6 Toward an Evolutionary Demography

Michael R. Rose

Introduction

Our quantitative understanding of the actuarial features of human populations has been dominated by ad hoc models from the field of demography, from Benjamin Gompertz in 1825 to the present day (e.g., Finch, 1990; Easton, 1995). This situation has continued despite the parallel development of an evolutionary theory for life history, including aging, from the 1930s to the present (see Charlesworth, 1994). On the one hand, we have the ad hoc models of demography, and on the other we have the a priori models of evolutionary theory. An obvious goal, then, would be to seek a synthesis of these two fields, a synthesis here termed ''evolutionary demography."

Naturally, there is resistance to the wholesale introduction of evolutionary theory into research on demography and aging. It is often supposed that demographic and aging patterns are fixed species properties, analogous to chromosome number or breeding system. This definition removes the topic from the reach of normal evolutionary theory. A hardy perennial is that aging is somehow good for the species, a theory that underemployed physicists seem to rediscover every decade. One side effect of this theoretical confusion is the displacement of evolutionary and demographic theories of aging by hypotheses from the realm of molecular or cellular biology. It has been argued that because aging is due to free radicals, the evolutionary history of the organism is irrelevant. Likewise, limited cell replication in vitro or a hypothalamic clock may be offered as the ultimate determinant of aging patterns. Elsewhere, I have published a lengthy critique of this type of reasoning (Rose, 1991) and will not repeat it here. My conclusion, in



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6 Toward an Evolutionary Demography Michael R. Rose Introduction Our quantitative understanding of the actuarial features of human populations has been dominated by ad hoc models from the field of demography, from Benjamin Gompertz in 1825 to the present day (e.g., Finch, 1990; Easton, 1995). This situation has continued despite the parallel development of an evolutionary theory for life history, including aging, from the 1930s to the present (see Charlesworth, 1994). On the one hand, we have the ad hoc models of demography, and on the other we have the a priori models of evolutionary theory. An obvious goal, then, would be to seek a synthesis of these two fields, a synthesis here termed ''evolutionary demography." Naturally, there is resistance to the wholesale introduction of evolutionary theory into research on demography and aging. It is often supposed that demographic and aging patterns are fixed species properties, analogous to chromosome number or breeding system. This definition removes the topic from the reach of normal evolutionary theory. A hardy perennial is that aging is somehow good for the species, a theory that underemployed physicists seem to rediscover every decade. One side effect of this theoretical confusion is the displacement of evolutionary and demographic theories of aging by hypotheses from the realm of molecular or cellular biology. It has been argued that because aging is due to free radicals, the evolutionary history of the organism is irrelevant. Likewise, limited cell replication in vitro or a hypothalamic clock may be offered as the ultimate determinant of aging patterns. Elsewhere, I have published a lengthy critique of this type of reasoning (Rose, 1991) and will not repeat it here. My conclusion, in

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any case, is that the proper ground for building theories of demography, aging, life history, and the like is evolutionary theory. Basic Theory Of Evolutionary Demography The fundamental starting point for evolutionary analysis is an ecologically determined demography: particular age-specific survival probabilities and fecundities, varying also with time, organismal size, population density, and a range of other factors (Charlesworth, 1994). Frequently, however, factors other than age are neglected in the theory, and I will follow this practice for the sake of convenience and clarity. Some of the literature on the other characters (e.g., size) is discussed in Steams (1992) and Roff (1992). For the present purposes, however, evolutionary demography starts from a simplified evolutionary situation defined by a set of age-dependent survival probabilities, P(x) and fecundities, m(x). When density-dependence can be neglected (cf. Charlesworth, 1994), population growth rate is given by the largest real-valued root, r, of where l(x) = Πy=0 P(y) and x is age as well as the upper limit of multiplication. This ecological situation, in turn, determines the evolution of P(x) and m(x), where the equations for gene frequency change have terms weighted by for selection coefficients involving In P(a) and m(a), with genetic effects at age a, respectively (Hamilton, 1966; Charlesworth, 1980; Rose, 1985). The s and s functions play a scaling role. When the scaling functions are large, selection is more powerful, and conversely, when these values are small, selection is weak. The forms of the s and s' scaling functions reveal the most important features of evolutionary demography in its crudest form. The form of s(a) is such that it remains at 1.0 for ages below the start of reproduction. But for ages after the start of reproduction, s(a) falls with age until it approaches zero. In terms of selection equations, this makes allelic effects on early survival of large impact on the evolutionary outcome, but allelic effects on late survival have little or no impact. Except for populations declining rapidly to extinction, similar patterns apply for s'(a), which will usually be large at early ages and small at late ages. Put simply. this situation is summarized as "the force of natural selection tends to fall with adult age" (Medawar, 1952). This basic idea is hinted at in the classic writings of R.A. Fisher and J.B.S. Haldane and then broadly sketched by P.B. Medawar (e.g., 1952). However, it wasn't adequately developed mathematically until the work of Hamilton (1966) and Charlesworth (e.g., 1980), as outlined above. The most obvious corollary derivable from this situation is that components of fitness should deteriorate at later adult ages, due to the weakness of natural selection,

