Should dispersers be fast learners? Modeling the role of cognition in dispersal syndromes

Abstract Both cognitive abilities and dispersal tendencies can vary strongly between individuals. Since cognitive abilities may help dealing with unknown circumstances, it is conceivable that dispersers may rely more heavily on learning abilities than residents. However, cognitive abilities are costly and leaving a familiar place might result in losing the advantage of having learned to deal with local conditions. Thus, individuals which invested in learning to cope with local conditions may be better off staying at their natal place. In order to disentangle the complex relationship between dispersal and learning abilities, we implemented individual‐based simulations. By allowing for developmental plasticity, individuals could either become a 'resident' or 'dispersal' cognitive phenotype. The model showed that in general residents have higher learning abilities than dispersers. Dispersers evolve higher learning ability than residents when dispersers have long life spans and when dispersal occurs either early or late in life, thereby maximizing the time in one habitat patch. Time is crucial here, because the longer an individual resides in a location where it can use its learned knowledge or behavior, the more often it profits from it and thus eventually obtains a net benefit from its investment into learning. Both, longevity and the timing of dispersal within lifecycles determine the time individuals have to recoup that investment and thus crucially influence this correlation. We therefore suggest that species' life history will strongly impact the expected cognitive abilities of dispersers, relative to their resident conspecifics, and that cognitive abilities might be an integral part of dispersal syndromes.

Dispersal is a complex process which can be divided into three phases: departure, transfer, and settlement (Bowler & Benton, 2005).
Because all three phases involve challenges that differ from the dayto-day challenges an individual faces when staying at its natal place, dispersing individuals may adjust their phenotypic traits accordingly.
Species differ quite strongly in their cognitive abilities, which are often positively correlated with longevity (e.g., Deaner et al., 2003;Sol, 2009). However, even short-living species are showing astonishing cognitive abilities, ranging from associative learning in nematodes (Sasakura & Mori, 2013), reversal learning in spiders (Liedtke & Schneider, 2014), to social learning and teaching in insects (Alem et al., 2016). In recent years, it has become clear that individuals of the same species differ in their cognitive abilities (Boogert et al., 2018;Cauchoix et al., 2018;Liedtke & Fromhage, 2019a), raising the question whether these between-individual differences may correlate with other traits such as dispersal, thus potentially being part of a 'dispersal syndrome' as described above.
Cognitive abilities may be beneficial during all three dispersal stages as they allow to, for example, gather information about and to compare unknown habitats (Clobert et al., 2009;Cote & Clobert, 2012;Delgado et al., 2014;Edelaar et al., 2017;Maspons et al., 2019;McNamara & Dall, 2011). Yet, there is not much known about how individual differences in cognitive abilities may relate to differences in dispersal tendencies. Furthermore, cognitive abilities, in general, are expensive (e.g., metabolic costs, Niven & Laughlin, 2008) and when dispersers settle in an environment in which these abilities are less needed, the costs may outweigh their benefits. Thus, under some circumstances it may be better for dispersers to have lower cognitive abilities in order to save these costs.
It is therefore conceivable that cognitive abilities can be adjusted for dispersal during development, thus being an integral part of 'dispersal syndromes'.
In another study, we showed that dispersal tendency and learning abilities can evolve in a correlated manner in a metapopulation setting (Liedtke & Fromhage, 2021), where distinct trait combinations emerged across different habitat (patch) types. That study, however, made the simplifying assumption that an individual's learning abilities were fully determined by its genotype, regardless of whether it dispersed or not. This essentially meant that different traits could not influence each other during development, thus precluding the evolution of an optionally expressed "dispersal syndrome" involving multiple traits. The present study is designed to relax this constraint. To this end, we model the evolution of a genotypic strategy that can encode two independently evolving alternative phenotypes-a "resident" and a "disperser" phenotype which are expressed in these respective contexts. Specifically, we assume that each individual faces a developmental switch with two options: either it expresses its genotypically encoded "resident" phenotype and is then destined not to disperse; or it expresses its genotypically encoded "disperser" phenotype and is then destined to disperse. These adjustments are irreversible and cannot be changed during an individuals' lifetime. This modeling approach seems especially appropriate for species where residents and dispersers differ in traits linked to dispersal, even among individuals originating from the same patch. Wing dimorphism, for example, is commonly found in insects, with large-winged (macropterous) individuals constituting the dispersal morph (Roff, 1986), which also may be linked to metabolism specialization (Van Belleghem & Hendrickx, 2014). In naked mole rats, young males can develop into a dispersing morph, including increased fat reserves and behavior adaptations, presumptively for increasing outbreeding (O'Riain et al., 1996). In common lizards, dispersal dimorphism is responsive to environmental change (e.g., fragmentation, Cote et al., 2017). Furthermore, whether the investment in cognitive abilities can be recouped, and thus can be adaptive, crucially depends on how much time animals have available to use these abilities (Liedtke & Fromhage, 2019b and refs. therein).
Longevity and timing of dispersal crucially influence the duration of this recouping phase by determining how long an individual will reside in one patch. We therefore investigate the effects of longevity and timing of dispersal on the interplay between cognitive abilities and dispersal. This allows us to assess the role of life-history traits in shaping dispersal syndromes. Because dispersal syndromes have mostly been documented for relatively short-lived species, we note that those are the species for which our present modeling approach may be most likely to be relevant. On the other hand, we see no compelling theoretical reason why the processes studied in our model should not occur, in a qualitatively similar form, in long-lived species too.

