An evolutionary model for simple ecosystems

In this review some simple models of asexual populations evolving on smooth landscapes are studied. The basic model is based on a cellular automaton, which is analyzed here in the spatial mean-field limit. Firstly, the evolution on a fixed fitness landscape is considered. The correspondence between the time evolution of the population and equilibrium properties of a statistical mechanics system is investigated, finding the limits for which this mapping holds. The mutational meltdown, Eigen's error threshold and Muller's ratchet phenomena are studied in the framework of a simplified model. Finally, the shape of a quasi-species and the condition of coexistence of multiple species in a static fitness landscape are analyzed. In the second part, these results are applied to the study of the coexistence of quasi-species in the presence of competition, obtaining the conditions for a robust speciation effect in asexual populations.Comment: 36 pages, including 16 figures, to appear in Annual Review of Computational Physics, D. Stauffer (ed.), World Scientific, Singapor

Multidimensional epistasis and the transitory advantage of sex

Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional fitness landscapes in the presence of sign epistasis. Here we present a comparative numerical study of sexual and asexual evolutionary dynamics of haploids on tunably rugged model landscapes under strong selection, paying special attention to the temporal development of the evolutionary advantage of recombination and the link between population diversity and the rate of adaptation. We show that the adaptive advantage of recombination on static rugged landscapes is strictly transitory. At early times, an advantage of recombination arises through the possibility to combine individually occurring beneficial mutations, but this effect is reversed at longer times by the much more efficient trapping of recombining populations at local fitness peaks. These findings are explained by means of well established results for a setup with only two loci. In accordance with the Red Queen hypothesis the transitory advantage can be prolonged indefinitely in fluctuating environments, and it is maximal when the environment fluctuates on the same time scale on which trapping at local optima typically occurs.Comment: 34 pages, 9 figures and 8 supplementary figures; revised and final versio

Rate of adaptation in sexuals and asexuals: A solvable model of the Fisher-Muller effect

The adaptation of large asexual populations is hampered by the competition between independently arising beneficial mutations in different individuals, which is known as clonal interference. Fisher and Muller proposed that recombination provides an evolutionary advantage in large populations by alleviating this competition. Based on recent progress in quantifying the speed of adaptation in asexual populations undergoing clonal interference, we present a detailed analysis of the Fisher-Muller mechanism for a model genome consisting of two loci with an infinite number of beneficial alleles each and multiplicative fitness effects. We solve the infinite population dynamics exactly and show that, for a particular, natural mutation scheme, the speed of adaptation in sexuals is twice as large as in asexuals. Guided by the infinite population result and by previous work on asexual adaptation, we postulate an expression for the speed of adaptation in finite sexual populations that agrees with numerical simulations over a wide range of population sizes and recombination rates. The ratio of the sexual to asexual adaptation speed is a function of population size that increases in the clonal interference regime and approaches 2 for extremely large populations. The simulations also show that the imbalance between the numbers of accumulated mutations at the two loci is strongly suppressed even by a small amount of recombination. The generalization of the model to an arbitrary number $L$ of loci is briefly discussed. If each offspring samples the alleles at each locus from the gene pool of the whole population rather than from two parents, the ratio of the sexual to asexual adaptation speed is approximately equal to $L$ in large populations. A possible realization of this scenario is the reassortment of genetic material in RNA viruses with $L$ genomic segments.Comment: Title has been changed. Supporting Information (animation) can be found in the source file. 53 pages. 10 figures. To appear in Genetic