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and thus aging occurs (Rose, 1991). No decline in the force of natural selection acting on age-specific mortality is expected until the onset of reproduction in a cohort of same-aged organisms. Once at ages having reproductive individuals, the force of natural selection acting on survival begins to decline, as indicated by the equation for s(a). There are analogous results for selection acting on age-specific fecundity, although they do not necessarily take the same form (Hamilton, 1966; Charlesworth, 1994). Overall, this might be described as the "basic" or "general" evolutionary theory for demography, aging, life history, and the like. There are many important special cases that depend on adding particular assumptions to this theory, some of which are discussed below. The foregoing should not be taken as a complete presentation of the theory of selection on age-structured populations, for which the best summary remains that of Charlesworth (1994). Empirical Evidence Concerning the Force of Natural Selection Unlike many other global theories in population biology, the basic evolutionary theory of demography leads to some directly testable theoretical predications. It is categorically not the case that evolutionary theory provides a mere backdrop for reductionist research on the real "causes" of aging. Indeed, some of the most elegant and powerful experimental designs in life-history research are derivable from this basic evolutionary theory. Edney and Gill (1968) were among the first to point out that altering imposed demographic regimes in the laboratory should lead to corresponding shifts in the organism's demographic pattern. Wattiaux (1968a, b) inadvertently performed two tests of this kind in Drosophila, and Mertz (1975) performed some Tribolium experiments along these lines. But the most important work has used laboratory populations of Drosophila melanogaster since the late 1970s (Rose and Charlesworth, 1980; Luckinbill et al., 1984; Rose, 1984a; Luckinbill and Clare, 1985; Partridge and Fowler, 1992; Leroi et al., 1994; and Fukui et al., 1995). Most of the Drosophila selection experiments have taken a broadly similar form and can be described generically. Normal fruit fly culture involves the production of a cohort of eggs from adults of similar age, where these eggs are typically laid on fresh fly medium. The adults are then discarded, and the eggs become larvae, pupae, and then young adults as a same-aged cohort. Typically, at 25 °C, the young adults are used to lay eggs for the next generation about 2 weeks after they were eggs themselves. With demographic manipulation, the period between emergence from pupa and egg laying to start the next generation is stretched—often to 8 weeks or more. Note that this procedure does not require the denial of copulation or egg laying in general. But any such eggs are discarded before they can contribute to the next generation. The typical experiment, then, combines these regimes: (i) controls in which reproduction is early, typically at

