Abstract
Computational models of evolutionary processes are increasingly required to incorporate multiple and diverse sources of data. A popular feature to include in population genetics models is spatial extension, which reflects more accurately natural populations than does a mean field approach. However, such models necessarily violate the mean field assumptions of classical population genetics, as do natural populations in the real world. Recently, it has been questioned whether classical approaches are truly applicable to the real world. Individual based models (IBM) are a powerful and versatile approach to achieve integration in models. In this study an IBM was used to examine how populations of plants deviate from classical expectations under spatial extension. Populations of plants that used three different mating strategies were placed in a range of arena sizes giving crowded to sparse occupation densities. Using a measure of population density, the pollen communication distance (Pcd), the deviation exhibited by outbreeding populations differed from classical mean field expectations by less than 5% when Pcd was less than 1, and over this threshold value the deviation significantly increased. Populations with an intermediate mating strategy did not have such a threshold and deviated directly with increasing isolation between individuals. Populations with a selfing strategy were influenced more by the mating strategy than by increased isolation. In all cases pollen dispersal was more influential than seed dispersal. The IBM model showed that mean field calculations can be reasonably applied to natural outbreeding plant populations that occur at a density in which individuals are less than the average pollen dispersal distance from their neighbors.
Highlights
Understanding the evolutionary process is increasingly requiring in the integration of sources of data that are typically beyond classical population genetics models [1]
We did not observe a clear threshold effect for seed dispersal. To our knowledge this is the only study where increasing spatial perturbations are made to examine the discrepancy between real observed values of population genetics variables, and those expected based on mean-field population genetics theory
The results we present here demonstrate that the deviation from classical population genetics introduced by the closer approximation to the real world through spatial extension is largely tractable, and different for different mating systems
Summary
Understanding the evolutionary process is increasingly requiring in the integration of sources of data that are typically beyond classical population genetics models [1]. Along with other simplifying assumptions such as non-overlapping generations and constant population sizes, such populations behave in tractable ways that can be described through deterministic approaches leading to features such as HardyWeinberg equilibria [2] and the Wright-Fisher model [3] The predictions of such models provide a useful starting point for evolutionary studies, for instance in establishing whether there has been significant deviation from neutrality indicative of selection. Mayr [4] observed that it was surprising how little classical population genetics has contributed to the understanding of one of the most important processes in evolution, speciation This is because a mean-field based model is essentially based on an anagenic evolutionary system, rather than a cladogenic one [5]. The evolutionary differentiation of populations, which leads to speciation, requires different selective environments
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