vol. 163, no. 4
the american naturalist
april 2004
Single-Generation Estimates of Individual Fitness as Proxies for
Long-Term Genetic Contribution
Jon E. Brommer,1,* Lars Gustafsson,2 Hannu Pietiäinen,1 and Juha Merilä3
1. Bird Ecology Unit, Department of Ecology and Systematics, P.O.
Box 65 (Viikinkaari 1), University of Helsinki, FIN-00014
Helsinki, Finland;
2. Department of Animal Ecology, Evolutionary Biology Centre,
Norbyvägen 18d, SE-75236 Uppsala, Sweden;
3. Evolutionary Genetics Research Unit, Department of Ecology
and Systematics, P.O. Box 65 (Viikinkaari 1), University of
Helsinki, FIN-00014 Helsinki, Finland
Submitted February 14, 2003; Accepted September 12, 2003;
Electronically published April 19, 2004
abstract: Individual fitness is a central evolutionary concept, but
the question of how it should be defined in empirical studies of
natural selection remains contentious. Using founding cohorts from
long-term population studies of two species of individually marked
birds (collared flycatcher Ficedula albicollis and Ural owl Strix uralensis), we compared a rate-sensitive (lind) and a rate-insensitive (lifetime reproductive success [LRS]) estimate of individual fitness with
an estimate of long-term genetic fitness. The latter was calculated as
the number of gene copies present in the population after more than
two generations, as estimated by tracing genetic lineages and accounting for the fact that populations were not completely closed.
When counting fledglings, rate-insensitive estimates of individual
fitness correlated better than rate-sensitive estimates with estimated
long-term genetic contribution. When counting recruits, both classes
of estimates performed equally well. The results support the contention that simple, rate-insensitive measures of fitness, such as LRS,
provide a valid and good estimate of fitness in evolutionary studies
of natural populations.
Keywords: individual fitness, life history, evolution, natural selection,
reproductive timing, rate sensitivity.
Fitness is a concept pivotal to any evolutionary inference
(Endler 1986). However, fitness is not necessarily easily
defined (Stearns 1976), and its definition is, in fact, highly
context dependent (Metz et al. 1992; Mylius and Diek* Corresponding author; e-mail: [email protected].
Am. Nat. 2004. Vol. 163, pp. 505–517. 䉷 2004 by The University of Chicago.
0003-0147/2004/16304-30038$15.00. All rights reserved.
mann 1995). Nevertheless, most authors agree that fitness
equates to some measure of genetic contribution to future
generations (Endler 1986; Charlesworth 1994). One aspect
of fitness, which complicates its practical use, is that it can
be measured on different hierarchical levels. For example,
the distinction between individual- and population-level
fitness permeates the life-history literature (table 1; McGraw and Caswell 1996; Link et al. 2002).
Theoretical studies usually consider fitness on the population level or at least of a group of individuals (clones)
with a certain life history (Roff 1992; Stearns 1992). Indeed, the recent development of invasibility as the master
fitness concept (Metz et al. 1992; Rand et al. 1994; Geritz
et al. 1998; van Dooren and Metz 1998; reviewed in Brommer 2000) highlights the growth rate of a distinct group
of mutants within a resident population. Empirical studies,
on the other hand, use an individual-based estimate of
fitness (Lande and Arnold 1983; Endler 1986; Roff 1997;
Lynch and Walsh 1998). Unfortunately, individual- and
population-level fitness estimates of growth rate do not
necessarily measure the same properties; for example, the
average individual fitness of all individuals is not necessarily the population growth rate (Lenski and Service 1982;
Bennington and McGraw 1995; Murray 1997; Cooch et
al. 2002). Some authors have argued that estimates of individual fitness are fundamentally hampered in their description of fitness (a population parameter) because they
are based on a sample of size one (Lenski and Service
1982; Link et al. 2002).
Two broad classes of fitness estimates can be distinguished. Rate-sensitive fitness estimates take into account
both the number of offspring produced and the age of the
parent when these offspring were produced. Rate-insensitive estimates only represent the number of offspring
produced and ignore the timing of reproduction. Examples
of the latter include the population measure R0 and its
individual analog lifetime reproductive success (LRS; table
1). Rate-sensitive estimates of fitness are, for example, lpop
(or r) and its individual analogue lind (table 1). The intrinsic rate of increase lpop is the fitness measure of choice
in most theoretical studies (e.g., Stearns 1992). In contrast,
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Table 1: Population estimates of fitness and their individual analogues
Name
Net reproductive ratio
Lifetime reproductive success
Intrinsic rate of increase
Age-discounted LRS
Description
Expected number of
same-sex offspring
Total number of offspring produced
Per time-unit increase
in number
Propensity of rate of
increase
Symbol
Level
Timing?
