Reproductive effort in viscous populations

Abstract.— Here I study a kin selection model of reproductive effort, the allocation of resources to fecundity versus survival, in a patch-structured population. Breeding females remain in the same patch for life. Offspring have costly, partial long-distance dispersal and compete for breeding sites, which become vacant upon the death of previous occupants. The main result is that the evolutionarily stable reproductive effort decreases as offspring dispersal rate increases. The result can be understood as follows: In a well-mixed population with global competition, neither adults nor juveniles compete with relatives, but in a patch-structured population with dispersal restricted to the juvenile phase, juveniles experience relatively less competition with relatives than adults, thus making juveniles relatively more valuable. Because this asymmetry between adults and juveniles decreases with the dispersal rate, so does the evolutionarily stable level of allocation to fecundity.     

Evolution of reproductive effort in a metapopulation with local extinctions and ecological succession

Abstract Using a metapopulation model, we study how local extinctions, limited population life span, and local demographic disequilibrium affect the evolution of the reproductive effort in a species with overlapping generations but no senescence. We show that in a metapopulation with saturation of all sites and an infinite deme maximal life span (no succession), local extinctions simply constitute an additional source of extrinsic mortality. When either the hypothesis of an infinite deme maximal life span or the saturation hypothesis is relaxed, nontrivial predictions arise. in particular, we find interactions between the evolutionarily stable reproductive effort strategy and the demographic dynamics in the metapopulation. We predict that larger reproductive effort may be selected for in habitats of poorer productivity, contrary to what would be predicted in a single population. Also, we predict that higher dispersal rates should favor selection for lower reproductive efforts. However, metapopulation parameters that favor high dispersal rates also favor larger reproductive efforts. Conflicting selection pressures in the metapopulation also allow maintaining evolutionarily stable polymorphism between a low and high reproductive effort for particular trade-offs between survival and fecundity.     

Coevolution between parasite virulence and host life-history traits

Epidemiological models generally explore the evolution of parasite life-history traits, namely, virulence and transmission, against a background of constant host life-history traits. However, life-history models have predicted the evolution of host traits in response to parasitism. The coevolution of host and parasite life-history traits remains largely unexplored. We present an epidemiological model, based on resource allocation theory, that provides an analysis of the coevolution between host reproductive effort and parasite virulence. This model allows for hosts with either a fixed (i.e., genetic) or conditional (i.e., a phenotypically plastic) response to parasitism. It also considers superinfections. We show that parasitism always favors increased allocation to host reproduction, but because of epidemiological feedbacks, the evolutionarily stable host reproductive effort does not always increase with parasite virulence. Superinfection drives the evolution of parasite virulence and acts on the evolution of the host through parasite evolution, generally leading to higher host reproductive effort. Coevolution, as opposed to cases where only one of the antagonists evolves, may generate correlations between host and parasite life-history traits across environmental gradients affecting the fecundity or the survival of the host. Our results provide a theoretical framework against which experimental coevolution outcomes or field observations can be contrasted.     

Cheating as a mixed strategy in a simple model of aggressive communication

The possibility that frequency-dependent cheating can persist in an evolutionarily stable communication system has frequently been proposed. Although there is empirical evidence for this idea, however, it has not been investigated in terms of game theory. In the present paper I show for a simple symmetric game that cheating can be part of a mixed evolutionarily stable strategy (ESS). Furthermore, despite the widespread assumption that cheaters must be rare, I show that most of the population can be cheaters, while the signalling system remains evolutionarily stable. Consequences for signalling theory and experiments to detect such mixed ESS are discussed. Copyright 2000 The Association for the Study of Animal Behaviour.     

The relationship between signal quality and physical condition: is sexual signalling honest in the three-spined stickleback?

Honest sexual signalling requires that the level of advertisement reveals mate quality. In the three-spined stickleback, Gasterosteus aculeatus, females base their mate choice mainly on the intensity of the males' red breeding coloration. Different results have, however, been obtained on the relationship between red breeding coloration and physical condition. In this study, the relationship was curvilinear in a natural population, with males in good and poor condition (measured as lipid content) having larger red areas than males of intermediate condition. By manipulating food intake and thus male condition prior to breeding, I further show that poor condition can induce an increase in signalling effort. This effect was further strengthened when the predation cost of signalling was increased by exposing the males to predators. This suggests that the reason for the high signalling effort of males in poor condition is their low probability of future reproduction and thus lower cost of signalling in terms of loss of future reproductive opportunities. Males in poor condition signal as a terminal effort and take larger risks and invest more in current reproduction than males in good condition. Finally, I discuss whether an effect of decreasing residual reproductive value on signalling effort could result in the breakdown of the honesty of the signal. Copyright 1999 The Association for the Study of Animal Behaviour.     

