TheWeight: A simple and flexible algorithm for simulating non‐ideal, age‐structured populations

Abstract

Abstract The Wright–Fisher model, which directs how matings occur and how genes are transmitted across generations, has long been a lynchpin of evolutionary biology. This model is elegantly simple, analytically tractable and easy to implement, but it has one serious limitation: essentially no real species satisfies its many assumptions. With growing awareness of the importance of jointly considering both ecology and evolution in eco‐evolutionary models, this limitation has become more apparent, causing many researchers to search for more realistic simulation models. A recently described variation retains most of the Wright–Fisher simplicity but provides greater flexibility to accommodate departures from model assumptions. This generalized Wright–Fisher model relaxes the assumption that all individuals have identical expected reproductive success by introducing a vector of parental weights w that specifies relative probabilities different individuals have of producing offspring. With parental weights specified this way, expectations of key demographic parameters are simple functions of w. This allows researchers to quantitatively predict the consequences of non‐Wright–Fisher features incorporated into their models. An important limitation of the Wright–Fisher model is that it assumes discrete generations, whereas most real species are age structured. Here I show how an algorithm (TheWeight) that implements the generalized Wright–Fisher model can be used to model evolution in age‐structured populations with overlapping generations. Worked examples illustrate simulation of seasonal and lifetime reproductive success and show how the user can pick vectors of weights expected to produce a desired level of reproductive skew or a desired Ne/N ratio. Alternatively, weights can be associated with heritable traits to provide a simple, quantitative way to model natural selection. Using TheWeight, it is easy to generate positive or negative correlations of individual reproductive success over time, thus allowing explicit modelling of common biological processes like skip breeding and persistent individual differences. Code is provided to implement basic features of TheWeight and applications described here, including one scenario implemented in SLiM. However, required coding changes to the Wright–Fisher model are modest, so the real value of the new algorithm is to encourage users to adopt its features into their own or others' models.