Invasion fitness for gene–culture co-evolution in family-structured populations and an application to cumulative culture under vertical transmission

AbstractHuman evolution depends on the co-evolution between genetically determined behaviors and socially transmitted information. Although vertical transmission of cultural information from parent to off-spring is common in hominins, its effects on cumulative cultural evolution are not fully understood. Here, we investigate gene-culture co-evolution in a family-structured population by studying the invasion fitness of a mutant allele that influences a deterministic level of cultural information (e.g., amount of knowledge or skill) to which diploid carriers of the mutant are exposed in subsequent generations. We show that the selection gradient on such a mutant, and the concomitant level of cultural information it generates, can be evaluated analytically under the assumption that the cultural dynamic has a single attractor point, thereby making gene-culture co-evolution in family-structured populations with multigenerational effects mathematically tractable. We apply our result to study how genetically determined phenotypes of individual and social learning co-evolve with the level of adaptive information they generate under vertical transmission. We find that vertical transmission increases adaptive information due to kin selection effects, but when information is transmitted as efficiently between family members as between unrelated individuals, this increase is moderate in diploids. By contrast, we show that the way resource allocation into learning trades off with allocation into reproduction (the “learning-reproduction trade-off”) significantly influences levels of adaptive information. We also show that vertical transmission prevents evolutionary branching and may therefore play a qualitative role in gene-culture co-evolutionary dynamics. More generally, our analysis of selection suggests that vertical transmission can significantly increase levels of adaptive information under the biologically plausible condition that information transmission between relatives is more efficient than between unrelated individuals.

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Invasion fitness, inclusive fitness, and reproductive numbers in heterogeneous populations

10.1101/036731 ◽

2016 ◽

Cited By ~ 1

Author(s):

Laurent Lehmann ◽

Charles Mullon ◽

Erol Akcay ◽

Jeremy Van Cleve

Keyword(s):

Growth Rate ◽

Mutant Allele ◽

Inclusive Fitness ◽

Weighted Average ◽

Structured Populations ◽

Basic Reproductive Number ◽

Reproductive Value ◽

Reproductive Number ◽

Invasion Fitness ◽

Fitness Measures

How should fitness be measured to determine which phenotype or "strategy" is uninvadable when evolution occurs in subdivided populations subject to local demographic and environmental heterogeneity? Several invasion fitness measures, such as basic reproductive number, lifetime dispersal success of a local lineage, or inclusive fitness have been proposed to address this question, but the relationships between them and their generality remains unclear. Here, we ascertain uninvadability (all mutant strategies always go extinct) in terms of the growth rate of a mutant allele arising as a single copy in a population. We show from this growth rate that uninvadability is equivalently characterized by at least three conceptually distinct invasion fitness measures: (i) lineage fitness, giving the average personal fitness of a randomly sampled mutant lineage member; (ii) inclusive fitness, giving a reproductive value weighted average of the direct fitness cost and relatedness weighted indirect fitness benefits accruing to a randomly sampled mutant lineage member; and (iii) three types of reproductive numbers, giving lifetime success of a local lineage. Our analysis connects approaches that have been deemed different, generalizes the exact version of inclusive fitness to class-structured populations, and provides a biological interpretation of selection on a mutant allele under arbitrary strength of selection.

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Origin of diversity in spatial social dilemmas

10.1101/2021.03.21.436334 ◽

2021 ◽

Author(s):

Christoph Hauert ◽

Michael Doebeli

Keyword(s):

Spatial Structure ◽

Adaptive Dynamics ◽

Social Dilemmas ◽

Finite Size ◽

Structured Populations ◽

Pair Approximation ◽

Evolutionary Diversification ◽

Invasion Fitness ◽

Population Structures ◽

Mixed Populations

Cooperative investments in social dilemmas can spontaneously diversify into stably co-existing high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be under-stood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavourable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

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Structured Populations and Games over Generations

Game Theory in Biology ◽

10.1093/oso/9780198815778.003.0010 ◽

2020 ◽

pp. 231-260

Author(s):

John M. McNamara ◽

Olof Leimar

Keyword(s):

Tail Length ◽

The State ◽

Structured Populations ◽

Reproductive Value ◽

Lifetime Reproductive Success ◽

Value Maximization ◽

Invasion Fitness ◽

Current State ◽

Mean Lifetime ◽

New Criterion

The actions and state of an individual in one generation can affect the state of offspring in the next generation, and hence the ability of these offspring to leave offspring themselves. This chapter deals with games in this multigenerational setting. Projection matrices are used to keep track of the state and number of descendants in successive years and generations. Invasion fitness is then defined in terms of the leading eigenvalue of the projection matrix. Simple examples illustrate these concepts and show how to apply them. Reproductive value is a function that measures how the ability to leave descendants in future generations depends on the current state. The Nash equilibrium condition is reformulated in terms of reproductive value maximization. This new criterion is used to justify the fitness proxy used in the analysis of sex allocation earlier in the book. The analysis is extended to the case where offspring may inherit aspects of their mother’s quality, with a focus on the question of whether high-quality mothers should produce sons or daughters. As a second application of reproductive value maximization, the co-evolution of female preference for a particular male trait and the trait itself is analysed, with the evolution of tail length in the widowbird as an illustrative application. Mean lifetime reproductive success is used as a fitness proxy in much of the book. Its use is finally justified in this chapter, where the fitness proxy is used to analyse the evolutionarily stable age of first reproduction in a population.

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Spatial social dilemmas promote diversity

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2105252118 ◽

2021 ◽

Vol 118 (42) ◽

pp. e2105252118

Author(s):

Christoph Hauert ◽

Michael Doebeli

Keyword(s):

Spatial Structure ◽

Adaptive Dynamics ◽

Social Dilemmas ◽

Finite Size ◽

Structured Populations ◽

Pair Approximation ◽

Evolutionary Diversification ◽

Invasion Fitness ◽

Population Structures ◽

Mixed Populations

Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

Download Full-text