299
Genetica 102/103: 299–314, 1998.
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
Other authors, including many in this volume, have
described how mutations can act not only as the source
of genetic variation on which selection acts, but may
even be the fundamental driving force in evolutionary
change, from the origin of sex (Kondrashov, 1998) to
the maintenance of sexually selected characters (Pomiankowski, Iwasa & Nee, 1991) to the ultimate decline
and disappearance of populations (Lande, this volume). Here we turn our attention to the evolution of
aging.
Many previous books and articles have provided
comprehensive reviews of the underlying theory for
the evolution of aging and the evidence that supports
or refutes this theory (Rose & Charlesworth, 1980; Partridge & Barton, 1993; Charlesworth, 1994; Curtsinger
et al., 1995). Rather than revisit this body of work, we
will touch on the theoretical background only briefly.
Our primary aim here is to integrate previous the-
oretical and empirical work in the field with recent
advances in the use of large-scale demography in studies of senescence (Carey et al., 1992; Curtsinger et al.,
1992; Vaupel, Johnson & Lithgow, 1994). In light of
these studies, we focus on the ways in which an explicitly demographic perspective can enhance our ability to
interpret studies of mutation accumulation and aging,
and guide research in the future.
Background
Aging is here defined as a persistent decline in agespecific fitness components of an organism (i.e., rates
of reproduction and survival) due to internal physiological deterioration (Rose, 1991). We expect to see an
age-related decline in all fitness components. For the
purpose of this present article we focus our attention
on age-specific mortality rates (Comfort, 1979; Finch,
Pike & Witten, 1990; Promislow, 1991; Curtsinger,
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300
1995), while acknowledging that other metrics of aging
exist (Curtsinger, 1995; Graves, 1995; Partridge &
Barton, 1996).
The evolutionary origins of senescence are generally explained by two widely-accepted theories–
mutation accumulation (Medawar, 1952) and antagonistic pleiotropy (Williams, 1957). We will confine
our focus here to the mutation accumulation model.
Medawar (1952) proposed that senescence arises
because the strength of selection declines with age. A
newly arising mutation in humans that reduces fertility by 50%, but that is only expressed after age 45,
would experience little selection against it. In the virtual absence of selection, it may increase in frequency through drift alone. The same deleterious mutation expressed at age 20 would be subject to very
strong selection. As a consequence, over many generations, late-acting deleterious mutations are more
likely to accumulate than early-acting ones. These
late-acting mutations will then cause an age-related
decline in fitness traits, including fecundity, fertility, and survival rates. This theory of aging has given
rise to specific micro-evolutionary predictions (Rose,
1985; Charlesworth, 1990). In particular, mathematical models of Medawar’s mutation accumulation theory predict an age-related increase in genetic variance
components (Charlesworth, 1990) and in inbreeding
load (Charlesworth & Hughes, 1996) for traits related
to fitness.
Charlesworth’s models (Charlesworth, 1990;
Charlesworth, 1994; Charlesworth & Hughes, 1996)
are based on assumptions about the nature of the effects
of mutations on fitness components. To make analysis tractable, while acknowledging that the assumptions underlying the model are not necessarily realistic,
Charlesworth has made the simplifying assumptions
that mutations act additively on age-specific survival
rates and that mutations are equally likely to act at any
age. We address the experimental evidence for these
assumptions in a later section of this paper.
Both mutation accumulation and antagonistic
pleiotropy theories have spawned a wealth of
experimental tests (recent reviews in Rose, 1991;
Charlesworth, 1994). But only very recently have biologists recognized that to understand the evolution of
aging fully, genetic studies of survival or fecundity
need to rest on large-scale demographic approaches
(e.g., Curtsinger et al., 1992; Curtsinger et al., 1995;
Fukui, Ackert & Curtsinger, 1996). With this in mind,
we first use a demographic perspective to evaluate
existing experimental evidence for the mutation accu-
mulation model of aging. Second, we explore the specific problem that arises in tests of aging due to the
way in which fruit flies – the work-horse of the field of
experimental demography – are maintained. And finally, we weigh the evidence in support of the underlying
assumptions of evolutionary models of aging.
Evidence for the mutation accumulation model
The mutation accumulation model gives rise to numerous predictions that can be tested experimentally: a)
variance for fitness traits should increase with age
(Rose & Charlesworth, 1981b; Charlesworth, 1990);
b) reverse selection for early fitness on lines produced
from selection for late-life fitness should only slowly revert to pre-selection age-specific phenotypes; c)
the controlled introduction of spontaneous or directed
mutations should alter patterns of senescence; and d)
inbreeding depression should increase with age (Tanaka, 1993; Charlesworth & Hughes, 1996).
A. Changes in variance with age
Under the mutation accumulation scenario, the relatively reduced force of natural selection permits an
age-dependent decrease in the selection-mutation balance. This should lead, in turn, to a greater amount of
additive genetic variance for fitness traits at late ages
compared to earlier ages. The prediction of an agerelated increase in genetic variance for fitness components is fundamental (though not necessarily exclusive,
see Charlesworth & Hughes, 1996) to the mutation
accumulation theory of aging. Many studies have now
tested this prediction for a variety of traits, including
age-specific fecundity (Rose & Charlesworth, 1981b;
Engström et al., 1989; Ebert, Yampolsky & Van
Noordwijk, 1993; Tanaka, 1993; Tatar et al., 1996),
age-specific mortality (Hughes & Charlesworth, 1994;
Hughes, 1995; Promislow et al., 1996), and male reproductive ability (Kosuda, 1985; Hughes, 1995), with
mixed results.
Fecundity
Rose and Charlesworth (1980, 1981b) first tested this
prediction by analyzing additive genetic variation for
fecundity in Drosophila melanogaster. Average additive genetic variance did not change with age. However, as has been previously pointed out, any realized
increase in variance may have been offset by the dif-
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301
ferential mortality of females with relatively high early fecundity, due to the costs of reproduction (Clark,
1987; Engström et al., 1989; Partridge & Barton,
1993).
In a later study, Engström et al. (1989) included
only those females that survived for the duration of
the experiment. Although they found that variance for
fecundity increased with age, the observed increase
may have been due to the fact that their data were logtransformed (G. Engström, personal communication;
Tatar et al., 1996), when the underlying raw data were
not log-normally distributed.
