The effects of animal personality on the ideal free distribution

Abstract

The ideal free distribution (IFD) has been used to predict the distribution of foraging animals in a wide variety of systems. However, its predictions do not always match observed distributions of foraging animals. Instead, we often observe that there are more consumers than predicted in low-quality patches and fewer consumers than predicted in high-quality patches (i.e. undermatching). We examine the possibility that animal personality is one explanation for this undermatching. We first conducted a literature search to determine how commonly studies document the personality distribution of populations. Second, we created a simple individual-based model to conceptually demonstrate why knowing the distribution of personalities is important for studies of populations of foragers in context of the IFD. Third, we present a specific example where we calculate the added time to reach the IFD for a population of mud crabs that has a considerable number of individuals with relatively inactive personalities. We suggest that animal personality, particularly the prevalence of inactive personality types, may inhibit the ability of a population to track changes in habitat quality, therefore leading to undermatching of the IFD. This may weaken the IFD as a predictive model moving forward.

1. Introduction

Animal habitats are changing at a rapid rate owing to global warming, habitat degradation and other anthropogenic drivers. Given these changes, understanding population distribution is more crucial than ever, as the ability of a species to adapt and respond to change through their distribution is key to their survival [1]. Thus, one of the main purposes in the field of ecology is to understand and explain the spatial distribution of animals [2]. The spatial distribution of animals is partially the result of foraging behaviour that is expressed on an individual level [3]. The ideal free distribution (IFD) is an ecological theory used to predict animal distribution based on resource availability and competition for those resources [4], and models based on the IFD have been able to successfully link individual foraging behaviour to population distribution [5–9]. This model assumes that fitness increases with patch quality and decreases with conspecific interference, and it predicts that each animal should position themselves so that no individual could improve its fitness by moving to another patch [10,11]. Because the model is based on resource consumption, tests of the IFD generally use consumption rate as a proxy for fitness. The theory further assumes that each individual has an ideal knowledge of the quality of all the resource patches in their environment, and that they are equally capable of moving between all patches and have equal competitive abilities [12].

In nature, one or more of the IFD assumptions are almost always violated, but consumer distributions predicted by this theory nonetheless match observed distributions in some cases. For instance, it has been demonstrated theoretically that the population distribution can still meet the IFD even when individuals have incomplete knowledge of patch quality, as long as they can migrate between patches repeatedly and so can overcome incorrect patch choices [11]. This same concept has been demonstrated in the specific instance of invasive European green crabs, Carcinus maenas, foraging across alcoves of differing quality [13]. Crabs with incomplete knowledge of patch quality were able to approximately match the predicted IFD very rapidly (within a matter of days) by following a simple patch-leaving rule and migrating repeatedly as necessary to maximize consumption [13].

In contrast with this, there are other cases where the distribution of consumers does not match the IFD. Instead, consumers are frequently distributed with fewer than the predicted number of individuals on patches of good quality and more than the predicted number of individuals on patches of poor quality. This has been termed ‘undermatching’ [14,15]. There have been multiple suggested causes for undermatching. For instance, undermatching may be caused by random movement, where individuals do not move based on consumption rate alone [16], or by incomplete knowledge, where individuals cannot comprehend the resource qualities of all habitat patches [14,17], or by individual differences in competitive abilities and susceptibility to predation [18]. These suggested explanations are all violations of the IFD's assumptions, yet there may also be explanations for undermatching that are independent of model assumptions.

Animal personalities, also referred to as behavioural syndromes or behaviour types, are defined as individual behavioural differences that persist through time and across contexts, and are widespread across taxa [19–22]. Historically, studies on personality were restricted to humans, primates, domesticated animals and laboratory rodents [23]. Recently, however, animal personality has been studied in a much broader scope of animals such as various mammals, birds, lizards, amphibians, fishes, molluscs, arthropods and other invertebrate phyla [21,24]. Animal personality can affect animal distribution by, for instance, influencing foraging behaviour, as has been shown abundantly. For example, some individuals that are more aggressive than others consistently do better in competitive interactions that occur when consumers are at high density [21], whereas other individuals that are less aggressive do not do as well in such high density and competitive habitats, and are therefore usually found in habitats with more refuges and fewer competitors [21,25]. Similarly, prey individuals with shy personalities are typically confined to habitats of low predation risks, when compared with bolder individuals that are less averse to foraging in habitats with a higher predation risk [26–28].

