Download Population Variation in Continuously Varying Traits as an Ecological

AMER. ZOOL., 21:795-811 (1981)
Population Variation in Continuously Varying
Traits as an Ecological Genetics Problem1
P. R. GRANT AND T. D. PRICE
Division of Biological Sciences, The University of Michigan, Ann Arbor, Michigan 48109
SYNOPSIS. The niche variation hypothesis is an adaptive explanation for variation within
populations and for,the differences in variation between populations in morphological,
physiological or behavioral traits. It has received only partial support from empirical tests
and has been criticized on theoretical grounds. Recent quantitative genetic models have
made an advance by exploring the effects of mutation, migration, mating pattern and
selection on phenotypic variance. These models are reviewed and their most important
features are integrated in a new model. In this model population variation is in a state of
balance between the opposing forces of mutation and immigration, which tend to elevate
variation, and selection and possibly genetic drift tending to decrease it. Populations exhibiting different levels of variation are interpereted as having different equilibrium
points, and it is the task of empirical studies to determine the relative magnitudes of the
opposing factors. An example is given from studies of Darwin's finches. Ceospiza fortis
varies more than G. scandens on Isla Daphne Major, Galapagos, in several morphological
traits including beak and body size. This is explained, assuming equal mutation rates in
the two species, as the result of more frequent genetic input to the G. fortis population,
through occasional hybridization with immigrant G. fuliginosa, and relaxed stabilizing
selection. Stabilizing selection is less intense on G.fortis than on G. scandens because the
G.fortis population has a broader niche; there is both a within-phenotype and betweenphenotype component to the broad niche of G.fortis. The success of theory in explaining
population variation is discussed, and it is concluded that empirical studies lag far behind
theory.
INTRODUCTION
ecologically important traits. For example,
additive genetic components of total phenotypic variance have been determined in
crustacean egg sizes (McLaren, 1976), avian clutch sizes (Perrins and Jones, 1974),
dipteran larval development times (Istock
et al., 1976) and dispersal distance from
birth place to breeding place in birds
(Greenwood et al., 1979). This means that
selection may be pervasive rather than
rare, and that averages are not necessarily
fixed. It also means that population variation is a subject worthy of study in its own
right.
In this paper we will review the major
explanations for the maintenance of continuous variation and for the fact that populations differ in variation for a given trait.
Since we will be concerned solely with continuous variation we will ignore sexual dimorphism, a special type of population
variation that may have relevance to our
primary question (Selander, 1966; Soule
and Stewart, 1970; Rothstein, 1973), because it may alternatively be the product
1
From the Symposium on Theoretical Ecology pre- of sexual selection or of natural selection
sented at the Annual Meeting of the American So- associated with differing reproductive
ciety of Zoologists, 27-30 December 1980, at Seattle,
roles of the sexes (Searcy, 1979; Lande,
Washington.
Ecologists are generally preoccupied
with the average characteristics of organisms, tending to view variation about the
mean as a nuisance in the search for precision (Grant, 1976). For many purposes
this is an appropriate attitude, as for example when the goal of a study is to determine how various demographic parameters contribute to the intrinsic rate of
increase of a population. It is not appropriate to view variation among organisms
in this way when the goal is to understand
why the population has these particular
demographic parameters. In this case an
evolutionary answer is sought, and can be
obtained by direct study of the effects of
environmental factors on variation in population growth characteristics if such variation is heritable. Recent studies give cause
for optimism that detectable heritable variation occurs in many organisms in many
795
796
P. R. GRANT AND T. D. PRICE
1980a). We will be concerned principally
with morphological traits, since these have
been investigated most often, but our discussion is fully applicable to ecological
traits which vary continuously. We will
concentrate on models which are amenable to testing. We find some explanations
to be unlikely on theoretical grounds, and
others to be not directly testable. We conclude by presenting a synthetic model and
show how it can be used.
T H E ADAPTIVE VARIATION HYPOTHESIS
Van Valen (1965) offered an adaptive
explanation for population variation. He
was concerned with the apparent conflict
between population adaptation in the
short term and adaptability in the long
term (see Mayr, 1963, chs. 8 and 9; Dobzhansky, 1970; also Thoday, 1953; Mather, 1953). If a single phenotype has maximum fitness, selection will be directed
against deviant phenotypes and thus a
phenotypic load will be incurred, with implications for population size and survival
(Crow, 1970; Wallace, 1970; Bulmer,
1980; Lande, 1980a). To the extent that
the variation is heritable, there will also be
a tendency towards reduction of that variation (Lande, 1976). Yet heritable variation maximizes the probability of longterm population survival in a changing environment.
Van Valen (1965) suggested that there
is no single optimum phenotype. Instead,
variants in the population are supposed to
have similar fitnesses by virtue of their
ability to differentially utilize parts of the
population's niche. Under these circumstances there will be little or no load, the
population will be polymorphic (polytypic)
and its size may be greater than that expected if it consisted solely of a single phenotype. Van Valen's suggestion has become known as the niche variation
hypothesis, but we will refer to it as the
adaptive variation hypothesis because we
believe this is both more general and more
meaningful.
Empirical tests of the adaptive
variation hypothesis
In general the hypothesis has been
tested by comparing populations exploit-
ing niches which are considered a priori to
differ in size. Then, to the extent that
some populations consist of specialist phenotypes (Van Valen and Grant, 1970;
Roughgarden, 1974), the prediction is that
those populations occupying wide niches
will vary more in traits functionally related
to the niches than those occupying narrow
niches. Birds have been employed most
often in tests, the traits being bill, tarsus
and body weight which have adaptive correlates that are readily interpretable, at
least interspecifically (Grant, 1965; Hespenheide, 1973).
Subjected to these tests, the hypothesis
has met with some success (e.g., Van Valen, 1965; Fretwell, 1969, 1977; Rothstein,
1973; Grant et ai, 1976; Abbott et al.,
1977; Lister, 1977; Davidson, 1978; Abbott, 1978; Bernstein, 1979) and some failure (e.g., Willson, 1969; Soule, 1972; Soule
and Stewart, 1970; Abbott, 1973; Willson
et al., 1975; Keast, 1976). This mixed success has stimulated debate on five aspects
of the tests.
First, statistical procedures for testing
morphological variation have been questioned (Banks, 1970; Rothstein, 1973;
Dow, 1976; Lande, 1977a). Second, the
choice of populations to compare has been
criticized on the grounds of inappropriateness (Van Valen and Grant, 1970; Beever,
1979; Grant, 1979a, b).
Third, tests involving poikilotherms
such as fish (Keast, 1977) and lizards
(Roughgarden, 1972, 1974) are complicated by slow and often intermittent and indeterminate growth. These complications
provide a non-genetic explanation for differences between phenotypes within populations, and can therefore result in trivial
explanations of differences in variation between populations (Lister and McMurtie,
1976).
Fourth, the difficulties of defining niche
width unambiguously have been discussed
by Soule and Stewart (1970) and Beever
(1979). This last area of concern reflects
the fact that most tests have been indirect.
Niche width has been defined by the number of habitats or associations of vegetation
occupied (Van Valen, 1965), by the abundance of a population on the assumption
of a positive correlation between popula-
POPULATION VARIATION
•
#
tion size and niche width (Rothstein, 1973;
see also McNaughton and Wolf, 1970), or
by the number of sympatric competitor
species on the assumption of a negative
correlation between this number and niche
width (Rothstein, 1973). Fifth, the estimation of population variation has been confounded to an unknown extent by the
lumping together of geographically differentiated samples of dead (Museum) specimens in some cases (Soule and Stewart,
1970; Beever, 1979; Grant, 1979a, b;
Wiens and Rotenberry, 1980).
