Why are some personalities less plastic?

Abstract

Individuals from the same population typically show consistent differences in behavioural traits that are frequently associated with differences in contextual plasticity. Yet such a correlation might arise either because some individuals are better able than others to detect environmental changes or because the benefits of being plastic are condition-dependent. To discriminate between these two competing hypotheses, I developed an individual-based model that simulates a population in which individuals of varying fighting ability compete by pairwise interactions using either the fixed hawk (aggressive) or dove (peaceful) strategies or a conditional assessment strategy. As anticipated, the model predicts that only individuals with low (and/or intermediate) fighting ability should use the assessment strategy, giving rise to a negative (or dome-shaped) relationship between aggressiveness and plasticity. The proportion of plastic individuals, however, should be affected not only by the environmental conditions in which individuals live but also by the mechanism that would maintain variation in the traits that determine the benefits of plasticity. In particular, if individual differences in fighting ability may be eroded by natural selection, it predicts that ecological conditions that cause assortative interactions (e.g. high predation risks) would contribute in maintaining variation among individuals in their fighting ability, thereby favouring greater plasticity.

1. Introduction

There is ample evidence that individuals within populations (or groups) can differ considerably among each other in their personality traits (i.e. behaviours, like boldness, exploration or aggressiveness, that are consistent across time and contexts [1–4]). Individuals from the same population also typically differ consistently in their propensities to alter their behaviour in response to changing conditions [5], and individual differences in contextual plasticity have been frequently found to be associated with differences in personality traits. Specifically, bold individuals (that are more aggressive and more exploratory) tend to be less plastic than shy individuals in the same population [6], despite the benefits of plasticity that should, as a consequence, promote increased plasticity [7,8]. Individuals capable of adjusting their behaviour to local conditions should, indeed, be expected to achieve higher fitness, particularly in variable environments, compared to less plastic individuals that cannot behave optimally in every situation. Accordingly, recent findings have demonstrated that individuals exhibiting greater plasticity may be more successful in terms of survival [9] or reproduction [10]. Yet, despite the numerous theoretical and empirical studies that have investigated the causes and consequences of consistent individual differences both in behavioural traits [11–13] and contextual plasticity [14–16], the link between personality and plasticity has seldom been examined (but see [17]). A key question, in particular, is why individuals with high personality scores (i.e. very aggressive, bold and active individuals) generally show limited plasticity. Two mechanisms could account for this effect.

On the one hand, the speed–accuracy trade-off hypothesis [18] suggests that bold individuals should be less capable of detecting changes in their environment (i.e. in external stimuli) because their exploring is rapid but inaccurate, contrary to shy individuals that are slow but thorough. Accordingly, the expression of behavioural plasticity would be constrained by cognitive limitations, becoming an intrinsic feature of individuals. On the other hand, the benefits of being plastic and/or the costs of being non-plastic could vary among individuals, depending on their condition or energetic needs, so that each individual would exhibit optimal plasticity. For instance, in changing environments, one should expect individuals with higher energetic demands to be more sensitive to external stimuli than individuals with lower metabolic rates, because they have to constantly modulate their behaviour in order to meet their resource requirements, hence suffering higher costs of being non-plastic. Alternatively, in a competitive context, the most plastic individuals should be those with the lowest fighting ability because they are likely to repeatedly meet stronger opponents against whom they would systematically lose if they do not retreat. If the benefits of being plastic are condition-dependent, the amount of contextual plasticity expressed by an individual could then vary depending on the context and the trait being measured.

