Download Selection in the presence of a genotype by environment interaction

Animal Science 2003, 76: 375-385
© 2003 British Society of Animal Science
1357-7298/03/22680375$20·00
Selection in the presence of a genotype by environment interaction :
response in environmental sensitivity
R. Kolmodin1†, E. Strandberg1, H. Jorjani1‡ and B. Danell1
1Department
of Animal Breeding and Genetics, PO Box 7023, S-750 07 Uppsala, Sweden
† E-mail: [email protected]
‡ Also a member of staff of the Interbull Centre.
Abstract
The effect of selection for high phenotypic value in the presence of a genotype by environment interaction (G ✕ E,
i.e. genetic variation for environmental sensitivity) and an improving environment was studied in a simulation.
Environmental sensitivity was evaluated by using reaction norms, which describe the phenotype expressed by a
genotype as a function of the environment. Three types of reaction norms (linear, quadratic and sigmoid), and two
selection schemes (mass selection and progeny test selection) were studied. Environmental sensitivity was measured
as the weighted average of the absolute value of the first derivative of the reaction norm function. Results showed
that environmental sensitivity increased in response to selection for high phenotypic value in the presence of G ✕ E
and an improving environment when reaction norms were linear or quadratic. For sigmoid reaction norms,
approximating threshold characters, environmental sensitivity increased within the environmental range
encompassing the threshold. With mass selection and/or non-linear reaction norms, environmental sensitivity
increased even without environmental change.
Keywords: genotype environment interaction, phenotypic plasticity, selection, simulation.
Introduction
that is often used in empirical studies (e.g. Finlay and
Wilkinson, 1963; Ceccarelli and Grando, 1991).
The term phenotypic plasticity is often used in
evolutionary biology. Phenotypic plasticity is the
ability of a genotype to alter its phenotypic
expression in response to environmental influences
(Bradshaw, 1965). In an animal breeding context the
term environmental sensitivity is more common. In
this paper, environmental sensitivity is defined to be
synonymous to phenotypic plasticity. The genetic
variation in environmental sensitivity is used as a
definition of genotype by environment interaction
(G ✕ E).
The reaction norm function can be used to predict
breeding values for a trait, given a certain
environment. Breeding values for reaction norm
parameters can be estimated, if phenotypic values of
a large number of offspring in a reasonably wide
range of environments are available (Kolmodin et al.,
2002). These breeding values could then be used to
monitor the environmental sensitivity of a trait in a
population, or to select for high or low
environmental sensitivity of a trait, in parallel to
genetic improvement of the mean level of the trait.
The reaction norm of a genotype describes the
phenotype expressed by that genotype over a range
of environments (e.g. Woltereck, 1909 in : Suzuki et
al., 1981; Stearns, 1989). A general measure of
environmental sensitivity in a specific environment is
the first derivative of the reaction norm function in
that environment (de Jong, 1995). For a linear
reaction norm function the first derivative equals the
slope, a measure of the environmental sensitivity
Empirical studies have shown that phenotypic
plasticity can change as a result of selection
(Falconer, 1990; Scheiner and Lyman, 1991;
Hillesheim and Stearns, 1991). However, in other
experiments, the response in plasticity was not
significant (Holloway and Brakefield, 1995;
Wijngaarden and Brakefield, 2001). Reported
estimates of genetic variation and heritability of
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Kolmodin, Strandberg, Jorjani and Danell
plasticity in several species vary from non-significant
to highly significant (e.g. Scheiner and Lyman, 1989;
Weis and Gorman, 1990; Holloway and Brakefield,
1995; Scheiner and Yampolski, 1998; Kolmodin et al.,
2002). In general, genetic variation of the plasticity of
a trait is considerably lower than the genetic
variation of the mean value of the trait (Scheiner,
1993). The study by de Jong and Bijma (2002) gives
an algebraic description of the response to selection
for a phenotypically plastic trait assuming a constant
environment.
Theoretically, a reaction norm may have any shape,
unless restricted by genetic constraints (Gavrilets and
Scheiner, 1993) or other costs and limits to plasticity
(reviewed by DeWitt et al., 1998). However, within
the range of environments normally encountered, it
is often reasonable to assume that reaction norms are
linear, as it has been described for gall size in the gall
fly, Eurosta solidaginis (Weis and Gorman, 1990) and
for milk protein production (Calus et al., 2002;
Kolmodin et al., 2002) and female fertility in dairy
cattle (Kolmodin et al., 2002).
Assume a population of animals having linear
reaction norms with individual variation in slope.
The two sires in Figure 1 have equal phenotypic
values when the environmental value is 2. If, in a
later generation, the environmental value has
increased one unit, the progeny of sire A will be
favoured over the progeny of sire B. These progeny
of sire A, having the steeper reaction norm, respond
more strongly to the changes in the environment.
Consequently, if the population is selected for high
phenotypic value, and the environment is
continuously improving, there is reason to believe
that the average phenotypic plasticity, or
environmental sensitivity, of the population will
increase. The described situation may be typical for
domestic animals in an intensive production system,
where feeding and management are continuously
improved, in addition to the genetic improvement.