Metapopulation dynamics and the evolution of sperm parasitism

Amazon molly (Poecilia formosa) females reproduce asexually, but they need sperm to initiate the process. Such gynogenetic reproduction can be called sperm parasitism since the DNA in the sperm is not used. Since all offspring of asexually reproducing females are females, they can locally outcompete sexually reproducing ones, but their persistence is threatened by the lack of males. Therefore, the existence of Amazon mollies is puzzling. A metapopulation structure has been suggested to enable the coexistence of gynogenetic and sexual species. Previously only Levins-type metapopulation models have been used to investigate this question, but they are not defined on the individual level. Therefore we investigate the evolution of sperm parasitism in a structured metapopulation model, which incorporates both realistic local population dynamics and individual-level dispersal. If the reproduction strategy is freely evolving in a large well-mixed population or in the structured metapopulation model, strong discrimination of asexually reproducing females by males results in evolution to full sexuality, whereas mild discrimination leads to too small probability of sexual reproduction, so that the lack of males causes the extinction of the evolving population, resulting in evolutionary suicide. This classification remains the same also when both sexual reproduction and dispersal are freely evolving. Sexual and asexual behaviour can be observed at the same time in this model in the presence of a trade-off between the reproduction and dispersal traits. However, we do not observe disruptive selection resulting in the evolutionarily stable coexistence of fully sexual and fully asexual females. Instead, the presence of sexual and asexual behaviour is due to females with a mixed reproduction trait.</p

A microscopic model of evolution of recombination

We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not related to the population itself, and a dynamic one that accounts for interactions between organisms e.g. competition. We focus on the dynamics of colonization of an empty niche. As competition is a function of the population, selection pressure rapidly changes in time. The simulations show that both in the case of flat and steep static fitness landscapes, recombination provides a high velocity of movement in the phenotypic space thus allowing recombinants to colonize the highest fitness regions earlier than non recombinants that are often driven to extinction. The stabilizing effects of competition and assortativity are also discussed. Finally, the analysis of phase diagrams shows that competition is the key factor for the evolution of recombination, while assortativity plays a significant role only in small populations.Comment: to appear in Physica

Speciation and the evolution of dispersal along environmental gradients

We analyze the joint evolution of an ecological character and of dispersal distance in asexual and sexual populations inhabiting an environmental gradient. Several interesting phenomena resulting from the evolutionary interplay of these characters are revealed. First, asexual and sexual populations exhibit two analogous evolutionary regimes, in which either speciation in the ecological character occurs in conjunction with evolution of short-range dispersal, or dispersal distance remains high and speciation does not occur. Second, transitions between these two regimes qualitatively differ between asexual and sexual populations, with the former showing speciation with long-range dispersal and the latter showing no speciation with short-range dispersal. Third, a phenotypic gradient following the environmental gradient occurs only in the last case, i.e., for non-speciating sexual populations evolving towards short-range dispersal. Fourth, the transition between the evolutionary regimes of long-range dispersal with no speciation and short-range dispersal with speciation is typically abrupt, mediated by a positive feedback between incipient speciation and the evolution of short-range dispersal. Fifth, even though the model of sexual evolution analyzed here does not permit assortative mating preferences, speciation occurs for a surprisingly wide range of conditions. This illustrates that dispersal evolution is a powerful alternative to preference evolution in enabling spatially distributed sexual populations to respond to frequency- dependent disruptive selection

Trade-offs drive resource specialization and the gradual establishment of ecotypes

Speciation is driven by many different factors. Among those are trade-offs between different ways an organism utilizes resources, and these trade-offs can constrain the manner in which selection can optimize traits. Limited migration among allopatric populations and species interactions can also drive speciation, but here we ask if trade-offs alone are sufficient to drive speciation in the absence of other factors. We present a model to study the effects of trade-offs on specialization and adaptive radiation in asexual organisms based solely on competition for limiting resources, where trade-offs are stronger the greater an organism's ability to utilize resources. In this model resources are perfectly substitutable, and fitness is derived from the consumption of these resources. The model contains no spatial parameters, and is therefore strictly sympatric. We quantify the degree of specialization by the number of ecotypes formed and the niche breadth of the population, and observe that these are sensitive to resource influx and trade-offs. Resource influx has a strong effect on the degree of specialization, with a clear transition between minimal diversification at high influx and multiple species evolving at low resource influx. At low resource influx the degree of specialization further depends on the strength of the trade-offs, with more ecotypes evolving the stronger trade-offs are. The specialized organisms persist through negative frequency-dependent selection. In addition, by analyzing one of the evolutionary radiations in greater detail we demonstrate that a single mutation alone is not enough to establish a new ecotype, even though phylogenetic reconstruction identifies that mutation as the branching point. Instead, it takes a series of additional mutations to ensure the stable coexistence of the new ecotype in the background of the existing ones, reminiscent of a recent observaComment: 19 pages, 3 figure