Birth-death symmetry in the evolution of a social trait

Evolution of epigenetic transmission when selection acts on fecundity versus viability

Existing theory on the evolution of parental effects and the inheritance of non-genetic factors has mostly focused on the role of environmental change. By contrast, how differences in population demography and life history affect parental effects is poorly understood. To fill this gap, we develop an analytical model to explore how parental effects evolve when selection acts on fecundity versus viability in spatio-temporally fluctuating environments. We find that regimes of viability selection, but not fecundity selection, are most likely to favour parental effects. In the case of viability selection, locally adapted phenotypes have a higher survival than maladapted phenotypes and hence become enriched in the local environment. Hence, simply by being alive, a parental phenotype becomes correlated to its environment (and hence informative to offspring) during its lifetime, favouring the evolution of parental effects. By contrast, in regimes of fecundity selection, correlations between phenotype and environment develop more slowly: this is because locally adapted and maladapted parents survive at equal rates (no survival selection), so that parental phenotypes, by themselves, are uninformative about the local environment. However, because locally adapted parents are more fecund, they contribute more offspring to the local patch than maladapted parents. In case these offspring are also likely to inherit the adapted parents' phenotypes (requiring pre-existing inheritance), locally adapted offspring become enriched in the local environment, resulting in a correlation between phenotype and environment, but only in the offspring's generation. Because of this slower build-up of a correlation between phenotype and environment essential to parental effects, fecundity selection is more sensitive to any distortions owing to environmental change than viability selection. Hence, we conclude that viability selection is most conducive to the evolution of parental effects. This article is part of the theme issue 'How does epigenetics influence the course of evolution?'

Kin discrimination, negative relatedness, and how to distinguish between selfishness and spite

Spiteful behaviors occur when an actor harms its own fitness to inflict harm on the fitness of others. Several papers have predicted that spite can be favored in sufficiently small populations, even when the harming behavior is directed indiscriminately at others. However, it is not clear that truly spiteful behavior could be favored without the harm being directed at a subset of social partners with relatively low genetic similarity to the actor (kin discrimination, causing a negative relatedness between actor and harmed recipient). Using mathematical models, we show that (1) the evolution of spite requires kin discrimination; (2) previous models suggesting indiscriminate spite involve scenarios where the actor gains a direct feedback benefit from harming others, and so the harming is selfish rather than spiteful; (3) extreme selfishness can be favored in small populations (or, more generally, under local competition) because this is where the direct feedback benefit of harming is greatest.

Fidelity of parent-offspring transmission and the evolution of social behavior in structured populations

The theoretical investigation of how spatial structure affects the evolution of social behavior has mostly been done under the assumption that parent-offspring strategy transmission is perfect, i.e., for genetically transmitted traits, that mutation is very weak or absent. Here, we investigate the evolution of social behavior in structured populations under arbitrary mutation probabilities. We consider populations of fixed size N, structured such that in the absence of selection, all individuals have the same probability of reproducing or dying (neutral reproductive values are the all same). Two types of individuals, A and B, corresponding to two types of social behavior, are competing; the fidelity of strategy transmission from parent to offspring is tuned by a parameter μ. Social interactions have a direct effect on individual fecundities. Under the assumption of small phenotypic differences (implying weak selection), we provide a formula for the expected frequency of type A individuals in the population, and deduce conditions for the long-term success of one strategy against another. We then illustrate our results with three common life-cycles (Wright-Fisher, Moran Birth-Death and Moran Death-Birth), and specific population structures (graph-structured populations). Qualitatively, we find that some life-cycles (Moran Birth-Death, Wright-Fisher) prevent the evolution of altruistic behavior, confirming previous results obtained with perfect strategy transmission. We also show that computing the expected frequency of altruists on a regular graph may require knowing more than just the graph's size and degree.

