Mutation and Senescence: Where Genetics and Demography Meet

Genetica 102/103: 299–314, 1998. 299

c 1998 Kluwer Academic Publishers. Printed in the Netherlands.

Mutation and senescence: where genetics and demography meet

Daniel E.L. Promislow1 & Marc Tatar2 1 Department of Genetics, University of Georgia, Athens, GA 30602-7223, USA (Phone: (706) 542-1715; Fax: (706) 542-3910; E-mail: [email protected]); 2 Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02912, USA (E-mail: mark [email protected])

Key words: mutation accumulation, senescence, demography, mortality

Abstract

Two evolutionary genetic models–mutation accumulation and antagonistic pleiotropy–have been proposed to explain the origin and maintenance of senescence. In this paper, we focus our attention on the mutation accumulation model. We re-examine previous evidence for mutation accumulation in light of new information from large-scale demographic experiments. After discussing evidence for the predictions that have been put forth from models of mutation accumulation, we discuss two critical issues at length. First, we discuss the possibility that classical fruit fly stock maintenance regimes may give rise to spurious results in selection studies of aging. Second, we consider evidence for the assumptions underlying evolutionary models of aging. These models assume that mutations act additively on age-specific survival rate, that there exist mutations whose effects are confined to late age-classes, and that all mutations have equal effects. Recent empirical evidence suggests that each of these three assumptions is unlikely to be true. On the basis of these results, we do not conclude that mutation accumulation is no longer a valid explanation for the evolution of aging. Rather, we suggest that we now need to begin developing more biologically realistic genetic models for the evolution of aging.

Introduction oretical and empirical work in the field with recent advances in the use of large-scale demography in stud- Other authors, including many in this volume, have ies of senescence (Carey et al., 1992; Curtsinger et al., described how mutations can act not only as the source 1992; Vaupel, Johnson & Lithgow, 1994). In light of of genetic variation on which selection acts, but may these studies, we focus on the ways in which an explic- even be the fundamental driving force in evolutionary itly demographic perspective can enhance our ability to change, from the origin of sex (Kondrashov, 1998) to interpret studies of mutation accumulation and aging, the maintenance of sexually selected characters (Pomi- and guide research in the future. ankowski, Iwasa & Nee, 1991) to the ultimate decline and disappearance of populations (Lande, this volume). Here we turn our attention to the evolution of Background aging. Many previous books and articles have provided Aging is here defined as a persistent decline in age- comprehensive reviews of the underlying theory for specific fitness components of an organism (i.e., rates the evolution of aging and the evidence that supports of reproduction and survival) due to internal physio- or refutes this theory (Rose & Charlesworth, 1980; Par- logical deterioration (Rose, 1991). We expect to see an tridge & Barton, 1993; Charlesworth, 1994; Curtsinger age-related decline in all fitness components. For the et al., 1995). Rather than revisit this body of work, we purpose of this present article we focus our attention will touch on the theoretical background only briefly. on age-specific mortality rates (Comfort, 1979; Finch, Our primary aim here is to integrate previous the- Pike & Witten, 1990; Promislow, 1991; Curtsinger,

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1995), while acknowledging that other metrics of aging mulation model of aging. Second, we explore the spe- exist (Curtsinger, 1995; Graves, 1995; Partridge & cific problem that arises in tests of aging due to the Barton, 1996). way in which fruit flies – the work-horse of the field of The evolutionary origins of senescence are gen- experimental demography – are maintained. And final- erally explained by two widely-accepted theories– ly, we weigh the evidence in support of the underlying mutation accumulation (Medawar, 1952) and antag- assumptions of evolutionary models of aging. onistic pleiotropy (Williams, 1957). We will confine our focus here to the mutation accumulation model. Medawar (1952) proposed that senescence arises Evidence for the mutation accumulation model because the strength of selection declines with age. A newly arising mutation in humans that reduces fertil- The mutation accumulation model gives rise to numer- ity by 50%, but that is only expressed after age 45, ous predictions that can be tested experimentally: a) would experience little selection against it. In the vir- variance for fitness traits should increase with age tual absence of selection, it may increase in frequen- (Rose & Charlesworth, 1981b; Charlesworth, 1990); cy through drift alone. The same deleterious muta- b) reverse selection for early fitness on lines produced tion expressed at age 20 would be subject to very from selection for late-life fitness should only slow- strong selection. As a consequence, over many gen- ly revert to pre-selection age-specific phenotypes; c) erations, late-acting deleterious mutations are more the controlled introduction of spontaneous or directed likely to accumulate than early-acting ones. These mutations should alter patterns of senescence; and d) late-acting mutations will then cause an age-related inbreeding depression should increase with age (Tana- decline in fitness traits, including fecundity, fertili- ka, 1993; Charlesworth & Hughes, 1996). ty, and survival rates. This theory of aging has given rise to specific micro-evolutionary predictions (Rose, A. Changes in variance with age 1985; Charlesworth, 1990). In particular, mathemati- cal models of Medawar’s mutation accumulation the- Under the mutation accumulation scenario, the rela- ory predict an age-related increase in genetic variance tively reduced force of natural selection permits an components (Charlesworth, 1990) and in inbreeding age-dependent decrease in the selection-mutation bal- load (Charlesworth & Hughes, 1996) for traits related ance. This should lead, in turn, to a greater amount of to fitness. additive genetic variance for fitness traits at late ages Charlesworth’s models (Charlesworth, 1990; compared to earlier ages. The prediction of an age- Charlesworth, 1994; Charlesworth & Hughes, 1996) related increase in genetic variance for fitness compo- are based on assumptions about the nature of the effects nents is fundamental(though not necessarily exclusive, of mutations on fitness components. To make analy- see Charlesworth & Hughes, 1996) to the mutation sis tractable, while acknowledging that the assump- accumulation theory of aging. Many studies have now tions underlying the model are not necessarily realistic, tested this prediction for a variety of traits, including Charlesworth has made the simplifying assumptions age-specific fecundity (Rose & Charlesworth, 1981b; that mutations act additively on age-specific survival Engstrom¨ et al., 1989; Ebert, Yampolsky & Van rates and that mutations are equally likely to act at any Noordwijk, 1993; Tanaka, 1993; Tatar et al., 1996), age. We address the experimental evidence for these age-specific mortality (Hughes & Charlesworth, 1994; assumptions in a later section of this paper. Hughes, 1995; Promislow et al., 1996), and male repro- Both mutation accumulation and antagonistic ductive ability (Kosuda, 1985; Hughes, 1995), with pleiotropy theories have spawned a wealth of mixed results. experimental tests (recent reviews in Rose, 1991; Charlesworth, 1994). But only very recently have biol- Fecundity ogists recognized that to understand the evolution of Rose and Charlesworth (1980, 1981b) first tested this aging fully, genetic studies of survival or fecundity prediction by analyzing additive genetic variation for need to rest on large-scale demographic approaches fecundity in Drosophila melanogaster. Average addi- (e.g., Curtsinger et al., 1992; Curtsinger et al., 1995; tive genetic variance did not change with age. How- Fukui, Ackert & Curtsinger, 1996). With this in mind, ever, as has been previously pointed out, any realized we first use a demographic perspective to evaluate increase in variance may have been offset by the dif- existing experimental evidence for the mutation accu-

