The evolution of morphological castes under decoupled control

Eusociality, where units that previously reproduced independently function as one entity, is of major interest in evolutionary biology. Obligate eusociality is characterized by morphologically differentiated castes and reduced conflict. We explore conditions under which morphological castes may arise in the Hymenoptera and factors constraining their evolution. Control over offspring morphology and behaviour seems likely to be decoupled. Provisioners (queens and workers) can influence offspring morphology directly through the nutrition they provide, while adult offspring control their own behaviour. Provisioners may, however, influence worker behaviour indirectly if offspring modify their behaviour in response to their morphology. If manipulation underlies helping, we should not see helping evolve before specialized worker morphology, yet empirical observations suggest that behavioural castes precede morphological castes. We use evolutionary invasion analyses to show how the evolution of a morphologically differentiated worker caste depends on the prior presence of a behavioural caste: specialist worker morphology will be mismatched with behaviour unless some offspring already choose to work. A mother's certainty about her offspring's behaviour is also critical-less certainty results in greater mismatch. We show how baseline worker productivity can affect the likelihood of a morphological trait being favoured by natural selection. We then show how under a decoupled control scenario, morphologically differentiated castes should be less and less likely to be lost as they become more specialized. We also suggest that for eusociality to be evolutionarily irreversible, workers must be unable to functionally replace reproductives and reproductives must be unable to reproduce without help from workers.

Nonlinear social evolution and the emergence of collective action

Organisms from microbes to humans engage in a variety of social behaviors, which affect fitness in complex, often nonlinear ways. The question of how these behaviors evolve has consequences ranging from antibiotic resistance to human origins. However, evolution with nonlinear social interactions is challenging to model mathematically, especially in combination with spatial, group, and/or kin assortment. We derive a mathematical condition for natural selection with synergistic interactions among any number of individuals. This result applies to populations with arbitrary (but fixed) spatial or network structure, group subdivision, and/or mating patterns. In this condition, nonlinear fitness effects are ascribed to collectives, and weighted by a new measure of collective relatedness. For weak selection, this condition can be systematically evaluated by computing branch lengths of ancestral trees. We apply this condition to pairwise games between diploid relatives, and to dilemmas of collective help or harm among siblings and on spatial networks. Our work provides a rigorous basis for extending the notion of "actor", in the study of social evolution, from individuals to collectives.

On the Interpretation of the Operation of Natural Selection in Class-Structured Populations

AbstractBiological adaptation is the outcome of allele-frequency change by natural selection. At the same time, populations are usually class structured as individuals occupy different states, such as age, sex, or stage. This is known to result in the differential transmission of alleles through nonheritable fitness differences called class transmission, which also affects allele-frequency change even in the absence of selection. How does one then isolate allele-frequency change due to selection from that due to class transmission? We decompose one-generational allele-frequency change in terms of effects of selection and class transmission and show how reproductive values can be used to reach a decomposition between any two distant generations of the evolutionary process. This provides a missing relationship between multigenerational allele-frequency change and the operation of selection. It also allows a measure of fitness to be defined summarizing the effect of selection in a multigenerational evolutionary process, which connects asymptotically to invasion fitness.

Symmetry in models of natural selection

Symmetry arguments are frequently used-often implicitly-in mathematical modelling of natural selection. Symmetry simplifies the analysis of models and reduces the number of distinct population states to be considered. Here, I introduce a formal definition of symmetry in mathematical models of natural selection. This definition applies to a broad class of models that satisfy a minimal set of assumptions, using a framework developed in previous works. In this framework, population structure is represented by a set of sites at which alleles can live, and transitions occur via replacement of some alleles by copies of others. A symmetry is defined as a permutation of sites that preserves probabilities of replacement and mutation. The symmetries of a given selection process form a group, which acts on population states in a way that preserves the Markov chain representing selection. Applying classical results on group actions, I formally characterize the use of symmetry to reduce the states of this Markov chain, and obtain bounds on the number of states in the reduced chain.

