On multilevel selection and kin selection: contextual analysis meets direct 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.

Even allocation of benefits stabilizes microbial community engaged in metabolic division of labor

Microbial communities execute metabolic pathways to drive global nutrient cycles. Within a community, functionally specialized strains can perform different yet complementary steps within a linear pathway, a phenomenon termed metabolic division of labor (MDOL). However, little is known about how such metabolic behaviors shape microbial communities. Here, we derive a theoretical framework to define the assembly of a community that degrades an organic compound through MDOL. The framework indicates that to ensure community stability, the strains performing the initial steps should hold a growth advantage (m) over the "private benefit" (n) of the strain performing the last step. The steady-state frequency of the last strain is then determined by the quotient of n and m. Our experiments show that the framework accurately predicts the assembly of our synthetic consortia that degrade naphthalene through MDOL. Our results provide insights for designing and managing stable microbial systems for metabolic pathway optimization.

A Note Against the Use of "Belonging To" Properties in Multilevel Selection Theory

In this short paper, I argue against what I call the "belonging to" interpretation of group selection in scenarios in which a group's fitness is defined as the per capita reproductive output of the individuals of the group. According to this interpretation, group selection acts on "belonging to" properties of individuals, i.e. on relational or contextual properties that all the individuals of a group share simply by belonging to that group; thus, if differences in the individuals' "belonging to" properties cause differences in their fitness, group selection sensu the "belonging to" interpretation is said to be at work. I argue that the main problem with the "belonging to" interpretation is that it confuses evolutionary changes due to differences in environmental quality with evolutionary changes due to selection. In other words, I argue that, in the majority of cases, this interpretation actually takes the "selection" out of the "group selection" notion it aims to interpret: by adopting this perspective, one implicitly commits to explaining the evolutionary change under consideration not by a kind of selection (be it individual or group selection), but by differences in the environmental quality experienced by individual types.

Evaluating kin and group selection as tools for quantitative analysis of microbial data

Kin selection and multilevel selection theory are often used to interpret experiments about the evolution of cooperation and social behaviour among microbes. But while these experiments provide rich, detailed fitness data, theory is mostly used as a conceptual heuristic. Here, we evaluate how kin and multilevel selection theory perform as quantitative analysis tools. We reanalyse published microbial datasets and show that the canonical fitness models of both theories are almost always poor fits because they use statistical regressions misspecified for the strong selection and non-additive effects we show are widespread in microbial systems. We identify analytical practices in empirical research that suggest how theory might be improved, and show that analysing both individual and group fitness outcomes helps clarify the biology of selection. A data-driven approach to theory thus shows how kin and multilevel selection both have untapped potential as tools for quantitative understanding of social evolution in all branches of life.

Explanatory goals and explanatory means in multilevel selection theory

It has become customary in multilevel selection theory to use the same terms (namely "multilevel selection 1" and "multilevel selection 2") to denote both two explanatory goals (explaining why certain individual- and, respectively, group-level traits spread) and two explanatory means (namely, two kinds of group selection we may appeal to in such explanations). This paper spells out some of the benefits that derive from avoiding this terminological conflation. I argue that keeping explanatory means and goals well apart allows us to see that, contrary to a popular recent idea, Price's equation and contextual analysis-the statistical methods most extensively used for measuring the effects of certain evolutionary factors (like individual selection, group selection etc.) on the change in the focal individual trait in multilevel selection scenarios-do not come with built-in notions of group selection and, therefore, the efficacy of these methods at analyzing various kinds of cases does not constitute a basis for deciding how group selection should best be defined. Moreover, contrary to another widely accepted idea, I argue that more than one type of group selection may serve as explanatory means when one's goal is that of explaining the evolution of individual traits in multilevel selection scenarios and I spell out how this explanatory role should be understood.

Group and individual selection during evolutionary transitions in individuality: meanings and partitions

The Price equation embodies the 'conditions approach' to evolution in which the Darwinian conditions of heritable variation in fitness are represented in equation form. The equation can be applied recursively, leading to a partition of selection at the group and individual levels. After reviewing the well-known issues with the Price partition, as well as issues with a partition based on contextual analysis, we summarize a partition of group and individual selection based on counterfactual fitness, the fitness that grouped cells would have were they solitary. To understand 'group selection' in multi-level selection models, we assume that only group selection can make cells suboptimal when they are removed from the group. Our analyses suggest that there are at least three kinds of selection that can be occurring at the same time: group-specific selection along with two kinds of individual selection, within-group selection and global individual selection. Analyses based on counterfactual fitness allow us to specify how close a group is to being a pseudo-group, and this can be a basis for quantifying progression through an evolutionary transition in individuality (ETI). During an ETI, fitnesses at the two levels, group and individual, become decoupled, in the sense that fitness in a group may be quite high, even as counterfactual fitness goes to zero. This article is part of the theme issue 'Fifty years of the Price equation'.