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2 weeks, and later reproduction is denied; and (ii) selected lines in which reproduction is later, typically at 10 weeks, and early reproduction is denied. In terms of the force of natural selection, these two regimes define two rectangular patterns for s(x), one truncated at 2 weeks and one truncated at 10 weeks. It should also be emphasized that these experiments often involve replication of the selected and control lines, up to five of these lines for each treatment. When such lines are created from a common ancestral stock, it can take as little as 10 generations for the late reproduced lines to evolve significantly increased longevity. After 50 or more generations of late reproduction, these lines may have 60-80 percent greater mean longevity, compared to the controls, and maximum longevity may be increased more than that. The general conclusion from this work has been that the laboratory evolution of aging broadly follows the expectations of basic evolutionary theory: when the force of natural selection at later ages is artificially prolonged by denying early reproductive opportunities, evolution progressively postpones aging (e.g., Rose, 1984a; Luckinbill et al., 1984; Partridge and Fowler, 1992). The force of natural selection can also be returned to its initial pattern by the simple expedient of returning late-reproduced lines, or derivatives of them, to early reproduction. Evolution then returns the population to its ancestral demography, with longevity falling back to its original value over subsequent generations (Graves et al., 1992). Other characters also tend to return to their original values, sometimes after considerable delay, sometimes not (Service et al., 1988; Graves et al., 1992). In any case, this is yet another case where demography effectively determines evolutionary destiny. By the standards of evolutionary biology, there is now a wide spectrum of experimental results of this kind, where the force of natural selection determines the pattern of evolution, only some of which is reviewed in Rose (1991). Broadly, this is the well-corroborated core of evolutionary demography: as predicted by theory, experimentally imposed demography determines the subsequent evolution of demography by changing the age-specific forces of natural selection. Indeed, this is one of the best instances of the application of the experimental method within evolutionary biology, a field that normally has to rely on very indirect inferences. At the same time, these results are also the best warrant for the introduction of evolutionary ideas into biodemography, in that these experimental systems dramatically reveal the interplay between selection and demography. One exemplary field study also deserves mention. Austad (1993) has studied natural populations of opossums in Virginia, one on the continental land mass, the other on islands that have been separated from the mainland for thousands of years. Island populations are exposed to less natural predation and suffer lower adult mortality rates, compared to mainland populations. Evolutionary theory predicts that the island populations should show slower aging. Austad's data corroborate this expectation: island populations show improved adult survivor-

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ship and later fertility, as well as ameliorated pathophysiology. In effect, the Virginia opossums have been a reasonable "natural experiment," like those in the laboratory with Drosophila. Theoretical Population Genetics Of Life-History Evolution But the force of natural selection does not entirely determine the pattern of demographic evolution. An additional determinant is the nature of the genetic mechanisms that affect particular life-history characters. These genetic mechanisms can be grouped under two broad headings: nonpleiotropic genetic effects and pleiotropic genetic effects. I discuss each further in turn. The most elegant possibility for the genetic mechanisms of demographic evolution is for each age-specific life-history character to evolve on its own, with the alleles that affect it lacking in effects on any other such character. It should be noted that this is a severe assumption, which is being offered here primarily for its simplicity. In particular, I do not wish to convey the impression that I think that this is the normal evolutionary situation where aging is concerned. At the same time, this severe constraint on allele action makes the mathematical specification of the evolutionary dynamics of life history, demography, etc. extremely elegant. Essentially, the entire evolutionary process reduces to two components: age-specific mutation and age-specific selection. In particular, because few beneficial alleles will be segregating at high frequencies at any one time, the evolutionary dynamics become mutation-selection balance, where there would typically be one favored allele and one or more deleterious alleles. For simplicity, the favored and deleterious alleles can be grouped into two allelic classes, and the frequency of the deleterious allele, when it is of minor effect and not fully recessive, can be approximated as where u is mutation rate from beneficial to deleterious alleles and the ij subscripts refer to genotypes having alleles i and j at the locus in question (Charlesworth, 1994). The beneficial allele is indicated by the numeral 1, and the deleterious allele is indicated by 2. Note that since the demography of the population will be determined largely by the homozygote of the fitter allele, the scaling function is specified by that demography. As discussed above, the scaling function is going to fall with age after the onset of reproduction. And because the scaling function is in the denominator of the allele-frequency formula, the frequency of deleterious alleles will theoretically increase enormously at later ages, producing a deterioration in survival probability. At early ages, of course, selection mutation should keep the frequency of deleterious alleles low, and thus age-specific survival would be high. An additional expectation, with this population genetic mechanism, is that the additive genetic variance for life-history characters should