Inclusive fitness in finite populations-effects of heterogeneity and synergy

I review recent results concerning the relationship between the inclusive fitness (IF) effect and standard measures of allele fitness in a finite-population, with attention to the effect of heterogeneity in population structure and nonadditive fitness effects. In both cases, existing theoretical work is somewhat technical and I try to provide a more transparent account. In a heterogeneous population it is known that inclusive fitness will generally fail to incorporate the effects of selection on the distribution of alleles among states unless a reproductive-value weighting is used. But even given that, recent work shows that under certain updating rules, the IF effect can fail to be equivalent to standard measures such as fixation probability. In terms of synergistic fitness effects, I review the result that in the finite population model, the IF effect can be calculated using only "additive" relatedness coefficients so that computational difficulties found in the infinite-population model do not arise. In my own work, there is an interaction here in that my 2012 work on synergy with Maciejewski made an assumption about inclusive fitness that my 2014 work on heterogeneity with Tarnita showed to be wrong. I include (Appendix C) a corrected argument for the 2012 result.

Models of social evolution: can we do better to predict 'who helps whom to achieve what'?

Models of social evolution and the evolution of helping have been classified in numerous ways. Two categorical differences have, however, escaped attention in the field. Models tend not to justify why they use a particular assumption structure about who helps whom: a large number of authors model peer-to-peer cooperation of essentially identical individuals, probably for reasons of mathematical convenience; others are inspired by particular cooperatively breeding species, and tend to assume unidirectional help where subordinates help a dominant breed more efficiently. Choices regarding what the help achieves (i.e. which life-history trait of the helped individual is improved) are similarly made without much comment: fecundity benefits are much more commonly modelled than survival enhancements, despite evidence that these may interact when the helped individual can perform life-history reallocations (load-lightening and related phenomena). We review our current theoretical understanding of effects revealed when explicitly asking 'who helps whom to achieve what', from models of mutual aid in partnerships to the very few models that explicitly contrast the strength of selection to help enhance another individual's fecundity or survival. As a result of idiosyncratic modelling choices in contemporary literature, including the varying degree to which demographic consequences are made explicit, there is surprisingly little agreement on what types of help are predicted to evolve most easily. We outline promising future directions to fill this gap.

Evolution of Cooperation on Spatial Network with Limited Resource

Considering the external resource offered by environment is limited, here, we will explore the cooperation on spatial networks with limited resource. The individual distributes the limited resource according to the payoffs acquired in games, and one with resource amounts is lower than critical survival resource level will be replaced by the offspring of its neighbors. We find that, for larger temptation to defect, the number of the dead decreases with the resource amount. However the cooperation behavior is interesting, the lower total resource and intermediate temptation to defect can greatly promote the cooperation on square lattice. Our result reveals that the limited resource contributes most to the cooperation.

Environmental evolutionary graph theory

Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have received relatively less attention. Here we present a structured population model where different individuals are best suited to different regions of their environment. The underlying structure is a graph: individuals occupy vertices, which are connected by edges. If an individual is suited for their vertex, they receive an increase in fecundity. This framework allows attention to be restricted to the spatial arrangement of suitable habitat. We prove some basic properties of this model and find some counter-intuitive results. Notably, (1) the arrangement of suitable sites is as important as their proportion, and (2) decreasing the proportion of suitable sites may result in a decrease in the fixation time of an allele.

Hamilton's inclusive fitness in finite-structured populations

Hamilton's formulation of inclusive fitness has been with us for 50 years. During the first 20 of those years attention was largely focused on the evolutionary trajectories of different behaviours, but over the past 20 years interest has been growing in the effect of population structure on the evolution of behaviour and that is our focus here. We discuss the evolutionary journey of the inclusive-fitness effect over this epoch, nurtured as it was in an essentially homogeneous environment (that of 'transitive' structures) having to adapt in different ways to meet the expectations of heterogeneous structures. We pay particular attention to the way in which the theory has managed to adapt the original constructs of relatedness and reproductive value to provide a formulation of inclusive fitness that captures a precise measure of allele-frequency change in finite-structured populations.