These empirical problems can be surmounted if careful attention is given to the
relevant niche parameters of living individuals of known phenotype in the population (Fretwell, 1969, 1977; Grant et al.,
1976; Bernstein, 1979; Davidson, 1978).
However, there still remain problems with
the hypothesis itself; it does not specify the
mechanisms of change in population variation or the precise conditions under
which specialization of phenotypes is to be
expected (Grant et al., 1976). Soule and
Stewart (1970) concluded that the hypothesis as stated is virtually irrefutable. A major reason for this is that the causal connections between environment and
organisms have not been developed sufficiently for the hypothesis to make clear-cut
predictions (Morse, 1971). This is a serious
problem because unexpected results can
be easily rationalized.
Thus the status of the adaptive variation
hypothesis hangs in the balance and it is in
danger of death through neglect as a result
of confusion in the empirical tests and theoretical inadequacies. We therefore turn to
recent theoretical models which have been
developed to explore the conditions and
mechanisms for the maintenance of continuous variation, and which can be modified to account for differing levels of variation between populations.
AN EXPLICIT POPULATION-GENETIC
APPROACH
™
There is no shortage of population-genetic models, but they are not all equally
useful to an ecologist.
We will consider a class of models which
make common assumptions that are derived from the theory and results of arti-
797
ficial breeding experiments (Falconer,
1960; Bulmer, 1980). Total phenotypic
variance is partitioned into genetic and
non-genetic (environmental) components.
Often a large part of the non-genetic com-'
ponent is not attributable to specific environmental variation (Falconer, 1960, pp.
143-149) and can be referred to as developmental noise. This will always be present. The genetic variance is partitioned
into additive and non-additive components. The additive component is important because it is that cause of the resemblance between relatives which determines
the response to selection. In domestic animals the proportion of the total variance
that is additively genetic {i.e., the narrowsense heritability) varies from 0.1 to 0.6 for
a variety of characters (Falconer, 1960, ch.
10). Henceforth we will use the term heritability to mean heritability in the narrow
sense. Heritability estimates for wild bird
populations are given in Table 1, and all
are high. Genotype-environment correlations have been partially disentangled in
two studies (Smith and Dhondt, 1980; Van
Noordwijck et al., 1980), and have been
shown to be unimportant.
Directional selection
It has been suggested that when characters are under directional selection variation may be "transiently released,"
through either the breakdown of canalization (Soule and Stewart, 1970) or the increase in frequency of rare alleles (Fisher,
1937). Canalization refers to the reduction
in phenotypic variation between two developmental bounds or thresholds (Waddington, 1957). Either there is no variation
between the thresholds, as in some cases of
discretely varying traits (Rendel, 1967,
1979), or there is less variation between the
thresholds than outside them, as occurs in
continuously varying traits. A breakdown
in the canalization of continuously varying
traits may not be of sustained importance
in nature, because in artificial breeding experiments the thresholds are reached apparently only when the population has low
mean fitness, for example under extreme
nutritional stress (Waddington, 1957), or
after prolonged and strong directional (artificial) selection (Falconer, 1960). In di-
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P. R. GRANT AND T. D. PRICE
TABLE 1. Heritabilities (estimated by mid-parent offspring regression) in wild bird populations.
Weight
Bill
length
Bill
depth
Tarsus
length
Medium ground finch, Geospiza fortis
Large cactus ground finch, Geospiza conirostns
Cactus ground finch, Geospiza scandens
85
95
.62
.48
.82
66
.43
.87
70
.51
.16
.77
Great tit, Parus major
59
—
—
.76
Van Noordwijk et al.
(1980); Garnett
(1981)
Song sparrow, Melospiza melodia
.04
.33
.51
.32
Smith and Zach (1979)
Boagand Grant (1978)
Grant (19816)
Boag(1981)
rectional selection experiments phenotypic cases of natural selection on continuously
variance commonly remains approximate- varying morphological traits we found in
ly constant over the first few generations a literature search, 15 were not explained
in terms of identified selection pressures,
(Slatkin and Lande, 1976).
Many of the variable populations dis- and of these 13 involved stabilizing seleccussed by Soule and Stewart (1970) are tion (examples in Johnson, 1976; see also
likely to have been in their environment Van Valen, 1963; Van Valen and Weiss,
for at least several hundred generations 1966; Bell, 1974).
Lerner (1954) gathered evidence from
{e.g., Grant, 1979ft), and any directional
selection resulting from a new colonization laboratory populations showing that hetshould have long ceased. Given typical erozygotes exhibited less environmental
heritabilities and strengths of stabilizing variation than homozygotes. This provides
selection, variances should have equilibrat- a basis whereby stabilizing selection acting
ed in this time. Van Valen (1969) considers directly on the character gives an advanthat there is no strong evidence for in- tage to heterozygotes and can result in the
creased variation in rapidly evolving fossil maintenance of additive genetic variation
lineages, despite some observations to the (Lerner, 1954; Lewontin, 1964ft; Mackay,
contrary {e.g., Guthrie, 1965). The effects 1980). Lande (1980ft) disputes the releof canalization breakdown might be seen vance of Lerner's observations to natural
in such lineages but only if the fossil record populations. It is not clear how common
is exceptionally good.
this mechanism is likely to be.
Heterozygote advantage
Models of continuous variation
Small amounts of variation can be maintained under stabilizing selection if alleles
act non-additively on the character involved (Lewontin, 1964a; Bulmer, 1971a;
summarized by Lande, 1976). However,
large amounts of variation can be maintained in a model in which alleles show
overdominance on a fitness scale {e.g., see
Berger, 1976) but are pleiotropically additive with respect to the phenotypic character being measured (Lerner, 1954; Lewontin, 1964ft; Robertson, 1977). Under
such conditions, there will be the appearance of stabilizing selection, but the selective forces are likely to remain unidentified. This may occur in nature. Out of 23
Other studies concerning the maintenance of continuous variation have been
based on one of three models (Slatkin,
1979). The first, a "phenotypic model"
{e.g., Slatkin, 1970; Roughgarden, 1972;
Slatkin and Lande, 1976) makes no assumptions about the detailed genetic basis
of the character and considers the equilibrium variance under conditions that vary
according to the question being asked. The
other two approaches discuss modifications of the additive genetic variance. Both
models assume a large but finite number
of loci. One model devised by Bulmer
(1971a, ft, c, 1972, 1974) considers just two
alleles at each locus, with each locus having
POPULATION VARIATION
equal effects. The other due to Lande
(1976, 19776) and based on earlier work by
Kimura (1965), assumes a potentially infinite range of allelic effects at each locus;
variation is introduced by mutation, and
the mean and variance of the mutational
input per generation can differ among
loci. In both models alleles are assumed to
act additively across and within loci, and
there are no gene-environment correlations or interactions. An important feature
of Lande's and the phenotypic models is
that modifications of the variance can be
considered independently of selection on
the mean (e.g., see Slatkin, 1978, 1979).
All the models are equilibrium models.
They can be used to make quantitative
predictions if the character is assumed to
be normally distributed. This assumption
is also usually made by empiricists in their
ubiquitous use of the F test (Van Valen,
1978). Extreme deviations such as multimodality do not usually occur in groups
standardized according to sex and age. In
any event qualitative predictions from the
models should not be greatly affected by
deviations from normality (e.g., Slatkin,
1978).
A further assumption is that the forces
of natural selection act on the character
whose variation is under study, or some
other character with which it has a high
additive genetic correlation. This assumption is important and justified in situations
where possible causes of selection can be
identified. Eight cases from the literature
which postulated a reasonable cause for
the selection are given in Table 2. The
models can be applied certainly to these
eight studies and possibly to the others,
although the overdominance fitness model
discussed earlier may be equally applicable
to the others.
