Proc. Natl. Acad. Sci. USA Vol. 93, pp. 6140-6145, June 1996 Genetics Age-specific inbreeding depression and components of genetic variance in relation to the evolution of senescence (mutation accumulation/antagonistic pleiotropy/aging) BRIAN CHARLESWORTH* AND KIMBERLY A. HUGHESt Department of Ecology and Evolution, University of Chicago, Chicago, IL 60637 Communicated by James F. Crow, University of Wisconsin, Madison, WI, February 26, 1996 (received for review October 25, 1995) ABSTRACT Two major theories of the evolution of senes- a population even if they have adverse affects on late perfor- cence (mutation accumulation and antagonistic pleiotropy) mance (3, 5, 7, 8, 10, 11). make different predictions about the relationships between Although there is widespread agreement that the general age, inbreeding effects, and the magnitude of genetic variance evolutionary theory of senescence provides a powerful tool for components of life-history components. We show that, under interpreting the genetics and comparative biology of aging, the mutation accumulation, inbreeding decline and three major relative contributions of mutation accumulation and antago- components of genetic variance are expected to increase with nistic pleiotropy to senescence have not been elucidated (2, 3, age in randomly mating populations. Under the simplest 7, 12). The two theories are clearly not mutually exclusive, but version ofthe antagonistic pleiotropy model, no changes in the it is legitimate to ask whether there is evidence for or against severity of inbreeding decline, dominance variance, or the either of them. Recent advances in the genetics of Alzheimer genetic variance of chromosomal homozygotes are expected, disease suggest that both mechanisms may contribute to this but additive genetic variance may increase with age. Age- aspect of senescence in humans (13). In Drosophila, there is specific survival rates and mating success were measured on evidence that both supports and casts doubt on the tradeoffs virgin males, using lines extracted from a population of postulated by the antagonistic pleiotropy model (3, 14, 15). Drosophila melanogaster. For both traits, inbreeding decline There is also conflicting evidence on the importance of and several components of genetic variance increase with age. mutation accumulation (16-20). In this paper, we show that The results are consistent with the mutation accumulation inbreeding depression is expected to increase with age under model, but can only be explained by antagonistic pleiotropy if the mutation accumulation model but not under antagonistic there is a general tendency for an increase with age in the size pleiotropy (unless the effects of segregating alleles themselves of allelic effects on these life-history traits. increase with age). We present data on inbreeding effects on survival and male mating success in Drosophila melanogaster Senescence is an almost universal feature of the life histories that are consistent with this prediction of the mutation accu- of species in which a clear distinction can be made between mulation model. We also provide theoretical results on the parent and offspring (1-3). Senescent decline in survival and expected behavior of components of genetic variance under reproductive performance appears to result from the deteri- the two alternative models and compare the models with the oration of many different biological parameters with age, and available data. Overall, the results are consistent with a role for it seems unlikely that there is a single proximate cause of this mutation accumulation in the evolution of senescence, but deterioration (1-3). The standard evolutionary theory of aging antagonistic pleiotropy is not ruled out. asserts that the ultimate cause of senescence is the decline with age in the net effect on Darwinian fitness of age-specific THEORETICAL ANALYSIS changes in survival or reproductive output (4-6). This means that, other things being equal, natural selection places a In this section, we will develop some simple models of muta- greater relative weight on changes in early survival or repro- tion accumulation and antagonistic pleiotropy and use them to duction than on changes at later ages. Provided that the predict the age-related patterns of inbreeding depression and appropriate genetic variability is available, this will lead to the genetic variance components. A randomly mating population evolution of a life history in which mortality increases and at equilibrium under mutation-selection balance (mutation reproductive performance declines with age (4-8). accumulation) or heterozygote advantage (antagonistic pleiot- There are two major models of the paths by which this ropy) will be assumed. age-specific selection pressure can cause the evolution of Inbreeding Effects Under Mutation Accumulation. Con- senescence. The mutation accumulation theory of senescence sider an age-specific trait z-e.g., survival from age x to x + 1 postulates that there