Example
R0
Population
No
Heesterbeek 2002
LRS
Individual
No
Clutton-Brock 1988
lpop (per)
Population
Yes
Stearns 1992
lind
Individual
Yes
McGraw and Caswell 1996
Note: Presented are short descriptions and the symbols for four commonly used estimates of fitness, the level on which these are used to describe
fitness, and whether they incorporate reproductive timing. Examples and discussion of their use can be found in the references given.
empirical studies usually use the rate-insensitive LRS (e.g.,
Roff 1997). Below, we explain the basis of individual fitness
estimates in more detail.
Although the rate-sensitive estimate of individual fitness
lind was introduced only recently, it has been used in several studies (reviewed in Brommer et al. 2002c). Because
lind incorporates the timing of reproduction, it ranks the
estimated fitness of individual life histories very differently
than the rate-insensitive LRS (Käär and Jokela 1998; Brommer et al. 2002c; fig. 1). Rate sensitivity will discount offspring production at later ages and thereby put a premium
on starting to reproduce early in life and make the relationship between LRS and lind curvilinear (e.g., fig. 1).
Hence, long-lived individuals with high LRS will typically
have a similar lind as individuals with a lower LRS. Especially when the fitness consequences of a differential
onset of reproduction are examined, lind will typically reveal strong selection for the earliest possible reproductive
age, whereas LRS will show little or no selection (e.g.,
McGraw and Caswell 1996; Brommer et al. 1998; Oli et
al. 2002).
The occurrence of conflicting patterns of selection, depending on which of the two different estimates of individual fitness is used, leads to the question of which fitness
estimate one should adhere to. Many authors have felt that
the rate-sensitive lind captures fitness significantly better
than the rate-insensitive estimate LRS (Käär and Jokela
1998; Korpelainen 2000; Cooch et al. 2002; Oli et al. 2002).
However, for an objective assessment of the accuracy of
any single-generation estimate of fitness, single-generation
estimates of fitness need to be compared with a more
complete estimate of individual fitness.
In this article, we use long-term data of marked individuals to explore the relationship between single-generation estimates of fitness (such as LRS and lind) and an
estimate of the long-term genetic contribution an individual makes to future generations. We use data on two
species with a markedly different life history: the collared
flycatcher Ficedula albicollis, a short-lived passerine, and
the Ural owl Strix uralensis, a long-lived bird of prey. By
tracing genetic lineages, we estimate the future number of
gene copies individuals in certain founding cohorts will
have left in the population after several generations. We
assume that our estimate of gene copies present in the
population after several generations describes an individual’s fitness better than estimates based only on a single
generation (such as LRS and lind). We then ask whether
rate-sensitive estimates of individual fitness are indeed better correlates of the estimated number of gene copies
found in future generations than rate-insensitive estimates
of fitness.
Material and Methods
Collared Flycatcher
Collared flycatchers were studied in the southern part of
the island of Gotland, Sweden. This article deals with data
collected during 1980–1999. Collared flycatchers are relatively short-lived, mainly monogamous small passerines
that in our study population have relatively short natal
and breeding dispersal distances (Pärt 1990; Pärt and Gustafsson 1991). The birds in the study population use nest
boxes provided in forest patches as breeding sites, and
most of the adults and their offspring have been individually marked and captured yearly since the study started.
We only used data from 12 central woodland plots and
discarded data from peripheral ones. Various experiments
have been performed in this population (e.g., Gustafsson
and Sutherland 1988). For more details on the general
methods and the dynamics of this population, see Gustafsson (1989) and Merilä and Sheldon (2000).
Ural Owl
From 1977 on, Ural owls were studied in a 1,500-km2 area
in southern Finland. The owls bred in boxes (n p 150–
180) that were 3–5 km apart. Ural owls are monogamous
Estimating Fitness 507
the incubation or early nestling period. All offspring were
ringed when they were 2–3 wk old. Unringed new females
were aged by their plumage characteristics as either 1, 2,
or 12 yr old (Pietiäinen and Kolunen 1986). This population has not been experimented with during the course
of this study. For more details on the methods and the
dynamics of this population, see Pietiäinen (1989) and
Brommer et al. (2002a).
Single-Generation Fitness Estimates and
Reproductive Timing
From the life-history data, we distilled several fitness measures. We distinguished between fledglings (offspring that
left the nest) and recruits (offspring that were recorded
breeding later in life). We only used local (within study
area) recruits because the capture probability of birds outside the study area is less efficient and is not standardized
between years. We only considered female recruits because
practically all females (but not all males) are trapped in
both species, genetic father⫺offspring relatedness is uncertain in the collared flycatcher (about 15% of offspring
are of extrapair origin; Sheldon and Ellegren 1999), and
paternal and maternal fitness cannot be separated in the
monogamous Ural owl, leading to pseudoreplication. Considering only the female part of a population is common
in life-history theory and is a valid simplification in case
the dynamics of both sexes do not differ (Stearns 1992).