A rather different pattern has been observed in two
more recent studies, one on the bean weevil Callosobruchus chinensis (Tanaka, 1993), and the other on a
large cohort of Drosophila (Tatar et al., 1996). In both
cases, the authors found significant additive genetic
variance for fecundity early in life, a subsequent drop
in variance, and then an increase at later age-classes.
At least for the finding of Tatar et al., this unexpected
result may be due in part to the way in which flies
are typically maintained in the lab. We discuss this
possibility later in this paper.
Mortality
Mortality rates are at the heart of our interest in aging,
yet only recently have researchers begun to estimate
genetic variance components for mortality. Hughes and
Charlesworth (1994) were the first to demonstrate a
significant increase in genetic variance for age-specific
mortality in Drosophila, which they argued showed
clear support for the mutation accumulation theory of
senescence. Subsequent work by others suggests that
their results tell only part of the story (Promislow et
al., 1996). When much larger cohorts are used in these
studies, variance components appear to decline at late
ages, counter to the most current predictions of the
mutation accumulation model (Promislow et al., 1996;
see also Pletcher, Houle & Curtsinger, 1998).
Male mating ability
In what is now perhaps the most widely cited study
to show an age-related increase in variance for fitness
traits, Kosuda (1985) found an age-related increase
in coefficient of variation for male mating ability
among lines of flies that were homozygous for different extracted second chromosomes. In addition, he
also showed that mating ability declined at a more
rapid rate in inbred than in outbred lines. Although
these results are based on analysis of genotypic vari-
ance, subsequent work by Hughes (1995) demonstrates
a similar increase in additive genetic variance for male
mating ability.
B. Demographic selection
Lines generated by demographic selection have been
used to assess whether mutation accumulation causes senescence. Service, Hutchinson and Rose (1988)
applied reverse selection to lines that had originally
been selected for postponed senescence. After reverse
selection they assessed early fecundity and three physiological variables that were characteristic of long lived
lines, including tolerance to starvation, desiccation,
and ethanol. Early fecundity responded directly to
reverse selection, and starvation resistance decreased
in the process. Desiccation resistance and ethanol tolerance, on the other hand, did not change after 22
generations and remained at elevated levels. They reasoned that desiccation resistance and ethanol tolerance
had improved originally in the long-lived lines, due
to the removal of late-acting age-specific deleterious
alleles present in the ancestral stocks (early deleterious
effects of the alleles would have precluded their accumulation). From the response of these traits, Service,
Hutchinson and Rose (1988) concluded that mutation
accumulation is a general mechanism for senescence
in D. melanogaster.
Let us consider their conclusion carefully. First,
Service, Hutchinson and Rose (1988) did not measure
how late fecundity or lifespan responded to reverse
selection, although the original improvement of these
demographic traits under selection for late fitness was
cited as the primary evidence for postponed senescence. Clearly, to understand the effect of reverse selection on senescence one should measure the return rate
of the demographic traits assayed originally. In particular, did lifespan rapidly return to the level of the control
population? If it did not, we would suggest that mutation accumulation is the primary underlying genetic
architecture that led to the eventual difference in senescence among the lines, rather than the more commonly
ascribed mechanism of antagonistic pleiotropy. In part
B of the following section we develop this idea further
when we discuss the effects of culture domestication
on mutation accumulation in D. melanogaster.
Second, Service, Hutchinson and Rose (1988) measured desiccation resistance and ethanol tolerance on
relatively young adults, those that were 6 days of age.
They observed no reverse selection response for these
age-specific traits. From this observation, Service et al.
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302
argued that mutation accumulation was the cause of the
deleterious expression of the traits in the ancestral controls, relative to the long-lived selected lines. However,
since the traits were measured at age 6 days, this argument requires that mutations affected fitness at ages
equal to or greater than 6 days, but that the mutations
had no effects on flies aged 0-5 days, ages that were
actively exposed to selection in the ancestral stocks.
As there is no evidence for such extreme asymmetry
in the age specificity of mutations, we should consider an alternative explanation, as suggested by Service,
Hutchinson and Rose (1988). The reverse selection
response may be due to epistasis combined with differences in genetic background among the ancestral
and long lived lines.
The footprint of mutation accumulation may be
inferred elsewhere from the recovery of late-age phenotypes when early-fitness selected lines are hybridized.
Mueller and Ayala (1981) created r lines based on
reproduction at young adult ages in discrete culture,
and K lines using higher density populations with overlapping generations. Purebred r lines have only 31%
of the week-four fecundity of purebred K lines, but
when hybrids within each selection regime are compared, the F1 r lines improve their week-four fecundity
to a level that is 74% that of the F1 K lines (Mueller,
1987). Mueller (1987) suggested that late fitness of the
r lines suffered from accumulation of deleterious mutations during the greater than 120 generations of their
selection on early fitness. Hybridization among the
independent r lines could at least partially restore late
fitness through dominance effects of non-mutant alleles
among the complementing lines. Further hybridization
analyses of this sort in terms of age-specific demographic traits may provide insight into the potential for
and prevalence of mutation accumulation as a cause of
senescence.
C. Mutation accumulation experiments
The above studies were concerned with understanding
the role of mutation accumulation in the past as a causal
factor in the evolution of senescence. An alternative
approach, discussed here, is to ask whether controlled
mutation is adequate to produce recognizable patterns
of senescence. To this end, recent studies have either
permitted the accumulation of spontaneous mutations,
or induced mutations with P-elements, and then analyzed the effects on patterns of aging.
Houle et al. (1994) created a set of mutation accumulation lines to estimate the effect of de novo muta-
tions on aging. In the early 1970s, Mukai and his colleagues first used this approach (Mukai et al., 1974), in
which one homologous chromosome is kept balanced
against another homologue with a dominant marker, a
recessive lethal gene, and multiple inversions (to prevent recombination). Thus, mutations with partially
or completely recessive deleterious effects can accumulate on the unmarked chromosome in the virtual
absence of selection. Subsequent studies have also used
the approach of maintaining lines under small effective
population size, which reduces the efficacy of selection
against mildly deleterious loci (Mackay et al., 1994;
Falconer & Mackay, 1996).
