inverted u hypothesis (yerkes and dodson 1908)

The Yerkes-Dodson Law of Arousal and Performance

Charlotte Nickerson

Research Assistant at Harvard University

Undergraduate at Harvard University

Charlotte Nickerson is a student at Harvard University obsessed with the intersection of mental health, productivity, and design.

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Editor-in-Chief for Simply Psychology

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Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Associate Editor for Simply Psychology

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On This Page:

The concept of optimal arousal in relation to performance on a task is depicted here. Performance is maximized at the optimal level of arousal, and it tapers off during under- and overarousal.

Key Takeaways

• The Yerkes-Dodson law states that there is an empirical relationship between stress and performance and that there is an optimal level of stress corresponding to an optimal level of performance. Generally, practitioners present this relationship as an inverted U-shaped curve.
• Research shows that moderate arousal is generally best; when arousal is very high or very low, performance tends to suffer (Yerkes & Dodson, 1908).
• Robert Yerkes (pronounced “Yerk-EES”) and John Dodson discovered that the optimal arousal level depends on the complexity and difficulty of the task to be performed.
• This relationship is known as the Yerkes-Dodson law, which holds that a simple task is performed best when arousal levels are relatively high, and complex tasks are best performed when arousal levels are lower.
• The Yerkes-Dodson law’s original formulation derives from a 1908 paper on experiments in Japanese dancing mice learning to discriminate between white and black boxes using electric shocks. This research was largely ignored until the 1950s when Hebb’s concept of arousal and the “U-shaped curve” led to renewed interest in the Yerkes-Dodson law’s general applications in human arousal and performance.
• The Yerkes-Dodson law has more recently drawn criticism for its poor original experimental design and it’s over-extrapolated scope to personality, managerial practices, and even accounts of the reliability of eyewitness testimony.

How the Law Works

The Yerkes-Dodson law describes the empirical relationship between stress and performance.

In particular, it posits that performance increases with physiological or mental arousal, but only up to a certain point. This is also known as the inverted U model of arousal.

When stress gets too high, performance decreases. To add more nuance, the shape of the stress-performance curve varies based on the complexity and familiarity of the task.

Task performance is best when arousal levels are in the middle range, with difficult tasks best performed under lower levels of arousal and simple tasks best performed under higher levels of arousal.

Original Experiments

The Yerkes-Dodson law has seen a number of interpretations since its inception in 1908. In their original paper, Robert Yerkes and John Dodson reported the results of two experiments involving “discrimination learning” – the ability to respond differently to different stimuli – and dancing mice (Teigen, 1994).

The mice received a non-injurious electric shock whenever they entered a white box but no shock when they entered the black box next to the white box.

In the first set of experiments, Yerkes and Dodson gave the mice very weak shocks; however, they found that these mice took two long to learn the habit of choosing the black box over the white box (choosing correctly 10/10 times over three consecutive days).

When the researchers increased the strength of the shock, the number of trials needed for the mice to learn the habit decreased – until they reached the third and strongest level of electric shock.

When the electric shock was at its strongest, the number of trials needed for the mice to learn which box to enter went up again. This finding went against Yerkes and Dodson” hypothesis that the rate of habit-formation would increase linearly with the increasing strength of the electric shock.

Instead, a degree of stimulation that was neither too weak nor too strong optimized the rate of learning (Yerkes and Dodson, 1908; Teigan, 1994).

Because of this unexpected result, Yerkes and Dodson elaborated on their original experimental design to provide “a more exact and thoroughgoing examination of the relation of strength of stimulus to rapidity of learning” (1908).

The researchers made it easier to discriminate between the white and black boxes by letting more light into the white box and used five rather than three levels of shock.

Contrary to what we now know as the Yerkes-Dodson law, the weakest stimulus gave the slowest rate of learning, while the strongest stimulus led to the fastest rate of learning.

This confused Yerkes and Dodson, who wrote, “The results of the second set of experiments contradict those of the first set. What does this mean?” (1908).

One hypothesis the researchers made was that these contradictory results came from the easiness of the discrimination task.

To test this hypothesis, Yerkes and Dodson made the discrimination task more difficult than in the first set of experiments by allowing less light into the white and black boxes.

The researchers used four levels of shock, but fewer mice in each condition than before – two rather than four. In this set of experiments, the most efficient learning seemingly occurred at the second-weakest shock level (Teigen, 1994).

From these three sets of experiments, Yerkes and Dodson concluded that both weak and strong stimuli can result in low rates of habit formation and that the stimulus level most conducive to learning depends on the nature of the task.

“As the difficultness of discrimination is increased, the strength of that stimulus which is most favorable to habit-formation approaches the threshold” (Yerkes and Dodson, 1908; Teigen, 1994).

Replication Studies

Following the original formulation of the Yerkes-Dodson law, researchers replicated the original study, using animals such as chicks (Cole, 1911) and kittens (Dodson, 1915).

Cole (1911) gave chicks an easy, medium, and difficult discrimination task, with four levels of shock for the medium task and three levels of shock for the other tasks.

In the easy task, the rapidity of learning increased with the strength of shock; in the medium-difficulty task, the strongest shock seemingly decreased the rate of learning, and in the difficult task, the strong shock increased the variability of performance – three chicks learned more rapidly due to the strong shock, while two others failed to learn the discrimination task (the sixth chick died over the course of the experiment).

Although Cole (1911) only observed one U-curve (in the medium-difficulty condition), he concluded that his results were in agreement with Yerkes-Dodson.

Dodson (1915), meanwhile, trained four kittens to discriminate between light and dark-colored boxes by giving them a “medium-strength” shock when they entered the darker box.

These kittens performed better at the discrimination task than those given a “strong” electric shock. When the task was made easier (again, by letting more light into the boxes), the strong and medium-strength shocks proved equally effective. With an easier task, learning improved with shock strength (Teigen, 1994).

Dodson himself later found that both the strength of rewards and punishments were related to the rapidity of learning in a U-shaped manner.

For example, rats who had been starved for up to 41 hours prior to the experiment showed higher rates of discrimination learning than those who were not. However, if they were starved longer (and food was more rewarding as a result), learning became less efficient (Dodson, 1917).

Later scholars generally agreed that the Yerkes-Dodson law was about the relationship between punishment and learning.

Young (1936), following a review of the research of Yerkes and Dodson (1908), Cole (1911), and Dodson (1915), added a later confounding study by Vaughn and Diserens (1930) showing that maze learning was more efficient in human subjects given either light or medium punishments in the form of electric shocks, but not with heavy punishment or no punishment.

To quote Young, “For the learning of every activity, there is an optimum degree of punishment” (1936). The 1930s and 1940s saw an evolution of the Yerkes-Dodson law.

Writers such as Thorndike (1932), Skinner (2019), and Estes (1944) did away with the idea of punishment as a fundamental learning principle, and others introduced a distinction between learning and performance (Teigen, 1994).

Researchers reinterpreted the Yerkes-Dodson law as describing the relationship between motivation and performance.

Some, such as Hilgard and Marquis (1961), concluded that the law was evidence that “under certain conditions, the drive may actually interfere” with learning.

Introductory textbooks as well as scholars on the subject, have described the Yerkes-Dodson law in terms of motivation and performance (e.g., Bourne and Ekstrand, 1973).

In these descriptions, the Yerkes-Dodson law has become more about motivated behavior in general than the psychology of learning.

The shape described by the Yerkes-Dodson law has also changed from U-curves to the inverted U: while learning (as measured by the number of trials needed for mastery) is optimal at the lowest point of a U-curve (the least trials needed), performance is optimal, at its highest, at the highest point of the inverted U-curve.

This expansion in scope, it has been argued, renewed interest in the Yerkes-Dodson law from 1955 to 1960 (Teigen, 1994).

Broadhurst (1957) replicated the original Yerkes-Dodson experiment with a better design by using four motivation levels and three difficulty levels with ten rats in each condition.

Again, the rats had to discriminate between light and dark boxes, but they were motivated by different levels of air deprivation: 0, 2, 4, or 8 seconds.

For the easy discrimination task, the highest performance was seen in the 4-second air deprivation group, while the optimum moved to 2 seconds for the medium and difficult task groups.

Broadhurst also proposed testing motivational differences in individual rats by conducting the experiment on rats differing in “emotionality” (Broadhurst, 1957; Teigen, 1994).

Eyewitness Testimony

Expert witnesses have cited the Yerkes-Dodson law in court.

Witness for the defense: The accused, the eyewitness, and the expert who puts memory on trial, Elizabeth Loftus, a psychologist and expert witness in memory and the fallibility of memory, eyewitness testimony explains,

“I approached the backboard located in front of the jury box and, with a piece of chalk, drew the upside-down U shape that represented the relationship between stress and memory known to psychologists as the Yerkes-Dodson law” (Loftus and Ketcham, 1991).

Although this curve bore more similarity to Hebb’s inverted U-curve of arousal, Loftus used the curve to relate arousal (or “stress”) to the efficiency of memory (rather than, as has been formulated by others, learning, performance, problem-solving, the efficiency of coping, or another concept).

The Yerkes-Dodson effect states that when anxiety is at low and high levels, eyewitness testimony is less accurate than if anxiety is at a medium level. Recall improves as anxiety increases up to an optimal point and then declines.

When we are in a state of anxiety, we tend to focus on whatever is making us feel anxious or fearful , and we exclude other information about the situation.

If a weapon is used to threaten a victim, their attention is likely to focus on it. Consequently, their recall of other information is likely to be poor.

Work Stress

The Yerkes-Dodson law has seen frequent citations in managerial psychology, particularly as researchers have argued that the increase in work stress levels is a “costly disaster” (Corbett, 2015).

Corbett (2015) examines the lineage of this law in business writing and questions its application, calling it a “folk method.”

In particular, Corbett criticizes how the law has been extrapolated from its initially limited animal experiments to almost every facet of human task performance, with studies examining tasks as unrelated as product development teamwork, piloting aircraft, competing in sports, and solving complex cognitive puzzles.

This has proved, Corbett argues, to create a situation where the law has become so ambiguous as to be unfalsifiable (2015).

Corbett argues that the generally uncritical portrayal of the Yerkes-Dodson law in textbooks has added a veneer of scientific legitimacy to the management practice of increasing work stress levels at a time when more robust research is increasingly showing that increasing levels of work-related stress corresponds to decreasing mental and physical health.

Corbett, taking an argument from Micklethwait and Wooldridge (1996) posits that management theory is generally incapable of self-criticism, has confusing terminology, rarely “rises above common sense,” and is riddled with contradictions (2015).

In response, he suggests that managerial psychology embraces evidence-based managerial practices.

Arousal and Performance

The renewal of interest in the Yerkes-Dodson law in the 1950s corresponded to the introduction of the concept of arousal (Teigen, 1994).

Hebb (1955), who wrote seminally on the concept of arousal, introduced the inverted U-curve to describe the relationship between arousal and performance.

This idea of arousal shifted the idea of “drive” from the body to the brain and could be framed as either a behavioral, physiological, or theoretical concept. Although not referenced in Hebb’s original paper, writers continued to describe the Yerkes-Dodson law in terms of arousal in textbooks and research literature (Teigen, 1994).

These reformulations of the Yerkes-Dodson law have used terms such as fear, anxiety, emotionality, tension, drive, and arousal interchangeably.

For example, Levitt (2015) holds that the Yerkes-Dodson law describes “that the relationship between fear, conceptualized as drive, and learning is curvilinear,” reporting findings on human maze learning as support for his view.

Using the arousal concept in the formulation of the Yerkes-Dodson law has also seen the law being linked to phenomena such as personality traits and the effects of physiological stimulants.

For instance, in accounting for the theoretical differences in intellectual performance between introverts and extroverts under time pressure, different noise conditions, and at different times of day (e.g., Revelle, Amaral, and Turriff, 1976; Geen, 1984; and Matthews, 1985) as well as participants differing in impulsivity working under the influence of caffeine (e.g., Anderson and Revelle, 1983).

Critical Evaluation

Yerkes and Dodsons’ original experimental design, scholars generally agree, was deeply flawed by modern standards – so much so that W. P. Brown wrote that the law should be “buried in silence” (Teigen, 1994; W. P. Brown, 1965).

Yerkes and Dodsons’ performance vs. stimulus curves were based on averages from just 2-4 subjects per condition; the researchers performed no statistical tests (Gigerenzer and Murray, 2015), and the highest level of shock used in 3, 4, and 5 shock conditions were of different strengths.

The authors assumed that the linear response curve in the second set of experiments (with the easily discriminated white and black boxes) was simply the first part of a U-curve, which would have been fully uncovered given that they had subjected the mice to higher levels of shocks (Teigen, 1994).

Indeed, this experimental design has been misreported by later scholars, such as Winton (1987), who described the original study as a 3 x 3 design with three different levels of discrimination difficulty and three levels of shock strength.