| ME THODS
This model is an extension of a previous model (Liedtke & Fromhage, 2021) about the joint evolution of cognitive styles and dispersal tendencies. The description of methods is therefore largely identical, except for the implementation of developmental plasticity (see below) and the exclusion of predation (for simplicity).
We implemented a metapopulation setting with N Patches habitat patches, which are connected through random global dispersal, that is, individuals have the same chance of reaching any of the N Patches patches when dispersing (list of abbreviations see Table 1). Carrying capacity of each patch is set to N Individuals and three traits are allowed to evolve independently for N Generations : learning ability L, exploration tendency E (i.e., explorative foraging within patch), and dispersal tendency D. All three traits are continuous with values between 0 and 1. At the end of each generation, individuals reproduce asexually in proportion to their fitness. Fitness of individuals is specified by the amount of resources they obtain during their lifetime. We assume an 'income breeder' system where individuals may reproduce independently of their survival until the end of season.
The length of a season (=generation) is defined by the number of days before dispersal T before , plus the number of days after dispersal T after . For simplicity, all dispersers will disperse at the same moment and dispersal does not consume any time. Cost of dispersal is implemented as mortality risk M during dispersal.
The lifecycle of individuals proceeds in four phases: (1) time before dispersal in which they can collect resources; (2) potential dispersal event, that is, moving with some probability from one patch to another, with a mortality risk defined by M; (3) time after dispersal for collecting resources; (4) asexual reproduction followed by death.
After the last phase, a new generation starts with offspring generated by the parent generation.

| Development
Because optimal traits values (L and E) may differ for residents and dispersers, we allow for developmental plasticity, by letting the expression of L and E to be conditional on dispersal. Whether or not an individual will disperse is determined at the very beginning of its life, depending on its trait value D and a threshold value between 0 and 1 randomly drawn from a uniform distribution. When the individual's dispersal tendency (D) is higher than that threshold, the individual will disperse later in life; otherwise, it will stay in its natal place. Depending on the now determined fate of individuals as either a resident or a disperser, they will develop different phenotypes, which are encoded by two independent loci: one locus determines the learning abilities for residents (L R ) and the other for dispersers (L D ). Similarly, there are two loci for exploration tendency with E R encoding exploration for residents and E D for dispersers. If the individual will be a resident, it expresses L R and E R ; if it will disperse, it expresses L D and E D , respectively. Traits do not change at the time of dispersal, but instead remain constant throughout an individual's life. Each locus underwent independent mutation as described below and thus could evolve independently.

| Environment
The environment of a patch is defined by its patch size N Individuals and the abundance (A Ri ) of different resource types R i . Abundances are defined as the maximal number of resource items of type R i which an individual can encounter in a given period of time (see below).
Patches can differ in their composition of available resources.
Furthermore, resources are defined by their value V Ri in terms of increasing fitness, their handling time H Ri, that is, how long individuals need to handle them before they can obtain their value, and their detectability C Ri , that is, how easy they are to find. For simplicity, we implemented simulations with two, equally frequent, patch types.

| Learning
Learning is implemented as a reduction in handling time (H Ri ) of resources due to gaining experience with specific resource types, reflecting the idea that some feeding techniques need to be practiced repeatedly before succeeding (such as tool use in primates (Boesch et al., 2019) and birds (Kenward et al., 2006), or hunting techniques in dolphins (Guinet & Bouvier, 1995)). Up to ten different resource types are implemented, with R 1 being a simple-to-access resource whose handling requires no learning. R 2 to R 10 are resources for which individuals need experience before they can exploit them. Therefore, individuals get better at exploiting resource items of type R 2 through R 10 with time. Learning experience with specific resource types can be carried over to new settlement patches if (and only if) dispersers will find the same resource type in the new patch. A detailed description of how learning was calculated follows below.

| Resource intake
First, we calculate the maximum number of resource items per type (R i ) an individual can collect before dispersal, by multiplying the abundances (A Ri ) in patch P i with the time it has to do so (i.e., T before ). Based on the results found in a previous study (Liedtke & Fromhage, 2019a), we assumed that individuals will explore their surroundings at least every second time step. Whether individuals would also move in the other timesteps depends on their exploration tendency (E i ). The higher its E i, the more likely an individual moves and encounters further resources, such that its maximum number of resource items of type R i is given by.

