Strong stability and density-dependent evolutionarily stable strategies

Stability conditions for equilibria of the evolution of population strategies in a single species are developed by comparing frequency and density dependent fitnesses of pairs of strategies. Stability of such equilibria is shown for general haploid frequency and density dynamics. It is also shown that this stability is stronger than that of multispecies population dynamical systems. A biological interpretation of the conditions is provided in terms of the fitness of invading subpopulations.     

Evolution of conditional dispersal: evolutionarily stable strategies in spatial models

We consider a two-species competition model in which the species have the same population dynamics but different dispersal strategies. Both species disperse by a combination of random diffusion and advection along environmental gradients, with the same random dispersal rates but different advection coefficients. Regarding these advection coefficients as movement strategies of the species, we investigate their course of evolution. By applying invasion analysis we find that if the spatial environmental variation is less than a critical value, there is a unique evolutionarily singular strategy, which is also evolutionarily stable. If the spatial environmental variation exceeds the critical value, there can be three or more evolutionarily singular strategies, one of which is not evolutionarily stable. Our results suggest that the evolution of conditional dispersal of organisms depends upon the spatial heterogeneity of the environment in a subtle way.     

Patterns of evolutionarily stable strategies: the maximal pattern conjecture revisited

A conflict is defined by a set of pure strategies [1,..., n] and a payoff matrix, and may have many evolutionarily stable strategies (ESSs). A collection of subsets of the set of pure strategies is called a pattern. If there is an n x n matrix which has ESSs whose supports match those of the pattern, then that pattern is said to be attainable. Much of the work on patterns of ESSs relied upon an unproved conjecture. Subject to some relaxation of the definition of attainability, this conjecture is proved.     

Descriptions of superparasitism by optimal foraging theory,evolutionarily stable strategies and quantitative genetics

Many parasitoids superparasitize, in which an insect attacks a previously parasitized host, laying an egg in the host even though only one offspring will emerge from the host. In this paper superparasitism is considered from the perspectives of optimal foraging theory, evolutionarily stable strategies, and quantitative genetics. The focal question is: at what point in its life should an individual parasitoid begin attacking previously parasitized hosts? Each of the three theoretical methods can be used to answer the question and by doing so, we see how the three methods are connected. Qualitative, empirical predictions based on the theories are described.     

Strong stability and evolutionarily stable strategies with two types of players

Static ESS conditions are developed for the frequency evolution of a two-species haploid system by analyzing the stability of the corresponding dynamics for two pairs of strategies. A dynamic strong stability concept is introduced and shown to be equivalent to the ESS conditions in all cases where a regularity assumption is satisfied.     

An explicit approach to evolutionarily stable dispersal strategies: no cost of dispersal

The evolution of dispersal is examined by looking at evolutionarily stable strategies (ESS) for dispersal parameters in discrete time multisite models without any cost of dispersal. ESS are investigated analytically, based on explicit results on sensitivity analysis of matrix models. The basic model considers an arbitrary number of sites and a single age class. An ESS for dispersal parameters is obtained when the spatial reproductive values, calculated at the density-dependent population equilibrium, are equal across sites. From this basic formulation, one derives equivalently that all local populations should be at equilibrium in the absence of migration, and that dispersal between sites should be balanced, i.e., the numbers of individuals arriving to and leaving a site are equal. These results are then generalized to a model with several age classes. Equal age-specific reproductive values do not however imply balanced dispersal in this case. Our results generalize to any number of sites and age classes those available ?M. Doebeli, Dispersal and dynamics, Theoret. Popul. 47 (1995) 82 for two sites and one age class.     

Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay

We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new players are born from parents who played in the past. We consider two-player games with two strategies and a unique mixed evolutionarily stable strategy. We show that in the first type of dynamics, it is asymptotically stable for small time delays and becomes unstable for big ones when the population oscillates around its stationary state. In the second type of dynamics, however, evolutionarily stable strategy is asymptotically stable for any size of a time delay.     

On evolutionarily stable strategies in populations with subpopulations having isolated strategy repertoires

The concept of a population with subpopulations that are isolated with respect to strategies is introduced and applied to a biologically important class of cases, showing that no proper mixed evolutionarily stable strategies can exist in such cases.     

