Viscous Populations Research Articles

LIFE HISTORY, HABITAT SATURATION AND THE EVOLUTION OF FECUNDITY AND SURVIVAL ALTRUISM

Hamilton's rule provides a general description of the conditions for the evolution of altruism. But altruism can take different forms depending on which life-history trait is affected by the helping behavior (fecundity vs. survival helping). In particular, these different forms of helping may have very different demographic consequences, which may feed back on evolution. We examine the interplay between various forms of helping and demography in viscous populations with empty sites. A key component of our analysis is the local density of empty sites experienced by a focal individual, which provides a measure of habitat saturation. Habitat saturation is shown to have contrasting effects depending on (1) whether the physiological costs and benefits of helping affect fecundity, survival or both; and (2) whether the costs of helping are paid in a density-dependent or density-independent manner. For a given level of habitat saturation and with density-dependent reproduction, we find that the conditions for the evolution of helping should be more favorable in the survival altruism life cycle with a cost on fecundity, and more stringent in the fecundity altruism life cycle with a cost on survival. More generally, our analysis stresses the importance of taking into account the feedback between population demography, life history, and kin selection when investigating the selective pressures on altruism.

The evolution of juvenile-adult interactions in populations structured in age and space

We study the evolution of a spatially structured population with two age classes using spatial moment equations. In the model, adults can either help juveniles by increasing their survival, or adopt a cannibalistic behaviour and consume juveniles. While cannibalism is the sole evolutionary outcome when the population is well-mixed, both cannibalism and parental care can be evolutionarily stable if the population is viscous. Our analysis allows us to make two main technical points. First, we present a method to define invasion fitness in class-structured viscous populations, which allows us to apply adaptive dynamics methodology. Second, we show that ordinary pair approximation introduces an important quantitative bias in the evolutionary model, even on random networks. We propose a correction to the ordinary pair approximation that yields quantitative accuracy, and discuss how the bias associated with this approach is precisely what allows us to identify subtle aspects associated with the evolutionary dynamics of spatially structured populations.

Nice natives and mean migrants: the evolution of dispersal‐dependent social behaviour in viscous populations

There has been much interest in the evolution of social behaviour in viscous populations. While low dispersal increases the relatedness of neighbours, which tends to promote the evolution of indiscriminate helping behaviour, it can also increase competition between neighbours, which tends to inhibit the evolution of helping and may even favour harming behaviour. In the simplest scenario, these two effects exactly cancel, so that dispersal rate has no impact on the evolution of helping or harming. Here, we show that dispersal rate does matter when individuals can adjust their social behaviour conditional on whether they have dispersed or whether they have remained close to their place of origin. We find that nondispersing individuals are weakly favoured to indiscriminately help their neighbours, whereas dispersing individuals are more readily favoured to indiscriminately harm their neighbours.

Stable public goods cooperation and dynamic social interactions in yeast

Despite long-standing theoretical interest in the evolution of cooperation, empirical data on the evolutionary dynamics of cooperative traits remain limited. Here, we investigate the evolutionary dynamics of a simple public goods cooperative trait, invertase secretion, using a long-term selection experiment in Saccharomyces cerevisiae. We show that average investment in cooperation remains essentially constant over a period of hundreds of generations in viscous populations with high relatedness. Average cooperation remains constant despite transient local selection for high and low levels of cooperation that generate dynamic social interactions. Natural populations of yeast show similar variation in social strategies, which is consistent with the existence of similar selective pressures on public goods cooperation in nature.

Cooperation in viscous populations—Experimental evidence

We experimentally investigate the effect of population viscosity (an increased probability to interact with others of one's type or group) on cooperation in a standard prisoner's dilemma environment. Subjects can repeatedly choose between two groups that differ in the defector gain in the associated prisoner's dilemma. Choosing into the group with the smaller defector-gain can signal one's willingness to cooperate. We find that viscosity produces an endogenous sorting of cooperators and defectors and persistently high rates of cooperation. Higher viscosity leads to a sharp increase in overall cooperation rates and in addition positively affects the subjects' preferences for cooperation.