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.     

Kin selection, local competition, and reproductive skew

In a spatially structured population, limited dispersal gives rise to local relatedness, potentially favoring indiscriminate helping behavior. However, it also leads to local competition, which reduces the benefits of helping local kin. This tension has become the focus for a growing body of theoretical work. Existing models, however, have focused chiefly on the net impact of limited dispersal on cooperative or competitive effort in a homogeneous population. Here, I extend existing models of kin selection in a group-structured population to allow for asymmetries in expected fecundity and reproductive success among group members. I explore the consequent impact of limited dispersal on the evolution of helping and harming behavior, and on the degree of reproductive inequality or skew. I show that when individuals in a group differ in their expected fecundity, limited dispersal gives rise to kin selection for harming behavior on the part of more fecund individuals, and for helping behavior on the part of less fecund individuals. As a result, philopatry tends to exaggerate differences in reproductive success, and so promotes greater reproductive skew.     

Dynamics of the caring family

When several individuals simultaneously provide for offspring, as in families, the effort of any one individual will depend on the efforts of the other family members. This conflict of interest among family members is made more complicated by their relatedness because relatives share genetic interest to some degree. The conflict resolution will also be influenced by the differences in reproductive value between breeders and helpers. Here, we calculate evolutionarily stable provisioning efforts in families with up to two helpers. We explicitly consider that the behavioral choices are made in a life-history context, and we also consider how group sizes change dynamically; this affects, for example, average relatedness among group members. We assume two different scenarios: intact families in which the breeder is 100% monogamous and stepfamilies in which the breeder shifts mate between breeding events. The average relatedness among family members is allowed to evolve in concert with changes in provisioning effort. Our model shows that an individual's provisioning effort is not easy to predict from either its relatedness to the offspring or its reproductive value. Instead, it is necessary to consider the inclusive fitness effect of provisioning, which is determined by a combination of relatedness, reproductive value, and the reproductive value of the offspring.     

Multiple infections,kin selection and the evolutionary epidemiology of parasite traits

The coinfection of a host by several parasite strains is known to affect selective pressures on parasite strategies of host exploitation. I present a general model of coinfections that ties together kin selection models of virulence evolution and epidemiological models of multiple infections. I derive an analytical expression for the invasion fitness of a rare mutant in a population with an arbitrary distribution of the multiplicity of infection (MOI) across hosts. When a single mutation affects parasite strategies in all MOI classes, I show that the evolutionarily stable level of virulence depends on a demographic average of within‐host relatedness across all host classes. This generalization of previous kin selection results requires that within‐host parasite densities do not vary between hosts. When host exploitation strategies are allowed to vary across classes, I show that the strategy of host exploitation in a focal MOI class depends on the relative magnitudes of parasite reproductive values in the focal class and in the next. Thus, in contrast to previous findings, lower within‐host relatedness in competitive parasite interactions can potentially correspond to either higher or lower levels of virulence.     

Parental effort and reproductive skew in coalitions of brood rearing female common eiders

Members of breeding groups face conflicts over parental effort when balancing antipredatory vigilance and feeding. Empirical evidence has shown disparate responses to manipulations of parental effort. We develop a model in which we determine the evolutionarily stable effort of partners given their body conditions, allowing the benefits of shared care to be unevenly divided, and we test this model's predictions with data on common eiders (Somateria mollissima). Eiders show uniparental female care; females may share brood rearing, or they may tend alone, and their body condition at hatching of the young shows large environmentally induced variation. The model predicts that parental effort (vigilance) in a coalition is lower than when tending alone, controlling for parental condition; this prediction is supported by the data. The parental effort in a coalition should be positively correlated with body condition, and this prediction is also supported. Finally, parental effort should increase when partner condition decreases and vice versa; this prediction is partially supported. The Nash bargaining game may provide promising avenues by which to determine the precise settlement of reproductive skew and effort between coalition partners in the future.     