Houle et al. (1994) analyzed 48 mutation accumulation lines for several traits related to aging, including
early and late fecundity, early and late male mating
ability, and age-specific mortality, measured in terms
of the slope and intercept of the Gompertz curve, (see
equation [4], below, for details of the Gompertz model). They found no significant mutational variance for
mortality rate parameters, although mutational variance for mean longevity and late-age reproduction was
evident. Houle et al. also observed that mutational
effects were positively correlated among the early and
late age classes, and from this they argued that mutation accumulation in general is inadequate to explain
the persistence of senescence at equilibrium. This conclusion, however, rests on the age-specific nature of de
novo mutations.
How do specific mutations affect senescence?
The spontaneous mutation accumulation approach
described above, and also used recently by Pletcher, Houle and Curtsinger (1998), cannot answer the
question, because each mutation may have an effect
too small to detect. Single-gene mutagenesis, however, may provide some answers to this question. For
example, Clark and Guadalupe (1995) used P-element
induced mutations in D. melanogaster to look at the
effects on survival of single mutations of substantial
effect. As with Houle et al.’s result, they found only
weak evidence for late-acting mutational effects.
Given the evidence to date, we have little doubt
that mutation accumulation plays a significant role in
the evolution and maintenance of senescence, at least
in laboratory population studies so far. The accumulation of deleterious mutations can lead to depression
of a variety of fitness traits and an increase in genetic variance for those traits late in life. However, at
least three major issues remain unresolved. First, how
important is mutation accumulation relative to antagonistic pleiotropy as a cause of senescence. Second,
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303
what is the nature of the effects of mutations with
respect to age. The claim that late-acting mutations are
more likely to accumulate assumes that there exists a
class of de novo mutations whose effects are confined
to late ages. The assumption remains virtually untested.
Third, are the data collected thus far based on statistically reliable demographic approaches. Recent studies based on very large-scale demographic approaches
suggest that we may need to re-evaluate conclusions
from previous studies on the role of mutation accumulation in aging. To answer these questions we must
overcome several specific theoretical, statistical and
empirical challenges
Challenges to testing the mutation accumulation
model
There are three critical issues that affect our ability
to test the mutation accumulation model for the evolution of senescence. First, our current predictive models
assume that life history traits are normally distributed,
and that means and variances are not correlated. These
assumptions are violated by major fitness parameters
and by mortality rate in particular. Second, most studies of evolutionary models of aging have relied on labdomesticated populations of the fruit fly, Drosophila
melanogaster. These populations are valued because
they are likely to be at some degree of demographic and
genetic equilibrium. However, the discrete-generation
protocol that has typically been used to maintain stocks
of flies may have unwittingly served as a generator
of late-age mutations, and so may have confounded
genetic studies of aging. Third, models for the evolution of senescence make specific assumptions about
the nature of the mutations that generate age-specific
changes. For example, de novo mutations are assumed
to have effects limited to specific ages, and to be more
prevalent at late ages. But only recently have studies
begun to test this assumption (Houle et al., 1994; Clark
& Guadalupe, 1995; Pletcher, Houle & Curtsinger,
1998), and the early evidence here suggests that the
age-distribution of the effects of novel mutations may
be more complex than previously thought.
A. Demography and variance in studies of aging
Several examples illustrate the necessity of accounting
for the complex statistics of demographic parameters
in tests of the mutation accumulation model.
The prevalent predictive models (e.g., Charlesworth,
1990; Charlesworth & Hughes, 1996) for the evolution
of aging assume that fitness traits — fecundity or survival — are normally distributed. If this assumption
is violated, one tends to observe strong mean-variance
correlations. For fecundity, survival, and male mating
ability, empirical results show them to be distinctly
non-normal. Male mating ability, at least as measured
in studies on aging (e.g., Kosuda, 1985), is binomially distributed (Promislow et al., submitted). A recent
study of age-specific fecundity found that egg counts
were approximately Poisson distributed (Tatar et al.,
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 isogenic individuals differ in their intrinsic risk of mortality due to environmental variance). Across ages within a
cohort, mortality rates increase exponentially. Among
different cohorts of the same-age, mortality is lognormally distributed. And finally, at very small sample
size or very low mortality rate, mortality can act as a
threshold character, such that it is not visible until the
mortality rate is greater than approximately the inverse
of the sample size. Failure to account for the complex
distribution of demographic parameters can mislead us
when we attempt to estimate age-specific changes in
genetic variance components.
Male mating ability
In 1985, Kosuda published the first study to show clear
evidence of an increase in genotypic variance for a fitness trait (Kosuda, 1985). In this case, the fitness trait
of interest was male mating activity (MMA). Kosuda used balancer stocks to isolate twenty-nine lines of
Drosophila melanogaster, each of which was homozygous for a different second chromosome extracted from
a natural population. For each line, he placed 1 virgin male and 12 virgin females in a vial and assayed
the number of inseminated females after 24 h. Twelve
males were tested for each of the twenty-nine lines.
Tests were conducted at ages 3 d (young) and 28 d
(old) post-eclosion. The mutation accumulation theory predicts that variance in fitness traits (such as
male mating ability) should be greater among old flies
(Charlesworth, 1990). Kosuda found that the MMA
declined from a mean of 0.535 to 0.185 (proportion of
females inseminated), and as predicted, the coefficient
of variation (CV) among lines increased from 49.6%
to 120%, an increase of a factor of 2.4.
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304
To interpret this result, we need an appropriate null
model. What is the expected change in variance with
age for MMA if there is no change in genotypic variance for the trait?
Given that MMA is binomially distributed, its
expected variance E( 2 ) = p(1-p)/N, where p is the
average MMA among lines, and N is the total number
of females sampled. Similarly, the expected coefficient
of variation
q
E (CVp ) =
p(1 p)
N
p
s
=
p)
Np
(1
(1)
The ratio of the CVs for these two variables is given
by CVEarly /CVLate
CVL
=
CVE
r
p E (1
pL (1
pL )
pE )
r
=
0:535
0:185
0 815 = 2 3
0 465
:
:
:
(2)
which is very close to the increase of 2.4 observed by
Kosuda.
One could use an arcsin transformation if the data
were truly binomial (see, for example, Hughes, 1995).
However, the distribution of male mating ability may
be slightly more complex. If isogenic males within
lines show intrinsic differences in mating ability, (due
to environmental variance, for example) the trait distribution may be beta-binomial, rather than simply binomial (Searle, Casella & McCulloch, 1992). To deal
with this complexity, future studies should use randomization procedures to determine whether the increase in
CV observed is significantly greater than that predicted
by chance alone.