Additionally, Yerkes and Dodson, as Teigen (1994) points out, failed to discuss the concepts involved in the speed of habit formation. Several of the original replicating studies, such as Dodson’s kitten experiment (1915), also showed poor experimental design.

In this experiment, there were only two kittens in the “less difficult” and “easy” discrimination conditions and no U-curves. Nonetheless, Dodson concluded that the results were compatible with the original Yerkes-Dodson experiment (Teigen, 1994).

Anderson, K. J., & Revelle, W. (1983). The interactive effects of caffeine, impulsivity and task demands on a visual search task. Personality and Individual Differences, 4(2), 127-134.

Bourne, L. E., & Ekstrand, B. R. (1973). Psychology: Its principles and meanings (Dryden, Hinsdale, IL).

Broadhurst, P. L. (1957). Emotionality and the Yerkes-Dodson law. Journal of experimental psychology, 54(5), 345.

Brown, W. P. (1965). The Yerkes-Dodson law repealed. Psychological reports, 17(2), 663-666.

Cole, L. W. (1911). The relation of strength of stimulus to rate of learning in the chick. Journal of Animal Behavior, 1(2), 111.

Corbett, M. (2015). From law to folklore: work stress and the Yerkes-Dodson Law. Journal of Managerial Psychology.

Dodson, J. D. (1915). The relation of strength of stimulus to rapidity of habit-formation in the kitten. Journal of Animal Behavior, 5(4), 330.

Dodson, J. D. (1917). Relative values of reward and punishment in habit formation. Psychobiology, 1(3), 231.

Estes, W. K. (1944). An experimental study of punishment. Psychological Monographs, 57(3), i.

Geen, R. G. (1984). Preferred stimulation levels in introverts and extroverts: Effects on arousal and performance. Journal of Personality and Social Psychology, 46(6), 1303.

Gigerenzer, G., & Murray, D. J. (2015). Cognition as intuitive statistics. Psychology Press.

Hebb, D. O. (1955). Drives and the CNS (conceptual nervous system). Psychological review, 62(4), 243.

Hilgard, E. R., & Marquis, D. G. (1961). Hilgard and Marquis” conditioning and learning.

Levitt, E. E. (2015). The psychology of anxiety.

Loftus, E., & Ketcham, K. (1991). Witness for the defense: The accused, the eyewitness, and the expert who puts memory on trial. Macmillan.

Matthews, G. (1985). The effects of extraversion and arousal on intelligence test performance. British Journal of Psychology, 76(4), 479-493.

Revelle, W., Amaral, P., & Turriff, S. (1976). Introversion/extroversion, time stress, and caffeine: Effect on verbal performance. Science, 192(4235), 149-150.

Skinner, B. F. (2019). The behavior of organisms: An experimental analysis. BF Skinner Foundation.

Teigen, K. H. (1994). Yerkes-Dodson: A law for all seasons. Theory & Psychology, 4(4), 525-547.

Thorndike, E. L. (1932). The fundamentals of learning.

Vaughn, J., & Diserens, C. M. (1930). The relative effects of various intensities of punishment on learning and efficiency. Journal of Comparative Psychology, 10(1), 55.

Winton, W. M. (1987). Do introductory textbooks present the Yerkes-Dodson Law correctly?. American Psychologist, 42(2), 202.

Yerkes, R. M., & Dodson, J. D. (1908). The relation of strength of stimulus to rapidity of habit-formation. Punishment: Issues and experiments, 27-41.

Young, P. T. (1936). Social motivation.

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Article • 10 min read

The Inverted-U Theory

Balancing performance and pressure with the yerkes-dodson law.

By the Mind Tools Content Team

Have you ever worked on a project with a tight-but-achievable deadline, where your unique knowledge and skills were vital for a successful result? Even though you found it challenging, you may well have done some of your very best work.

Or, think back to a task where you felt little pressure to deliver. The deadline may have been flexible, or perhaps the work wasn't challenging. Chances are, you did an average job at best.

There's a subtle relationship between pressure and performance. When people experience the right amount of pressure, they often perform brilliantly. However, if there's too much or too little pressure, performance can suffer.

In this article, you'll learn how the Inverted-U Theory – also known as the Yerkes-Dodson Law – can help you to understand the relationship between pressure and performance. The result will be that you'll get the best from a happy and engaged team!

Click here to watch our video on the Inverted-U Theory/Yerkes-Dodson Law.

What Is the Inverted-U Theory?

The Inverted-U Theory was created by psychologists Robert Yerkes and John Dodson in 1908. Despite its age, it's a model that has stood the test of time. [1]

The theory describes a clear relationship between pressure and performance. In the original research, pressure was exerted by electric shocks – to motivate rats to escape from a maze!

The Inverted-U Theory gets its name from the curve created when the correlation between pressure (or "arousal") and performance is shown on a graph. See figure 1, below.

Figure 1: The Inverted-U Curve.

From " The Relation of Strength of Stimulus to Rapidity of Habit‐Formation " by Robert Yerkes and John Dodson. Published in the Journal of Comparative Neurology (1908). Work now in the public domain.

According to Yerkes and Dodson, peak performance is achieved when the level of pressure we experience is appropriate for the work we're doing. When we're under too much or too little pressure, performance declines, sometimes severely.

Understanding the Inverted-U Curve

The left hand side of the graph, above, shows the situation where people aren't being challenged. Here, they see no reason to work hard at a task, or they're in danger of approaching their work in a "sloppy," unmotivated way.

The middle of the graph shows where people work at peak effectiveness. They're sufficiently motivated to work hard, but they're not so overloaded that they're starting to struggle. This is where people can experience "flow," the enjoyable and highly productive state in which they can do their best work. (For more on this, see our article, The Flow Model .)

The right hand side of the graph shows where they're starting to fall apart under pressure. They're overwhelmed by the volume and scale of competing demands on their attention, and feeling a serious lack of control over their situation. They may exhibit signs of hurry sickness , stress, or out-and-out panic.

In reality, the exact shape of the curve will depend on both the individual and their situation. It's also important to recognize that seemingly small changes in professional or personal life can lead to rapid repositioning on the curve.

What's the Difference Between Pressure and Stress?

The Inverted-U Theory shows that pressure can be positive – up to a point. Stress, however, is never positive, and it's important not to confuse the two ideas.

When the levels of pressure we're experiencing are right for the work we're doing, we're stimulated in a beneficial way: motivated, engaged, and excited about doing our best. But stress happens when people feel out of control, and it's a wholly negative thing.

The Inverted-U Theory is about using pressure wisely, always aware of where the benefits end and stress begins.

For more information about how to identify and manage stress, see our article, Minimizing Workplace Stress .

You can take steps to manage the way you experience pressure by using techniques such as Relaxation Imagery , Centering , and Deep Breathing . You can also use Affirmations to maintain a positive outlook and control. Consider teaching these techniques to your teams, too – though you'll also need to have the right organizational processes in place to ensure that pressure levels remain beneficial.

The Four Influencers of the Inverted-U Theory

The impact of pressure can be complex. But four key factors, or "influencers," affect how the Inverted-U Theory plays out in practice*:

• Skill Level.
• Personality.
• Trait Anxiety.
• Task Complexity.

1. Skill Level

Someone's level of skill with a given task will directly influence their performance, in terms of both their attitude and their results.

For a while, a new task is likely to be challenging enough. Later, if it starts to feel too easy, some form of extra pressure might be needed to help the person re-engage with their role.

Don't worry about people becoming too skilled or too confident. You can use the other influencers to balance this, so that they feel the optimum amount of positive pressure. Increased skill and confidence can only bring benefits to individuals and organizations.

2. Personality

A person's personality also affects how well they perform.

For instance, some psychologists believe that people who are extroverts are likely to perform better in high-pressure situations. People with an introverted personality, on the other hand, may perform better with less pressure.

The Inverted-U Theory prompts us to match our own personalities – and those of our people – to appropriate tasks. Observation, detailed knowledge of individuals, and open communication, are all important when we're allocating roles and responsibilities.

Although not addressed directly within the Inverted-U Theory, it's important to remember that people can experience various forms of personal pressure (from their family lives, for instance, or from underlying concerns about their role or organization). Try to bear these pressures in mind when setting deadlines and allocating tasks.

3. Trait Anxiety

Think of trait anxiety as the level of a person's "self-talk." People who are self-confident are more likely to perform better under pressure. This is because their self-talk is under control, which means that they can stay "in flow," and they can concentrate fully on the situation at hand.

By contrast, people who criticize or question themselves are likely to be distracted by their self-talk, which can cause them to lose focus in more challenging situations.

The more that people are able to lower their anxiety about a task (with practice, or with positive thinking, for example) the better they'll perform.

4. Task Complexity

Task complexity describes the level of attention and effort that people have to put into a task in order to complete it successfully. People can perform simple activities under quite high levels of pressure, while complex activities are better carried out in a calm, low-pressure environment.

But even when someone's skill levels are high, they may still benefit from a calm environment in which to carry out their most complex work. Conversely, people carrying out low-complexity tasks may need extra stimulation in order to feel motivated and achieve their potential.

Using the Inverted-U Theory

The simplest way to use the Inverted-U Theory is to be aware of it when you allocate tasks and projects to people on your team, and when you plan your own workload.

Start by thinking about existing pressures. If you're concerned that someone might be at risk of overload, see if you can take some of the pressure off them. This is a simple step to help them improve the quality of their work.

By contrast, if anyone is underworked, it may be in everyone's interest to shorten some deadlines, increase key targets, or add extra responsibilities – but only with clear communication and agreement.

From there, balance the factors that contribute to pressure, so that your people can perform at their best. Remember, too little pressure can be just as stressful as too much!

Try to provide team members with tasks and projects of an appropriate level of complexity, and work to build confidence in the people who need it.

Also, manage any negativity in your team, and train your people so that they have the skills they need to do the jobs they're given. Our article on Training Needs Assessment (TNA) will help you do this. Tools like the Four Dimensions of Relational Work can also help you match tasks to people's personalities and interpersonal skills.

However, bear in mind that you won't always be able to balance the "influencers." Motivate and empower your people so that they can make effective decisions for themselves.

The Inverted-U Theory illustrates the relationship between pressure and performance. Also known as the Yerkes-Dodson Law, it explains how to find the optimum level of positive pressure at which people perform at their best. Too much or too little pressure can lead to decreased performance.

Various factors affect how much people react to pressure in different situations. There are "four influencers" that can affect how much pressure people feel:

The Inverted-U Theory helps you to observe and manage these four factors, aiming for a balance that supports engagement, well-being, and peak performance.

You can use the model by managing these four influencers, and by being aware of how they can positively or negatively influence your people's performance.

*Originator unknown. If you know the originator of the "Four Influencers," please contact us.

[1] Yerkes, R.M. and Dodson, J.D. (1908). 'The Relation of Strength of Stimulus to Rapidity of Habit-Formation,' Journal of Comparative Neurology and Psychology, 18(5), 459-482. Available here .

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Inverted-U Theory of Stress (Yerkes & Dodson)

Inverted-U Theory: this article explains Inverted-U Theory , developed by Robert Yerkes and John Dodson in a practical way. Next to what it is, this article also highlights the interpreting of the model, the four influencing factors and responding to stress and pressure. After reading, you’ll understand the basics of this stress management theory . Enjoy reading!

What is Inverted-U Theory?

Inverted-U Theory is a theory that sheds light on the relation between performance and pressure or arousal. In the original study, rats were given electric shocks as motivation for escaping from a maze.

The Inverted-U Theory owes its name to the line, in the form of an inverted U, that appears when there is a correlation between pressure and performance. This is illustrated in the graph presented in this article.

Figure 1 – the nverted-U theory model

A quick look at the curve reveals that performance lags behind when there’s little pressure, and that performance is positively influenced when there’s some more pressure.

If even more pressure is added, performance is negatively influenced and efficiency decreases. The worker’s efficiency and performance can reach an optimal point if the pressure or arousal have reached an optimal point.

Inverted-U Theory was developed by psychologists Robert Yerkes and John Dodson in 1908. Despite the fact that the model was developed long ago, it continues to be relevant.

Interpreting the Model

When looking at the left-hand side of the graph, it’s notable that low pressure or low stress levels result in a stress response corresponding to ‘boredom or lack of challenge’.

Even if the task itself is a critical activity, the attention, concentration, and precision required to properly execute a task is absent in the absence of an appropriate level of pressure or stress.

On the right-hand side of the graph from the Inverted-U Theory, we can see that extreme pressure levels or high stress levels don’t automatically result in good performance.

The opposite is true: if pressure gets too high, or a too high stress level is activated, this results in a feeling of unhappiness, stressfulness, and anxiety. These are all results of overwhelming stress.