Optimal floating and queuing strategies: consequences for density dependence and habitat loss

Field studies of many vertebrates show that some individuals (floaters) do not defend territories even when there is space for them to do so. We show that the evolutionarily stable strategy (ESS) for the threshold territory quality at which floating takes place is that which maximizes the size of the floating population (but not the total population, breeding population, or reproductive output). The ESS is solved separately for two assumptions: whether individuals wait to occupy a single territory or multiple territories and whether queuing rules are strict or if all waiting individuals are equally likely to obtain the next territory. The four combinations of these assumptions all give the same evolutionarily stable population size of both floaters and breeders. At the ESS, only territories with expected lifetime reproductive success (LRS) exceeding 1 should be occupied, which introduces a limit to ideal habitat selection. The behavioral decision to float alters the shape of the density-dependent response, reduces the equilibrium population size, and affects the response of the population to habitat loss. Specifically, the floater: breeder ratio is directly related to average breeding habitat quality, and the floater population size will decrease more than the breeding population size if better than average quality habitat is lost.     

Reproductive asynchrony increases with environmental disturbance

While it is widely recognized that the manner in which organisms adjust their timing of reproduction reflects evolutionary strategies aimed at minimizing offspring mortality or maximizing reproductive output, the conditions under which the evolutionarily stable strategy involves synchronous or asynchronous reproduction is a matter of considerable discord. A recent theoretical model predicts that whether a population displays reproductive synchrony or asynchrony will depend on the relative scales of intrinsic regulation and environmental disturbance experienced by reproducing individuals. This model predicts that, under conditions of negligible competition and large-scale environmental perturbation, evolution of a single mixed strategy will result in asynchronous reproduction. We tested this prediction using empirical data on large-scale climatic fluctuation and the annual timing of reproduction by three species of flowering plants covering 1300-population-years and four degrees of latitude in Norway. In agreement with model predictions, within populations of all three species reproductive asynchrony increased with the magnitude of large-scale climatic perturbation, but bore no relation to the strength of local density dependence. These results suggest that mixed evolutionarily stable strategies can arise from the interplay of combinations of agents of selection and the scale at which they operate; hence it is fruitless to associate synchronous versus asynchronous timing with particular single factors like climate, competition, or predation.     

Reproductive Effort and Reproductive Values in Periodic Environments

Life-history theory concerns the optimal spread of reproduction over an organism's life span. In variable environments, there may be extrinsic differences between breeding periods within an organism's life, affecting both offspring and parent and giving rise to intergenerational trade-offs. Such trade-offs are often discussed in terms of reproductive value for parent and offspring. Here, we consider parental life-history optimization in response to varying offspring values of a population regulated by territoriality, where the quality of the environment varies periodically. Periods are interpreted as either within-year (seasonality) or between-years variation (cyclicity). The evolutionarily stable strategy in a general model with two-phased periodicity in the environment can generate either higher or lower effort in the more favorable of the two phases; hence knowing survival prospects of offspring does not suffice for predicting reproductive effort-the future of all descendants and the parent must be tracked. We also apply our method to data on the Ural owl Strix uralensis, a species preying on cyclically fluctuating voles. The observed dynamics are best predicted by assuming delayed reproductive costs and Type II functional response. Accounting for varying offspring values can lead to cases where both reproductive effort and recruitment of offspring are higher in the phase when voles are not maximally abundant, a pattern supported by our data.     

The island syndrome in isolated populations of a tropical forest rodent

I examined population traits of eight isolated populations of a tropical forest rodent (Proechimys semispinosus, the Central American spiny rat) for 1 year in central Panamá. Populations were sampled by monthly live-trapping, and seven traits (density, population growth rate, adult survival, reproductive effort, age structure, sex ratio, and body mass) were compared among populations. I also compared results with published data from nearby mainland populations. Each isolated population showed characteristics typical of island populations when compared with mainland populations, including higher and more stable densities, reduced reproductive effort, and greater body mass. Densities were the highest yet recorded for this species, and biomass of these island populations was among the highest of any tropical rodent yet studied. Population traits varied not only between island and mainland populations but also among island populations. P. semispinosus have traits that allow individuals in a population to rapidly respond to temporal changes in habitat quality or resource abundance. These traits include a high reproductive rate and an ability to adjust reproductive effort to changes in density. P. semispinosus are therefore able to quickly reach and maintain high densities under favorable conditions, thereby allowing close tracking of temporally and spatially varying resources. This flexibility is predicted for habitat generalists and presumably promotes abundance and persistence in temporally and spatially heterogeneous environments. P. semispinosus, often the most abundant and widely distributed species of rodent in forests throughout their geographic range, therefore have traits that are similar to those of generalist rodents in temperate forests.     