Frequency dependent selection
We turn to models concerned with the
selective maintenance of variation through
a frequency dependence among phenotypes. In what is probably thought of as the
niche variation model (Roughgarden,
1972; Emlen, 1975; Slatkin, 1979), phenotypes are assumed to be best adapted to one point along a continuously vary-
799
ing environmental gradient such as a
resource spectrum, according to their phenotypic measure, with competition between phenotypes being a decreasing
function of their difference (Roughgarden, 1972; Bulmer, 1974; Slatkin, 1979).
Slatkin (1979) reviewed these models, and
showed that genetic variation (particularly
when the variance is not constrained by the
mean) will be maintained at equilibrium
provided the resource function (or niche
width) is sufficiently broad and the competition function is not too large. This formalizes the idea that differences in population variation will be correlated with
differences in niche breadth only if the
degree of specialization (or the competition function) remains relatively constant
(Van Valen and Grant, 1970).
Slatkin (1979) showed that, in the absence of mutation, all phenotypes are expected to have approximately equal fitnesses at equilibrium when resource,
competition and phenotypic variation
functions are relatively smooth (usually
normal); but he also showed that fitnesses
vary substantially among phenotypes at
equilibrium when the resource function
assumes an unusual shape. However it is
important to note that even in models of
frequency dependence where all phenotypes have equal fitness at equilibrium, selection is still required to maintain the
equilibrium (Crow, 1970). Moreover the
effect of mutation is to increase the variance above the equilibrium, and stabilizing
selection will act on this variation.
Although the models are plausible,
there are several reasons for doubting that
selection acts regularly in nature in the
above manner. Wilson (1975) reviewed intraspecific differences in feeding efficiency
associated with body size, and concluded
that the models may be applicable to organisms segregating along a food-size resource axis, but a competitive gradient favoring large individuals could override the
frequency dependence. Moreover in stochastic environments selection may be frequency independent sometimes, and this
will obscure the frequency dependent
component. Keast (1977) has offered the
opinion that differences of a few percent
TABLE 2. Cases of observed selection for which a reasonable cause for the selection has been prescribed.
Organism
Characters
Method of examining selection
Tvpe of
selection
Cause of
selection
Reference
Water snakes
Banding patterns
Compare age
classes
Mainly
directional
Predation
Camin and Ehrlich, 1958;
Beatson, 1976
Sticklebacks
Lateral plate numbers,
gill raker numbers
Sampling from a
single cohort
Stabilizing,
directional
Predation
Hagen and Gilbertson,
1973
Snails
Size
Differential
mortality
Directional
Predation
Bantock and Bayley,
1973
Humans
Height
Mating success
Stabilizing
Mate choice
Cavalli-Sforza and
Bodmer, 1971
Darwin's finches
Length measures
Survival through
drought
Directional
Feeding
ability
Great tits
Body size
Population
through time
Directional
House sparrows
Body size, length
measures
Differential
mortality
Directional
and stabilizing
Reduced
competition
for nest sites
Dominance
hierarchy
Boag and Grant,
1981
Dhondt elal, 1979
Brown-headed
cowbirds
Wing and tarsus
length
Differential
mortality
Directional
Temperature
stress
Grant, 1972
Johnson et al, 1980
POPULATION VARIATION
between morphs cannot regularly have
ecological significance. In addition resources will sometimes not follow a continuum and exploitation efficiencies will likewise not vary continuously, so a discrete
niche model (see below) will be more appropriate.
Hespenheide (1975) has pointed out a
further difficulty. If a population consists
of territorial individuals during critical selection periods, there will be little opportunity for a frequency dependent distribution of phenotypes when resource
variation among territories is much less
than variation within territories, as is likely
to be generally true. The population is
then expected to consist of monomorphic
generalists solely on ecological grounds.
However, critical selection periods for terrestrial vertebrates are most likely to occur
outside the breeding season at a time when
territoriality is minimal or absent (Fretwell,
1972; Smith et al., 1978).
801
dominants (e.g., Krebs, 1971). However,
Grant et al. (1976) found segregation of
finches by beak shape to two habitats, and
Fretwell (1969) found segregation of sparrows on the basis of tarsus length. On the
basis of dimensions of other species present in each habitat these authors prescribed selective advantages to the two
groups within each species. Despite these
observations, it is an open question whether conditions for the maintenance of
polymorphism and, by extension, large
continuous variation in heterogeneous environments will be commonly met.
Temporal heterogeneity
As a final possibility for the selective
maintenance of variation, we consider
temporally varying selection. Slatkin and
Lande (1976) modelled a stabilizing selection function on a phenotypic trait with the
optimum fluctuating across generations.
They showed that the variance will converge to that predicted by the selection
Spatial heterogeneity
function unless the optima are so far apart
Frequency dependence may be im- that much of the population has very low
posed, alternatively, by the structure of the fitness. This was confirmed by simulation
environment. Beginning with Levene (Maynard Smith, 1979). Positive autocor(1953), there have been many single locus relation among environments can relax
models proposed for the maintenance of the conditions. Where there is a degree of
genetic variation in an environment with specialization among phenotypes in a poptwo niches (reviews by Felsenstein, 1976; ulation subject to density independent seHedrick et al, 1976). Bulmer (19716) has lection, a positive correlation is expected
extended these results to his models, dis- between the amplitude of the fluctuations
and the variance of a character affected by
regarding linkage disequilibrium.
Conditions for the maintenance of poly- those fluctuations (Slatkin and Lande,
morphism with a complete mixing of phe- 1976). Nevertheless, the general conclunotypes in the niches in each generation sion is that fluctuating environmental conare restrictive (Felsenstein, 1976; Maynard ditions can slow the loss of variation (LeSmith and Hoekstra, 1980), although they wontin, 19646) but are not likely to
have been met in laboratory experiments maintain it in the absence of mutation
with Drosophila (Thoday, 1972). The main- (Lande, 19776; Maynard Smith, 1979).
tenance of the polymorphism is enhanced
With models based on one locus, it is
by a reduced gene flow between niches, possible to find conditions for the maine.g., as a result of assortative mating or tenance of polymorphism (e.g., Haldane
through patch selection (Maynard Smith, and Jayakar, 1963), but these appear quite
1966, 1970).
restrictive. In reality, temporal fluctuaThere have been several field studies in- tions may actually erode variation (e.g., see
dicating preferential segregation of phe- Hedrick et al., 1976). Similar difficulties
notypes to different habitats (e.g., Nisbet for the role of temporal and spatial hetand Medway, 1972), but in many instances erogeneity in maintaining variation have
this is the result of displacement of sub- been observed using a quite different apordinate types to suboptimal habitat by proach—the modelling of the mainte-
802
P. R. GRANT AND T. D. PRICE
nance of sex (Hamilton et al., 1981; Williams, 1975).
We conclude that although mechanisms
for the maintenance of variation in heterogeneous environments may operate in
nature, in populations approaching panmixis they will act mainly to retard the loss
of variation. The population structure is
crucially important, and we suggest that
the determination of this should be a
priority in future empirical studies. We
earlier alluded to the problems caused by
the lumping of geographically differentiated samples in previous tests of the
adaptive variation hypothesis. In distinguishing between the models presented it
is important that this be eliminated as a
complicating factor.
Stabilizing selection
We now turn to those types of selection
actually observed in nature. It is generally
thought that most characters are under
stabilizing selection (Lande, 1976; Johnson, 1976), which may be frequency dependent, the rationale being that artificial
(directional) selection can rapidly alter
mean positions yet rapid change in means
is rarely observed in nature (Lewontin,
1964a). Of the eight cases of selection with
identified selective factors listed in Table
2, seven are concerned with only one component of total fitness, namely survival,
and seven involve mainly directional selection, not stabilizing selection. If this is a
common pattern, overall stabilizing selection will presumably occur as a result of
fluctuating directional selection within
generations. Opposing selection may occur
at different stages of the life cycle. This is
sometimes referred to as endocyclic selection (Dowdeswell, 1971). Alternatively,
changing environmental conditions from
year to year may shift the optimum at the
same stage of the life cycle (Grant et al.,
1976), an excellent example being the initial egg laying date in the Great Tit (Van
Noordwijk et al., 1980). In addition, stabilizing selection may occur at a given life
cycle stage through the operation of opposing forces such as predation and sexual
selection (Endler, 1980).