A rate-sensitive estimate of fitness (lind) was calculated
as the unique positive real root in the equation
1p
冘
x
Figure 1: Estimates of lind plotted against estimates of lifetime reproductive success (LRS) for 1,414 collared flycatcher females. Census was
based either on fledglings (A, lind(fp) vs. lifetime fledgling production
[LFP]) or on recruits (B, lind(rp) vs. lifetime recruit production [LRP]).
The fitness values of females that started to breed as 1-yr-olds are indicated with an open dot, and the fitness of those that started to breed
at later ages are indicated with filled dots. Lifetime fledgling production
is calculated as half the total number of fledglings produced in a female’s
lifetime, and LRP is calculated as half the number of female recruits
produced in a lifetime. Note that measures of LRS and lind are equal for
values of 0 and 1 and that many points may overlap for these fitness
values.
site-tenacious birds with a low divorce rate: they basically
live and breed in the same territory their whole reproductive life (Saurola 1987). Practically all females were
trapped each year by netting them from the box during
1 ⫺x
fl ,
2 x ind
(1)
where x is the age of the individual considered and fx the
production of offspring (McGraw and Caswell 1996). Offspring production is scaled by the parent-offspring relatedness of 1/2 (McGraw and Caswell 1996). Again, we calculated estimates of lind based on counting offspring fx as
fledglings (lind(fp)), and on recruits (lind(rp)). In practice,
equation (1) is most easily solved by using matrix algebra
and an appropriate software package. The value lind is the
dominant eigenvalue of a matrix that has for each age x
the fx /2 values in its first row and 1 in its subdiagonal
(McGraw and Caswell 1996).
Measures of LRS were counted as half the total sum of
fledglings (lifetime fledgling production [LFP]) or half the
sum of recruits (lifetime recruit production [LRP]) that
an individual produced during its entire breeding career.
We followed the above outlined practice for calculating
lind and also incorporated the factor 1/2 in calculating
measures of LRS. In this way, when two offspring (either
fledglings or female recruits) are produced, LRS p
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l ind p 1 (e.g., fig. 1). Note that this way of calculating
measures of LRS differs from what is usual in the literature
but that scaling offspring production in this manner does
not affect the proportional relationship between the performance of two different life histories for a linear measure
such as LRS, whereas lind is highly sensitive to such scaling
(Brommer et al. 2002c).
Long-Term Fitness
We calculated a third long-term estimate of fitness by following lineages of descendants. This estimate is based on
the concept of future descendants (Houston and McNamara 1999) and estimates the number of gene copies of
a focal individual y years after it hatched. Long-term fitness
wg(y) is based on the sum of all descendants (including
the focal individual itself) weighted by their relatedness of
1/2 to the focal individual. Hence,
冘()
G
wg(y) p
1 G
D ,
2 y
(2)
where the factor (1/2)G denotes the relatedness (for diploids) between the focal individual and a descendant of
the Gth generation (self: G p 0, relatedness p 1; F1 offspring: G p 1, relatedness p 1/2; F2 offspring: G p 2,
relatedness p 1/4; etc.) and DyG the number of descendants in the Gth generation alive in year y. Again, when
counting the number of descendants we only considered
females for the reasons outlined above.
Estimating long-term fitness requires taking into account uncertainty due to dispersal. The study populations
are not closed, and a certain fraction of F1 offspring disperses away and may recruit outside the study population
in each season. Their descendants cannot be identified.
Hence, the number of observed descendants of a focal
individual in the study population continually diminishes
as time proceeds, although the actual number of descendants could (in principle) be stable or even increasing
during the given time period. Because the uncertainty in
the number of descendants builds up over time, the explanatory power of the observed number of descendants
will become increasingly low. We incorporated this uncertainty by using a simulation approach in three steps.
First, for each reproductive event, we assumed there was
a probability d of F1 offspring to successfully disperse outside the study population and recruit there. We estimated
d by iteration. We calculated the cohort-specific rate of
population increase lcoh by solving the Euler-Lotka equation 1 p 冘 (1 ⫹ d) Fx L x l⫺x
coh, where Fx is the average number of local female recruits produced by a female of age
x and Lx the proportion of females in the cohort still alive
at age x. In calculating population growth rate, we only
considered females as usual in life-history theory (Stearns
1992). We assumed that the long-term growth rate of the
population (i.e., the harmonic mean of the lcoh’s including
dispersal over all the study years) would be 1 (e.g., Tuljapurkar 1989) and chose parameter d accordingly. Second,
outside-recruitment probability d was assumed to be a
random binomially distributed probability per brood produced. Hence, for each reproductive event, there were a
number (0, 1, 2, 3, …) of simulated outside recruits. To
any such “invisible” individual we randomly assigned the
life history (i.e., age-specific production of fledglings and
recruits) of an individual of the same birth cohort from
our data set. In the same fashion, random life histories
were drawn for all remaining putative descendants. Hence,
we make the strong assumption that the environment outside the study area allows for similar reproductive output
as inside the study area. Third, step 2 was repeated 250
times. For each run, we calculated the estimated number
of descendants as wg(y) p 冘 (1/2)G DyG ⫹ 冘 (1/2)G E (DyG),
where the first term is as in equation (2), and the second
term, E (DyG), is the expected number of descendants of
generation G at yr y, based on the simulation approach
described above.
