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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 35 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 36 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. 16 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. 37 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 38