A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment

Based on a population genetic model of mixed strategies determined by alleles of small effect, we derive conditions for the evolution of social learning in an infinite-state environment that changes periodically over time. Each mixed strategy is defined by the probabilities that an organism will commit itself to individual learning, social learning, or innate behavior. We identify the convergent stable strategies (CSS) by a numerical adaptive dynamics method and then check the evolutionary stability (ESS) of these strategies. A strategy that is simultaneously a CSS and an ESS is called an attractive ESS (AESS). For certain parameter sets, a bifurcation diagram shows that the pure individual learning strategy is the unique AESS for short periods of environmental change, a mixed learning strategy is the unique AESS for intermediate periods, and a mixed learning strategy (with a relatively large social learning component) and the pure innate strategy are both AESS's for long periods. This result entails that, once social learning emerges during a transient era of intermediate environmental periodicity, a subsequent elongation of the period may result in the intensification of social learning, rather than a return to innate behavior.     

The evolution of conformist transmission in social learning when the environment changes periodically

Conformity is often observed in human social learning. Social learners preferentially imitate the majority or most common behavior in many situations, though the strength of conformity varies with the situation. Why has such a psychological tendency evolved? I investigate this problem by extending a standard model of social learning evolution with infinite environmental states (Feldman, M.W., Aoki, K., Kumm, J., 1996. Individual versus social learning: evolutionary analysis in a fluctuating environment. Anthropol. Sci. 104, 209-231) to include conformity bias. I mainly focus on the relationship between the strength of conformity bias that evolves and environmental stability, which is one of the most important factors in the evolution of social learning. Using the evolutionarily stable strategy (ESS) approach, I show that conformity always evolves when environmental stability and the cost of adopting a wrong behavior are small, though environmental stability and the cost of individual learning both negatively affect the strength of conformity.     

Adaptive evolution of foraging-related traits in a predator-prey community

In this paper, with the method of adaptive dynamics and geometric technique, we investigate the adaptive evolution of foraging-related phenotypic traits in a predator-prey community with trade-off structure. Specialization on one prey type is assumed to go at the expense of specialization on another. First, we identify the ecological and evolutionary conditions that allow for evolutionary branching in predator phenotype. Generally, if there is a small switching cost near the singular strategy, then this singular strategy is an evolutionary branching point, in which predator population will change from monomorphism to dimorphism. Second, we find that if the trade-off curve is globally convex, predator population eventually branches into two extreme specialists, each completely specializing on a particular prey species. However, if the trade-off curve is concave-convex-concave, after branching in predator phenotype, the two predator species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist. The analysis reveals that an attractive dimorphism will always be evolutionarily stable and that no further branching is possible under this model.     

Evolution of learning capacities and learning levels

Humans strongly depend on individual and social learning, both of which are highly effective and accurate. I study the effects of environmental change on the evolution of the effectiveness and accuracy of individual and social learning (individual and social learning levels) and the number of pieces of information learned individually and socially (individual and social learning capacities) by analyzing a mathematical model. I show that individual learning capacity decreases and social learning capacity increases when the environment becomes more stable; both decrease when the environment becomes milder. I also show that individual learning capacity increases when individual learning level increases or social learning level decreases, while social learning capacity increases when individual or social learning level increases. The evolution of high learning levels can be triggered when the environment becomes severe, but a high social learning level can evolve only when a high individual learning level can simultaneously evolve with it.     

Evolutionarily stable dispersal of a waterstrider in a temporally and spatially heterogeneous environment

Summary Evolutionary stable dispersal and wing muscle histolysis strategies are studied in the waterstriderGerris thoracicus. These strategies relate to spreading reproductive risk. Overwintering individuals have the choice of dispersing to either a brackish sea bay or a rock pool habitat. The former is reproductively more favorable than the latter during warm dry years and less favorable during cool wet years. After spring migration, individuals may histolyse their flight muscles and lay all their eggs in one pool or they may retain their flight ability and lay fewer eggs in total but spread them in several pools. We use a simple two-habitat model to examine the question of habitat dispersal. Our results indicate that, although the value of the evolutionary stable dispersal depends on the degree of variability in the environment and on the probability of local extinctions in either habitat, the population always disperses to both habitats as a consequence of density dependent growth. We use a more detailed multiple-rockpool habitat model to examine the question of wing muscle histolysis as a response to density dependence. Our results indicate that a wing muscle histolysis response to population density is an evolutionarily stable strategy when compared with the two alternatives of females always histolysing or never histolysing their flight muscles. The application of evolutionarily stable theory to stochastic problems presents a number of difficulties. We discuss these difficulties in the context of computing evolutionarily stable strategies for the problems at hand.     