When the reaction norms are non-linear, the
plasticity is not the same over the entire
environmental gradient. Non-linear reaction norms
have been estimated for milk production traits in
dairy cattle (M. P. L. Calus and R. F. Veerkamp,
personal communication), and for several traits in
relation to temperature for Drosophila (e.g. David et
al., 1997; Morin et al., 1999; Gibert and de Jong, 2001).
Second degree polynomial functions are used when
there is an optimal environmental value that
maximizes the phenotypic value (Delpuech et al.,
1995; Morin et al., 1999).
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Phenotypic value
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80
60
40
20
0
1
2
Environmental value
3
Figure 1 Reaction norms of two sires (sire A
, sire
B
). Arbitrary units of phenotypic and environmental
values.
A sigmoid shaped reaction norm may describe a
threshold character with two phenotypic classes (e.g.
Roff, 1994; Fairbairn and Yadlovski, 1997) or a
situation, where the range of phenotypic values of
the trait of interest has upper and lower asymptotes
within the studied environmental interval. Sigmoid
shaped reaction norms have been found for wing/
thorax ratio (David et al., 1994; Morin et al., 1999) and
abdominal pigmentation in Drosophila (David et al.,
1990; Gibert et al., 1996).
Our objective was to study the effect on
environmental sensitivity of selection for high
phenotypic value in combination with a
continuously improving environment, when there
was genetic variation for environmental sensitivity.
The relevance of the question is demonstrated by a
study of G ✕ E in Nordic Red dairy cattle (Kolmodin
et al., 2002). Linear reaction norms were found for
milk protein production and female fertility, and
there was genetic variation for the environmental
sensitivity of these traits. As dairy cattle are selected
for high production of milk protein and fertility, and
as animal husbandry is improved in parallel, there is
reason to believe that the environmental sensitivity
of high-producing dairy cattle will increase.
The hypothesis of this study was that the average
environmental sensitivity of a population selected for
high phenotypic value in a continuously improving
environment, and in the presence of G ✕ E, would
increase. The hypothesis was tested in a simulation
of selection in combination with different levels of
environmental change. The three types of reaction
norms reported in the literature, linear, quadratic and
sigmoid, were studied.
Environmental sensitivity in populations under selection
Material and methods
Reaction norms were simulated for a population of
20 000 animals. Selection was practised for 10
generations and the experiment was replicated 100
times. When simulating quadratic or sigmoid
reaction norms, the simulation was allowed to run
for up to 100 generations to study the development
of the shape of the reaction norms.
In the base population the average environmental
value (xt) was zero on an arbitrary environmental
scale with s.d. 30 units. For each generation, xt was
increased (∆E) by 0·0, 0·1, 0·5, 5·0 or 10·0 units. The
environmental value simulated for each individual
was a random deviation, xi, from the average
environment of each generation. The generations
were not overlapping and the environment was
assumed to be constant from birth to selection within
each generation. No systematic environmental effects
within any one generation were simulated.
Two alternative selection schemes were used to select
individuals to parent the next generation : (1) mass
selection scheme (designated by M) : 10% of both
males and females were selected in each generation
based on their phenotypic values (yi|xt, + xi), and (2)
progeny test scheme (designated by P) : 5% of the
males were selected based on their expected
phenotypic value in the average environment of each
generation (yi|xt), i.e. the expectation of the reaction
norm function. This value corresponds to an
estimated breeding value based on a large number of
offspring normally distributed over all possible
environments. In the progeny test scheme there was
no selection among females. Mating among selected
animals was at random and each mating resulted in
an equal number of offspring.
To assess the effect of genetic drift, simulations were
also run with random selection of individuals to
parent
the
next
generation
and
without
environmental change. The same numbers of parents
as in the mass selection and progeny test schemes
were selected.
Genetic variances for the parameters of the linear
reaction norms corresponded to those estimated for
milk protein production in Nordic Red dairy cattle
(Kolmodin et al., 2002). The variances of the
parameters of the non-linear reaction norms were
chosen to result in approximately the same
phenotypic variation as for the linear reaction norms.
The reaction norm parameters, the individual
environmental deviations (xi) and the residuals (ei)
were independently normally distributed with an
expectation of zero. The environmental and residual
variances were 900 and 500, respectively.
377
Expectations and variances of the reaction norm
parameters were allowed to change in response to
selection.
Linear reaction norms (experiments L0 M, L1 M, L0P and
L1P)
Linear reaction norms (designated by L) were
simulated as
(1)
yit = ai + (bf + bi)(xt + xi) + ei
where
yit is the phenotype of individual i in generation t,
and in the given environment, ai is the intercept
(level) of the reaction norm of individual i, bf is
the regression coefficient of a fixed regression
of phenotypic value on environmental value
(fixed slope), bi is the corresponding random
regression coefficient (random slope) of individual i,
xt is the average environment in generation t, xi is the
random deviation from the average environment of
individual i, and ei is the random residual.
The base population variances of the intercept and
random slope were 100 and 0·02, respectively. The
corresponding
phenotypic
variance
was
approximately 618. In experiments L0M and L0P the
fixed slope was set to zero, i.e. on average there was
no environmental sensitivity in the base population
and no environment gave a higher average
phenotypic value than any other. In experiments L1M
and L1P the fixed slope was set at 1·0, to define
higher environmental values as favourable, i.e. the
base population was on average environmentally
sensitive.