These personality differences can also influence group situations. For instance, highly active individuals that are consistently more mobile are more likely to be situated on the edge of a herd, with less active individuals in the centre [29]. In some group foraging settings, the composition of bold and shy individuals influences where the group decides to forage, therefore affecting the distribution of the entire group [30]. Additionally, a group with more bold individuals in it makes the group more prone to splitting off into subgroups, even at smaller numbers, because the bold individuals are more likely to move away and explore new areas of the habitat [31]. Animal personality, habitat quality and animal distribution can also interact, with some personalities being expressed more readily in high-quality habitats that support groups of individuals than when individuals are more isolated in low-quality habitats [32]. Thus, animal personality can influence and interact with the distribution of individuals and of groups of individuals within and across foraging habitats. Knowing how animal personalities are distributed across habitats is crucial for a better understanding of population dynamics, and may be important for understanding undermatching of the IFD.

Our study has three components to it. A prerequisite for understanding how personality influences the IFD is being able to first quantify the personality distribution within a population. We, therefore, first conducted a literature search to determine how common it is to understand the personality distribution in studies where personality is examined. Second, we created a simple individual-based model to conceptually demonstrate why knowing the distribution of personalities is important for studies of populations of foragers in context of the IFD. Third, we present a specific example where we calculate the added time to reach the IFD for a population of mud crabs, given their known personality distribution using previously published data. We suggest that animal personality, particularly the prevalence of inactive personality types in the population, may inhibit the ability of the population to track changes in habitat quality, therefore leading to undermatching of the IFD. Specifically, we show that as the prevalence of inactive personality types increases, the time to reach the IFD increases.

2. Material and methods

(a). How common is it to understand the personality distribution of a population?

We used the Web of Science database to search for papers that showed the distribution of personalities, or that provided the information necessary to determine the distribution (e.g. by providing graphical data that could be digitized to determine the personality distribution). We performed a search using the following terms for all available years: ‘personality’ AND ‘population’, OR ‘behavioural syndromes' AND ‘population’, OR ‘behaviour types’ AND ‘population’. This search identified 40 466 papers. We then refined our search by limiting it to only articles published in ecology journals. This reduced the number to 2447 papers. Next, we searched through the titles and abstracts of each of these 2447 papers and identified those that measured the personality of individual animals, yielding a total of 181 papers. We searched each of these papers, focusing on the results and identified all papers that presented a distribution of personalities within the study population, or that provided graphs where it would be possible to extract the data to get a personality distribution. The list of 181 papers that we examined is given in the electronic supplementary material, S1.1.

(b). Demonstration of why the personality distribution is important

We used the agent-based modelling system Netlogo (v. 6.0.2) to create a simple model that we use to demonstrate the influence of animal personality on the ability of consumers to match the IFD. We describe the model below using the overview, design concepts, and details (ODD) protocol for agent-based models [33].

(i). Purpose

The purpose of this model was to conceptually demonstrate how the relative abundance of personalities within a consumer population (i.e. proportion of active versus inactive individuals) affects the ability of consumers to match the IFD. According to the IFD, consumers should distribute themselves such that no individual could increase their consumption rate by moving to another location [4]. We reasoned that the time required to reach this distribution would depend on the proportion of active versus inactive individuals because individuals with inactive personalities would be less likely to leave a patch that offered a suboptimal consumption rate, leading to more consumers than expected on poor patches and fewer consumers than expected on good patches (i.e. undermatching).

(ii). Variables and scales

Individual consumers were characterized by personality type (i.e. active or inactive). Personality type controlled the probability of moving if a better consumption rate was possible elsewhere, with active individuals having a higher probability of moving (probability 0.8) than inactive individuals (probability 0.2). Other than personality, consumers were identical. We used 50 consumers in each model simulation. There were 49 habitat patches, arranged in a 7 × 7 array, that were each characterized by resource quantity, or the amount of food resources the patch contained. Resource quantity was assigned to each patch randomly for each model run using a value ranging from 1 to 9, with 9 being the highest amount of resources. Resource quantity on each patch was assumed to be constant within a model run (i.e. consumption did not deplete resources).