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increase substantially at later ages, subject to comparability in the number of loci affecting each age class, as well as showing roughly uniform mutation rates over age classes and similar magnitude effects of the individual alleles over age classes. Of course, if these ceteris paribus conditions are violated, the additive genetic variance may not increase with age. But that is a typical caveat for population genetics theory. Essentially all other possible population mechanisms fall under the pleiotropic heading. When pleiotropic effects are in the same direction, such that one allele is beneficial for all affected life-history characters, then evolution is somewhat analogous to that in the case with nonpleiotropy. The balance between selection and mutation will be determined primarily by genetic effects at early ages, and the form of the equation determining allele frequency will be much more complicated, but qualitatively the results will be similar. One complication, however, might be a reduction in the genetic variance at later ages, if early, stronger, selective forces are determining allele-frequency equilibria. If allelic effects are opposed among life-history characters, then antagonistic pleiotropy arises. Under these conditions, selection will often be the dominating factor in the evolutionary outcome, favoring alleles that are beneficial at early ages but deleterious later (Williams, 1957; Charlesworth, 1980; Rose, 1985). Overall, both mutation-selection balance and pleiotropy can act so that aging evolves. They can also maintain genetic variability for demographic characters. However, these two mechanisms have different implications for the nature of that genetic variability. With mutation-selection balance, genetic variance should increase with age (Charlesworth, 1990, 1994), all other things being equal, while with pleiotropy it may or may not. Antagonistic-pleiotropy models also require that there be antagonistic genetic effects between some life-history characters, which may (Rose, 1985) or may not (Houle, 1991) be manifest as negative genetic correlations between some life-history characters. Fortunately, these corollaries are testable in experimental systems. Experimental Population Genetics Of Life-History Evolution The first thing to be said about the experimental population genetics of life history is that additive genetic variation is maintained for a variety of demographic characters in a variety of species (Rose, 1991; Roff, 1992). This is a corollary of both of the theoretical population genetic mechanisms described above. Beyond this point most of our experimental information comes from Drosophila. In that genus, at least, there are some cases in which genetic variances increase with age (e.g., Hughes and Charlesworth, 1994), and other cases where it does not (Rose and Charlesworth, 1981; Promislow et al., 1996). There are some cases where negative genetic correlations between life-history characters have been inferred (Rose and Charlesworth, 1981: Rose, 1984a: Luckinbill et

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al., 1984; Luckinbill and Clare, 1985) and other cases where they have not been (Partridge and Fowler, 1992). Still other studies find evidence both for and against antagonistic pleiotropy, as well as for and against mutation accumulation (Service et al., 1988; Leroi et al., 1994; Promislow et al., 1996; Tatar et al., 1996). The question is, then, how these results reflect on the validity of the two mechanisms of demographic evolution. Many of the aforementioned studies have been plagued by artifacts. Indeed, it may be that almost all experiments of this kind are afflicted to at least some degree by problems like inbreeding depression, inadequate replication, genotype-by-environment interaction, and so on (Rose and Service, 1985). Nonetheless, it is sometimes possible for further experimentation to sort out many of these problems (e.g., Rose, 1984b; Service and Rose, 1985; Leroi et al., 1994; Chippindale et al., 1994). Another point to make is that the experimental evidence can't plausibly be viewed as an either-or competition between mutation and pleiotropy models. There is some empirical support for both, some of it coming from the same experiments (e.g., Service et al., 1988; Tatar et al., 1996). Therefore, the only balanced point of view is that both of these genetic mechanisms are somewhat supported. They may both be involved in the evolution of demography, but neither is necessarily involved. Either is, in any case, sufficient for the evolution of demography to be dominated by the force of natural selection. Gompertz Models: Phenomenological Theory From age 15 years or so, the rate of mortality accelerates exponentially in long-industrialized human populations, and this has been a commonplace of both demography and gerontology (e.g., Comfort, 1964). The Gompertz equation attempts to summarize this pattern using what amounts to a linear regression of the logarithm of the mortality rate (µ) on age, x, where a gives the slope of that regression and α is the initial rate of mortality. It has been argued that this ad hoc demographic model is key to understanding aging (e.g., Finch et al., 1990; Finch, 1990), and it certainly has much to recommend it, particularly in comparison with alternative indices, like mean or maximum life span, when the data are collected under dubious conditions. My colleagues at the University of California, Irvine, and I have recently explored the extent to which the Gompertz model can be used to predict accurately the demography of experimental Drosophila populations (Mueller et al., 1995; Nusbaum et al., 1996). We did so because we do not regard human data as a particularly good way to test any general population-level theory; there is too much complexity introduced by culture and history. We also have reservations concerning the uncritical use of field data. We began with considerable doubts