Quadratic reaction norms (experiments QM and QP)
In experiments QM and QP, quadratic reaction
norms (designated Q) were simulated as a second
degree polynomial function:
(2)
yit = ai + bi (xt + xi) + ci (xt + xi) + ei
where ai, bi and ci are the reaction norm parameters
of individual i, and yit, xt + xi and ei are defined as
above.
Base population variances of ai, bi, and ci, were 80,
0·02, and 0·00001, respectively. The corresponding
phenotypic variance was approximately 617. The
relations between the variance components for the
intercept and the slope, and the slope and the
quadratic coefficient were chosen to be similar to the
relation between the variances of the intercept and
the slope of the linear reaction norms estimated from
dairy cattle field data (Kolmodin et al., 2002). A
restriction ci ≤ 0 was imposed on the curvature of the
reaction norm, to ensure that a maximum phenotypic
value existed. Hence, the parameter ci had a
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Kolmodin, Strandberg, Jorjani and Danell
truncated normal distribution with an expected
value of –0·0025 in the base population.
Sigmoid reaction norms (experiments SM and SP)
Sigmoid reaction norms (designated by S) were
simulated as
yit = ai + bi ✕ eci + di (xt + xt)/(l + eci + di (xt + xt)) + ei
(3)
where ai, bi, ci, and di are the reaction norm
parameters of individual i, and yit, xt, xi, and ei are
defined as above.
The high levels of environmental change (∆E 5·0 to
10·0) were assumed to be relevant for farm animals
in an intensive production system, where
competition and market demands drive the need for
continuous improvement of technology, food quality,
health care, etc., as well as a genetic progress. Fast
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(a)
90
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60
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40
30
20
10
–50
–100
0
0
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50
Environmental value
200
(b)
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100
Results and discussion
The response to selection and environmental change
will be reported for ES and individual reaction norm
parameters. The response in phenotypic values
across the environmental scale will not be dealt with
as that was not the main focus of this study.
The costs of plasticity or biological restrictions were
not accounted for in this simulation. In biological
systems it is probable that such restrictions not only
exist but have an effect on the shape of the reaction
norm. A simulation including such restrictions could
give different results from those found in this study.
Environmental change
The low levels of environmental change (∆E 0·0 to
0·5) were assumed to be relevant for populations
Phenotypic value
Measure of environmental sensitivity
The environmental sensitivity of an individual in a
specific environment was measured as the first
derivative of the reaction norm function with respect
to (xt + xi) evaluated at xi. The fixed slopes of the
linear reaction norms were not included. The overall
environmental sensitivity of each individual was
measured as the weighted average of the absolute
value of the derivative over the environmental range
of ± 3 environmental s.d. units (i.e. ± 90 units) from
the generation mean. The weights were the values of
the probability density function of the environmental
distribution in the interval. The population average
environmental sensitivity (ES) was the average of the
overall environmental sensitivities of all individuals
in each generation.
Phenotypic value
The base population variances of ai, bi, ci and di, were
50, 180, 1·5 and 0·02, respectively. The corresponding
phenotypic variance was approximately 620. The
relations between the variance components of the
reaction norm parameters were chosen to get more
variation in the relative levels of the two asymptotes
of the reaction norm function, than in the slope at the
inflexion point. This was in accordance with the
larger variance in level than in slope of the linear
reaction norms estimated from dairy cattle field data
(Kolmodin et al., 2002).
living under natural conditions, in harsh climates
and/or in developing countries, where the rate of
improvement of animal husbandry may be low.
Absence of or slow environmental change may also
be relevant for populations kept under standardized
conditions, e.g. in test stations, laboratories, or
specific pathogen free farms.
50
–100
–50
0
50
100
150
0
200
Environmental value
Figure 2 Average reaction norms (average level and slope
of 100 replicates of 20 000 individuals per generation) in
generation 0 ( ✕ ), 2 ( ■ ), 4 ( ▲ ), 6 (
), 8 (
)
and 10 (
) for experiment L0P (linear reaction norms,
progeny test selection scheme, fixed slope 0·0) plotted over
the expected range of environments for each generation (±3
environmental s.d. units from generation average). (a). ∆E =
0·5, (b) ∆E = 10·0.
Environmental sensitivity in populations under selection
environmental change may also occur when an
extensive production system is being upgraded to a
more intensive system.
Reaction norm parameters and the shape of the reaction
norms
Short term effects. In the base generation, the average
linear reaction norm, as described by the average
values of level and slope, was flat (equation 1, Figure
2). The average intercept, ai (equation 1), increased
over generations, showing the selection response in
the average value of the trait, in all simulated
combinations of value of fixed slope, selection
scheme and ∆E (not shown). The increase was
smaller at higher levels of environmental change
(Figure 2a and b). The average random slope of the
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(a)
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40
20
0
Phenotypic value
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–20
–100
–50
0
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–40
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Environmental value
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(b)
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linear reaction norm, bi (equation 1) became steeper
and steeper with selection in an improving
environment (∆E ≥ 0·1, not shown). The increase in
slope was larger at higher levels of environmental
change (Figure 2a and b).
