Null expectation of spatial correlograms under a stochastic process of genetic divergence with small sample sizes

Abstract

An Ornstein-Uhlenbeck process was used to simulate the exponential relationship between genetic divergence and geographic distances, as predicted by stochastic processes of population differentiation, such as isolation-by-distance, stepping-stone or coalescence models. These simulations were based only on the spatial coordinates of the local populations that defined a spatial unweighted pair-group method using arithmetic averages (UPGMA) link among them. The simulated gene frequency surfaces were then analyzed using spatial autocorrelation procedures and Nei’s genetic distances, constructed with different numbers of variables (gene frequencies). Stochastic divergence in space produced strong spatial patterns at univariate and mutivariate levels. Using a relatively small number of local populations, the correlogram profiles varied considerably, with Manhattan distances greater than those defined by other simulation studies. This method allows one to establish a range of correlogram profiles under the same stochastic process of spatial divergence, thereby avoiding the use of unnecessary explanations of genetic divergence based on other microevolutionary processes.