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Division of labor exists at different levels of biological organization - from cell colonies to human societies. One of the simplest examples of the division of labor in multicellular organisms is germ-soma specialization, which plays a key role in the evolution of organismal complexity. Here we formulate and study a general mathematical model exploring the emergence of germ-soma specialization in colonies of cells. We consider a finite population of colonies competing for resources. Colonies are of the same size and are composed by asexually reproducing haploid cells. Each cell can contribute to activity and fecundity of the colony, these contributions are traded-off. We assume that all cells within a colony are genetically identical but gene effects on fecundity and activity are influenced by variation in the microenvironment experienced by individual cells. Through analytical theory and evolutionary agent-based modeling we show that the shape of the trade-off relation between somatic and reproductive functions, the type and extent of variation in within-colony microenvironment, and, in some cases, the number of genes involved, are important predictors of the extent of germ-soma specialization. Specifically, increasing convexity of the trade-off relation, the number of different environmental gradients acting within a colony, and the number of genes (in the case of random microenvironmental effects) promote the emergence of germ-soma specialization. Overall our results contribute towards a better understanding of the role of genetic, environmental, and microenvironmental factors in the evolution of germ-soma specialization., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

More than half a century has now elapsed since coalition or alliance formation theory (CAFT) was first developed. During that time, researchers have amassed a vast amount of detailed and high-quality data on coalitions or alliances among primates and other animals. But models have not kept pace, and more relevant theory is needed. In particular, even though CAFT is primarily an exercise in polyadic game theory, game theorists have devoted relatively little attention to questions that motivate field research, and much remains largely unexplored. The state of the art is both a challenge and an opportunity. In this review we describe a variety of game-theoretic and related modelling approaches that have much untapped potential to address the questions that field biologists ask., (Copyright © 2010 Elsevier Ltd. All rights reserved.)

We study how correlations in the random fitness assignment may affect the structure of fitness landscapes, in three classes of fitness models. The first is a phenotype space in which individuals are characterized by a large number n of continuously varying traits. In a simple model of random fitness assignment, viable phenotypes are likely to form a giant connected cluster percolating throughout the phenotype space provided the viability probability is larger than 1/2(n). The second model explicitly describes genotype-to-phenotype and phenotype-to-fitness maps, allows for neutrality at both phenotype and fitness levels, and results in a fitness landscape with tunable correlation length. Here, phenotypic neutrality and correlation between fitnesses can reduce the percolation threshold, and correlations at the point of phase transition between local and global are most conducive to the formation of the giant cluster. In the third class of models, particular combinations of alleles or values of phenotypic characters are "incompatible" in the sense that the resulting genotypes or phenotypes have zero fitness. This setting can be viewed as a generalization of the canonical Bateson-Dobzhansky-Muller model of speciation and is related to K-SAT problems, prominent in computer science. We analyze the conditions for the existence of viable genotypes, their number, as well as the structure and the number of connected clusters of viable genotypes. We show that analysis based on expected values can easily lead to wrong conclusions, especially when fitness correlations are strong. We focus on pairwise incompatibilities between diallelic loci, but we also address multiple alleles, complex incompatibilities, and continuous phenotype spaces. In the case of diallelic loci, the number of clusters is stochastically bounded and each cluster contains a very large sub-cube. Finally, we demonstrate that the discrete NK model shares some signature properties of models with high correlations.

The paper entitled "Sympatric speciation," which was published by John Maynard Smith in 1966, initiated the development of mathematical models aiming to identify the conditions for sympatric speciation. A part of that paper was devoted to a specific two-locus, two-allele model of sympatric speciation in a population occupying a two-niche system. Maynard Smith provided some initial numerical results on this model. Later, Dickinson and Antonovics (1973) and Caisse and Antonovics (1978) performed more extensive numerical studies on the model. Here, I report analytical results on the haploid version of the Maynard Smith model. I show how the conditions for sympatric and parapatric speciation and the levels of resulting genetic divergence and reproductive isolation are affected by the strength of disruptive selection and nonrandom mating, recombination rate, and the rates of male and female dispersal between the niches.

We study a general dynamical model describing coevolution of two haploid populations with two alleles at a single locus under weak linear symmetric frequency-dependent selection. A novel and more realistic element of our modeling approach is that both species are allowed to evolve. We analyse conditions for "evolutionary chase" between two phenotypically similar species in which one species evolves to decrease its resemblance with the other species while this other species evolves to increase its resemblance with the first species. We apply our results to a series of simple population genetics models describing classical Müllerian and Batesian mimicries as well as intermediate cases. We show that one of the most important factors influencing the plausibility of non-equilibrium dynamics in systems of mimicry is the relationship between the strength of between-species and within-species interactions. This indicates that this relationship should be the focus of both experimental and theoretical work. Our results suggest that systematic studies of frequencies of different mimicry morphs through time may be very useful.

I study the dynamics of a simple quantitative genetic model describing coevolution of two antagonistic species of the victim-exploiter type. In this model, individuals are different with respect to an additive polygenic character that is under direct stabilizing selection and which also determines the strength of within and between species interactions. The model assumes that between species interactions are most intense when the victim's and exploiter's phenotypes match. I show that a cyclic coevolutionary chase is possible under a broad range of conditions. In most cases, the system cycles if the "victim" has a stronger incentive to win and/or a larger genetic variance, and is under stronger stabilizing selection than the "exploiter". The results presented here provide counter-examples to recent studies that (1) question the applicability of "Red Queen" and "arms race" metaphors for continuously varying traits; (2) argue for the existence of crucial differences between major and minor loci dynamics; and (3) attribute a stabilizing role to coevolution.

We study the structure and properties of adaptive landscapes arising from the assumption that genotype fitness can only be 0 (inviable genotype) or 1 (viable genotype). An appropriate image of resulting ("holey") fitness landscapes is a (multidimensional) flat surface with many holes. We have demonstrated that in the genotype space there are clusters of viable genotypes whose members can evolve from any member by single substitutions and that there are "species" defined according to the biological species concept. Assuming that the number of genes, n, is very large while the proportion of viable genotypes among all possible genotypes, p, is very small, we have deduced many qualitative and quantitative properties of holey adaptive landscapes which may be related to the patterns of speciation. Relationship between p and n determines two qualitatively different regimes: subcritical and supercritical. The subcritical regime takes place if p is extremely small. In this case, the largest clusters of viable genotypes in the genotype space have size of order n and there are many of such size; typical members of a cluster are connected by a single ("evolutionary") path; the number of different (biological) species in the cluster has order n; the expected number of different species in the cluster within k viable substitutions from any its member is of order k. The supercritical regime takes place if p is small but not extremely small. In this case, there exists a cluster of viable genotypes (a "giant" component) that has size of order 2n/n; the giant component comes "near" every point of the genotype space; typical members of the giant component are connected by many evolutionary paths; the number of different (biological) species on the "giant" component has at least order n2; the expected number of different species on the "giant" component within k viable substitution from any its member is at least of order kn. At the boundary of two regimes all properties of adaptive landscapes undergo dramatic changes, a physical analogy of which is a phase transition. We have considered the most probable (within the present framework) scenario of biological evolution on holey landscapes assuming that it starts on a genotype from the largest connected component and proceeds along it by mutation and genetic drift. In this scenario, there is no need to cross any "adaptive valleys"; reproductive isolation between populations evolves as a side effect of accumulating different mutations. The rate of divergence is very fast: a few substitutions are sufficient to result in a new biological species. We argue that macroevolution and speciation on "rugged" fitness landscapes proceed according to the properties of the corresponding holey landscapes.