In the middle of the graph, however, is a region where the worker performs best. This area is where an optimal amount of pressure is applied. In this region, the moderate pressure leads to an optimal stress level, which is manageable as well. Eventually, this results in the highest performance level for the user.

The optimal level of pressure or arousal is influenced by a number of factors.

Four Influencing Factors of the Inverted-U Theory

It can be hard to determine how much impact pressure, and stress have because the desired amount of pressure is influenced by four factors. These factors are also known as influencers. Inverted-U Theory recognises the following four influencers:

Personality

Different personality types benefit from different levels of stress or pressure.

Generally, extraverted personalities are more resistant to stress and better able to keep their head above water when stressed than introverted personalities. Introverted people usually have a higher chance of performing well in environments with little stress or excitement.

There are also factors, of course, that can cause temporary pressure or stress. These may be professional matters or matters in private life. The duration of the period in which stress or pressure are present may differ as well.

Task Difficulty

The degree of complexity of a task relates to the level of attention and effort a person requires to successfully complete it. People are generally able to carry out simple activities even when pressure is high, but complex tasks are better taken care of in quiet surroundings.

A shop manager and an accountant have completely different jobs. Each has more knowledge of the work they do individually than of the other’s job.

If they would swap jobs, the challenge and the pressure would be so high in the beginning that it would strongly motivate them. After a while, when tasks get easier, they would have to use a new form of pressure to keep their performance up.

Inverted-U Theory shows that fear can also have an effect on performance. This mainly relates to the ability to set aside or ignore feelings of fear in order to be able to keep one’s focus on the situation and the tasks.

People who are better at this also perform better under pressure. People who are not good at it will enter into challenging situations more often.

Complexity and Motivation

In situations that require carrying out tasks with a high level of complexity, or solving complex problems, motivation plays an important role.

There have been various situations in which the relation between motivation and complex problem solving was studied. These have yielded several theories, such as McClelland’s motivation theory and Maslow’s hierarchy of needs .

Stress Management: 40+ easy ways to deal with stress Stress relief and burnout prevention. Don’t let stress control your life. Beat anxiety and worries. Live, Laugh, Love.    >> More information

Inverted-U Theory: difference between pressure and stress

The terms ‘pressure’ and ‘stress’ are often used interchangeably, as if they refer to the same thing. ‘I work in a high-pressure environment’ , or ‘I have a stressful job’ . According to science, however, there definitely is a difference between pressure and stress. These two things reappear regularly in Inverted-U Theory.

‘Stress’ refers to situations that demand a lot from someone who has few resources such as money, time, energy, or manpower.

Pressure, on the other hand, is a situation in which someone notices that there are extensive consequences to the outcome of a certain action. It’s the feeling that something is at stake, depending on one’s performance. Stress can create several problems that can lead to feelings of overload and, in the most extreme case, even a occupational burnout .

Stress on the job is caused by things such as late meetings, long lists of emails that have to be answered, approaching deadlines, or emergency situations.

Pressure often becomes apparent from signals such as anxiety and the feeling that a situation is life-or-death.

A job interview, too, is an example of a situation where one’s actions may have far-reaching consequences, which is why it is not described as a stressful situation.

Inverted-U Theory: responding to stress and pressure

Different stress levels or feelings of pressure cause different reactions and approaches in people. In an extraordinarily stressful situation, a person’s goal is to feel less overwhelmed. In a situation of pressure, the goal is to perform well.

There are various things that can be done to reduce stress. Going for a walk after a long day in the office is good for you, and spending time on hobbies on the weekend also lowers stress.

In a high-pressure situation, these same options are often unavailable. A special forces soldier who is involved in a rescue mission has no time to relax and settle down, but may have to react instinctively and adequately without changing their stress levels.

Now It’s Your Turn

What do you think? Do you recognise the explanation about Inverted-U Theory? What do you think are important points when it comes to using this tool? How do you experience the influence of pressure on your performance? Are you facing excessive stress, or rather little or no pressure? Do you have any tips or additional comments?

Share your experience and knowledge in the comments box below.

More information

• Broadhurst, P. L. (1957). Emotionality and the Yerkes-Dodson law . Journal of experimental psychology, 54(5), 345.
• Broadhurst, P. L. (1959). The interaction of task difficulty and motivation: The Yerkes Dodson law revived . Acta Psychologica, Amsterdam.
• Cohen, R. A. (2011). Yerkes–Dodson Law . Encyclopedia of clinical neuropsychology, 2737-2738.
• Teigen, K. H. (1994). Yerkes-Dodson: A law for all seasons . Theory & Psychology, 4(4), 525-547.

How to cite this article: Janse, B. (2019). Inverted-U Theory of Stress (Yerkes & Dodson) . Retrieved [insert date] from Toolshero: https://www.toolshero.com/human-resources/inverted-u-theory/

Original publication date: 09/18/2019 | Last update: 12/25/2023

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Ben Janse is a young professional working at ToolsHero as Content Manager. He is also an International Business student at Rotterdam Business School where he focusses on analyzing and developing management models. Thanks to his theoretical and practical knowledge, he knows how to distinguish main- and side issues and to make the essence of each article clearly visible.

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Table of Contents

The theory of inverted u: a comprehensive exploration.

Dive deep into the theory of Inverted U, also known as the Yerkes-Dodson Law. Understand how it affects performance, productivity, and stress management across various life aspects.

Understanding the Inverted U Theory: An Introduction

The Theory of Inverted U , also known as the Yerkes-Dodson Law , is a critical psychological concept that explores the complex relationship between arousal, stress, and performance. Introduced by psychologists Robert Yerkes and John Dodson in 1908, the law suggests that a certain level of stress can enhance performance, but there's a threshold beyond which performance deteriorates.

This theory is a fundamental framework to understand productivity, stress management, decision making, and even motivation. This article aims to present an in-depth exploration of this mental model with relatable examples and practical applications.

Unpacking the Inverted U Model

The Inverted U model visualizes the correlation between pressure (stress or arousal) and performance. This correlation is divided into three primary phases:

Ascending Phase (Increasing Returns) : At this stage, as stress or stimulation increases, performance also improves. The pressure can act as a catalyst to drive focus and energy.

Peak Point (Optimal Performance) : This is the ideal stress-performance equilibrium. At this point, an individual or system is at their peak performance—the right amount of stress fuels motivation and focus without causing overwhelm.

Descending Phase (Decreasing Returns) : Past the optimal point, any additional stress results in deteriorating performance. Here, stress outweighs the individual's coping mechanisms, leading to errors, decreased productivity, or even burnout.

A Day in the Life: The Inverted U Model in Action

To better grasp this theory, imagine a regular workday. In the morning, as you sip your coffee, your arousal levels gradually increase. You start working and as the pressure mildly intensifies, you find yourself becoming more efficient - this is the ascending phase of the model.

Come mid-day, you're entirely engrossed in your work, handling tasks effectively - you're at the peak point of the inverted U, experiencing optimal stress levels and showcasing your best performance.

As the day progresses, if the workload continues to pile up, you might start feeling overwhelmed. The excessive stress leads to fatigue and mistakes - you've entered the descending phase of the model, where increased stress leads to decreased performance.

Practical Applications of the Inverted U Theory

Understanding the theory of Inverted U allows us to optimize performance and well-being in various contexts, from personal growth to professional environments, education, and even sports training.

Workplace Productivity

Effective stress management is crucial in the workplace. Leaders and managers can utilize this model to ensure employees aren't overloaded with work and to prevent burnout. For instance, setting realistic deadlines, promoting a healthy work-life balance, and recognizing employees' efforts can help maintain an optimal stress-performance balance.

Education and Learning

The Yerkes-Dodson law is equally applicable in the realm of education. It helps teachers, parents, and students understand the impact of stress on academic performance. Moderate pressure can encourage students to study and prepare well for exams. However, excess stress might impair focus, memory recall, and overall learning.

Sports and Performance Psychology

In sports, the right amount of arousal can boost performance. Athletes often perform their best when they're mildly stressed - it enhances focus and adrenaline flow. However, too much anxiety can lead to poor performance. Coaches and athletes can use this model to devise optimal training strategies, taking care to avoid overtraining and promoting proper rest and recovery.

Conclusion: Harnessing the Power of the Inverted U Theory

The Theory of Inverted U or the Yerkes-Dodson Law offers vital insights into the intricate interplay of stress and performance. By understanding this relationship, we can strive for balance, optimizing productivity without compromising well-being.

Whether you're a professional trying to maximize your work output, a student seeking to optimize study habits, or a sports coach aiming to improve team performance, this mental model offers a powerful framework to inform your strategy.

Remember, the goal isn't to eliminate stress, but to harness it - striking the right balance is the key to unlocking peak performance.

Yerkes-Dodson Law: The Relationship Between Stress And Performance

Many people feel that their performance improves when they feel pressured. For example, it is likely that you have been surprised more than once by the ease with which you have managed to memorize the syllabus of an exam despite studying it only the day before, compared to other occasions in which you have dedicated much more time.

In this article we will talk about the Yerkes-Dodson law, as the inverted U model is commonly called on the relationship between activation level and performance. This hypothesis was proposed by Robert Yerkes and John Dodson more than a century ago; However, it is still in force today due to the notable solidity it has demonstrated.

Table of Contents

The Yerkes-Dodson law or inverted U model

In 1908, psychologists Robert Mearns Yerkes and John Dillingham Dodson published their inverted U model, the result of studies they carried out on the influence of pressure (which can be understood as the level of stress, activation or physiological alertness). and cognitive) in performance on tasks that involve complex mental operations.

The Yerkes and Dodson model states that the relationship between stress and performance can be represented in the shape of an inverted U. This means that performance will be optimal if the activation level is moderately high ; On the other hand, if it is too high or too low it will have a negative impact on the result of the task.

Thus, the Yerkes-Dodson law states that the best way to enhance performance is to increase motivation to carry out the objective tasks, although it is equally important to ensure that the workload does not become difficult to manage, since that this interferes with the natural development of the activity and generates unpleasant feelings.

When we carry out tasks with a low level of stress or alertness, we often become bored or the lack of pressure reduces our productivity; If the demands are excessive we tend to experience feelings of anxiety and general psychological distress. On the other hand, when the task is stimulating and challenging we concentrate to a greater extent.

In this sense we can relate the Yerkes-Dodson law with another very popular psychological concept: the state of flow (or “flow”) described by Mihály Csíkszentmihályi. According to this author, stimulating tasks, appropriate to the level of ability, with clearly delimited objectives and immediate feedback generate complete and rewarding mental involvement.

Influential factors in the relationship between stress and performance

There are at least four factors that have a very relevant role in the relationship between the level of activation and productivity : the complexity of the task, the skill level of the person completing it, their personality in general, and the trait-anxiety factor in particular. Each of them modulates the effects of the Yerkes-Dodson law in a key way.

1. Complexity of the task

If the task we have to carry out is difficult, we will need to invest more cognitive resources (related, for example, to attention or working memory) than if it were not. Consequently, complex tasks require a lower level of pressure to achieve optimal performance than the simple ones, since they are stimulating in themselves.

From this arises the idea that it is important to adapt environmental pressure levels to the difficulty of the task in order to enhance productivity, so that quiet environments are more recommended when carrying out challenging activities, while a quiet environment enriched can help improve quality when tackling easy tasks.

2. Skill level

As with the difficulty of the tasks, taking into account the subject’s skill level is essential when determining what the ideal environmental pressure is. We can say that Practice in a domain reduces the difficulty of the tasks included in it so relating these two variables can be useful when applying the Yerkes-Dodson law.

3. Personality

It would be reductionist to think that simply modifying the level of stimulation or environmental pressure can allow us to reliably influence the performance of other people: if we did so, we would be ignoring something as important as the personality of each individual.

Thus, for example, if we follow the neurobiological theory of personality proposed by Hans Eysenck we can deduce that Extraverted people tend to need a higher level of brain activation to achieve optimal performance, while biologically introverted people typically prefer minimal environmental pressure.

4. Trait Anxiety

The personality factor we know as “trait anxiety” refers to the tendency to experience negative emotions related to anxiety, such as restlessness, fear, and worry. Trait anxiety constitutes the core of the Neuroticism construct ; In this sense it is opposed to the Emotional Stability factor.

As can be assumed, people who have a very marked tendency to feel anxious practically always react negatively to increased stress levels. As is the case with introverted people, it can be a serious mistake to ignore the fact that people with this characteristic work better with low levels of stimulation.

