Variance additivity of genetic populational parameter estimates obtained through bootstrapping

Abstract

Studying the genetic structure of natural populations is very important for conservation and use of the genetic variability available in nature. This research is related to genetic population structure analysis using real and simulated molecular data. To obtain variance estimates of pertinent parameters, the bootstrap resampling procedure was applied over different sampling units, namely: individuals within populations (I), populations (P), and individuals and populations simultaneously (I, P). The considered parameters were: the total fixation index (F or F IT), the fixation index within populations (f or F IS) and the divergence among populations or intrapopulation coancestry (theta or F ST). The aim of this research was to verify if the variance estimates of <IMG SRC="/img/fbpe/sa/v60n1/14549x09.gif">, <IMG SRC="/img/fbpe/sa/v60n1/14549x10.gif">and <IMG SRC="/img/fbpe/sa/v60n1/14549x11.gif">, found through the resampling over individuals and populations simultaneously (I, P), correspond to the sum of the respective variance estimates obtained from separated resampling over individuals and populations (I+P). This equivalence was verified in all cases, showing that the total variance estimate of <IMG SRC="/img/fbpe/sa/v60n1/14549x09.gif">, <IMG SRC="/img/fbpe/sa/v60n1/14549x10.gif">and <IMG SRC="/img/fbpe/sa/v60n1/14549x11.gif">can be obtained summing up the variances estimated for each source of variation separately. Results also showed that this facilitates the use of the bootstrap method on data with hierarchical structure and opens the possibility of obtaining the relative contribution of each source of variation to the total variation of estimated parameters.