Lande (1976) has shown that given a
mutation rate which increases the total
variance by about 0.1% of the environmental variance per generation (which appears reasonable for polygenic characters;
Lande, 1976) large amounts of additive
genetic variance can be maintained even
under quite strong stabilizing selection.
Furthermore Lande (19776) reviewed experimental evidence that levels of variation
in experimental populations can increase
through mutation beyond that observed in
nature. This complements the direct evidence of stabilizing selection in nature.
Variation is also increased by immigration. In nature, this is suggested by the inverse correlation between population variation and degree of isolation (Soule, 1972;
Grant, 19796). For example, in the Azores
archipelago the least variable Chaffinch
(Fringilla coelebs) populations are the most
isolated and also the most differentiated;
populations on the Canary Islands are
more differentiated than on the Azores,
and consistently less variable (Grant,
19796).
It is generally thought that the mean is
more strongly affected by natural selection
than by immigration (Ehrlich and Raven,
1969; Sokal, 1978; Lande, 19806), whereas
the variance is more sensitive than the
mean to immigration (Endler, 1977). Typically, artificial (directional) selection on
the mean is successful (Falconer, 1960, ch.
12; Lewontin, 1974, pp. 86-94) but selection on the variance is less effective and
gives inconsistent results (e.g., Falconer,
1957; Scharloo, 1970; Thoday, 1972). The
generation of linkage disequilibrium causes
a temporary change in the genetic variance
(Bulmer, 197ld, 1976; Robertson, 1977)
and reduces the impact of selection on the
variance. Linkage disequilibrium is always
transient however, being broken down by
recombination. Under the assumption of
an infinite number of loci, variation is reduced to but not below an equilibrium value by stabilizing selection acting on the
variation regenerated by recombination;
in contrast the mean continuously responds to directional selection because it
is dependent only on the heritability (Bulmer, 197 Id).
803
POPULATION VARIATION
A DYNAMIC EQUILIBRIUM MODEL
The preceding considerations lead us to
propose a model of phenotypic variation
which is in a state of balance between
forces tending to increase the variation,
principally mutation and introgression or
immigration (input), and those tending to
decrease it, mainly selection (output: Fig.
1). If we compare two populations of assumed equal mutation rates, we can use
the model to account for differences in
variation in terms of a difference in the
immigration-selection balance. For the
purposes of illustration, input (horizontal
unbroken line) is assumed independent of
the amount of variation present in the
population. Lande (19776) has reviewed
evidence which shows this to be reasonable
for mutation; however with immigration,
input is likely to decrease as maintained
variation increases. The curved unbroken
line represents variation lost due to a stabilizing selection function. As variation increases more will be lost, because more of
the population is then in the low fitness
tails of the selection function. A is the equilibrium point between input and output
for population 1. Population 2 is more
variable, either as a result of a relaxation
of selection (curved dashed line, intersection at B) or an increase in immigration
(horizontal dashed line, intersection at C).
The simultaneous operation of both processes results in an even higher level of
variation maintained (population 3). Note
that increased immigration entails an increase in loss through selection.
Thus increased levels of variation in one
population over another can be accounted
for by an increase in immigration, a relaxation of selection or some combination of
the two. We ignore the effects of drift on
the level of variation maintained because
Lande (19806) has shown them to be of
minor importance in a selection-mutation
balance system. We first consider the influence of immigration, and then consider
how selection may be relaxed.
Felsenstein (1977) and Slatkin (1978)
have considered the effect of gene exchange (immigration) on clinal variation
using a model based on Lande's (1976).
Slatkin (1978) showed that, with weak se-
c
A
FIG. 1. The equilibrium maintained as a result of a
balance between forces tending to increase population variation (mainly immigration and mutation, the
input) and those tending to decrease it (mainly selection, the output). Four different intersections of input and output (A, B, C, D) give rise to three equilibrial levels of variation (1,2, 3). See text for further
details.
lection, for there to be an appreciable increase in variance at any one locality, the
variance in the means of the exchanging
populations must be similar to the variance
expected in one locality after selection.
Bulmer (1971c) has provided a similar
analysis for his model.
There are several ways in which selection may be relaxed. Selection may be relaxed or even absent when a species enters
a new environment. The population increases in size, the absolute fitness is raised
above one and phenotypes that would not
normally survive have their fitnesses raised
to or above one. This can only be transient.
A possible example is the population of
Great Skuas, Catharacta skua, in Scotland
(Furness, 1977), which is growing exponentially following cessation of human
persecution. Another example is the Cattle
Egret, Casmerodius alba, which has grown
exponentially following recent immigration to the U.S. (Bock and Lepthien, 1976).
Fluctuations in selective optima within
and across generations also slow the loss of
variation, and increasing the amplitude of
the fluctuation has the effect of relaxing
the overall stabilizing selection. The top of
the selection function becomes flattened,
and phenotypes assume nearly equal fitnesses over a wide range of conditions.
The total effect on the character may be
nearly neutral. With a further increase in
804
P. R. GRANT AND T. D. PRICE
TABLE 3. Heritabiltfies and coefficients of variation for the two species of Darwin's finches on Isla Daphne Major.
Bill depth
G. fortis
G. scandens
Body weight
Bill length
h1
x
CV
CVg
h!
x
CV
CVg
h*
X
CV
CVg
.82
.16
9.39
9.19
9.10
5.68
8.24
2.27
.62
.51
10.70
14.45
7.24
4.75
6.10
3.40
.84
.70
15.67
19.90
11.31
8.65
10.36
7.25
Data for G. fortis are from Boag and Grant (1978, unpublished) and for G. scandens adapted from Boag
(1981). h2 = heritability estimates based on mid-parent offspring regression, x = mean. CV = coefficient of
variation. CVg = coefficient of genetic variation. CVg is calculated by dividing the square root of the product
of the phenotypic variance and the heritability by the mean phenotype, assumed also to be the mean genotype.
Sample sizes for CV estimates are 1,100 in G. fortis and 177 in G. scandens. Measurements for bill characters
are in millimeters, for body weight in grams.
amplitude, the overall selection function
dips in the middle and there will be disruptive selection. Since the selective intensity is high this is a more extreme condition
and hence it may be relatively rare.
Segregation of phenotypes to different
niches can slow the loss of variation. Slatkin (1978), on the basis of Lande's (1976)
model, explicitly considered this as a
means of relaxing selection. He showed
that if the variance in the selective optima
across niches is approximately the same as
the variance in the selection function in
one niche there will be an appreciable increase in variance over the whole population. Spatial heterogeneity is likely to be
far more effective than temporal heterogeneity in influencing levels of variation
because (1) conditions for maintenance of
polymorphisms are less restrictive, and (2)
temporal fluctuations only slow the reduction of variation to that expected within an
environment (Slatkin and Lande, 1976),
while spatial heterogeneity determines the
expected variation within that environment.
Populations composed of generalist phenotypes all of which exploit a large variety
of resources may be subject to less intense
stabilizing selection than populations of
specialist phenotypes all exploiting the
same narrow range of resources (Rothstein, 1973). Unlike the original formulation of the adaptive variation hypothesis
(e.g., see Van Valen and Grant, 1970), this
type of relaxation should lead to increased
variation even when there is no betweenphenotype component to niche breadth
(Rothstein, 1973). However, we emphasize
that the postulated relationship between
generalist habits and relaxed stabilizing selection is an assumption that needs to be
tested.