Age-specific mortality rates
Although the mutation accumulation model was developed to explain the age-related increase in mortality
(Medawar, 1952), only recently have scientists turned
their attention to this key variable. The first such study
was conducted by Hughes and Charlesworth (Hughes
& Charlesworth, 1994; Hughes, 1995). To estimate
genetic variance components for age-specific mortality, Hughes and Charlesworth extracted 40 wild-type
chromosomes from an outbred population of Drosophila melanogaster. They crossed these lines in a partial
diallel design (Comstock & Robinson, 1952) and estimated mortality rates in the progeny for three different
ages (0-3 wk, 5-7 wk, 9-11 wk). From these data, they
were able to determine genetic variance components
for age-specific mortality rate. This study provided the
first evidence that additive genetic variance for mortality rates did, in fact, increase with age.
Promislow et al. (1996) suggested that the increase
in variance observed by Hughes and Charlesworth may
have been due to artifacts of the distributional properties of mortality rate coupled with insufficient sample
size. As with MMA, we require a null model to determine how we expect estimated variance of mortality
rate to change with age when the underlying genetic
variance is indeed constant across ages, given a particular rate of increase in mortality and a particular
age-dependent sample size. At issue is the fact that
when sample size N is small relative to mortality (such that < 1/N) we are likely to underestimate
the true variance in mortality, but when mortality rate
increases with age the true underlying genetic variance becomes apparent, and we thus observe a trend of
increasing genetic variance with age. Under the null
model assumption of no increase in variance, only
when initial cohort sizes are very large do we have statistical power to see that genetic variance at young ages
is the same as at ages where mortality rates are relatively high. Thus, to test predictions, we require demographic studies based on much larger sample sizes.
This requirement motivated Promislow and colleagues to conduct an experiment similar to that of
Hughes and Charlesworth, but with substantially larger sample sizes. Similar to Hughes’ and Charlesworth’s
original experiment, Promislow et al. (1996) observed
an initial, age-specific increase in additive variance for
mortality. In this case, the increase does not appear to
be due to insufficient sample size. At late ages, however, variance components for mortality declined, contrary to what is predicted by standard mutation accumulation models. This result is a novel observation
that challenges the basic assumptions of predictions
for the mutation accumulation model of senescence.
No model exists yet that would explain this result.
As with early ages, the reduction in the number
of live individuals could potentially lead to an erroneous apparent reduction in variance at later ages. In
Promislow et al.’s (1996) experiment, sampling error
at late ages may have led to an underestimate of mortality rates. To control for the potential effect of sampling error, Frank Shaw (personal communication) has
developed a statistical technique, based on maximum
likelihood, that accounts not only for the unusual statistical distribution of age-specific mortality, but also for
the effects of sample size. Shaw’s analysis of the mortality data using this technique further supports Promislow et al.’s original interpretation–variance compo-
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305
nents for mortality do, indeed, decline at late ages, even
after accounting for the effect of sampling error. The
decline in genetic variance for mortality observed by
Promislow et al. could have several other explanations.
The age specificity of mutational effects is unknown.
Mutations may have limited effects at advanced ages,
which would preclude the accumulation of additive
variance among the oldest old. Alternatively, heterogeneity of reproductive costs among genotypic cohorts
may produce a decline in variance once all groups reach
post-reproductive ages (Promislow et al., 1996).
A recent study by Sergey Nuzhdin and colleagues
(Nuzhdin et al., 1997) provides additional evidence
of the need to analyse mortality, rather than survivorship. Nuzhdin et al. (1997) compared survivorship curves among 98 recombinant inbred lines of
D. melanogaster. To test the mutation accumulation
model, they asked whether the coefficient of additive genetic variance (CVG ) for survivorship increased
with age. Survivorship, the percentage of individuals
in a cohort alive at a given age, necessarily declines
with age. To control for the decline in mean survivorship, the authors rescaled survivorship by dividing the
age-specific survivorship for each line by the mean
age-specific survivorship among all lines. They then
calculated the variance among the rescaled lines, and
to obtain CVG , divided the scaled variance by the
unscaled mean. However, because the unscaled mean
of survivorship is smaller at late ages, the value of CVG
increases with age. Thus, the increase that Nuzhdin et
al. observed may have been an artefact of using agespecific survivorship, rather than mortality rates, to
estimate age-specific variance.
Inbreeding load and the mutation accumulation model
Charlesworth and Hughes (1996) point out that both
genetic models of aging–mutation accumulation and
antagonistic pleiotropy–predict an age-related increase
in additive genetic variance for fitness traits, at least
under certain conditions. Thus, an analysis of additive
variance at different ages does not necessarily provide
a mutually exclusive prediction that would allow us to
distinguish between the two models.
Fortunately, there may be a genetic prediction that
is specific to mutation accumulation. Under mutation
accumulation, if deleterious mutations with effects on
late-age fitness traits have a higher frequency than those
with effects on early-age fitness traits, and if mutations are partially or fully recessive (Simmons & Crow,
1977), then inbreeding depression should be less for
fitness traits early in life than late in life.
The first test of this prediction is provided by Tanaka (1993), who compared age-specific fecundity at ten
ages (at 2-day intervals) in the bean weevil, Callosobruchus chinensis. He regressed differences in the logtransformed values of outbred minus inbred fecundity
versus age and found no significant increase. This failure to find an increase is even more notable given that
Tanaka was basing the analysis on differences between
log-transformed values of fecundity. Because fecundity in Callosobruchus takes on a Poisson distribution
and declines monotonically with age (C. Fox, personal communication), for statistical reasons alone one
would expect an apparent increase in the difference
between inbred and outbred fecundity with age, under
a null model of no actual increase in the difference
between the two groups.
The prediction was also evaluated by Charlesworth
and Hughes (1996), who developed an explicit model for inbreeding load under mutation accumulation.
They assume that mutations act additively on survival,
such that the deleterious mutation rate at the ith locus
with effects on survival rate z is given as ui and has
effect zi . Their model predicts that inbreeding load, L,
defined as the ratio of age-specific survival in outbred
flies (zO ) to age-specific survival in inbred flies (zI )
should increase with age, t. That is,
zO
d
1n
> 0:
dt
zI
(3)
Survival rate is related to mortality rate, , as z = e .