(iii). Process overview and scheduling

The model used discrete time steps. Within each time step, all consumers first calculated their own consumption rate according to the quality of patch they were on and the number of competing individuals on that same patch (see the Submodels section below for description of consumption rate calculation). Next, the possible consumption rate that each patch could offer was calculated. One individual at a time (randomly ordered) had the opportunity to move if the individual could improve on its consumption rate by moving to another patch. Movement probability was determined by personality type as described above. Movement is an appropriate metric for personality (i.e. active versus inactive) here because it has been suggested to control population dynamics [34], the spread of diseases [35], dispersal patterns [36], invasion advancements via controlling the consumption rate of prey [37], the capacity to expand to novel habitats [38], and the tendency to interact with other individuals [39].

If an individual did move, it randomly moved directly to one of the patches that offered the highest consumption rate. Individuals did not move if their consumption rate on their current patch was equal to or greater than the consumption rate available on any other patch. The model simulation stopped when all individual consumers stopped moving (we included a buffer of 50 additional time steps after the final movement to ensure that all movement was complete), meaning that no other patch could improve their consumption and the modelled consumers had, therefore, reached the IFD. While the movement patterns described here may not match the movement patterns seen in many natural systems, they are consistent with the assumptions of the IFD (i.e. ideal knowledge of patch quality and equally free to move to all patches), which is what we were testing in this study.

(iv). Design concepts

The distribution of consumers across the patches emerged from the distribution of patches with different quality, individual personalities and efforts of each individual to maximize consumption. Individuals were assumed to have a persistent expression of personality and to know the quality of each patch, so that they migrated accordingly.

We used model results from 11 000 simulations to examine the time it took to reach the IFD based on the proportion of active versus inactive individuals. We varied the relative number of active versus inactive individuals from 0 to 50 in increments of 5 (i.e. 50 : 0, 45 : 5, 40 : 10, …), and conducting 1000 model simulations at each of these 11 possible combinations. At the conclusion of each model run, the model returned the following information for each of the 49 patches: patch quality, the number of active and inactive individuals on each patch and the number of time steps required to achieve the IFD.

(v). Initialization

To start an individual simulation, the habitat patches were randomly assigned their habitat qualities and the consumers were randomly distributed across patches.

(vi). Submodels

Consumption rate on patches with consumers was calculated as the ratio of habitat quality and the total number of consumers on the patch (i.e. calculation followed a ratio-dependent type I functional response, aR/C, where a is the foraging efficiency and is set to 1.0, R is the resource quantity on a given patch and C is the number of competing consumers on that same patch) [40]. This approach adds resource competition to the model and assumes that all competitors are equal. The possible consumption rate on empty patches was equivalent to the consumption rate that would occur if a single individual alone moved onto that patch and did not have to share the resources.

(vii). Sensitivity analysis

We conducted additional model simulations to examine the sensitivity of the model to the parameter ranges chosen. Specifically, we varied the total number of consumers (25–75), number of patches (25–81) and the different probabilities of moving (0.6–0.9 for active consumers and 0.1–0.4 for inactive consumers) separately in model simulations and compared the resulting qualitative patterns to those of the primary model simulations described above. See a full description of the sensitivity analysis in the TRACE document [41] (electronic supplementary material, S1.2). All code for implementing the model in Netlogo is provided in the electronic supplementary material, S1.3.

 Finally, we also conducted two additional model simulations in an effort to somewhat increase the reality of our model conditions. Specifically, in the model reported here, we used a type I functional response and a static environment in an effort to simplify the model as much as possible. Our first additional model simulation instead used a type II (i.e. saturating) functional response, which occurs more frequently. Our second additional model simulation used a variable environment, where the quality of habitats periodically changed so that consumers were trying to track a moving target. See the electronic supplementary material, S1.4 and S1.5 for a full description of these two additional models and their results, respectively.

