The age-specific force of natural selection and biodemographic walls of death

Abstract

celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full nonlinear demographic model for mutation accumulation recently developed by Evans, Steinsaltz, and Wachter, we find surprising differences. Nonlinear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine predictions in other cases, and allow walls of death at ages before the end of reproduction. Haldane's principle for genetic load has an exact but unfamiliar generalization.biodemography | hazard functions | senescence T he best-known formula at the intersection of genetics and demography is doubtless W. D. Hamilton's "age-specific force of natural selection," the starting point for the models in ref. 1 applied in this paper. Hamilton (2, 3) differentiated a measure of fitness, Lotka's intrinsic rate of natural increase, with respect to an increment to age-specific mortality at an age a. Thus, he obtained a linear approximation for loss in fitness due to any deleterious mutations that raised mortality at an age a. The greater the loss in fitness, the faster should mutant alleles be selected out of a population, and the fewer should be found at equilibrium as recurring mutations balance natural selection.By this route, Sir Peter Medawar's concept of mutation accumulation as an evolutionary reason for senescence takes on mathematical form. As in refs. 4-6, richly developed in ref. 7, the idea involves genetic load produced by large numbers of mildly deleterious mutations occurring at widely separated loci, each with some small age-specific effect on vital schedules.Hamilton's work has been assessed and extended by Baudisch (8). Sophisticated genetic models of mutation-selection balance are available (9). Demographers mainly put up with less sophisticated models of the genome in return for more refined treatments of agespecific structure, as we do here. Age-specific predictions for vital schedules may be robust to details of genetic specification, in line with a principle of Haldane (10), which equates the population loss in fitness from genetic load to the total mutation rate, independent of the form of action of mutations.Current interest has been stimulated by the expansion of biodemography, reviewed in refs. 11-14, and by the appreciation of two widely occurring cross-species commonalities in graphs of mortality rates as functions of age: exponential increase at adult ages (the "Gompertz-Makeham" mortality pattern) and plateaulike shapes at older ages. Working with an appealingly simple specification, Brian Charlesworth (15) gave an elegant demonstration that Gompertz-Makeham mortality could be predicted exactly by the Hamilton-based linear approximate model. He also proposed an optional fix that would lead to plateaus at extreme ages. In Charlesworth's setting, a "wall of death" with infinite mortality rates and zero survivorship ...

Evolution of maternal effect senescence

“…This is likely an overly simplistic model of reality, but it is a sensible place to start to understand the evolution of IGE senescence. We may infer from DGE senescence models that positive genetic correlations across ages-of-effects will lower rates of aging (3,57), and negative genetic correlations will intensify these (4,44). Clearly, an understanding of the genetic architecture underpinning age-dependent variation in maternally influenced traits in natural populations will be essential for predicting senescence trajectories.…”

Mutations and the age pattern of death

“…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 Fig.…”

“…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.…”

“…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).…”

“…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.…”