A two level mutation-selection model of cultural evolution and diversity

Cultural evolution is a complex process that can happen at several levels. At the level of individuals in a population, each human bears a set of cultural traits that he or she can transmit to its offspring (vertical transmission) or to other members of his or her society (horizontal transmission). The relative frequency of a cultural trait in a population or society can thus increase or decrease with the relative reproductive success of its bearers (individual’s level) or the relative success of transmission (called the idea’s level). This article presents a mathematical model on the interplay between these two levels. The first aim of this article is to explore when cultural evolution is driven by the idea’s level, when it is driven by the individual’s level and when it is driven by both. These three possibilities are explored in relation to (a) the amount of interchange of cultural traits between individuals, (b) the selective pressure acting on individuals, (c) the rate of production of new cultural traits, (d) the individual’s capacity to remember cultural traits and to the population size. The aim is to explore the conditions in which cultural evolution does not lead to a better adaptation of individuals to the environment. This is to contrast the spread of fitness-enhancing ideas, which make individual bearers better adapted to the environment, to the spread of “selfish” ideas, which spread well simply because they are easy to remember but do not help their individual bearers (and may even hurt them). At the same time this article explores in which conditions the adaptation of individuals is maximal. The second aim is to explore how these factors affect cultural diversity, or the amount of different cultural traits in a population. This study suggests that a larger interchange of cultural traits between populations could lead to cultural evolution not improving the adaptation of individuals to their environment and to a decrease of cultural diversity.     

Dispersal and the evolution of specialisation in a two-habitat type metapopulation

Metapopulation theory for the evolution of specialisation is virtually absent. In this article, therefore, we study a metapopulation model for consumers with a fitness trade-off between two habitats. We focus on effects of habitat abundance, dispersal rate and trade-off strength on the evolution of specialisation under two types of trade-off. Adaptation affects either the intrinsic growth rates r or the carrying capacities K. Depending on dispersal rate and trade-off strength, evolution can result in one generalist, one specialist or two specialist types. Higher dispersal rate and a weaker trade-off favour the evolution of a generalist, for both trade-off structures. However, we also find differences between the two trade-off structures. Our results are qualitatively similar to analyses of two-patch models, suggesting that insights from such simpler models can be extrapolated to metapopulation models. Additional effects, however, occur because in classical metapopulations patch lifetime depends on extinction rate. Counterintuitively, this favours the evolution of specialisation when the trade-off affects r.     

The effect of metapopulation dynamics on the survival and spread of a novel, conspicuous prey

Animals that deploy chemical defences against predators often signal their unprofitability using bright colouration. This pairing of toxicity and conspicuous patterning is known as aposematism.Explaining the evolution and spread of aposematic traits in previously cryptic species has been the focus of much empirical and theoretical work over the last two decades. Existing research concerning the initial evolution of aposematism does not however properly consider that many aposematic species (such as members of the hymenoptera, the lepidoptera, and amphibia) are highly mobile. We argue in this paper that the evolution of aposematic displays is therefore often best understood within a metapopulation framework; hence in this paper we present the first explicit metapopulation model of the evolution of aposematism. Our most general finding is that migration tends to reduce the probability that an aposematic prey can increase from rarity and spread across a large population. Hence, the best case scenarios for the spread of aposematism required fixation of the aposematic form in one or more isolated sub-habitats prior to some event which subsequently enabled migration. We observed that changes in frequency of new aposematic forms within source habitats are likely to be nonmonotonic. First, aposematic prey tend to decline in frequency as they migrate outwards from the source habitat to neighbouring sink habitats, but subsequently they increase in relative abundance in the source, as the descendents of earlier migrants migrate back from newly converted sub-populations. This pattern of initial loss and subsequent gain between new source and neighbouring sink habitats is then repeated as the aposematic form spreads via a moving cline.     

The effects of large and small-scale random events on the synchrony of metapopulation dynamics: a theoretical analysis

We present an analysis of the conditions under which migration and global random factors may determine large scale synchrony in the dynamics of spatially structured populations. We derive an analytic approximation which describes how the desynchronizing influence of local environmental stochasticity combines with the synchronizing influences of larger scale environmental stochastic variation and migration to determine population cross correlation coefficients. Despite the simplifications made by this analysis, computer simulations show that the behaviour of more complicated models is well described by our approximation over considerable regions of parameter space. We conclude that population synchrony is largely determined by the coefficients of variation (CVs) of the local and larger scale stochastic processes, and that migration alone is only likely to maintain population synchrony when the CV of the local stochastic process is very small.     