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about the robustness of the Gompertz model. However, when the model is fitted using maximum-likelihood or nonlinear-regression methods, as opposed to conventional numerical approaches, we find that Gompertz parameters can be used to predict the mortality patterns of experimental populations of Drosophila after just 20-30 percent of the deaths of an observed cohort. The fit of these predictions can achieve respectable levels of accuracy, placing such parameters as mean longevity and 95 percent mortality within tight 95 percent confidence intervals. In effect, once the two Gompertz parameters have been fit to the data, there is usually only a little residual pattern to be modeled in the age-specific mortality data. Moreover, there is a high degree of correlation between the a parameter of the Gompertz model and other measures of aging, like maximum life span (Nusbaum et al., 1996), over diverse replicated populations. Having started as skeptics, we became convinced of the practical value of the Gompertz model in uncomplicated demographic situations. (However, as will be discussed, we remain concerned about the model's failures.) Results like these, as well as those of many other investigators, show that the Gompertz model and its comparable first-order demographic equivalents (e.g., the Weibull model) are accurate representations of the demography of some experimental populations. In effect, Gompertz models are outstanding phenomenological models for some biodemographic situations. The Oldest Old However, this situation may break down in human populations at extremely advanced ages (Comfort, 1964; Finch, 1990; Gavrilov and Gavrilova, 1991; Vaupel, in this volume, among others). Among these "oldest old," the probability of dying may not increase with age. This phenomenon has recently been demonstrated dramatically in various diptera, as well (e.g., Carey et al., 1992: Curtsinger et al., 1992). This problem of the oldest-old survival rates clearly merits serious attention. In particular, it makes continued reliance on the Gompertz model uncertain. Somehow, demographic theory needs to be refashioned. Note, however, that the cases where the oldest old break from Gompertzian patterns may involve the latest-age classes only, when few individuals are still alive. For this reason, there is no necessary incongruence between the many cases in which the Gompertz model works to within reasonable limits of accuracy and the few cases where the model breaks down. Most cases where the model seems to work involve too few organisms to detect a late-life deviation from Gompertz expectations. In other words, the violations of the Gompertz model have usually arisen in unusual circumstances, in which the detailed data are either much more extensive or extensive and of very high quality. The analogy that suggests itself is that of relativistic mechanics, which is based on cases that are usually not important in physical systems, most obviously