In the collared flycatcher study population, some individuals were subjected to an experimental alteration of
a life-history component at some point in their life. Because of carryover effects of such manipulations (Gustafsson and Sutherland 1988; Gustafsson and Pärt 1990),
we only used the life-history data for such an individual
until the year in which it was experimented with. The
remaining life history (i.e., age-specific production of recruits and parental survival) of such an experimental bird
was, starting with the year of the experiment, assumed to
follow the life history of a randomly drawn nonexperimental bird of equal age breeding in the same year.
In the Ural owl, we randomized the age distribution of
birds that could not be aged reliably (i.e., those that were
aged by plumage characteristics as being 3 yr or older when
they first bred). We assumed that their ages followed the
average distribution of age at first breeding of ringed birds
that started to breed at 3 yr or older (62% at 3 yr; 21%
at 4 yr; 10% at 5 yr; 7% at 6 yr; Brommer et al. 1998).
We included this uncertainty by randomly assigning these
unreliably aged birds a certain age at first breeding for
each randomization round. Because of age discounting,
rate-sensitive individual fitness is rather insensitive to
changes in the age at first breeding for birds that started
to breed as 3-yr-olds or older.
Data and Analysis
Because we are interested in counting descendants over a
multigeneration time span, we focused on individuals in
Estimating Fitness 509
early (founding) cohorts of the population. We considered
females, which had not been subjected to any experiment
and were unrelated, from all cohorts (i.e., individuals
hatched) before 1988 in the Ural owl and from 1980 to
1989 for the collared flycatcher. We calculated all fitness
estimates described above for these individuals. We considered single-generation estimates of individual fitness
(LRS, lind) for each life-history stage (fledgling, recruit)
separately. Single-generation estimates were correlated
with the estimated number of gene copies left after y years
(y p 1, 2, 3, …). We used Spearman rank correlations
with significance corrected according to the number of
years tested (for k years, a p 0.05/k) and sample size set
by the number of individuals considered. We calculated a
correlation for each run separately and present box plots
in correlation diagrams. To aid in comparing results for
the two different life histories of the species used, we considered their generation time. Generation time was calculated as the average age of females producing a clutch
(Stearns 1992; Charlesworth 1994) during the whole study
period. The sensitivity of our results to uncertainty in our
dispersal parameter d was addressed by a sensitivity analysis. Uncertainty in d may be considered as testing the
sensitivity of our results to violations of our assumptions
that the total population is stable over time or that the
performance of recruits outside the study area is the same.
Results
The consequences of incorporating rate sensitivity into
estimates of individual fitness are readily apparent. In the
collared flycatcher, most females (78%, 1,103/1,414)
started to breed as 1-yr-olds. Such an early start gives high
estimates of lind, especially when fledglings are considered
(open vs. closed dots in fig. 1A). A similar fitness was
rarely achieved by individuals that postponed for at least
1 additional year, although early and late first breeders did
not differ in their total production of fledglings (fig. 1A;
t p 1.0, df p 1, 412, P p .3). In terms of recruits, ratesensitive (lind(rp)) and rate-insensitive (LRP) estimates of
individual fitness were highly correlated (fig. 1B). In general, lind will increase only modestly after a certain number
of offspring have been produced (fig. 1A; cf. Brommer et
al. 2002c for data on Ural owl). There was a clear difference
in the life histories of the two species of bird (table 2).
The collared flycatchers started to breed earlier, had a
shorter generation time, and produced fewer fledglings
(but more recruits) during their lives than Ural owls (table
2).
We estimated the long-term fitness of founding females
and simulated to account for uncertainty in our fitness
estimates. In the Ural owl data set, the age at first breeding
was randomized for 62/176 females that started to breed
Table 2: Descriptive data (mean Ⳳ SE) comparing the life
histories of the collared flycatcher and the Ural owl
Trait
Sample size
Generation time
Age at first production
LFP
lind(fp)
LRP
lind(rp)
Collared flycatcher
1,414
1.8 Ⳳ .02
1.3 Ⳳ .01
2.8 Ⳳ .06
1.9 Ⳳ .03
.15 Ⳳ .008
.17 Ⳳ .009
Ural owl
176
6.4 Ⳳ
3.5 Ⳳ
4.3 Ⳳ
1.2 Ⳳ
.10 Ⳳ
.09 Ⳳ
.1
.1
.3
.03
.02
.02
Note: Generation time is the average age of reproducing females during
the study period. Fitness estimates include half the sum of offspring
produced (counted either as fledglings—lifetime fledgling production
[LFP]—or as female recruits—lifetime recruit production [LRP]) and
age-discounted production of offspring (fledglings: lind(fp); female recruits: lind(rp)). See text for details on how these measures are defined.