On the role of body size in a tri-trophic metapopulation model

 A particular tri-trophic (resource, prey, predator) metapopulation model with dispersal of preys and predators is considered in this paper. The analysis is carried out numerically, by finding the bifurcations of the equilibria and of the limit cycles with respect to prey and predator body sizes. Two routes to chaos are identified. One is characterized by an intriguing cascade of flip and tangent bifurcations of limit cycles, while the other corresponds to the crisis of a strange attractor. The results are summarized by partitioning the space of body sizes in eight subregions, each one of which is associated to a different asymptotic behavior of the system. Emphasis is put on the possibility of having different modes of coexistence (stationary, cyclic, and chaotic) and/or extinction of the predator population. Received 1 August 1995; received in revised form 8 January     

Variation,selection and evolution of function-valued traits

We describe an emerging framework for understanding variation, selection and evolution of phenotypic traits that are mathematical functions. We use one specific empirical example – thermal performance curves (TPCs) for growth rates of caterpillars – to demonstrate how models for function-valued traits are natural extensions of more familiar, multivariate models for correlated, quantitative traits. We emphasize three main points. First, because function-valued traits are continuous functions, there are important constraints on their patterns of variation that are not captured by multivariate models. Phenotypic and genetic variation in function-valued traits can be quantified in terms of variance-covariance functions and their associated eigenfunctions: we illustrate how these are estimated as well as their biological interpretations for TPCs. Second, selection on a function-valued trait is itself a function, defined in terms of selection gradient functions. For TPCs, the selection gradient describes how the relationship between an organism's performance and its fitness varies as a function of its temperature. We show how the form of the selection gradient function for TPCs relates to the frequency distribution of environmental states (caterpillar temperatures) during selection. Third, we can predict evolutionary responses of function-valued traits in terms of the genetic variance-covariance and the selection gradient functions. We illustrate how non-linear evolutionary responses of TPCs may occur even when the mean phenotype and the selection gradient are themselves linear functions of temperature. Finally, we discuss some of the methodological and empirical challenges for future studies of the evolution of function-valued traits.     

Patterns of rectrix rachis modification in pintails and the evolution of sexually selected traits

In order to transmit aerodynamic forces to the rest of the body, tail feathers need to be stiff to resist lift forces with minimum deformation. Because delta-wing theory predicts that such feathers do not produce lift forces beyond the point of the maximum continuum width of the tail, species with pintails should not require stiff central rectrices distal to that point. We tested this prediction by comparing the relative thickness of the central rectrix rachis in taxa with pintails and triangular tails. Fourteen pairs of closely related species or species groups belonging to the families Phaethontidae, Phalacrocoracidae, Anatidae, Stercorariidae, Psittacidae, Trochilidae, Alcedinidae, Momotidae, Meropidae, Bucerotidae, Tyrannidae, Pipridae and Nectariniidae were compared. Twelve of the phylogenetically independent comparisons showed that the taxa with triangular tails have higher relative rachis thickness (RRT) than their pintailed relatives just behind the point of the maximum continuum width of the tail. In contrast, two taxa with pintails showed proportionately higher RRT than their triangular-tailed relatives. Triangular tails showed an approximately linear relationship between RRT and relative rachis length, which contrasts with a proportionately greater increase in RRT from distal to proximal parts of the feather in 12 pintailed taxa. These results show that in most of the pintailed taxa studied the distal part of the central rectrix rachis has not been selected to resist lift forces and may be adaptively reduced to attenuate the costs of a hypertrophied ornament. However, the presence of distally reinforced rachices in Eumomota superciliosa and Colonia colonus suggests that a different explanation may be required to account for the design of pintail structure in other taxa.  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 86 , 477–485.     