Thus, we can restate mutation load as L = I – O .
Charlesworth and Hughes tested this prediction
with data collected by Hughes as part of a larger study
on the genetics of fitness in male D. melanogaster
(Hughes, 1995). They found that the inbreeding load
increased with age, in direct support of the mutation
accumulation theory for the evolution of senescence.
But as with previous studies we have discussed so far,
in this case the statistical and demographic nature of
mortality makes these observations difficult to interpret.
First, as with standing genetic variance discussed
above, at early ages, mortality rates tend to be very
low. Over a large range of ages, mortality rates may
be non-zero, but significantly lower than the measurable threshold of one death per cohort of size N
(i.e., x < 1/Nx , where Nx is the number of individuals in a cohort of age x). If mortality rates differ
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between inbred and outbred lines, but are both below
this threshold, then we will not be able to detect a difference between the two. At later ages, as mortality
rates increase above the threshold, we will more easily
detect a difference between inbred and outbred lines.
Thus, even in the absence of any real increase in difference between inbred and outbred mortality, we might
expect to find an apparent increase with age, because
of an age-related increase in our ability to detect a
difference.
Second, because mortality is log-normally distributed, there is a strong positive mean-variance correlation, so the distance between lines on an absolute
scale necessarily increases. To illustrate, we can simply model mortality with a Gompertz curve, such that
x = ex;
(4)
where is the Initial Mortality Rate (IMR), and is
the actuarial rate of aging. For now we safely ignore
the fact that late-life mortality departs significantly
from this pattern (Abrams, 1991; Carey et al., 1992;
Curtsinger et al., 1992; Vaupel, Johnson & Lithgow,
1994).
Consider two cohorts, one inbred and one outbred,
that are identical in their actuarial rate of aging (i.e.,
O = I = ), but differ in their IMR component, with
I > O . In this case, the difference between mortality curves of two cohorts that vary only in alpha will
necessarily increase with age, as will the age-specific
inbreeding load, L[x] = I – O = (I – O )ex .
B. Demography of fly culture
Until now, we have stressed the importance of careful
use of demographic approaches in studies of mutation
accumulation. We have argued that standard demographic designs can lead to biased results in a variety of studies. The problems may actually be even
more complex. Many selection studies were initiated
from base stocks laden with late-expressed mutations
that accumulated prior to selection. We suggest that
this complicates how we interpret direct and correlated
selection responses and, in turn, may bias our interpretations of the evidence for antagonistic pleiotropy
theories of senescence. Our comments here are extensions of observations first made by Clark (1987).
To illustrate genetic trade-offs in senescence, many
researchers have selected on late-age fitness and have
observed increased life expectancy and, as predicted
by the antagonistic pleiotropy theory of senescence,
reduced early-expressed traits such as fecundity or
development rate (e.g., Wattiaux, 1968a, 1968b; Rose
& Charlesworth, 1980; Rose, 1984). Furthermore,
some have observed increases in other late-life traits
including late-fecundity and stress tolerance (Service
& Rose, 1985; Service, Hutchinson & Rose, 1988;
Chippindale et al., 1993). These data are widely used
to argue that antagonistic pleiotropy is a primary basis
for the evolution of senescence, and that certain physiological traits underlie variation in longevity.
In almost all cases, these selection programs used
laboratory adapted base stocks. This was done to avoid
spurious positive genetic correlations that might arise
due to gene-environment interactions when wild flies
are introduced into the novel laboratory environment
(Service & Rose, 1985). In practice, however, laboratory adaptation may have introduced more problems
than it solved. In particular, laboratory adapted stocks
are commonly maintained in a 2-week discrete culture. Unfortunately, this practice constitutes a de facto mutation accumulation experiment, allowing lateacting deleterious mutations to increase in frequency
in the base stock in the absence of selection. We believe
that these novel mutations in the base stock may have
provided the genetic variation upon which much of the
observed selection response in previous experiments
was based.
In 2-week culture, adult flies are transferred into a
fresh vessel at reference day 0. At the time of transfer, eggs must be laid immediately since the adults are
often removed after several hours. Even if they remain
for several days, only those eggs laid within 36-48 h
are likely to contribute to the following generation (D.
Houle and L. Rowe, pers. comm.). Typically, the most
rapidly developing individuals pupate no earlier than
at reference day 8, while the modal emergence is at day
9 or 10 (Ashburner, 1989). Emergence continues until
reference day 14, at which time the accumulated adults
are transferred to the next day 0 vessel. Up to a maximum of 4 days of age, all eggs laid by adults before
transfer make no contribution towards lifetime reproductive success. Then, within 24 h, all flies experience
a narrow window of potential reproductive opportunity. As a consequence, genes for adult fitness traits
expressed after 4 days of age are not directly exposed
to selection.
Although little is known about fitness traits in natural populations of Drosophila, it is likely that reproductive value remains high beyond 4 days of age. If
this is the case, then when wild flies are introduced
to a 2-week regime as a prelude to conducting selec-
gene441.tex; 26/05/1998; 15:02; v.7; p.8
307
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
name
(Rose & Charleston, 1981; ‘Ives’
Rose, 1984) and
all current derivates
Base stock Culture population Founding population Interval of
selection No. generations
founded
structure
max. estimate Ne
discrete culture initiated selection intitated
(yr)
after base founded
1970
Discrete
unknown
14 days
1980
> 130
(Luckinbill et al., 1984)
‘Michigan Orchard’ unknown
Discrete
< 50
7–14 days
ca. 1981
12
(Engström, Liljedahl &
Björkland, 1992)
‘Swedish Stock
Center Hybrid’
unknown
Discrete
unknown
16 days
unknown
> 10 once hybrid
(Partridge &
Fowler, 1992)
‘Brighton’
1984
Overlapping
unknown
NA
1985
kept with overlapping
generations
(Partridge &
Fowler, 1992)
‘Dahomey’
1970
Overlapping
unknown
NA
1986
kept with overlapping
generations
(Zwaan, Bijlsma &
Hoekstra, 1995a;
Zwaan, Bijlsma &
Hoekstra, 1995b)
‘Groningen 1983’
1983
Discrete
403 isofemale
lines
14 days
1990
unknown
(Zwaan, Bijlsma &
Hoekstra, 1995a;
Zwaan, Bijlsma &
Hoekstra, 1995b)
‘Groningen 1983’
1983
Discrete
403 isofemale
lines
14 days
1991
unknown
unknown before
tion experiments on longevity, we release this later
part of their natural life history from direct selection.
