Stochastic slowdown in evolutionary processes

We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but non--vanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes.Comment: 8 pages, 3 figures, accepted for publicatio

Generalized Urn Models of Evolutionary Processes

Generalized Polya urn models can describe the dynamics of finite populations of interacting genotypes. Three basic questions these models can address are: Under what conditions does a population exhibit growth? On the event of growth, at what rate does the population increase? What is the long-term behavior of the distribution of genotypes? To address these questions, we associate a mean limit ordinary differential equation (ODE) with the urn model. Previously, it has been shown that on the event of population growth, the limiting distribution of genotypes is a connected internally chain recurrent set for the mean limit ODE. To determine when growth and convergence occurs with positive probability, we prove two results. First, if the mean limit ODE has an ``attainable'' attractor at which growth is expected, then growth and convergence toward this attractor occurs with positive probability. Second, the population distribution almost surely does not converge to sets where growth is not expecte

Ecological and evolutionary processes at expanding range margins

Many animals are regarded as relatively sedentary and specialized in marginal parts of their geographical distributions. They are expected to be slow at colonizing new habitats. Despite this, the cool margins of many species' distributions have expanded rapidly in association with recent climate warming. We examined four insect species that have expanded their geographical ranges in Britain over the past 20 years. Here we report that two butterfly species have increased the variety of habitat types that they can colonize, and that two bush cricket species show increased fractions of longer-winged (dispersive) individuals in recently founded populations. Both ecological and evolutionary processes are probably responsible for these changes. Increased habitat breadth and dispersal tendencies have resulted in about 3- to 15-fold increases in expansion rates, allowing these insects to cross habitat disjunctions that would have represented major or complete barriers to dispersal before the expansions started. The emergence of dispersive phenotypes will increase the speed at which species invade new environments, and probably underlies the responses of many species to both past and future climate change

Eco-evolutionary dynamics of social dilemmas

Social dilemmas are an integral part of social interactions. Cooperative actions, ranging from secreting extra-cellular products in microbial populations to donating blood in humans, are costly to the actor and hence create an incentive to shirk and avoid the costs. Nevertheless, cooperation is ubiquitous in nature. Both costs and benefits often depend non-linearly on the number and types of individuals involved -- as captured by idioms such as `too many cooks spoil the broth' where additional contributions are discounted, or `two heads are better than one' where cooperators synergistically enhance the group benefit. Interaction group sizes may depend on the size of the population and hence on ecological processes. This results in feedback mechanisms between ecological and evolutionary processes, which jointly affect and determine the evolutionary trajectory. Only recently combined eco-evolutionary processes became experimentally tractable in microbial social dilemmas. Here we analyse the evolutionary dynamics of non-linear social dilemmas in settings where the population fluctuates in size and the environment changes over time. In particular, cooperation is often supported and maintained at high densities through ecological fluctuations. Moreover, we find that the combination of the two processes routinely reveals highly complex dynamics, which suggests common occurrence in nature.Comment: 26 pages, 11 figure

Integrating the processes in the evolutionary system of domestication

Genetics has long been used as a source of evidence to understand domestication origins. A recent shift in the emphasis of archaeological evidence from a rapid transition paradigm of hunter-gatherers to agriculturalists, to a protracted transition paradigm has highlighted how the scientific framework of interpretation of genetic data was quite dependent on archaeological evidence, resulting in a period of discord in which the two evidence types appeared to support different paradigms. Further examination showed that the discriminatory power of the approaches employed in genetics was low, and framed within the rapid paradigm rather than testing it. In order to interpret genetic data under the new protracted paradigm it must be taken into account how that paradigm changes our expectations of genetic diversity. Preliminary examination suggests that a number of features that constituted key evidence in the rapid paradigm are likely to be interpreted very differently in the protracted paradigm. Specifically, in the protracted transition the mode and mechanisms involved in the evolution of the domestication syndrome have become much more influential in the shape of genetic diversity. The result is that numerous factors interacting over several levels of organization in a domestication system need to be taken into account in order to understand the evolution of the process. This presents a complex problem of integration of different data types which is difficult to describe formally. One possible way forward is to use Bayesian approximation approaches that allow complex systems to be measured in a way that does not require such formality