gene441.tex; 26/05/1998; 15:02; v.7; p.2 301 ferential mortality of females with relatively high ear- ance, subsequent work by Hughes (1995) demonstrates ly fecundity, due to the costs of reproduction (Clark, a similar increase in additive genetic variance for male 1987; Engstrom¨ et al., 1989; Partridge & Barton, mating ability. 1993). In a later study, Engstrom¨ et al. (1989) included B. Demographic selection only those females that survived for the duration of the experiment. Although they found that variance for Lines generated by demographic selection have been fecundity increased with age, the observed increase used to assess whether mutation accumulation caus- may have been due to the fact that their data were log- es senescence. Service, Hutchinson and Rose (1988) transformed (G. Engstrom,¨ personal communication; applied reverse selection to lines that had originally Tatar et al., 1996), when the underlying raw data were been selected for postponed senescence. After reverse not log-normally distributed. selection they assessed early fecundity and three physi- A rather different pattern has been observed in two ological variables that were characteristic of long lived more recent studies, one on the bean weevil Calloso- lines, including tolerance to starvation, desiccation, bruchus chinensis (Tanaka, 1993), and the other on a and ethanol. Early fecundity responded directly to large cohort of Drosophila (Tatar et al., 1996). In both reverse selection, and starvation resistance decreased cases, the authors found significant additive genetic in the process. Desiccation resistance and ethanol tol- variance for fecundity early in life, a subsequent drop erance, on the other hand, did not change after 22 in variance, and then an increase at later age-classes. generations and remained at elevated levels. They rea- At least for the finding of Tatar et al., this unexpected soned that desiccation resistance and ethanol tolerance result may be due in part to the way in which flies had improved originally in the long-lived lines, due are typically maintained in the lab. We discuss this to the removal of late-acting age-specific deleterious possibility later in this paper. alleles present in the ancestral stocks (early deleterious effects of the alleles would have precluded their accu- Mortality mulation). From the response of these traits, Service, Mortality rates are at the heart of our interest in aging, Hutchinson and Rose (1988) concluded that mutation yet only recently have researchers begun to estimate accumulation is a general mechanism for senescence genetic variance components for mortality.Hughes and in D. melanogaster. Charlesworth (1994) were the first to demonstrate a Let us consider their conclusion carefully. First, significant increase in genetic variance for age-specific Service, Hutchinson and Rose (1988) did not measure mortality in Drosophila, which they argued showed how late fecundity or lifespan responded to reverse clear support for the mutation accumulation theory of selection, although the original improvement of these senescence. Subsequent work by others suggests that demographic traits under selection for late fitness was their results tell only part of the story (Promislow et cited as the primary evidence for postponed senes- al., 1996). When much larger cohorts are used in these cence. Clearly, to understand the effect of reverse selec- studies, variance components appear to decline at late tion on senescence one should measure the return rate ages, counter to the most current predictions of the of the demographictraits assayed originally. In particu- mutation accumulation model (Promislow et al., 1996; lar, did lifespan rapidly return to the level of the control see also Pletcher, Houle & Curtsinger, 1998). population? If it did not, we would suggest that mutation accumulation is the primary underlying genetic Male mating ability architecture that led to the eventual difference in senes- In what is now perhaps the most widely cited study cence among the lines, rather than the more commonly to show an age-related increase in variance for fitness ascribed mechanism of antagonistic pleiotropy. In part traits, Kosuda (1985) found an age-related increase B of the following section we develop this idea further in coefficient of variation for male mating ability when we discuss the effects of culture domestication among lines of flies that were homozygous for dif- on mutation accumulation in D. melanogaster. ferent extracted second chromosomes. In addition, he Second, Service, Hutchinson and Rose (1988) mea- also showed that mating ability declined at a more sured desiccation resistance and ethanol tolerance on rapid rate in inbred than in outbred lines. Although relatively young adults, those that were 6 days of age. these results are based on analysis of genotypic vari- They observed no reverse selection response for these age-specific traits. From this observation, Service et al.

gene441.tex; 26/05/1998; 15:02; v.7; p.3 302 argued that mutation accumulation was the cause of the tions on aging. In the early 1970s, Mukai and his col- deleterious expression of the traits in the ancestral con- leagues first used this approach (Mukai et al., 1974), in trols, relative to the long-lived selected lines. However, which one homologous chromosome is kept balanced since the traits were measured at age 6 days, this argu- against another homologue with a dominant marker, a ment requires that mutations affected fitness at ages recessive lethal gene, and multiple inversions (to pre- equal to or greater than 6 days, but that the mutations vent recombination). Thus, mutations with partially had no effects on flies aged 0-5 days, ages that were or completely recessive deleterious effects can accu- actively exposed to selection in the ancestral stocks. mulate on the unmarked chromosome in the virtual As there is no evidence for such extreme asymmetry absence of selection. Subsequent studies have also used in the age specificity of mutations, we should consid- the approach of maintaining lines under small effective er an alternative explanation, as suggested by Service, population size, which reduces the efficacy of selection Hutchinson and Rose (1988). The reverse selection against mildly deleterious loci (Mackay et al., 1994; response may be due to epistasis combined with dif- Falconer & Mackay, 1996). ferences in genetic background among the ancestral Houle et al. (1994) analyzed 48 mutation accumu- and long lived lines. lation lines for several traits related to aging, including The footprint of mutation accumulation may be early and late fecundity, early and late male mating inferred elsewhere from the recovery of late-age pheno- ability, and age-specific mortality, measured in terms types when early-fitness selected lines are hybridized. of the slope and intercept of the Gompertz curve, (see Mueller and Ayala (1981) created r lines based on equation [4], below, for details of the Gompertz mod- reproduction at young adult ages in discrete culture, el). They found no significant mutational variance for and K lines using higher density populations with over- mortality rate parameters, although mutational vari- lapping generations. Purebred r lines have only 31% ance for mean longevity and late-age reproduction was of the week-four fecundity of purebred K lines, but evident. Houle et al. also observed that mutational when hybrids within each selection regime are com- effects were positively correlated among the early and pared, the F1 r lines improve their week-four fecundity late age classes, and from this they argued that muta- to a level that is 74% that of the F1 K lines (Mueller, tion accumulation in general is inadequate to explain 1987). Mueller (1987) suggested that late fitness of the the persistence of senescence at equilibrium. This con- r lines suffered from accumulation of deleterious muta- clusion, however, rests on the age-specific nature of de tions during the greater than 120 generations of their novo mutations. selection on early fitness. Hybridization among the How do specific mutations affect senescence? independent r lines could at least partially restore late The spontaneous mutation accumulation approach fitness through dominance effects of non-mutant alleles described above, and also used recently by Pletch- among the complementing lines. Further hybridization er, Houle and Curtsinger (1998), cannot answer the analyses of this sort in terms of age-specific demo- question, because each mutation may have an effect graphic traits may provide insight into the potential for too small to detect. Single-gene mutagenesis, howev- and prevalence of mutation accumulation as a cause of er, may provide some answers to this question. For senescence. example, Clark and Guadalupe (1995) used P-element induced mutations in D. melanogaster to look at the C. Mutation accumulation experiments effects on survival of single mutations of substantial effect. As with Houle et al.’s result, they found only The above studies were concerned with understanding weak evidence for late-acting mutational effects. the role of mutation accumulation in the past as a causal Given the evidence to date, we have little doubt factor in the evolution of senescence. An alternative that mutation accumulation plays a significant role in approach, discussed here, is to ask whether controlled the evolution and maintenance of senescence, at least mutation is adequate to produce recognizable patterns in laboratory population studies so far. The accumu- of senescence. To this end, recent studies have either lation of deleterious mutations can lead to depression permitted the accumulation of spontaneous mutations, of a variety of fitness traits and an increase in genet- or induced mutations with P-elements, and then ana- ic variance for those traits late in life. However, at lyzed the effects on patterns of aging. least three major issues remain unresolved. First, how Houle et al. (1994) created a set of mutation accu- important is mutation accumulation relative to antag- mulation lines to estimate the effect of de novo muta- onistic pleiotropy as a cause of senescence. Second,

