Download A general model of the relation between phenotypic selection and

J. evol.
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7: l-12
(1994)
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Mini-review
A general model of the relation
and genetic response
P. H. van Tienderen’,2
between phenotypic
selection
and G. de Jong3
‘Netherlands Institute of Ecology, Centre for Terrestrial Ecology, Department of
Plant Population Biology, P.O. Box 40, 6666 ZG Heteren, The Netherlands
‘Department of Genetics, Agricultural
University Wageningen
3Department of Plant Ecology and Evolutionary Biology, University of Utrecht
Key words:
Quantitative
genetics; selection; heritability;
trade-offs;
birds.
Abstract
The phenotypic view of selection assumes that genetic responses can be predicted
from selective forces and heritability - or in the classical quantitative genetic equation:
R = h2S. However, data on selection in bird populations show that often no selection
response is found, despite consistent selective forces on phenotypes and significant
heritable variation. Such discrepancies may arise due to the assumption that selection
only acts on observed phenotypes. We derive a general selection equation that takes
into account the possibility that some relevant (internal or external) traits are not
measured. This equation shows that the classic equation applies if selection directly
acts on the measured, phenotypic traits. This is not the case when, for instance, there
are unknown internal genetic trade-offs, or unknown common environmental factors
affecting both trait and fitness. In such cases, any relationship between phenotypic
selection and genetic response is possible. Fortunately, the classical model can be tested
by comparing phenotypic and genetic covariances between traits and fitness; an
indication that important internal or external traits are missing can thus be obtained.
Such an analysis was indeed found in the literature; for selection on fledging weight
in Great Tits it yielded valuable extra information.
Introduction
Genetic changes in a population can be predicted by tracing the flow of genes
from one generation to the next. Robertson’s
secondary theorem of natural
2
van Tienderen
and de Jong
selection states this more precisely: ‘the change in any character produced by a
selection process is equal to the additive genetic covariance between fitness and the
character itself’ (Robertson,
1968; Crow and Nagylaki,
1976). When selection is
due to differences in viability, the covariance between trait and relative fitness is
simply the difference in mean breeding value before and after selection. More
generally, this covariance sums up the additive effects of the genes affecting the
trait, taking into account their expected frequencies in the next generation (i.e.
weighted by relative fitness). The secondary theorem lacks an explicit reference to
selection at the phenotypic level, and follows a ‘genetic approach’.
However,
natural selection is often seen as the result of (i) heritable phenotypic variation and
(ii) consistent fitness differences between phenotypes (Endler, 1986). This ‘phenotypic approach’ is summarized in the familiar quantitative genetic formula R = h2S,
with R the response to selection, h2 the heritability and S the selection differential
(Falconer, 198 I), or in its multivariate form R = GP- ‘S in which R and S are now
vectors of responses and selection differentials, and G and P genetic and environmental covariance matrices, respectively (Lande, 1982). The phenotypic approach
suggests that selection can be adequately described by combining measurements of
selection on phenotypic traits, and estimates of heritabilities and genetic correlations. The empirical appeal is evident: field studies can measure selective forces on
phenotypes, phenotypic optimization models can be used to derive optimal strategies, and the population should show a response in the predicted direction, towards
a peak in the fitness landscape, provided that there is adequate genetic variation.
Problems with this phenotypic approach have been detected in numerous studies
of selection in bird populations (Boyce and Perrins, 1987: Rockwell,
Findlay and
Cooke, 1987; Gibbs, 1988; Price, Kirkpatrick
and Arnold, 1988; Price and Liou,
1989; Alatalo, Gustafsson and Lundberg, 1990; Cooke et al., 1990). Unlike many
other organisms birds allow an integrated analysis of selection and genetic variation
in natural populations. These papers reported directional selection and significant
heritabilities,
without
any indication of a selection response. Apparently,
the
observed phenotypic correlation between trait and fitness was not accompanied by
a genetic correlation between trait and fitness (unless the selection response was
exactly counterbalanced by changes in conditions over time, cf. Cooke et al., 1990).