How to make an inclusive-fitness model

Social behaviours are typically modelled using neighbour-modulated fitness, which focuses on individuals having their fitness altered by neighbours. However, these models are either interpreted using inclusive fitness, which focuses on individuals altering the fitness of neighbours, or not interpreted at all. This disconnect leads to interpretational mistakes and obscures the adaptive significance of behaviour. We bridge this gap by presenting a systematic methodology for constructing inclusive-fitness models. We find a behaviour's 'inclusive-fitness effect' by summing primary and secondary deviations in reproductive value. Primary deviations are the immediate result of a social interaction; for example, the cost and benefit of an altruistic act. Secondary deviations are compensatory effects that arise because the total reproductive value of the population is fixed; for example, the increased competition that follows an altruistic act. Compared to neighbour-modulated fitness methodologies, our approach is often simpler and reveals the model's inclusive-fitness narrative clearly. We implement our methodology first in a homogeneous population, with supplementary examples of help under synergy, help in a viscous population and Creel's paradox. We then implement our methodology in a class-structured population, where the advantages of our approach are most evident, with supplementary examples of altruism between age classes, and sex-ratio evolution.

Evolutionarily stable preferences

The 50-year old concept of an evolutionarily stable strategy provided a key tool for theorists to model ultimate drivers of behaviour in social interactions. For decades, economists ignored ultimate drivers and used models in which individuals choose strategies based on their preferences-a proximate mechanism for behaviour-and the distribution of preferences in the population was taken to be fixed and given. This article summarizes some key findings in the literature on evolutionarily stable preferences, which in the past three decades has proposed models that combine the two approaches: individuals inherit their preferences, the preferences determine their strategy choices, which in turn determine evolutionary success. One objective is to highlight complementarities and potential avenues for future collaboration between biologists and economists. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Evolutionarily stable strategy analysis and its links to demography and genetics through invasion fitness

Evolutionarily stable strategy (ESS) analysis pioneered by Maynard Smith and Price took off in part because it often does not require explicit assumptions about the genetics and demography of a population in contrast to population genetic models. Though this simplicity is useful, it obscures the degree to which ESS analysis applies to populations with more realistic genetics and demography: for example, how does ESS analysis handle complexities such as kin selection, group selection and variable environments when phenotypes are affected by multiple genes? In this paper, I review the history of the ESS concept and show how early uncertainty about the method lead to important mathematical theory linking ESS analysis to general population genetic models. I use this theory to emphasize the link between ESS analysis and the concept of invasion fitness. I give examples of how invasion fitness can measure kin selection, group selection and the evolution of linked modifier genes in response to variable environments. The ESSs in these examples depend crucially on demographic and genetic parameters, which highlights how ESS analysis will continue to be an important tool in understanding evolutionary patterns as new models address the increasing abundance of genetic and long-term demographic data in natural populations. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Genetic conflicts and the case for licensed anthropomorphizing

The use of intentional language in biology is controversial. It has been commonly applied by researchers in behavioral ecology, who have not shied away from employing agential thinking or even anthropomorphisms, but has been rarer among researchers from more mechanistic corners of the discipline, such as population genetics. One research area where these traditions come into contact—and occasionally clash—is the study of genetic conflicts, and its history offers a good window to the debate over the use of intentional language in biology. We review this debate, paying particular attention to how this interaction has played out in work on genomic imprinting and sex chromosomes. In light of this, we advocate for a synthesis of the two approaches, a form of licensed anthropomorphizing. Here, agential thinking’s creative potential and its ability to identify the fulcrum of evolutionary pressure are combined with the rigidity of formal mathematical modeling.

Multiple social encounters can eliminate Crozier's paradox and stabilise genetic kin recognition

Crozier’s paradox suggests that genetic kin recognition will not be evolutionarily stable. The problem is that more common tags (markers) are more likely to be recognised and helped. This causes common tags to increase in frequency, and hence eliminates the genetic variability that is required for genetic kin recognition. It has therefore been assumed that genetic kin recognition can only be stable if there is some other factor maintaining tag diversity, such as the advantage of rare alleles in host-parasite interactions. We show that allowing for multiple social encounters before each social interaction can eliminate Crozier’s paradox, because it allows individuals with rare tags to find others with the same tag. We also show that rare tags are better indicators of relatedness, and hence better at helping individuals avoid interactions with non-cooperative cheats. Consequently, genetic kin recognition provides an advantage to rare tags that maintains tag diversity, and stabilises itself.

Crozier’s paradox suggests that genetic kin recognition will not be evolutionarily stable. Here, the authors show that allowing for multiple social encounters before each social interaction can eliminate Crozier’s paradox and stabilise genetic kin recognition.