gene441.tex; 26/05/1998; 15:02; v.7; p.4 303 what is the nature of the effects of mutations with The prevalent predictive models (e.g.,Charlesworth, respect to age. The claim that late-acting mutations are 1990; Charlesworth & Hughes, 1996) for the evolution more likely to accumulate assumes that there exists a of aging assume that fitness traits — fecundity or sur- class of de novo mutations whose effects are confined vival — are normally distributed. If this assumption to late ages. The assumption remains virtually untested. is violated, one tends to observe strong mean-variance Third, are the data collected thus far based on statis- correlations. For fecundity, survival, and male mating tically reliable demographic approaches. Recent stud- ability, empirical results show them to be distinctly ies based on very large-scale demographic approaches non-normal. Male mating ability, at least as measured suggest that we may need to re-evaluate conclusions in studies on aging (e.g., Kosuda, 1985), is binomial- from previous studies on the role of mutation accu- ly distributed (Promislow et al., submitted). A recent mulation in aging. To answer these questions we must study of age-specific fecundity found that egg counts overcome several specific theoretical, statistical and were approximately Poisson distributed (Tatar et al., empirical challenges 1996). And age-specific mortality rates have a more complex distribution. For a given age within a cohort, variance is binomial (or possibly beta-binomial, if iso- Challenges to testing the mutation accumulation genic individuals differ in their intrinsic risk of mortali- model ty due to environmentalvariance). Across ages within a cohort, mortality rates increase exponentially. Among There are three critical issues that affect our ability different cohorts of the same-age, mortality is log- to test the mutation accumulation model for the evolu- normally distributed. And finally, at very small sample tion of senescence. First, our current predictive models size or very low mortality rate, mortality can act as a assume that life history traits are normally distributed, threshold character, such that it is not visible until the and that means and variances are not correlated. These mortality rate is greater than approximately the inverse assumptions are violated by major fitness parameters of the sample size. Failure to account for the complex and by mortality rate in particular. Second, most stud- distribution of demographic parameters can mislead us ies of evolutionary models of aging have relied on lab- when we attempt to estimate age-specific changes in domesticated populations of the fruit fly, Drosophila genetic variance components. melanogaster. These populations are valued because they are likely to be at some degree of demographic and Male mating ability genetic equilibrium. However, the discrete-generation protocol that has typically been used to maintain stocks In 1985, Kosuda published the first study to show clear of flies may have unwittingly served as a generator evidence of an increase in genotypic variance for a fit- of late-age mutations, and so may have confounded ness trait (Kosuda, 1985). In this case, the fitness trait genetic studies of aging. Third, models for the evo- of interest was male mating activity (MMA). Kosu- lution of senescence make specific assumptions about da used balancer stocks to isolate twenty-nine lines of the nature of the mutations that generate age-specific Drosophila melanogaster, each of which was homozy- changes. For example, de novo mutations are assumed gous for a different second chromosome extracted from to have effects limited to specific ages, and to be more a natural population. For each line, he placed 1 vir- prevalent at late ages. But only recently have studies gin male and 12 virgin females in a vial and assayed begun to test this assumption (Houle et al., 1994; Clark the number of inseminated females after 24 h. Twelve & Guadalupe, 1995; Pletcher, Houle & Curtsinger, males were tested for each of the twenty-nine lines. 1998), and the early evidence here suggests that the Tests were conducted at ages 3 d (young) and 28 d age-distribution of the effects of novel mutations may (old) post-eclosion. The mutation accumulation the- be more complex than previously thought. ory predicts that variance in fitness traits (such as male mating ability) should be greater among old flies A. Demography and variance in studies of aging (Charlesworth, 1990). Kosuda found that the MMA declined from a mean of 0.535 to 0.185 (proportion of Several examples illustrate the necessity of accounting females inseminated), and as predicted, the coefficient for the complex statistics of demographic parameters of variation (CV) among lines increased from 49.6% in tests of the mutation accumulation model. to 120%, an increase of a factor of 2.4.

gene441.tex; 26/05/1998; 15:02; v.7; p.5 304

To interpret this result, we need an appropriate null first evidence that additive genetic variance for mortal- model. What is the expected change in variance with ity rates did, in fact, increase with age. age for MMA if there is no change in genotypic vari- Promislow et al. (1996) suggested that the increase ance for the trait? in variance observed by Hughes and Charlesworth may Given that MMA is binomially distributed, its have been due to artifacts of the distributional proper- 2 expected variance E( )=p(1-p)/N,wherepis the ties of mortality rate coupled with insufficient sample average MMA among lines, and N is the total number size. As with MMA, we require a null model to deter- of females sampled. Similarly, the expected coefficient mine how we expect estimated variance of mortality of variation rate to change with age when the underlying genetic

variance is indeed constant across ages, given a par-

( p)

p 1ticular rate of increase in mortality and a particular

( p)

N 1

(CV )= = E age-dependent sample size. At issue is the fact that

p (1)

p Np

when sample size N is small relative to mortality < The ratio of the CVs for these two variables is given (such that 1/N) we are likely to underestimate by CV /CV the true variance in mortality, but when mortality rate Early Late increases with age the true underlying genetic vari-

ance becomes apparent, and we thus observe a trend of r

r increasing genetic variance with age. Under the null

p ( p )