Required parental investment and mating patterns: A quantitative analysis in the context of evolutionarily stable strategies

Abstract

Much social psychological research has been dedicated to understanding mating strategies from the standpoint of genetic‐fitness payout (e.g., Simpson and Gangestad, 2000). The current work is designed to provide a coherent, quantitative model for predicting different classes of mating strategies in both males and females. Specifically, the framework developed in this paper is an elaboration of Dawkins’ (1989) quantitative assessment of different male and female mating strategies. Dawkins suggests that the prevalence of different strategies employed should be predictable in terms of evolutionary stable strategies. In the current work, a quantitative analysis predicting the prevalence of different mating strategies within each sex was conducted. The mathematical functions derived suggest that variability in the costs associated with raising offspring affects the expected prevalence of mating strategies differently for males and females. According to the present model, variability in female strategies should be less affected by changes in parental investment (PI) than variability in male strategies. Important predictions regarding male and female mating strategies across cultures are discussed.     

Required parental investment and mating patterns: a quantitative analysis in the context of evolutionarily stable strategies

Much social psychological research has been dedicated to understanding mating strategies from the standpoint of genetic-fitness payout (e.g., Simpson and Gangestad, 2000). The current work is designed to provide a coherent, quantitative model for predicting different classes of mating strategies in both males and females. Specifically, the framework developed in this paper is an elaboration of Dawkins' (1989) quantitative assessment of different male and female mating strategies. Dawkins suggests that the prevalence of different strategies employed should be predictable in terms of evolutionary stable strategies. In the current work, a quantitative analysis predicting the prevalence of different mating strategies within each sex was conducted. The mathematical functions derived suggest that variability in the costs associated with raising offspring affects the expected prevalence of mating strategies differently for males and females. According to the present model, variability in female strategies should be less affected by changes in parental investment (PI) than variability in male strategies. Important predictions regarding male and female mating strategies across cultures are discussed.     

Modelling evolutionarily stable strategies in oviposition site selection, with varying risks of predation and intraspecific competition

Many ovipositing mosquitoes, as well as other species, can detect biotic factors that affect fitness. However, a female mosquito seeking a high quality oviposition site (e.g. one with low risk of predation and competition to her progeny) must often balance the competing risk of increasing probability of mortality to herself while she continues to search, against increased probability of finding a high quality site. Such oviposition site selection may affect adult population size. We examined a female mosquito’s expected strategy of oviposition site selection under conditions of varying predator prevalence and adult mortality risk, by combining a detailed structured population model with a Markov chain implementation of the adult behavioural process. We used parameter values from the specific mosquito-predator system, Culiseta longiareolata-Notonecta maculata, although the overall results can be generalised to many mosquito species. Our model finds the evolutionarily stable strategy of oviposition site selection for different parameter combinations. Our model predicts that oviposition strategy does not vary smoothly with varying environmental risk of adult mortality, but that certain oviposition strategies become unstable at some parameter values. Mosquitoes will distribute their reproductive effort between breeding sites of varying predation risk only when adult mortality is low or larval competition high. Our model predicts that females will continue searching for predator-free pools, rather than oviposit in the first site encountered, regardless of the risk of mortality to the adult. The ecological basis for a reproductive strategy with alternative behaviours is important for understanding the effect of biotic factors on the population dynamics of mosquitoes, and for the development of biological control strategies, such as the dissemination of predator-cue chemicals.     

Genomic organization of evolutionarily correlated genes in bacteria: limits and strategies

The need for efficient molecular interplay in time and space within a cell imposes strong constraints that could be partially relaxed if relative gene positions along chromosomes were appropriate. Comparative genomics studies have demonstrated the short-scale conservation of gene proximity along bacterial chromosomes. Additionally, the long-range periodic positioning of evolutionarily correlated genes within Escherichia coli has recently been highlighted. To gain further insight into these different genetic organizations, we examined the compromise between chromosomal proximity and periodicity for all available eubacterial genomes by evaluating groups of evolutionarily correlated genes from a benchmark data set. In enterobacteria, strict chromosomal proximity is found to be limited to groups under 20 genes, whereas periodicity is significant in all groups over 50. The E. coli K12 genome bears 511 periodic genes (12% of the genome), whose orthologs are found to be periodic in all eubacterial phyla. These periodic genes predominantly function in macromolecular synthesis and spatial organization of cellular components. They are enriched in essential and housekeeping genes and tend to often be constitutively expressed. On this basis, it is argued that chromosomal proximity and periodicity are ubiquitous complementary genomic strategies that favor the build-up of local concentrations of co-functional molecules. In particular, the periodic layout may facilitate chromosome folding to spatially organize the construction of major cell components. The transition at 20 genes is reminiscent of the size of the longest operons and of topological microdomains. The range for which DNA neighborhood optimizes biochemical interactions might therefore be defined by DNA topology.     