The shape of the average quadratic reaction norm
remained quadratic after ten generations of selection,
with the peak performance within the expected
environmental range of each generation (±3
environmental s.d. units from generation average,
Figure 3). There was significant selection response in
the mean level of the trait, as seen in the increase in ai
(equation 2, Figure 3a and b) from first to tenth
generation for all levels of environmental change
(including ∆E = 0·0) and for both selection criteria
(not shown). The linear coefficient, bi, of the
quadratic reaction norm increased significantly from
first to tenth generation when the environment was
improving (not shown), indicating an increasing
environmental sensitivity. The quadratic coefficient,
ci, became more negative after selection, increasing
the curvature of the reaction norm for mass selection
with ∆E ≤ 5·0 and progeny test or random selection
for all levels of ∆E (not shown). The quadratic
coefficient in generation 10 was more negative with
decreasing environmental change, indicating that
reaction norms resulting in a maximum performance
in an optimum environment could be favourable
when the conditions of animal husbandry change
slowly. With mass selection and a rapidly changing
environment (∆E = 10·0) instead, the curvature of the
reaction norm diminished, indicating that a reaction
norm with an optimum within the observed
environmental range was less favourable.
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40
20
0
Phenotypic value
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–20
–100
–50
0
50
100
150
–40
200
Environmental value
Figure 3 Average reaction norms (average reaction norm
parameters of 100 replicates of 20 000 individuals per
generation) in generation 0 ( ✕ ), 2 ( ■ ), 4 ( ▲ ), 6
(
), 8 (
) and 10 (
) for experiment QP (quadratic
reaction norms, progeny test selection scheme) plotted over
the expected range of environments for each generation (±3
environmental s.d. units from generation average). (a) ∆E =
0·5, (b) ∆E = 10·0.
With the sigmoid reaction norm function the average
reaction norm was flat in the base population (Figure
4a, b and c). The average reaction norm parameters
ai, bi, ci, and di (equation 3) all increased significantly
from base to tenth generation for all levels of
environmental change (except for di, which did not
change significantly with progeny test selection and
∆E = 0·0).
At low levels of environmental change (∆E ≤ 0·1) the
average sigmoid reaction norm remained more or
less flat over generations (Figure 4a). With ∆E ≥ 0·5,
the average reaction norm assumed a sigmoid shape
after selection (Figure 4b and c). The inflexion point
of the average reaction norm did not alter its position
on the environmental scale, although the position
was not restricted by the reaction norm function.
After a large environmental change (∆E = 10·0), the
threshold was outside the normal environmental
range of the population. With ∆E = 10·0, the average
reaction norm in generation 10 was also flat (Figure
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Kolmodin, Strandberg, Jorjani and Danell
140
(a)
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(b)
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Phenotypic value
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Phenotypic value
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60
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0
0
–50
0
50
–50
100
Environmental value
Figure 4 Average reaction norms (average reaction norm
parameters of 100 replicates of 20 000 individuals per
generation) in generation 0 ( ✕ ), 2 ( ■ ), 4 ( ▲ ), 6
( ◆ ), 8 (
) and 10 (
) for experiment SP (sigmoid
reaction norms, progeny test selection scheme) plotted over
the expected range of environments for each generation (±3
environmental s.d. units from generation average) (solid
lines). Dotted lines represent the average reaction norm
function plotted over ±3 environmental s.d. units from 0·0,
i.e. the base generation average. (a) ∆E = 0·0, (b) ∆E = 0·5
(c) ∆E = 10·0.
4c, solid lines), because in the range of environments
that this generation was expected to encounter the
expressed phenotypes were at the upper asymptote
of the reaction norm function (equation 3).
Gavrilets and Scheiner (1993) predict that a
population under stabilizing selection in an
environment varying temporally within generations
50
100
140
(c)
120
100
80
60
40
20
–100
Long term effects. When the simulation of the
population with the quadratic reaction norm
function was run for further generations of selection
in an improving environment, the linear coefficient,
bi, increased continuously (mass selection and
progeny test selection). The decrease in ci during the
first 10 generations of selection turned to an increase
towards zero. The consequence was that the average
reaction norm approached linearity within the
environmental range expected after 50 or 100
generations of environmental change (∆E ≥ 0·5 or
∆E = 0·1, respectively, both selection schemes, not
shown). This indicates that a reaction norm with an
optimum environment could not be maintained over
a long period of environmental change. The constant
environmental improvement assumed in this study
may not be realistic over a time period of 50
generations, although the constancy of the
environmental change may not be crucial.
0
Environmental value
Phenotypic value
–100
–100
–50
0
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Environmental value
will converge on a linear reaction norm, even if nonlinear reaction norms are possible. If directional and
stabilizing selection in environments varying
between or within generations cause non-linear
reaction norms to approach linearity, then one
conclusion could be that non-linear reaction norms
are transitional states. However, a linear increase in
the phenotypic value would probably not be found,
for biological reasons, over very large environmental
ranges. Extrapolation of estimated reaction norms
outside the environmental range of the data should
be done with caution.