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Learning under stress: The inverted-U-shape function revisited

• Basira Salehi ,
• M. Isabel Cordero and
• Carmen Sandi 1
• Laboratory of Behavioral Genetics, Brain Mind Institute, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland

Although the relationship between stress intensity and memory function is generally believed to follow an inverted-U-shaped curve, strikingly this phenomenon has not been demonstrated under the same experimental conditions. We investigated this phenomenon for rats’ performance in a hippocampus-dependent learning task, the radial arm water maze (RAWM). Variations in stress intensity were induced using different water temperatures (25°C, 19°C, and 16°C), which elicited increased plasma corticosterone levels. During spatial training over three consecutive days, an inverted-U shape was found, with animals trained at 19°C making fewer errors than animals trained at either higher (16°C) or lower (25°C) stress conditions. Interestingly, this function was already observed by the last trial of day 1 and maintained on the first day trial of day 2. A long-term recall probe test administered under equal temperature conditions (20°C) revealed differences in performance according to the animals’ former training conditions; i.e., platform searching for rats trained at 25°C was less accurate than for rats trained at either 16°C or 19°C. In reversal learning, groups trained at both 19°C and 25°C showed better performance than the 16°C group. We also found an interaction between anxiety and exploration traits on how individuals were affected by stressors during spatial learning. In summary, our findings confirm, for the first time, the existence of an inverted-U-shape memory function according to stressor intensity during the early learning and memory phases in a hippocampus-dependent task, and indicate the existence of individual differences related to personality-like profiles for performance at either high or low stress conditions.

Physiological stress responses are used by organisms to adapt to changing, demanding circumstances, so these responses are of enormous adaptive value ( Lightman 2008 ). However, survival success depends not only on the immediate ability to respond to threat, but also on the integration of previously acquired knowledge and skills into effective strategies to facilitate coping with similar demands in the future. This view provides an evolutionary explanation for stress effects on learning and memory processes.

Understanding the nature of stress–memory interactions has attracted significant attention in recent years. Surprisingly, despite much investigation, it is still not known how stress severity affects memory function. It is generally believed that the relationship between stress intensity and memory function follows an inverted-U-shaped curve, with memory increasing with stress to an optimal point, above or below which memory decreases. However, this stress–memory relationship seems to not apply to classical (Pavlovian) conditioning processes (for review, see Sandi and Pinelo-Nava 2007 ). Rather, current evidence supports a linear relationship between stressor intensity and the strength of the fear-conditioned memory formed, with an asymptotic waveform for high-to-very-high stress intensities ( Fanselow and Bolles 1979 ; Shors and Servatius 1997 ; Beylin and Shors 1998 ; Cordero et al. 1998 ; Radulovic et al. 1998 ; Anagnostaras et al. 2000 ; Merino et al. 2000 ; Laxmi et al. 2003 ).

The inverted U-shape function was originally proposed by Yerkes and Dodson (1908) to explain the relationship between stimulus strength and the rapidity of habit formation for “difficult” discrimination learning tasks in mice. In their experimental conditions, as with those of Broadhurst (1957) , “easy” tasks followed a linear relationship, as discussed above for classical conditioning. Hence, the so-called Yerkes-Dodson law implies that cognitive performance in difficult tasks is best when an individual is under optimal stress; performance would be impaired under conditions above or below optimal stress levels ( Yerkes and Dodson 1908 ; Broadbent 1965 ; Mendl 1999 ). Despite the great popularity of the inverted-U curve, or the Yerkes-Dodson law, to describe the relationship between stress and performance ( Diamond 2005 ), the validity of the law has been criticized due to significant methodological problems in the study performed by Yerkes and Dodson (1908) and their data being judged insufficient to substantiate conclusions, among other reasons ( Brown 1965 ; Baumler and Lienert 1993 ; Baumler 1994 ; Teigen 1994 ; Hancock and Ganey 2003 ; Diamond et al. 2007 ). In 1957, Broadhurst provided further evidence for the inverted-U-shape function using more refined methods and a visual discrimination task similar to that used by Yerkes and Dodson (1908) . In Broadhurst's experiments, variations in stress levels were achieved by exposing rats to different lengths of air deprivation just before the start of each trial. Therefore, stress was applied within the learning context, but did not originate from elements related to the cognitive task, so the stress could be considered “extrinsic” to the learning task. In the field of animal learning, it is surprising to note that not a single report has described an inverted-U-shape function for the relationship between “intrinsic” stress (i.e., induced by elements related to the cognitive task) and learning under the same experimental conditions ( Morris 2006 ; Sandi and Pinelo-Nava 2007 ). For example, recent proposals of an inverted-U-shaped function during spatial learning in rodents are based on independent, composite observations from different experimental settings and laboratories examining different parts (ascending or descending) of the function ( Mendl 1999 ; Morris 2006 ; Park et al. 2006 ; Sandi and Pinelo-Nava 2007 ).

Here we aimed to evaluate, for the first time, the validity of the inverted-U-shape function to account for the impact of variations in intrinsic stressor intensity on memory processes in a spatial learning task. We used the radial six-arm water maze (RAWM), in which animals learn to find a hidden escape platform located at the end of one of the arms with the help of extramaze visual cues. This task was chosen because it was previously shown to be both hippocampus dependent and sensitive to modulation by stress ( Diamond et al. 1999 ). To evaluate the effect of stressor intensity on task learning, we trained rats at different water temperatures, which produce different plasma corticosterone levels, and explored the rats' performance throughout each memory phase (learning acquisition, long-term memory retention, and reversal learning).

Furthermore, in line with the pioneering work by Eysenck (1955) , who questioned the role of personality in stress-influenced performance during learning tasks, as well as our own work relating anxiety-like trait with differences in spatial learning abilities ( Herrero et al. 2006 ) and behavioral and neurobiological vulnerability to stress ( Jakobsson et al. 2008 ; Sandi et al. 2008 ; Luksys et al. 2009 ), we set a second goal of capturing individual differences in the relationship between intrinsic stress and learning based on rat's personality traits.

Plasma corticosterone levels induced by swimming at different water temperatures

Our first step was to select three water temperatures that represent a gradation of physical stressor intensities when rats are placed in a pool without concomitant spatial learning. Based on pilot and previous experiments ( Sandi et al. 1997 ; Akirav et al. 2001 , 2004 ), 16°C, 19°C, and 25°C were chosen, and plasma levels of the stress hormone corticosterone were evaluated after submitting animals to one cued training session in the RAWM (i.e., cued platform) at one of the three water temperatures ( n = 6 rats/temperature; Fig. 1 A). A one-way ANOVA indicated an effect of temperature ( F (2,15) = 5.29, P < 0.05), with corticosterone levels from animals trained at 16°C being significantly higher than levels from animals trained at 25°C ( P < 0.05), and levels from animals trained at 19°C falling between the other two levels. A linear regression analysis confirmed the existence of a significant negative relationship between water temperature and corticosterone levels ( P < 0.005; Fig. 1 B), indicating that plasma corticosterone levels increased linearly as water temperature decreased. No differences were found among the groups for the number of errors across all trials (data not shown). Furthermore, to ensure that the low water temperatures used in this study did not induce hypothermia, rectal temperatures were measured immediately after training in the water maze at different temperatures. No differences in body temperature were observed between the groups (Supplemental Fig. S1).

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( A ) Corticosterone levels measured 45 min after the first trial in the RAWM. Overall ANOVA: P < 0.05; (*) P < 0.05 vs. 16°C. ( B ) Regression analysis confirmed the existence of a significant negative relationship between water temperature level and corticosterone level. Data are the mean ± SEM.

Learning in the RAWM at different water temperatures

Rats were trained in the spatial version of the RAWM under the three selected water temperatures (16°C, n = 35; 19°C, n = 50; or 25°C, n = 37) over three consecutive days ( Fig. 2 A). A repeated-measures ANOVA on the arm entry errors revealed an effect of training days ( F (2,238) = 26.78, P < 0.0001), confirming that animals progressively learned the spatial location of the platform across the training sessions. ANOVA also revealed an effect of water temperature ( F (2,119) = 12.38, P < 0.0001). This effect was further confirmed when performance across the three training days was averaged ( F (2,119) = 12.38, P < 0.0001; Fig. 2 B). Interestingly, post-hoc analyses indicated the existence of an inverted-U-shaped function, with animals trained at 19°C making less errors to find the platform than those trained at either 16°C ( P < 0.0001) or 25°C ( P < 0.0001). No difference in performance was found between rats trained at either 16°C or 25°C water temperature. A repeated-measures ANOVA on data represented in Figure 2 A yielded no interaction between water temperature and training day ( F (4,238) = 0.74, n.s). Separate ANOVAs for each training day indicated that on each training day, rats trained at 19°C outperformed those trained at either 16°C or 25°C ( P < 0.01). To examine possible differences in motor performance that may have been caused by the different water temperatures, the swimming speed of the different groups was compared. No significant differences were found between swimming speeds of groups trained at different temperatures ( F (2,119) = 0.12, n.s.; Supplemental Fig. S2). It is important to note that the different patterns of performance observed at the different water temperatures were already observed on the first training day, but not on the first training trial, in which no significant differences were found among the different groups (Supplemental Fig. S3). However, on the last trial (Trial 4) of day 1, animals trained at 19°C performed significantly better than animals trained at either 16°C or 25°C (Supplemental Fig. S3).

Effect of water temperature on performance, as indicated by the number of arm entry errors, in the RAWM during spatial learning ( A–C ) or cued training ( D–F ). ( A ) Spatial learning: When compared with the 19°C group, rats trained at either 16°C or 25°C showed delayed acquisition (**) P < 0.01 vs. 19°C for 16°C and 25°C in each training day. ( B ) Average error values collapsed for performance across the three training days. (***) P < 0.001 vs. 16°C and 25°C. ( C ) Number of errors incurred on the first training trial of day 2. (*) P < 0.05 vs. 16°C and 25°C. ( D ) Cued training: No differences were found in reaching the cued platform for groups trained at different water temperatures. ( E ) Average arm entry errors made to reach the platform collapsed over the three cued training days reveals no differences among groups. ( F ) No differences were found in performance on the first trial of the second cued training day. Data are the mean ± SEM.

Evaluation of motivational factors in animals trained at different water temperatures

A critical issue was whether the differences in path length observed in rats trained at different water temperatures were due to differential motivation to escape from the water (i.e., to find the platform) or to genuine differences in spatial learning capabilities. To address this issue, a similar experiment was carried out on a new set of animals ( n = 9/temperature group), although here the platform was visible (not submerged) and cued. A repeated-measures ANOVA indicated an effect of training days ( F (2,48) = 5, P < 0.05), confirming that rats progressively reached the platform after shorter navigation distances. In contrast, there was no effect for water temperature ( F (2,24) = 1.5, n.s) and no interaction between the two factors ( F (4,48) = 0.37, n.s; Fig. 2 D). Similar findings were obtained when data from the three training days were averaged, yielding no differences in the number of errors to find a cued platform among groups of rats trained at different temperatures ( F (2,24) = 1.5, n.s; Fig. 2 E).

Evaluation of long-term retention

Long-term retention was tested both during and after the initial spatial training by applying different testing opportunities. First, we analyzed data from the first trial of the second training day, because this trial can be considered the earliest long-term memory test ( Fig. 2 C) (note that this was not a probe trial, but a regular training trial). An ANOVA indicated an effect of water temperature ( F (2,119) = 3.3, P < 0.05), and post-hoc analyses confirmed that the data followed a U-shape function, with animals trained at 19°C making a significantly lower number of arm entry errors to find the platform than those trained at either 25°C or 16°C ( P < 0.05). When the same analysis was performed on data from the cued platform version, no differences in performance were found among animals trained at different temperatures on the first trial of day 2 ( F (2,24) = 0.65, n.s; Fig. 2 F).

On day 8 (i.e., 5 d after the last training session), rats were administered a probe test in which the platform was removed and the water temperature was kept equal (20°C ± 0.5°C) for all groups. Different parameters were analyzed for the duration of the probe trial (60 sec) and for the first and second half of the test trial. No significant differences were found in the arm entry errors to reach the virtual platform among animals that had been trained at the different water temperatures ( F (2,119) = 2.06, P = 0.13; Supplemental Fig. S4). However, an interesting finding arose when animals' strategies (i.e., whether they spent more time in the error arms, the target arm, or the center of the pool) were evaluated in a time-dependent fashion (i.e., the first and last 30 sec of the probe trail analyzed separately; Fig. 3 ). An ANOVA on the amount of time spent in the target arm over the first 30 sec indicated a significant difference among the groups ( F (2,119) = 3.24, P < 0.05). Post-hoc analyses indicated that rats trained at 25°C spent less time in the target arm than rats trained at 16°C ( P < 0.05) or 19°C ( P < 0.05; Fig. 3 A). Furthermore, an ANOVA for the amount of time spent in the error arms during the first 30 sec revealed a significant difference of the three groups ( F (2,119) = 4.1, P < 0.05; Fig. 3 C); animals trained at 16°C and 19°C spent significantly less time in the error arms than those trained at 25°C ( P < 0.05). Finally, an ANOVA of the time spent in the center of the pool during the last 30 sec indicated a difference among the three groups ( F (2,119) = 3.41, P < 0.05; Fig. 3 F). Specifically, rats trained at 19°C spent significantly more time in the center of the pool than animals trained at 25°C ( P < 0.05). All together, these data indicate that when tested under identical experimental conditions (i.e., the same water temperature), animals previously trained at different water temperatures differ in their behavioral pattern, with the most significant differences appearing between animals trained at 19°C and 25°C and the latter displaying a more erratic search pattern. In other words, the animals trained at 25°C spent more time in the error arms and less time in the target arm than 19°C-trained animals. However, performance of the animals trained at 16°C was similar to those trained at 19°C, showing performance significantly superior to animals trained at 25°C during the first 30 sec.