The very few experimental studies that have measured plasticity in multiple traits or contexts on the same individuals found relatively low levels of consistency among measures [19–21] (but see [22]), supporting the idea that behavioural plasticity would not be a general feature. That said, the questions as to why certain behavioural traits affect the level of plasticity and how differences in these traits are maintained remain unclear. Here, I set out a model that allows predicting when individuals' differences in their plasticity should be related to differences in their personality and determining which conditions would be necessary to maintain individual differences in behavioural traits and plasticity. To address these questions, I use the hawk–dove game, a classical example of the game-theoretical approach that predicts the proportion of aggressive (i.e. hawk players) and non-aggressive (i.e. dove players) contestants within a population when animals compete by pairwise contests [23]. When contestants are symmetric (in terms of fighting ability or resource holding potential), the model predicts that hawk is an evolutionarily stable strategy (ESS) when the value of winning is larger than the cost of losing an aggressive encounter. Otherwise, hawk and dove players coexist as a mixed ESS. In the case of asymmetric contestants, however, individuals may benefit from being plastic and adjusting their behaviour from one interaction to the next, based on their probability of winning a fight [24,25], despite assessment of relative fighting ability being cognitively and energetically costly [26]. More precisely, the assessor strategy, which consists in playing dove if the opponent is more likely to win and hawk otherwise, is predicted to reach fixation when assessment is cheap relative to the cost of escalated fighting. Given that the costs of escalated fighting, and hence the benefits of assessment, may vary among individuals, however, it should be rather expected, under most circumstances, that the frequency at which the contestants use the conditional assessor strategy, is dependent on their relative fighting ability. Here, I use an individual-based computer model to explore the evolution of hawk, dove and assessor strategies, when initial individual differences in fighting ability are maintained throughout the simulation period, irrespective of fitness differences, or may be eroded by natural selection. I demonstrate that tactic use should vary among individuals and that the expected proportion of assessor (plastic) individuals should be greatest among individuals with low and/or intermediate fighting ability (and with presumably low and/or intermediate levels of boldness and risk-taking [27]). Thus the model supports the idea that individuals that benefit the most from being plastic should exhibit greater plasticity. Yet the link between personality traits and plasticity should be affected not only by the environmental conditions in which individuals live but also by the mechanism that would maintain variation in those traits.

2. The model

(a). Less successful individuals are replaced by individuals with similar fighting ability

The population consists of n individuals that compete by pairwise interactions (see the list of the model parameters in table 1). At the beginning of a simulation, each individual i is randomly assigned a fighting ability α_i (a discrete number varying from 0 to 5) and a strategy (i.e. dove, hawk or assessor). While dove and hawk players always behave the same way, Assessors adjust their behaviour to their opponent's strategy and relative fighting ability. All individuals keep their fighting ability throughout the simulation. However, I allow one individual of each fighting ability to switch its strategy at the end of each time step, and repeat the process for 1000 time steps to ensure that the proportion of hawk, dove and assessor players reach equilibrium frequencies. Because several stochastic events occur at each time step (e.g. individuals are paired partly randomly or the value of the contested resources is randomly chosen), a simulation may converge towards different equilibrium. To take into account these stochastic events, each simulation is then replicated 100 times and results are averaged across replicates.

Table 1.

List of model parameters.

symbol	parameter	range of tested values or default value
n	population size (number of individuals)	360
V	mean value of the contested resource	5–20
σv	measure of deviation around the mean value of the resource	0–10
CF	cost of losing a fight	0–20
εi	risk of making an assessment error	0–0.5
ε0	minimum error rate	0–0.5
δ	magnitude of the difference in error rates between individuals with a fighting ability of αi and αi + 1	0–0.2
CA	energetic cost of playing assessor	0–5
q	maximal difference in fighting ability between two opponents	0–5
T	length of the simulation (number of time steps)	1000

At the beginning of each simulation time step, all individuals are successively paired with one opponent that is randomly chosen among the individuals that are not yet in pairs and whose fighting ability does not differ by more than q from that of the considered individual. The maximal difference between two opponents in terms of fighting ability can vary from 0 to 5 so that the interactions occur randomly when q is equal to 5 but become more assortative as q decreases. For each pair j of contestants, the value of the contested resource V_j is randomly chosen among all possible values ranging from (V − σ_v) and (V + σ_v), with σ_v being the range of deviations around the average patch value, and the expected gain of each individual (W_i) is then calculated. The gain expected by an individual is conditional on its strategy and that of its opponent (table 2). For instance, an individual playing dove never escalates. As a consequence, a dove only shares the contested resource with another dove opponent but systematically retreats, leaving the resources to its contestant, when it meets a hawk or assessor player.

Table 2.