An example
We now illustrate the application of this
simple model to a field study. In conjunction with P. T. Boag, we have been studying two species of Darwin's finches (Geospizafortis, the Medium Ground Finch, and
G. scandens, the Cactus Ground Finch) on
Isla Daphne Major, Galapagos since 1975.
The two species are very closely related
(they have been known to interbreed but
the hybrids did not survive). Coefficients of
variation of morphological characters are
up to 1.6 times greater in G. fortis than in
G. scandens, and their coefficients of genetic variation differ by even more (Table
3).
Selection. In 1977 there was a drought on
the island: Population sizes are estimated
to have decreased from about 1,200 to 180
in G. fortis and from 280 to 110 in G. scandens (Grant and Grant, 1980; Boag and
Grant, 1981). We have analyzed selection
on the variance associated with this mortality independent of selection on the
mean, for three morphological traits (Boag
and Grant, 1981). The separation is assumed in models and often observed in
practice (Slatkin and Lande, 1976; Lande,
1976, 1977). Variation in the three beak
and body size characters considered here
has a fairly well understood adaptive significance with respect to metabolic rate
and particularly feeding ability (Grant et
ai, 1976; Grant, 1981a). We restrict ourselves to a univariate analysis. Despite a
high phenotypic correlation between the
805
POPULATION VARIATION
TABLE
4. Selectionon the variances by species and sex.
Bill depth
G.fortis, males
G.fortis, females
G. scandens, males
G. scandens, females
NB
NA
VB
390
105
74
34
114
30
33
16
.63
.63
.19
.21
Bill length
vA
.58
.60
.11*
.13
VB
.59
.59
.42
.22
Body weight
vA
V,
VA
.55
.59
.33
.11*
2.8
2.7
2.2
1.6
3.0
2.3
1.9
0.7*
The comparison is between birds of known sex alive in 1976 with those that survived to 1977. Data are
from Boag and Grant (unpublished) and Boag (1981). N refers to sample sizes and V to variances. The
subscript B refers to before the drought, and A to after the drought.
* Decreases in the variance between survivors and dead significant at the 5% level (F test).
three characters (r varies from 0.69 to
0.86) selection on a composite character is
likely to be more intense, but is more difficult to interpret ecologically.
Changes in variance for each species and
sex are given in Table 4. An unweighted
average of the variances in each sex is used
to give an estimate of the intensity of stabilizing selection (Table 5). Stabilizing selection over the drought appears to have
been more intense on G. scandens than on
G. fortis, despite the lower variability and
mortality of G. scandens and almost no
change in its mean. This can be related to
the wider range of food types exploited by
G.fortis, both between phenotypes (associated with patch selection, Grant et al., 1976;
Grant, 1981a; Boag and Grant, 1981) and
within phenotypes (Smith et al., 1978;
Grant and Grant, 1980).
The calculated selective losses are high
in G. scandens and low in G. fortis. Using
Figure 2 of Lande (1976) and assuming a
normal fitness function, we estimate that
heritabilities in the two species should be
maintained at about 0.4 to 0.5 in G. scandens and slightly higher in G. fortis; this
procedure also assumes the rates of mutation given by Lande (1976) for polygenic
characters are applicable. Stabilizing selection over the whole life cycle is likely to be
more intense: we have not considered survival to maturity or differences in fecundity. An examination of the breeding population in 1978 shows that fecundity
differences may have an important effect.
The sex ratio in both species in 1978 was
skewed heavily in favor of males. All females on the island bred monogamously,
and those males they bred with formed a
less variable subset of the total male population in both species (Table 6). It is likely
that the inclusion of selection over the
whole life cycle would result in expected
maintained heritabilities of 0.3 to 0.5 in
each species (from Fig. 2 in Lande, 1976).
Immigration. G. fortis, G. fuliginosa (the
Small Ground Finch), and G. magnirostris
(the Large Ground Finch) and possibly G.
scandens regularly immigrate, probably
from neighboring Isla Santa Cruz (Price,
unpublished; Grant et al., 1975), but only
G. fuliginosa have been known to stay and
breed. They hybridize solely with G.fortis,
TABLE 5. Selection over the drought period.
Analysis of selection
Bill depth
G.fortis
G. scandens
Body weight
Bill length
F
Load
F
Load
F
Load
1.07
1.65
3.2
22.3
1.04
1.42
1.7
15.9
1.03
1.44
.02
16.9
' selective
F values for the variance changes are given as an unweighted average of males and females. T h e Jo
mortality or phenotypic load is defined by Lande (1976) as 100 (1 - V(&>2/(&>2 + crp2))), based on a normal fitness function, up- is a measure of the width of the fitness function; a large o>2 implies weak selection. It can be
calculated using formulae in O'Donald (1970), again assuming a normal fitness function, ap2 is the phenotypic
variance before selection.
806
P. R. GRANT AND T. D. PRICE
TABLE 6. Variances at the start of the breeding season.
Breeding males
Bill depth
NT
VT
Bill length
Body weight
VT
G.fortis, males
81
26
.73
.59
.61
.34*
2.4
2.1
G. scandens, males
46
23
.18
.15
.45
.26*
2.3
1.9
The relative variances of all males (subscript T) and breeding males (subscript BD) by species in 1978. N
refers to numbers, V to variances.
* Variance decreases between breeders and nonbreeders significant at the 5% level (F test).
and hybrid pairs comprise approximately
3% of all pairs (Boag, 1981). We use the
character bill depth to illustrate the impact
of this hybridization on population variation.
We assume a pairing between the mean
phenotypes (by assumption also the mean
genotypes) of fuliginosa (bill depth 6.95
mm) and Daphne fortis (9.39 mm). A hybrid offspring at the mean position (expected bill depth 8.17 mm) will increase
the genotypic variance in the Daphne fortis
population by 1.77%, and the phenotypic
variance by 1.45% for every 100 fortis individuals; these calculations are based on
the observed heritability of 0.82 (Table 1).
The final effect of hybridization is difficult
to calculate because it depends, among
other things, on the probability of hybrids
surviving to breed successfully, the number of loci involved and the decay of linkage disequilibrium.
A bird thought to be a hybrid on the
basis of measurements bred successfully in
1976 (Boag, 1981). Two out of 55 male
fortis offspring surviving into 1979 from
1978 were hybrids. Their presence increased the variance in the juvenile male
component of the population by 6.5%,
which is in rough agreement with the calculation above.
The expected increase in phenotypic
variance per generation due to hybridization is between one and two orders of magnitude greater than that expected from
mutation alone (=£0.1%; Lande, 1976), and
it is sufficient to account for the higher
heritabilities in G. fortis than those predicted earlier without this immigration
(see Lande, 1976, Fig. 2 for details).
Therefore the greater variation in G.
fortis than in G. scandens is probably asso-
ciated with both relaxed selection and
higher levels of immigration. It is impossible to apportion the relative importance
of the two at this stage of the study. Nevertheless, it appears that there is some decrease in selective losses per unit variance
maintained in G. fortis. This is in accord
with the adaptive variation hypothesis.
DISCUSSION: RETURN TO THE
THEME OF THE SYMPOSIUM
This symposium asks: To what extent
has theoretical ecology contributed to our
understanding of nature? We have considered one aspect of nature, variation within
populations, and have discussed the major
theories to account for it. To what extent
have the theories been successful? A few
comments on the role of theory are needed before we answer this question.
Theoretical activities vary in methods
and purposes, but they can be artificially
dichotomized for convenience into two
classes which we refer to as operational
theory and pure theory. By operational
theory we mean those constructs which,
with little or no modification, can be applied to real world situations. By pure theory we mean those constructs which cannot be made useful in an applied sense
without much simplification or other qualification. Both classes of theory are valuable; neither should be thought of as more
important than the other and typically
there is fruitful exchange between them.
