Quantifying random drift in a multi-level selection model

Abstract

Random drift – stochastic effects leading to evolutionary change – is one of the major forces within evolution. Its effects are more significant for smaller populations. Since it has been shown that group-structured populations undergoing multi-level selection have a significantly lower effective population size (Ne), one would expect to see a more significant impact of random drift in these type of systems. Although there are some quantities available that are greatly influenced by drift, e.g. fixation probability or the fluctuations around a mutation-selection equilibrium, random drift has not often been quantified directly. The aim of this study is to quantify random drift in a group-structured population undergoing multi-level selection. First, we will present a new framework based on Price’s equation that is able to do quantify both random drift and natural selection on multiple levels. Secondly, we will apply this framework on a model based on Traulsen and Nowak (2006). Then we will study how the fixation probability of a mutant and the fluctuations around a mutation-selection equilibrium change for varying number of groups in the group-structured population of our model. Finally, we will try to explain these effects using the terms from our newly presented framework. We have found that our framework is able to properly describe the evolutionary change due to drift in our model. Furthermore, we can identify some trends in the patterns of within-group and among-group drift corresponding to the behaviour of the system and are able to explain these. However, it has still proven difficult to explain directly how changes in fixation probability are affected directly by the drift terms. Future research could study the implications of the different terms from our framework more extensively, considering more quantities of random drift or perhaps studying the terms in more models.