FLUCTUATING POPULATION SIZE AND THE RATIO OF EFFECTIVE TO CENSUS POPULATION SIZE.

The effective size of a population (Ne) quantifies the rate at which genetic diversity is eroded by genetic drift (i.e., 112Ne per generation), a fundamental process of evolutionary change. Genetic diversity and its rate of decay have been linked with key components of population fitness (Allendorf and Leary 1987; Ralls et al. 1988; Briscoe et al. 1992; Newman and Pilson 1997; but see Britten 1996). Ne is thus a central parameter both in studies aimed at understanding evolution (Falconer and Mackay 1996) and in the field of conservation genetics (Lande and Barrowclough 1987; Nunney and Campbell 1993; Nunney and Elam 1994). Unfortunately, accounting for all factors that influence Ne is notoriously difficult (reviewed by Caballero 1994). This difficulty is apparently responsible for significant disagreement between theoretical (Nunney 1993) and observed values of the ratio, Ne/N (Frankham 1995). Here we investigate whether this disagreement can be reconciled by incorporating the effect of a factor long known to reduce Ne, namely temporal fluctuations in population size (FPS; Wright 1938). More specifically, we consider the extent to which Ne/N is depressed by FPS over the range of fluctuations observed in wild animal populations. In addition, we present a method for predicting Ne/N from a standard measure of population variability, and we discuss the implications of this theoretical relationship. Several factors affect the effective size of a population: fluctuations in size, variance in fecundity, sex ratio, and the degree to which generations overlap (Crow and Kimura 1970). One difficulty in estimating Ne is that no single formula simultaneously accounts for all these factors. This difficulty would be largely inconsequential if the ratio Ne/N were known to fall consistently within a narrow range. Estimating Ne would be trivial because N is often relatively easily estimated. Theoretical and empirical studies have searched for such a range of Ne/N. Theoretical studies have explored the plausible range of Ne/N through analysis of a reparameterized version of Hill's (1972) expression for Ne (Nunney 1991, 1993, 1996). This reparameterization provides several advantages. Ne is expressed in parameters that are biologically interpretable, and for which typical ranges are known. In addition, the parameters can be estimated from data commonly available from single-season studies of real populations (Nunney and Elam 1994). Through thorough numerical exploration of the parameter space, these studies led to the conclusion that Ne/N is usually close to 0.5 and only rarely outside the range 0.250.75 (Nunney 1991, 1993, 1996; hereafter, referred to as the theoretical expectation.) In contrast with this theoretical expectation, a review of 192 empirical estimates (based on a variety of demographic and genetic methods) revealed that Ne/N was usually less than 0.5 (Frankham 1995; hereafter, referred to as empirical estimates.) In fact, approximately one-third of the Ne/N estimates were less than 0.25, and a subset of these estimates (37 from animal taxa) accounting for all factors that influence Ne had an average Ne/N of 0.15 (median = 0.08). By contrast, a subset of estimates (27 from animal taxa) accounting for all factors except FPS had an average Ne/N of 0.38 (median = 0.38). The discrepancy between theoretical expectation and empirical estimates may thus be largely attributable to the fact that the theoretical expectation is based on the assumption of constant N. The theoretical expectation may provide a reasonable estimate of the short-term Ne/N, but the longerterm ratio may often be less than 0.25, owing to the effect of FPS. A long-term estimate of Ne that accounts for FPS is obtained by transforming a series of short-term effective sizes (Wright 1938; see also Crow and Kimura 1970; Lande and Barrowclough 1987):