The value of pure theory, theory for the
theoretician, is extremely difficult to assess
in terms of its contribution to our understanding of nature because its benefits are
indirect. It provides a framework in which
to organize our thoughts and may enable
us to pose sharp questions that would oth-
807
POPULATION VARIATION
erwise never occur to us. By contrast operational theory can be more readily evaluated because the tests of its predictions
show it to be satisfactory or inadequate as
an explanation of nature. However, ultimately all theory must be measured
against an empirical yardstick, so the final
verdict on its usefulness will be rendered
by empirical studies. In the words of J. B.
S. Haldane: "No scientific theory is worth
anything unless it enables us to predict
something which is actually going on. Until
that is done, theories are a mere game of
words, and not such a good game as poetry" (Haldane, 1937, p. 7).
Understanding phenotypic variation
within populations is both an ecological
and a genetics problem, but most of the
theory has been developed by population
geneticists, and much of it is pure theory.
Van Valen's (1965) hypothesis was the first
attempt to offer a testable explanation for
differences between populations in levels
of continuous variation. It drew upon prevailing views on the maintenance of genetic variation in single locus models,
which are not appropriate for continuously varying phenotypic traits. Fifteen
years later we have more useful, multilocus
models that offer the opportunity of exploring the effects of ecological variables
on levels of continuous variation. We have
taken a small step towards translating
them into operational form by presenting
a model which integrates the main effects
from these multilocus models. It can make
predictions and it can be shown to be
wrong. In the example we gave to illustrate
its use, we might have found G.fortis, the
more variable species, to receive no immigration and to be subject to stronger stabilizing selection than G. scandens. In this
case the model would have been clearly
wrong: as it turned out, the facts were consistent with the model. The model should
also be applicable to other populations in
the archipelago, and in fact there is indirect evidence of an association between
large variation and relaxed selection
among other populations of fortis (Grant,
1967).
tinuous variation. Without the theory it is
doubtful if the problem would have ever
been recognized. Therefore in this area,
and probably many others, it is not correct
to say "Practice has caught up with theory
in ecology" (Odum, 1971, p. vii). Rather,
empirical studies lag far behind theory in
this important but complex subject. While
theory will undoubtedly continue to be
elaborated and refined, even without feedback from empirical studies, what we really
need at the moment are testable alternative theories, and data to test them from
ecological studies of marked individuals.
Empirical studies are needed to assess
the importance of those features identified
by theory as being of primary importance
in determining population variation; spatial and temporal heterogeneity, population structure in its widest sense, immigration and selection—its cause, direction and
whether it occurs in a frequency dependent fashion or not. Alternative theories
are needed to avoid the main weakness of
single theory testing: when there is only
one theory and the data do not entirely fit,
a process of altering the theory takes place
to bring it more into line with the facts.
Such essentially curve-fitting manipulation
has sound theoretical justification; after all
the theory may be basically correct, but at
its worst it is no more than a post hoc rationalization of a poor theory.
A limitation of our model is that it encompasses several selection processes without being specific about how or when they
occur: It does not specify the conditions
under which the different types of relaxed
selection are expected to occur. We intend
to make such refinements as this and then
set the model in opposition to other explanatory schemes for variation, such as
the more phenomenological suggestions of
ecologists based on considerations of environmental heterogeneity and population
control (McNaughton and Wolf, 1970;
Murton, 1972; see also Grant, 1971), to see
which one is most consistent with the natural world.
ACKNOWLEDGMENTS
In our judgment, theory has contributed
Our research on Darwin's finches has
substantially to our understanding of con- been funded by NRC (Canada) Grant
808
P. R. GRANT AND T. D. PRICE
A2920 and by NSF Grants DEB 77-23377
and DEB 79-21119 to P.R.G. We thank
numerous colleagues for discussion and
for reading manuscripts, including J. P.
Adams, P. T. Boag, J. A. Endler, B. R.
Grant, J. Felsenstein, R. Lande, N. A. Moran, D. Schluter, C. Sing, M. Slatkin and P.
Smouse.
Bulmer, M. G. 1971c. Stable equilibria under the
migration matrix model. Heredity 27:419-430.
Buhner, M. G. 1971rf. The effect of selection on genetic variability. Amer. Natur. 105:201-211.
Bulmer, M. G. 1972. The genetic variability of polygenic characters under optimizing selection, mutation and drift. Genet. Res., Camb. 19:17-25.
Bulmer, M. G. 1974. Density dependent selection
and character displacement. Amer. Natur.
108:45-58.
Bulmer, M. G. 1976. The effection of selection on
genetic variability: A simulation study. Genet.
Res., Camb. 28:101-117.
REFERENCES
Bulmer, M. G. 1980. The mathematical theory of quantitative genetics. Clarendon Press, Oxford.
Abbott, I. 1973. Birds of Bass Strait. Evolution and
Camin.J. H. and P. R. Ehrlich. 1958. Natural selececology of the avifaunas of some Bass Strait Istion in water snakes (Natrix sipedon L.) on islands
lands, and comparison with those of Tasmania
on Lake Erie. Evolution 12:504-511.
and Victoria. Proc. Roy. Soc. Viet. 85:197-224.
Cavalli-Sforza, L. L. and W. F. Bodmer. 1971. The
Abbott, I. 1978. The significance of morphological
genetics of human populations. W. H. Freeman and
variation of the finch species on Gough, InaccesCo., San Francisco.
sible and Nightingale Islands, South Atlantic Crow, J. F. 1970. Genetic loads and the cost of natOcean. J. Zool. London 184:119-125.
ural selection. In K. I. Kojima (ed.), Mathematical
Abbott, I., L. K. Abbott, and P. R. Grant. 1977.
topics in population genetics, pp. 128-177. SpringComparative ecology of Galapagos ground
er-Verlag, Heidelberg.
finches (Geospiza Gould): Evaluation of the im- Davidson, D. W. 1978. Size variability in the worker
portance of floristic diversity and interspecific
caste of a social insect (Veromessor pergandei Mayr)
competition. Ecol. Monogr. 47:151-184.
as a function of the competitive environment.
Banks, R. C. 1970. On ecotypic variation in birds.
Amer. Natur. 112:523-532.
Evolution 24:829-831.
Dhondt, A. A., R. Eyckeman, and J. Huble. 1979.
Bantock, C. R. and J. A. Bayley. 1973. Visual selecWill great tits become little tits? Biol. J. Linn. Soc.
tion for shell size in Cepaea (Held.). J. Anim.
11:289-294.
Ecol. 42:247-261.
Dobzhansky, Th. 1970. Genetics of the evolutionary proBeatson, R. R. 1976. Environmental and genetical
cess. Columbia University Press, New York and
correlates of disruptive coloration in the water
London.
snake, Natrtx s. sipedon. Evolution 30:241-252.
Dow, D. D. 1976. The use and misuse of the coefBeever, J. W. 1979. The Niche-Variation hypothesis:
ficient of variation in analyzing geographical
An examination of assumptions and organisms.
variation in birds. Emu 76:25—29.
Evolutionary Theory 4:181-191.
Dowdeswell, W. H. 1971. Ecological genetics and
Bell, G. 1974. The reduction of morphological varibiology teaching. In R. Creed (ed.), Ecological
ation in natural populations of smooth newt largenetics and evolution: Essays in honour ofE. B. Ford,
vae. J. Anim. Ecol. 43:115-128.
pp. 363-378. Blackwells, Oxford.
Berger, E. 1976. Heterosis and the maintenance of
Ehrlich, P. R. and P. H. Raven. 1969. Differentiation
enzyme polymorphism. Amer. Natur. 110:823of populations. Science 165:1228-1232.