at age 12 yr but could not be reliably aged. In the flycatcher
data set, offspring that were subjected to an experimental
alteration of their life history were assigned a random life
history. For both species, the results are qualitatively the
same if these individuals are fully omitted from the analysis. Measures of LRS based on the production of fledglings
proved to be good correlates of long-term genetic contribution to the population in both species (fig. 2A, 2C). The
rate-sensitive estimates of individual fitness lind generally
performed less well. In the short-lived collared flycatcher,
LFP was a good correlate of long-term fitness for 4–6 yr
(i.e., two to three times the generation time) but became
insignificant in the long run (fig. 2A). Similarly, in the
long-lived Ural owl, LFP remained a good correlate of
long-term genetic contribution for up to 15 yr (i.e., about
two times the generation time of this species). For both
life histories, fitness estimates based on recruits proved to
be better correlates of long-term genetic contribution than
fitness estimates based on fledglings, especially in the long
run (fig. 2). The LRP and lind based on recruits are highly
correlated because these two estimates of individual fitness
are identical for most parents (LRP and lind(rp) are equal
for values of 1 and 0; fig. 1B). In the collared flycatcher,
lind(rp) tended to correlate slightly better with our estimate
of long-term genetic contribution than LRP after about
two generations (3–5 yr), but there were no differences in
the strength of correlations of LRP and lind(rp) with longterm fitness in either species after more than two generations (fig. 2B, 2C).
One reason that rate-sensitive estimates of fitness based
on fledglings correlated less well with long-term fitness
than rate-insensitive estimates was due to the fact that the
rate-sensitive estimate discounted reproduction later in the
life of the parent. The correlation between the two fitness
estimates and long-term fitness after about two generations (4 yr for the flycatcher and 12 yr for the Ural owl)
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Figure 2: Correlogram of long-term fitness and measures of lifetime reproductive success and lind for collared flycatcher (CF, panels A and B) and
Ural owl (UO, panels C and D) data without dispersal. Data are presented separately for fitness estimates calculated on the basis of fledglings (A,
C) and recruits (B, D). Box plots indicate the median, quartiles, and spread of 250 simulations. In the Ural owl data set, the age at first breeding
was randomized for 62/176 females that started to breed at age 12 yr but could not be reliably aged. In the flycatcher data set, offspring that were
subjected to an experimental alteration of their life history were assigned a random life history. Filled boxes indicate correlations for the rate
insensitive fitness estimate (lifetime fledgling production, lifetime recruit production); open boxes indicate the rate-sensitive fitness estimates (lind).
The dashed line indicates the Bonferroni-corrected significance threshold of these correlations.
showed a clear contrast (fig. 3). The difference in longterm fitness between females with high LFP and those with
lower LFP produced a good correlation between these two
traits (fig. 3A, 3C). However, because of age discounting,
females with a high LFP had a similar lind(fp) (cf. fig. 1A).
As a consequence the correlation between lind(fp) and
long-term fitness was lower, especially for the long-lived
Ural owl (fig. 3C, 3D).
The decrease in correlations between the estimates of
individual fitness and long-term fitness as time goes by
Estimating Fitness 511
Figure 3: Correlation between long-term fitness (number of gene copies after approximately two generations) and two single-generation estimates
of individual fitness for the collared flycatcher (A, B) and the Ural owl (C, D). The number of gene copies was estimated for the flycatcher after 4
yr and for the Ural owl after 12 yr. Data were chosen from the randomized set so as to have the average correlation (see fig. 2). This estimate of
long-term fitness was plotted against lifetime fledgling production (panels A and C) and lind based on fledglings (lind(fp); panels B, D).