Equilibrium Distributions of Populations of Biological Species on Networks of Social Sites

ABSTRACT

We investigate the problem of how a population of biological species would distribute over a given network of social sites so that their social contacts through the connected sites can be maximized (or minimized). This problem has applications in modelling the behaviours of social (or solitary) species such as the development of social groups in human society and the spread of solitary animals in distant habitats. We show that this problem can be formulated as an evolutionary game, with the equilibrium state of the game corresponding to a strategy for choosing the residing sites, each with a certain probability, or equivalently, to a distribution of the population on these sites. The game has a symmetric payoff matrix, and can therefore be analyzed via the solution of a corresponding quadratic programme: An equilibrium strategy of the game is a KKT point of the quadratic programme, which may be a local maximizer, local minimizer, or saddle point, but it is evolutionarily stable if and only if it is a strict local maximizer. In general, with a goal to maximize the social contacts, the species tend to spread on network sites where there are dense connections such as a complete subnetwork or in other words, a network clique. We show that at equilibrium, the population may or may not distribute on a network clique, but the stability of the equilibrium state does depend on the structure of the selected subnetwork. In particular, we show that the distribution of the population on a maximal network clique is evolutionarily stable unless the clique is ‘attached’ to another clique of the same or larger size, when the population may be able to switch or expand to the neighbouring clique to increase or at least maintain its total amount of contacts. However, the distribution of the population on a non-clique subnetwork is always evolutionarily unstable or weakly evolutionarily stable at the very best, for the population can always move away from its current distribution without decreasing its total amount of contacts. We conclude that the strategies to spread on maximal network cliques are not only equilibrium strategies but also evolutionarily more stable than those on non-clique subnetworks, thus theoretically reaffirming the evolutionary advantages of joining social cliques in social networks for social species.     

The evolution of dispersal in a two-patch system: some consequences of differences between migrants and residents

We investigate how age-structure and differences in certain demographic traits between residents and immigrants of a single species act to determine the evolutionarily stable dispersal strategy in a two-patch environment that is heterogeneous in space but constant in time. These two factors have been neglected in previous models of the evolution of dispersal, which generally consider organisms with very simple life-cycles and assume that, whatever their origin, individuals in a given habitat have the same bio-demographic characteristics. However, there is increasing empirical evidence that dispersing individuals have different demographic properties from phylopatric ones. We develop a matrix model in which recruitment depends on local population densities. We assume that dispersal entails a proportional cost to immigrant fecundity, which can be compensated by differences in survival rates between immigrants and residents. The evolutionarily stable strategies (ESS) for dispersal are identified using a combination of analytical expressions and numerical simulations. Our results show that philopatry is selected (1) when dispersal rates do not vary in space, (2) when the metapopulation is a source-sink system and (3) when dispersal rates vary in space (asymmetric dispersal) and immigrants do not compensate for their reduced fecundity. We observe that non-zero asymmetric dispersal rates may be evolutionarily stable when (1) immigrants and residents are demographically alike and (2) immigrants compensate totally for their reduced fecundity through an increase in adult survival. Under these conditions, we find that the ESS occurs when the fitnesses at equilibrium in the two habitats, measured in our model by the realized reproductive rates, are each equal to unity. A comparison with previous studies suggests a unifying rule for the evolution of dispersal: the dispersal rates which permit the spatial homogenization of fitnesses are ESSs. This condition provides new insight into the evolutionary stability of source-sink systems. It also supports the hypothesis that immigrants have adapted demographic strategies, rather than the hypothesis that dispersal is costly and immigrants are at a disavantage compared with residents.     