839.
Emlen.J. M. 1975. Niches and genes; some further
Bernstein, R. A. 1979. Evolution of niche breadth
thoughts. Amer. Natur. 109:472-476.
in populations of ants. Amer. Natur. 114:533Endler, J. A. 1977. Geographic variation, speciation,
544.
and dines. Princeton Univ. Press, Princeton.
Boag, P. T. 1981. Morphological variation in the
Endler, J. A. 1980. Natural selection on color patDarwin's finches (Geospizinae) of Daphne Major
terns in Poecilia reticulata. Evolution 34:76-91.
Island, Galapagos. Ph.D. Diss., McGill UniverFalconer, D. S. 1957. Selection for phenotypic intersity.
mediates in Drosophila. J. Genet. 55:551-561.
Boag, P. T. and P. R. Grant. 1978. Heritability of
Falconer, D. S. 1960. Introduction to quantitative geexternal morphology in Darwin's finches. Nature
netics. Ronald Press, New York.
274:793-794.
Felsenstein, J. 1976. The theoretical population geBoag, P. T. and P. R. Grant. 1981. Intense natural
netics of variable selection and migration. Ann.
selection in a population of Darwin's finches. SciRev. Genetics 10:253-280.
ence 213. (In press)
Felsenstein, J. 1977. Multivariate normal genetic
Bock, C. E. and L. W. Lepthien. 1976. Population
models with a finite number of loci. In E. Pollak,
growth in the Cattle Egret. Auk 93:164-166.
O. Kempthorne, and T. B. Bailey (eds.). ProceedBulmer, M. G. 1971a. The stability of equilibria unings of the International Conference on Quantitative
der selection. Heredity 27:157-162.
genetics, pp. 227-246. Iowa State Univ. Press,
Ames.
Bulmer, M. G. 19716. Stable equilibria under the
two island model. Heredity 27:321-330.
Fretwell, S. 1969. Ecotypic variation in the non-
POPULATION VARIATION
809
breeding season in migratory populations: A
study of tarsal length in some Fringillidae. Evolution 23:406^420.
1981. Fluctuation of environment and coevolved
entagonistic polymorphism as factors in the maintenance of sex. In R. D. Alexander and D. W.
Fretwell, S. D. 1972/ Populations in a seasonal environ-
Tinkle (eds.), Natural selection and social behavior,
ment. Princeton Univ. Press, N.J.
Fretwell, S. 1977. Stabilizing selection in field sparrows—a retraction. Amer. Natur. I l l : 1209—
1210.
Furness, R. 1977. Studies on the breeding biology
and population dynamics of the great skua Catharacla skua. Ph.D. Diss., University of Durham.
Garnett, M. C. 1981. Body size, its heritability and
influence on juvenile survival among great tits,
Parus major. Ibis 123:31-41.
Grant, P. R. 1965. The adaptive significance of some
size trends in island birds. Evolution 19:355-367.
Grant, P. R. 1967. Bill length variability in birds of
the Tres Marias islands, Mexico. Can. J. Zool.
45:805-815.
Grant, P. R. 1971. Variation in the tarsus length of
birds in island and mainland regions. Evolution
25:599-614.
Grant, P. R. 1972. Centripetal selection and the
house sparrow. Systematic Zoology 21:23—30.
Grant, P. R. 1976. Population variation on islands.
Proc. 16th Int. Orn. Congr., pp. 603-615.
Grant, P. R. 1979a. Ecological and morphological
variation of Canary Island blue tits, Parus caeruleus (Aves: Paridae). Biol. J. Linn. Soc. 11:103129.
Grant, P. R. 19796. Evolution of the chaffinch, Fringilla coelebs, on the Atlantic Islands. Biol. J. Linn.
Soc. 11:301-332.
Grant, P. R. 1981a. The feeding of Darwin's finches
on Tnbulus cistoides (L.) seeds. Anim. Behav. 29:
785-793.
Grant, P. R. 19816. Patterns of growth in Darwin's
finches. Proc. Roy. Soc. (London) B. 212:403432.
Grant, P. R. and B. R. Grant. 1980. Annual variation
in finch numbers, foraging and food supply on
Isla Daphne Major, Galapagos. Oecologia (Berl.)
46:55-62.
Grant, P. R., B. R. Grant, J. N. M. Smith, I. J. Abbott,
and L. K. Abbott. 1976. Darwin's finches: Population variation and natural selection. Proc. Nat.
Acad. Sci. U.S.A. 73:257-261.
Greenwood, P. J., P. H. Harvey, and C. M. Perrins.
1979. The role of dispersal in the great tit (Parus
major): The causes, consequences and heritability
of natal dispersal. J. Anim. Ecol. 48:123-142.
Guthrie, R. D. 1965. Variability in characters
undergoing rapid evolution, an analysis of Microtus molars. Evolution 19:214-233.
Hagen, D. W. and L. A. Gilbertson. 1973. Selective
predation and the intensity of selection acting
upon the lateral plates of three spine sticklebacks. Heredity 30:273-287.
Haldane, J. B. S. 1937. Adventures of a biologist. Harper and Brothers, New York.
Haldane, J. B. S. and S. D. Jayakar. 1963. Polymorphism due to selection of varying direction. J.
Genet. 58:237-242.
Hamilton, W. D., P. A. Henderson, and N. A. Moran.
pp. 363-381. Chiron Press, New York and Concord.
Hedrick, P. W., M. E. Ginevan, and E. P. Ewing.
1976. Genetic polymorphism in heterogeneous
environments. Ann. Rev. Ecol. Syst. 7:1-32.
Hespenheide, H. A. 1973. Ecological inferences
from morphological data. Ann. Rev. Ecol. Syst.
4:213-229.
Hespenheide, H. A. 1975. Prey characteristics and
predator niche width. In M. L. Cody and J. M.
Diamond (eds.), Ecology and evolution of commu-
nities, pp. 158—180. Belknap Press, Harvard.
Istock, C. A., J. Zisfein, and K. J. Vavra. 1976. Ecology and evolution of the pitcher-plant mosquito.
2. The substructure of fitness. Evolution 30:535—
547.
Johnson, C.
1976. Introduction to natural selection.
Univ. Park Press, Baltimore, Md.
Johnson, D. M., A. L. Stewart, M. Corley, R. Ghrist,
J. Hagner, A. Keteses, B. McDonnell, W. Newsora, E. Owen, and P. Samuels. 1980. Brownheaded cowbird (Molothrus ater) mortality in an
urban winter roost. Auk 97:299-320.
Keast, A. 1976. Ecological opportunities and adaptive evolution on islands with special reference
to evolution on the isolated forest outliers of
southern Australia. Proc. 16th Int. Orn. Congress: 573-584.
Keast, A. 1977. Mechanisms expanding niche width
and minimizing intraspecific competition in two
centrarchid fishes. Evol. Biol. 10:333-395.
Kimura, M. 1965. A stochastic model concerning the
maintenance of genetic variability in quantitative
characters. Proc. Nat. Acad. So. U.S.A. 54:731736.
Krebs,J. R. 1971. Territory and breeding density in
the great tit, Parus major. Ecology 52:1-22.
Lande, R. 1976. The maintenance of genetic variability by mutation in a polygenic character with
linked loci. Genet. Res., Camb. 26:221-235.
Lande, R. 1977a. On comparing coefficients of variation. Syst. Zool. 26:214-217.
Lande, R. 19776. The influence of the mating system
on the maintenance of genetic variability in polygenic characters. Genetics 86:485-498.
Lande, R. 1980a. Sexual dimorphism, sexual selection and adaptation in polygenic characters. Evolution 34:292-305.
Lande, R. 19806. Genetic variation and phenotypic
evolution during allopatric speciation. Amer.
Natur. 116:463-479.