(fig. 2) stems from the loss of genetic lineages. Loss of a
genetic lineage is inevitable because we only considered
the female part of the breeding population, but it is also
partly due to dispersal outside the study area. The flycatcher pedigree allowed following some lineages for up
to seven generations (i.e., F6 offspring), and the Ural owl
pedigree allowed for lineages of three generations. Nevertheless, few maternal lineages remained in the popula-
tion after three times the generation time. Hence, correlations decreased, as there was little contrast across
individuals in their long-term fitness. We incorporated an
estimate of the individuals lost through dispersal in order
to check the validity of our correlations of estimates of
individual fitness and genetic contributions on a longer
timescale (i.e., larger than twice the generation time). Results show that when dispersal was incorporated, estimates
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Figure 4: Correlogram of long-term fitness and measures of lifetime reproductive success and lind for collared flycatcher (CF, panels A and B) and
Ural owl (UO, panels C and D) including hypothetical dispersal outside the study area. Data are presented separately for fitness estimates calculated
on the basis of fledglings (A, C) and recruits (B, D). Symbols and dashed line as in figure 2. Simulation included the hypothetical life histories of
a fraction d of F1 offspring assumed to successfully recruit outside the study area. For Ural owls, d p 0.1 , and for flycatchers, d p 0.125 . In addition,
the randomizations described in the caption of figure 2 are performed.
based on LRS still performed equally well (in case of recruits; fig. 4B, 4D) or better (in case of fledglings; fig. 4A,
4C) than rate-sensitive estimates of individual fitness. Especially for the long-lived Ural owl, the differences between
LFP and lind remained substantial in the long term (fig.
4C). In both species, there was no difference in the strength
of correlation of LRP and lind(rp) with our estimate of
long-term fitness at any timescale once dispersal was incorporated (fig. 4B, 4D).
The differences between the correlations of the two types
of fitness estimates and our estimate of long-term fitness
were robust to variation in the probability d to recruit
outside the study area (fig. 5). The correlations of lind
based on fledglings and LFP with estimated long-term fit-
Estimating Fitness 513
ness increased in unison with increasing values of d.
Hence, conclusions appear robust to violations of our assumptions underlying the simulation of dispersal (equal
performance inside and outside the study area, stable population growth), which would be reflected in either underor overestimation of the dispersal parameter d. When dispersal was incorporated, estimates of individual fitness
based on recruits tended to correlate less with long-term
fitness than estimates based on fledglings (fig. 4), and the
strength of this correlation decreased with increasing values of d (fig. 5). Closer inspection of the correlations
showed that this reduction was due to individuals without
local recruits having (simulated) descendants. Hence, this
result was a direct consequence of simulating outside recruitment as a binomial function of brood size and showed
the potential error in assigning any individual a fitness
value of 0.
Discussion
Fitness is typically thought to be related to the rate of
spread of a gene in the population (Charlesworth 1994).
We have estimated an individual’s genetic contribution to
future generations spanning three generations in the Ural
owl and seven generations in the collared flycatcher. We
have compared a rate-insensitive (LRS) and a rate-sensitive
(lind) estimate of individual fitness based on a census of
fledglings and of recruits with this long-term estimate of
individual fitness. Our aim was to provide an empirical
test for how well an individual’s genetic contribution to
future generations can be captured by single-generation
estimates based on data on the production of F1 descendants and what the importance of reproductive timing is
for estimating individual fitness. For both the short-lived
(collared flycatcher) and the long-lived (Ural owl) life histories, our results show that single-generation estimates of
fitness capture the long-term genetic contribution to the
population. Further, when counting fledglings, rate-insensitive estimates of individual fitness correlate better than
rate-sensitive estimates with estimated long-term genetic
contribution. When counting recruits, both classes of estimates perform equally well. Hence, we find little evidence
that rate-sensitivity as incorporated by lind significantly
improves estimates of individual fitness.
Although all estimates of fitness are based on the production of offspring, studies differ substantially in the time
at which offspring are counted. Measures of LRS have been
calculated by counting offspring that are still dependent
on their parents (Clutton-Brock 1988; Newton 1989), independent offspring (Käär and Jokela 1998; Gaillard et al.
2000; Korpelainen 2000; Kruuk et al. 2000), or breeding
offspring (Clutton-Brock 1988; Merilä and Sheldon 2000).
Our results support the intuitive notion that estimates of
Figure 5: Sensitivity analysis for dispersal parameter d. The parameter
d was varied by 30% with steps of 5% from its original value (see legend
to fig. 4). Average correlation with long-term fitness after about two
generations (4 yr for the collared flycatcher and 12 yr for the Ural owl)
is indicated for lifetime fledgling production (filled circle), lind (filled
square), and lifetime recruit production (open circle). Confidence intervals
(95%) are based on 100 simulation runs each.
LRS based on offspring that are recorded breeding (recruits) correlate better with estimated genetic contribution
to the population than estimates based on dependent offspring (fledglings). However, recruitment is notoriously
difficult to measure, and recruitment outside the study
area is one reason that our estimate of the number of
descendants alive in the local population decreases over
time. We have here captured some uncertainty in recruit-
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ment due to dispersal. In doing so, we have made the
assumption that the reproductive output of individuals
that have recruited outside the study area is equal to those
that stayed. This assumption probably does not hold: collared flycatchers that move away from their natal site have
reduced breeding performance (Pärt and Gustafsson
1991), and Ural owls that immigrate from outside the
study area have a poorer lifetime performance than local
individuals (H. Pietiäinen, unpublished data). This would
mean that we have underestimated losses due to dispersal.