are numerous loci subject to mutation to in a discrete age-class model. Assume for simplicity that deleterious alleles, whose effects on survival or other compo- mutations at several loci affect only this trait and have no effect nents of fitness are restricted to narrow bands of ages (3, 4, on performance at any other age. Let the mutation rate of the 7-9). The equilibrium frequencies of such deleterious alleles wild-type allele at the ith locus that affects z be ui and the will be higher the later in life in which they act (8) because of homozygous effect of a mutation at this locus be zi (measured the decline in the of net fitness to in survival as the reduction in z relative to the value for wild-type). The sensitivity changes in z or with This will cause both a decline in sensitivity of fitness to a change trait is S(z), such that the reproduction age (6). reduction in fitness due to a mutation at locus i mean performance with age (senescence) and a corresponding homozygous increase in variance The alternative in- is S(z)Szi. S(z) is the partial derivative of net fitness with respect genetic (7, 9). path to z to the value for volves "antagonistic pleiotropy," according to which genes that z, setting equal wild-type homozygotes (8). increase early performance are likely to become established in *To whom reprint requests should be addressed at: Department of Ecology and Evolution, University of Chicago, 1101 East 57th Street, The publication costs of this article were defrayed in part by page charge Chicago, IL 60637. e-mail: [email protected]. payment. This article must therefore be hereby marked "advertisement" in tPresent address: Department of Life Sciences, Arizona State Uni- accordance with 18 U.S.C. §1734 solely to indicate this fact. versity West, Phoenix, AZ 85069. 6140 Downloaded by guest on September 26, 2021 Genetics: Charlesworth and Hughes Proc. Natl. Acad. Sci. USA 93 (1996) 6141 Under most circumstances, S(z) is a decreasing function of age the value of ln(zo/zi)for F = 1, which is sometimes referred to (6). It will thus be highest for traits expressed early in the as the inbreeding load (24). The use of balancer chromosomes reproductive portion of the life history and lowest for traits in Drosophila enables direct measurements of this for the expressed late in life (it is zero for postreproductive traits). We effects of single chromosomes on fitness components (25). We assume that mutant alleles are partially recessive, such that the have reduction in trait value in heterozygotes is hi&zi, where hi is the dominance coefficient and 0 < hi < 0.5. There is good evidence 2 1S from to this last - -1} [3b] Drosophila support assumption (21, 22). a(z)S(z) i i2hi Under these conditions, the equilibrium allele frequency at the ith locus is qi - ui/S(z)hi&zi (8). We assume that mutant Provided that there are no systematic differences in mutation alleles are always rare, so that qi << 1. Because the population rate or dominance coefficients among genes affecting different mean is then mainly affected by the heterozygous carriers of ages, these results shows that inbreeding depression and the mutations, the mean trait value relative to the value for inbreeding load should increase as S(z) declines with age. wild-type homozygotes is reduced below one by approximately Genetic Variance Components Under Mutation Accumula- 2qihikii = 2ui/S(z). With multiplicative interactions between tion. The above model can also be used to predict variance alleles at different loci, the mean trait value for the equilibrium components. Its application to the standard formula for ad- population is ditive genetic variance (26) implies that the additive genetic 2 variance, VA, in a trait z contributed by a single locus is zo X exp - S( Ui [1] 2qi(hizi)2 (27). If the genetic variance from all sources is small, as is usually the case, the multiplicative model can be well approximated by an additive one. Substituting the equilibrium This result shows that, as expected intuitively, age-specific gene frequency under mutation selection balance into this mutational effects lead to senescent decline in a randomly expression and summing over loci, yields the expression in mating population, because S(z) declines with age (7, 9). If Table 1 for VA, scaled relative to the outbred mean value. inbreeding leads to the production of individuals with inbreed- Similar expressions for the dominance variance, VD (26), and ing coefficient F, without any change in allele frequencies, the the genetic variance among completely inbred lines, VG (22), ith locus causes a reduction in mean trait value for the inbred are also given in Table 1. It will be seen that the variance population below that for the wild-type homozygote of ap- components other than VD are inversely proportional to S(z), proximately {2(1 - F)hi + F}qi&i (23). With multiplicative as is the inbreeding load, whereas VD is inversely proportional effects, the net trait value for the inbreds is then to S(z)2.