How to distinguish altruism from spite (and why we should bother)

Social behaviour is often described as altruistic, spiteful, selfish or mutually beneficial. These terms are appealing, but it has not always been clear how they are defined and what purpose they serve. Here, I show that the distinctions among them arise from the ways in which fitness is partitioned: none can be drawn when the fitness consequences of an action are wholly aggregated, but they manifest clearly when the consequences are partitioned into primary and secondary (neighbourhood) effects. I argue that the primary interaction is the principal source of adaptive design, because (i) it is this interaction that determines the fit of an adaptation and (ii) it is the actor and primary recipients whom an adaptation foremost affects. The categories of social action are thus instrumental to any account of evolved function.

Can natural selection favour altruism between species?

Darwin suggested that the discovery of altruism between species would annihilate his theory of natural selection. However, it has not been formally shown whether between-species altruism can evolve by natural selection, or why this could never happen. Here, we develop a spatial population genetic model of two interacting species, showing that indiscriminate between species helping can be favoured by natural selection. We then ask if this helping behaviour constitutes altruism between species, using a linear-regression analysis to separate the total action of natural selection into its direct and indirect (kin selected) components. We show that our model can be interpreted in two ways, as either altruism within species, or altruism between species. This ambiguity arises depending on whether or not we treat genes in the other species as predictors of an individual's fitness, which is equivalent to treating these individuals as agents (actors or recipients). Our formal analysis, which focuses upon evolutionary dynamics rather than agents and their agendas, cannot resolve which is the better approach. Nonetheless, because a within-species altruism interpretation is always possible, our analysis supports Darwin's suggestion that natural selection does not favour traits that provide benefits exclusively to individuals of other species.

An inclusive fitness analysis of synergistic interactions in structured populations

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or 'synergistic' fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term--that is, over all possible allele frequencies--and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects--for example, hawk-dove and prisoner's dilemma games--frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p. We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk-dove game.

Origins of altruism diversity I: The diverse ecological roles of altruistic strategies and their evolutionary responses to local competition

Nature abounds with a rich variety of altruistic strategies, including public resource enhancement, resource provisioning, communal foraging, alarm calling, and nest defense. Yet, despite their vastly different ecological roles, current theory typically treats diverse altruistic traits as being favored under the same general conditions. Here, we introduce greater ecological realism into social evolution theory and find evidence of at least four distinct modes of altruism. Contrary to existing theory, we find that altruistic traits contributing to "resource-enhancement" (e.g., siderophore production, provisioning, agriculture) and "resource-efficiency" (e.g., pack hunting, communication) are most strongly favored when there is strong local competition. These resource-based modes of helping are "K-strategies" that increase a social group's growth yield, and should characterize species with scarce resources and/or high local crowding caused by low mortality, high fecundity, and/or mortality occurring late in the process of resource-acquisition. The opposite conditions, namely weak local competition (abundant resource, low crowding), favor survival (e.g., nest defense) and fecundity (e.g., nurse workers) altruism, which are "r-strategies" that increase a social group's growth rate. We find that survival altruism is uniquely favored by a novel evolutionary force that we call "sunk cost selection." Sunk cost selection favors helping that prevents resources from being wasted on individuals destined to die before reproduction. Our results contribute to explaining the observed natural diversity of altruistic strategies, reveal the necessary connection between the evolution and the ecology of sociality, and correct the widespread but inaccurate view that local competition uniformly impedes the evolution of altruism.

Resistance and relatedness on an evolutionary graph

When investigating evolution in structured populations, it is often convenient to consider the population as an evolutionary graph-individuals as nodes, and whom they may act with as edges. There has, in recent years, been a surge of interest in evolutionary graphs, especially in the study of the evolution of social behaviours. An inclusive fitness framework is best suited for this type of study. A central requirement for an inclusive fitness analysis is an expression for the genetic similarity between individuals residing on the graph. This has been a major hindrance for work in this area as highly technical mathematics are often required. Here, I derive a result that links genetic relatedness between haploid individuals on an evolutionary graph to the resistance between vertices on a corresponding electrical network. An example that demonstrates the potential computational advantage of this result over contemporary approaches is provided. This result offers more, however, to the study of population genetics than strictly computationally efficient methods. By establishing a link between gene transfer and electric circuit theory, conceptualizations of the latter can enhance understanding of the former.