An evolutionarily stable strategy for aggressiveness in feeding groups

Animals searching for food in groups display highly variabledegrees of aggressiveness. In this paper I present an individual-basedgame theoretical model of how gregarious animals should adjusttheir level of aggressiveness to their environmental conditions.In accordance with behavioral observations, the predicted levelof aggressiveness increases progressively with decreasing foodavailability and increasing animal density. The proposed modelalso predicts a positive influence of food energy value andhandling time on the level of aggressiveness within the group.In addition, the model provides information about the influenceof aggressive behavior on individual foraging success, interference,and population dynamics. Adaptive behavioral rules for aggressivenessin consumers are predicted to respond to both competitors andfood density in a way that contributes to stabilization of thedynamics of population systems.     

Mating group size and evolutionarily stable pattern of sexuality in barnacles

Barnacles, marine crustaceans, have various patterns of sexuality depending on species including simultaneous hermaphroditism, androdioecy (hermaphrodites and dwarf males), and dioecy (females and dwarf males). We develop a model that predicts the pattern of sexuality in barnacles by two key environmental factors: (i) food availability and (ii) the fraction of larvae that settle on the sea floor. Populations in the model consist of small individuals and large ones. We calculate the optimal resource allocation toward male function, female function and growth for small and large barnacles that maximizes each barnacle's lifetime reproductive success using dynamic programming. The pattern of sexuality is defined by the combination of the optimal resource allocations. In our model, the mating group size is a dependent variable and we found that sexuality pattern changes with the food availability through the mating group size: simultaneous hermaphroditism appears in food-rich environments, where the mating group size is large, protandric simultaneous hermaphroditism appears in intermediate food environments, where the mating group size also takes intermediate value, the other sexuality patterns, androdioecy, dioecy, and sex change are observed in food-poor environments, where the mating group size is small. Our model is the first one where small males can control their growth to large individuals, and hence has ability to explain a rich spectrum of sexual patterns found in barnacles.     

Evolutionary branching and evolutionarily stable coexistence of predator species: Critical function analysis

On the ecological timescale, two predator species with linear functional responses can stably coexist on two competing prey species. In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate under what conditions such a coexistence is also evolutionarily stable, and whether the two predator species may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in capture rates and a predator with a high capture rate for one prey has a low capture rate for the other and vice versa. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly convex in the vicinity of the singular strategy and the interspecific prey competition is not strong, then this singular strategy is an evolutionary branching point, near which the resident and mutant predator populations can coexist and diverge in their strategies. Second, we find that after branching has occurred in the predator phenotype, if the trade-off curve is globally convex, the predator population will eventually branch into two extreme specialists, each completely specializing on a particular prey species. However, in the case of smoothed step function-like trade-off, an interior dimorphic singular coalition becomes possible, the predator population will eventually evolve into two generalist species, each feeding on both of the two prey species. The algebraical analysis reveals that an evolutionarily stable dimorphism will always be attractive and that no further branching is possible under this model.     

Short- vs. long-range disperser: the evolutionarily stable allocation in a lattice-structured habitat

The population dynamics of two types of organisms in a lattice-structured habitat are studied and the evolutionarily stable allocation between short- and long-range disperser is calculated. Offsprings of short-range dispersal stay in the vicinity of their parent and cause local competition. Using pair approximation, I derive a closed system of ordinary differential equations of global and local densities (or mean crowding), and calculate the condition for one type to invade the population dominated by the other type. The evolutionarily stable strategy (ESS) of resource allocation is derived for the case in which there is a linear trade-off between short- and long-range dispersers. The maximum equilibrium abundance of the population may be achieved by a mixture of both types of dispersers, but it is in general different from the ESS resource allocation calculated from the invasibility condition. For the same parameter values, the ESS invests a larger fraction of resources to short-range disperser than the optimal allocation which maximizes the equilibrium population density. This difference can be explained by the fact that long-range disperser is more effective in the preoccupation of space than short-range disperser. The predictions are confirmed by the direct computer simulations of the lattice stochastic models. Copyright 1999 Academic Press.