Lerner, I. M. 1954. Genetic homeostasis. Oliver and
Boyd, London.
Levene, H. 1953. Genetic equilibrium when more
than one ecological niche is available. Amer. Natur. 87:331-333.
Lewontin, R. C. 1964a. The interaction of selection
and linkage. I. General considerations; Heterotic
models. Genetics 49:49-67.
Lewontin, R. C. 19646. The interaction of selection
810
P. R. GRANT AND T. D. PRICE
and linkage. II. Optimum models. Genetics
50:757-782.
Rothstein, S. I. 1973. The niche variation model—is
it valid? Amer. Natur. 107:598-620.
Lewontin, R. C. 1974. The genetic basis of evolutionary Roughgarden, J. 1972. Evolution of niche width.
change. Columbia Univ. Press, New York.
Amer. Natur. 106:683-718.
Lister, B. C. 1976. The nature of niche expansion Roughgarden, J. 1974. Niche width: Biogeographic
in West Indian Anolis lizards II: Evolutionary
patterns among Anolis lizard populations. Amer.
Natur. 108:429-442.
components. Evolution 30:677-692.
Lister, B. C. and R. E. McMurtie. 1976. On size vari- Scharloo, W. 1970. Stabilizing and disruptive selection on a mutant character in Drosophila. III.
ation in anoline lizards. Amer. Natur. 110:311314.
Polymorphism caused by a developmental switch
mechanism. Genetics 65:693-705.
Mackay, T. F. C. 1980. Genetic variance, fitness, and
homeostasis in varying environments: An exper- Searcy, W. A. 1979. Sexual selection and body size
imental check of the theory. Evolution 34:1219in male redwinged blackbirds. Evolution 33:649—
1222.
661.
Mather, K. 1953. The genetical structure of popu- Selander, R. K. 1966. Sexual dimorphism and diflations. Symp. Soc. Exp. Biol. 7:66—95.
ferential niche utilization in birds. Condor
68:113-151.
Mayr, E. 1963. Animal species and evolution. Harvard
Univ. Press, Cambridge.
Slatkin, M. 1970. Selection and polygenic characters.
Maynard Smith, J. 1966. Sympatric speciation.
Proc. Nat. Acad. Sci. U.S.A. 66:87-93.
Amer. Natur. 100:637-650.
Slatkin, M. 1978. Spatial patterns in the distributions
Maynard Smith, J. 1970. Genetic polymorphism in
of polygenic characters. J. Theor. Biol. 70:213—
a varied environment. Amer. Natur. 104:487228.
490.
Slatkin, M. 1979. Frequency and density-dependent
selection on a quantitative character. Genetics
Maynard Smith, J. 1979. The effects of normalizing
93:755-771.
and disruptive selection on genes for recombination. Genet. Res., Camb. 33:121-128.
Slatkin, M. and R. Lande. 1976. Niche width in a
fluctuating environment-density independent
Maynard Smith, J. and R. Hoekstra. 1980. Polymormodel. Amer. Natur. 110:31-55.
phism in a varied environment: How robust are
Smith, J. N. M. and A. A. Dhondt. 1980. Experithe models? Genet. Res., Camb. 35:45-57.
mental confirmation of heritable morphological
McLaren, I. A. 1976. Inheritance of demographic
variation in a natural population of song sparand production parameters in the marine coperows. Evolution 34:1155-1160.
pod Eurytemora herdmam. Biol. Bull. 151:200213.
Smith, J. N. M., P. R. Grant, B. R. Grant, I. J. Abbott,
McNaughton, S. J. and L. L. Wolf. 1970. Dominance
and L. K. Abbott. 1978. Seasonal variation in
and the niche in ecological systems. Science
feeding habits of Darwin's ground finches. Ecol167:131-139.
ogy 59:1137-1150.
Morse, D. H. 1971. The niche-variation hypothesis: Smith, J. N. M. and R. Zach. 1979. Heritability of
A test and alternatives (review). Bird Banding
some morphological characters in a song sparrow
42:57-58.
population. Evolution 33:460-467.
Murton, R. K. 1972. The control of bird popula- Sokal, R. R. 1978. Population differentiation: Sometions. Le Gerfaut 62:63-81.
thing new or more of the same? In P. F. Brussard
Nisbet, I. C. T. and Lord Medway. 1972. Disper(ed.), Ecological genetics: The interface, pp. 2 1 5 sion, population ecology and migration of east239. Springer-Verlag, N.Y.
ern great reed warblers, Acrocephalus onentalis Soule, M. 1972. Phenetics of natural populations.
wintering in Malaysia. Ibis 114:451—494.
III. Variation in insular populations of a lizard.
O'Donald, P. 1970. Change of fitness by selection
Amer. Natur. 106:429-446.
for a quantitative character. Theor. Popul. Biol.
Soule, M. and B. R. Stewart. 1970. The niche vari1:219-232.
ation hypothesis: A test and alternatives. Amer.
O d u m , E. P. 1971. Fundamentals of ecology. W. B.
Natur. 104:85-97.
Saunders, Philadelphia.
Perrins, C. M. and P.J.Jones. 1974. The inheritance Thoday, J. M. 1953. Components of fitness. Symp.
Soc. Exp. Biol. 7:96-113.
of clutch size in the great tit (Parus major L.).
Thoday, J. M. 1972. Disruptive selection. Proc. Roy.
Condor 76:225-229.
Soc. (London) B. 182:109-143.
Rendel, J. M. 1967. Canalisation and gene control. AcVan Noordwijk, A.J., J. H. van Balen, and W. Scharademic Press, N.Y.
loo. 1980. Heritability of ecologically important
Rendel, J. M. 1979. Canalisation and selection. In J.
traits in the great tit, Parus major. Ardea 68:
N. M. Thompson and J. M. Thoday (eds)., Quan193-203.
titative genetic variation, pp. 139—156. Academic
van Valen, L. 1963. Intensities of selection in natPress, N.Y.
ural populations. Proc. 11th Int. Cong. Genet.
Robertson, A. 1977. Artificial selection with a large
1:153.
number of linked loci. In E. Pollak, O. Kempthorne, and T. B. Bailey (eds.), Proceedings of the Van Valen, L. 1965. Morphological variation and
International Conference on Quantitative Genetics,
width of the ecological niche. Amer. Natur.
pp. 307-322. Iowa State Univ. Press, Ames.
99:377-390.
POPULATION VARIATION
811
Van Valen, L. 1969. Variation genetics of extinct
ceptual aspects. Prentice-Hall, Englewood Cliffs,
animals. Amer. Natur. 103:193-224.
N.J.
Van Valen, L. 1978. The statistics of variation. Evo- Wiens, J. A. and J. T. Rotenberry. 1980. Patterns of
lutionary Theory 4:33-43.
morphology and ecology in grassland and shrubVan Valen, L. and P. R. Grant. 1970. Variation and
steppe bird populations. Ecol. Monogr. 50:287niche width reexamined. Amer. Natur. 104:587308.
590.
Williams, G. C. 1975. Sex and evolution. Princeton
Van Valen, L. and R. Weiss. 1966. Selection in natUniversity Press, Princeton.
ural populations. V. Indian rats. Genet. Res., Willson, M. F. 1969. Avian niche size and morphoCamb. 8:261-267.
logical variation. Amer. Natur. 103:531-542.
Waddington, C. H. 1957. The strategy of the genes; a Willson, M. F., J. R. Karr, and R. R. Roth. 1975.
discussion of some aspects of theoretical biology.
Ecological aspects of avian bill-size variation.
MacMillan, N.Y.
Wilson Bull. 87:32-44.
Wallace, B. 1970. Genetic load. Its biological and con- Wilson, D. S. 1975. The adequacy of body size as a
niche difference. Amer. Natur. 109:769-784.