Percolation on fitness landscapes: effects of correlation, phenotype, and incompatibilities

We study how correlations in the random fitness assignment may affect the structure of fitness landscapes. We consider three classes of fitness models. The first is a continuous phenotype space in which individuals are characterized by a large number of continuously varying traits such as size, weight, color, or concentrations of gene products which directly affect fitness. The second is a simple model that explicitly describes genotype-to-phenotype and phenotype-to-fitness maps allowing for neutrality at both phenotype and fitness levels and resulting in a fitness landscape with tunable correlation length. The third is a class of models in which particular combinations of alleles or values of phenotypic characters are "incompatible" in the sense that the resulting genotypes or phenotypes have reduced (or zero) fitness. This class of models can be viewed as a generalization of the canonical Bateson-Dobzhansky-Muller model of speciation. We also demonstrate that the discrete NK model shares some signature properties of models with high correlations. Throughout the paper, our focus is on the percolation threshold, on the number, size and structure of connected clusters, and on the number of viable genotypes.Comment: 31 pages, 4 figures, 1 tabl

Dynamics of alliance formation and the egalitarian revolution

Arguably the most influential force in human history is the formation of social coalitions and alliances (i.e., long-lasting coalitions) and their impact on individual power. In most great ape species, coalitions occur at individual and group levels and among both kin and non-kin. Nonetheless, ape societies remain essentially hierarchical, and coalitions rarely weaken social inequality. In contrast, human hunter-gatherers show a remarkable tendency to egalitarianism, and human coalitions and alliances occur not only among individuals and groups, but also among groups of groups. Here, we develop a stochastic model describing the emergence of networks of allies resulting from within-group competition for status or mates between individuals utilizing dyadic information. The model shows that alliances often emerge in a phase transition-like fashion if the group size, awareness, aggressiveness, and persuasiveness of individuals are large and the decay rate of individual affinities is small. With cultural inheritance of social networks, a single leveling alliance including all group members can emerge in several generations. Our results suggest that a rapid transition from a hierarchical society of great apes to an egalitarian society of hunter-gatherers (often referred to as "egalitarian revolution") could indeed follow an increase in human cognitive abilities. The establishment of stable group-wide egalitarian alliances creates conditions promoting the origin of cultural norms favoring the group interests over those of individuals.Comment: 37 pages, 15 figure

speciation. 2. Palms on an oceanic island

A recent study of a pair of sympatric species of palms on the Lord Howe Island is viewed as providing probably one of the most convincing examples of sympatric speciation to date. Here we describe and study a stochastic, individual-based, explicit genetic model tailored for this palms system. Overall, our results show that relatively rapid (< 50 000 generations) colonization of a new ecological niche, and sympatric or parapatric speciation via local adaptation and divergence in flowering periods are theoretically plausible if (i) the number of loci controlling the ecological and flowering period traits is small; (ii) the strength of selection for local adaptation is intermediate; and (iii) an acceleration of flowering by a direct environmental effect associated with the new ecological niche is present. We discuss patterns and time-scales of ecological speciation identified by our model, and we highlight important parameters and features that need to be studied empirically in order to provide information that can be used to improve the biological realism and power of mathematical models of ecological speciation

Dynamics of clade diversification on the morphological hypercube

Understanding the relationship between taxonomic and morphological changes is important in identifying the reasons for accelerated morphological diversification early in the history of animal phyla. Here, a simple general model describing the joint dynamics of taxonomic diversity and morphological disparity is presented and applied to the data on the diversification of blastozoans. I show that the observed patterns of deceleration in clade diversification can be explicable in terms of the geometric structure of the morphospace and the effects of extinction and speciation on morphological disparity without invoking major declines in the size of morphological transitions or taxonomic turnover rates. The model allows testing of hypotheses about patterns of diversification and estimation of rates of morphological evolution. In the case of blastozoans, I find no evidence that major changes in evolutionary rates and mechanisms are responsible for the deceleration of morphological diversification seen during the period of this clade's expansion. At the same time, there is evidence for a moderate decline in overall rates of morphological diversification concordant with a major change (from positive to negative values) in the clade's growth rate.Comment: 8 pages, Latex, 2 postscript figures, submitted to Proc.R.Soc.Lond.

diseases with ecological speciation

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Convergence to consensus in heterogeneous groups and the emergence of informal leadership

When group cohesion is essential, groups must have efficient strategies in place for consensus decisionmaking. Recent theoretical work suggests that shared decision-making is often the most efficient way for dealing with both information uncertainty and individual variation in preferences. However, some animal and most human groups make collective decisions through particular individuals, leaders, that have a disproportionate influence on group decision-making. To address this discrepancy between theory and data, we study a simple, but general, model that explicitly focuses on the dynamics of consensus building in groups composed by individuals who are heterogeneous in preferences, certain personality traits (agreeability and persuasiveness), reputation, and social networks. We show that within-group heterogeneity can significantly delay democratic consensus building as well as give rise to the emergence of informal leaders, i.e. individuals with a disproportionately large impact on group decisions. Our results thus imply strong benefits of leadership particularly when groups experience time pressure and significant conflict of interest between members (due to various between-individual differences). Overall, our models shed light on why leadership and decision-making hierarchies are widespread, especially in human groups

Kinship can hinder cooperation in heterogeneous populations

Kin selection and direct reciprocity are two most basic mechanisms for promoting cooperation in human society. Generalizing the standard models of the multi-player Prisoner's Dilemma and the Public Goods games for heterogeneous populations, we study the effects of genetic relatedness on cooperation in the context of repeated interactions. Two sets of interrelated results are established: a set of analytical results focusing on the subgame perfect equilibrium and a set of agent-based simulation results based on an evolutionary game model. We show that in both cases increasing genetic relatedness does not always facilitate cooperation. Specifically, kinship can hinder the effectiveness of reciprocity in two ways. First, the condition for sustaining cooperation through direct reciprocity is harder to satisfy when relatedness increases in an intermediate range. Second, full cooperation is impossible to sustain for a medium-high range of relatedness values. Moreover, individuals with low cost-benefit ratios can end up with lower payoffs than their groupmates with high cost-benefit ratios. Our results point to the importance of explicitly accounting for within-population heterogeneity when studying the evolution of cooperation