A review of the discovery of the surprising dynamical properties of evolutionary amplifiers (Lieberman, Hauert & Nowak, 2005). In the spatial Moran process the geometrical arrangement of individuals can have surprising effects on the evolutionary dynamics. The key determinants of the evolutionary process in finite populations are the fixation probabilities and times. Both can be significantly...
Moran process is a classic random process that models the competition of two or more types of individuals on a network-structured population. The individuals reproduce, the offspring migrate along the edges of the network, and they replace the neighbors. In the absence of mutation, one of the types eventually triumphs over the whole network. We survey the existing results on the time (that is,...
David Brewster, Martin Nowak, Josef Tkadlec
Computing the rate of evolution in spatially structured populations is difficult. A key quantity is the fixation time of a single mutant with relative reproduction rate r which invades a population of residents. We say that the fixation time is "fast" if it is at most a polynomial function in terms of the population size N. Here we study fixation...
Suppose that mutant invasion starts with
In another setting, suppose that selection pressure is only present on a few locations in a population structure, therefore mutants have an advantage only when reproducing on these...
Petros Petsinis, Andreas Pavlogiannis, Josef Tkadlec, Panagiotis Karras
The Moran process is a classic stochastic process that models the rise and takeover of novel traits in network-structured populations. In biological terms, a set of mutants, each with fitness m∈(0,∞) invade a population of residents with fitness 1. Each agent reproduces at a rate proportional to its fitness and each...
Evolutionary dynamics are sensitive to the type of ecological interactions that drive reproduction and death. In this talk I will discuss how spatial interactions may change the laws of evolution. First I will describe spatial invasion dynamics and derive a number of scaling laws that describe the growth of disadvantageous, neutral, and advantageous mutants in growing populations. Applications...
Evolutionary graph theory has shown that population structure can strongly impact evolution, in particular by affecting the fixation probability of mutants. Natural microbial populations often have complex spatial structures, where these effects can be crucial. However, making the link with update rules is not always easy. We proposed a model for describing deme-structured populations on...
Ernesto Berríos-Caro and Hildegard Uecker
Meta-populations often exhibit complex spatial structures. Migration between environments plays a crucial role in shaping mutant dynamics. Motivated by bacterial evolution experiments, we develop a model of spatially structured populations on graphs, incorporating between-deme migration and periodic bottlenecks. We explore two key scenarios: one...
Natural populations are often spatially structured, meaning they are best described as metapopulations composed of subpopulations connected by migration. We know little about how the topology of connections in metapopulations impacts adaptive evolution. Models based on evolutionary graph theory suggest topologies that concentrate dispersing individuals through a central hub can accelerate...
George Berry, Christoph Hauert
We investigate an extension to the Moran process which adds ecological aspects through variable population sizes. For the original Moran process, birth and death events are correlated to maintain a constant population size. Here we decouple the two events and derive the stochastic differential equation that represents the dynamics in a well-mixed population...
Certain defense mechanisms of phages against the immune system of their bacterial host rely on cooperation of phages. Motivated by this example we analysed in [BP] the spread of cooperative parasites in host populations that were structured according to a configuration model. Building on these results we consider the case of a host population which is (genuinely spatially) structured according...
The adaptation of a population to a novel environment proceeds through the fixation of beneficial mutations and the purging of deleterious ones. Although most novel mutations are deleterious, in well-mixed populations their effects become largely negligible at large population size. By contrast, in structured populations deleterious mutations can dominate the behavior even in the limit of...
Evolution in finite populations is often modelled using the classical Moran process and this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such population is whether a rare mutant has a higher or lower fixation probability than the Moran probability, i.e. that from the original Moran model, which represents an unstructured...
Diogo L. Pires, Mark Broom
Community organization permeates both social and biological complex systems. To study its interplay with behavior emergence, we model mobile structured populations with multiplayer interactions. We derive general analytical methods for evolutionary dynamics under high home fidelity when populations self-organize into networks of asymptotically isolated...
Natalya Slyeptsova, Christopher Overton
Evolutionary graph theory (EGT) considers evolutionary dynamics in a structured population that is represented by a graph. Fixation probability is a measure of probability that a mutation takes over the resident population. One of the major questions EGT tries to answer is how the graph structure impacts the fixation probability. It has been found...
Kieran Sharkey, Chris Overton
As ecosystems evolve, species can become extinct due to fluctuations in the environment. This leads to the evolutionary adaption known as bet-hedging, where species hedge against these fluctuations to reduce their likelihood of extinction. Environmental variation can be either within or between generations. Previous work has shown that selection for...
Evolutionary dynamics are sensitive to the type of ecological interactions that drive reproduction and death. In this talk I will discuss how spatial interactions may change the laws of evolution. First I will describe spatial invasion dynamics and derive a number of scaling laws that describe the growth of disadvantageous, neutral, and advantageous mutants in growing populations. Applications...