A model of dominance and resource division among a group of animals of differing quality

Individuals of many species spend a large portion of their lives within groups of conspecifics. Within such groups, there can be considerable diversity in size and other traits, with some, perhaps larger or stronger, animals laying claim to a greater than fair share of available resources. We use the word quality as a single measure of individual animal phenotypes within such a group and develop a model of resource division through contests between animals of differing quality. We investigated the effect of varying environmental factors on the level of aggressiveness used in such contests and the division of resources among the group. A numerical example shows that maximum discriminations between individuals on the basis of quality occur for medium-sized costs of aggressive encounters, but resources are divided more equitably at either extreme, when costs are either high or low. Received: April 9, 2001 / Accepted: September 16, 2001     

A model for predicting the emergence of dragonflies in a changing climate

1. Precise models for the phenology of different species are essential for predicting the potential effects of any temporal mismatch of life cycles with environmental parameters under different climate change scenarios. Here we investigated the effects of ambient water temperature on the onset and synchrony of emergence for a widespread European riverine dragonfly, Gomphus vulgatissimus .
2. Long-term field data on the annual emergence from two rivers in northern Germany, and additional data from a laboratory experiment with different temperature regimes, were used to develop a model that predicted the onset of emergence by using mainly the temperature sum (degree days) as a parameter.
3. Model predictions of the onset of emergence fitted the observations well and could be transferred between localities. This was particularly so when weighting early winter temperature data by using a day length and a temperature-response function, implying potential additional control mechanisms for the onset of emergence.
4. We simulated effects of different winter temperature regimes on the emergence curves in order to predict the effects of climate change. These indicated an acceleration of emergence by 6–7 days per 1 °C temperature increase, which is corroborated by the laboratory data and is in the upper range of data published for other dragonflies.     

The ideal free distribution: a review and synthesis of the game-theoretic perspective

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16-32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the “habitat selection game”. Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species.For a single species, the article briefly reviews existing results. It also develops a new perspective for Parker’s matching principle, showing that this can be viewed as the IFD of the habitat selection game that models consumer behavior in several resource patches and analyzing complications involved when the model includes resource dynamics as well. For two species, the article first demonstrates that the connection between IFD and ESS is now more delicate by pointing out pitfalls that arise when applying several existing game-theoretic approaches to these habitat selection games. However, by providing a new detailed analysis of dispersal dynamics for predator-prey or competitive interactions in two habitats, it also pinpoints one approach that shows much promise in this general setting, the so-called “two-species ESS”. The consequences of this concept are shown to be related to recent studies of population dynamics combined with individual dispersal and are explored for more species or more patches.     

The application of a model of glucose and insulin dynamics to explain an observed effect of leptin administration in reversal of developmental programming

A dynamical model describing the glucose-insulin physiological system was applied to an experiment on the administration of the adipokine leptin between neonatal days 3 and 13 to rats whose dams were subject to different levels of nutrition during gestation. The effect of leptin treatment on the glucose-insulin equilibrium point and on the levels of other associated metabolites showed a significant change in direction that depended on the level of prenatal nutrition. Leptin has been shown to affect two factors that affect the equilibrium levels of glucose and insulin, gluconeogenesis and insulin sensitivity. Each effect is described by a parameter in the dynamical model. Mathematical analysis shows that changes in these parameters in the manner promoted by leptin would indeed increase or decrease the glucose-insulin equilibria depending on their initial equilibrium levels which might be induced by the level of prenatal nutrition. This analysis explains the results of the leptin experiment in the context of the dynamics of the glucocorticoid system. It also proposes a physiological mechanism for the expression of plasticity in the organism based on the status of the glucose and insulin equilibria.     

Evolutionarily stable transition rates in a stage-structured model. An application to the analysis of size distributions of badges of social status

This paper deals with the adaptive dynamics associated to a hierarchical non-linear discrete population model with a general transition matrix. In the model, individuals are categorized into n dominance classes, newborns lie in the subordinate class, and it is considered as evolutionary trait a vector eta of probabilities of transition among classes. For this trait, we obtain the evolutionary singular strategy and prove its neutral evolutionary stability. Finally, we obtain conditions for the invading potential of such a strategy, which is sufficient for the convergence stability of the latter. With the help of the previous results, we provide an explanation for the bimodal distribution of badges of status observed in the Siskin (Carduelis spinus). In the Siskin, as in several bird species, patches of pigmented plumage signal the dominance status of the bearer to opponents, and central to the discussion on the evolution of status signalling is the understanding of which should be the frequency distribution of badge sizes. Though some simple verbal models predicted a bimodal distribution, up to now most species display normal distributions and bimodality has only been described for the Siskin. In this paper, we give conditions leading to one of these two distributions in terms of the survival, fecundity and aggression rates in each dominance class.     