Correlated evolution of multivariate traits: detecting co-divergence across multiple dimensions

Tests of correlated evolution typically treat phenotypic characters as univariate variables, even though different trait attributes may contribute to their association with other traits. In this study, patterns of character covariation among species are analysed in a multivariate framework to test for both correlated rates and directions of evolutionary change in traits forming the genitalic complex of male grasshoppers. Although the covariation structure differs among traits, and among the constituent species of two grasshopper clades, significant co-divergence was detected among the most closely interacting genitalic traits (i.e. intromittent characters) in both clades. Co-divergence across shape space is not accompanied by similar rates of evolution among species, although the intromittent characters tend to show accelerated evolution (relative to nonintromittent characters). Differences in the evolutionary trajectories among traits may relate to their varied roles during mating. The study emphasizes the importance of a multivariate framework for detecting macroevolutionary patterns of correlated change.     

The evolution of static allometry in sexually selected traits

Although it has been the subject of verbal theory since Darwin, the evolution of morphological trait allometries remains poorly understood, especially in the context of sexual selection. Here we present an allocation trade-off model that predicts the optimal pattern of allometry under different selective regimes. We derive a general solution that has a simple and intuitive interpretation and use it to investigate several examples of fitness functions. Verbal arguments have suggested cost or benefit scenarios under which sexual selection on signal or weapon traits may favor larger individuals with disproportionately larger traits (i.e., positive allometry). However, our results suggest that this is necessarily true only under a precisely specified set of conditions: positive allometry will evolve when the marginal fitness gains from an increase in relative trait size are greater for large individuals than for small ones. Thus, the optimal allometric pattern depends on the precise nature of net selection, and simple examples readily yield isometry, positive or negative allometry, or polymorphisms corresponding to sigmoidal scaling. The variety of allometric patterns predicted by our model is consistent with the diversity of patterns observed in empirical studies on the allometries of sexually selected traits. More generally, our findings highlight the difficulty of inferring complex underlying processes from simple emergent patterns.     

The quantitative genetics of sexually selected traits,preferred traits and preference: a review and analysis of the data

The maintenance of variation in sexually selected traits is a puzzle that has received increasing attention in the past several decades. Traits that are related to fitness, such as life‐history or sexually selected traits, are expected to have low additive genetic variance (and hence, heritability) due to the rapid fixation of advantageous alleles. However, previous analyses have suggested that the heritabilities of sexually selected traits are on average higher than nonsexually selected traits. We show that the heritabilities of sexually selected traits are not significantly different from those of nonsexually selected traits overall or when separated into the three trait categories: behavioural, morphological and physiological. In contrast with previous findings, the heritability of preference is quite low (h² = 0.25 ± 0.06) and is in the same range as life‐history traits. We distinguish preferred traits as a category of sexually selected traits and find that the heritability of the former is not significantly different than sexually selected traits overall (0.48 ± 0.04 vs. 0.46 ± 0.03). We test the hypothesis that the heritability of sexually selected traits is negatively correlated with the strength of sexual selection. As predicted, there is a significant negative correlation between the heritabilities of sexually selected traits and the strength of selection. This suggests that heritabilities do indeed decrease as sexual selection increases but sexual selection is not strong enough to cause heritabilities of sexually selected traits to deviate from the same type of nonsexually selected traits.     

Effects of population subdivision and catastrophes on the persistence of a land snail metapopulation

We modeled the dynamics of a metapopulation of the land snail Arianta arbustorum in north-eastern Switzerland to investigate the effect of population subdivision on the persistence of a land snail metapopulation and to analyze the interaction between spatial factors, population subdivision, and catastrophes. We developed a spatially structured, stochastic, age-structured metapopulation model with field data from previous studies on the metapopulation in Switzerland and experimental and meteorological data. The model incorporated distance-dependent dispersal through stream banks, correlated environmental fluctuations, and catastrophes resulting from heavy rains. The results point to various complex interactions among factors involved in metapopulation dynamics and suggest that in some cases population subdivision may act to decrease threats from environmental fluctuations and catastrophes.     

