Mutations and the age pattern of death

The age pattern of death is what biologists and demographers think about when they consider mortality (or immortality). As everyone knows, human lives on average have nearly doubled in length over the past century (1), yet human mortality still increases exponentially fast (Fig. 1) as people age past 40. Not surprisingly, the health of older people is now a major concern (2), often focused on proximate factors, biological, economic and social, that affect health (3–5). However, a deeper question is, how did evolution shape the age pattern of mortality? In particular, is the rise in old-age mortality driven by an increase in the number and frequency of deleterious (i.e., bad for you) alleles? In PNAS, Wachter et al. (6) show how to compute the equilibrium distribution of deleterious mutant alleles in a large, age-structured, and genetically heterogeneous population. Their analysis is a significant advance over previous work on this question (7, 8).

Fig. 1.

The logarithm of age-specific probabilities of death, for single years of age, for the US population (both sexes) together, plotted against age. Note the exponential (straight line) rise after age about 40, and the slowing-down, suggesting a plateau, at very late ages. The high infant mortality remains a subject of study whereas the late-age pattern is thought to be the result of the accumulation of deleterious mutations. Data are from the Human Mortality Database (www.mortality.org).

The problem that Wachter et al. (6) consider is a general one in population genetics. In any population, every individual experiences a continuing flux of mutations at a small rate, almost all deleterious in effect. The carrier of a deleterious mutant allele arising at one gene has a selective disadvantage and is eventually swept away. Recurrent mutation can repeatedly introduce a mutant allele so that, in the population, the frequency of the mutant allele is kept above zero by the balance between selection and mutation. There are other processes (9) by which alleles that sometimes (e.g., in some combinations) confer a selective disadvantage can be maintained in a population; this is not always a bad thing because evolution requires variation. However, any such process means, of course, that the population contains genotypes that are less fit than others, and so on the average fitness is not as high as it could be. The reduction in average fitness is called the genetic load (9).

A single deleterious mutant allele can be held in a balance between mutation that injects new copies and selection that removes old ones. The equilibrium frequency depends on the fitness loss experienced by carriers of the mutation, and that loss depends on how the mutation affects individuals. For most plants and animals, fitness depends on the age pattern of reproduction and survival, and fitness is measured by the long-run growth rate or, for a population held at some limits, by the net reproductive rate. Hamilton (7) made a major breakthrough by answering the question: what is the loss in fitness produced by a mutation that has age-specific effect, i.e., reduces survival or increases fertility at just one age? One of his main conclusions was that such reductions had declining effect with age. Charlesworth (8) started from these results to compute the equilibrium distribution of mutations at each age. He assumed linearity of selection—the selective disadvantage of three copies of a mutation is three times that of a single copy—and predicted a rise in the frequency of deleterious mutations with age, as well as an eventual leveling-off that can result if every mutation affects many ages, not just one. His deservedly influential results provide an evolutionary reason for the pattern of old-age mortality (Fig. 1). This result is satisfying on the face of it but raises at least two questions that need answering.

Is it reasonable to assume linear selection when, for example, we compare an individual carrying say three deleterious alleles (which need not be the same) to another with just one? And, because mutations strike at random, shouldn’t we analyze a heterogeneous population in which individuals differ by the number and kind of mutant alleles they carry? This is where Wachter et al. (6) come in. They measure selective cost for a genotype carrying some set of deleterious mutant alleles by (i) adding the age-specific changes produced by those alleles on fertility and/or mortality, just as in refs. 7 and 8, but then (ii) computing the effect of this cumulative change on the net reproductive rate of the mutant, which will in general be nonlinear in the number and kind of mutations. Next they start, as is reasonable, with a Poisson distribution for the arrival of deleterious mutations and show that the heterogeneous population that you end up with, at equilibrium, is also described by a Poisson distribution over the number and kind of mutant alleles. This is a remarkable mathematical result; even better, it comes with a computable expression for the equilibrium. That equilibrium in turn tells us what the population’s equilibrium age pattern of mortality and reproduction should be.

So where does this get us? The first thing we can do is to turn assumptions, or better yet, measurements, of the rate and distribution of mutations into predicted equilibrium age patterns of mortality. As shown by examples (6), mutations can indeed generate patterns of rising mortality consistent with observations (as in Fig. 1). However, these results also give sharp form to a deeper existence question. That question is related to what I call the “stone tablet” aspect of the Hamilton theory: we always begin by assuming that we are given, a priori, the age pattern of reproduction, or at least the last age at which reproduction is possible. Then deleterious mutations must be most frequent at ages that are late in the sense of being close to this last age of reproduction. In a heterogeneous population, the average realized fertility at late ages must then be decreased; this decline in turn might weaken selection against new deleterious mutations, leading to a further fall in fertility, and so on. Can such declines lead to a progressive chipping away of the original

Wachter et al. show how to compute the equilibrium distribution of deleterious mutant alleles in a large, age-structured, and genetically heterogeneous population.

fertility pattern so that the age of last reproduction falls slowly but inexorably, until we reach a bacterial limit (9) of short reproductive lives? Wachter et al. (6) show that such cumulative change is indeed possible and that an age-structured life history can unravel under the onslaught of deleterious mutations.

These developments are a welcome, indeed essential, step forward in the theory of life history evolution. The tools that are now available (6) suggest ways of tackling not just the problem of predicting age patterns of mortality but of analyzing the more general question of how mortality and fertility coevolve (10–12). In particular, we must consider how mutations of positive effect, even rarer than deleterious ones, are distributed. The constructive role of positive mutations (which may act in combinations, and whose effects may be constrained by tradeoffs and environments) has generally been studied in isolation from the destructive effects of deleterious mutations, but now a joint analysis may be feasible.