Fluctuation induces evolutionary branching in a modeled microbial ecosystem

The impact of environmental fluctuation on species diversity is studied with a model of the evolutionary ecology of microorganisms. We show that environmental fluctuation induces evolutionary branching and assures the consequential coexistence of multiple species. Pairwise invasibility analysis is applied to illustrate the speciation process. We also discuss how fluctuation affects species diversity.Comment: 4 pages, 4 figures. Submitted to Physical Review Letter

Adaptive Evolution of Cooperation through Darwinian Dynamics in Public Goods Games

The linear or threshold Public Goods game (PGG) is extensively accepted as a paradigmatic model to approach the evolution of cooperation in social dilemmas. Here we explore the significant effect of nonlinearity of the structures of public goods on the evolution of cooperation within the well-mixed population by adopting Darwinian dynamics, which simultaneously consider the evolution of populations and strategies on a continuous adaptive landscape, and extend the concept of evolutionarily stable strategy (ESS) as a coalition of strategies that is both convergent-stable and resistant to invasion. Results show (i) that in the linear PGG contributing nothing is an ESS, which contradicts experimental data, (ii) that in the threshold PGG contributing the threshold value is a fragile ESS, which cannot resist the invasion of contributing nothing, and (iii) that there exists a robust ESS of contributing more than half in the sigmoid PGG if the return rate is relatively high. This work reveals the significant effect of the nonlinearity of the structures of public goods on the evolution of cooperation, and suggests that, compared with the linear or threshold PGG, the sigmoid PGG might be a more proper model for the evolution of cooperation within the well-mixed population

A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.Comment: 21 pages, 2 figures, as accepted to J Math Biol 2013/03/1

Where Two Are Fighting, the Third Wins: Stronger Selection Facilitates Greater Polymorphism in Traits Conferring Competition-Dispersal Tradeoffs

A major conundrum in evolution is that, despite natural selection, polymorphism is still omnipresent in nature: Numerous species exhibit multiple morphs, namely several abundant values of an important trait. Polymorphism is particularly prevalent in asymmetric traits, which are beneficial to their carrier in disruptive competitive interference but at the same time bear disadvantages in other aspects, such as greater mortality or lower fecundity. Here we focus on asymmetric traits in which a better competitor disperses fewer offspring in the absence of competition. We report a general pattern in which polymorphic populations emerge when disruptive selection increases: The stronger the selection, the greater the number of morphs that evolve. This pattern is general and is insensitive to the form of the fitness function. The pattern is somewhat counterintuitive since directional selection is excepted to sharpen the trait distribution and thereby reduce its diversity (but note that similar patterns were suggested in studies that demonstrated increased biodiversity as local selection increases in ecological communities). We explain the underlying mechanism in which stronger selection drives the population towards more competitive values of the trait, which in turn reduces the population density, thereby enabling lesser competitors to stably persist with reduced need to directly compete. Thus, we believe that the pattern is more general and may apply to asymmetric traits more broadly. This robust pattern suggests a comparative, unified explanation to a variety of polymorphic traits in nature.ope

Direct competition results from strong competiton for limited resource

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka-Volterra direct competition model, describes competitive interactions leading to concentrated distributions of species in continuous trait space. Here we assume a very fast dynamics for the supply of the resource and a fast dynamics for death and uptake rates. In this regime we show that factors that are independent of the resource competition become as important as the competition efficiency and that the direct competition model is a good approximation of the chemostat. Assuming these two timescales allows us to establish a mathematically rigorous proof showing that our resource-competition model with continuous traits converges to a direct competition model. We also show that the two timescales assumption is required to mathematically justify the corresponding classic result on a model consisting of only finite number of species and resources (MacArthur, R. Theor. Popul. Biol. 1970:1, 1-11). This is performed through asymptotic analysis, introducing different scales for the resource renewal rate and the uptake rate. The mathematical difficulty relies in a possible initial layer for the resource dynamics. The chemostat model comes with a global convex Lyapunov functional. We show that the particular form of the competition kernel derived from the uptake kernel, satisfies a positivity property which is known to be necessary for the direct competition model to enjoy the related Lyapunov functional

Species Invasion History Influences Community Evolution in a Tri-Trophic Food Web Model

