Unicellular-Multicellular Evolutionary Branching Driven by Resource Limitations

Multicellular life forms have evolved many times in our planet, suggesting that this is a common evolutionary innovation. Multiple advantages have been proposed for multicellularity (MC) to emerge. In this paper we address the problem of how the first precondition for multicellularity, namely "stay together" might have occurred under spatially limited resources exploited by a population of unicellular agents. Using a minimal model of evolved cell-cell adhesion among growing and dividing cells that exploit a localised resource with a given size, we show that a transition occurs at a critical resource size separating a phase of evolved multicellular aggregates from a phase where unicellularity (UC) is favoured. The two phases are separated by an intermediate domain where where both UC and MC can be selected by evolution. This model provides a minimal approach to the early stages that were required to transition from Darwinian individuality to cohesive groups of cells associated with a physical cooperative effect: when resources are present only in a localised portion of the habitat, MC is a desirable property as it helps cells to keep close to the available local nutrients.

Two-dimensional adaptive dynamics of evolutionary public goods games: finite-size effects on fixation probability and branching time

Public goods games (PGGs) describe situations in which individuals contribute to a good at a private cost, but others can free-ride by receiving a share of the public benefit at no cost. The game occurs within local neighbourhoods, which are subsets of the whole population. Free-riding and maximal production are two extremes of a continuous spectrum of traits. We study the adaptive dynamics of production and neighbourhood size. We allow the public good production and the neighbourhood size to coevolve and observe evolutionary branching. We explain how an initially monomorphic population undergoes evolutionary branching in two dimensions to become a dimorphic population characterized by extremes of the spectrum of trait values. We find that population size plays a crucial role in determining the final state of the population. Small populations may not branch or may be subject to extinction of a subpopulation after branching. In small populations, stochastic effects become important and we calculate the probability of subpopulation extinction. Our work elucidates the evolutionary origins of heterogeneity in local PGGs among individuals of two traits (production and neighbourhood size), and the effects of stochasticity in two-dimensional trait space, where novel effects emerge.

On the importance of evolving phenotype distributions on evolutionary diversification

Evolutionary branching occurs when a population with a unimodal phenotype distribution diversifies into a multimodally distributed population consisting of two or more strains. Branching results from frequency-dependent selection, which is caused by interactions between individuals. For example, a population performing a social task may diversify into a cooperator strain and a defector strain. Branching can also occur in multi-dimensional phenotype spaces, such as when two tasks are performed simultaneously. In such cases, the strains may diverge in different directions: possible outcomes include division of labor (with each population performing one of the tasks) or the diversification into a strain that performs both tasks and another that performs neither. Here we show that the shape of the population’s phenotypic distribution plays a role in determining the direction of branching. Furthermore, we show that the shape of the distribution is, in turn, contingent on the direction of approach to the evolutionary branching point. This results in a distribution–selection feedback that is not captured in analytical models of evolutionary branching, which assume monomorphic populations. Finally, we show that this feedback can influence long-term evolutionary dynamics and promote the evolution of division of labor.

Effects of pollution on individual size of a single species

In this paper, we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species. The invasion fitness function of a monomorphic species is given, which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system, which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate. We conclude that the pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size, while the opposite is more likely to generate evolutionary branching and promote species diversity. The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs.

Branching and extinction in evolutionary public goods games

Public goods games (PGGs) describe situations in which individuals contribute to a good at a private cost, but others can free-ride by receiving their share of the public benefit at no cost. PGGs can be nonlinear, as often observed in nature, whereby either benefit, cost, or both are nonlinear functions of the available public good (PG): at low levels of PG there can be synergy whereas at high levels, the added benefit of additional PG diminishes. PGGs can be local such that the benefits and costs are relevant only in a local neighborhood or subset of the larger population in which producers (cooperators) and free-riders (defectors) co-evolve. Cooperation and defection can be seen as two extremes of a continuous spectrum of traits. The level of public good production, and similarly, the neighborhood size can vary across individuals. To better understand how distinct strategies in the nonlinear public goods game emerge and persist, we study the adaptive dynamics of production rate and neighborhood size. We explain how an initially monomorphic population, in which individuals have the same trait values, could evolve into a dimorphic population by evolutionary branching, in which we see distinct cooperators and defectors emerge, respectively characterized by high production and low neighborhood sizes, and low production and high neighborhood sizes. We find that population size plays a crucial role in determining the final state of the population, as smaller populations may not branch, or may observe extinction of a subpopulation after branching. Our work elucidates the evolutionary origins of cooperation and defection in nonlinear local public goods games, and highlights the importance of small population size effects on the process and outcome of evolutionary branching.

Evolution of dispersal in a spatially heterogeneous population with finite patch sizes

Dispersal is one of the fundamental life-history strategies of organisms, so understanding the selective forces shaping the dispersal traits is important. In the Wright’s island model, dispersal evolves due to kin competition even when dispersal is costly, and it has traditionally been assumed that the living conditions are the same everywhere. To study the effect of spatial heterogeneity, we extend the model so that patches may receive different amounts of immigrants, foster different numbers of individuals, and give different reproduction efficiency to individuals therein. We obtain an analytical expression for the fitness gradient, which shows that directional selection consists of three components: As in the homogeneous case, the direct cost of dispersal selects against dispersal and kin competition promotes dispersal. The additional component, spatial heterogeneity, more precisely the variance of so-called relative reproductive potential, tends to select against dispersal. We also obtain an expression for the second derivative of fitness, which can be used to determine whether there is disruptive selection: Unlike the homogeneous case, we found that divergence of traits through evolutionary branching is possible in the heterogeneous case. Our numerical explorations suggest that evolutionary branching is promoted more by differences in patch size than by reproduction efficiency. Our results show the importance of the existing spatial heterogeneity in the real world as a key determinant in dispersal evolution.

Evolutionary branching of function-valued traits under constraints

Some evolutionary traits are described by scalars and vectors, while others are described by continuous functions on spaces (e.g., shapes of organisms, resource allocation strategies between growth and reproduction along time, and effort allocation strategies for continuous resource distributions along resource property axes). The latter are called function-valued traits. This study develops conditions for candidate evolutionary branching points, referred to as CBP conditions, for function-valued traits under simple equality constraints, in the framework of adaptive dynamics theory (i.e., asexual reproduction and rare mutation are assumed). CBP conditions are composed of conditions for evolutionary singularity, strong convergence stability, and evolutionary instability. The CBP conditions for function-valued traits are derived by transforming the CBP conditions for vector traits into those for infinite-dimensional vector traits.

Evolutionary branching in distorted trait spaces

Biological communities are thought to have been evolving in trait spaces that are not only multi-dimensional, but also distorted in a sense that mutational covariance matrices among traits depend on the parental phenotypes of mutants. Such a distortion may affect diversifying evolution as well as directional evolution. In adaptive dynamics theory, diversifying evolution through ecological interaction is called evolutionary branching. This study analytically develops conditions for evolutionary branching in distorted trait spaces of arbitrary dimensions, by a local nonlinear coordinate transformation so that the mutational covariance matrix becomes locally constant in the neighborhood of a focal point. The developed evolutionary branching conditions can be affected by the distortion when mutational step sizes have significant magnitude difference among directions, i.e., the eigenvalues of the mutational covariance matrix have significant magnitude difference.