Gains expected by an individual when interacting with an opponent of lower (first line of each cell) or higher (second line of each cell) fighting ability and depending on their tactic use.

	hawk	dove	assessor
hawk	Vj	Vj	Vj
	−C	Vj	ε × Vj − (1 − ε) × C
dove	0	Vj/2	0
	0	Vj/2	0
assessor	(1 − ε) × Vj	Vj	(1 − ε) × Vj + ε(1 − ε) × Vj/2
	ε(−C)	Vj	ε (1 − ε) × [Vj/2 − C] + ε2 × Vj

Conversely, an individual playing assessor systematically escalates against a dove opponent. However, if an assessor player meets an opponent that plays hawk or assessor, it escalates only if it considers that its fighting ability is higher than its opponent's, or behaves like a dove otherwise. Each individual has a probability (1 − ε_i) of correctly assessing its relative fighting ability and a probability ε_i of making an assessment error, where ε_i = ε₀ + (α_i × δ). The parameter ε₀ corresponds to the minimum error rate while δ reflects a possible trade-off between the fighting capacity of an individual and its cognitive abilities [28]. According to this expression, individuals with higher fighting ability are then more likely to make assessment errors, particularly if ε₀ is small and δ is large. The probability of making an assessment error, however, is considered independent of the magnitude of the difference in fighting ability between two opponents. When two players decide to escalate, the winner of the fight (i.e. the contestant with the highest fighting ability) gets the whole contested resource, while the loser suffers a cost of C_F units. Assessor players also systematically suffer a cost of assessment C_A that reduces their fitness, regardless of the outcome of the interaction.

Finally, an individual playing hawk systematically escalates, and hence obtains the whole contested resource, if either its opponent playing dove or assessor retreats, or if it wins against an aggressive competitor (i.e. a hawk or assessor player that escalates) of lower fighting ability. Note that in the case where two aggressive contestants have exactly the same fighting ability, each has a 50% chance of winning and a 50% chance of losing.

At the end of each time step, I estimate the average gain of dove, assessor and hawk players for individuals of every fighting ability, and then for each ability, I randomly choose one individual that uses the least successful strategy and replace it by another individual of the same fighting ability that uses the most successful strategy. The model was implemented in C++ (the code is available as electronic supplementary material as well as a description of the model following the ODD protocol [29]).

(b). Less successful individuals are replaced by individuals with the highest pay-off regardless of their competitive ability

As above, all individuals are randomly assigned at the beginning of a simulation a fighting ability α_i and a strategy (i.e. dove, hawk or assessor). However, in this model version, I consider that individual differences in fighting ability may be eroded by natural selection to explore the conditions that should promote among-individual variation in behavioural traits and plasticity. Therefore, at the end of each time step, I estimate the average gain of each type of individuals (i.e. individuals with the same fighting ability and using the same strategy) and I randomly replace one individual from the least successful type by another individual from the most successful one.

Results from both models were analysed qualitatively as p-values, which are determined by statistical power (i.e. replication), can be arbitrarily high in a simulation context and are then meaningless unless accompanied with measures of effect size and statistical power [30].

3. Predictions

(a). Less successful individuals are replaced by individuals with similar abilities

The assessor strategy should be favoured when the cost of losing a fight is large compared to the value of the resource, while individuals should mainly use the aggressive hawk strategy in the opposite case. The model also predicts that the average proportion of individuals using the assessor strategy at equilibrium should decrease as both the cost of assessment (figure 1a) and the probability of making an assessment error (figure 1b) increase. By contrast, the range of deviations around the average patch value (σ_v) and the magnitude of the difference in error rates between individuals with low and high fighting ability (δ) should have no effect on the expected proportion of each strategy, while increasing the probability of assortative interactions (q) should only very slightly decrease the assessor strategy use.

Figure 1.

Average proportion of dove, assessor and hawk players at equilibrium in relation to (a) the cost of assessment (C_A) and (b) the risk of making an assessment error (ε₀), when individual differences in fighting ability cannot be eroded by natural selection. In both panels: V = 10, σ_v = 0, C = 10, δ = 0 and q = 5.

