The effect of the dispersal kernel on isolation-by-distance in a continuous population

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.

在隔离距离模型（isolation-by-distance）下，种群结构由成对基因间的血统同一性（identity-by-descent）概率决定，该概率与基因间的地理距离直接相关。经充分验证的解析理论表明，地理距离与遗传距离之间的关联主要取决于种群邻域大小（neighborhood size）——这一指标是衡量基因流（gene flow）的标准化尺度。为验证该理论预测，我们采用七种扩散核（dispersal kernels），对二维景观（two-dimensional landscape）上单倍体个体（haploid individuals）的局域扩散过程进行建模，所涉及的分布包括瑞利分布（Rayleigh）、指数分布（exponential）、半正态分布（half-normal）、三角分布（triangular）、伽马分布（gamma）、洛马克斯分布（Lomax）与帕累托分布（Pareto）。当邻域大小保持恒定时，各扩散分布均呈现出相似的隔离距离模式，验证了前述预测。基于上述结果，我们提出将三角分布作为隔离距离研究的适宜空分布（null distribution）。在三角分布假设下，个体扩散在邻域范围内呈均匀分布，这表明将邻域大小视作有效局域泛交种群衡量指标的通用表述，对于主流扩散分布族而言是成立的。我们进一步展示了如何高效地从三角分布中抽取随机变量，并主张在关注计算效率的相关研究中应当采用该分布。