When the simulation of sigmoid reaction norms was
run for 50 generations of selection in an improving
environment (∆E ≥ 0·5), the range increased between
the two asymptotes of the sigmoid reaction norm
function. With ∆E < 0·1, the sigmoid reaction norms
remained more or less flat.
381
Environmental sensitivity in populations under selection
Roff (1994) studied the population level reaction
norm for the proportion of individuals in one of the
categories of a categorical trait. With the model
assumptions that the threshold point is normally
distributed in the population and the underlying
trait distribution is fixed, this reaction norm has a
sigmoid shape and selection can change the location
of the threshold, i.e. the inflexion point, but not the
shape of the reaction norm. This environmental
threshold model has some experimental support
from studies on wing dimorphic insects. Owing to
different model assumptions the results of the
present study are not directly comparable to the
results of Roff (1994).
Environmental sensitivity
Linear reaction norms. The results corroborated the
hypothesis of increased environmental sensitivity in
response to selection for high phenotypic value in a
continuously improving environment. In general, the
ES of a population having linear reaction norms
increased over generations and increased more with
higher levels of environmental change (Figure 5a and
b). ES increased more with the mass selection scheme
than with the progeny test scheme at low levels of
environmental change (∆E ≤ 0·5). At high levels (∆E ≥
5·0) ES increased more with the progeny test scheme.
The standard errors were 0·1 to 0·5% of the value of
the ES in the different generations, selection schemes
and levels of ∆E.
With the mass selection scheme, ES increased with or
without environmental change. The increased ES
even without environmental change can be
explained as follows. Directional mass selection is an
example of what Falconer (1990) refers to as
synergistic selection, i.e. selection and environmental
effects act to change the phenotype in the same
direction. Synergistic selection is expected to increase
environmental sensitivity because ‘The individuals
selected are those that have experienced a favourable
environment and have the genetic ability to perform
well in that environment’ (Falconer, 1990).
(c)
(a)
0·7
0·4
0·3
0·2
QP 10·0
QM 10·0
QP 0·5
QP 0·0
QP 0·1
QP 5·0
QM 5·0
QM 0·5
QM 0·1
QM 0·0
0·3
ES
0·5
ES
0·4
L0M 10·0
L1M 10·0
L1M 5·0
L0M 5·0
L1M 0·5
L1M 0·1
L1M 0·0
L0M 0·5
L0M 0·1
L0M 0·0
0·6
0·2
0·1
0·0
0
2
4
6
Generation
8
0·1
10
0
(b)
0·4
ES
ES
0·6
0·5
LP 10·0
LP 5·0
LP 0·5
LP 0·1
LP 0·0
0·3
0·3
0·2
0·2
0·1
0·0
0·1
0
8
10
SP 0·5
SP 0·1
SP 0·0
SM 0·0
SM 0·1
SM 0·5
SP 5·0
SM 5·0
SP 10·0
SM 10·0
0·7
0·4
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6
Generation
(d)
0·7
0·6
0·5
2
2
4
6
Generation
8
10
0·0
0
2
4
6
Generation
8
10
Figure 5 Average environmental sensitivity (ES) in generations 0 to 10 for different levels (0·0, 0·1, 0·5, 5·0 and 10·0) of
environmental change per generation. (a) Linear reaction norms, mass selection scheme and a fixed slope of 0·0 (L0M) and
1·0 (L1M), (b) linear reaction norms and progeny test selection scheme (LP), (c) quadratic reaction norms, mass selection
(QM) and progeny test (QP) selection scheme, (d) sigmoid reaction norms, mass selection (SM) and progeny test (SP)
selection scheme. ES for environmental change of 0·0, 0·1 or 0·5 units per generation are indistinguishable, or nearly so, from
each other.
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Kolmodin, Strandberg, Jorjani and Danell
With the simulated mass selection scheme, parents
were selected based on the phenotype they would
have in an environment with a random deviation
from the average value. The ES of a population
having linear reaction norms was, by definition, the
average of the absolute value of the random slope,
|bi |. With a fixed slope, bf, of 0·0, three
combinations of environmental deviations and
random slopes resulted in high phenotypic values : a
positive environmental deviation and a positive
random slope, a negative environmental deviation
and a negative random slope, and a high intercept
combined with a small environmental deviation
from the average value. Because both individuals
with positive and negative random slopes could be
selected, the variance of the slopes increased. Thus,
the average absolute value of the slope (ES)
increased, although bi did not increase significantly.
This means that there were more animals with steep
reaction norms in the later generations.
Without environmental change, with mass selection
and bf = 1·0 the individuals selected were those with
a positive environmental deviation and a positive
random slope. Hence, bi and |bi | both increased
with selection for high phenotypic value, and the
difference between them was small.
The resulting increase in ES seen in this study when
linear reaction norms were simulated has some
support in the literature. Simmonds (1981) reported
that newer varieties of cereals, developed in
environments of high yield potential, were more
responsive than older varieties and reached the
conclusion that ‘historically rising E (environment)
has apparently evoked responsive genotypes’. For
potatoes, though, no such trend was seen. Simmonds
(1991) simulated selection for high yield of cultivars
in environments of constant high, medium or low
yield potential, respectively. After two cycles of
selection in an environment of high yield potential,
the slope of a regression of cultivar yield on the
environmental value, measured as the mean yield of
a set of cultivars (i.e. a linear reaction norm for
cultivar yield) had increased significantly.