The model predicts that tactic use should vary among individuals (figure 2): individuals with the highest fighting ability should mainly use the hawk strategy while the expected proportion of assessor (plastic) individuals should be greatest among individuals with low and/or intermediate fighting ability. More precisely, when the cost of assessment is low, assessor is the best strategy for individuals with low and intermediate fighting ability, while the frequency of dove at equilibrium should increase among individuals with low fighting ability with the cost of assessment.

Figure 2.

Average strategy use of individuals with (a) low (i.e. α_i = 0 or 1), (b) intermediate (i.e. α_i = 2 or 3) or (c) high (i.e. α_i = 4 or 5) fighting ability, in relation to the cost of assessment, and when individual differences in fighting ability cannot be eroded by natural selection. In all panels: V = 10, σ_v = 0, C = 10, ε₀ = 0, δ = 0 and q = 5.

(b). Less successful individuals are replaced by individuals with the highest pay-off regardless of their fighting ability

When natural selection can erode individual differences in fighting ability, the model predicts that the assessor strategy should be systematically eliminated if individuals interact randomly with each other (figure 3a), and so even if the conditions favour the maintenance of individual differences in fighting ability (figure 4a). Specifically, when the cost of losing a fight is smaller than the benefit of winning (i.e. when C_F < V), individuals with the highest fighting ability do better than those with lower abilities that, consequently, tend to be progressively eliminated from the population (figure 4a), thereby making plasticity obsolete. Under these conditions, therefore, pure hawk is an ESS (figure 3a). Conversely, when the cost of losing is greater than the value of winning (i.e. when C_F > V), the population should be made up of individuals with low and high fighting ability that should play dove and hawk, respectively (figure 3a). The use of the assessor strategy, on the other hand, is never favoured under such conditions because the chance that individuals with relatively low fighting abilities encounter a weaker opponent is too unlikely.

Figure 3.

Average proportion of dove, assessor and hawk players at equilibrium in relation to the cost of losing an escalated fight when individual differences in fighting ability can be eroded by natural selection. The maximum difference in fighting ability between two opponents (q) is equal to (a) 5 or (b) 1. In both panels: V = 10, σ_v = 0, ε₀ = 0, δ = 0 and C_A = 1.

Figure 4.

Effect of the cost of losing an escalated fight on (a) the amount of among-individual variation in fighting ability (estimated as the standard deviation around the mean from results of the 100 simulations obtained in the last time step) and (b) average expected gain of individuals in the last time step of each simulation. The maximum difference in fighting ability between two opponents (q) is equal to 5 (dark bars) or 1 (light bars). In both panels: V = 10, σ_v = 0, ε₀ = 0, δ = 0 and C_A = 1.

Conversely, when individuals interact with opponents that are more similar in terms of fighting ability, assessor may coexist with at least one other strategy when the cost of losing is greater than the mean value of the contested resource (figure 3b). Such conditions, indeed, favour a great amount of variation among individuals in their fighting ability (figure 4a) and therefore lead to an increased use of the assessor strategy by individuals of intermediate fighting ability. The more frequent use of the assessor and dove strategies when interactions are non-random serves to diminish conflicts between population members and thereby is associated with a higher average expected gain (figure 4b).

4. Discussion

In compliance with previous game-theoretical analyses [24,25], the model explored here predicts that individuals may benefit from adjusting their aggressive behaviour to the characteristics of their opponent when the cost of losing is high and individuals, therefore, take advantage of retreating when they face a strong rival. For that reason, however, the simulation model predicts that assessor would never exist as a pure ESS, but would mostly be used by individuals with the lowest fighting ability that are likely to repeatedly meet stronger opponents. This prediction is consistent with observations that individuals within a group typically differ in the amount of plasticity expressed or degree of social specialization [31]. The link between individual differences in consistent traits (such as fighting ability) and plasticity should nevertheless be affected not only by the environmental conditions in which individuals live but also by the mechanism that would maintain variation in those traits.