Metacommunities, fitness and gradual evolution

We analyze the evolution of a multidimensional quantitative trait in a class-structured focal species interacting with other species in a wider metacommunity. The evolutionary dynamics in the focal species as well as the ecological dynamics of the whole metacommunity is described as a continuous-time process with birth, physiological development, dispersal, and death given as rates that can depend on the state of the whole metacommunity. This can accommodate complex local community and global metacommunity environmental feedbacks owing to inter- and intra-specific interactions, as well as local environmental stochastic fluctuations. For the focal species, we derive a fitness measure for a mutant allele affecting class-specific trait expression. Using classical results from geometric singular perturbation theory, we provide a detailed proof that if the effect of the mutation on phenotypic expression is small ("weak selection"), the large system of dynamical equations needed to describe selection on the mutant allele in the metacommunity can be reduced to a single ordinary differential equation on the arithmetic mean mutant allele frequency that is of constant sign. This invariance on allele frequency entails the mutant either dies out or will out-compete the ancestral resident (or wild) type. Moreover, the directional selection coefficient driving arithmetic mean allele frequency can be expressed as an inclusive fitness effect calculated from the resident metacommunity alone, and depends, as expected, on individual fitness differentials, relatedness, and reproductive values. This formalizes the Darwinian process of gradual evolution driven by random mutation and natural selection in spatially and physiologically class-structured metacommunities.

Realistic genetic architecture enables organismal adaptation as predicted under the folk definition of inclusive fitness

A fundamental task of evolutionary biology is to explain the pervasive impression of organismal design in nature, including traits benefiting kin. Inclusive fitness is considered by many to be a crucial piece in this puzzle, despite ongoing discussion about its scope and limitations. Here, we use individual-based simulations to study what quantity (if any) individual organisms become adapted to maximize when genetic architectures are more or less suitable for the presumed main driver of biological adaptation, namely cumulative multi-locus evolution. As an expository device, we focus on a hypothetical situation called Charlesworth's paradox, in which altruism is seemingly predicted to evolve, yet altruists immediately perish along with their altruistic genes. Our results support a recently proposed re-definition of inclusive fitness, which is concerned with the adaptive design of whole organisms as shaped by multi-locus evolution, rather than with selection for any focal gene. They also illustrate how our conceptual understanding of adaptation at the phenotypic level should inform our choice of genetic assumptions in abstract simplified models.

Long-term overlap of social and genetic structure in free-ranging house mice reveals dynamic seasonal and group size effects

Associating with relatives in social groups can bring benefits such as reduced risk of aggression and increased likelihood of cooperation. Competition among relatives over limited resources, on the other hand, can induce individuals to alter their patterns of association. Population density might further affect the costs and benefits of associating with relatives by altering resource competition or by changing the structure of social groups; preventing easy association with relatives. Consequently, the overlap between genetic and social structure is expected to decrease with increasing population size, as well as during times of increased breeding activity. Here, we use multi-layer network techniques to quantify the similarity between long-term, high resolution genetic, and behavioral data from a large population of free-ranging house mice (Mus musculus domesticus), studied over 10 years. We infer how the benefit of associating with genetically similar individuals might fluctuate in relation to breeding behavior and environmental conditions. We found a clear seasonal effect, with decreased overlap between social and genetic structure during summer months, characterized by high temperatures and high breeding activity. Though the effect of overall population size was relatively weak, we found a clear decrease in the overlap between genetic similarity and social associations within larger groups. As well as longer-term within-group changes, these results reveal population-wide short-term shifts in how individuals associate with relatives. Our study suggests that resource competition modifies the trade-off between the costs and benefits of interacting with relatives.

The Price equation and reproductive value

The Price equation is widely recognized as capturing conceptually important properties of natural selection, and is often used to derive versions of Fisher's fundamental theorem of natural selection, the secondary theorems of natural selection and other significant results. However, class structure is not usually incorporated into these arguments. From the starting point of Fisher's original connection between fitness and reproductive value, a principled way of incorporating reproductive value and structured populations into the Price equation is explained, with its implications for precise meanings of (two distinct kinds of) reproductive value and of fitness. Once the Price equation applies to structured populations, then the other equations follow. The fundamental theorem itself has a special place among these equations, not only because it always incorporated class structure (and its method is followed for general class structures), but also because that is the result that justifies the important idea that these equations identify the effect of natural selection. The precise definitions of reproductive value and fitness have striking and unexpected features. However, a theoretical challenge emerges from the articulation of Fisher's structure: is it possible to retain the ecological properties of fitness as well as its evolutionary out-of-equilibrium properties? This article is part of the theme issue 'Fifty years of the Price equation'.