Natural selection of altruism in inelastic viscous homogeneous populations

Biological explanations are given of three main uninterpreted theoretical results on the selection of altruism in inelastic viscous homogeneous populations, namely that non-overlapping generations hinder the evolution of altruism, fecundity effects are more conducive to altruism than survival effects, and one demographic regime (so-called death–birth) permits altruism whereas another (so-called birth–death) does not. The central idea is ‘circles of compensation’, which measure how far the effects of density dependence extend from a focal individual. Relatednesses can then be calculated that compensate for density dependence. There is very generally a ‘balancing circle of compensation’, at which the viscosity of the population slows up selection of altruism, but does not affect its direction, and this holds for altruism towards any individual, not just immediate neighbours. These explanations are possible because of recent advances in the theory of inclusive fitness on graphs. The assumption of node bitransitivity in that recent theory is relaxed to node transitivity and symmetry of the dispersal matrix, and new formulae show how to calculate relatedness from dispersal and vice versa.

Self‐structuring in spatial evolutionary ecology

Spatial self-structuring has been a focus of recent interest among evolutionary ecologists. We review recent developments in the study of the interplay between spatial self-structuring and evolution. We first discuss the relative merits of the various theoretical approaches to spatial modelling in ecology. Second, we synthesize the main theoretical studies of the evolution of cooperation in spatially structured populations. We show that population viscosity is generally beneficial to cooperation, because cooperators can reap additional benefits from being clustered. A similar mechanism can explain the evolution of honest communication and of reduced virulence in host-parasite interactions. We also discuss some recent innovative empirical results that test these theories. Third, we show the relevance of these results to the general field of evolutionary ecology. An important conclusion is that kin selection is the main process that drives evolution of cooperation in viscous populations. Many results of kin selection theory can be recovered as emergent properties of spatial ecological dynamics. We discuss the implications of these results for the study of multilevel selection and evolutionary transitions. We conclude by sketching some perspectives for future research, with a particular emphasis on the topics of evolutionary branching, criticality, spatial fluctuations and experimental tests of theoretical predictions. Space is the place - Sun Ra.

Local Interactions Select for Lower Pathogen Infectivity

Theory suggests that the current rapid increase in connectivity and consequential changes in the structure of human, agricultural, and wildlife populations may select for parasite strains with higher infectivity. We carried out a test of this spatial theory by experimentally altering individual host movement rates in a model host/pathogen system by altering the viscosity of their environment. In our microevolutionary selection experiments, the infectivity of the virus was, as predicted by the theory, reduced in the most viscous populations. We therefore provide empirical support for the theory that population structure affects the evolution of infectious organisms.

Various remarks on Lehmann and Keller's article

Various remarks on Lehmann and Keller's article

Habitat geometry, population viscosity and the rate of genetic drift

In all natural populations, individuals located close to one another tend to interact more than those further apart. The extent of population viscosity can have important implications for ecological and evolutionary processes. Here we develop a spatially explicit population model to examine how the rate of genetic drift depends upon both spatial population structure and habitat geometry. The results show that the time to fixation for a new and selectively neutral mutation is dramatically increased in viscous populations. Furthermore, in viscous populations the time to fixation depends critically on habitat geometry. Fixation time for populations of identical size increases markedly as landscape width decreases and length increases. We suggest that similar effects will also be important in metapopulations, with the spatial arrangement of subpopulations and their connectivity likely to determine the rate of drift. We argue that the recent increases in computer power should facilitate major advances in our understanding of evolutionary landscape ecology over the next few years, and suggest that the time is ripe for a unification of spatial population dynamics theory, landscape ecology and population genetics.

Evolution of contingent altruism when cooperation is expensive

The ubiquity of cooperation has motivated a major research program over the last 50 years to discover ever more minimal conditions for the evolution of altruism. One important line of work is based on favoritism toward those who appear to be close relatives. Another important line is based on continuing interactions, whether between individuals (e.g., reciprocity) or between lines of descent in a viscous population. Here, we use an agent-based model to demonstrate a new mechanism that combines both lines of work to show when and how favoritism toward apparently similar others can evolve in the first place. The mechanism is the joint operation of viscosity and of tags (heritable, observable, and initially arbitrary characteristics), which serve as weak and potentially deceptive indicators of relatedness. Although tags are insufficient to support cooperation alone, we show that this joint mechanism vastly increases the range of environments in which contingent altruism can evolve in viscous populations. Even though our model is quite simple, the subtle dynamics underlying our results are not tractable using formal analytic tools (such as analysis of evolutionarily stable strategies), but are amenable to agent-based simulation.

Viscous populations and their support for reciprocal cooperation.