(c). Specific example of increased time to reach the ideal free distribution when personality is a factor

We mathematically examined the mud crab Panopeus herbstii to determine the extra time expected for this species to distribute across individual oyster reefs according to IFD expectations, given the personality of this species. The density and size distribution of mud crabs was previously determined across 30 different oyster reefs in the Winyah Bay, SC, that differed in habitat quality (reef complexity and density of small bivalves that serve as food for mud crabs) [42]. Overall, Griffen & Norelli [42] sampled 264 mud crabs across 30 reefs, and we used these mud crabs here. Specifically, we created 10 000 replicate bootstrap samples of crab sizes, n = 264 for each, by resampling with replacement from this observed size distribution. While the size of these crabs is known, the personality is not. However, activity level generally increases with body size in this species, with body size explaining 36% of variation and with the remaining variation being attributable to personality [43]. In figure 1a, we show data from Toscano et al. [43] that depicts the relationship between personality and body size, and provides the overall personality distribution of crabs in this same population.

Figure 1.

Personality–size relationship for the mud crab P. herbstii as measured by Toscano et al. [43] (a), and as predicted for the body size distribution of 264 crabs sampled from oyster reefs within Winyah Bay, SC, by Griffen & Norelli [42] (b).

The β distribution is generally used to model proportions, probabilities or other continuous data with a range restricted to (0,1) [44]. We used logistic regression (betareg function in the betareg package in R) to determine how activity level was influenced by crab carapace width. The β regression model assumes that all values fall between 0 and 1 and that these two endpoints of this distribution are not included. However, the data on activity level from Toscano et al. [43] did include the extremes 0 and 1. We, therefore, used the following transformation to rescale the data to exclude these extremes: (y × (n–1) + 0.5)/n, where n is the sample size [45]. We initially used a variable dispersion model where both the mean and the dispersion were allowed to vary with carapace width. However, the parameter estimate for carapace width in the dispersion model was not significant, and a likelihood ratio test revealed that the variable dispersion model was not a better fit than a fixed dispersion model (p = 0.247). We, therefore, used a fixed dispersion model using a ‘loglog’ link in the mean model, and a ‘sqrt’ link for the precision model. We then used this model fitted to the measured activity levels for crabs by Toscano et al. [43] to predict the activity levels based on carapace width for the 264 crabs in each of our 10 000 bootstrap samples that were based on the crabs sampled by Griffen & Norelli [42]. Dispersal from oyster reefs as a function of personality (activity level) was previously measured for this species in a field experiment [46]. Belgrad & Griffen [46] showed that dispersal probability increased with activity level. We, therefore, used these results to determine the probability of dispersal for each of the 264 crabs in each of the 10 000 replicate distributions as a function of their predicted, size-dependent personality. The standard IFD assumes that individuals with unacceptably low consumption rates on a given food patch will leave that food patch with probability of 1.0. Therefore, the ratio of this ideal free probability of leaving a patch and the estimated dispersion probability for our 264 crabs yields the relative increase in time to reach the IFD across oyster reefs for the crabs in each of our 10 000 replicate calculations for this population.

3. Results

(a). How common is it to understand the personality distribution of a population?

Of the 181 papers we identified that could potentially include personality distributions for populations, we found that only 10 included the distribution explicitly or included the information necessary to derive the personality distribution [43,46–53].

(b). Demonstration of why the personality distribution is important

We found that before the model reached the IFD, there were less consumers than expected on higher quality patches and more consumers than expected on lower quality patches, consistent with undermatching (figure 2). We also found, consistent with our hypothesis, that as the proportion of consumers with an inactive personality increased in the model, it took more time for the population to reach the IFD (figure 3).

Figure 2.

Demonstration of undermatching in the modelled consumer distribution before the IFD is reached during a single, representative model simulation. (a) Key to demonstrate the expected pattern for undermatching. Undermatching occurs when the ratio of expected/observed consumers falls mainly in quadrants designated by ‘undermatching’. (b–e) Decreasing levels of undermatching as the simulation progressed. (f) Consumer distribution matched the IFD and so the expected/observed distribution on all patches was equal to 1.0. Individual box plots show the median (heavy black line), the upper and lower quartiles (box), values that fall within the central 95% of the distribution (whiskers) and outliers that fall outside of this 95% window (circles).

Figure 3.

Number of model time steps required to reach the IFD (y-axis) decreased as the proportion of consumers that have an active personality type increased (x-axis). Individual boxplot interpretation as described in figure 2 caption.