Specifically, when differences among individuals in their fighting ability are preserved, regardless of whether they are associated with fitness differences, the model predicts that, under most conditions, individuals with low (and/or intermediate) fighting ability should assess their relative fighting ability before deciding to escalate or retreat, thereby exhibiting plasticity in their aggressive behaviour from one interaction to the next. By contrast, individuals with greater fighting ability should consistently use an aggressive strategy, giving rise to a negative (or dome-shaped) relationship between aggressiveness and plasticity. When individual differences in fighting ability can be eroded by natural selection, however, such an association is less likely to occur even if the capacity of individuals to accurately assess their chances of winning trades off with their fighting ability. Findings from the present model therefore strongly suggest that the amount of behavioural plasticity expressed by an individual would not be an intrinsic feature, but would rather result from a decision based, mostly, on the cost of not being plastic. In other words, individual differences in plasticity would essentially be maintained by condition-dependent selection when conditions favour the maintenance of differences in the traits that determine the costs of not being plastic and/or the benefits of being plastic. This prediction contradicts the widespread idea that the proximate factors underlying individual differences in behavioural plasticity would be the same for any measure of plasticity, but is consistent with experimental evidence that the most plastic individuals in a given context are not necessarily the same in another context [20].

Even when individuals with different behavioural traits (and that, consequently, exhibit different levels of plasticity) differ in fitness, one may expect such variation to be maintained, if, for example, an individual that has low fitness in one context has high fitness in another context [32,33] or if the trait is genetically correlated with other traits by pleiotropic or physical linkage. In that case, one would expect a significant proportion of individuals to express plasticity in their aggressive behaviour, particularly if the cost of losing is high relative to the value of winning. Conversely, when the trait that determines plasticity is the direct target of selection and fitness differences are persistent across contexts, the proportion of plastic assessor individuals should be much lower. Nevertheless, when the cost of losing an escalated fight exceeds the value of the contested resource, the assessor strategy can never be totally eliminated, although such conditions promote differences in microhabitat use among individuals with different traits [34]. This prediction is due to the fact that increased niche specialization reduces conflicts [35]. For that reason, I found that individuals, on average, had a larger gain if they encountered an opponent with relatively similar traits than if interactions occurred randomly. As niche specialization contributes to maintaining among-individual variation in intrinsic traits [36,37], some individuals should still be expected to exhibit behavioural plasticity, despite interactions being more likely between similar opponents. Individuals with intermediate fighting ability might especially benefit from being plastic as they may encounter opponents of either lower or higher fighting ability, contrary to individuals with low or high ability that interact almost exclusively with stronger or weaker opponents, respectively. Increased individual specialization in microhabitat use, therefore, would not necessarily imply increased social specialization. Several studies using a network approach found evidence that populations may exhibit strong phenotypic assortment [38]. Behavioural data currently available, however, do not allow to test whether populations where individuals are more likely to interact with similar opponents show greater plasticity. This is because network analyses typically are based on physical interactions only, and consequently ignore cases where one individual decides to retreat without escalating or both contestants share the resource without fighting. Experimental studies manipulating the degree of assortativity, therefore, could be useful to further explore the link between network structure and social specialization.

In conclusion, although there is some evidence suggesting that the amount of behavioural plasticity expressed by individuals may have important fitness consequences at both the individual and population levels, the mechanisms underlying these effects remain unclear. In particular, we still ignore, for most (if not all) species, (1) to what extent the expression of behavioural plasticity is constrained by physiological or cognitive limitations or results from an individual decision, and (2) which conditions favour the maintenance of individual differences in plasticity. If, as predicted by the present model, the spatial distribution of individuals in their environment is a key determinant of the amount of among-individual variation in intrinsic traits and individual specialization, other factors than intra-specific competition should affect these two components as well. Predation pressure, for instance, might contribute in maintaining variation among individuals through determining the degree of assortativity [39]. Specifically, under high predation risk, shy and less competitive individuals should concentrate their activities in safe zones, thereby increasing their probability of encountering opponents with similar traits. As a consequence, we would predict that populations with higher predation pressure should be composed of individuals that are more variable in their phenotypic traits and that would exhibit (at least for some of them) greater behavioural plasticity compared with populations with low predations risks. Fieldwork and comparative studies would therefore be needed to better understand variations among individuals and populations in their degree of specialization.

Data accessibility

The code is available as electronic supplementary material as well as a description of the model following the ODD protocol.

Competing interests

I declare I have no competing interests.

Funding

I received a research grant (Discovery Grants Program) from the Natural Sciences and Engineering Council of Canada for this study.