The Price equation and the unity of social evolution theory

The Price equation has been entangled with social evolution theory from the start. It has been used to derive the most general versions of kin selection theory, and Price himself produced a multilevel equation that provides an alternative formulation of social evolution theory, dividing selection into components between and within groups. In this sense, the Price equation forms a basis for both kin and group selection, so often pitted against each other in the literature. Contextual analysis and the neighbour approach are prominent alternatives for analysing group selection. I discuss these four approaches to social evolution theory and their connections to the Price equation, focusing on their similarities and common mathematical structure. Despite different notations and modelling traditions, all four approaches are ultimately linked by a common set of mathematical components, revealing their underlying unity in a transparent way. The Price equation can similarly be used in the derivation of streamlined, weak selection social evolution modelling methods. These weak selection models are practical and powerful methods for constructing models in evolutionary and behavioural ecology; they can clarify the causal structure of models, and can be easily converted between the four social evolution approaches just like their regression counterparts. This article is part of the theme issue 'Fifty years of the Price equation'.

Allee effects drive the coevolution of cooperation and group size in high reproductive skew groups

The evolution of cooperation between conspecifics is a fundamental evolutionary puzzle, with much work focusing on the evolution of cooperative breeding. Surprisingly, although we expect cooperation to affect the population structures in which individuals interact, most studies fail to allow cooperation and population structure to coevolve. Here, we build two models containing group-level Allee effects (positive density dependence at low group sizes) to study the coevolution of cooperation and group size. Group-level Allee effects, although common in cooperatively breeding species, remain understudied for their evolutionary implications. We find that a trait that affects group size can cause increased cooperation to be favored evolutionarily even in a group with complete reproductive skew. In particular, we find a single evolutionarily stable attractor in our model corresponding to moderate helpfulness and group size. In general, our results demonstrate that, even in groups with complete reproductive skew, Allee effects can be important for the evolution of cooperation and that the evolution of cooperation may be closely linked to the evolution of group size. Further, our model matches empirical data in African wild dogs (Lycaon pictus), suggesting that it may have an application in understanding social evolution in this endangered species.

Assortment and the analysis of natural selection on social traits

A central problem in evolutionary biology is to determine whether and how social interactions contribute to natural selection. A key method for phenotypic data is social selection analysis, in which fitness effects from social partners contribute to selection only when there is a correlation between the traits of individuals and their social partners (nonrandom phenotypic assortment). However, there are inconsistencies in the use of social selection that center around the measurement of phenotypic assortment. Here, we use data analysis and simulations to resolve these inconsistencies, showing that: (i) not all measures of assortment are suitable for social selection analysis; and (ii) the interpretation of assortment, and how to detect nonrandom assortment, will depend on the scale at which it is measured. We discuss links to kin selection theory and provide a practical guide for the social selection approach.

Deconstructing Superorganisms and Societies to Address Big Questions in Biology

Social insect societies are long-standing models for understanding social behaviour and evolution. Unlike other advanced biological societies (such as the multicellular body), the component parts of social insect societies can be easily deconstructed and manipulated. Recent methodological and theoretical innovations have exploited this trait to address an expanded range of biological questions. We illustrate the broadening range of biological insight coming from social insect biology with four examples. These new frontiers promote open-minded, interdisciplinary exploration of one of the richest and most complex of biological phenomena: sociality.

Multilevel Selection in Kin Selection Language

Few issues have raised more debate among evolutionary biologists than kin selection (KS) versus multilevel selection (MLS). They are formally equivalent, but use different-looking mathematical approaches, and are not causally equivalent: for a given problem KS can be a more suitable causal explanation than MLS, and vice versa. Methods for analyzing a given model from both viewpoints would therefore be valuable. I argue that there is often an easy way to achieve this: MLS can be written using the components of KS. This applies to the very general regression approach as well as to the practical evolutionarily stable strategy (ESS) maximization approach, and can hence be used to analyze many common ESS models from a multilevel perspective. I demonstrate this with example models of gamete competition and limitation.

