Abstract
Under models of isolation-by-distance, population structure is determined by the probability of identity-by-descent between pairs of genes according to the geographic distance between them. Well established analytical results indicate that the relationship between geographical and genetic distance depends mostly on the neighborhood size of the population which represents a standardized measure of gene flow. To test this prediction, we model local dispersal of haploid individuals on a two-dimensional landscape using seven dispersal kernels: Rayleigh, exponential, half-normal, triangular, gamma, Lomax and Pareto. When neighborhood size is held constant, the distributions produce similar patterns of isolation-by-distance, confirming predictions. Considering this, we propose that the triangular distribution is the appropriate null distribution for isolation-by-distance studies. Under the triangular distribution, dispersal is uniform over the neighborhood area which suggests that the common description of neighborhood size as a measure of an effective, local panmictic population is valid for popular families of dispersal distributions. We further show how to draw random variables from the triangular distribution efficiently and argue that it should be utilized in other studies in which computational efficiency is important.
Highlights
For many populations, individuals do not exist in discrete patches or demes; instead they are spread across a continuous landscape
There are no barriers separating individuals, dispersal distances are often limited, and individuals that are near one another in space will be more similar genetically than individuals further apart. This phenomenon is known as isolation-by-distance and introduces a spatial component that should be considered when studying population genetic processes (Jongejans, Skarpaas & Shea, 2008)
The average squared parent–offspring dispersal distance, s2, observed for each distribution was very similar with a relative error of less than 5% from the expected σ 2 value (Table 1); the distribution of these values over sampled generations varied (Fig. S3A)
Summary
Individuals do not exist in discrete patches or demes; instead they are spread across a continuous landscape. There are no barriers separating individuals, dispersal distances are often limited, and individuals that are near one another in space will be more similar genetically than individuals further apart. This phenomenon is known as isolation-by-distance and introduces a spatial component that should be considered when studying population genetic processes (Jongejans, Skarpaas & Shea, 2008). Many researchers have turned to spatially-explicit, individual-based computer simulations which offer a more flexible way to incorporate spatial complexity into biological models (e.g., Barton et al, 2013; Cartwright, 2009; Epperson, 2003; Novembre & Stephens, 2008; Rousset, 2004; Slatkin, 1993).
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