Under this condition, the selection-mutation balance
for genetic effects expressed in late-life is altered and
mutation accumulation for late-express traits will likely take place. The expected effect of the accumulation of late-acting, age-specific mutations would be to
reduce many late expressed fitness traits, including life
expectation, fecundity, and stress tolerance.
Over a few generations of relaxed late-age selection, the rate of decline in fitness due to novel mutations will be virtually unmeasurable. However, in previous studies, many of the base stocks used as selection material were maintained in 2-week culture for
over 120 generations (Table 1). Given a per-generation
decline in fitness of between 0.1 and 1% due to mutation accumulation (Mukai et al., 1974; Houle et al.,
1994; Falconer & Mackay, 1996), over a hundred
or more generations one would expect to see a substantial decline in late-life fitness, perhaps as great as
50%. This assumes that the mutations have additive
and independent effects, and that mutations are not
totally purged by correlated expression with traits at
ages less than 4 days old. Covariance between ages
(Houle et al., 1994) would reduce the magnitude of the
estimated loads, but the load could still be substantial
if correlations are age limited, as suggested by the data
of Pletcher, Houle and Curtsinger (1998).
What is the consequence of the base stock’s demographic history in the context of demographic selection on longevity? In selection experiments designed to
study senescence, demographic selection for longevity
is applied initially to a base stock by propagating with
adults that are at least 14 days old, an age that we now
recognize has been sheltered from selection in standard culture. Therefore, substantial additive variance
for traits at this age may exist due to mutation accumulation in the base stock, and we should expect a rapid
response in the selection lines as deleterious mutations
are purged. And since deleterious mutations produce
positive genetic covariance among fitness traits, we
should expect many late-age expressed fitness traits
to improve with the direct selection response. It is
important to realize here that selection responses are
measured relative to the original base stock or to a concurrent control population derived from the base stock
that is still maintained on a discrete 2-week culture.
To an unknown extent, the base and control stocks
are effectively mutation accumulation lines, and the
observed selection response represents a purging of
accumulated mutations.
gene441.tex; 26/05/1998; 15:02; v.7; p.9
308
The effect of subsequent selection on base-stock
mutations confounds how we interpret the data
with respect to antagonistic pleiotropy. Antagonistic
pleiotropy is inferred from selection studies from the
negative correlations between directly selected late-age
traits and associated changes in early-age traits. These
correlations are thought to be caused by pleiotropic
loci. Linkage disequilibrium can produce similar patterns, but previous interpretations assumed that the
base populations were at genetic and demographic
equilibrium as a result of their long period of laboratory adaptation. If this were the case, then standing
genetic covariance could largely reflect polymorphism
maintained by antagonistic pleiotropy, and the correlated selection response would reflect this underlying
genetic architecture. The heart of our concern is that
the assumption of genetic equilibrium prior to selection is violated by the 2-week culture practice: late-age
life histories of the base stocks were not in genetic equilibrium. Thus, correlated selection responses,
both negative and positive, could result from linkage
disequilibrium between newly accumulated mutations
and early- or late-age traits that were under direct selection.
Consider the evidence for a genetic trade-off
between early reproduction and survival in the selection data of Rose (1984; Rose & Charlesworth, 1981a).
Rose selected on late-age survival and observed a correlated response of decreased early fecundity relative
to a control. We suggest that the negative correlated response between survival and early reproduction
among the Rose lines (short lived ‘B’, and long-lived
‘O’) may be due to linkage disequilibrium. We surmise that the Ives stocks from which Rose’s lines
were derived contained a substantial mutation load
expressed only at late ages and that, due to removal
of these deleterious mutations, the survival in the ‘O’
lines would have increased relative to the control ‘B’
lines. In addition, during domestication and throughout the experiment, the ‘B’ lines were strongly selected for early reproductive effort. If total reproductive
effort is a deterministic or ‘zero-sum’ quantity (Bell &
Koufopanou, 1985), then upon selecting for late reproduction in the ‘O’ lines, there would be a decline in
early reproduction. Therefore, changes in reproductive
schedule need not be pleiotropic with survival; they
could result from linkage disequilibrium between loci
affecting fecundity and accumulated late-acting mutations.
In light of this argument, we may need to devise
new experiments and models to distinguish the corre-
lations that arise in selection experiments due to antagonistic pleiotropy from correlations that arise due to
linkage disequilibrium and mutation accumulation. In
particular, there are four outstanding issues that need
to be addressed.
First, we do not yet understand the extent to which
inadvertent mutation accumulation has occurred in
each of the initial base stocks, although it is useful to
recognize that not all base stocks are suspect (Table 1,
e.g., Luckinbill et al., 1984; Partridge & Fowler, 1992).
Second, we cannot determine the extent to which
an observed selection response is due to the purging of
base-stock accumulated mutations versus a response
due to changes in gene frequency of polymorphic loci
that were segregating in the natural population (or
maintained under balancing selection in the lab culture). Consequently we cannot attribute the cause of
apparent supernormal longevity of selected lines: are
they really long-lived or are the base stocks relatively sick? It is widely known, for example, that wildcaught flies brought into the lab are more robust than
lab strains that have been maintained under lab conditions for extended periods (Dobzhansky, Lewontin &
Pavlovsky, 1964).
Third, we have yet to describe adequately the agespecific distribution of mutational effects on fitness
traits. Knowledge of these distributions is required to
predict the extent to which mutation accumulation can
lead to linkage disequilibrium in base stocks relative
to selected lines.
Fourth, most selection studies have not maintained
adequate control stocks to measure selection responses. A control population would be one at genetic and
demographic equilibrium. The many derived selection
and control lines of Rose and colleagues present a special challenge in this respect, because each control line
retained a discrete generation culture regime similar to
that of the ancestral base stock.
It should be apparent that mutation accumulation
and demography are inextricably intertwined, with
causal arrows drawn in both directions. In previous
sections of this paper, we showed how careful use of
demography was needed to test the model of mutation accumulation. In the present section, we argue
that the demographic regime imposed on domesticated
base stocks can alter the balance of mutation accumulation and selection. Much like Heisenberg’s uncertainty
principle, in the very process of examining Drosophila
populations for evidence of mutation accumulation we
inadvertently induce the process we seek to test.
gene441.tex; 26/05/1998; 15:02; v.7; p.10
309
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
senescence.