CVL E 1 L 0:535 0 815

= = :

= 2 3(2) model assumption of no increase in variance, only

( p ) : : CVE pL 1 E 0 185 0 465 when initial cohort sizes are very large do we have sta- which is very close to the increase of 2.4 observed by tistical power to see that genetic variance at young ages Kosuda. is the same as at ages where mortality rates are rela- One could use an arcsin transformation if the data tively high. Thus, to test predictions, we require demo- were truly binomial (see, for example, Hughes, 1995). graphic studies based on much larger sample sizes. However, the distribution of male mating ability may This requirement motivated Promislow and col- be slightly more complex. If isogenic males within leagues to conduct an experiment similar to that of lines show intrinsic differences in mating ability, (due Hughes and Charlesworth, but with substantially larg- to environmental variance, for example) the trait distri- er sample sizes. Similar to Hughes’ and Charlesworth’s bution may be beta-binomial, rather than simply bino- original experiment, Promislow et al. (1996) observed mial (Searle, Casella & McCulloch, 1992). To deal an initial, age-specific increase in additive variance for with this complexity, future studies should use random- mortality. In this case, the increase does not appear to ization procedures to determine whether the increase in be due to insufficient sample size. At late ages, how- CV observed is significantly greater than that predicted ever, variance components for mortality declined, con- by chance alone. trary to what is predicted by standard mutation accumulation models. This result is a novel observation Age-specific mortality rates that challenges the basic assumptions of predictions Although the mutation accumulation model was devel- for the mutation accumulation model of senescence. oped to explain the age-related increase in mortality No model exists yet that would explain this result. (Medawar, 1952), only recently have scientists turned As with early ages, the reduction in the number their attention to this key variable. The first such study of live individuals could potentially lead to an erro- was conducted by Hughes and Charlesworth (Hughes neous apparent reduction in variance at later ages. In & Charlesworth, 1994; Hughes, 1995). To estimate Promislow et al.’s (1996) experiment, sampling error genetic variance components for age-specific mortal- at late ages may have led to an underestimate of mor- ity, Hughes and Charlesworth extracted 40 wild-type tality rates. To control for the potential effect of sam- chromosomes from an outbred population of Drosophi- pling error, Frank Shaw (personal communication) has la melanogaster. They crossed these lines in a partial developed a statistical technique, based on maximum diallel design (Comstock & Robinson, 1952) and esti- likelihood, that accounts not only for the unusual statis- mated mortality rates in the progeny for three different tical distribution of age-specific mortality, but also for ages (0-3 wk, 5-7 wk, 9-11 wk). From these data, they the effects of sample size. Shaw’s analysis of the mor- were able to determine genetic variance components tality data using this technique further supports Promis- for age-specific mortality rate. This study provided the low et al.’s original interpretation–variance compo-

gene441.tex; 26/05/1998; 15:02; v.7; p.6 305 nents for mortality do,indeed, decline at late ages, even 1977), then inbreeding depression should be less for after accounting for the effect of sampling error. The fitness traits early in life than late in life. decline in genetic variance for mortality observed by The first test of this prediction is provided by Tana- Promislow et al. could have several other explanations. ka (1993), who compared age-specific fecundity at ten The age specificity of mutational effects is unknown. ages (at 2-day intervals) in the bean weevil, Calloso- Mutations may have limited effects at advanced ages, bruchus chinensis. He regressed differences in the log- which would preclude the accumulation of additive transformed values of outbred minus inbred fecundity variance among the oldest old. Alternatively, hetero- versus age and found no significant increase. This fail- geneity of reproductive costs among genotypic cohorts ure to find an increase is even more notable given that may produce a decline in variance once all groups reach Tanaka was basing the analysis on differences between post-reproductive ages (Promislow et al., 1996). log-transformed values of fecundity. Because fecundi- A recent study by Sergey Nuzhdin and colleagues ty in Callosobruchus takes on a Poisson distribution (Nuzhdin et al., 1997) provides additional evidence and declines monotonically with age (C. Fox, person- of the need to analyse mortality, rather than sur- al communication), for statistical reasons alone one vivorship. Nuzhdin et al. (1997) compared survivor- would expect an apparent increase in the difference ship curves among 98 recombinant inbred lines of between inbred and outbred fecundity with age, under D. melanogaster. To test the mutation accumulation a null model of no actual increase in the difference model, they asked whether the coefficient of addi- between the two groups.

tive genetic variance (CV G ) for survivorship increased The prediction was also evaluated by Charlesworth with age. Survivorship, the percentage of individuals and Hughes (1996), who developed an explicit mod- in a cohort alive at a given age, necessarily declines el for inbreeding load under mutation accumulation. with age. To control for the decline in mean survivor- They assume that mutations act additively on survival, ship, the authors rescaled survivorship by dividing the such that the deleterious mutation rate at the ith locus

age-speciﬁc survivorship for each line by the mean with effects on survival rate z is given as u i and has age-speciﬁc survivorship among all lines. They then effect zi . Their model predicts that inbreeding load, L,

calculated the variance among the rescaled lines, and deﬁned as the ratio of age-speciﬁc survival in outbred

O I to obtain CV G , divided the scaled variance by the flies (z ) to age-specific survival in inbred flies (z ) unscaled mean. However, because the unscaled mean should increase with age, t.Thatis,

of survivorship is smaller at late ages, the value of CV G

d z

increases with age. Thus, the increase that Nuzhdin et O

> :

al. observed may have been an artefact of using age- 1 n 0 (3)

dt z I

speciﬁc survivorship, rather than mortality rates, to

estimate age-speciﬁc variance. Survival rate is related to mortality rate, ,asz= .

O Thus, we can restate mutation load as L = I – . Inbreeding load and the mutation accumulation model Charlesworth and Hughes tested this prediction Charlesworth and Hughes (1996) point out that both with data collected by Hughes as part of a larger study genetic models of aging–mutation accumulation and on the genetics of fitness in male D. melanogaster antagonistic pleiotropy–predictan age-related increase (Hughes, 1995). They found that the inbreeding load in additive genetic variance for fitness traits, at least increased with age, in direct support of the mutation under certain conditions. Thus, an analysis of additive accumulation theory for the evolution of senescence. variance at different ages does not necessarily provide But as with previous studies we have discussed so far, a mutually exclusive prediction that would allow us to in this case the statistical and demographic nature of distinguish between the two models. mortality makes these observations difficult to inter- Fortunately, there may be a genetic prediction that pret. is specific to mutation accumulation. Under mutation First, as with standing genetic variance discussed accumulation, if deleterious mutations with effects on above, at early ages, mortality rates tend to be very late-age fitness traits have a higher frequency than those low. Over a large range of ages, mortality rates may with effects on early-age fitness traits, and if muta- be non-zero, but significantly lower than the mea-