Tradeoffs limit the evolution of male traits that are attractive to females

Tradeoffs occur between a variety of traits in a diversity of organisms, and these tradeoffs can have major effects on ecological and evolutionary processes. Far less is known, however, about tradeoffs between male traits that affect mate attraction than about tradeoffs between other types of traits. Previous results indicate that females of the variable field cricket, Gryllus lineaticeps, prefer male songs with higher chirp rates and longer chirp durations. In the current study, we tested the hypothesis that a tradeoff between these traits affects the evolution of male song. The two traits were negatively correlated among full-sibling families, consistent with a genetically based tradeoff, and the tradeoff was stronger when nutrients were limiting. In addition, for males from 12 populations reared in a common environment, the traits were negatively correlated within populations, the strength of the tradeoff was largely invariant across populations, and the within-population tradeoff predicted how the traits have evolved among populations. A widespread tradeoff thus affects male trait evolution. Finally, for males from four populations assayed in the field, the traits were negatively correlated within and among populations. The tradeoff is thus robust to the presence of environmental factors that might mask its effects. Together, our results indicate there is a fundamental tradeoff between male traits that: (i) limits the ability of males to produce multiple attractive traits; (ii) limits how male traits evolve; and (iii) might favour plasticity in female mating preferences.     

A new group-selection model for the evolution of homosexuality

Abstract. Scientists have long puzzled over how homosexual orientation has evolved, given the assumed low relative fitness of homosexual individuals compared to heterosexual individuals. A number of theoretical models for the evolution of homosexuality have been postulated including balance polymorphism, "Fertile females", hypervariability of DNA sequences, kin selection, and "parental manipulation". In this paper, I propose a new group-selection model for the evolution of homosexuality which offers two advantages over existing models: (1) its non-assumption of genetic determinism, and (2) its lack of dependency on an inefficient altruism relation and family dynamics theory.     

The evolution of life-history traits in parasitic and free-living platyhelminthes: a new perspective

Parasite life histories have been assumed to be shaped by their particular mode of existence. To test this hypothesis, we investigate the relationships between life-history traits of free-living and parasitic platyhelminthes. Using phylogenetically independent contrasts we examine patterns of interspecific covariation in adult size, progeny volume, daily fecundity, total reproductive capacity, age at first reproduction and longevity. The correlations obtained indicate a similar causal chain of life history variations for free-living and parasitic platyhelminthes. These results suggest that increased longevity favours delayed reproduction. Furthermore, growth pattern determines adult body size and age at maturity. For platyhelminthes, whether free-living or parasitic, the total reproductive capacity is found to be directly determined by the size of the worm. Within this group the parasitic way of life does not seem to influence the basic patterns of life history evolution. Received: 20 September 1997 / Accepted: 1 March 1998     

Virulence and transmission modes in metapopulations: when group selection increases virulence

Individuals that are infected by a pathogen can transmit it to unrelated conspecifics (horizontal transmission) or to their progeny when they reproduce (vertical transmission). The mechanisms of these two routes of transmission are different and this difference impacts the way virulence evolves in pathogens. More precisely, horizontal transmission depends on the probability that an infected host contacts susceptible conspecifics, and therefore on its lifespan. Vertical transmission additionally depends on the host's fecundity. This additional dependence in vertically transmitted pathogens results in a decrease in their evolutionarily stable (ES) virulence.Spatial structure is another factor that is often supposed to decrease pathogens’ ES virulence, mostly because it impedes competition for transmission in local populations of hosts. In this paper, using the adaptive dynamics framework, we show that spatial structure can increase ES virulence when pathogens are mostly vertically transmitted. This is due to the difference in how pathogens compete for transmission in local population of hosts, depending on how they are transmitted. We also show that symbionts that are horizontally transmitted should respond more to a change in spatial structure than symbionts that are vertically transmitted.     

Costly dispersal can destabilize the homogeneous equilibrium of a metapopulation

I investigate the stability of the homogeneous equilibrium of a discrete-time metapopulation assuming costly dispersal with arbitrary (but fixed) spatial pattern of connectivity between the local populations. First, I link the stability of the metapopulation to the stability of a single isolated population by proving that the homogeneous metapopulation equilibrium, provided that it exists, is stable if and only if a single population, which is subject to extra mortality matching the average dispersal-induced mortality of the metapopulation, has a stable fixed point. Second, I demonstrate that extra mortality may destabilize the fixed point of a single population. Taken together, the two results imply that costly dispersal can destabilize the homogeneous equilibrium of a metapopulation. I illustrate this by simulations and discuss why earlier work, arriving at the opposite conclusion, was flawed.     

