Genetic drift, the chance loss of genetic variation due to small or finite population size, can be the result of continuous small or finite population size, bottlenecks, or founder effects. For all of these situations, there may be sex differences in genetic drift due to differences in the female and male effective population sizes, *N*_{ef} and *N*_{em}. In addition, the impact of mutation, recombination, selection, and gene flow in finite populations are often given as the product of the effective population size and the parameters for these factors. Assuming sex-specific values for all these factors, the general differences between the sexes can be given for mutation as *N*_{ef}u_{f} and *N*_{em}u_{m}, for recombination as *N*_{ef}c_{f} and *N*_{em}c_{m}, for selection as *N*_{ef}s_{f} and *N*_{em}s_{m}, and for gene flow as *N*_{ef}m_{f} and *N*_{em}m_{m}. For example, sex-specific impacts of mutation, recombination, selection, or gene flow may be increased or decreased by sex differences in the effective population size.

#### POPULATION GENETIC IMPLICATIONS

Genetic drift resulting from finite population size is recognized as an important factor in the evolution of small populations and for large, finite populations over evolutionary time for neutral variants. The expected extent of genetic drift is inversely related to the effective population size, a concept thoroughly reviewed by Cabarello (1994). Here we introduce the general differences expected for genes with different types of inheritance and sex differences in effective population size. Considering different numbers of the two sexes, the effective population size for an autosomal gene is

- ((15a))

where *N*_{f} and *N*_{m} are the number of females and males in the population, and *N*_{f}+*N*_{m}=*N*, the total number of adults in the population. Frequently, the number of males contributing progeny may be smaller than the number of females because some males mate more than once. When one male mates with all the females in a population, *N*_{e.A} is a maximum of only 4. In other words, because each sex must contribute half the genes to the progeny, restricting the number of breeding males (or females) can greatly reduce the effective population size and increase genetic drift.

Nomura (2002) showed that for harem polygamy, assuming that all the females mate with one male (no variance in female mating success) and that the males have a Poisson distribution in mating success, the effective population size becomes

- ((15b))

The ratio of equation (15a) to (15b) is *N*_{m}/*N*+1 so that the ratio of these effective sizes is a decreasing function of the proportion of males. For example, if *N*_{m}/*N*= 0.2, then harem polygamy would reduce the effective size by 17%. This impact is further increased if the variance in male-mating success is greater than the variance given the Poisson distribution (Nomura 2002) (see also Nunney 1993).

It has often been assumed that in polygynous vertebrates, where one male controls a female group, such as in bighorn sheep or elephant seals, that he is the father of all the progeny (harem polygamy). However, the observed breeding behavior often is not supported genetically. For example, behavioral observations in the southern elephant seal estimated that the sex ratio was about 40 females per male but the effective sex ratio from genetic data was estimated to be only 4 or 5 females per male (Slade et al. 1998). The difference in these estimates appears to result from both an overestimate of breeding success in the behavioral estimate and the short time that a male is dominant (1 or 2 years).

For an X-linked gene (or one in a haplo–diploid organism), because females contain two-thirds and males one-third of the alleles, the effective population size is

- (16)

(Wright 1931; Cabarello 1995). If there are equal numbers of females and males (*N*_{f}=*N*_{m}= 1/2*N*), then *N*_{e.X}= 3/4*N* because the males are haploid. In other words, the effective population size for an X-linked gene is generally expected to be 75% that of an autosomal gene in the same species. When there is only one breeding male for an X-linked gene, then the maximum *N*_{e.X}= 4.5, somewhat larger than for an autosomal gene. In some social Hymenoptera, there may be only one breeding female or queen so that the effective population size is a maximum of only 2.25. When there is harem polygamy, Nomura (2002) also showed that the effective size for an X-linked gene is reduced by variance in male-mating success.