Plausible hypotheses concerning the absence of selection response were given. For
instance, Price and Liou (1989) argued that apparent selection on clutch size was in
fact due to a correlation between the non-heritable nutritional state and clutch size;
Alatalo, Gustafsson and Lundberg (1990) argued that selection was acting on the
environmental component of tarsus length rather than on the phenotype.
In more general terms, there are two reasons why the phenotypic approach may
be too simple. Firstly, expectations are based on a model with specific assumptions
about the genetics underlying quantitative traits, concerning number of loci, allelic
effects, polygenic mutation rates, pleiotropy and epistasis. Our knowledge of the
actual genetics of quantitative traits is very limited (Barton and Turelli, 1989)
genetic details may matter (Turelli, 1988) and simple expectations may be wrong.
Here we focus on an entirely different complicating factor, the fact that we observe
only a subset of the traits under selection. The purpose of this paper is to show how
Phenotypic
selection
and genetic
response
3
the relationship between observed selection forces and genetic responses is affected
by lack of information.
We derive a general equation for the relationship between
apparent selection and genetic response.
A general framework
for selection
A morphological
or behavioural trait is affected by a complex network of genes
and their products, interacting with the ambient environmental conditions (Endler
and McLellan, 1988; Wade and Kalisz, 1990; Rausher, 1992) (Fig. 1). A functional
explanation can often be given for the relationship between the external phenotype
and fitness. For instance, the optimal timing of breeding in Great Tits depends on
the peak in caterpillar density when rearing the chicks (Perrins, 1991). This might
be called ‘external selection’, as selection depends on conditions in the external
environment.
‘Internal
selection’ on the genes, mechanisms
and ‘intermediate
structures’ (Stearns, 1981) that underlie the external phenotype may also affect the
outcome of selection. For example, genes that cause early breeding may have effects
on fitness other than those mediated by the breeding data and its effect on the
Fig. 1. Example of a simple network
of traits: genes affect internal traits, that affect external traits (e.g.
morphology,
behaviour)
and/or fitness components
(e.g. viability,
fecundity).
Arrows
indicate translations from one level to the next, that may be affected by environmental
factors E (no arrows drawn for
clarity here). At each level there may be variation
within the population.
The subset of observed traits
is given by thick boxes. It is usually impossible
to cover all relevant traits and pathways.
For instance,
gene G3 affects internal
trait 13, hence traits 22, 23 and fitness component
W3. Consequently,
the
observed
correlation
between 22 and fitness is due to (i) external
selection on the phenotype
(path
Z2-W2-W)
and (ii) genes such as G3 that affect both 22 (path G3-13-22)
and, but independently,
W
(path G3-13-23.W3
or C3-13-W3).
4
van Tienderen
and de Jong
clutch, e.g. due to an internal metabolic cost of breeding early. The external and
internal selective forces may also interact. Females that breed early in the season
may be confronted with low temperatures and limited food supplies; this in turn
may result in relatively high metabolic costs of laying the clutch. In contrast, a
female that starts early because she lives in a warmer habitat with an earlier food
supply may not pay extra costs for earliness. Therefore the relationship between
earliness and fitness may critically depend on whether earliness is due to genetic or
to environmental factors.