Falconer (1990) reviewed experiments on mice, pigs
and a number of plant species, selected for increased
or decreased phenotypic value in favourable or
unfavourable environments. He found that, in
general, selection for high phenotypic value in a
favourable, though not improving, environment
increased the environmental sensitivity.
With the progeny test selection scheme ES increased
significantly over generations with ∆E ≥ 0·5 (Figure
5b). As expected, ES did not change with zero or very
low environmental change (∆E ≤ 0·1), as selection
was based on the expected phenotypic value in the
average environment. Without environmental
improvement, this average environment remained
the same (zero) in all generations. The phenotypic
value in an environment of value zero depended
only on the intercept, ai (equation 1). As ES did not
depend on ai, selection should not affect ES. This
means that without a systematic change in the
environment, a progeny test selection scheme for
high phenotypic value or selection on predicted
breeding values mainly based on progeny
information, should not result in an increase in ES,
unless there is a correlation between the level and the
slope of the reaction norm.
When parents were selected according to the
progeny test scheme, the value of the fixed slope, bf ,
had no effect on the estimated reaction norm
parameters and hence not on ES. With random
selection of parents there was no significant change
in ES or reaction norm parameters (not shown).
Quadratic reaction norms. The ES increased
significantly from base to tenth generation for all
levels of environmental change (Figure 5c). The ES
increased more with the progeny test selection
scheme than with mass selection. In general, the
increase in ES was larger with higher levels of
environmental change. The standard errors were 0·1
to 0·2% of the value of the ES in the different
generations, selection schemes and levels of ∆E.
The increase in ES when there was no environmental
change can be explained by genetic drift of the linear
and quadratic coefficients, bi and ci (equation 2,
ES = weighted average of |bi + 2ci (xt + xi)|). Also
with random selection of parents, ES increased from
base to tenth generation. Although bi did not change
significantly with ∆E = 0·0, the variation between
replicates increased as expected due to random drift
occurring independently in the different replicates
(Falconer and Mackay, 1996). As ES was a measure of
absolute values, the increased variation between
replicates also increased the ES. The random drift of
ci was asymmetric, because of the restriction ci ≤ 0.
The replicate average of ci could increase only to
asymptotically approach zero, but could decrease
indefinitely. Thus the average ci became more
negative by random drift, and ES increased.
An example of a quadratic reaction norm, with
relevance to animal production, may be found for
growth rate in broilers with respect to ambient
temperature. Broilers between 4 and 8 weeks of age
have maximal growth rate between 18ºand 20ºC
(Yalcin et al., 2001), which can be thought of as a
Environmental sensitivity in populations under selection
quadratic reaction norm. Heat stress, reducing
growth performance, has a larger effect in broilers
with high growth potential than in slower-growing
chickens (e.g. Cahaner and Leenstra, 1992; Yunis and
Cahaner, 1999; Yalcin et al., 2001). High sensitivity to
heat stress may be a correlated response to selection
for increased growth rate (Cahaner and Leenstra,
1992; Yunis and Cahaner, 1999). It could also be an
example of the results seen in this study, if one thinks
of the selection for high phenotypic value as
selection for increased growth rate, of the
environment as a temperature gradient, and of heat
stress as environmental sensitivity. The scenario of
∆E = 0·0, would correspond to a situation where the
breeding population has been kept in conditions of
well regulated temperature for several generations.
The simulated environmental improvement would
correspond to improvements of control and
optimization of the ambient temperature.
Sigmoid reaction norms. At low and intermediate
levels of environmental change (∆E ≤ 0·5) ES
increased significantly over generations with mass
and progeny test selection. ES was higher after
progeny test selection than after mass selection. The
ES increased even without environmental change
(Figure 5d), because the parameters that increased
the phenotypic value in the environment of value
zero also increased the ES. The standard errors of ES
were 0·1 to 0·8% of the value of the ES in the different
generations, selection schemes and levels of ∆E.
With high levels of environmental change (∆E ≥ 5·0),
the ES increased for some generations and then
decreased (Figure 5d). In the later generations,
sensitivity to environmental change occurred more in
the less frequent environments, because the
threshold was not close to the average environment
of the population (Figure 4c). However, there was
variation in individual ES, even when the average
reaction norm was flat. With random selection of
parents there was no significant change in ES or
reaction norm parameters (not shown).
The dotted lines in Figure 4c illustrate the reaction
norms over the environmental range encountered in
the base generation. As can be seen in Figure 4c, all
generations showed environmental sensitivity in the
environmental range encompassing the threshold.
The interpretation of this result is that a large
decrease in the environmental value, beyond the
range of environments that the later generations of
the population are expected to encounter, could have
drastic effects on the average phenotypic value of the
population. For example, in a population living in a
very good environment, all animals may be healthy.
If, for some reason, the population encounters a
383
worse environment, the disease incidence could
increase dramatically, reducing the average
phenotypic value of health.
