Interact box 9.4 Effective population size and genotypic variation in a neutral quantitative trait

In PopGene.S2, open the QTL simulation module and then explore how the effective population size influences the level of genotypic variation for a selectively neutral quantitative trait. The key parameter to adjust is the number of individuals in the population. Try N = 50 and then N = 500 while the other parameters are set at nQTL = 10, mutation rate = 0.00001, generations = 100, VE = 0.1, Maximum genotypic value = 10.0, and Selection threshold = 0.0 (this last parameter value sets the truncation point so that all individuals reproduce each generation, effectively removing natural selection).

How much genotypic variance (Vc) do you find with these two effective population sizes? How variable are the levels of VG over time with N = 50 or N = 500? How do the mutation rate and the environmental variance (VE) in the trait influence the long-term heritability for each effective population size?

This recommendation for an effective population size target of 500 sparked a debate that centered around the numerous assumptions about the nature and causes of quantitative trait variation in natural populations. Lande (1995) pointed out that VM ~ 0.001 VE was probably too high since the mutation rate needed to be discounted for the number of mutations that were highly deleterious and a more realistic assumption was VM ~ 0.0001 VE by counting only nearly neutral mutations. This change in the mutational input of quantitative genetic variance each generation substantially increases the required effective population size to approximately 5000. Franklin and Frankham (1998) countered that assuming a heritability of 0.5 was larger than necessary because heritabilities for fitness-related traits were often around 0.1 (see also Frankham and Franklin 1998). They reasoned that even if VM ~ 0.0001 VE, an effective population size of about 550 was sufficient to maintain a heritability of 0.1.

In contrast, inferred -VL ratios were observed in a vM

range of organisms to be between 30 and 300 which implies that Ne is between 15 and 150 (Houle et al. 1996; Lynch & Lande 1998). Since this effective population size is definitely too low for some of the species studied by Houle et al. (1996), such as Drosophila, these findings then called into question the very assumptions of neutral drift-mutation equilibrium. An alternative explanation is that stabilizing natural selection is operating and causing reduced variation in quantitative traits and could explain the -VLratios rather than such low effective p vM

population sizes.

The perspective of neutral evolution for quantitative traits has also been employed to make inferences about the nature of the total genotypic variation (VG). Genetic drift that occurs during genetic bottlenecks and founder events as well as consanguineous mating impacts the components of genotypic variation for neutral quantitative traits. In a seeming contradiction, genetic drift can produce a transient increase in additive genotypic variance for neutral quantitative traits that exhibit dominance (VD) or epistasis (Vj) genotypic variance (Robertson 1952; Goodnight 1987, 1988; Willis & Orr 1993; Barton & Turelli 2004). For quantitative traits that exhibit only VA and VD, higher heterozygote frequencies produce more VD and less VA when the dominance coefficient (d) increases. Genetic drift causes an increase in homozygosity as allele frequencies change toward fixation and loss on average under random sampling. An increase in homozygosity is also a decrease in heterozygosity and thereby a decrease in VD. For a single generation bottleneck of Ne = 2 and assuming no epistasis, Willis and Orr (1993) showed that the expected value of VA over many replicate populations increases if d > 0.29. They also showed that as Ne during a bottleneck increases, the threshold dominance coefficient for VA to increase approaches d > 0.20. The increase in VA is greater for larger d and for lower initial frequencies of the recessive allele. These increases in VA translate into increases in the heritability that also depend on the magnitude of VE for the trait. Consanguineous mating also acts to increase homozygosity while not altering allele frequencies, and so can also cause a reduction in VD that leads to a relative increase in VA.

These predictions about changes in heritability after genetic drift or consanguineous mating lead to a test of whether quantitative traits have geno-typic variation that is exclusively additive or is a combination of additive and non-additive genotypic variation. Van Buskirk and Willi (2006) reviewed the results of numerous studies that estimated herit-ability and VA from both small or inbred populations as well as large randomly mated populations. They found that phenotypes closely associated with fitness (e.g. viability, fecundity, body size) often did show an increase in heritability after consanguineous mating or population bottlenecks. In contrast, phenotypes not associated with fitness (e.g. morphological traits, bristle number, oil content) showed only declines in heritability after consanguineous mating or population bottlenecks. This result is consistent with the explanation that VG in fitness-related phenotypes was caused by both allele and genotype variation whereas VG in non-fitness phenotypes was caused by alleles alone in the organisms studied.

9.3 Quantitative trait loci (QTL)

• QTL mapping with single marker loci.

• QTL mapping with multiple marker loci.

• Limitations of QTL mapping studies.

• Biological significance of QTL mapping.

Thus far in this chapter, quantitative traits have been described based on the mean and variance of values in a population. Quantities like the components of the total genotypic variance and the heritability illuminate population-level average qualities of phenotypes. However, the numerous loci that each contribute to such population variation have not been identified nor described. This final section of the chapter introduces the concepts and some methods needed to identify the individual loci that ultimately contribute to variation in quantitative traits.

Using the basic framework of phenotypic values and the population mean already established, and joining it with genetic marker data for individuals, it is possible to identify individual regions in a genome that contribute to quantitative trait variation. The genomic regions that contribute to variation in quantitative traits are called quantitative trait loci or QTLs. In the simplest idealized case, individual QTLs are single genes that contribute to the value of a quantitative trait and have alternate alleles with different effects on phenotypic value. The trait mean and variance would then be the sum of the mean and variance contributed by each gene that affects the trait. In reality, QTLs are not necessarily individual genes but can be larger chromosomal regions held together by linkage that may contain several or many genes. It is these linkage blocks, each of which contains a genetic marker, that can be associated with an effect on the variance of a quantitative trait.

