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AAABG Vol 15
THE EFFECT OF ARTIFICIAL SELECTION ON THE DISTRIBUTION OF QTL EFFECTS
M.E. Goddard1,2 and B. Hayes1
Victorian Institute of Animal Science, Department of Primary Industries, Attwood, Victoria, 3049,
2
Institute of Land and Food Resources, University of Melbourne, Parkville, Victoria, 3052
1
SUMMARY
Simulation of natural selection and artificial selection for a quantitative trait is used to explain the
surprising finding that quantitative trait loci (QTL) of moderate effect are found segregating for traits
that have long been subject to selection. The model predicts that 20 generations of intense selection in
a population of effective size 100 or less will cause a marked decrease in genetic variance, due to a
decrease in the number of genes segregating. Despite this, the proportion of segregating genes with
moderate to large effects remains almost the same, due to rare alleles being more likely to survive if
they are favourable and due to new mutations.
Keywords:. Segregating QTL, artificial selection, QTL effect
INTRODUCTION
During the last decade much research has been devoted to detecting and mapping genes or QTL for
economically important, quantitative traits. To be detected as significant a gene must have at least a
moderate effect (Bovenhuis and Shrooten 2002), and must be segregating with allele frequencies that
are not too extreme, or else the probability of one of the small number of sires used being
heterozygous is too low. However for traits such as milk yield in dairy cows and fatness in pigs, that
have been subject to consistent selection for some generations, one would expect that the genes with
largest effect would have been pushed near to fixation and so QTL experiments for these traits would
find nothing. In fact, QTL detection experiments do find segregating QTL of moderate effects (e.g.
Georges et al 1995). How can we explain the continued segregation (at intermediate allele
frequencies) of genes with moderate effects on highly selected traits?
In an attempt to explain this observation we have simulated the evolution of the genes underlying a
quantitative trait and then simulated artificial selection for that trait. Ideally, results from our
simulation would also agree with two other puzzling observations from livestock populations.
Firstly, if variation at QTL was due to mutation and drift, the genetic variance should be proportional
to effective population size, but there is no evidence that this is the case. Caballero and Keightley
(1994) used a model where natural selection against mutant alleles at QTL was correlated with the
size of the effect on the quantitative trait. However they still predicted genetic variance for the
quantitative trait would increase indefinitely with effective population size. We have used a similar
model but with an additional restriction that the natural selection coefficient cannot be less than a
certain amount. This eliminates the existence of neutral QTL of large effect on the quantitative trait.
Secondly selection, by driving QTL of the largest effect to near fixation, should reduce genetic
variance. This is not observed despite many years of selection in dairy cattle and pigs.
This paper models the evolution of a quantitative trait and the effect of artificial selection on the
segregation of QTL with different sizes of effect. The aim was to gain some insight into the
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Using QTL
distribution of effects of QTL which affect a quantitative trait, following artificial selection for that
trait.
MATERIALS AND METHODS
The population experienced 1000 generations of natural selection, followed by 20 generations of
artificial selection. Each animal had a genome of 5 chromosomes each 100 cM long, each of which
contained 100 quantitative trait loci (QTL). Each QTL allele had an effect on both fitness and the
quantitative trait sampled from a bi-variate gamma distribution with shape parameter 0.5. To create
an offspring, for each parent in a mating pair, a gamete was formed from its chromosome pairs by
sampling the number of crossovers for each chromosome pair from a Poisson distribution. Crossover
points were randomly positioned along chromosome pairs. The haploid gametes were mutated
(mutation rate = .000028), and if a locus was mutated, a new allele was added. Fitness effects were
always deleterious. Quantitative effects were given a negative sign with probability 0.5. The
correlation of absolute value of fitness effects with the absolute value of the effect on the quantitative
trait was 0.4. If the sampled value for the effect on the quantitative trait was larger than the effect on
fitness, the quantitative effect was set as equal to the effect on fitness. The quantitative value for an
offspring was calculated by summing the effects of the QTL alleles over all loci. An individual’s
fitness was calculated similarly, but the effects of the QTL were multiplied. Artificial selection in
generation 1001 to 1020 was on phenotype, where phenotype for individual i was
y i = ai + ran * Ve, , where ran is a random normal deviate and Ve was the environmental
variance of the quantitative trait = 10 in all populations with artificial selection. During the 20
generations of artificial selection 1500 offspring were bred each generation from which either 26
males and 525 females were selected (Ne=100) or 5 males and 100 females were selected (Ne=20).
The evolution of gene frequencies depends mainly on Ne s, Ne c and Neµ, where Ne is the effective
population size, s is the coefficient of selection, c is the average number of recombinations per
chromosome per gametogenesis and µ is the per locus mutation rate at QTL. To reduce computer
times, large populations were simulated by reducing Ne and increasing the other parameters.
RESULTS AND DISCUSSION
Prior to selection, the genetic variance had reached an equilibrium of 11-14 when Ne=10,000 and 3-4
when ne=1000. Thus the model, like most other models, predicts that genetic variance increases with
Ne. This is inconsistent with observation and indicates the need for modification of the model
perhaps to include a greater intensity of natural selection.