Environmental sensitivity as a breeding goal trait
More knowledge is needed about the shape of
reaction norms for important traits in our domestic
animal populations. The (co)variation of reaction
norm parameters for different environmental
descriptors needs to be studied. With this
knowledge, a decision could be made as to whether
to include the environmental sensitivity of a trait in
the breeding goal. This would be possible if reaction
norms for the sires of the breeding population were
routinely estimated from field data. The first
derivative of the reaction norm function for a certain
trait would then give the predicted breeding value
for environmental sensitivity for this trait.
In this study environmental sensitivity was
measured as the absolute value of the first derivative
of the reaction norm function averaged over the
environmental range of interest and weighted by the
environmental probability density function. This was
relevant because the study was focused on the
average environmental sensitivity of a population
that encounters a range of environments. If the
interest is in the environmental sensitivity of each
individual, or if a certain response to environmental
change is expected or desired, one could instead use
the actual value of the derivative of the reaction
norm function (de Jong, 1995) in the environment of
each individual, because it distinguishes between
individuals with positive and negative derivatives of
the reaction norm function.
In an intensive farming system, where the
environment can be kept adequate, a high sensitivity
(responsiveness) towards environmental change may
be desired. The benefit from improvements of for
example management and feeding would be
substantial. The risk of environmental deterioration,
causing drastic reduction in the value of the
responsive trait, would be relatively low. However,
the system would be susceptible to disturbances, e.g.
food quality problems or disease. Breeding for high
sensitivity could be of ethical concern, if animals as a
result became restricted to highly controlled
environments for their welfare or even survival.
Low sensitivity of production traits could be useful
in agricultural systems where the environment is
unpredictable and cannot be controlled, as may be
the case for subsistence farmers in developing
countries. In such situations yield stability is of
paramount importance to minimize the risk of crop
failure (Ceccarelli, 1994). Similarly, the livestock must
384
Kolmodin, Strandberg, Jorjani and Danell
be tolerant to harsh conditions. The disadvantage of
breeding animals for low environmental sensitivity
would be a lesser incentive for actions to improve
animal husbandry, because of the less sensitive
animals’ small response to improved conditions.
Also, breeding for low sensitivity could be of ethical
concern, if animals as a result lost their ability to
react and respond to stressful treatment.
Conclusion
We detected significant selection response in
environmental sensitivity, or phenotypic plasticity,
when selection was for high phenotypic value in an
improving
environment.
The
environmental
sensitivity of traits having linear or quadratic
reaction norms can be expected to increase, as a
result of traditional selection programmes combined
with environmental improvements in animal
husbandry. Environmental sensitivity may increase
even with small environmental changes, as might be
experienced by populations living under natural or
standardized conditions.
Sigmoid reaction norms, approximating threshold
characters, showed environmental sensitivity in the
environmental range encompassing the threshold.
After a large environmental change, the environment
of the population was not in the range of the
threshold. The reaction norms appeared flat,
although the reaction norm function did not
approach linearity. This means that if the
environment was to deteriorate, environmental
sensitivity would be expressed and the average
performance of the population would be reduced
drastically.
Even when the average environment is not in a state
of change, there is a random variation of the
environment experienced by each individual. With
mass selection, environmental sensitivity may
increase as a result of selecting individuals that are
able to take advantage of a favourable environment.
References
Bradshaw, A. 1965. Evolutionary significance of phenotypic
plasticity in plants. Advances in Genetics 13: 115-155.
Cahaner, A. and Leenstra, F. 1992. Effects of high
temperature on growth and efficiency of male and female
broilers from lines selected for high weight gain, favourable
feed conversion, and high or low fat content. Poultry Science
71: 1237-1250.
Calus, M. P. L., Groen, A. F. and Jong, G. de. 2002.
Genotype x environment interaction for protein yield in
Dutch dairy cattle as quantified by different models. Journal
of Dairy Science 85: 3115-3123.
Ceccarelli, S. 1994. Specific adaptation and breeding for
marginal conditions. Euphytica 77: 205-219.
Ceccarelli, S. and Grando, S. 1991. Selection environment
and environmental sensitivity in barley. Euphytica 57:
157-167.
David, J. R., Capy, P. and Gauthier, J. 1990. Abdominal
pigmentation and growth temperature in Drosophila
melanogaster: similarities and differences in the norms of
reaction of successive segments. Journal of Evolutionary
Biology 3: 429-445.
David, J. R., Gibert, P., Gravot, E., Petavy, G., Morin, J.,
Karan, D. and Moretau, B. 1997. Phenotypic plasticity and
developmental temperature in Drosophila: analysis and
significance of reaction norms of morphometrical traits.
Journal of Thermal Biology 22: 441-451.
David, J. R., Moretau, B., Gauthier, J. P., Pétavy, G.,
Stockel, A. and Imasheva, A. G. 1994. Reaction norms of
size characters in relation to growth temperature in
Drosophila melanogaster: an isofemale analysis. Genetics,
Selection, Evolution 26: 229-251.
Delpuech, J., Moretau, B., Chiche, J., Pla, E., Vouidibio, J.
and David, J. R. 1995. Phenotypic plasticity and reaction
norms in temperate and tropical populations of Drosophila
melanogaster: ovarian size and developmental temperature.
Evolution 49: 670-675.
DeWitt, T. J., Sih, A. and Wilson, D. S. 1998. Costs and
limits to phenotypic plasticity. Trends in Ecology and
Evolution 13: 77-81.