Bubonic plague: a metapopulation model of a zoonosis.

Bubonic plague (Yersinia pestis) is generally thought of as a historical disease; however, it is still responsible for around 1000-3000 deaths each year worldwide. This paper expands the analysis of a model for bubonic plague that encompasses the disease dynamics in rat, flea and human populations. Some key variables of the deterministic model, including the force of infection to humans, are shown to be robust to changes in the basic parameters, although variation in the flea searching efficiency, and the movement rates of rats and fleas will be considered throughout the paper. The stochastic behaviour of the corresponding metapopulation model is discussed, with attention focused on the dynamics of rats and the force of infection at the local spatial scale. Short-lived local epidemics in rats govern the invasion of the disease and produce an irregular pattern of human cases similar to those observed. However, the endemic behaviour in a few rat subpopulations allows the disease to persist for many years. This spatial stochastic model is also used to identify the criteria for the spread to human populations in terms of the rat density. Finally, the full stochastic model is reduced to the form of a probabilistic cellular automaton, which allows the analysis of a large number of replicated epidemics in large populations. This simplified model enables us to analyse the spatial properties of rat epidemics and the effects of movement rates, and also to test whether the emergent metapopulation behaviour is a property of the local dynamics rather than the precise details of the model.     

Multilevel selection: the evolution of cooperation in non-kin groups

Hamiltons (1964a, 1964b) landmark papers are rightly recognized as the formal basis for our understanding of the evolution of altruistic traits. However, Hamiltons equation as he originally expressed it is simplistic. A genetically oriented approach to studying multilevel selection can provide insights into how the terminology and assumptions used by Hamilton can be generalized. Using contextual analysis I demonstrated that Hamiltons rule actually embodies three distinct processes, group selection, individual selection, and transmission genetics or heritability. Whether an altruistic trait will evolve depends the balance of all of these factors. The genetical approach, and particularly, contextual analysis provides a means of separating these factors and examining them one at a time. Perhaps the greatest issue with Hamiltons equation is the interpretation of r. Hamilton (1964a) interpreted this as relatedness. In this paper I show that what Hamilton called relatedness is more generally interpreted as the proportion for variance among groups, and that many processes in addition to relatedness can increase the variance among groups. I also show that the evolution of an altruistic trait is driven by the ratio of the heritability at the group level to the heritability at the individual level. Under some circumstances this ratio can be greater than 1. In this situation altruism can evolve even if selection favoring selfish behavior is stronger than selection favoring altruism.     

Effects of information and group structure on evolution of altruism: analysis of two-score model by covariance and contextual analyses

An altruistic individual has to gamble on cooperation to a stranger because it does not know whether the stranger is trustworthy before direct interaction. Nowak and Sigmund (Nature 393 (1998a) 573; J. Theor. Biol. 194 (1998b) 561) presented a new theoretical framework of indirect reciprocal altruism by image scoring game where all individuals are informed about a partner's behavior from its image score without direct interaction. Interestingly, in a simplified version of the image scoring game, the evolutionarily stability condition for altruism became a similar form of Hamilton's rule, i.e. inequality that the probability of getting correct information is more than the ratio of cost to benefit. Since the Hamilton's rule was derived by evolutionarily stable analysis, the evolutionary meaning of the probability of getting correct information has not been clearly examined in terms of kin and group selection. In this study, we applied covariance analysis to the two-score model for deriving the Hamilton's rule. We confirmed that the probability of getting correct information was proportional to the bias of altruistic interactions caused by using information about a partner's image score. The Hamilton's rule was dependent on the number of game bouts even though the information reduced the risk of cooperation to selfish one at the first encounter. In addition, we incorporated group structure to the two-score model to examine whether the probability of getting correct information affect selection for altruism by group selection. We calculated a Hamilton's rule of group selection by contextual analysis. Group selection is very effective when either the probability of getting correct information or that of future interaction, or both are low. The two Hamilton's rules derived by covariance and contextual analyses demonstrated the effects of information and group structure on the evolution of altruism. We inferred that information about a partner's behavior and group structure can produce flexible pathways for the evolution of altruism.