Gains from 20 generations of artificial selection were 10.3σg (Ne= 1000 for natural selection/
Ne=100 for artificial selection), 10.0σg (Ne=1000 / 20), 15.7σg (Ne=10,000 / 100) and 15.4σg
(Ne=10,000 / 20). Figure 1 shows the genetic variance during artificial selection. There is an initial
fall due to the Bulmer effect, then a plateau and then a further fall. The decline in genetic variance
occurs sooner and is greater if Ne=20 than if Ne =100. The plateau is expected because during this
phase genes that were initially at low frequency, are moving towards frequency = 0.5 and so the
variance they contribute is increasing and offsetting decreased variance due to genes moving towards
fixation. The decline in genetic variance is greater than expected from inbreeding, so most of it is due
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AAABG Vol 15
to selection. This pattern may be realistic, as in some selection experiments response or genetic
variance does decline with time. However there is little evidence of this in commercial livestock,
perhaps because populations are not completely closed for 20 generations and/or selection objectives
vary over time.
Table 1 shows the distribution of QTL effects before and after 20 generations of artificial selection.
Prior to selection there are many genes of small effect and a few of moderate to large effect. This is
broadly in agreement with experimental results but there may be less genes of moderate effect (.3σp)
than observed (Hayes and Goddard 2000). The effect of selection is to reduce the number of genes
segregating but there is little effect on the distribution of effects ie there is still the same proportion of
genes of moderate to large effect that could be detected by QTL mapping experiments.
Figure 2 A shows that for populations with Ne=1000 prior to artificial selection, allele frequencies are
more commonly close to 0 or 1.0 than 0.5. Selection decreases the proportion of favourable alleles at
very low frequency. Figure 2 B shows that before artificial selection, there was no correlation
between gene frequency and size of effect. Selection pushed the genes with larger effects to higher
frequencies. Trends for Ne=10000 during natural selection were very similar.
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1000_100
1000_20
10000_100
10000_20
14
Genetic Variance
12
10
8
6
4
2
0
0
5
10
15
20
Generation
Figure 1. Change in genetic variance over generations in four populations. The first number
indicates the effective population size during natural selection, followed by the effective size of
the population during 20 subsequent generations of artificial selection.
Putting these results together we can describe the effect of selection as follows. Genes with
favourable alleles at frequencies above 0.5, increase in frequency (some to fixation) causing a
decrease in genetic variance. Genes with favourable alleles at very low frequency may lose the
favourable allele due to genetic drift or it may increase in frequency, which is more likely if its effect
is large, causing an increase in genetic variance at least for a few generations. Thus the genes of
moderate to large effect that are still segregating after 20 generations of selection, presumably
represent genes at initially low frequency plus a small number of new favourable mutations.
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Using QTL
Table 1. Percentage of segregating QTL of a particular size (gene substitution effect expressed
in phenotypic standard deviations)
Population
1000
1000_100
1000_20
10000 10000_100 10000_20
No. of genes segregating
219
176
103
494
456 269
Gene substitution effect*
Effect<0.1
86.4
85.8
86.3
91.8
89.5
91.7
0.1<effect<0.2
8.7
9.3
9.6
6.1
6.9
5.9
0.2<effect<0.3
3.2
3.1
2.3
1.5
2.5
1.9
0.3<effect<0.4
1
1.1
1
0.4
0.9
0.4
0.4<effect<0.5
0.3
0.4
0.5
0.1
0.1
0.1
0.5<effect<0.6
0.2
0.1
0
0
0
0
0.6<effect<0.7
0.1
0.1
0.1
0
0.1
0
Effect >0.7
0
0
0.1
0
0
0
*In phenotypic standard deviations
A
B
0.07
Gene substitution effect (phenotypic standard
deviations)
0.4
1000
0.35
Proportion of genes
1000_100
0.3
1000_20
0.25
0.2
0.15
0.1
0.05
1000
0.06
1000_100
1000_20
0.05
0.04
0.03
0.02
0.01
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
Frequency of favourable allele
0.2
0.4
0.6
0.8
1
Frequency of favourable allele
Figure 2. A. Frequency of favourable allele for three populations, 1000 (natural selection only
in a population of Ne=1000), 1000_100 (natural selection in a population of Ne=1000 followed
by artificial selection with Ne=100) and 1000_20 (natural selection in a population of Ne=1000
followed by artificial selection with Ne=20). B. Plot of the gene substitution effect (phenotypic
standard deviations) against the frequency of the favourable allele, across all segregating QTL
in the genome, for populations 1000, 1000_100 and 1000_20 (populations described above).
The results from our simulations are encouraging for QTL mapping experiments, suggesting that at
least a small number of QTL of moderate to large effect (and therefore detectable) should be
segregating in artificially selected populations, even for quantitative trait that have been under strong
artificial selection.
REFERENCES
Bovenhuis, H., Shrooten, C (2002) Proc. 7th World Congr. Genet. Appl. Livest. Prod., 09-07.
Caballero, A. and Keightley, P. D. (1994) Genetics 138: 883-900.
Georges, M. et al. (1995) Genetics 139: 907-920
Hayes, B. and Goddard, M. E. (2003) Livest. Prod. Sci. Accepted
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