Evolutionary syndromes linking dispersal and mating system: the effect of autocorrelation in pollination conditions

Self-fertilization is classically thought to be associated with propagule dispersal because self-fertilization is a boon to colonizers entering environments devoid of pollinators or potential mates. Yet, it has been theoretically shown that random fluctuations in pollination conditions select for the opposite association of traits. In nature, however, various ecological factors may deviate from random variations, and thus create temporal correlation in pollination conditions. Here, we develop a model to assess the effects of pollination condition autocorrelation on the joint evolution of dispersal and self-fertilization. Basically, two syndromes are found: dispersing outcrossers and nondispersing (partial) selfers. Importantly, (1) selfers are never associated with dispersal, whereas complete outcrossers are, and (2) the disperser/outcrosser syndrome is favored (resp. disfavored) by negative (resp. positive) autocorrelation in pollination conditions. Our results suggest that observed dispersal/mating system syndromes may depend heavily on the regime of pollination condition fluctuations. We also point out potential negative evolutionary effects of anthropic management of the environment on outcrossing species.     

Chaos and the (un)predictability of evolution in a changing environment

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency‐dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco‐evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability.     

Landscape dynamics and evolution of colonizer syndromes: interactions between reproductive effortand dispersal in a metapopulation

The evolutionary consequences of changes in landscape dynamics for the evolution of life history syndromes are studied using a metapopulation model. We consider in turn the long-term effects of a change in the local disturbance rate, in the maximal local population persistence, in habitat productivity, and in habitat fragmentation. We examine the consequences of selective interactions between dispersal and reproductive effort by comparing the outcome of joint evolution to a situation where the species has lost the potential to evolve either its reproductive effort or its dispersal rate. We relax the classical assumption that any occupied site in the metapopulation reaches its carrying capacity immediately after recolonization. Our main conclusions are the following: (1) genetic diversity modifies the range of landscape parameters for which the metapopulation is viable, but it alters very little the qualitative evolutionary trends observed for each trait within this range. Although they are both part of a competition/colonization axis, reproductive effort and dispersal are not substitutable traits: their evolution reflects more directly the change in the landscape dynamics, than a selective interaction among them. (2) no general syndrome of covariation between reproductive effort and dispersal can be predicted: the pattern of association between the two traits depends on the type of change in landscape dynamics and on the saturation level. We review empirical evidence on colonizer syndromes and suggest lines for further empirical work. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: An assessment of three methods

In recent years, three related methods have been used to model the phenotypic dynamics of traits under the influence of natural selection. The first is based on an approximation to quantitative genetic recursion equations for sexual populations. The second is based on evolution in asexual lineages with mutation-generated variation. The third method finds an evolutionarily stable set of phenotypes for species characterized by a given set of fitness functions, assuming that the mode of reproduction places no constraints on the number of distinct types that can be maintained in the population. The three methods share the property that the rate of change of a trait within a homogeneous population is approximately proportional to the individual fitness gradient. The methods differ in assumptions about the potential magnitude of phenotypic differences in mutant forms, and in their assumptions about the probability that invasion or speciation occurs when a species has a stable, yet invadable phenotype. Determining the range of applicability of the different methods is important for assessing the validity of optimization methods in predicting the evolutionary outcome of ecological interactions. Methods based on quantitative genetic models predict that fitness minimizing traits will often be evolutionarily stable over significant time periods, while other approaches suggest this is likely to be rare. A more detailed study of cases of disruptive selection might reveal whether fitness-minimizing traits occur frequently in natural communities.     

Foraging strategy of a non-omniscient predator in a changing environment (I) model with a data window and absolute criterion

1. Almost all the models so far presented assume that predators are omniscient in the sense that they always have complete information about the spatial distribution of prey abundance and its change over time. But this type of model cannot cover the situation where the prey abundance in each patch changes over time due to factors other than predation. The model with a data window and absolute criterion (SAC) here enables us to treat such situations.
2. The strategy of non-omniscient predators can be generally devided into four procedures; collection of information, its memorization, decision of tactics and its execution. SAC involves only two tactics; to stay another time period in the patch the predator is staying presently or to move to another patch chosen at random. The choice of either one of the two tactics is made by comparing the profitability of the current patch estimated by the data window with a pre-determined absolute criterion.
3. Three changing patterns of prey abundance are considered. In the most general pattern good patches have a higher mean profitability than poor patches, but the profitability changes cyclically in each of patches.
4. There are only two possibilities for an optimal strategy; the “patch choice strategy” in which once the predator has taken a good patch, it tries to stay there even when the state becomes poor, and the ‘state choice strategy” in which the predator seeks for only good states in good patches. The condition for which either of the two foraging strategies is superior to the other is specified analytically.