The levels of selection debate: taking into account existing empirical evidence

Por más de cinco décadas la visión neo-darwinista dominante de la selección natural es que esta actúa únicamente a nivel génico y organísmico, pero la ignorada evidencia empírica de selección multinivel ocurriendo en la naturaleza obtenida durante los últimos cincuenta años no es consecuente. Un largo intercambio de argumentaciones matemáticas y teóricas sobre los niveles en los que actúa la selección natural constituye lo que se denomina como el “debate de los niveles de selección”. La gran cantidad de evidencia empírica, estudiada mediante métodos de genética cuantitativa, específicamente el análisis contextual, indica que la selección natural actúa en niveles de la jerarquía biológica por encima y por debajo del nivel del gen y organismo, desde el nivel molecular hasta el ecosistémico, apoyando así lo que se denomina la teoría de selección multinivel. Más allá de argumentos teóricos, si se examina cuidadosamente la evidencia empírica de selección multinivel y los resultados del análisis contextual, se resuelve de forma sencilla el debate de los niveles de selección: la selección natural ocurre en la naturaleza en diferentes niveles de la jerarquía biológica. Este texto ofrece una revisión general de dicha evidencia empírica.

Ecology and multilevel selection explain aggression in spider colonies

Progress in sociobiology continues to be hindered by abstract debates over methodology and the relative importance of within‐group vs. between‐group selection. We need concrete biological examples to ground discussions in empirical data. Recent work argued that the levels of aggression in social spider colonies are explained by group‐level adaptation. Here, we examine this conclusion using models that incorporate ecological detail while remaining consistent with kin‐ and multilevel selection frameworks. We show that although levels of aggression are driven, in part, by between‐group selection, incorporating universal within‐group competition provides a striking fit to the data that is inconsistent with pure group‐level adaptation. Instead, our analyses suggest that aggression is favoured primarily as a selfish strategy to compete for resources, despite causing lower group foraging efficiency or higher risk of group extinction. We argue that sociobiology will benefit from a pluralistic approach and stronger links between ecologically informed models and data.

Kin and multilevel selection in social evolution: a never-ending controversy?

Kin selection and multilevel selection are two major frameworks in evolutionary biology that aim at explaining the evolution of social behaviors. However, the relationship between these two theories has been plagued by controversy for almost half a century and debates about their relevance and usefulness in explaining social evolution seem to rekindle at regular intervals. Here, we first provide a concise introduction into the kin selection and multilevel selection theories and shed light onto the roots of the controversy surrounding them. We then review two major aspects of the current debate: the presumed formal equivalency of the two theories and the question whether group selection can lead to group adaptation. We conclude by arguing that the two theories can offer complementary approaches to the study of social evolution: kin selection approaches usually focus on the identification of optimal phenotypes and thus on the endresult of a selection process, whereas multilevel selection approaches focus on the ongoing selection process itself. The two theories thus provide different perspectives that might be fruitfully combined to promote our understanding of the evolution in group-structured populations.

Multilevel selection theory and evidence: a critique of Gardner, 2015

Gardner (2015) recently developed a model of a 'Genetical Theory of Multilevel Selection, which is a thoughtfully developed, but flawed model. The model's flaws appear to be symptomatic of common misunderstandings of the multi level selection (MLS) literature and the recent quantitative genetic literature. I use Gardner's model as a guide for highlighting how the MLS literature can address the misconceptions found in his model, and the kin selection literature in general. I discuss research on the efficacy of group selection, the roll of indirect genetic effects in affecting the response to selection and the heritability of group-level traits. I also discuss why the Price multilevel partition should not be used to partition MLS, and why contextual analysis and, by association, direct fitness are appropriate for partitioning MLS. Finally, I discuss conceptual issues around questions concerning the level at which fitness is measured, the units of selection, and I present a brief outline of a model of selection in class-structured populations. I argue that the results derived from the MLS research tradition can inform kin selection research and models, and provide insights that will allow researchers to avoid conceptual flaws such as those seen in the Gardner model.

