Behavior of popular indices of genetic diversity in simulated expanding populations

Protecting genetic diversity is an integral component of food security, fishery management, and biodiversity conservation, and thus the ability to model and predict the distribution of genetic diversity is valuable. Population genetic theory predicts that genetic diversity will be greatest in the largest populations at mutation-drift equilibrium, implying that efforts to preserve diversity would be best focused on keeping populations as large as feasibly possible. Natural populations, however, are rarely in equilibrium, because their sizes can fluctuate due to a variety of processes, e.g., populations that have had a recent bottleneck or invaded a new habitat. To predict patterns of genetic diversity in natural populations, it has become increasingly important to understand how populations behave in non-equilibrium scenarios. Here we report the effects of mutation rate (µ), initial population size (Ne0), and final population size (Ne1) on the genetic diversity in expanding populations using a Wright-Fisher forward time model built with SLiM2. Using a 300 bp sequence to simulate modern genome-wide surveys of genetic variation (RAD), a range of naturally occurring mutation rates, and population sizes, multiple models were created to cover a broad portion of parameter space, and six commonly reported measures of genetic diversity estimated. As previously reported, genetic diversity increased with increasing population size given a similar set of circumstances, but there are broad swaths of parameter space where small populations exhibit greater diversity than large populations, making historical context critical in population genetics analysis. Depending on population size and mutation rate, the different diversity indices (nucleotide diversity, gene diversity, number of haplotypes, effective number of haplotypes, number of heterozygotes, and number of substitutions) progressed towards equilibrium at different rates. Furthermore, different diversity indices had different levels of sensitivity to changes in diversity at different times. To better describe the change in diversity with time, logistic growth models were used to estimate the equilibrium diversity (Deq), initial diversity value (D0), amount of time required to reach halfway to genetic equilibrium (t50eq), growth parameter (Φ3), maximum rate of genetic diversity increase (r), and time required to reach 95% of the equilibrium value (t95) in populations that expand from Ne0 to Ne1. We employed both linear and non-linear model fitting and used AIC to identify the best models describing the logistic growth parameters with varying Ne0, Ne1, and µ. In most cases, the models fit the simulated data well as the relative bias is low, ranging from +/- 3%, but the models did not perform as well when Ne0, Ne1, and µ, are small, with relative bias as high as 20%. The best models were used to create a tool that estimates the diversity of a population given the time since the onset of expansion, Ne0, Ne1, and µ. The prediction model performed best when using the Ne0, Ne1, and µ used in the simulations but could give misleading diversities when interpolating, so a switch was created to restrict the tool to only accept the predefined set of parameter values. This tool can be used to get a rough approximation of how long it will take for genetic diversity to accumulate and determine why there might be deviations from the neutral expectation that large populations have more diversity without running time consuming simulations and subsequent analysis.