     

Coexistence in a fluctuating environment by the effect of relative nonlinearity: A minimal model

The minimal model of the “relative nonlinearity” type fluctuation-maintained coexistence is investigated. The competing populations are affected by an environmental white noise. With quadratic density dependence, the long-term growth rates of the populations are determined by the average and the variance of the (fluctuating) total density. At most two species can coexist on these two “regulating” variables; competitive exclusion would ensue in a constant environment. A numerical study of the expected time until extinction of any of the two species reveals that the criterion of mutual invasibility predicts the parameter range of long-term coexistence correctly in the limit of zero extinction threshold. However, any extinction threshold consistent with a realistic population size will allow only short-term coexistence. Therefore, our simulations question the biological relevance of mutual invasibility, as a sufficient condition of coexistence, for large density fluctuations. We calculate the average and the variance of the fluctuating density of the coexisting populations analytically via the moment-closure approximation; the results are reasonably close to the simulated behavior. Based on this treatment, robustness of coexistence is studied in the limit of infinite population size. We interpret the results of this analysis in the context of necessity of niche segregation with respect to the regulating variables using a framework theory published earlier.     

Foraging strategy of a non-omniscient predator in a changing environment (II) model with two data windows and a relative comparison criterion

1. The model with two data windows and the relative comparison criterion (SRC) is proposed based on a Dynamic Programming problem. The model deals with predators whith remember separately the profitability of each patch and visit patches repeatedly. The model predator can remember foraging results that have occurred within the duration of memory (D_m). But when the number of foraging results in one patch exceeds the capacity of the memory chamber (C_m), older results are deleted from memory. C_m is the short data window for patches searched recently and D_m is the long one for patches searched in the past, but not recently. The model predator always searches at the patch with the highest estimation of profitability.
2. The validity of SRC was checked by the experiment with great tits ofSmith andSweatman (1974). SRC could describe satisfactorily weil the experimental result that great tits at first searched almost uniformly and then concentrated their foraging efforts to good patches but they could not detect the new good patch after changes in food distribution. These analyses showed that great tits did not forage in an optimal manner in the experimental conditions ofSmith andSweatman (1974).
3. Differences of SRC from the exploration and exploitation model ofKrebs et al. (1978) and from the model with one data window and the absolute criterion (SAC) of Inoue (1983) were discussed to show characteristics of the two extreme strategies for sampling the patchy environment.

     

An individual-based model for predicting the emergence period of sea trout fry in a Lake District stream

The objective of this study was to predict interannual fluctuations in the emergence period of sea trout fry, using models developed from field data for 70 excavated redds, and laboratory data on egg and alevin development at 30 constant temperatures (range 1·5–10·5° C with 100 naturally fertilized eggs at each temperature). Egg weight and numbers per redd both increased with female length; a power function described the relationship. Early spawners were the largest females laying the largest and most numerous eggs, whilst late spawners were the smallest females laying the smallest and least numerous eggs; middle spawners being intermediate between these two extremes. Mean values for egg weight and numbers of eggs per redd were obtained for these three groups. Hatching and emergence times in the laboratory decreased with increasing temperature. Of five models tested for hatching time, the best fit was provided by a three-parameter hyperbolic model which formed the asis of the individual-based model used to predict egg hatching and fry emergence. Model development was described in detail and the final equations predicted the times taken for 5, 50 and 95% of the fry to emerge, and hence the period over which 90% of the fry emerged. Analogous models were obtained for egg hatching. All models were excellent fits to the laboratory data. Hatching times for eggs kept in perforated boxes in the stream were almost identical to those kept at similar mean temperatures in the laboratory. Model predictions of fry emergence times were validated by field data for 8 years (1967–1971, 1974, 1975, 1980). The chief objective was therefore fulfilled, and predictions for the 30-year study (1967–1996) revealed a large variation in the timing of emergence (extremes: 11 March–4 April 1989, 15–20 May 1979). Most of the variation in median emergence date was due to variations in water temperature, with spawning dates as a secondary factor; the latter, however, had a greater effect on the length of the emergence period.