tions are partially or fully recessive (Simmons & Crow, surable threshold of one death per cohort of size N

x x (i.e., x 1/N ,whereN is the number of individuals in a cohort of age x). If mortality rates differ

gene441.tex; 26/05/1998; 15:02; v.7; p.7 306 between inbred and outbred lines, but are both below reduced early-expressed traits such as fecundity or this threshold, then we will not be able to detect a dif- development rate (e.g., Wattiaux, 1968a, 1968b; Rose ference between the two. At later ages, as mortality & Charlesworth, 1980; Rose, 1984). Furthermore, rates increase above the threshold, we will more easily some have observed increases in other late-life traits detect a difference between inbred and outbred lines. including late-fecundity and stress tolerance (Service Thus, even in the absence of any real increase in differ- & Rose, 1985; Service, Hutchinson & Rose, 1988; ence between inbred and outbred mortality, we might Chippindale et al., 1993). These data are widely used expect to ﬁnd an apparent increase with age, because to argue that antagonistic pleiotropy is a primary basis of an age-related increase in our ability to detect a for the evolution of senescence, and that certain phys- difference. iological traits underlie variation in longevity. Second, because mortality is log-normally distrib- In almost all cases, these selection programs used uted, there is a strong positive mean-variance corre- laboratory adapted base stocks. This was done to avoid lation, so the distance between lines on an absolute spurious positive genetic correlations that might arise scale necessarily increases. To illustrate, we can sim- due to gene-environment interactions when wild ﬂies ply model mortality with a Gompertz curve, such that are introduced into the novel laboratory environment (Service & Rose, 1985). In practice, however, labo-

x ratory adaptation may have introduced more problems

= e ;

x (4)

than it solved. In particular, laboratory adapted stocks where is the Initial Mortality Rate (IMR), and is are commonly maintained in a 2-week discrete cul- the actuarial rate of aging. For now we safely ignore ture. Unfortunately, this practice constitutes a de fac- the fact that late-life mortality departs signiﬁcantly to mutation accumulation experiment, allowing late- from this pattern (Abrams, 1991; Carey et al., 1992; acting deleterious mutations to increase in frequency Curtsinger et al., 1992; Vaupel, Johnson & Lithgow, in the base stock in the absence of selection. We believe 1994). that these novel mutations in the base stock may have Consider two cohorts, one inbred and one outbred, provided the genetic variation upon which much of the

that are identical in their actuarial rate of aging (i.e., observed selection response in previous experiments

O = = ), but differ in their IMR component, with was based.

> O I . In this case, the difference between mortal- In 2-week culture, adult ﬂies are transferred into a ity curves of two cohorts that vary only in alpha will fresh vessel at reference day 0. At the time of trans-

necessarily increase with age, as will the age-speciﬁc fer, eggs must be laid immediately since the adults are

O I O inbreeding load, L[x]= I – =( – )e . often removed after several hours. Even if they remain for several days, only those eggs laid within 36-48 h B. Demography of fly culture are likely to contribute to the following generation (D. Houle and L. Rowe, pers. comm.). Typically, the most Until now, we have stressed the importance of careful rapidly developing individuals pupate no earlier than use of demographic approaches in studies of mutation at reference day 8, while the modal emergence is at day accumulation. We have argued that standard demo- 9 or 10 (Ashburner, 1989). Emergence continues until graphic designs can lead to biased results in a vari- reference day 14, at which time the accumulated adults ety of studies. The problems may actually be even are transferred to the next day 0 vessel. Up to a max- more complex. Many selection studies were initiated imum of 4 days of age, all eggs laid by adults before from base stocks laden with late-expressed mutations transfer make no contribution towards lifetime repro- that accumulated prior to selection. We suggest that ductive success. Then, within 24 h, all flies experience this complicates how we interpret direct and correlated a narrow window of potential reproductive opportu- selection responses and, in turn, may bias our inter- nity. As a consequence, genes for adult fitness traits pretations of the evidence for antagonistic pleiotropy expressed after 4 days of age are not directly exposed theories of senescence. Our comments here are exten- to selection. sions of observations first made by Clark (1987). Although little is known about fitness traits in nat- To illustrate genetic trade-offs in senescence, many ural populations of Drosophila, it is likely that repro- researchers have selected on late-age fitness and have ductive value remains high beyond 4 days of age. If observed increased life expectancy and, as predicted this is the case, then when wild flies are introduced by the antagonistic pleiotropy theory of senescence, to a 2-week regime as a prelude to conducting selec-

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Table 1. Population culture characteristics of lines of Drosophila melanogaster that have been used for studies of senescence. Under discrete culture, ﬂies older than 4–6 days have no reproductive value. Mutations with effects conﬁned to this age or later experience no selection, and so accumulate through drift (see text for more detailed discussion)

Study Base stock Base stock Culture population Founding population Interval of selection No. generations name founded structure max. estimate Ne discrete culture initiated selection intitated (yr) after base founded

(Rose & Charleston, 1981; ‘Ives’ 1970 Discrete unknown 14 days 1980 > 130 Rose, 1984) and all current derivates

(Luckinbill et al., 1984) ‘Michigan Orchard’ unknown Discrete < 50 7–14 days ca. 1981 12

(Engstr¨om, Liljedahl & ‘Swedish Stock unknown Discrete unknown 16 days unknown > 10 once hybrid Bj¨orkland, 1992) Center Hybrid’ unknown before (Partridge & ‘Brighton’ 1984 Overlapping unknown NA 1985 kept with overlapping Fowler, 1992) generations (Partridge & ‘Dahomey’ 1970 Overlapping unknown NA 1986 kept with overlapping Fowler, 1992) generations (Zwaan, Bijlsma & ‘Groningen 1983’ 1983 Discrete 403 isofemale 14 days 1990 unknown Hoekstra, 1995a; lines Zwaan, Bijlsma & Hoekstra, 1995b) (Zwaan, Bijlsma & ‘Groningen 1983’ 1983 Discrete 403 isofemale 14 days 1991 unknown Hoekstra, 1995a; lines Zwaan, Bijlsma & Hoekstra, 1995b)