Environmental
effects on the phenotype are not easy to discern, and measuring
all relevant (especially internal) traits may not be possible at all. Simplifying
assumptions have to be made. One possible simplification
is that the relationship
between the external phenotype and fitness is independent of the factors causing
phenotypic variation. However, this is not a fortunate choice: there are inevitably
genes that affect (i) the phenotype of a focal trait and hence fitness and (ii)
fitness(-components)
by independent pathways (Fig. 1). Such genes have independent pleiotropic effects on trait and fitness, and cause a correlation between trait
and fitness that is not tied to the functional relationship between fitness and focal
trait (Price and Langen, 1992). Similarly, environmental
factors may affect both
phenotype and fitness independently (Rausher, 1992). This situation applies to the
explanation given for selection on clutch size and breeding data (Price, Kirkpatrick
and Arnold, 1988; Price and Liou, 1989): if nutritional state is not heritable, but
affects both the trait and component(s)
of fitness, an apparent selection differential
can be shown to persist at equilibrium
(i.e. without
a genetic response). The
observed phenotypic correlation may not be due to a direct causal relationship
between phenotype and fitness. If we focus on selection on a single trait, we can
simplify the complex network of Fig. 1 to six relations (Fig. 2): the phenotype as
affected by (1) genetic, (2) environmental,
and (3) other factors, and the relations
between (4) phenotype and fitness (i.e. external selection), (5) the genes that affect
both the focal trait and - independently
from the focal trait - fitness, and (6)
environmental
factors that affect both trait and, independently, fitness. Whenever
Fig. 2. Possible relationships
between a focal trait (Z), its genetic (G) and environmental
(E) component, and fitness (IV). The standard
model assumes that only relationships
t-4 exist: selection on
phenotypes,
and variation
in phenotypes
partly determined
by additive genetic variation.
Arrows
5 and
6 exist when genes or environmental
factors affect fitness not only via the phenotype
Z, but also by
independent
pathways.
Phenotypic
selection
and genetic
response
5
genes or environmental
factors affect fitness in other ways than mediated by the
focal trait (5 or 6) the standard model will not be applicable. For instance, for
artificial selection it is well-known
that the selection response cannot be adequately
predicted if there is additional selection on a genetically correlated trait (e.g. Lerner
and Dempster,
195 1; Falconer, 198 1). Natural selection can only be adequately
described if all the relevant traits and constraints
among traits are taken into
account (Lande and Arnold, 1983; Burger, 1986; Arnold, 1992). It seems important
to safeguard ourselves against situations in which this is uncertain.
Model specifications
For simplicity,
the model focuses on one trait only. The approach allows
derivation of more complex formulae for selection on multiple traits, but if only
part of the complex system of traits is observed similar problems are expected. We
assume that fitness may not only be related to the phenotype per se, but also, and
independently, to the underlying genetic and environmental
components of variation. These relations are quantified as partial regression coefficients of fitness on
phenotype, on breeding value and on environmental
deviation, respectively. The
regression of fitness on phenotype, b,+, measures the direct causal effects of the
phenotype on fitness, i.e. regardless of the genetic and environmental
background
of the phenotype. The partial regression of fitness on genotypic value, bwlc,
measures residual effects on fitness of the genes affecting the focal trait that are not
attributable to a causal link between trait and fitness (cf. Fig. 2). Similarly, bWJE
measures the effects on fitness of those environmental factors that influence one or
more fitness components through other pathways than via the focal trait. Once
these regression coefficients are defined, further derivation is straightforward
if we
assume that the multivariate
distribution
of breeding values and environmental
deviations is Gaussian, and that the regression of offspring phenotypes on the
mid-parental breeding values is linear (for conditions implicit to these assumptions
see Turelli, 1988; Nagylaki, 1992). When we compare the final equation of Table 1
with R = h2S we see that the equation for the selection response is much more
complex; the selection response can be in an opposite direction to that of the
selection differential, for instance, leading to a negative realized heritability (R/S).
It appears that the classical model is valid for conditions common to artificial
selection, but perhaps uncommon in natural selection. In artificial selection, the
‘fitness’ of an individual (or group of individuals) is assigned on the basis of their
phenotype. For instance, if the phenotype is less than a certain threshold value, the
individual is excluded from the selection lines. In this case the partial regression
coefficients on genotype and on environmental
deviation are absent, and the
realized heritability reduces to Cov,,/l/,,
with Cov,, = V, + Cov,,.
Furthermore, in plant or animal breeding, genotypes are usually randomized over environments, so that environmental
and genetic values are not correlated (Cov,, = 0).