Nevertheless, our sensitivity analysis shows that the difference in the correlations of measures of LRS and measures of lind with (dispersal-corrected) long-term fitness
is qualitatively not affected by the extent of dispersal.
Our simulations have by no means captured all possible
uncertainty. In particular, demographic stochasticity in the
sex ratio of offspring creates error. Long-term fitness is
based on females only, and single-generation estimates
should therefore also be based on females only. In terms
of fledglings, we can only consider both sexes. Although
sex ratios in birds do not deviate much from 50% (Sheldon
1998), stochastic differences across individuals in the proportion of daughters produced per lifetime will lead to
error in the correlation of single-generation and our longterm estimates of fitness. Significantly, LFP and lind based
on fledglings are not equally biased by demographic stochasticity in the sex ratio of fledglings; lind is less sensitive
than LFP to changes over most of the range of lifetime
production (e.g., fig. 1; Brommer et al. 2002a). Of all
offspring produced, chance events may also make it so
that only sons are recruited. Because we only consider
maternal lineages, male-only recruitment at some point
along a lineage would lead to the erroneous conclusion
that the genetic lineage goes extinct. A diploid individual
will have genetically replaced itself in the population if it
recruits two offspring during its lifetime. Hence, not incorporating both sexes adds to the disappearance of our
genetic lineages. Other uncertainty in our long-term estimate of fitness includes the way we incorporated dispersal
in a uniform way. Estimates of lifetime recruitment have
been shown to be biased with respect to the spatial position
of the site of birth within the study area because loss rates
are higher at the edge than in the core (Lambrechts et al.
1999).
Interpreting our result in terms of how fitness should
be quantified depends on the accuracy of our estimates of
individual fitness. The most critical requirement for an
estimate of individual fitness is to separate the genetic
signal from the noise. Environmental and demographic
stochasticity form two aspects of noise that affect both our
single-generation and long-term estimates of individual
fitness. The profound effect of stochasticity on estimates
of individual fitness is evident from studies that have
shown that the low heritability of estimates of individual
fitness is caused by high environmental or nonadditive
variance and not by low additive genetic variance (e.g.,
Kruuk et al. 2000; Merilä and Sheldon 2000). Given such
demographic and environmental noise, it is encouraging
that we can detect a correlation of single-generation estimates of fitness with our estimate of long-term fitness
(r is about 0.3–0.6 after two to three generations depending
on when the offspring is counted). Nevertheless, this correlation may be lower in other populations or species than
the ones used in this article. In a comparison with 38
populations of 18 species of birds, the two bird populations
used in this article were relatively stable (they had a high
estimated time to extinction), mainly due to their relatively
high growth rate (a function of local recruitment and life
span) and relatively low environmental stochasticity (B.
Saether et al., unpublished manuscript). In addition, demographic stochasticity in the Ural owl population was
lowest of all 38 populations (but about average for the
collared flycatcher population). In general, stochastic effects therefore seem to play a more important role in other
bird populations than the populations used in this article,
and the correlation of individual fitness and long-term
performance may therefore be even less in other populations than what we have recorded here.
Benton and Grant (2000) showed in a theoretical study
that rate-sensitive population estimates of fitness performed worse than rate-insensitive estimates in populations that fluctuated around equilibrium (due to either
overcompensatory density dependence or environmental
stochasticity). Such population dynamics are probably
common in natural populations. Hence, for natural scenarios, rate sensitivity does not seem to improve estimates
of either population-level fitness (Benton and Grant 2000)
or individual-level fitness (this article). These results stand
in strong contrast to the predominant view in the current
literature where rate-sensitive estimates of individual fitness are considered better estimates than rate-insensitive
estimates independent of when offspring are counted
(Käär and Jokela 1998; Korpelainen 2000; Cooch et al.
2002; Oli et al. 2002). We see three main reasons why
sensitivity to reproductive timing may not increase the
accuracy of individual fitness estimates.
First, the fitness payoff from offspring produced late in
life is too strongly de-emphasized by rate sensitivity. Offspring of both first and later clutches contribute equally
to LRS, but rate sensitivity discounts reproduction by the
age at which an offspring (either fledgling or recruit) was
produced. Large values of LRS do not translate into large
values of lind. Lifetime reproductive success and lind have
a curvilinear relationship; individuals with an LRS above
a certain critical value differ little in their lind (Käär and
Jokela 1998; Brommer et al. 2002c; this article). Our results
Estimating Fitness 515
show that individuals that contribute most in the long
term have high values of LFP. However, lind based on the
production of fledglings insufficiently contrasted these
successful individuals. In fact, these successful individuals
are the long-lived ones, as LFP is largely determined by
life span (Clutton-Brock 1988; Newton 1989; Ural owl:
Brommer et al. 1998; collared flycatcher: Gustafsson 1989).