The context-dependent effect of multiple paternity on effective population size

Effective population size (N(e)) is important because it describes how evolutionary forces will affect a population. The effect of multiple sires per female on N(e) has been the subject of some debate, at the crux of which is the effects of monandry and multiple-paternity (MP) on male variance in reproductive success. In both mating systems, females mate with several males over their lifetimes, but sire offspring with one male at a time in the former and have several sires per clutch in the latter. First, I theoretically show that whether the annual male variance in reproductive success in an MP population is greater or less than that of a monandrous population depends on the distributions of within-clutch paternity. Then, I simulated different distributions of within-clutch paternity under a range of parameters that characterize natural populations to show that an MP population can have an N(e) smaller or larger than that of a monandrous population with otherwise equal dynamics. The N(e(MP)):N(e(Monandry)) ratio increased with mating frequency and female variance in reproductive success, was equalized by long generation times, and was affected by the distribution of within-clutch paternities. The results of this model provide a unifying framework for the debate.     

A new demographic function maximized by life-history evolution

A goal of life-history theory has been to understand what combination of demographic traits is maximized by natural selection. In practice, researchers usually choose either density-independent population growth rate, lambda, or lifetime reproductive success, R0 (expected number of offspring produced in a lifetime). Others have shown that the maxima of density-independent lambda and R0 are evolutionarily stable strategies under specific density-dependent conditions: population regulation by equal density dependence among all age classes for lambda and by density dependence on a single age class for R0. Here I extend these connections between density-independent optimization models and density-dependent invasion function models in two ways. First, I derive a new demographic function for which a maximum corresponds to attainability of the equilibrium strategy or stability of the mean rather than stability of the variance of the strategy distribution. Second, I show explicitly a continuous range of cases with maxima between those for the lambda and R0. Graphical and biological interpretations are given for an example model. Finally, exceptions to a putative life-history generality (from lambda and R0 models), that high early-life mortality selects for high iteroparity, are shown.     

Life-history variation in contrasting habitats: flowering decisions in a clonal perennial herb (Veratrum album)

Quantifying intraspecific demographic variation provides a powerful tool for exploring the diversity and evolution of life histories. We investigate how habitat-specific demographic variation and the production of multiple offspring types affect the population dynamics and evolution of delayed reproduction in a clonal perennial herb with monocarpic ramets (white hellebore). In this species, flowering ramets produce both seeds and asexual offspring. Data on ramet demography are used to parameterize integral projection models, which allow the effects of habitat-specific demographic variation and reproductive mode on population dynamics to be quantified. We then use the evolutionarily stable strategy (ESS) approach to predict the flowering strategy-the relationship between flowering probability and size. This approach is extended to allow offspring types to have different demographies and density-dependent responses. Our results demonstrate that the evolutionarily stable flowering strategies differ substantially among habitats and are in excellent agreement with the observed strategies. Reproductive mode, however, has little effect on the ESSs. Using analytical approximations, we show that flowering decisions are predominantly determined by the asymptotic size of individuals rather than variation in survival or size-fecundity relationships. We conclude that habitat is an important aspect of the selective environment and a significant factor in predicting the ESSs.     

Optimal Floating and Queuing Strategies: The Logic of Territory Choice

This is a response to a recent article by Hanna Kokko and William J. Sutherland (American Naturalist 152:354-366), who consider evolutionarily stable territory acceptance rules for animals that face the decision between settling on a poor territory now (which is then retained for life) or waiting for better habitat to become available later (taking a chance of dying before reproducing). In contrast to these authors, we argue that the evolutionarily stable threshold quality above which territories are acceptable does depend on whether individuals compete for a single territory (queuing) or for multiple territories (floating) and also on whether access to territories is determined by a hierarchy among waiting individuals. More specifically, we show the following: First, if the choice is between floating and settling, the evolutionarily stable acceptance threshold is such that threshold territories yield an expected lifetime reproductive success (LRS) of 1-μF, the survival probability of a floater. Second, if the choice is between queuing and settling, the evolutionarily stable threshold may correspond to any LRS between 1-μF and unity. Third, the number of nonbreeding individuals in the population is maximized at a threshold of unity. In other words, the evolutionarily stable threshold does not maximize the nonbreeding fraction of the population. We argue that models of territory choice should carefully specify the mechanism of choice because some choice processes (e.g., indiscriminate habitat use above the threshold) do not admit an evolutionarily stable acceptance rule.