Performance of animals trained in the spatial RAWM version at different water temperatures when administered a probe trial on day 8 at identical temperature conditions (20°C ± 0.5°C). Results are shown for the first and last 30 sec of the probe trial and are represented as the percent time in the target arm ( A , B ), the error arms ( C , D ), and the center of the pool ( E , F ). Data are the mean ± SEM. (*) P < 0.05 vs. 25°C.

The impact of increasing psychogenic stress: Reversal learning

After a further training day (day 9; no differences in performance were found among the groups; data not shown), on which animals were retrained as on days 1–3, all groups were submitted to a reversal learning session on day 10 using water temperatures that matched temperatures from previous training days (16°C, 19°C, or 25°C) ( Fig. 4 ). An ANOVA on the arm entry errors from trials 2–4 (the first trial was novel to all animals and not indicative of learning processes, so it was excluded from analyses) indicated a significant effect of temperature ( F (2,119) = 3.55, P < 0.05), and post-hoc analyses indicated that animals trained at 16°C made significantly more errors to reach the platform than those trained at either 19°C ( P = 0.05) or 25°C ( P < 0.05).

The effect of water temperature on performance in the reversal learning session. Rats trained at 16°C showed poor performance compared with rats trained at either 19°C or 25°C. Data are the mean number of arm entry errors ± SEM. (*) P < 0.05 vs. 16°C.

Individual differences and the inverted-U shape

One of the goals set for this study was to evaluate whether animals showing different behavioral profiles differ in how stress affects their performance during learning and memory tests. Data from principal component analyses performed on tests administered for behavioral characterization were used to classify animals into dichotomized variables for each behavioral trait (i.e., locomotion, anxiety, and exploration) (see Materials and Methods for details on the principal component analyses performed and the extracted factors, and Supplemental Tables S1–S3). Thus, animals were classified according to whether their score was above or below the mean for each factor into groups of low (LL) or high (HL) locomotion, low (LA) or high (HA) anxiety, and low (LE) or high (HE) exploration. Mean comparisons on the scores for each variable confirmed that the dichotomized groups representing high and low scores for each trait differed significantly (all Student t -tests; P < 0.01; Supplemental Fig. S5). RAWM performance of these groups was then compared using parametric analyses on the learning and memory data.

A factorial ANOVA, with temperature and the three behavioral traits extracted from the principal component analyses as the factors, performed on data from the first three RAWM training days, revealed a lack of significant interaction (n.s.). There was also no effect of each personality factor (n.s.). Further factorial ANOVAs performed on combinations of two behavioral traits and water temperature as factors did not yield statistical significance, except when anxiety and exploration were combined ( F (2,110) = 4.64, P < 0.05). Next, simple main effect analyses were performed to evaluate the impact of water temperature on RAWM learning for each behavioral profile resulting from the dichotomized groups of anxiety and exploration (HA-HE, LA-HE, HA-LE, LA-LE; Fig. 5 ). These analyses confirmed a U-shape relationship for the HA-HE profile, with animals trained at 19°C performing significantly better than those trained at 16°C ( P < 0.05) or 25°C ( P < 0.01). Among both the LA-HE and the HA-LE profiles, the group trained at 16°C performed significantly worse than the 19°C group ( P < 0.01), whereas performance at 25°C did not differ significantly from either of the other groups (n.s). Interestingly, a different pattern was observed for the LA-LE profile; animals trained at 25°C performed significantly worse than those trained at 19°C ( P < 0.01) or 16°C ( P < 0.05). Furthermore, an analysis of performance at each water temperature for the different personality groups revealed an effect of personality profiles at 25°C, with superior performance being observed for the HA-LE and LA-HE groups relative to the HA-HE and LA-LE groups (Supplemental Fig. S6).

Performance in the RAWM during the first training day at different water temperatures according to the personality profiles of high anxiety-high exploration (HA-HE), low anxiety-high exploration (LA-HE), high anxiety-low exploration (HA-LE), and low anxiety-low exploration (LA-LE). Only the HA-HE group displayed a U-shape learning response at different water temperatures. (*) P < 0.05 and (**) P < 0.01 vs. 19°C, (#) P < 0.05 vs. 16°C.

We report here, for the first time, the existence of an inverted-U-shape relationship between intrinsic stress intensity and performance in a hippocampus-dependent learning task, the RAWM. Various stress intensities were achieved using water temperatures of 25°C, 19°C, and 16°C to elicit increasing plasma corticosterone levels. By submitting rats to different training and testing protocols, we confirmed the existence of an inverted-U-shape function for performance at training; animals trained at 19°C made less errors to find the platform than animals trained at either higher (16°C) or lower (25°C) stress conditions. However, a long-term memory (probe) test performed 1 wk after training under equal temperature conditions (20°C ± 0.5°C) revealed a different performance pattern ( Fig. 3 ). Although the groups did not significantly differ in the number of errors made before reaching the virtual platform, analysis of the behavioral profile displayed during the test revealed that rats trained at 25°C were less accurate in platform searching than rats trained at either 16°C or 19°C, while no difference in searching was found for the latter two groups. When a cognitive challenge was subsequently introduced by changing the platform location (reversal learning), the groups trained at both 19°C and 25°C showed better performance than rats trained at 16°C, suggesting that cognitive difficulty affects the cognitive impact of “physical” stress. Furthermore, we presented evidence supporting the view that stress does not affect spatial learning and memory uniformly in all individuals. Rather, performance at either the high- or the low-stress levels is differentially affected in individuals with different personality-like profiles.

Previous studies using the Morris water maze ( Morris 1984 ) showed that rats trained at 19°C perform better than rats trained at 25°C, and corticosterone levels after the first training session were higher in rats trained at the colder water temperature ( Sandi et al. 1997 ; Akirav et al. 2004 ). A similar association among water temperature, learning and memory rate, and post-training corticosterone levels was also recently described in mice ( Conboy and Sandi 2010 ). Selden et al. (1990) presented evidence for impaired training at lower water temperatures (12°C) in rats, and they implicated coeruleo-cortical noradrenergic projections in the impairing effects of high stress on spatial learning. Here, we confirm the ascending portion of the U-shaped curve for the RAWM acquisition phase at 25°C (low stress) and 19°C (optimal stress) water temperature. Moreover, we show evidence supporting the existence of the descending portion of the U-shaped curve in animals trained at 16°C (high stress, or physical conditions leading to highest corticosterone levels) under otherwise identical experimental conditions. Importantly, differences in performance between animals trained at different temperatures seem to be related to the spatial learning nature of the RAWM task, previously reported to be hippocampus dependent ( Diamond et al. 1999 ), since no differences were found when animals were trained in the nonhippocampus-dependent cued platform version. These results are in agreement with pioneering observations by Wever (1932) , who observed no differences in latency to escape from a nonspatial water task in rats trained at temperatures ranging from 10°C to 25°C. Therefore, we show evidence for the existence of an inverted-U-shape function between stressor intensity and performance, specifically for spatial learning and in the memory test administered 24 h after the first training session.

While this curvilinear function was not captured in earlier work using intrinsic stress approaches, studies involving manipulations of the noradrenergic ( Introini-Collison et al. 1994 ) and glucocorticoid ( Lupien and McEwen 1997 ; Conrad 2005 ; Joëls 2006 ) systems have successfully substantiated the inverted-U-shape relationship between increasing glucocorticoid levels/function and both learning and synaptic plasticity. Glucocorticoids are adrenal hormones released into the bloodstream that, due to their lipophilic nature, can enter the brain, where they can influence brain function and cognition through genomic and nongenomic effects ( de Kloet et al. 1999 , 2005 ). Glucocorticoid receptors [GR] (mineralocorticoid receptors [MR]) are expressed in different brain areas, including regions that are central to learning and memory formation (e.g., hippocampus, amygdala, and prefrontal cortex) ( Sandi 1998 ; de Kloet et al. 1999 ). In chicks ( Sandi and Rose 1997 ), ground squirrels ( Mateo 2008 ), rats ( Roozendaal et al. 1999 ; Okuda et al. 2004 ), and humans ( Andreano and Cahill 2006 ), either very low or high glucocorticoid levels were reported to be associated with poor performance in a variety of learning and memory tasks ( Park et al. 2006 ). Similarly, the magnitude of hippocampal primed burst potentiation (i.e., a physiological type of synaptic plasticity) was shown to follow an inverted-U function relative to serum corticosterone levels (manipulated through adrenalectomy and different corticosterone concentrations delivered through subcutaneous pellets) ( Diamond et al. 1992 ). In agreement with this finding, opposite effects were described for activation of MR and GR in hippocampal long-term potentiation ( Pavlides et al. 1995 , 1996 ) and in a spatial learning task in rats ( Conrad et al. 1997 ), with activation of the MR exerting facilitatory and GR exerting inhibitory effects. However, despite this congruent evidence supporting a U-shape relationship between glucocorticoids and cognitive function, the full story is likely more complex than presented here. For example, cognitive effects depend on many factors, such as surrounding context ( de Kloet et al. 1999 ; Joëls et al. 2006 ), memory phase ( Roozendaal 2003 ), sex ( Conrad et al. 2004 ; Andreano and Cahill 2006 ), estrus cycle in females ( Andreano et al. 2008 ), previous experience, and emotional state ( de Quervain 2008 ; de Quervain et al. 2009 ).

A key question arising from the observed differences in performance of learning and memory tasks when animals were trained under different stress levels is whether these differences translate into differences in the strength of the long-term memory developed. To address this question, all groups were administered a probe test under equal temperature conditions. Strikingly, despite the inferior performance shown during training by the 16°C-trained group (i.e., the high-stress group), their behavioral pattern during the long-term probe test was very similar to that of the 19°C-trained group, which performed optimally during training. However, the group that was trained at 25°C (i.e., the low-stress group) showed during the first 30 sec the most erratic search patterns of the three groups, being the group that spent the most time in the error arms and the least time in the target arm. These data suggest that the 16°C-trained rats formed a stronger memory for the platform location than the 25°C-trained rats. The contribution of state-dependent mechanisms in this latter group cannot be discarded, since this group was the only one that was tested in the probe trial at a lower temperature than in previous sessions, and this difference might have produced an additional stress contributing to the impairing effect during this testing session. These findings also suggest that the deficits observed during the training phase in the 16°C group were probably due not only to impaired learning but also to impaired performance, particularly toward the final phase of training. This possibility would agree with a proposal by de Kloet et al. (1999) and Joëls et al. (2006) , both of whom suggested that when individuals are confronted with high stress levels, their strategy switches from an information-processing mode to a more opportune response that is adapted to the actual condition. More specifically, animals tested at a lower temperature in the probe trial may have changed strategies to conserve energy at the expense of navigation. Although this interpretation is plausible, we were surprised to find no differences in the speed at which the different water temperature groups swam and, hence, find no evidence for a change in a metabolic-related behavioral strategy. Furthermore, we did not find differences among groups in body temperature following training at different temperatures. Moreover, the fact that no differences were observed in the cued platform version of the task further suggests that the training deficits found in the 16°C and 25°C groups were, at least in part, related to the spatial orientation learning nature of the task and not to nonspecific effects related, for example, to swimming ability, hypothermia, or tracking down the relevant cues. Importantly, these results also strongly support the current view that stress (and glucocorticoids) facilitates memory consolidation ( Oitzl and de Kloet 1992 ; Sandi and Rose 1994 ; Sandi 1998 ; Roozendaal et al. 1999 , 2008 ; Sandi and Pinelo-Nava 2007 ; de Quervain et al. 2009 ).

We also found that in a subsequent training session using temperatures matching initial training, all groups achieved similar performance levels, suggesting that the observed inverted-U-shape relationship might be related to the initial stages of learning acquisition. With overtraining, initial differences due to variations in stress level seem to disappear. Then, when a new cognitive challenge was introduced (i.e., change of platform location in the reversal learning session), the 16°C group became impaired not only relative to the 19°C group, but also relative to the 25°C group, and performance of the 25°C group resembled the 19°C optimally performing group. This result is in agreement with studies testing the prediction from the Yerkes-Dodson law that the optimal stress or arousal state decreases with increasing task difficulty ( Mendl 1999 ). Therefore, the increase in task difficulty produced by the platform change would have extended the level of optimal stress for this type of learning from 19°C to 25°C ( Hancock and Ganey 2003 ).