Our result thus reflects the classic notion that the optimal
life-history strategy is to live long and produce as many
offspring as possible (Law 1979). Notably, this notion is
not supported by rate-sensitive estimates that discount
reproductive output by parental age, as individual fitness
then rapidly converges to a semiasymptotic value (fig. 1;
Käär and Jokela 1998; Brommer et al. 2002c). Hence, additional reproduction at later ages erroneously contributes
little to the value of age-discounting fitness estimates.
Second, in addition to the sheer number of offspring
produced, offspring may vary in their (reproductive) value.
The inability to accurately incorporate such variation in
offspring value hampers all single-generation estimates of
individual fitness. Part of an offspring’s value includes
genetic effects (e.g., Sheldon et al. 1997 for evidence of
genetically determined quality differences among collared
flycatcher offspring), although it will also reflect environmental conditions. For example, in birds, within-season
variation in the timing of laying affects the value of offspring produced (Ural owl: Brommer et al. 2002b; collared
flycatcher: Sheldon et al. 2003). In addition, among-year
variation in environmental conditions generates a cohort
effect (e.g., Lindström 1999), which will create pronounced
differences in performance across offspring produced in
different reproductive seasons during the life of a parent.
In contrast to single-generation estimates of individual
fitness, our estimate of long-term genetic contribution
does include offspring value because it incorporates not
only the performance of the parent but also the performance of its offspring and all further descendants. In fact,
in theoretical studies reproductive value is measured by
tracing the number of descendants after several generations (Houston and McNamara 1999). Rate sensitivity’s
emphasis on reproduction early in life may produce severe
errors if offspring value increases as a function of parental
age. Typically, a parent will gain advantages during its
lifetime (e.g., in terms of experience [e.g., Nol and Smith
1987] or a better territory [Newton 1989]) that may be
transferred to its offspring. Parents may also increase their
reproductive effort with age because their residual reproductive value is reduced (terminal reproductive effort, e.g.,
Schaffer 1974; see Gustafsson and Pärt 1990 for collared
flycatcher). Offspring produced early in the life of the
parent (especially in the first breeding attempt) may therefore be of poorer value than offspring produced later. Incorporating timing by weighing offspring production with
parental age (as lind does) may thus both overestimate the
fitness contribution of early reproduction and underestimate the fitness contributions of later broods. Lifetime
reproductive success also does not consider variation in
offspring value, but measures of LRS may still provide a
better fitness estimate than lind because rate insensitivity
will buffer it against erroneously inflating the fitness contributions of offspring of different value produced during
the life of the parent.
Third, population dynamical feedback is largely ignored.
Only in a growing population is reproduction early in life
favored by selection, while delaying reproduction to later
in life is favored in a shrinking population (Stearns 1992).
Populations will typically fluctuate, alternatively increasing
and decreasing in size. Hence, reproductive timing will
certainly be an important selective force at times, but its
magnitude (and sign) may change on a shorter timescale
than the life span of an individual parent. Fluctuations in
population dynamics shorter than a generation may mean
that the importance of reproductive timing is unlikely to
be captured as a function of age alone (as lind assumes).
Measures of LRS or lind based on either fledglings or recruits do not incorporate such population dynamical feedback. Lifetime reproductive success may provide a better
estimate of individual fitness, possibly because its rate insensitivity will make it less sensitive when fitness is averaged out over several periods of change in population
size that occur during the life of a parent. In this respect,
further work on estimating individual fitness is needed,
and an individual-based theoretical exploration of the difference in predictive power of the various estimates of
individual fitness that we used in this article will be
interesting.
In conclusion, we have shown that by using long-term
individual-based data, one can trace genetic lineages in
order to gain a more objective insight into the predictive
power of proxy estimates of fitness. Such proxy estimates
are essential for quantification of individual performance
in a population. Contrasting the performance of individuals is an intrinsic element in evolutionary biology and in
applied ecological problems such as conservation biology.
Here, we have addressed a classic dichotomy in the measurement of fitness and focused on comparing two broad
classes of individual fitness, rate sensitive and rate insensitive. We find that the latter often performs equally well
or better than the former, depending on when in the organism’s life cycle offspring are counted. Further studies
utilizing species with different life histories are, of course,
needed to verify the generality of our results and
conclusions.
516
The American Naturalist
Acknowledgments
We thank J. M. McNamara (November 23, 2001) and T.
Benton for providing food for thought. Comments by two
anonymous reviewers substantially improved the quality
of this article. We are very grateful to all those who have
over the years helped out in the field. Our research was
supported by the Swedish Natural Science Research Council (L.G., J.M.), the Academy of Finland (J.E.B., J.M., H.P.),
and the Finnish Cultural Foundation (J.E.B.).
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Associate Editor: Ben C. Sheldon