Lecture 18. Genetics of complex traits (quantitative genetics)PHENOTYPES ARE NOT ALWAYS A DIRECT REFLECTION OF GENOTYPESSome alleles are only expressed in some environments, or have variable expression for other reasons..Temperature-sensitive mutations.The effects of these mutations are usually only apparent at high temperatures. Siamese cats have amutation in the C gene controlling dark pigment formation. The ch allele of this gene is heat sensitive.The ch allele can make dark pigment at low but not high temperatures. The permissivetemperature for dark-color occurs at the extremities, and a restrictive temperature occurs inthe body core.Nutritional effectsPhenylketonuria is a human nutritional defect that can lead to severe physical and mental disorders inchildren, but only if they consume phenylalanine. The mutation prevents individuals frommetabolizing this amino acid. The disease phenotype can be avoided by eliminating phenylalanine fromthe diet.18.1. QUANTITATIVE TRAITSMost phenotypic traits in plants and animals are affected by many genes (size, weight, shape, lifespan,physiological traits, fecundity). Often, it is not feasible to determine the number of genes affecting aparticular trait, and the individual effects of genes on the phenotype. Many of these traits can be measuredon a quantitative, rather than a qualitative, scale. This is where the terms quantitative trait and quantitativegenetics come from.Quantitative traits:1. Have continuous distributions, not discrete classes2. Are usually affected by many genes (polygenic)3. Are also affected by environmental factorsEXAMPLE: COLOR OF WHEAT KERNELSThis trait is determined by two genes that contribute “doses” of red pigment, and display partial dominance(heterozygotes intermediate). Each allele with the subscript "1" contributes 1 dose of red pigment. This traitdemonstrates additive effects among different alleles at a single locus, and among alleles at differentgenetic loci. Genes with subscript "2 " don't contribute any red pigment. With two additive genes you havefive phenotypic classes in the F2 offspring of true-breeding strains, instead of the three classes you wouldsee if you had only one additive gene. Some classes are composed of several genotypes that areindistinguishable in phenotype. The number of phenotypic classes expected when there are n diallelicadditive loci is (2n+1). So, if have four additive genes, you should expect nine phenotypic classes in the F2offspring of pure-breeding strains.As the number of additive genes increases, the distribution of phenotypes becomes more continuous. Inaddition, as stated above, most quantitative traits are also affected by the environment. Environmentaleffects may obscure genetically-caused differences between phenotypic classes. For example, nutritionaffects the adult size in many organisms. The distribution of phenotypes then becomes even morecontinuous. The distribution of quantitative traits often approximates a bell-shaped curve when you plotphenotypic value (height, for example) against the frequency of individuals in particular phenotypic classes.Such a plot is called a frequency histogram.EXAMPLE: DISTRIBUTION OF HEIGHT IN 5000 BRITISH WOMEN:# of Women0250500750100012501500 56 58 60 62 64 66 68 70 72Height (inches)Mean = 63.1 inchesIn this graph, the column designated "62" includes all individuals with heights between 61 and 63 inches,"64" includes all individuals with heights between 63 and 65 inches, and so on.This curve has two easily measured properties--the MEAN (average), and the VARIANCE (variation about themean). Curves with the same mean may have very different variances.If you were to measure the heights of a sample of about 5000 different British women, you would get a curvesimilar to the one shown above. To calculate the mean of a distribution, you need to sum up all the differentheights, then divide by the number of individuals:mean = average = sum of heights / number of women: x = Σ (xi)/N = 63.1 inches. Another way ofcalculating the mean directly from a histogram (if you don't have available a list of the heights of all 5000women, for example) is x = ∑i=1n=#classesfixi/∑infiThe variance is calculated from the sum of squared deviations of individuals from the mean:Var = Σ (xi - x)2/(N-1) = 7.24 in2 or Var = ∑i=1nfi(xi- x)2/(N- 1)where N = total number of individuals (5000). We will use this concept of variance extensively in ourdiscussion of quantitative genetics.Quantitative traits are influenced by genetics and by the environment. Under some circumstances, we canpartition the phenotypic variance in quantitative traits into variance that is associated with genetic effects,and variance that is associated with environmental effects:VP = VG + VEWhere VP is the total phenotypic variance, VG is the genetic variance, and VE is the environmentalvariance.18.2. MODELS OF QUANTITATIVE INHERITANCEHERITABILITY, GENETIC AND PHENOTYPIC VARIANCESome genetic variation is heritable because it can be passed from parent to offspring. Some geneticvariation is not strictly heritable, because it is due to dominance or epistatic interactions that are not directlypassed from parent to offspring. For example, if one allele is dominant to another, the phenotype of aheterozygous parent is determined in part by the dominance interaction between the two alleles. Since asexually-reproducing parent only passes on a single allele to its offspring, the offspring does not inherit itswhole genotype from a single parent. So it does not inherit the dominance interaction, just the effect of asingle allele.For example, assume that the size of a bird (measured as wing span) is determined by two genes, one withcomplete dominance of one allele over the other, and one with additive effects. Interactions betweenthe two different genes are additive. Birds of genotype aabb have 16 cm long wing spans, and birds withother genotypes are somewhat larger, depending upon which alleles they have at each locus. The followingtable shows the increase in wing span conferred by different genotypes at each locus:Dominance effectsAdditive effectsAAAaaaBBBbbb+2+2+0+2+1+0F1:Aa BbxAa Bb19 cm19 cmF2 Genotypes:AABBAABbAAbbAaBBAaBbAabbaaBBaaBbaabbGenotypicEffects+4+3+2+4+3+2+2+1+0Phenotype(cm)201918201918181716F2 proportions:1/162/161/162/164/162/161/162/161/16What is the phenotypic mean and