Do mutations act additively on age-specific survival?
The first of these assumptions concerns the way in
which mutations affect survival rate. Models of both
mutation accumulation and antagonistic pleiotropy
have assumed that genetic effects on age-specific survival rate, Px , are additive on P or on the log of P
(Hamilton, 1966; Charlesworth, 1990; Charlesworth
& Hughes, 1996) for any age x. We can evaluate this
assumption in two ways. First, we can ask whether phenotypic manipulations of any sort alter survival rate in
an additive fashion across ages. Alternatively, we can
take a more direct approach, and ask whether novel
mutations affect survival rates additively.
In the first case, we could measure survival rate at
several ages in cohorts with and without some manipulation. If the manipulation acts additively and instantaneously on survival rate, then the effect should be
similar across all ages. This sort of manipulation has
been done for a variety of factors, including limited reproduction, (Partridge & Andrews, 1985; Tatar,
Carey & Vaupel, 1993; Tatar & Carey, 1995), dietary
restriction (Weindruch & Walford, 1982; Yu, Masoro
& McMahan, 1985; Tatar & Carey, 1995), and transgenic alteration (Orr & Sohal, 1994; Tatar, Khazaeli &
Curtsinger, in prep).
Data from such experiments suggest that, at least
for the manipulations examined thus far, these factors
act additively not on Px , or even on log(Px ), but rather
on the log of instantaneous mortality rate, x (ln(ln[Px]). To take one illustrative case, we have replotted the data from a classic dietary restriction experiment. Although many of these studies have claimed
Figure 1. This figure shows the relationship between Ln(mortality)
and age for rats fed a restricted diet (open squares) and rats fed an adlib diet (filled squares). These data were taken from the survivorship
curves presented in figure 1B of Weindruch and Walford (1982),
with a sample size for each cohort of approximately 70.
that dietary restriction can decelerate the rate of aging
(Weindruch & Walford, 1982), data are typically presented in terms of age-specific survival. By converting these data into mortality curves, one can see that
dietary restriction (e.g., Weindruch & Walford, 1982),
displays a proportional effect on mortality at all ages
(Figure 1). Life span is increased, but the rate of aging
(as defined by the rate of increase in the slope of the
line) does not change. This suggests that at least in
the case of dietary restriction, the manipulation acts
additively on the log of mortality.
However, we can only infer indirectly from these
results whether genetic changes are likely to act additively on Px , ln(Px) or ln(x ). To do this more directly,
we need to assess the effect of de novo mutations on
age-specific mortality rates. If mutations act additively on the log of mortality, for example, then amongcohort variation in log(mortality) due to novel mutations should be normally distributed. Two such datasets
exist that provide at least some preliminary information in this regard (Clark & Guadalupe, 1995; Pletcher,
Houle & Curtsinger, 1998).
Clark and Guadalupe (1994) conducted an analysis of the effects of novel mutations on aging. They
used a P-element construct and the JSK jumpstarter
stock of Drosophila melanogaster to induce mutations
at random genes. The P-element inserts were then
made homozygous using balancer chromosomes and
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
for each of three blocks for which data were available.
These included data on 20 lines in each of two blocks
and 11 lines in a third block. For each age-class and
block, distributions of ln(mortality) did not depart significantly from normality, based on a sequential Bonferroni test of Shapiro-Wilks W with = 0.05 (Promislow and Tatar, unpublished analysis). This result suggests that P-element induced mutations act additively
on ln(mortality). However, we recognize the potential for Type II error in this situation–with the available
sample sizes (N=11 or N=20), the test may fail to detect
departures from normality.
Further information is available from the recent
experiment by Pletcher and colleagues (Pletcher,
Houle and Curtsinger, 1998). The authors analyzed the
effects of de novo mutations on age-specific mortality
rates. They estimated variation in age-specific mortality across ages among 29 mutation accumulation lines
and a control from which the 29 lines were derived.
The analysis included ages at death for 109,860 flies.
Using a Shapiro-Wilks test, the authors determined that
for both males and females, and for each of seven ageclasses, ln(x ) is normally distributed. For one case,
(females at six weeks), W = 0.92, and P = 0.01. However, this is not significant after a sequential Bonferroni
correction for multiple hypothesis tests. In contrast,
distributions of age-specific survival at most ages differed significantly from a normal distribution.
In sum, data from both phenotypic and genetic
manipulations, as well as from mutation accumulation
experiments, suggest that factors which alter survival
lead to proportional changes in mortality rate (i.e., the
additive effect is on the log of mortality rate). It would
be worth creating models based on this more biologically realistic assumption.
Do novel mutations exhibit age-specificity in their
effects?
In the most predictive model to date, Charlesworth
(1990) assumed that there exist de novo mutations with
age-specific effects and that the age of onset of these
mutations is distributed equally across all age-classes.
This assumption gave rise to the prediction that genetic
variance components for fitness should increase with
age. Results from Promislow et al.’s (1996) study called
into question the assumption that there are mutations
with very late-acting effects on fitness traits. However,
this inference is taken from indirect evidence, based on
the standing genetic variance in a population assumed
to be at genetic equilibrium.
Pletcher, Houle and Curtsinger’s (1998) analysis
of mutation accumulation lines was designed to estimate the age-specificity of mutation variance. From
this analysis, they hoped to infer, at least indirectly, the
extent to which novel mutations exhibit age-specific
effects. Pletcher, Houle and Curtsinger (1998) found
that mutational variance was high at early ages, and
then showed a significant decline late in life. There
was only weak evidence of an increase in mutational
variance during the first two weeks.
These results suggest that while there may be agespecific mutations whose effects are seen later in life,
there are no mutations with effects confined solely to
very late ages, and in fact, there may be no mutational
effects whatsoever on traits at very late ages. This result
is concordant with the age-related decline in additive
genetic variance for age-specific mortality observed
by Promislow et al. (1996). However, as both Pletcher,
Houle and Curtsinger (1998) and Promislow et al. point
out, the decline in late-age variance could be confounded by the diminishing effects of reproduction late in
life. Furthermore, the lack of late-age mutational variance in Pletcher, Houle and Curtsinger’s study could
also have been due to the base stock from which the
mutation accumulation lines were derived. The base
stock had been in two-week culture for many hundreds
of generations. As discussed in the previous section,
this may have led to extremely high mutation loads
for late-age fitness traits, to the point that subsequent
mutations would have only minor effect.