Candidate loci Loci that have known or inferred function and therefore are hypothesized to be causal contributors to genetic variation in a quantitative trait. Genetic architecture The number of loci that underlie a quantitative trait and the magnitude of their contributions to quantitative trait genetic variation. Quantitative trait locus or QTL A gene, or more often a genome region associated by linkage, possessing multiple alleles that affect the average value of a quantitative trait in a defined population associated through linkage with a genetic marker.

A major goal in identifying and describing the individual QTLs that cause quantitative genetic variation is to understand the genetic architecture of continuous phenotypes. By one definition, genetic architecture is all of the genetic and environmental factors that contribute to a quantitative trait, as well as their magnitude and their interactions (National Institute of General Medical Sciences 1998). More narrowly, genetic architecture often refers to the number of QTLs and the size of their effects on a quantitative traits. Identification of the number and phenotypic effects of QTLs has applications in many areas of biology. Identification of QTLs helps test the role, if any, of candidate loci (identified through independent molecular biology research or sequence analyses, for example) in explaining a portion of the genetic variance in quantitative traits. The reverse is also true, since loci identified by QTL mapping (which is described below) as causing some of the genetic variation in a quantitative trait are often further studied to better understand their function. In clinical settings, QTL mapping helps identify genes and alleles that cause disease conditions as well as genetic markers associated with disease QTLs that can be used to screen for disease risk. Identifying QTLs can improve the efficiency of animal and plant breeding, such as in the development of genetic markers associated with QTLs that can be used to screen individuals early in life for traits that may only be manifest later in life. One example would be screening tree seedlings for mature wood characteristics and planting those individuals with genetic marker genotypes associated with desirable phenotypes that appear only after many years of growth.

The number of QTLs and the size of their effects on a quantitative trait also have profound implications for evolutionary change such as the response to natural selection and the amount of variation generated by mutation. QTL mapping has the potential to deconstruct phenomena in quantitative genetics that have traditionally only been analyzed via variance components. In principle at least, QTL mapping can distinguish the specific causes of genetic correlations (pleiotropy or linkage), identify the loci and alleles that demonstrate dominance and epistasis, and show how specific loci involved in genotype-by-environment interactions respond to their environments.

QTL mapping with single marker loci

The process of identifying quantitative trait loci is called QTL mapping because it is based on the technique of linkage mapping that establishes the linear order of loci on chromosomes based on recombination frequencies. QTL mapping takes basic linkage mapping one step further by determining whether any of the mapped loci are associated with variation in a quantitative trait. QTL mapping requires variation for a quantitative trait within or between populations and numerous polymorphic genetic marker loci that are spread across the genome of the organism. The mapping is carried out for the marker loci, since after all the QTLs are unknown. QTLs are identified by differences in the mean phenotype of groups of individuals with different marker locus genotypes. Any association between phenotypic means and marker genotypes is caused by gametic disequilibrium between QTLs and marker loci when the two types of loci are close enough on a chromosome to be linked. Thus, QTL mapping uses known marker loci to detect the phenotypic signature of unknown QTLs that are in the same linkage block.

Genetic marker loci are a critical ingredient in QTL mapping. First and foremost, marker loci should be both independent of the phenotype(s) being mapped (i.e. not a QTL themselves) and also selectively neutral so that genotype frequencies are determined only by mating and recombination but not by viability or fecundity selection. Marker loci must be polymorphic because they are only informative when individuals with different phenotypic values possess distinct maker locus genotypes. Codominant marker loci where all possible genotypes are detectable present the easiest case to consider, although mating designs exist that can utilize dominant marker loci. Before the present age of genomics, only loci with phenotypic effects or protein polymorphisms were used as markers and OTL mapping was generally limited by the small number and low polymorphism of such marker loci. In the present day, OTL mapping can employ a full battery of DNA markers such as restriction fragment length polymorphisms (RFLPs), amplified fragment length polymorphisms (AFLPs), microsatellites, and single nucleotide polymorphisms (SNPs). The numerous genome-sequencing projects that have been completed or are planned lead to the identification of marker loci spread across the entire genome. Linkage maps based on many molecular markers are also now available for humans as well as model and agricultural species.

Experimental mating designs are a major component of OTL mapping. One of the most basic breeding schemes for OTL mapping in organisms that can be raised and mated in captivity is called the F2 design or recombinant inbred line design (Fig. 9.15). It starts with a population, perhaps in the wild, that has considerable phenotypic variation as well as genetic variation at numerous molecular marker loci. From this original population, individuals are sampled to start inbred lines or subpopulations. The inbred lines are maintained by some type of consanguineous mating (e.g. selfing, brother-sister mating) for numerous generations. The inbred lines eventually contain individuals with a high probability of homo-zygosity for different alleles at the loci that cause variation in the phenotype (O1 and O2) as well as for the different alleles present at the genetic marker loci (M1 and M2). An individual is sampled from each of two inbred lines that exhibit different values for the phenotype(s) of interest as well as different homozygous genotypes at the marker locus. These individuals form the P1 generation in Fig. 9.15.

When the P1 individuals are mated, they produce progeny that are all heterozygotes for both the OTL and the marker locus. Note that recombination events do not alter the gametes produced because each P1 individual is a double homozygote. The progeny of the P1 generation form the F1 generation. Figure 9.15 shows the four gametes that are produced by the F1 individuals and transmitted after

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