Finally, we examined whether all individuals equally displayed the U-shape effects that we observed during training and the 24-h memory test. Previously, we reported that certain behavioral traits, such as anxiety, render subjects more sensitive to the behavioral and neurobiological effects of stress ( Jakobsson et al. 2008 ; Sandi et al. 2008 ; Luksys et al. 2009 ) and influence spatial learning abilities ( Herrero et al. 2006 ). Here, we considered whether more than one personality trait could contribute to differential performance under stress. To do so, we first extracted personality traits by applying principal component analyses to a series of behavioral tests for spontaneous behavior of rats. While the factor “locomotion” did not contribute to defining individuals with different responsiveness, the combination of the factors “anxiety” and “exploration” resulted in a meaningful interaction, yielding four personality-like profiles (HA-HE, HA-LE, LA-HE, and LA-LE). Animals falling into each of these different profiles showed different patterns of “learning under stress.” Highly anxious and highly explorative animals (HA-HE) were the only animals whose learning under different stress levels exhibited the U-shape function. Interestingly, among the remaining three profiles, two (HA-LE and LA-HE) showed optimal performance in the low-stress condition (25°C water) and impaired performance in the high-stress condition (16°C water), but one profile (LA-LE) showed the opposite pattern (i.e., optimal performance in the high-stress condition and impaired performance in the low-stress condition). These opposite response patterns to the different stress levels explain why an inverted-U shape is observed at the population level. In addition, these findings raise many interesting questions and, given the lack of similar studies in humans, raise the interest of addressing similar questions in humans. One interesting implication to extract from this study is that different personality types may be differentially affected in their cognitive functioning under varying stress levels. Therefore, the precise shape of the inverted-U-shape curve may vary for different personality types from a narrow bell revealing that performance is maximal only within a limited range of stimulus intensities (as observed in the HA-HE group) to curves that show maximal performance at either low (LA-HE, HA-LE) or high (LA-LE) stress levels (Supplemental Fig. S7). Interestingly, a physiological treatment that results in decreased anxiety to novelty ( Vataeva et al. 2001 ) was found to improve learning in the water maze at a temperature of 16°C–17°C, whereas performance was impaired at 23°C–24°C ( Vataeva et al. 2005 ). Accordingly, our study supports the conclusion that stress effects on hippocampus-dependent learning tasks vary for different personality profiles. Furthermore, our findings provide an attractive behavioral model to characterize the neurobiological mechanisms involved in the differential impact of stress levels in cognitive performance as well as the intrinsic interactions among personality, stress, and cognitive processes.

• Materials and Methods

Adult male Wistar rats (Charles River Laboratories, Lyon, France), weighing 200–225 g at the beginning of the experiments, were housed in groups of three per cage. They were maintained under light (12 h light/dark cycle; lights on at 7:00 am) and temperature (22°C ± 2°C)-controlled conditions. Food and water were available ad libitum. Animal care procedures were approved through a license issued by the Cantonal Veterinary Authorities (Vaud, Switzerland).

General procedure

All experiments were conducted between 9:00 and 14:00 h. Approximately 2 wk after arrival, each rat was handled for 3 d, 2 min per day, just before the behavioral characterization started. The behavioral characterization included, first testing in the elevated plus maze, and 4 d afterward testing in the open field and novel object reactivity test. One week afterward, animals were distributed into three groups that were balanced for behavioral traits and body weights, and each group was submitted to training in the RAWM at a different water temperature (16°C, 19°C, or 25°C). Water-maze training was performed using either a cued-platform version or a spatial learning version. In all behavioral tests, the behavior of each rat was monitored using a video camera located on the ceiling, and movements of the rats were automatically registered and analyzed with a computerized tracking system (Ethovision 3.1.16, Noldus IT).

Behavioral characterization

Elevated plus maze (epm).

The first behavioral test was the elevated plus-maze ( Herrero et al. 2006 ), which is widely used to evaluate animals' anxiety-related behaviors. The elevated plus maze consists of two opposing open arms (45 × 10 cm) and two closed arms (45 × 10 × 50 cm) that extend from a central platform (10 × 10 cm), elevated 65 cm above the floor. The rats were placed individually on the central platform, always facing the same enclosed arm, and were allowed to freely explore the maze for 5 min. Different parameters were evaluated with the video tracking system: total distance moved (centimeters), distance moved (centimeters), and time spent (seconds) in the open and closed arms, and number of times the animal entered each type of arm. The floor of the apparatus was washed after each testing with 1% acetic acid solution to remove odors left by previous subjects.

Open field (OF) and novel object reactivity (NOR) tests

Animals' behavior was also assessed in the open field test (OF), which involves placing the animals in a circular open arena (100-cm diameter, 32-cm high). For analysis, the floor was divided into three virtual concentric parts, with a center zone in the middle of the arena (20-cm diameter), an interior zone (60-cm diameter), and an exterior zone made up of the remaining area along the sidewalls. At the start of the test, animals were placed in the center of the arena, and their behavior monitored for 10 min using a video camera mounted on the ceiling above the center of the arena. Different parameters were evaluated with the video tracking system: distance moved (centimeter) and time spent (seconds) in each zone.

Immediately after the open field test, rats were submitted to the novel object reactivity (NOR) test. For this purpose, a small, white plastic bottle (3 × 1.5 × 5 cm) was placed into the center of the open field while the rat was inside. Rats were then given 5 min to freely explore the novel object. Different parameters were evaluated with the video tracking system: time spent (seconds) in the center and the periphery of the compartment, number and latency of entries to the center, total distance moved (centimeters) in the center and in the whole compartment. The time spent exploring (touching) the novel object and the freezing time were recorded manually from the video recordings ( Jakobsson et al. 2008 ).

The apparatus used for testing spatial memory was a round black Plexiglas tank that was filled with clear water. The tank had a diameter of 170 cm and a height of 45 cm. Within the tank were Plexiglas walls that extended from the floor to a height of 43 cm and had a length of 60 cm. The walls were positioned to produce six swim paths radiating out of an open central area. A black metal platform (11-cm diameter) positioned 1.5 cm below the surface of the water was located at the end of one of the swim paths (arms), and the platform edge was ∼8 cm from the tank wall. When the rats swam to the end of this arm (referred to as the “target” arm) they could climb onto the platform to get out of the water. The tank was located in the middle of a well-lit testing room. Visually distinct cues were attached to the walls adjacent to the tank. All animals from each home cage were tested under the same water temperature condition. They were taken individually from the adjacent housing room and directly tested in the water maze.

The following parameters were evaluated with the video tracking system: latency (seconds) to find the platform, distance (centimeters) traveled to find the platform, and swim speed. The number of arm entry errors was determined according to the criteria established by Diamond et al. (1999) as the number of arm entries that did not result in the rat finding the escape platform. An arm entry was defined as a rat having all four paws extended out of the center area into an arm. An error was committed if a rat entered an arm that did not contain the platform or if a rat entered the correct arm but did not find the platform. Since we observed a very high correlation for the parameters “distance” to find the platform and “arm entry errors” ( r = 0.92, P < 0.001) and confirmed that the data for “distance” and “latency” gave similar results to analyses on “arm entry errors,” we only present the data corresponding to the “arm entry errors” parameter.

Animals were trained in either a cued or a spatial version of the RAWM. In the cued version, the platform is elevated slightly over the surface of the water and signaled with a 10-cm flag. This version is not sensitive to hippocampal lesions, so it is considered a hippocampus-independent task. Performance in the spatial version (in which the escape platform is hidden) is sensitive to hippocampal damage, so it is considered a hippocampus-dependent task. In each of these tasks, three different groups of animals were trained at different water temperatures that were selected with the goal of representing different stressor intensities (i.e., low, moderate, high stress). The temperatures of 19°C and 25°C were previously shown to be appropriate temperatures to elicit different stress levels in rats. The temperature of 16°C was added to enhance stressor intensity. Two independent experiments were performed with the cued version paradigm, one designed to evaluate plasma corticosterone levels immediately after the first training session at the different water temperatures ( n = 6/group), and a second one to evaluate motivational factors and performance over consecutive days ( n = 9/group). As to the spatial version protocol, a higher number of animals per group than in conventional studies was required to perform analyses, taking into account the combination of personality traits (final number of animals per group: 16°C, n = 35; 19°C, n = 50; 25°C, n = 37). A total of five replication experiments were performed, three of them including all water temperatures ( n = 8–9/group for each replication) and two of them involving two water temperature conditions (19°C in both cases and either 16°C or 25°C in each of the replications; n = 12/group for each replication). In each replication experiment, all water-temperature groups included were sequentially tested on the same days in a single RAWM. The order at which the different groups were run on each training day was counterbalanced both for different training days within each replication experiment and for each of the training days across the different replication experiments following a semirandom schedule. Every day, water temperature was easily changed by either adding hot water (available through the tap water) or ice obtained from an ice-making machine located in the animal facilities.

The acquisition phase of the spatial task consisted of a block of four trials per day run on each of three consecutive days. Four different starting arms were equally chosen around the perimeter of the pool. On each day, all four start positions were used once in a random sequence that was held constant for all rats. A trial began by placing the rat into the water facing the center of the pool at one of the starting points. If the animal failed to escape within 90 sec, it was manually guided to the platform. The animal was allowed to remain on the platform for 15 sec and was then placed into a holding cage under a warming lamp for 30 sec until the start of the next trial. After a rest period, on day 8 rats received a 60-sec free-swim period, during which the platform was removed from the maze (probe trial). At the end of the probe trial, the platform was reinserted into the pool and rats remained on it for 15 sec. On day 9, rats were retrained with another four-trial training session under the same conditions as described above. One day later (day 10), a reversal learning session was conducted, in which the platform position was changed to a different arm. Similar to the first 3 d of the experiment, the reversal session included four trials. After the last trial on each day, the rats were carefully dried with a towel and placed in the heated waiting cage for 10 min. Rats were then returned to their home cages.

Corticosterone analysis

Trunk blood was collected by decapitation 45 min after the beginning of a 1-d cued training session. The experiment was performed between 10 am and 1 pm. Samples were centrifuged (4000 rpm for 20 min at 4°C), and the serum was extracted and stored at −20°C. Corticosterone levels were assayed by ELISA (Assay Design) according to the manufacturer's instructions.

Statistical analyses

Results are expressed as mean ± SEM. The SPSS 13.0 statistical package was used for the statistical analyses.

Parametric statistics

Mean comparisons were carried out with either one-way or factorial ANOVAs; simple main effects analyses or post-hoc comparisons were made with LSD tests when appropriate. Normality and homogeneity of variance was tested, and adjusted statistics were used if required. Unless otherwise indicated, analyses of behavioral parameters excluded the first training trial (when no learning has as yet taken place).

Principal component analyses (PCA)

PCAs were applied to characterize animals according to their behaviors from the EPM, OF, and NOR tests. For the factorial analysis, which was twofold, the number of extracted factors was not predefined. Rather, PCAs were applied separately to a range of extracted parameters from the EPM (Supplemental Table 1) and the OF-NOR tests (Supplemental Table 2). Then, an overall principal component analysis was performed on the extracted factors, which revealed three factors that were termed “locomotion,” “anxiety,” and “exploration” according to the parameters that defined them (Supplemental Table 3). A continuous, interval scale score was calculated for each factor using principal components as the extraction method and varimax rotation with Kaiser normalization rotation. Then, individual factor scores were calculated for each subject through the relative weight and orientation (eigen values) of the parameters for each factor. Scores were generated using a Z distribution, where the value 0 corresponds to the mean, and values are expressed in terms of standard deviations. Animals were matched for their scores in the different factors and classified into the different experimental groups to yield groups with similar personality traits. In addition, data from the factorial analyses were used to investigate the modulatory effect of factor score differences on the learning measures investigated. For this study, animals were classified into groups such that scores laid either above or below the mean for each of the factors.

• Acknowledgments

This work has been supported by grants from the EU (FP7-HEALTH-F2M-2008-201600, MemStick), the Swiss National Science Foundation (310000-120791), and intramural funding from the EPFL. We thank Cristina Marquez and Coralie Siegmund for technical assistance and the Laboratory of Behavioral Genetics at the EPFL for helpful discussions.

↵ 1 Corresponding author.

E-mail carmen.sandi{at}epfl.ch ; fax 41-21-6939636.