Clark and Guadalupe’s study (1995) provides us
with yet further evidence for age-specific mutations.
They point out in their study that mortality rates leveled
off at late ages, and they offer as one interpretation
the possibility that mutations with deleterious effects
confined to very late ages do not occur. To test Clark
and Guadalupe’s claim more directly, we present a
reanalysis of Clark and Guadalupe’s data here. Using
their original dataset, we estimated variance among
lines for age-specific mortality rate. Mortality rate was
estimated per five days. In each of three blocks for
which there were sufficient data to calculate mortality
rates, we found that among line variance was initially
high and then declined. In two of the three blocks,
variance showed a subsequent increase at later ages
(Figures 2 and 3), though not to original levels.
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).
Figure 3. Ln(mortality) versus age for data from Block 2 of Clark
and Guadalupe’s (1995) study, showing an apparent increase in variance both early and late in life. Mortality data were smoothed on
a 3-day running average. Lines differ with respect to P-element
induced mutations, though both environmental and genetic components contribute to total variation in this figure.
minor effects after day 10 or so. The data are also consistent with alternative interpretations. For example,
environmental variation, rather than genetic variation,
may have initially been relatively high, perhaps due
to the effects of experimental setup, and genetic variance over much of the life span was relatively constant.
There is some evidence for this – in many of the lines,
mortality rates are initially high and then drop for 510 days before increasing (Figure 2, and Clark and
Guadalupe, unpublished data).
Although mortality rates in this experiment level
off late in life (Clark & Guadalupe, 1995), data from
blocks 1 and 2 suggest an increase in variance at late
ages (Figures 2 and 3). (Block 4 had insufficient data
to estimate variance components after day 30). The
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
striking decline in variance late in life. It is possible
that, on closer inspection, we will find that P-element
induced mutations have dramatic effects both early
and late in life, and minimal effects at intermediate
ages. This would be the opposite of the age-specific
effects suggested by recent experiments on variation
due to spontaneous mutations (Promislow et al., 1996;
Pletcher, Houle & Curtsinger, 1998). Clearly we need
experiments designed to test directly the possibility
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,
1996), but also in terms of their age-specificity.
In Houle et al.’s (1994) work described above, the
authors analyzed the mutational covariance between
age classes. Although they did not try to estimate specific ages at which de novo mutations act, they argued
that weak or no mutational covariance between ageclasses would support the existence of mutations with
age-specific effects. In contrast, they found strong positive correlations between ages for age-specific fecundity (r 0.6). They argue that this result fails to support the mutation accumulation model. If mutational
effects acting late in life are highly correlated with
mutational effects acting early in life, then selection
on early-acting mutations will act as de facto selection
on late-acting mutations.
Finally, recent work by Rogina and Helfand (1995,
1996) provides some direct molecular evidence that
genes with age-specific patterns of expression exist in
adult flies and that the pattern of expression is correlated 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
initial increase in expression followed by a subsequent
decline, and the timing of these changes appeared to be
linked with physiological age of the organism. A second gene (Rogina & Helfand, 1996) showed complex
age-related expression linked more to chronological
age than to physiological age.
Further quantitative and molecular genetic studies
are clearly necessary to obtain information about the
overall pattern of expression of novel mutation.
Do all mutations have equal effects?
In the past few years, Peter Keightley has developed
models to determine the distribution of the magnitude
of effects of novel mutations. He has estimated the distribution of mutational effects based on analyses of relative larval viability (Keightley, 1996), using a model
that assumes additivity among loci. Keightley’s results
suggest that the vast majority of mutations are of very
weak deleterious effect, with a very small fraction of
mutations that have substantial deleterious effects on
fitness. The distribution of mutational effects is highly skewed. However, this skew in mutational effects
in viability is consistent with a normal distribution of
mutational effects on log(mortality). To demonstrate
this, we have plotted the distribution of simulated data,
assuming that deleterious mutations act additively on
the logarithm of larval mortality rates, ln(larv ), which
are assumed to be constant with larval age. The same
data are also shown in terms of larval viability (Figure 4A, 4B). We assume a 10-day developmental period, such that larval viability
llarv = e
larv 10
(5)
This distribution of viabilities is remarkably similar
to that determined by Keightley (1996) for previously
published data (Mukai et al., 1974). Thus, the skew
observed by Keightley may be due, at least in part, to
the choice of variable studied.
In addition, Keightley’s work focused on mutational effects on larval viability. But we know that in many
cases there is little genetic concordance between fitness
traits in the larval stage and those in adults (Chippindale et al., 1994; Zwaan, Bijlsma & Hoekstra, 1995).
Thus, we need to know how the effects of novel mutations are distributed with respect to mortality rates at
all life stages.
Conclusion
Taken together, these data on the way in which mutations affect mortality, the age-specificity of mutations,
and the distribution of effects of new mutations suggest
that we need to re-evaluate our previous assumptions
of how mutations affect survival. In closing, we suggest that in light of much new information, it is time
to design models with a set of new, more biologically realistic of assumptions. First, we have previously
assumed that mutations have instantaneous effects on
life history traits. Perhaps it is more realistic (albeit
less mathematically tractable) to assume that mutations that ‘turn on’ at a particular age then stay on.
This assumption leads to a second assumption that the
effects of novel mutations will be positively correlated across ages. Third, the data suggest that mutations
act additively not on survival, but rather on the log of
age-specific mortality.
This new set of assumptions may help us to explain
a series of new demographic findings that are inconsistent with theoretical expectation. These observations include a) leveling off in late-age mortality; b)
a decrease in genetic variance for mortality late in
life; and c) convergence of mortality curves late in
life among cohorts.
Incorporating realistic assumptions about how
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 empiricists in the design and interpretation of evolutionary
studies of aging.
Acknowledgments
We gratefully acknowledge Andy Clark and Scott
Pletcher for generously sharing their data with us, and
Locke Rowe and two anonymous reviewers for helpful comments. Support during the course of this work
was provided by the separate American Federation of
Aging grants to DP and MT, and National Institute on
Aging Grant R29 AG14027 to DP.
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