Site-specific group selection drives locally adapted group compositions

Group selection may be defined as selection caused by the differential extinction or proliferation of groups. The socially polymorphic spider Anelosimus studiosus exhibits a behavioural polymorphism in which females exhibit either a 'docile' or 'aggressive' behavioural phenotype. Natural colonies are composed of a mixture of related docile and aggressive individuals, and populations differ in colonies' characteristic docile:aggressive ratios. Using experimentally constructed colonies of known composition, here we demonstrate that population-level divergence in docile:aggressive ratios is driven by site-specific selection at the group level--certain ratios yield high survivorship at some sites but not others. Our data also indicate that colonies responded to the risk of extinction: perturbed colonies tended to adjust their composition over two generations to match the ratio characteristic of their native site, thus promoting their long-term survival in their natal habitat. However, colonies of displaced individuals continued to shift their compositions towards mixtures that would have promoted their survival had they remained at their home sites, regardless of their contemporary environment. Thus, the regulatory mechanisms that colonies use to adjust their composition appear to be locally adapted. Our data provide experimental evidence of group selection driving collective traits in wild populations.

Queller's separation condition explained and defended

The theories of inclusive fitness and multilevel selection provide alternative perspectives on social evolution. The question of whether these perspectives are of equal generality remains a divisive issue. In an analysis based on the Price equation, Queller argued (by means of a principle he called the separation condition) that the two approaches are subject to the same limitations, arising from their fundamentally quantitative-genetical character. Recently, van Veelen et al. have challenged Queller's results, using this as the basis for a broader critique of the Price equation, the separation condition, and the very notion of inclusive fitness. Here we show that the van Veelen et al. model, when analyzed in the way Queller intended, confirms rather than refutes his original conclusions. We thereby confirm (i) that Queller's separation condition remains a legitimate theoretical principle and (ii) that the standard inclusive fitness and multilevel approaches are indeed subject to the same limitations.

Ecological causes of multilevel covariance between size and first-year survival in a wild bird population

Estimates of selection in natural populations are frequent but our understanding of ecological causes of selection, and causes of variation in the direction, strength and form of selection is limited. Here, we apply a multilevel framework to partition effects of great tit fledging mass on first-year survival to hierarchical levels and quantify their ecological dependence using a data set spanning 51 years. We show that estimates of the effect of fledging mass on first-year survival decline threefold from year- to brood- to individual level, so that estimates of selection depend strongly on the level at which they are calculated. We identify variables related to summer and winter food availability as underlying higher-level effects of fledging mass on first-year survival and show experimentally that brood-level effects originate early in development. Further, we show that predation and conspecific density modulate individual-level effects of fledging mass on first-year survival. These analyses demonstrate how correlations between traits, fitness and environment influence estimates of selection and show how partitioning trait effects between levels of selection and environmental factors is a promising approach to identify potential agents of selection.

Continuous-time models of group selection, and the dynamical insufficiency of kin selection models

Traditionally, the process of group selection has been described mathematically by discrete-time models, and analyzed using tools like the Price equation. This approach makes implicit assumptions about the process that are not valid in general, like the central role of synchronized mass-dispersion and group re-formation events. In many important examples (like hunter-gatherer tribes) there are no mass-dispersion events, and the group-level events that do occur, like fission, fusion, and extinction, occur asynchronously. Examples like these can be fully analyzed by the equations of two-level population dynamics (described here) so their models are dynamically sufficient. However, it will be shown that examples like these cannot be fully analyzed by kin selection (inclusive fitness) methods because kin selection versions of group selection models are not dynamically sufficient. This is a critical mathematical difference between group selection and kin selection models, which implies that the two theories are not mathematically equivalent.

Hamiltonian inclusive fitness: a fitter fitness concept

In 1963-1964 W. D. Hamilton introduced the concept of inclusive fitness, the only significant elaboration of Darwinian fitness since the nineteenth century. I discuss the origin of the modern fitness concept, providing context for Hamilton's discovery of inclusive fitness in relation to the puzzle of altruism. While fitness conceptually originates with Darwin, the term itself stems from Spencer and crystallized quantitatively in the early twentieth century. Hamiltonian inclusive fitness, with Price's reformulation, provided the solution to Darwin's 'special difficulty'-the evolution of caste polymorphism and sterility in social insects. Hamilton further explored the roles of inclusive fitness and reciprocation to tackle Darwin's other difficulty, the evolution of human altruism. The heuristically powerful inclusive fitness concept ramified over the past 50 years: the number and diversity of 'offspring ideas' that it has engendered render it a fitter fitness concept, one that Darwin would have appreciated.