(i). Model sensitivity analysis

Regardless of the parameter that we changed while using a type I consumer functional response, we found that the time to reach the IFD always increased as the proportion of inactive consumers increased. While this trend was always observed when using a type I functional response, we found that the pattern was reversed when consumers used a type II functional response. Additionally, there was still some variation in this general trend as we modified the different parameters in our sensitivity analysis. Specifically, the time to reach the IFD increased when we increased the total number of consumers from 50 to 75 (figure 4a). Conversely, the IFD was reached more quickly when we decreased the total number of consumers from 50 to 25 (figure 4b). The time to reach the IFD changed less dramatically when we increased the total number of patches from 49 to 81 (figure 4c), while the time to reach the IFD shifted more dramatically when we decreased the total number of patches from 49 to 25 (figure 4d). There was a unimodal change in the time to reach the IFD with changes in personality distribution when we maximized the difference in the probability of moving in consumers by simultaneously increasing the probability of moving for active individuals to 0.9 and decreasing the probability of moving for inactive individuals to 0.1 (Figure 4e). Finally, the influence of personality distribution on the time to reach the IFD became much weaker when we reduced the difference in the probability of moving in consumers by simultaneously decreasing the probability of moving for active individuals to 0.6 and increasing the probability of moving for inactive individuals to 0.4 (figure 4f). Considering that in most natural systems, there are many more consumers than patches, we also ran model simulations with an extreme number of consumers compared to patches, nine patches and 100 consumers. When we made this change, the same general pattern emerged, although the time to reach the IFD increased overall because of the increased competition; additionally, the influence of personality distribution was less extreme because the increased time steps to reach the IFD meant that there was always a lot of movement regardless of the proportion of active individuals present.

Figure 4.

The variation in the general trend that as the proportion of active consumers increases, the time to reach the IFD decreases as we modified the different parameters from our sensitivity analysis. (a) The variation from increasing the number of consumers, (b) from decreasing the number of consumers, (c) from increasing the number of patches, (d) from decreasing the number of patches, (e) from maximizing the difference in the probability of moving by consumers, and (f) from minimizing the difference in the probability of moving by consumers.

Not surprisingly, the use of a type II functional response and the use of temporally variable patch quality caused the model to yield very different results (see the electronic supplementary material, S1.4 and S1.5 for a full description of results of these additional models). However, neither of these two sets of more realistic conditions altered the main conclusion that the distribution of personality types within the population is important for determining the time required to reach the IFD.

(c). Specific example of increased time to reach the ideal free distribution when personality is a factor

The results of a β regression provide two component parts: a mean model and a precision model. The fixed-precision mean model showed that activity level increased with carapace width (parameter estimate = 0.114 ± 0.011, z = 10.75, p < 0.0001). (The full model results, including both the mean and precision model output, are shown in the electronic supplementary material, S1.6.) Using this model to predict the activity levels of the 264 mud crabs sampled by Griffen & Norelli [42] based on their carapace widths yielded the activity levels shown in figure 1b. Based on the 10 000 bootstrapped replicate size distributions and the personality distribution for each, calculated using the β regression model described above, we estimated that it would take 27.6% ± 0.9% longer for mud crabs to reach the IFD than if personality had no effect on the likelihood of dispersion (figure 5).

Figure 5.

Per cent increase in the calculated time for mud crabs P. herbstii to reach the IFD in 10 000 bootstrapped replicate analyses, compared to a hypothetical population of crabs where movement is not influenced by personality. Boxplot is as described in figure 2 caption.

4. Discussion

The IFD has been a useful tool in predicting the distribution of foraging animals. However, there are some populations whose distributions deviate from its predictions, and undermatching is a particularly common deviation [14,15]. We examined the effects of animal personality on the IFD as a possible cause for undermatching. We showed that in the literature, there are currently very few studies that provide the distribution of individual personalities. We found that the majority of studies on animal personality simply document the presence of personalities and do not give the personality distribution in their study population. For the purposes of the IFD and for many other applications of personality in ecological systems, it is necessary to understand not just that personalities exist, but to have a quantitative measure of the personality distribution. Thus, personality studies need to more consistently report this distribution.