The effective population size is a function of the variance in progeny number and the effective population size is

- (17)

where and *V*_{k} are the mean and variance in the number of progeny. Using sex-specific values of and *V*_{k} for females and males, then *N*_{e} values for females (*N*_{ef}) and males (*N*_{em}) can be calculated (Lande and Barrowclough 1987; Engen et al. 2007). The overall effective population size for an autosomal or X-linked gene can then be calculated by using *N*_{ef} and *N*_{em} in the equations above as given in Table 2.

The effect of different ratios of female and male effective population size on the relative effective population size for genes on different chromosomes is given in Figure 4. Notice that for autosomal genes when the ratio of the input of either sex is low, the overall effect is largest, unlike the additive effect for mutation, recombination, or gene flow. To determine when the effective population size for autosomal and X-linked genes is the same, we can set these equations equal to each other and find that when *N*_{em}=*N*_{ef}/7, *N*_{e.A}=*N*_{e.X}. Or, whenever *N*_{em} < *N*_{ef}/7, the effective population size for an X-linked gene is slightly larger than for an autosomal gene in the same population.

For genes that are inherited only through one sex such as mtDNA, cpDNA, and the Y chromosome, the effective population size for the appropriate sex determines the effect of genetic drift on those genes. In all of these cases, if there is an equal sex ratio, and random progeny production for both sexes, the expected effective population size is *N*_{e}/4 because these genes are transmitted in only one sex and they are haploid. Without these assumptions and because mtDNA and cpDNA are generally maternally inherited, their effective sizes are

- ((18a))

If the number of males breeding or the male effective population size is small, then the effective size for such a gene may actually be greater than for an autosomal gene in the same population (Fig. 4). For example, if *N*_{m} is 1, then *N*_{e} for an autosomal gene is a maximum of 4 but because *N*_{ef} can be much larger than 8, *N*_{e} for an organellar gene can be larger than for an autosomal gene. Interestingly, *N*_{e.mt}=*N*_{e.A}=*N*_{e.X} when *N*_{em}=*N*_{ef}/7, that is, when *N*_{em}/(*N*_{em}+*N*_{ef}) = 0.125, and the effective population sizes for autosomal, X-linked, and mtDNA genes are the same.

The Y chromosome effective population size, and for mtDNA when it is inherited paternally as in conifers or mussels, is

- ((18b))

In organisms with a low male effective size, the effective size for such a gene could be much smaller than that of an autosomal gene in the same organism. Only if *N*_{em}/(*N*_{em}+*N*_{ef}) > 0.875 or > 0.8 is it larger for an autosomal or X-linked gene, respectively (Fig. 4). Wade and Shuster (2004) suggest that the variance in fitness may be much larger in males than in females (higher *V*_{k}) because of sexual selection. Therefore, *N*_{em} may be much smaller than *N*_{ef} and consequently *N*_{e.Y} may be much smaller than *N*_{e.mt}.

Using simulations, Storz et al. (2001) estimated the impact of life-history variation in a baboon population and a tribal human population on the effective population size for genes with different inheritance. Although *N*_{e}/*N* was 0.33 and 0.79 for baboon and human populations, due primarily to variance in male fitness, X, Y, and mtDNA effective population sizes were not different from the expected ratios with autosomal *N*_{e} (0.75, 0.25, and 0.25) assuming Poisson variance in reproduction. These results are consistent with the theoretical conclusion of Charlesworth (2001) that extreme differences between the sexes in survival and fecundity are necessary to cause major departures from these expected ratios.

With the availability of genetic markers on chromosomes with different inheritance, in recent years there have been a number of studies examining the effective population and the amount and pattern of genetic variation (Hellborg and Ellegren 2004; Sundström et al. 2004; Balaresque et al. 2006; Eriksson et al. 2006; Lawson Handley et al. 2006; Baines and Harr 2007). In many such studies, it is difficult to disentangle the additional impact of differences between the markers in selective sweeps, background selection, and other sex-specific processes (Betancourt et al. 2004). Wilder et al. (2004b) examined variation in human mtDNA and nonrecombining Y chromosome genes and estimated that the time to most recent common ancestor for mtDNA is twice as old as for the Y. As a result, they concluded that this difference appears to result in an approximate twofold larger effective population size for females than for males.