TA B L E 1 Abbreviations
This formulation implies that individuals with E i = 0 move at a slow pace and gain maximally half of what individuals with E i = 1 gain.
Next, we take into account the individuals' exploration tendency E i and the detectability of resource types C Ri . We assume that the faster an individual explores, the less thoroughly it can search; and the harder the items are to detect (i.e., low C Ri ), the less likely the individual will find a resource. This changes the calculation of collected resources as: Thereafter, we take into account each individual's efficiency of handling resources as influenced by its learning speed L and the number of resource items collected, that is, how much experience it gained with a specific resource type. This changes the calculation of collected resources as: where H Ri is the handling time of R i . This formula was selected because it describes a decline of handling time at a decelerating rate. This functional shape appears biologically plausible because perfection may often be difficult to reach, which may slow progress down once more progress has been made. Note that resources with high H need to be handled multiple times before they can be exploited by a given individual.
Finally, we take into account intraspecific competition over resources within a patch. First, we estimate the maximum total amount of resources Rmax i potentially collected by all individuals in a given patch, adjusted by a competition factor Ф that controls the severity of the competition: Then, we divide this by the sum of resources collected by all individuals as estimated by Equation 3, to obtain the ratio

Ri
. If this ratio is <1, then the focal resource type is completely depleted, and the share collected per individual is reduced by competition as: For example, if (according to precompetition calculations) resource type R 2 was collected 10 times more often than its Rmax i value for this patch, then for every individual in this patch its amount of collected R 2 items is multiplied by 0.1.

| Dispersal
After this foraging phase, individuals could disperse to a randomly chosen patch. An individual's decision to disperse or not was determined at the beginning of its life as described above. Due to the stochasticity of this process some patches may have lower, others higher numbers of individuals after the dispersal phase. Dispersal costs are implemented as mortality risk M which was set to 0.01 in all cases.
Whenever an individual attempts to disperse, a random number between 0 and 1 is drawn from an uniform distribution. If this number is lower than M, the individual dies; otherwise, it successfully disperses.
After the dispersal phase, surviving individuals are allowed to collect resources again. Resource intake and competition are calculated as in the predispersal phase (Equations 1-5) with the only difference being that the duration of the postdispersal phase is defined by T after . Note that dispersers may need to learn how to gain hardto-access resources again, if a different resource type is found in the settlement patch. Since residents stay in their natal patch, they need to learn only one type of hard-to-access resource type (with given settings presented in this study).

| Reproduction
After estimating the total resource income of all individuals, reproductive success (fecundity) is calculated as: where L is an individual's learning ability, α a cost coefficient which specifies the cost of learning, and V Total is the sum of value of all resources collected by this individual. We do not include any explicit cost of E because costs of exploration are implicit in the risks of overlooking resources. The next generation is recruited in each patch independently, by using local individuals' F value as the independent sampling probability. Thus, the higher F of a focal individual is compared to all other individuals in the same patch, the more likely it contributes offspring to the total N Individuals .

| Mutation
Mutation probabilities for all three traits (L, E, D) are set to μ = 0.1.
Traits evolve independently and new values are chosen randomly from a normal distribution with the parental trait value as mean and SD of 0.1. (1)

| Extinction
To increase the incentive to disperse, it is common practice in modeling studies to implement random extinction of patches (Poethke et al., 2003). We do so by erasing, with a given frequency, all individuals of a randomly selected patch at the end of a generation. The empty patch can then only be recolonized by emigrants from other patches within the metapopulation.

| Initialization
Initially, we heuristically explored the parameter space in order to find parameter settings allowing the evolution of different cognitive styles which can coexist both within (compare Liedtke & Fromhage, 2019a) and between patches.
For simplicity, the main results presented here are derived from simulations in which detectabilities of resources (C Ri ) were the same and thus E of all individuals evolved to be similar. This allows us to concentrate on the effects of learning abilities on dispersal and vice versa, which is our main interest here.
Parameter settings for each of the presented simulation sets are given in Tables 2 and 3. All simulations presented were replicated 10 times with identical parameter settings. All replicate runs produced qualitatively similar results.
To compare learning abilities (L) between residents and dispersers, we applied paired t tests. Separately for each season length (S = 4 to 4,000), we used the mean values of L of residents and dispersers of each replicated simulation run as independent datapoints (degrees of freedom = 9).
All traits reached equilibrium-as judged by visual inspectionwell within given generations numbers.