Viscous populations (those whose members are spatially distributed and have limited mobility and locality of interaction and mating) have been proposed to support the evolution of reciprocal cooperation among self-interested individuals. Here we present a model of such a population and describe how its examination yielded the realization that different classes of viscous populations exist with differing levels of support for reciprocal cooperation. Specifically we find from our model that, in a spatially distributed population with increased viscosity, the reciprocally cooperative tit-for-tat strategy may not be globally stable due to a corresponding increase in local population density.

Vicious fig wasps in viscous populations

Understanding when interacting individuals should conflict or cooperate is an enduring topic in evolutionary ecology. Cooperation can be favoured through kin selection when those interacting are genetic relatives. Because high levels of relatedness can be generated in ‘viscous’ populations, characterized by limited dispersal, it has often been assumed that population viscosity will lead to cooperation. However, the same viscosity might also increase resource competition between relatives, and recent theory predicts that this might oppose the evolution of cooperation. The predicted and opposing influences of relatedness and competition can be difficult to disentangle in practice but a new comparative study on male–male conflicts in fig wasps shows that fighting is correlated with resource competition rather than with genetic relatedness 1xTesting Hamilton's rule with competition between relatives. West, S.A et al. Nature. 2001; 409: 510–513Crossref | PubMed | Scopus (170)See all

The spatial spread of altruism versus the evolutionary response of egoists.

Several recent models have shown that altruism can spread in viscous populations, i.e. in spatially structured populations within which individuals interact only with their immediate neighbours and disperse only over short distances. I first confirm this result with an individual-based model of a viscous population, where an individual can vary its level of investment into a behaviour that is beneficial to its neighbours but costly to itself. Two distinct classes of individuals emerge: egoists with no or very little investment into altruism, and altruists with a high level of investment; intermediate levels of altruism are not maintained. I then extend the model to investigate the consequences of letting interaction and dispersal distances evolve along with altruism. Altruists maintain short distances, while the egoists respond to the spread of altruism by increasing their interaction and dispersal distances. This allows the egoistic individuals to be maintained in the population at a high frequency. Furthermore, the coevolution of investment into altruism and interaction distance can lead to a stable spatial pattern, where stripes of altruists (with local interactions) alternate with stripes of egoists (with far-reaching interactions). Perhaps most importantly, this approach shows that the ease with which altruism spreads in viscous populations is maintained despite countermeasures evolved by egoists.

Role of male dispersal in the evolution of female altruistic behavior in viscous populations

A computer simulation was conducted to examine the effect of differential dispersal of sexes on the evolution of altruism in viscous populations. First, a basic model, which was regarded as a purely viscous population model, was constructed. The model was assumed to be the same as the simulation model of Wilson et al. (1992), except that it assumed sexual reproduction and that only females show altruistic behavior toward females. For the basic model, altruism could not evolve when b/N ≤ c, where b is the benefit of the altruism to the recipient, c is the cost to the altruist, and N is the number of interacting neighbors. The male dispersal model I assumed that females disperse to nine neighboring sites including the natal site, but males disperse to eight sites farther than females do. For this model, altruistic alleles could evolve when b/N was equal to c or b/N was slightly smaller than c only when the male dispersal distance was slightly larger than those of females. The male dispersal model II assumed that the male dispersal distance follows a normal probability distribution. The Vole model was based on actual data of the gray‐sided vole, Clethironomys rufocanus bedfordiae, whose frequency distribution of dispersal distance was similar to a normal distribution. For these models, altruism could evolve under the condition that b/N was slightly smaller than c when the dispersal distances of males were larger than those of females. The results indicate that the differential dispersal of sexes, in which females are philopatric and males disperse farther than females, can somewhat increase the probability of spreading altruistic alleles in viscous populations.

