The Effect of Nonindependent Mate Pairing on the Effective Population Size

The effective population size (N_e) quantifies the effectiveness of genetic drift in finite populations. When generations overlap, theoretical expectations for N_e typically assume that the sampling of offspring genotypes from a given individual is independent among successive breeding events, even though this is not true in many species, including humans. To explore the effects on N_e of nonindependent mate pairing across breeding events, we simulated the genetic drift of mitochondrial DNA, autosomal DNA, and sex chromosome DNA under three mating systems. Nonindependent mate pairing across breeding seasons has no effect when all adults mate pair for life, a small or moderate effect when females reuse stored sperm, and a large effect when there is intense male–male competition for reproduction in a harem social system. If adult females reproduce at a constant rate irrespective of the type of mate pairing, the general effect of nonindependent mate pairing is to decrease N_e for paternally inherited components of the genome. These findings have significant implications for the relative N_e values of different genomic regions, and hence for the expected levels of DNA sequence diversity in these regions.THE effective population size (N_e) is a fundamental parameter of population genetics, which quantifies the effect of genetic drift, the stochastic change in allele frequencies over time in a population of finite size (Wright 1931). The magnitude of N_e affects both the level of genetic variability within a population and the efficiency with which populations retain mildly beneficial mutations and purge mildly deleterious ones. This influences a myriad of genetic phenomena, such as the level of DNA sequence polymorphism, the rate of substitution of nonsynonymous and functional noncoding nucleotide positions, the abundance of transposable elements, levels of variation, and the rate of evolution of gene expression, the persistence of duplicate genes, and genome size and organization (Lynch 2007; Charlesworth 2009). There are a variety of definitions of N_e; here we use the definition in terms of the mean coalescence time of a pair of neutral alleles, which is given by 2N_e (Charlesworth 2009). This definition has the useful feature that the expected pairwise nucleotide site diversity under the widely used infinite sites model is equal to 4N_eμ, where μ is the neutral mutation rate (Kimura 1971).As a result of differences in their ploidy level and mode of inheritance, autosomal DNA (aDNA), the X chromosome (xDNA), the Y chromosome (yDNA), and maternally transmitted organelle DNA such as mitochondrial DNA (mtDNA) generally have a different N_e values. Under certain conditions, such as constant population size, discrete generations, a Poisson distribution of reproductive success, and a sex ratio equal to one, the relative N_e values of these genomic regions (N_e-a, N_e-x, N_e-mt, and N_e-y) are expected to be 4:3:1:1 (Charlesworth 2009). This is because aDNA is biparentally inherited and diploid; xDNA is biparentally inherited, diploid in females, and haploid in males (with female heterogamety, the reverse applies to the Z chromosome), and yDNA (the W chromosome, with female heterogamety) and mtDNA are both effectively uniparentally inherited and haploid in most species.However, several characteristics of natural populations, such as unequal numbers of males and females and nonrandom variation in reproductive success, can affect the value of N_e, even for populations with discrete generations (reviewed in Caballero 1994; Hedrick 2007; Charlesworth 2009). In addition, natural selection at sites linked to neutral markers also has the potential to increase N_e (under balancing selection) (Charlesworth 2006) or to decrease N_e (with background selection or selective sweeps) (Hudson and Kaplan 1988; Charlesworth et al. 1993). Because the nature of natural selection varies in different genomic regions, especially in relation to the rate of recombination, N_e may also vary among unlinked regions with the same ploidy and mode of inheritance, for example, different portions of an autosomal chromosome (Gossmann et al. 2011). In natural populations, these factors can skew the relative N_e values away from the 4:3:1:1 expectation. Even when the effects of natural selection and “nonideal” demography are ignored, the 4:3:1:1 relation still has a large variance when applied to individual loci (Hudson and Turelli 2003).When generations overlap, an additional source of possible deviations from these idealized relations arises from variation among individuals in survival and reproductive success among breeding seasons (Felsenstein 1971; Hill 1972, 1979; Johnson 1977) and from sex differences in demographic parameters and stochastic changes in population size (Engen et al. 2007). In contrast, the effect of a high variance in reproductive success caused by male–male competition is lessened when generations overlap for many breeding seasons (Nunney 1993; Charlesworth 2001). Conversely, overlapping generations with nonindependent mate pairing across breeding seasons could increase the variance in reproductive success. For example, in humans, paternity is correlated with paternal confidence in paternity (Anderson 2006), and married individuals tend to repeatedly produce offspring with each other more frequently than expected by chance. Nonindependent mate pairing among breeding seasons occurs in many other species as well—for example, long-term pair bonding in prairie voles (DeVries et al. 1995), harems in gorillas (Gatti et al. 2004), and sperm storage in fruit flies (Neubaum and Wolfner 1999).Current theoretical models that allow calculation of the effective population size with overlapping generations and age structure make several simplifying assumptions, notably constant sizes of each age class, sufficiently large numbers of individuals in each age class that second-order terms in their reciprocals can be neglected, and independent sampling of offspring genotypes from the same individual reproducing at different times (Hill 1972; Nunney 1991, 1993; Caballero 1994; Charlesworth 1994, 2001). The latter assumption in particular makes it difficult to provide accurate expressions for species such as humans and Drosophila, which reproduce nonindependently because of long-term pair bonds and sperm storage, respectively (Charlesworth 2001).The goal of this study is therefore to explore the consequences of nonindependence of reproductive events across time in different social systems and with different age structures, using simulations of genetic drift in two types of age-structured populations, under different scenarios of independent and nonindependent mate pairing among breeding events. We have explored how these scenarios affect the relative values of N_e-a, N_e-x, N_e-mt, and N_e-y using the infinite alleles model of mutation (Kimura and Crow 1964), with particular emphasis on comparisons of similar mating systems that differ in the extent of nonindependence among breeding events.