[Supplemental material is available online at http://www.learnmem.org. ]

• Received June 18, 2010.
• Accepted July 27, 2010.
• © 2010 Cold Spring Harbor Laboratory Press
• Richter-Levin G
• Kozenicky M ,
• Anagnostaras SG ,
• Josselyn SA ,
• Frankland PW ,
• Andreano JM ,
• Arjomandi H ,
• Baumler G ,
• Beylin AV ,
• Broadbent DE
• Broadhurst PL
• Conrad CD ,
• Lupien SJ ,
• Thanasoulis LC ,
• Jackson JL ,
• Wieczorek L ,
• Harman JS ,
• Wright RL ,
• Cordero MI ,
• Merino JJ ,
• de Kloet ER ,
• de Quervain DJ
• de Quervain DJF ,
• Schelling G ,
• Roozendaal B
• Diamond DM ,
• Bennett MC ,
• Fleshner M ,
• Campbell AM ,
• Halonen J ,
• Fanselow MS ,
• Hancock PA ,
• Herrero AI ,
• Introini-Collison IB ,
• Castellano C ,
• Jakobsson J ,
• Groner AC ,
• Busskamp V ,
• Bensadoun J-C ,
• Mansuy IM ,
• Wiegert O ,
• Lightman SL
• Gerstner W ,
• de Kloet ER
• Roozendaal B ,
• Woodson JC ,
• Pavlides C ,
• Watanabe Y ,
• Magarinos AM ,
• Radulovic J ,
• Kammermeier J ,
• Nguyen BT ,
• Barsegyan A ,
• Pinelo-Nava MT
• Loscertales M ,
• Ugolini A ,
• Caberlotto L ,
• Selden NRW ,
• Everitt BJ ,
• Servatius RJ
• Vataeva LA ,
• Kostkin VB ,
• Makukhina GV ,
• Khozhai LI ,
• Tyul'kova EI ,
• Samoilov MO ,
• Yerkes RM ,

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Inverted-U Theory (Yerkes-Dodson Law)

The Inverted-U Theory is a psychological model that suggests that there is an optimal level of arousal for peak performance.

The theory was first proposed by Robert Yerkes and John Dodson in 1908 , and it has since been supported by empirical evidence.

What is the Inverted-U Theory (Yerkes-Dodson Law)?

The Inverted-U Theory is also known as the Yerkes-Dodson law.

It is a psychological model which suggests that there is an optimal level of arousal for peak performance. The theory states that as arousal levels increase, so does performance, but only up to a point.

Once arousal levels become too high, performance begins to decline. The Inverted-U Theory can help to explain why some people perform better under pressure and why some crumble.

It also has implications for education, training, and job design. For example, if a task is too easy, it may not provide enough stimulation to lead to peak performance. On the other hand, if a task is too difficult, it may lead to anxiety and suboptimal performance.

Thus, the goal is to find the Goldilocks zone of challenge: not too hard and not too easy, but just right. When this sweet spot is found, it can lead to peak performance on both an individual and organizational level.

What is the Yerkes-Dodson Curve?

The Yerkes-Dodson curve is a graphical representation of the Inverted-U Theory. It shows how performance improves with increasing levels of arousal, but only up to a point.

Once arousal levels become too high, performance begins to decline. The Yerkes-Dodson curve is a valuable tool for understanding the optimal performance and how it can be achieved.

Yerkes-Dodson curve is a supporting tool for psychologists and others who need to understand how different levels of arousal can impact performance. It can also be used to help individuals identify their own optimum level of arousal for different tasks.

Low Arousal and Performance

If arousal levels are too low, it can lead to boredom and apathy. When people are bored, they may daydream or become disengaged from the task at hand. This can direct to poor performance and even accidents. For example, if a driver is bored, they may not pay attention to the road and may have an accident.

High Arousal and Performance

If arousal levels are too high, it can lead to anxiety and poor performance. When people are anxious, they may make mistakes or freeze up. This can lead to suboptimal performance on both an individual and organizational level.

The Optimal Level of Arousal

The optimal level of arousal for peak performance is often referred to as the “Goldilocks zone.” This is because it is not too high and not too low, but just right. When people are in the Goldilocks zone, they are able to perform at their best. This can lead to better results on both an individual and organizational level.

How Can You Tell if You Are in the Goldilocks Zone?

There is no single answer to this question as it will vary from person to person. However, some known signs that you may be in the Goldilocks zone include feeling focused and alert, feeling like you have enough energy to complete the task at hand, and being able to think clearly.

If you are experiencing anxiety or stress, this may be a sign that you are outside of the Goldilocks zone.

What Are Some Ways to Stay in the Goldilocks Zone?

There are a few different things you can do to stay in the Goldilocks zone.

• First, it is essential to find a balance between challenge and skill. If a task is too easy, it may not provide enough stimulation to lead to peak performance.
• Second, you can try to keep your arousal levels in check by using relaxation techniques such as deep breathing or visualization.
• Finally, it is essential to be aware of your own individual stress triggers and to avoid them if possible. If you know that certain things tend to increase your stress levels, try to avoid them or at least be prepared for them.

What Are Some Real-World Examples of the Inverted-U Theory?

The Inverted-U Theory can be seen in a variety of real-world situations. For example, athletes often use it to understand how different levels of arousal affect their performance.

Individuals who are taking a test or giving a presentation may also use the Inverted-U Theory to find the optimal level of arousal for peak performance.

Finally, the Inverted-U Theory can be used to help individuals find the optimal level of arousal for their specific goals.

Difference Between Pressure and Stress

It is important to understand the difference between pressure and stress.

Pressure is a normal part of life that can lead to improved performance. Stress is a negative response to pressure that can lead to poor performance.

Pressure is a necessary ingredient for peak performance. It can help us to focus and do our best. Stress is an unhelpful response to pressure that can lead to anxiety and poor performance.

Pressure is a normal part of life, but it is vital to learn how to cope with it in a healthy way.

Stress is a negative response to pressure that can be harmful to our physical and mental health. It is essential to learn how to manage stress in a healthy way.

What Are the Limitations of the Inverted-U Theory?

The Inverted-U Theory is a helpful model for understanding optimal performance, but it is not without its limitations. One limitation is that it does not take into account individual differences.

Some people may perform better at higher levels of arousal than others, and this is not captured by the theory. Another limitation is that it only applies to relatively simple tasks.

For more complex tasks, the relationship between arousal and performance is more likely to be U-shaped, with both low and high levels of arousal leading to suboptimal performance.

Despite its limitations, the Inverted-U Theory is a valuable tool for understanding how different levels of arousal affect performance and for finding the optimal level of arousal for peak performance.

Conclusion: Inverted-U Theory (Yerkes-Dodson law)

The Yerkes-Dodson law is a cognitive principle that suggests there is an inverted-U relationship between arousal and performance.

In other words, as arousal levels increase, productivity or performance levels also increase up to a point. After that point, however, further increases in arousal lead to decreases in productivity.

This theory has been used extensively in the field of sports psychology to help athletes achieve the optimal level of arousal for competition.

The inverted-U curve can be seen in many different areas of life, such as work stressors and emotions. It’s important to note that each individual experiences this relationship differently, and you may have to experiment with different levels of stimulation to find what works best for you.

We hope this article has helped you better understand the Yerkes-Dodson law (Inverted-U Theory) and how it applies to your own life.

Frequently Asked Questions

How does the inverted-u theory apply to workplace productivity.

It suggests an optimal arousal level for peak performance, implying that too little or too much pressure can decrease productivity.

Can the Inverted-U Theory help in personal stress management?

Yes, by identifying optimal stress levels, individuals can manage stress for better performance and well-being.

What role does arousal play in the Inverted-U Theory?

Arousal influences performance; moderate arousal levels are ideal for optimal performance, while too high or low levels can hinder it.

How can organizations use the Inverted-U Theory?

Organizations can tailor tasks and environments to maintain optimal arousal levels among employees, enhancing efficiency and satisfaction.

What are the limitations of the Inverted-U Theory?

It doesn’t account for individual differences in stress tolerance or task complexity, affecting its application’s universality.

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Le Corbusier’s triumphant return to Moscow

The exhibition of French prominent architect Le Corbusier, held in The Pushkin Museum, brings together the different facets of his talent. Source: ITAR-TASS / Stanislav Krasilnikov

The largest Le Corbusier exhibition in a quarter of a century celebrates the modernist architect’s life and his connection with the city.

Given his affinity with Moscow, it is perhaps surprising that the city had never hosted a major examination of Le Corbusier’s work until now. However, the Pushkin Museum and the Le Corbusier Fund have redressed that discrepancy with the comprehensive exhibition “Secrets of Creation: Between Art and Architecture,” which runs until November 18.

Presenting over 400 exhibits, the exhibition charts Le Corbusier’s development from the young man eagerly sketching buildings on a trip around Europe, to his later years as a prolific and influential architect.

The exhibition brings together the different facets of his talent, showing his publications, artwork and furniture design alongside photographs, models and blueprints of his buildings.

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Irina Antonova, director of the Pushkin Museum, said, “It was important for us to also exhibit his art. People know Le Corbusier the architect, but what is less well know is that he was also an artist. Seeing his art and architecture together gives us an insight into his mind and his thought-processes.”

What becomes obvious to visitors of the exhibition is that Le Corbusier was a man driven by a single-minded vision of how form and lines should interact, a vision he was able to express across multiple genres.

The upper wings of the Pushkin Museum are separated by the central stairs and two long balconies. The organizers have exploited this space, allowing comparison of Le Corbusier’s different art forms. On one side there are large paintings in the Purist style he adapted from Cubism, while on the other wall there are panoramic photographs of his famous buildings.

Le Corbusier was a theorist, producing many pamphlets and manifestos which outlined his view that rigorous urban planning could make society more productive and raise the average standard of living.

It was his affinity with constructivism, and its accompanying vision of the way architecture could shape society, which drew him to visit the Soviet Union, where, as he saw it, there existed a “nation that is being organized in accordance with its new spirit.”

The exhibition’s curator Jean-Louis Cohen explains that Le Corbusier saw Moscow as “somewhere he could experiment.” Indeed, when the architect was commissioned to construct the famous Tsentrosoyuz Building, he responded by producing a plan for the entire city, based on his concept of geometric symmetry.

Falling foul of the political climate

He had misread the Soviet appetite for experimentation, and as Cohen relates in his book Le Corbusier, 1887-1965, drew stinging attacks from the likes of El Lissitsky, who called his design “a city on paper, extraneous to living nature, located in a desert through which not even a river must be allowed to pass (since a curve would contradict the style).”

Not to be deterred, Le Corbusier returned to Moscow in 1932 and entered the famous Palace of the Soviets competition, a skyscraper that was planned to be the tallest building in the world.

This time he fell foul of the changing political climate, as Stalin’s growing suspicion of the avant-garde led to the endorsement of neo-classical designs for the construction, which was ultimately never built due to the Second World War.

Situated opposite the proposed site for the Palace of the Soviets, the exhibition offers a tantalizing vision of what might have been, presenting scale models alongside Le Corbusier’s plans, and generating the feeling of an un-built masterpiece.

Despite Le Corbusier’s fluctuating fortunes in Soviet society, there was one architect who never wavered in his support . Constructivist luminary Alexander Vesnin declared that the Tsentrosoyuz building was the "the best building to arise in Moscow for over a century.”

The exhibition sheds light on their professional and personal relationship, showing sketches and letters they exchanged. In a radical break from the abstract nature of most of Le Corbusier’s art, this corner of the exhibition highlights the sometimes volatile architect’s softer side, as shown through nude sketches and classical still-life paintings he sent to Vesnin.

“He was a complex person” says Cohen. “It’s important to show his difficult elements; his connections with the USSR, with Mussolini. Now that relations between Russia and the West have improved, we can examine this. At the moment there is a new season in Le Corbusier interpretation.” To this end, the exhibition includes articles that have never previously been published in Russia, as well as Le Corbusier’s own literature.

Completing Le Corbusier’s triumphant return to Russia is a preview of a forthcoming statue, to be erected outside the Tsentrosoyuz building. Even if she couldn’t quite accept his vision of a planned city, Moscow is certainly welcoming him back.

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Yerkes-Dodson Law

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References and Readings

Easterbrook, J. A. (1959). The effect of emotion on cue utilization and the organization of behavior. Psychological Review, 66 (3), 183–201.

Article   Google Scholar  

Mateo, J. M. (2007, December 27). Inverted-U shape relationship between cortisol and learning in ground squirrels. Neurobiology of Learning and Memory (online ), 89 , 582–590.

Yerkes, R. M., & Dodson, J. D. (1908). The relationship of strength of stimulus to rapidity of habit formation. Journal of Comparative Neurology and Psychology, 18 , 459–482.

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In Transit: Notes from the Underground

Jun 06 2018.

Spend some time in one of Moscow’s finest museums.

Subterranean commuting might not be anyone’s idea of a good time, but even in a city packing the war-games treasures and priceless bejeweled eggs of the Kremlin Armoury and the colossal Soviet pavilions of the VDNKh , the Metro holds up as one of Moscow’s finest museums. Just avoid rush hour.