Background: Recent experimental studies have demonstrated the importance of invasion history for evolutionary formation of community. However, only few theoretical studies on community evolution have focused on such views. Methodology and Principal Findings: We used a tri-trophic food web model to analyze the coevolutionary effects of ecological invasions by a mutant and by a predator and/or resource species of a native consumer species community and found that ecological invasions can lead to various evolutionary histories. The invasion of a predator makes multiple evolutionary community histories possible, and the evolutionary history followed can determine both the invasion success of the predator into the native community and the fate of the community. A slight difference in the timing of an ecological invasion can lead to a greatly different fate. In addition, even greatly different community histories can converge as a result of environmental changes such as a predator trait shift or a productivity change. Furthermore, the changes to the evolutionary history may be irreversible. Conclusions and Significance: Our modeling results suggest that the timing of ecological invasion of a species into a focal community can largely change the evolutionary consequences of the community. Our approach based on adaptive dynamics will be a useful tool to understand the effect of invasion history on evolutionary formation of community

Speciation Along Environmental Gradients

Traditional discussions of speciation are based on geographical patterns of species ranges. In allopatric speciation, long-term geographical isolation generates reproductively isolated and spatially segregated descendant species. In the absence of geographical barriers, diversification is hindered by gene flow. Yet a growing body of phylogenetic and experimental data suggests that closely related species often occur in sympatry or have adjacent ranges in regions over which environmental changes are gradual and do not prevent gene flow. Theory has identified a variety of evolutionary processes that can result in speciation under sympatric conditions, with some recent advances concentrating on the phenomenon of evolutionary branching. Here we establish a link between geographical patterns and ecological processes of speciation by studying evolutionary branching in spatially structured populations. We show that along an environmental gradient, evolutionary branching can occur much more easily than in non-spatial models. This facilitation is most pronounced for gradients of intermediate slope. Moreover, spatial evolutionary branching readily generates patterns of spatial segregation and abutment between the emerging species. Our results highlight the importance of local processes of adaptive divergence for geographical patterns of speciation, and caution against pitfalls of inferring past speciation processes from present biogeographical patterns

The effect of extrinsic mortality on genome size evolution in prokaryotes

Mortality has a significant role in prokaryotic ecology and evolution, yet the impact of variations in extrinsic mortality on prokaryotic genome evolution has received little attention. We used both mathematical and agent-based models to reveal how variations in extrinsic mortality affect prokaryotic genome evolution. Our results suggest that the genome size of bacteria increases with increased mortality. A high extrinsic mortality increases the pool of free resources and shortens life expectancy, which selects for faster reproduction, a phenotype we called ‘scramblers’. This phenotype is realised by the expansion of gene families involved in nutrient acquisition and metabolism. In contrast, a low mortality rate increases an individual’s life expectancy, which results in natural selection favouring tolerance to starvation when conditions are unfavourable. This leads to the evolution of small, streamlined genomes (‘stayers’). Our models predict that large genomes, gene family expansion and horizontal gene transfer should be observed in prokaryotes occupying ecosystems exposed to high abiotic stress, as well as those under strong predator- and/or pathogen-mediated selection. A comparison of genome size of cyanobacteria in relatively stable marine versus more turbulent freshwater environments corroborates our predictions, although other factors between these environments could also be responsible

Competition-Colonization Trade-Offs, Competitive Uncertainty, and the Evolutionary Assembly of Species

We utilize a standard competition-colonization metapopulation model in order to study the evolutionary assembly of species. Based on earlier work showing how models assuming strict competitive hierarchies will likely lead to runaway evolution and self-extinction for all species, we adopt a continuous competition function that allows for levels of uncertainty in the outcome of competition. We then, by extending the standard patch-dynamic metapopulation model in order to include evolutionary dynamics, allow for the coevolution of species into stable communities composed of species with distinct limiting similarities. Runaway evolution towards stochastic extinction then becomes a limiting case controlled by the level of competitive uncertainty. We demonstrate how intermediate competitive uncertainty maximizes the equilibrium species richness as well as maximizes the adaptive radiation and self-assembly of species under adaptive dynamics with mutations of non-negligible size. By reconciling competition-colonization tradeoff theory with co-evolutionary dynamics, our results reveal the importance of intermediate levels of competitive uncertainty for the evolutionary assembly of species