tion experiments on longevity, we release this later if correlations are age limited, as suggested by the data part of their natural life history from direct selection. of Pletcher, Houle and Curtsinger (1998). Under this condition, the selection-mutation balance What is the consequence of the base stock’s demo- for genetic effects expressed in late-life is altered and graphic history in the context of demographic selec- mutation accumulation for late-express traits will like- tion on longevity? In selection experiments designed to ly take place. The expected effect of the accumula- study senescence, demographic selection for longevity tion of late-acting, age-specific mutations would be to is applied initially to a base stock by propagating with reduce many late expressed fitness traits, including life adults that are at least 14 days old, an age that we now expectation, fecundity, and stress tolerance. recognize has been sheltered from selection in stan- Over a few generations of relaxed late-age selec- dard culture. Therefore, substantial additive variance tion, the rate of decline in fitness due to novel muta- for traits at this age may exist due to mutation accumu- tions will be virtually unmeasurable. However, in pre- lation in the base stock, and we should expect a rapid vious studies, many of the base stocks used as selec- response in the selection lines as deleterious mutations tion material were maintained in 2-week culture for are purged. And since deleterious mutations produce over 120 generations (Table 1). Given a per-generation positive genetic covariance among fitness traits, we decline in fitness of between 0.1 and 1% due to muta- should expect many late-age expressed fitness traits tion accumulation (Mukai et al., 1974; Houle et al., to improve with the direct selection response. It is 1994; Falconer & Mackay, 1996), over a hundred important to realize here that selection responses are or more generations one would expect to see a sub- measured relative to the original base stock or to a con- stantial decline in late-life fitness, perhaps as great as current control population derived from the base stock 50%. This assumes that the mutations have additive that is still maintained on a discrete 2-week culture. and independent effects, and that mutations are not To an unknown extent, the base and control stocks totally purged by correlated expression with traits at are effectively mutation accumulation lines, and the ages less than 4 days old. Covariance between ages observed selection response represents a purging of (Houle et al., 1994) would reduce the magnitude of the accumulated mutations. estimated loads, but the load could still be substantial

gene441.tex; 26/05/1998; 15:02; v.7; p.9 308

The effect of subsequent selection on base-stock lations that arise in selection experiments due to antag- mutations confounds how we interpret the data onistic pleiotropy from correlations that arise due to with respect to antagonistic pleiotropy. Antagonistic linkage disequilibrium and mutation accumulation. In pleiotropy is inferred from selection studies from the particular, there are four outstanding issues that need negative correlations between directly selected late-age to be addressed. traits and associated changes in early-age traits. These First, we do not yet understand the extent to which correlations are thought to be caused by pleiotropic inadvertent mutation accumulation has occurred in loci. Linkage disequilibrium can produce similar pat- each of the initial base stocks, although it is useful to terns, but previous interpretations assumed that the recognize that not all base stocks are suspect (Table 1, base populations were at genetic and demographic e.g., Luckinbill et al., 1984; Partridge & Fowler, 1992). equilibrium as a result of their long period of labo- Second, we cannot determine the extent to which ratory adaptation. If this were the case, then standing an observed selection response is due to the purging of genetic covariance could largely reflect polymorphism base-stock accumulated mutations versus a response maintained by antagonistic pleiotropy, and the corre- due to changes in gene frequency of polymorphic loci lated selection response would reflect this underlying that were segregating in the natural population (or genetic architecture. The heart of our concern is that maintained under balancing selection in the lab cul- the assumption of genetic equilibrium prior to selec- ture). Consequently we cannot attribute the cause of tion is violated by the 2-week culture practice: late-age apparent supernormal longevity of selected lines: are life histories of the base stocks were not in genet- they really long-lived or are the base stocks relative- ic equilibrium. Thus, correlated selection responses, ly sick? It is widely known, for example, that wild- both negative and positive, could result from linkage caught flies brought into the lab are more robust than disequilibrium between newly accumulated mutations lab strains that have been maintained under lab condi- and early- or late-age traits that were under direct selec- tions for extended periods (Dobzhansky, Lewontin & tion. Pavlovsky, 1964). Consider the evidence for a genetic trade-off Third, we have yet to describe adequately the age- between early reproduction and survival in the selec- specific distribution of mutational effects on fitness tion data of Rose (1984; Rose & Charlesworth, 1981a). traits. Knowledge of these distributions is required to Rose selected on late-age survival and observed a cor- predict the extent to which mutation accumulation can related response of decreased early fecundity relative lead to linkage disequilibrium in base stocks relative to a control. We suggest that the negative correlat- to selected lines. ed response between survival and early reproduction Fourth, most selection studies have not maintained among the Rose lines (short lived ‘B’, and long-lived adequate control stocks to measure selection respons- ‘O’) may be due to linkage disequilibrium. We sur- es. A control population would be one at genetic and mise that the Ives stocks from which Rose’s lines demographic equilibrium. The many derived selection were derived contained a substantial mutation load and control lines of Rose and colleagues present a spe- expressed only at late ages and that, due to removal cial challenge in this respect, because each control line of these deleterious mutations, the survival in the ‘O’ retained a discrete generation culture regime similar to lines would have increased relative to the control ‘B’ that of the ancestral base stock. lines. In addition, during domestication and through- It should be apparent that mutation accumulation out the experiment, the ‘B’ lines were strongly select- and demography are inextricably intertwined, with ed for early reproductive effort. If total reproductive causal arrows drawn in both directions. In previous effort is a deterministic or ‘zero-sum’ quantity (Bell & sections of this paper, we showed how careful use of Koufopanou, 1985), then upon selecting for late repro- demography was needed to test the model of muta- duction in the ‘O’ lines, there would be a decline in tion accumulation. In the present section, we argue early reproduction. Therefore, changes in reproductive that the demographic regime imposed on domesticated schedule need not be pleiotropic with survival; they base stocks can alter the balance of mutation accumula- could result from linkage disequilibrium between loci tion and selection. Much like Heisenberg’s uncertainty affecting fecundity and accumulated late-acting muta- principle, in the very process of examining Drosophila tions. populations for evidence of mutation accumulation we In light of this argument, we may need to devise inadvertently induce the process we seek to test. new experiments and models to distinguish the corre-

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C. Measuring effects of novel mutations

Evolutionary studies of aging have been driven by a small set of model-based predictions. But the assumptions that underlie these models remain untested. In particular, these models have assumed that a) mutations act additively on survival; b) there exists a class of mutations that act only at late ages; and c) all mutations have equal effects. In the following section, we present results from some recent studies, and also from a reconsideration of previously published data, that shed light on each of these assumptions. It is hoped that an understanding of the actual effects of mutations on fitness traits will allow us to create the most biologically realistic models possible, and so help us to understand the evolution of Figure 1. This figure shows the relationship between Ln(mortality) and age for rats fed a restricted diet (open squares) and rats fed an ad- senescence. lib diet (filled squares). These data were taken from the survivorship curves presented in figure 1B of Weindruch and Walford (1982), Do mutations act additively on age-specific survival? with a sample size for each cohort of approximately 70. The first of these assumptions concerns the way in which mutations affect survival rate. Models of both mutation accumulation and antagonistic pleiotropy that dietary restriction can decelerate the rate of aging have assumed that genetic effects on age-specific sur- (Weindruch & Walford, 1982), data are typically pre-