The Metro is stunning and provides an unrivaled insight into the city’s psyche, past and present, but it also happens to be the best way to get around. Moscow has Uber, and the Russian version called Yandex Taxi , but also some nasty traffic. Metro trains come around every 90 seconds or so, at a more than 99 percent on-time rate. It’s also reasonably priced, with a single ride at 55 cents (and cheaper in bulk). From history to tickets to rules — official and not — here’s what you need to know to get started.

A Brief Introduction Buying Tickets Know Before You Go (Down) Rules An Easy Tour

A Brief Introduction

Moscow’s Metro was a long time coming. Plans for rapid transit to relieve the city’s beleaguered tram system date back to the Imperial era, but a couple of wars and a revolution held up its development. Stalin revived it as part of his grand plan to modernize the Soviet Union in the 1920s and 30s. The first lines and tunnels were constructed with help from engineers from the London Underground, although Stalin’s secret police decided that they had learned too much about Moscow’s layout and had them arrested on espionage charges and deported.

The beauty of its stations (if not its trains) is well-documented, and certainly no accident. In its illustrious first phases and particularly after the Second World War, the greatest architects of Soviet era were recruited to create gleaming temples celebrating the Revolution, the USSR, and the war triumph. No two stations are exactly alike, and each of the classic showpieces has a theme. There are world-famous shrines to Futurist architecture, a celebration of electricity, tributes to individuals and regions of the former Soviet Union. Each marble slab, mosaic tile, or light fixture was placed with intent, all in service to a station’s aesthetic; each element, f rom the smallest brass ear of corn to a large blood-spattered sword on a World War II mural, is an essential part of the whole.

The Metro is a monument to the Soviet propaganda project it was intended to be when it opened in 1935 with the slogan “Building a Palace for the People”. It brought the grand interiors of Imperial Russia to ordinary Muscovites, celebrated the Soviet Union’s past achievements while promising its citizens a bright Soviet future, and of course, it was a show-piece for the world to witness the might and sophistication of life in the Soviet Union.

It may be a museum, but it’s no relic. U p to nine million people use it daily, more than the London Underground and New York Subway combined. (Along with, at one time, about 20 stray dogs that learned to commute on the Metro.)

In its 80+ year history, the Metro has expanded in phases and fits and starts, in step with the fortunes of Moscow and Russia. Now, partly in preparation for the World Cup 2018, it’s also modernizing. New trains allow passengers to walk the entire length of the train without having to change carriages. The system is becoming more visitor-friendly. (There are helpful stickers on the floor marking out the best selfie spots .) But there’s a price to modernity: it’s phasing out one of its beloved institutions, the escalator attendants. Often they are middle-aged or elderly women—“ escalator grandmas ” in news accounts—who have held the post for decades, sitting in their tiny kiosks, scolding commuters for bad escalator etiquette or even bad posture, or telling jokes . They are slated to be replaced, when at all, by members of the escalator maintenance staff.

For all its achievements, the Metro lags behind Moscow’s above-ground growth, as Russia’s capital sprawls ever outwards, generating some of the world’s worst traffic jams . But since 2011, the Metro has been in the middle of an ambitious and long-overdue enlargement; 60 new stations are opening by 2020. If all goes to plan, the 2011-2020 period will have brought 125 miles of new tracks and over 100 new stations — a 40 percent increase — the fastest and largest expansion phase in any period in the Metro’s history.

Facts: 14 lines Opening hours: 5 a.m-1 a.m. Rush hour(s): 8-10 a.m, 4-8 p.m. Single ride: 55₽ (about 85 cents) Wi-Fi network-wide

Buying Tickets

• Ticket machines have a button to switch to English.
• You can buy specific numbers of rides: 1, 2, 5, 11, 20, or 60. Hold up fingers to show how many rides you want to buy.
• There is also a 90-minute ticket , which gets you 1 trip on the metro plus an unlimited number of transfers on other transport (bus, tram, etc) within 90 minutes.
• Or, you can buy day tickets with unlimited rides: one day (218₽/ US$4), three days (415₽/US$7) or seven days (830₽/US$15). Check the rates here to stay up-to-date.
• If you’re going to be using the Metro regularly over a few days, it’s worth getting a Troika card , a contactless, refillable card you can use on all public transport. Using the Metro is cheaper with one of these: a single ride is 36₽, not 55₽. Buy them and refill them in the Metro stations, and they’re valid for 5 years, so you can keep it for next time. Or, if you have a lot of cash left on it when you leave, you can get it refunded at the Metro Service Centers at Ulitsa 1905 Goda, 25 or at Staraya Basmannaya 20, Building 1.
• You can also buy silicone bracelets and keychains with built-in transport chips that you can use as a Troika card. (A Moscow Metro Fitbit!) So far, you can only get these at the Pushkinskaya metro station Live Helpdesk and souvenir shops in the Mayakovskaya and Trubnaya metro stations. The fare is the same as for the Troika card.
• You can also use Apple Pay and Samsung Pay.

Rules, spoken and unspoken

No smoking, no drinking, no filming, no littering. Photography is allowed, although it used to be banned.

Stand to the right on the escalator. Break this rule and you risk the wrath of the legendary escalator attendants. (No shenanigans on the escalators in general.)

Get out of the way. Find an empty corner to hide in when you get off a train and need to stare at your phone. Watch out getting out of the train in general; when your train doors open, people tend to appear from nowhere or from behind ornate marble columns, walking full-speed.

Always offer your seat to elderly ladies (what are you, a monster?).

An Easy Tour

This is no Metro Marathon ( 199 stations in 20 hours ). It’s an easy tour, taking in most—though not all—of the notable stations, the bulk of it going clockwise along the Circle line, with a couple of short detours. These stations are within minutes of one another, and the whole tour should take about 1-2 hours.

Start at Mayakovskaya Metro station , at the corner of Tverskaya and Garden Ring,  Triumfalnaya Square, Moskva, Russia, 125047.

1. Mayakovskaya.  Named for Russian Futurist Movement poet Vladimir Mayakovsky and an attempt to bring to life the future he imagined in his poems. (The Futurist Movement, natch, was all about a rejecting the past and celebrating all things speed, industry, modern machines, youth, modernity.) The result: an Art Deco masterpiece that won the National Grand Prix for architecture at the New York World’s Fair in 1939. It’s all smooth, rounded shine and light, and gentle arches supported by columns of dark pink marble and stainless aircraft steel. Each of its 34 ceiling niches has a mosaic. During World War II, the station was used as an air-raid shelter and, at one point, a bunker for Stalin. He gave a subdued but rousing speech here in Nov. 6, 1941 as the Nazis bombed the city above.

Take the 3/Green line one station to:

2. Belorusskaya. Opened in 1952, named after the connected Belarussky Rail Terminal, which runs trains between Moscow and Belarus. This is a light marble affair with a white, cake-like ceiling, lined with Belorussian patterns and 12 Florentine ceiling mosaics depicting life in Belarussia when it was built.

Transfer onto the 1/Brown line. Then, one stop (clockwise) t o:

3. Novoslobodskaya.  This station was designed around the stained-glass panels, which were made in Latvia, because Alexey Dushkin, the Soviet starchitect who dreamed it up (and also designed Mayakovskaya station) couldn’t find the glass and craft locally. The stained glass is the same used for Riga’s Cathedral, and the panels feature plants, flowers, members of the Soviet intelligentsia (musician, artist, architect) and geometric shapes.

Go two stops east on the 1/Circle line to:

4. Komsomolskaya. Named after the Komsomol, or the Young Communist League, this might just be peak Stalin Metro style. Underneath the hub for three regional railways, it was intended to be a grand gateway to Moscow and is today its busiest station. It has chandeliers; a yellow ceiling with Baroque embellishments; and in the main hall, a colossal red star overlaid on golden, shimmering tiles. Designer Alexey Shchusev designed it as an homage to the speech Stalin gave at Red Square on Nov. 7, 1941, in which he invoked Russia’s illustrious military leaders as a pep talk to Soviet soldiers through the first catastrophic year of the war.   The station’s eight large mosaics are of the leaders referenced in the speech, such as Alexander Nevsky, a 13th-century prince and military commander who bested German and Swedish invading armies.

One more stop clockwise to Kurskaya station,  and change onto the 3/Blue  line, and go one stop to:

5. Baumanskaya.   Opened in 1944. Named for the Bolshevik Revolutionary Nikolai Bauman , whose monument and namesake district are aboveground here. Though he seemed like a nasty piece of work (he apparently once publicly mocked a woman he had impregnated, who later hung herself), he became a Revolutionary martyr when he was killed in 1905 in a skirmish with a monarchist, who hit him on the head with part of a steel pipe. The station is in Art Deco style with atmospherically dim lighting, and a series of bronze sculptures of soldiers and homefront heroes during the War. At one end, there is a large mosaic portrait of Lenin.

Stay on that train direction one more east to:

6. Elektrozavodskaya. As you may have guessed from the name, this station is the Metro’s tribute to all thing electrical, built in 1944 and named after a nearby lightbulb factory. It has marble bas-relief sculptures of important figures in electrical engineering, and others illustrating the Soviet Union’s war-time struggles at home. The ceiling’s recurring rows of circular lamps give the station’s main tunnel a comforting glow, and a pleasing visual effect.

Double back two stops to Kurskaya station , and change back to the 1/Circle line. Sit tight for six stations to:

7. Kiyevskaya. This was the last station on the Circle line to be built, in 1954, completed under Nikita Khrushchev’ s guidance, as a tribute to his homeland, Ukraine. Its three large station halls feature images celebrating Ukraine’s contributions to the Soviet Union and Russo-Ukrainian unity, depicting musicians, textile-working, soldiers, farmers. (One hall has frescoes, one mosaics, and the third murals.) Shortly after it was completed, Khrushchev condemned the architectural excesses and unnecessary luxury of the Stalin era, which ushered in an epoch of more austere Metro stations. According to the legend at least, he timed the policy in part to ensure no Metro station built after could outshine Kiyevskaya.

Change to the 3/Blue line and go one stop west.

8. Park Pobedy. This is the deepest station on the Metro, with one of the world’s longest escalators, at 413 feet. If you stand still, the escalator ride to the surface takes about three minutes .) Opened in 2003 at Victory Park, the station celebrates two of Russia’s great military victories. Each end has a mural by Georgian artist Zurab Tsereteli, who also designed the “ Good Defeats Evil ” statue at the UN headquarters in New York. One mural depicts the Russian generals’ victory over the French in 1812 and the other, the German surrender of 1945. The latter is particularly striking; equal parts dramatic, triumphant, and gruesome. To the side, Red Army soldiers trample Nazi flags, and if you look closely there’s some blood spatter among the detail. Still, the biggest impressions here are the marble shine of the chessboard floor pattern and the pleasingly geometric effect if you view from one end to the other.

Keep going one more stop west to:

9. Slavyansky Bulvar.  One of the Metro’s youngest stations, it opened in 2008. With far higher ceilings than many other stations—which tend to have covered central tunnels on the platforms—it has an “open-air” feel (or as close to it as you can get, one hundred feet under). It’s an homage to French architect Hector Guimard, he of the Art Nouveau entrances for the Paris M é tro, and that’s precisely what this looks like: A Moscow homage to the Paris M é tro, with an additional forest theme. A Cyrillic twist on Guimard’s Metro-style lettering over the benches, furnished with t rees and branch motifs, including creeping vines as towering lamp-posts.

Stay on the 3/Blue line and double back four stations to:

10. Arbatskaya. Its first iteration, Arbatskaya-Smolenskaya station, was damaged by German bombs in 1941. It was rebuilt in 1953, and designed to double as a bomb shelter in the event of nuclear war, although unusually for stations built in the post-war phase, this one doesn’t have a war theme. It may also be one of the system’s most elegant: Baroque, but toned down a little, with red marble floors and white ceilings with gilded bronze c handeliers.

Jump back on the 3/Blue line  in the same direction and take it one more stop:

11. Ploshchad Revolyutsii (Revolution Square). Opened in 1938, and serving Red Square and the Kremlin . Its renowned central hall has marble columns flanked by 76 bronze statues of Soviet heroes: soldiers, students, farmers, athletes, writers, parents. Some of these statues’ appendages have a yellow sheen from decades of Moscow’s commuters rubbing them for good luck. Among the most popular for a superstitious walk-by rub: the snout of a frontier guard’s dog, a soldier’s gun (where the touch of millions of human hands have tapered the gun barrel into a fine, pointy blade), a baby’s foot, and a woman’s knee. (A brass rooster also sports the telltale gold sheen, though I am told that rubbing the rooster is thought to bring bad luck. )

Now take the escalator up, and get some fresh air.

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