The covariance between genotype and phenotype Cov,, is then equal to the genetic
variance V,, and consequently the realizable heritability equals the ratio additive
van Tienderen and de Jong
6
Table 1. The phenotype Z is written as the sum of an additive genetic component (G) or
breeding value, an environmental component (E), and an error term (e) that, for instance,
can be due to non-additive genetic effects or developmental noise. More complex models
can be made in a similar fashion. Tbe model is defined as follows:
Model
Z=G+E+&
GEE
Additive Genetic, Environmental and srror component
W
Relative fitness
v,
VG vE
Phenotypic, Genetic, Environmental and error varianees
v,
CovzG Cov,
Cove, Corresponding eovarianees (all covariances with error component
assumed absent)
h/z
Partial regression coefficient of relative fitness OK) on Z, G and E,
bwlc hvla
holding the other components constant
s = cov,
Selection differential
R = Cov,
Expected Selection Response
Define a vector of covsrianees x = (Cov,
regression coefficients $ = (bwlz
bw,,
Cov,
bw,dT.
COV,,)~, and a vector of partial
Assume a multivariate gaussisn
distribution for Z and its components G, E and E, with A tbe varianee/covariance matrix
of Z, G and E. Using the definition of the multiple regression coefficients we get: $ =
A-’ x or & = A b. Expanding the first two elements of x in full, we get:
covGW
=
covZG
hflZ+
vG
hVjG+
CovGEblE
covzw
=
v,
hVlZ+
covZG
bVIG+
covZE
hVfE
and after rearranging
R
covZG
hVlZ
+
vG
bVlG
+
covGE
bwlE
vz
hVlZ
+
CovZG
hlG
+
covZE
b.'JE
=
S
genetic to phenotypic
variance.
For artificial selection the secondary theorem and
h2S are equivalent,
since Cov,,/Cov,,
= V,/Vz
= h2. For natural
the prediction
selection the equation
may not reduce to a simpler form, due to (i) non-random
distribution
of genotypes over environments,
e.g. if some form of habitat choice is
present (Cov,, # 0), (ii) direct selection on unmeasured,
internal
traits that are
genetically
correlated
(bWIG # 0), or (iii) environmental
factors that affect both the
phenotype
and fitness (bWIE # 0).
Phenotypic
selection
Complications
and genetic
response
for the classical approach
Genotype-Environment
Covariance
Genotype-environment
covariance can arise due to non-random distribution
of
genotypes over environments (Falconer, 1981). It leads to a covariance term in the
selection equation that can inflate or attenuate the selection response (Tab. 1). In
general, negative covariances reduce, and positive covariances increase the selection
response. When individuals with high breeding values do not have above average
phenotypic values due to a negative genotype-environment
covariance that nullifies
the genetic covariance (Cov,,
= V, + Cov,, = 0), no selection response is expected at all. If the covariance is strongly negative, the selection response can be
opposite in direction to the selection differential.
Selection on unmeasured, genetically
correlated
traits
In Fig. 3, we assumed external directional selection for higher phenotypic values.
In addition, we assumed a genetic link between focal trait and fitness that was not
mediated by the phenotype, e.g. due to a genetic correlation
with a second,
unmeasured trait under selection (b wlc # 0). This may be the result of an internal
cost: genes that result in a higher phenotype may also cause a reduction in a
component of fitness. Without this link, the classical model applies and R = h2S
Fig. 3. The effects of independent
selection
on the genetic component
of variation.
The scale for
phenotypic
variation
is taken as b‘= = 1. External
selection of the phenotype
is taken as constant, with
the partial selection differential
due to selection on the phenotype
bwlz = 1, the narrow-sense
heritability
hZ = 0.5, and no selection on the environmental
component
of variation,
b,lE = 0.