Fairbairn, D. J. and Yadlovski, D. E. 1997. Coevolution of
traits determining migratory tendency: correlated response
to selection on wing morphology. Journal of Evolutionary
Biology 10: 495-513.
Falconer, D. S. 1990. Selection in different environments:
effects on environmental sensitivity (reaction norm) and on
mean performance. Genetical Research 56: 57-70.
Falconer, D. S. and Mackay, T. F. C. 1996. Introduction to
quantitative genetics, fourth edition. Longman Group, Essex.
Finlay, K. W. and Wilkinson, G. N. 1963. The analysis of
adaptation in a plant-breeding programme. Australian
Journal of Agricultural Research 14: 742-754.
Gavrilets, S. and Scheiner, S. M. 1993. The genetics of
phenotypic plasticity. V. Evolution of reaction norm shape.
Journal of Evolutionary Biology 6: 31-48.
Gibert, P. and Jong, G. de. 2001. Temperature dependence
of development rate and adult size in Drosophila species:
biophysical parameters. Journal of Evolutionary Biology 14:
267-276.
Gibert, P., Moretau, B., Moretau, J. and David, J. R. 1996.
Growth temperature and adult pigmentation in two
Drosophila sibling species: an adaptive convergence of
reaction norms in sympatric populations? Evolution 50:
2346-2353.
Hillesheim, E. and Stearns, S. C. 1991. The responses of
Drosophila melanogaster to artificial selection on body weight
and its phenotypic plasticity in two larval food
environments. Evolution 45: 1909-1923.
Holloway, G. J. and Brakefield, P. M. 1995. Artificial
selection of reaction norms of wing pattern elements in
Bicyclus anynana. Heredity 74: 91-99.
Environmental sensitivity in populations under selection
385
Jong, G. de. 1995. Phenotypic plasticity as a product of
selection in a variable environment. The American Naturalist
145: 493-512.
Simmonds, N. W. 1991. Selection for local adaptation in a
plant breeding programme. Theoretical and Applied Genetics
82: 363-367.
Jong, G. de and Bijma, P. 2002. Selection and phenotypic
plasticity in evolutionary biology and animal breeding.
Livestock Production Science 78: 195-214.
Stearns, S. C. 1989. The evolutionary significance of
phenotypic plasticity. BioScience 39: 436-445.
Kolmodin, R., Strandberg, E., Madsen, P., Jensen, J. and
Jorjani, H. 2002. Genotype by environment interaction in
Nordic dairy cattle studied using reaction norms. Acta
Agriculturæ Scandinavica, Section A, Animal Science 52: 11-24.
Morin, J. P., Moretau, B., Petavy, G. and David, J. R. 1999.
Divergence of reaction norms of size characters between
tropical and temperate populations of Drosphila melanogaster
and D. simulans. Journal of Evolutionary Biology 12: 329-339.
Roff, D. A. 1994. The evolution of dimorphic traits:
predicting the genetic correlation between environments.
Genetics 136: 395-401.
Scheiner, S. M. 1993. Genetics and evolution of phenotypic
plasticity. Annual Review of Ecology and Systematics 24: 35-68.
Scheiner, S. M. and Lyman, R. F. 1989. The genetics of
phenotypic plasticity. I. Heritability. Journal of Evolutionary
Biology 2: 95-107.
Scheiner, S. M. and Lyman, R. F. 1991. The genetics of
phenotypic plasticity. II. Response to selection. Journal of
Evolutionary Biology 4: 23-50.
Scheiner, S. M. and Yampolski, L. Y. 1998. The evolution of
Daphnia pulex in a temporally varying environment.
Genetical Research 72: 25-37.
Simmonds, N. W. 1981. Genotype (G), environment (E) and
GE components of crop yields. Experimental Agriculture 17:
355-362.
Suzuki, D. T., Griffiths, A. J. F. and Lewontin, R. C. 1981.
An introduction to genetic analysis. W. H. Freeman and
Company, San Francisco.
Weis, A. E. and Gorman, W. L. 1990. Measuring selection
on reaction norms: an exploration of the Eurosta-solidago
system. Evolution 44: 820-831.
Wijngaarden, P. J. and Brakefield, P. M. 2001. Lack of
response to artificial selection on the slope of reaction
norms for seasonal polyphenism in the butterfly Bicyclus
anynana. Heredity 87: 410-420.
Woltereck,
R.
1909.
Weitere
experimentelle
Untersuchungen über Artveränderung, speziell über das
Wesen quantitativer Artunterschiede bei Daphniden.
Verhandlungen der Deutschen Zoologischen Gesellschaft 1909:
110-172.
Yalcin, S., Özkan, S., Türkmut, T. and Siegel, P. B. 2001.
Responses to heat stress in commercial and local broiler
stocks. 1. Performance traits. British Poultry Science 42:
149-152.
Yunis, R. and Cahaner, A. 1999. The effects of the Naked
Neck (Na) and Frizzle (F) genes on growth and meat yield
of broilers and their interactions with ambient temperatures
and potential growth rate. Poultry Science 78: 1347-1352.
(Received 30 May 2002—Accepted 3 February 2003)