vival rate, Px , are additive on P or on the log of P sented in terms of age-specific survival. By convert- (Hamilton, 1966; Charlesworth, 1990; Charlesworth ing these data into mortality curves, one can see that & Hughes, 1996) for any age x. We can evaluate this dietary restriction (e.g., Weindruch & Walford, 1982), assumption in two ways. First, we can ask whether phe- displays a proportional effect on mortality at all ages notypic manipulations of any sort alter survival rate in (Figure 1). Life span is increased, but the rate of aging an additive fashion across ages. Alternatively, we can (as defined by the rate of increase in the slope of the take a more direct approach, and ask whether novel line) does not change. This suggests that at least in mutations affect survival rates additively. the case of dietary restriction, the manipulation acts In the first case, we could measure survival rate at additively on the log of mortality. several ages in cohorts with and without some manip- However, we can only infer indirectly from these

ulation. If the manipulation acts additively and instan- results whether genetic changes are likely to act addi-

x x taneously on survival rate, then the effect should be tively on P x ,ln(P )orln( ). To do this more directly, similar across all ages. This sort of manipulation has we need to assess the effect of de novo mutations on been done for a variety of factors, including limit- age-speciﬁc mortality rates. If mutations act additive- ed reproduction, (Partridge & Andrews, 1985; Tatar, ly on the log of mortality, for example, then among- Carey & Vaupel, 1993; Tatar & Carey, 1995), dietary cohort variation in log(mortality) due to novel muta- restriction (Weindruch & Walford, 1982; Yu, Masoro tions should be normally distributed.Two such datasets & McMahan, 1985; Tatar & Carey, 1995), and trans- exist that provide at least some preliminary informa- genic alteration (Orr & Sohal, 1994; Tatar, Khazaeli & tion in this regard (Clark & Guadalupe, 1995; Pletcher, Curtsinger, in prep). Houle & Curtsinger, 1998). Data from such experiments suggest that, at least Clark and Guadalupe (1994) conducted an analy-

for the manipulations examined thus far, these factors sis of the effects of novel mutations on aging. They x

act additively not on Px ,orevenonlog(P ), but rather used a P-element construct and the JSK jumpstarter

on the log of instantaneous mortality rate, x ( ln(- stock of Drosophila melanogaster to induce mutations

ln[P x ]). To take one illustrative case, we have replot- at random genes. The P-element inserts were then ted the data from a classic dietary restriction experi- made homozygous using balancer chromosomes and ment. Although many of these studies have claimed assayed for early fecundity and age-speciﬁc survival. Using Clark and Guadalupe’s original data, we cal-

gene441.tex; 26/05/1998; 15:02; v.7; p.11 310 culated age-specific mortality rates per 5-day interval the standing genetic variance in a population assumed for each of three blocks for which data were available. to be at genetic equilibrium. These included data on 20 lines in each of two blocks Pletcher, Houle and Curtsinger’s (1998) analysis and 11 lines in a third block. For each age-class and of mutation accumulation lines was designed to esti- block, distributions of ln(mortality) did not depart sig- mate the age-specificity of mutation variance. From nificantly from normality, based on a sequential Bon- this analysis, they hoped to infer, at least indirectly, the

ferroni test of Shapiro-Wilks W with =0.05(Promis- extent to which novel mutations exhibit age-specific low and Tatar, unpublished analysis). This result sug- effects. Pletcher, Houle and Curtsinger (1998) found gests that P-element induced mutations act additively that mutational variance was high at early ages, and on ln(mortality). However, we recognize the poten- then showed a significant decline late in life. There tial for Type II error in this situation–with the available was only weak evidence of an increase in mutational sample sizes (N=11 or N=20),the test may fail to detect variance during the first two weeks. departures from normality. These results suggest that while there may be age- Further information is available from the recent specific mutations whose effects are seen later in life, experiment by Pletcher and colleagues (Pletcher, there are no mutations with effects confined solely to Houle and Curtsinger, 1998). The authors analyzed the very late ages, and in fact, there may be no mutational effects of de novo mutations on age-specific mortality effects whatsoever on traits at very late ages. This result rates. They estimated variation in age-specific mortal- is concordant with the age-related decline in additive ity across ages among 29 mutation accumulation lines genetic variance for age-specific mortality observed and a control from which the 29 lines were derived. by Promislow et al. (1996). However, as both Pletcher, The analysis included ages at death for 109,860 flies. Houle and Curtsinger (1998) and Promislow et al. point Using a Shapiro-Wilks test, the authors determined that out, the decline in late-age variance could be confound-

for both males and females, and for each of seven age- ed by the diminishing effects of reproduction late in classes, ln( x ) is normally distributed. For one case, life. Furthermore, the lack of late-age mutational vari- (females at six weeks), W = 0.92, and P = 0.01. Howev- ance in Pletcher, Houle and Curtsinger’s study could er, this is not significant after a sequential Bonferroni also have been due to the base stock from which the correction for multiple hypothesis tests. In contrast, mutation accumulation lines were derived. The base distributions of age-specific survival at most ages dif- stock had been in two-week culture for many hundreds fered significantly from a normal distribution. of generations. As discussed in the previous section, In sum, data from both phenotypic and genetic this may have led to extremely high mutation loads manipulations, as well as from mutation accumulation for late-age fitness traits, to the point that subsequent experiments, suggest that factors which alter survival mutations would have only minor effect. lead to proportional changes in mortality rate (i.e., the Clark and Guadalupe’s study (1995) provides us additive effect is on the log of mortality rate). It would with yet further evidence for age-specific mutations. be worth creating models based on this more biologi- They point out in their study that mortality rates leveled cally realistic assumption. off at late ages, and they offer as one interpretation the possibility that mutations with deleterious effects Do novel mutations exhibit age-specificity in their confined to very late ages do not occur. To test Clark effects? and Guadalupe’s claim more directly, we present a In the most predictive model to date, Charlesworth reanalysis of Clark and Guadalupe’s data here. Using (1990) assumed that there exist de novo mutations with their original dataset, we estimated variance among age-specific effects and that the age of onset of these lines for age-specific mortality rate. Mortality rate was mutations is distributed equally across all age-classes. estimated per five days. In each of three blocks for This assumption gave rise to the prediction that genetic which there were sufficient data to calculate mortality variance components for fitness should increase with rates, we found that among line variance was initially age. Results from Promislow et al.’s (1996) study called high and then declined. In two of the three blocks, into question the assumption that there are mutations variance showed a subsequent increase at later ages with very late-acting effects on fitness traits. However, (Figures 2 and 3), though not to original levels. this inference is taken from indirect evidence, based on On the face of it, Clark and Guadalupe’s data suggest that P-element induced mutations are most likely to affect mortality rates early in life and have relatively

gene441.tex; 26/05/1998; 15:02; v.7; p.12 311

Figure 2. Variance among 20 lines (blocks 1 and 2) or 11 lines (block 4), for log-transformed values of age-speciﬁc mortality, estimated on ﬁve-day intervals, based on data from Clark and Guadalupe (1995).