8
van Tienderen
and de Jong
(Fig. 3, on the ordinate). If selection on the genetic component is positive, i.e. in the
same direction as selection at the phenotypic level, the response is faster than
predicted, and the realized heritability R/S is higher than the narrow-sense
heritability Vc /V, (in this case 0.5) for the trait. If selection on the genetic component
is in an opposite direction, the selection response is slower. At some point a
response is absent, the realized heritability has dropped to zero, while directional
selection is still observed. The population is in equilibrium, and selection at the
phenotypic level is offset by selection on the genetic component of variation. For
instance, genes that cause earlier egg-laying may also have negative pleiotropic
effects on the survival of the adult (b,+ > 0); in contrast, environmental
factors
causing early breeding (e.g. microclimate) may not have such negative effects. The
pleiotropic effects may then counteract possible benefits of earlier breeding due to
a better synchronization
with food availability when rearing the chicks (bWlz < 0).
If selection on the genetic component is even more negative (e.g. due to stronger
selection on the correlated trait) a positive selection differential coincides with a
negative response. Finally, for very negative values of selection against large
genotypic values, the selection differential
is absent, but a negative selection
response is expected. The external selection for higher phenotypic values is then
completely masked by the internal selection for lower genetic trait values.
Environmental
factors
afleeting phenotype and$tness
Effects on an environmental correlation due to environmental factors that affect
both the focal phenotype and fitness (via other pathways) are shown in Fig. 4. In
this example, the external selection on the phenotype was assumed to be constant,
and the genetic covariance between trait and fitness was fixed. Thus, the environmental correlation between trait and fitness (b + # 0) affects the selection differential but not the genetic response. In the absence of such a correlation,
on the
ordinate of the graph, the standard model applies. If the environmental correlation
works in the same direction as the phenotypic selection, the selection differential
and hence the prediction h2S is increased. If the environmental correlation works in
the opposite direction, the selection differential is reduced, eventually to negative
values.
These examples show several things. Firstly, the absence of a selection response
despite selection differentials
and heritable variation,
as observed in the bird
examples, may have several causes. However, problems with the phenotypic approach are not restricted to this situation. There can also be no phenotypic
selection, but a genetic response, without a change in environment between generations. Or the selection response can be in the opposite direction than that expected.
These discrepancies are due to a lack of knowledge of the interplay of environments
and genes on the one hand, and phenotypes
and fitness on the other. Any
relationship
between observed phenotypic
selection and selection response is
possible.
Phenotypic
selection
and genetic
9
response
Fig. 4. The effects of spurious correlations
between environmental
factors that determine
trait value and
fitness. The scale for phenotypic
variation
is taken as V z = 1. External
selection on the phenotype
is
assumed constant,
with the partial selection differential
due to selection on the phenotype
b,lz = 1, the
narrow-sense
heritability
hZ = 0.2, and no selection at the genotypic
level other than that mediated by the
phenotype,
!I,,, = 0.
Tests to estimate different expectations
for selection response
The genetic and environmental components of variation are not directly observable. Additive genetic covariances between trait and fitness can be estimated from
data on relatives such as parent-offspring
combinations,
or sib-families.
This
assumes that the additive genetic component can be estimated from the covariance
between relatives; obviously, complications
arise when the covariances between
relatives are also affected by non-genetic factors (e.g. maternal effects, or a common
environment) (Falconer, 1981). Assuming that the additive genetic covariances are
measured correctly, they can be compared with a predicted response from phenotypic selection differential and heritability (Rausher, 1992). Van Noordwijk
(1988)
performed such a regression analysis for selection of fledging weight in Great Tits,
using survival in the first three months after fledging as a component of fitness.
Regression was calculated not only for the focal trait of the chick but also for the
mean of its parents (Tab. 2). Parent-offspring
regressions of fledging weight gave
estimates of heritabilities in the period under study, so that independent estimates
of S, h2 and the additive genetic covariance between (mid)parental
trait and
offspring survival were obtained. The latter measured the expected genetic response
in the focal trait due to selection in the life-cycle stage studied. The results suggested
that the selection on the phenotype was not associated with selection on genes (Tab.