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cases where velocities approach the speed of light or very high masses are involved. Normally, Newtonian theory "works." But we know now that this is because it is only a first-order approximation to the truth, which is better approached by relativistic mechanics. The strategy that Laurence D. Mueller and I have adopted is to look for a theory that can naturally, without forcing, generate phenomena like plateaus in mortality rates among the oldest old. This theory is thus the analog of relativistic mechanics in physics. We feel that we have taken the first significant steps toward developing such theory, but I do not have the opportunity to introduce this theory for evolutionary demography here. Abrams and Ludwig (1995) have recently published an optimality approach to the kind of the theory that Mueller and I have tried to develop using population genetics. As a population geneticist, I have long had grave reservations about the use of optimality models for biological situations that are not defined by "free choices," such as those of sex allocation (Charnov, 1982), for example, in which there seems little reason to doubt that an optimal phenotype can evolve. Life-history evolution, instead, involves material resources and genetic constraints that may entirely prevent the attainment of any optimal phenotype (cf. Gould and Lewontin, 1979), and it is at least arguable that the evolution of actual life histories does not proceed toward optimal outcomes (Rose et al., 1987). For example, is it likely that the later life history will evolve toward optimal values if the allelic variation that shapes it is subject to very weak natural selection or none at all, given recurrent mutation pressure? For these reasons, we have proceeded instead to develop a population genetics theory for demography. Conclusion Recent work on age-specific mortality rates strongly suggests that conventional demographic models are in need of repair. Rather than resorting to yet another ad hoc tuning up of the same mathematical tools, consider the alternative approach provided by the population genetics theory of age-structured populations. This theory has been well-characterized mathematically and has been extensively supported in experimental genetic systems, although neither theory nor experiment are complete or perfect. Results obtained from evolutionary theory offer the best prospects for the development of demographic models, in general. In this way, demography could leave its ad hoc traditions behind and join together with evolutionary biology to forge a much stronger theoretical foundation. While the Gompertz model is an excellent approximation to mortality rates for most individuals from some iteroparous populations, it appears inadequate for the description of even the qualitative pattern of the full life history of most organisms, granting that such full life histories are not usually adequately observed. Biodemography should now move on to the task of developing proper evolutionary foundations.

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Acknowledgments I am grateful to the other members of the National Research Council Biodemography of Aging group for their helpful comments. In particular, I thank C.E. Finch for his editorial advice. The aging research of the author has recently been supported by U.S. Public Health Service PO] Grant AG0-9970. References Abrams, P.A., and D. Ludwig 1995   Optimality theory, Gompertz' Law, and the disposable soma theory of senescence. Evolution 49:1055-1066. Austad, S.A. 1993   Retarded senescence in an insular population of Virginia opossums Didelphis virginiana. Journal of Zoology 229:695-708. Carey, J.R.. P. Liedo, D. Orozco. and J.W. Vaupel 1992   Slowing of mortality rates at older ages in large medfly cohorts. Science 258:457-461. Charlesworth, B. 1980 Evolution in Age-Structured Populations. London: Cambridge University Press. 1990 Optimization models, quantitative genetics, and mutation. Evolution 44:520-538. 1994 Evolution in Age-Structured Populations, 2nd ed. London: Cambridge University Press. Charnov, E.L. 1982 The Theory of Se Allocation. Princeton, NJ: Princeton University Press. Chippindale, A.K., D.T. Hoang, P.M. Service, and M.R. Rose 1994 The evolution of development in Drosophila melanogaster selected for postponed senescence. Evolution 48:1880-1899. Comfort, A. 1964   Ageing, The Biology of Senescence, 2nd ed. London: Routledge. Curtsinger, J.W., H.H. Fukui, D.R. Townsend, and J.W. Vaupel 1992   Demography of genotypes: Failure of the limited life span paradigm in Drosophila melanogaster. Science 258:461-463. Easton, D.M. 1995   Gompertz survival kinetics: Fall in number alive or growth in number dead? Theoretical Population Biology 48:1-6. Edney, E.B., and R.W. Gill 1968   Evolution of senescence and specific longevity. Nature 220:281-282. Finch, C.E. 1990   Longevity, Senescence, and the Genome. Chicago: University of Chicago Press. Finch, C.E., M.C. Pike, and M. Witten 1990   Slow increases of the Gompertz mortality rate during aging in certain animals approximate that of humans. Science 249:902-905. Fukui, H.H., S.D. Pletcher, and J.W. Curtsinger 1995   Selection for increased longevity in Drosophila melanogaster: A response to Baret and Lints. Gerontology 41:65-68. Gavrilov, L.A., and N.S. Gavrilova 1991   The Biology of Life span, A Quantitative Approach. Chur, Switzerland: Harwood Academic Publishers. Gould, S.J., and R.C. Lewontin 1979   The sprandrels of San Marco and the Panglossian Paradigm: A critique of the adaptationist programme. Proceedings of the Royal Society of London Series B. Biological Sciences 205:581-598.

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