In our simple model, the distribution of consumers showed undermatching before the IFD was achieved. As inactive personality types became more common in our modelled population, the time that undermatching was observed (i.e. the time required to reach the IFD) increased. Different personality types within the population resulted in differing abilities of foragers to track resource availability. The distribution of personality types proved to be a key component in the population's ability to match the IFD. However, we realized our model looked at a very narrow range of simplified conditions, so we used our sensitivity analysis and additional model simulations to look at a much broader range of ecological conditions that would influence the speed with which a population achieves the IFD. Based on the results of the sensitivity analysis described above, we can surmise that the ability to reach the IFD by tracking changes in habitat quality through time will decrease with the number of individuals in the population because individuals will be forced to move around more until they find a habitat patch of good quality that is not already saturated with consumers (figure 3a,b). Individual personality should have a stronger impact on the ability to reach the IFD as the number of habitat patches decreases for a given population size because movements to new patches are more likely to be contested by conspecific competitors (figure 3c,d). With increasing anthropogenic influence and resulting habitat destruction across many types of natural habitats, this condition is a growing reality for many mobile consumers. Consequently, we should expect that habitat destruction will further reduce the use of the IFD as a predictive tool for understanding forager distribution.

In the specific application of personality to mud crab movement, we showed that personality increased the time for mud crabs to reach the IFD by approx. approximately 28%, compared to a hypothetical population where movement is independent of personality. However, this increased time to reach the IFD is a highly conservative estimate, as personality can influence factors associated with dispersal other than just the likelihood of moving. In this particular population of crabs that we examined, there are at least five additional mechanisms by which personality could further complicate the ability to achieve the IFD. First, personality also influences dispersal distance [46], and thus which habitats an individual disperses to (a violation of the ‘free’ assumption of the IFD). Second, personality also influences the consumption rate of individuals at a site [27], and thus, the impetus to disperse in the first place. Third, personality expression (activity level in this case) is influenced by safety in numbers [32], and thus at high consumer density, the distribution of personality types will vary, as shy individuals become bolder. Fourth, expression of personality varies with the level of predation risk, and thus the likelihood of dispersing to a new site will depend on the level of predation risk in the matrix habitat between patches. Fifth, personality influences predation risk [46] and consequently alters the distribution of personality types within populations. Several mechanisms related to personality, therefore, influence the likelihood of dispersing from an unfavourable patch and the consequences once that dispersal decision is made. Failure to account for personality distributions in natural populations may, therefore, be a ubiquitous contributing factor to undermatching of the IFD.

In most systems, the IFD is a moving target owing to temporal environmental variation and directional change (i.e. habitat degradation). Resource abundance across habitat patches may change through several mechanisms [54]. For instance, the consumptive activities of consumers themselves are likely to change the quality of patches in a non-uniform manner: it should be expected that high-quality patches will be altered (deteriorated) faster than low-quality patches because of the relative abundance of consumers using these different patches. Habitat quality is also strongly influenced by human activities [1] that degrade habitats, reducing the quality of foraging patches, or destroy individual habitat patches, forcing consumers to aggregate within ever-declining numbers of foraging sites. The ability of animals to match the IFD will, therefore, depend on their ability to track that target relative to the rate that it changes (electronic supplementary material, S1.5). All of these changes in habitat quality will influence the ability of consumers to match the IFD via two mechanisms. First, these changes may reduce the ability of consumers to maintain a knowledge of habitat quality, thus increasing the likelihood that the ‘ideal knowledge’ assumption of the IFD will be violated. Second, as described above, even in the absence of ideal knowledge, consumers that can repeatedly move between habitats may still match IFD expectations [11,13]. The success of tracking this moving target will depend on the personality distribution within a given population. The less active the consumers are on average, the harder time they will have keeping up with the rate of environmental change.

Consumer personality is essential to consider when trying to understand and use the IFD, as we have shown conceptually in a model, as well as in a natural population of mud crabs. Time to reach the IFD increased in our study with the prevalence of relatively inactive consumers. Conditions that natural populations face, such as habitat destruction, only exacerbate this effect and weaken the IFD as a predictive model when these factors are ignored.

Data accessibility

This article has no additional data.

Authors' contributions

B.D.G. conceived the study, guided the work and wrote the paper. E.R.D. performed the literature review and individual-based modelling and wrote the paper.

Competing interests

We declare we have no competing interests.

Funding

This work was supported by funds from Brigham Young University.