Figure 4. A) The ﬁgure shows a frequency distribution of simulated larval mortality rates among mutation accumulation lines. B) The distribution of larval viabilities that would result from the underlying distribution of mortality rates shown in (4A).

Although mortality rates in this experiment level Figure 3. Ln(mortality) versus age for data from Block 2 of Clark off late in life (Clark & Guadalupe, 1995), data from and Guadalupe’s (1995) study, showing an apparent increase in vari- blocks 1 and 2 suggest an increase in variance at late ance both early and late in life. Mortality data were smoothed on a 3-day running average. Lines differ with respect to P-element ages (Figures 2 and 3). (Block 4 had insufficient data induced mutations, though both environmental and genetic compo- to estimate variance components after day 30). The nents contribute to total variation in this figure. observed increase in variance is somewhat surprising in light of results by both Pletcher, Houle and Curtsinger (in press) and Promislow et al. (1996), which show a minor effects after day 10 or so. The data are also con- striking decline in variance late in life. It is possible sistent with alternative interpretations. For example, that, on closer inspection, we will find that P-element environmental variation, rather than genetic variation, induced mutations have dramatic effects both early may have initially been relatively high, perhaps due and late in life, and minimal effects at intermediate to the effects of experimental setup, and genetic vari- ages. This would be the opposite of the age-specific ance over much of the life span was relatively constant. effects suggested by recent experiments on variation There is some evidence for this – in many of the lines, due to spontaneous mutations (Promislow et al., 1996; mortality rates are initially high and then drop for 5- Pletcher, Houle & Curtsinger, 1998). Clearly we need 10 days before increasing (Figure 2, and Clark and experiments designed to test directly the possibility Guadalupe, unpublished data). that these two types of mutations differ in effect not

gene441.tex; 26/05/1998; 15:02; v.7; p.13 312 only in terms of their magnitude (see also Keightley, are assumed to be constant with larval age. The same 1996), but also in terms of their age-speciﬁcity. data are also shown in terms of larval viability (Fig- In Houle et al.’s (1994) work described above, the ure 4A, 4B). We assume a 10-day developmental peri- authors analyzed the mutational covariance between od, such that larval viability

age classes. Although they did not try to estimate spe-

ciﬁc ages at which de novo mutations act, they argued lar v

l = e

lar v (5) that weak or no mutational covariance between age- classes would support the existence of mutations with This distribution of viabilities is remarkably similar age-speciﬁc effects. In contrast, they found strong pos- to that determined by Keightley (1996) for previously itive correlations between ages for age-speciﬁc fecun- published data (Mukai et al., 1974). Thus, the skew

dity (r 0.6). They argue that this result fails to sup- observed by Keightley may be due, at least in part, to port the mutation accumulation model. If mutational the choice of variable studied. effects acting late in life are highly correlated with In addition, Keightley’s work focused on mutation- mutational effects acting early in life, then selection al effects on larval viability. But we know that in many on early-acting mutations will act as de facto selection cases there is little genetic concordance between fitness on late-acting mutations. traits in the larval stage and those in adults (Chippin- Finally, recent work by Rogina and Helfand (1995, dale et al., 1994; Zwaan, Bijlsma & Hoekstra, 1995). 1996) provides some direct molecular evidence that Thus, we need to know how the effects of novel muta- genes with age-specific patterns of expression exist in tions are distributed with respect to mortality rates at adult flies and that the pattern of expression is correlat- all life stages. ed with life span. Expression of two separate genes was shown to exhibit clear patterns of age-specificity. In one case (Rogina & Helfand, 1995), a gene showed an Conclusion initial increase in expression followed by a subsequent decline, and the timing of these changes appeared to be Taken together, these data on the way in which muta- linked with physiological age of the organism. A sections affect mortality, the age-specificity of mutations, ond gene (Rogina & Helfand, 1996) showed complex and the distribution of effects of new mutations suggest age-related expression linked more to chronological that we need to re-evaluate our previous assumptions age than to physiological age. of how mutations affect survival. In closing, we sug- Further quantitative and molecular genetic studies gest that in light of much new information, it is time are clearly necessary to obtain information about the to design models with a set of new, more biological- overall pattern of expression of novel mutation. ly realistic of assumptions. First, we have previously assumed that mutations have instantaneous effects on Do all mutations have equal effects? life history traits. Perhaps it is more realistic (albeit In the past few years, Peter Keightley has developed less mathematically tractable) to assume that muta- models to determine the distribution of the magnitude tions that ‘turn on’ at a particular age then stay on. of effects of novel mutations. He has estimated the dis- This assumption leads to a second assumption that the tribution of mutational effects based on analyses of rel- effects of novel mutations will be positively correlat- ative larval viability (Keightley, 1996), using a model ed across ages. Third, the data suggest that mutations that assumes additivity among loci. Keightley’s results act additively not on survival, but rather on the log of suggest that the vast majority of mutations are of very age-specific mortality. weak deleterious effect, with a very small fraction of This new set of assumptions may help us to explain mutations that have substantial deleterious effects on a series of new demographic findings that are incon- fitness. The distribution of mutational effects is high- sistent with theoretical expectation. These observa- ly skewed. However, this skew in mutational effects tions include a) leveling off in late-age mortality; b) in viability is consistent with a normal distribution of a decrease in genetic variance for mortality late in mutational effects on log(mortality). To demonstrate life; and c) convergence of mortality curves late in this, we have plotted the distribution of simulated data, life among cohorts.

assuming that deleterious mutations act additively on Incorporating realistic assumptions about how the logarithm of larval mortality rates, ln( lar v ), which mutations affect mortality, and new observation about mortality trajectories, should provide an exciting chal-

gene441.tex; 26/05/1998; 15:02; v.7; p.14 313 lenge for theoreticians and a clearer guide for empiri- Curtsinger, J.W., H.H. Fukui, A.A. Khazaeli, A. Kirscher, S.D. cists in the design and interpretation of evolutionary Pletcher, D.E.L. Promislow & M. Tatar, 1995. Genetic variation studies of aging. and aging. Annual Review of Genetics 29: 553–75. Curtsinger, J.W., H.H. Fukui, D.R. Townsend & J.W. Vaupel, 1992. Demography of genotypes: Failure of the limited life-span para- digm in Drosophila melanogaster. Science 258: 461–463. Acknowledgments Dobzhansky, T., R.C. Lewontin & O. Pavlovsky, 1964. The capacity for increase in chromosomally polymorphic and monomorphic populations of Drosophila pseudoobscura. Heredity 19: 597– We gratefully acknowledge Andy Clark and Scott 614. Pletcher for generously sharing their data with us, and Ebert, D., L. Yampolsky & A.J. Van Noordwijk, 1993. Genetics of Locke Rowe and two anonymous reviewers for help- life-history in Daphnia magna. 2. 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