2). On average, the heritability was 0.35, a higher survival rate of larger chicks
resulted in a positive selection differential of 0.4g, hence an expected genetic
10
van Tienderen
and de Jong
Table 2. Selection on nestling weight of Great Tits during three months after fledging.
Data reproduced
from Van Noordwijk
(1988).
Comparison
of mean nestling weight of
h2
hzS
parents, and survival of their offspring
Average
nestling
s
weight (g)
cov,
CW
1975
16.38
0.24
0.38
0.09
0.00
1976
16.90
0.68
0.47
0.32
0.03
1977
17.55
0.16
0.26
0.04
0.06
1978
17.06
0.53
0.29
0.15
0.05
0.40
0.35
0.14
0.03
ML?ZUl
response of 0.14g. However, the covariance between the survival of the young and
the average weight of the parent was only 0.03. Van Noordwijk
concluded that the
observed phenotypic selection was not translated into a genetic response. A similar
analysis could be employed for sib-data, by estimating genetic covariances between
traits and fitness (components),
and comparing these to the expectation from h2
and selection differentials. Selection due to differential survival in the succeeding
winter was also studied. There appeared to be no discrepancy (Van Noordwijk,
1988).
Discussion
Lande and Arnold (1983) warned that predictions from (multivariate)
selection
models were inadequate if selection acted on an unmeasured, correlated trait. Of
course, one cannot know if such traits exist, or know when to stop measuring more
traits. However, one can check whether selection is adequately described by the
selective forces, heritabilities and genetic covariances of the set of traits that one is
measuring. In fact the approach is identical to using the multivariate
selection
equation R = GP-~‘S = Gb (Lande, 1982), but with fitness as one of the traits in the
analysis, rather than an external entity; in this way, both fundamental theorems
resurface (Van Tienderen, 1989). The partial regression of fitness on fitness equals
one, that of fitness on other traits equals zero: the response in fitness itself becomes
equal to the additive genetic variance in fitness, the response in an arbitrary trait
becomes equal to the additive genetic covariance between trait and fitness, i.e.
Fisher’s first and secondary fundamental theorems. These derivations are based on
quantitative genetic models with many assumptions
about the actual genetics
involved (Nagylaki,
1992). Although the details may differ, we believe that the
complexity of the relation between selection on the external phenotype and at the
Phenotypic
selection
and genetic
11
response
genetic level causes fundamental problems. An important suggestion is to measure
the genetic variances and covariances of traits and fitness or components of fitness
directly.
Absence of a selection response can have several causes. Obviously, without
additive genetic variation there cannot be a response. Secondly, selection on the
phenotype may be in one direction (say for earlier breeding), while selection on the
genetic component of variation is in an opposite direction (for later breeding). For
instance, internal genetic tradeoffs may counterbalance
external selection on the
phenotype. Thirdly, if the observed selection differential is solely due to a correlation between fitness and the environmental
component of the phenotype, no
selection response is expected unless there is genotype-environment
covariance (e.g.
genetically above-average individuals occupy territories that are above average both
in environmental effects on the focal trait and in fitness). Finally, individuals with
high breeding values may have average phenotypic values (Cov,,
= 0) due to a
negative genotype-environment
covariance. Of course, more complex, hybrid situations may also occur.
The current analysis is not only relevant to situations in which a selection
response is absent. Any selective force we observe in nature is the result of causal
relations between external phenotype and fitness, and indirect correlations due to
pleiotropic effects of genes or spurious environmental correlations. It appears that
a study of natural selection needs to assess these possibilities, and empiricists may
want to take them into account. Unfortunately,
observing phenotypic selection on
a trait, and estimating heritabilities and genetic covariances may not be sufficient to
understand how selection changes a population. The real challenge, should discrepancies be found, comes with detection of the responsible external or internal
mechanisms.
Acknowledgements
We would like to thank A. J. van Noordwijk,
comments
on previous
drafts.
T. Price, J. M. Tinbergen
and J. A. Shykoff
for valuable
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Received 5 June 1993;
accepted 29 July 1993.
Corresponding
Editor: G. Wagner