Lecture 18 Genetics of complex traits quantitative genetics PHENOTYPES ARE NOT ALWAYS A DIRECT REFLECTION OF GENOTYPES Some 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 a mutation 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 permissive temperature for dark color occurs at the extremities and a restrictive temperature occurs in the body core Nutritional effects Phenylketonuria is a human nutritional defect that can lead to severe physical and mental disorders in children but only if they consume phenylalanine The mutation prevents individuals from metabolizing this amino acid The disease phenotype can be avoided by eliminating phenylalanine from the diet 18 1 QUANTITATIVE TRAITS Most 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 a particular trait and the individual effects of genes on the phenotype Many of these traits can be measured on a quantitative rather than a qualitative scale This is where the terms quantitative trait and quantitative genetics come from Quantitative traits 1 Have continuous distributions not discrete classes 2 Are usually affected by many genes polygenic 3 Are also affected by environmental factors EXAMPLE COLOR OF WHEAT KERNELS This 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 trait demonstrates additive effects among different alleles at a single locus and among alleles at different genetic loci Genes with subscript 2 don t contribute any red pigment With two additive genes you have five phenotypic classes in the F2 offspring of true breeding strains instead of the three classes you would see if you had only one additive gene Some classes are composed of several genotypes that are indistinguishable in phenotype The number of phenotypic classes expected when there are n diallelic additive loci is 2n 1 So if have four additive genes you should expect nine phenotypic classes in the F2 offspring of pure breeding strains As the number of additive genes increases the distribution of phenotypes becomes more continuous In addition as stated above most quantitative traits are also affected by the environment Environmental effects may obscure genetically caused differences between phenotypic classes For example nutrition affects the adult size in many organisms The distribution of phenotypes then becomes even more continuous The distribution of quantitative traits often approximates a bell shaped curve when you plot phenotypic 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 Mean 63 1 inches 1500 1250 1000 750 of Women 500 250 0 56 58 60 62 64 66 68 70 72 Height inches In 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 the mean 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 curve similar to the one shown above To calculate the mean of a distribution you need to sum up all the different heights then divide by the number of individuals mean average sum of heights number of women x xi N 63 1 inches Another way of calculating the mean directly from a histogram if you don t have available a list of the heights of all 5000 women for example is n classes x n f x f i 1 i i i i The variance is calculated from the sum of squared deviations of individuals from the mean Var xi x 2 N 1 7 24 in2 n Var or f x x N 1 i 1 2 i i where N total number of individuals 5000 We will use this concept of variance extensively in our discussion of quantitative genetics Quantitative traits are influenced by genetics and by the environment Under some circumstances we can partition the phenotypic variance in quantitative traits into variance that is associated with genetic effects and variance that is associated with environmental effects V P VG VE Where VP is the total phenotypic variance VG is the genetic variance and VE is the environmental variance 18 2 MODELS OF QUANTITATIVE INHERITANCE HERITABILITY GENETIC AND PHENOTYPIC VARIANCE Some genetic variation is heritable because it can be passed from parent to offspring Some genetic variation is not strictly heritable because it is due to dominance or epistatic interactions that are not directly passed from parent to offspring For example if one allele is dominant to another the phenotype of a heterozygous parent is determined in part by the dominance interaction between the two alleles Since a sexually reproducing parent only passes on a single allele to its offspring the offspring does not inherit its whole genotype from a single parent So it does not inherit the dominance interaction just the effect of a single allele For example assume that the size of a bird measured as wing span is determined by two genes one with complete dominance of one allele over the other and one with additive effects Interactions between the two different genes are additive Birds of genotype aabb have 16 cm long wing spans and birds with other genotypes are somewhat larger depending upon which alleles they have at each locus The following table shows the increase in wing span conferred by different genotypes at each locus Dominance effects AA Aa aa 2 2 0 F1 Additive effects BB Bb bb 2 1 0 Aa Bb 19 cm x Aa Bb 19 cm F2 Genotypes Genotypic Effects AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabb 4 3 2 4 3 2 2 1 0 Phenotype cm 20 19 18 20 19 18 18 17 16 F2 proportions 1 16 2 16 1 16 2 16 4 16 2 16 1 16 2 16 1 16 What is the phenotypic mean and variance assuming we have exactly 16 F2 offspring in the proportions given above n classes x n f x f i 1 i i i n i Var f x x N 1 i 1 2 i i Mean 20 3 19 6 18 4 17 2 16 1 16