Asymptotic behavior of joint distributions of characteristics of apair of randomly chosen individuals in discrete-time Fisher-Wrightmodels with mutations and drift

摘要

This is a continuation of the series of articles (C.R. Rao, D.N. Shanbhag (Eds.), Handbook of Statistics 19: Stochastic Processes: Theory and Methods, Elsevier Science, Amsterdam, 2001 (Chapter 8); Math. Biosci. 175 (2002) 83; Math. Meth. Appl. Sci. 26 (2003) 1587; Adv. Appl. Probab. 36 (2004) 57) devoted to a study of the interplay between two of the main forces of population genetics, mutations and drift, in the Fisher-Wright model. We provide discrete-time versions of theorems describing asymptotic behavior of joint distributions of characteristics of a pair of individuals in this model; their continuous-time counterparts were presented in the previous papers. Furthermore, we show that imbalance index, introduced in Kimmel et al. (Genetics 148 (1998) 1921) and King et al. (Mol. Biol. Evol. 17(12) (2000) 1895) in the context of continuous-time models, may also be used in discrete-time models to detect past population growth.