The Unit of Selection in Viscous Populations and the Evolution of Altruism

Group selection can overcome individual selection for selfishness and favour altruism if there is variation among the founders of the spatially distinct groups, and groups with many altruists become substantially larger (or exist longer) than groups with few. Whether altruism can evolve in populations that do not have an alternation of local population growth and global dispersal (“viscous populations”) has been disputed for some time. Limited dispersal protects the altruists from the non-altruists, but also hinders the export of altruism. In this article, we used the Pair Approximation technique (tracking the dynamics of pairs of neighbours instead of single individuals) to derive explicit invasion conditions for rare mutants in populations with limited dispersal. In such viscous populations, invading mutants form clusters, and ultimately, invasion conditions depend on the properties of such clusters. Thus there is selection on a higher level than that of the individual; in fact, invasion conditions define the unit of selection in viscous populations. We treat the evolution of altruism as a specific example, but the method is of more general interest. In particular, an important advantage is that the spatial aspects can be incorporated into game theory in a straightforward fashion; we will specify the ESS for a more general model.The invasion condition can be interpreted in terms of inclusive fitness. In contrast with Hamilton's model, the coefficient of relatedness is not merely a given genetical constant but depends on local population dynamical processes (birth, dispersal and death of individuals). With a simple birth rate function, Hamilton's rule is recovered: the cost to the donor should be less than the benefit to the recipient weighted with the coefficient of relatedness. As the coefficient of relatedness is roughly proportional to an individual's number of neighbours, benefits to the recipient must be substantial to outweigh the costs, confirming earlier studies. We discuss the consequences for the evolution of dispersal and outline how the method may be extended to study evolution in interacting populations.

Genetic consequences of restricted dispersal and incest avoidance in a cooperatively breeding wren

Can restricted dispersal in a family-structured population produce conditions that favor the evolution of helping behavior by kin selection? To address this question a numerical model of a population of cooperatively breeding stripe-backed wrens ( Campylorhynchus nuchalis) was developed. The model incorporated the demography and social dynamics of a natural population under long-term study in Venezuela. Replicated simulations followed uniquely labelled copies of alleles for 100 annual cycles, in order to estimate coefficients of kinship between mates and between helpers and the young they raised in relation to overall levels of inbreeding in the population. The consequences of restricted dispersal and incest avoidance were investigated, under different rates of migration. The results indicated that close incest occurred too infrequently to influence genetic structure significantly. Restricted dispersal, on the other hand, even in combination with relatively high rates of immigration (10–20%), like those observed in the natural population, tended to produce genetically viscous populations. Relatedness between mates was significantly greater than 0, and relatedness among members of different groups decreased with distance. The relatedness between mates tended to increase both the relatedness of individuals to their own progeny and the relatedness of helpers to the young they raised. The latter effect predominated, so the genetic consequences of restricted dispersal, in relation to the overall level of inbreeding, tended to favor the evolution of helping by kin selection. Mutually reinforcing consequences of short-range dispersal, on the one hand, and delayed dispersal, on the other, could thus result in accelerating evolution of cooperative breeding.

Does seed dormancy benefit the mother plant by reducing sib competition?

Seed dormancy has been considered, almost without exception, as a bet-hedging strategy in a temporally varying environment. However, in this paper we show that seed dormancy can improve the reproductive success of the mother plant when competition between sibling seedlings and adult plants is intense even if the environment is temporally invariable. We allow a cohort of sibling seeds to germinate simultaneously in the same patch and assume a density dependent survival and fecundity of seedlings. In the model, the mother plant is assumed to control the germination behaviour of the seeds, e.g. by enclosing the seeds in coats of different hardiness. When sib competition is intense, a postponed germination of her seeds can increase the reproductive success of the mother plant up to four times, measured in terms of the number of grandchildren. Consequently, our results suggest that postponed germination may function as a mechanism that alters local interactions in viscous plant populations with limited dispersal.

Genetic relatedness in viscous populations

Hamilton's inclusive fitness rule shows that the evolution of altruism is facilitated by high genetic relatedness of altruists to their beneficiaries. But the evolution of altruism is inhibited when the beneficiaries are also close competitors of the altruist, as will often be true in structured or viscous populations. However, Hamilton's rule still gives the correct condition for the evolution of altruism if relatedness is measured with respect to the local competitive neighbourhood.

Inclusive fitness in a homogeneous environment

A general formulation of inclusive fitness is proposed which specifically accounts for competitive effects between relatives. As an example, for an asexual population in a homogeneous inelastic environment, such as is found in a stepping-stone model of dispersal, the inclusive fitness of a breeding female, under weak selection, is independent of her direct effect on the fitness of other individuals in the population. More precisely, suppose a female acts in a way that changes not only her own fitness but the fitness of several other females in the population who may be relatives (i.e. she changes the number of their offspring). I call these changes the direct effects of the action. There will also be indirect effects on the fitness of these and other females which come from the competitive impact of the extra offspring in the next generation. The principal result is that these indirect effects exactly cancel all the direct effects except the direct effect of the actor on herself.