| RE SULTS
Season length (i.e., T before + T after ; equivalent to life span) crucially determines whether dispersers had higher or lower L than residents (see Figure 1, Table A1). With very short life spans, individuals did not invest into higher learning speed and both L R and L D were low accordingly. However, since dispersal tendency D was very high, there were only very few residents present and thus selection for L R was low. Due to mutation-selection balance (Crow & Kimura, 1970), L R was pushed upwards (Figure 1, Season length (S) = 4 and 10), that is, closer to the value 0.5 expected for a selectively neutral trait. With slightly longer season length, residents, which by definition stayed in their birth patch their whole life, became able to exploit hard-toaccess resources if they invested strongly into learning abilities (i.e., L R ). This led to a huge increase in L R compared to learning abilities of dispersers (i.e., L D ) which were unable to exploit hard-to-access resources within their given time (Figure 1, S = 20 and 30). When increasing the total season length further, also dispersers were able to exploit hard-to-access resources (both in their natal and new settlement patches) and invested highly into L. As a result, the differences between L R and L D first becomes insignificant ( Figure 1, Table 2, SL = 50) and then, with increased SL, reverses direction, that is, L R becomes significantly lower than L D (Figure 1, Table 2  dispersers had time to adapt to at least one set of local conditions, hence investing in L similarly to but slightly lower than residents ( Figure 2a) and dispersal tendencies increased again (Figure 2b).  This results in low costs for dispersal and high dispersal rates. Yet, once life span is long enough to permit effective learning, residents have the advantage of being faster in exploiting hard-to-access resources and thus outcompete dispersers, which first need to learn how to handle the new hard-to-access resources. This increases the costs of dispersal, leading to lower mean dispersal rates. Only with longer life spans, dispersers can become similarly efficient in exploiting hard-to-access resources at the settlement patch and thus are able to compete with residents. At this point, dispersal rates start to increase with longevity again (S > 50, in Figure 1). In conclusion, we have shown that the interplay of cognitive abilities and dispersal can be complex. In our simulations, time is a crucial determinant of whether dispersers should be fast learners to adjust quickly to new environments, or whether dispersal interferes with the ability to reap the potential benefits of learning. More generally speaking, plasticity allows individuals to adjust to local conditions which, however, induces also costs. Whether these costs can be recouped depends on how much time the dispersers have after settlement. We therefore predict that a species' life span and the timing of dispersal within the lifecycle crucially influence the correlation between dispersal and cognitive abilities, supporting other findings underlining the importance of lifecycles when considering the evolution of dispersal (e.g., Massol & Débarre, 2015).

| D ISCUSS I ON
In this study, we simulated an annual life cycle resembling shortlived species such as insects or spiders, and parameters like longevity or duration of learning a task were implemented accordingly. Yet we expect that the general principles of the interaction between learning, dispersal, and longevity will remain the same for longer-lived species such as vertebrates. The crucial point is how long individuals need to learn a task in relation to their available time as determined by their ecology. However, since learning speed should depend on the frequency with which similar tasks are encountered, it should also depend on the degree of environmental complexity and predictability.
Thus, an interesting avenue for further research would be to investigate how life-history traits such as life span and timing of dispersal coevolve under variation of these environmental aspects.

ACK N OWLED G M ENTS
We thank M. Bruneaux for helping with coding and D. Bonte for commenting on the model and on an earlier version of the manuscript.

CO N FLI C T O F I NTE R E S T
None declared.

AUTH O R CO NTR I B UTI O N S
Jannis Liedtke: Conceptualization (lead); data curation (lead); funding acquisition (lead); investigation (lead); methodology (lead); F I G U R E 2 (a) Mean trait values L (=learning speed) for residents (L R in blue, with matching contour colours to make colours discernible despite low variances) and dispersers (L D in red). Note that these phenotypes are encoded by different loci, only one of which is expressed in any given individual. (b) Mean dispersal tendency of whole population. Boxplots represent the results of ten replicated runs where the mean of each simulation serves as one datapoint. The season length (i.e. in 'days') was 20 in total in each case but the time point of dispersal differed.
On the left-hand side dispersal was allowed after the second, in the middle after the ninth and on the right-hand side after the 18th 'day'