15 The Genetic Basis of Complex Inheritance 1

Multifactorial Traits • Multifactorial traits are determined by multiple genetic and environmental factors acting together • Multifactorial = complex traits = quantitative traits • Most traits that vary in the population, including common human diseases with the genetic component, are complex traits • Genetic architecture of a complex trait = specific effects and combined interactions of all genetic and environmental factors 2

Quantitative Inheritance • Quantitative traits = phenotypes differ in quantity rather than type (such as height) • In a genetically heterogeneous population, genotypes are formed by segregation and recombination • Variation in genotype can be eliminated by studying inbred lines = homozygous for most genes, or F 1 progeny of inbred lines = uniformly heterozygous • Complete elimination of environmental variation is impossible 3

Quantitative Inheritance • Continuous traits = continuous gradation from one phenotype to the next (height) • Categorical traits = phenotype is determined by counting (hen’s eggs) • Threshold traits = only two, or a few phenotypic classes, but their inheritance is determined by multiple genes and environment (adult-onset diabetes) 4

Multiple gene hypothesis: range of phenotypes can be accounted for by cumulative effect of many alleles. Polygenes: Additive allele; nonadditive allele 1 phenotypic traits can be measured eg. weight or height 2 two or more loci (genes) could account for phenotype in an additive or cumulative way 3 each loci may be occupied by an additive allele, which contributes a constant amount to the phenotype, or a nonadditive allele which does not 4 The contribution by each allele may be small and is approx equal 5 together the alleles contribute to a single phenotypic character with substantial variation. 5

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Distributions • Distribution of a trait in a population = proportion of individuals that have each of the possible phenotypes • Mean = peak of distribution x = ∑xi /N • Variance = spread of distribution estimated by squared deviation from the mean s 2=∑(xi - x )2/N-1 • Standard deviation = square root of the variance s =√ s 2 7

Normal Distribution • Normal distribution = symmetrical curve produced by data in which half points are above and half points are below mean ~68% of a population have a phenotype within one standard deviation (s) of the mean ~95% - within 2 s ~99. 7% - within 3 s • The distribution of a trait in a population implies nothing about its inheritance 8

Fig. 15. 5 9

Phenotypic Variation • Variation of a trait can be separated into genetic and environmental components • Genotypic variance g 2 = variation in phenotype caused by differences in genotype • Environmental variance e 2 = variation in phenotype caused by environment • Total variance p 2 = combined effects of genotypic and environmental variance p 2 = g 2 + e 2 + 2 cov ge 10

Analysis of a quant trait: Tomato fruit P 1 ave=6 oz P 2 ave=18 oz F 1 ave = 1/n Σ ( Xi) =626/52 =12. 04 F 2 ave = 1/n Σ ( Xi) =626/52 =12. 11 F 1 var = 1/(n-1) Σ ( Xi-X)2 =1. 29 F 2 var = 1/(n-1) Σ ( Xi-X)2 =4. 27 F 1 st dev = sqrt(var) =1. 13 F 2 st dev = sqrt(var) =2. 06 11

Phenotypic Variation • Genotype and environment can interact or they can be associated • Genotype-environment (G-E) interaction = environmental effects on phenotype differ according to genotype • Genotype-by-sex interaction: same genotype produces different phenotype in males and females (distribution of height among women and men) 12

Genetic Variation • Genotype-environment (G-E) association = certain genotypes are preferentially associated with certain environments • There is no genotypic variance in a genetically homogeneous population g 2 = 0 • When the number of genes affecting a quantitative trait is not too large, the number, n, of genes contributing to the trait is n = D 2/8 g 2 D = difference between parental strains 13

Fig. 15. 10 14

Broad-Sense Heritability • Broad-sense heritability (H 2) includes all genetic effects combined H 2 = g 2 / p 2 = g 2 / g 2 + e 2 • Knowledge of heritability is useful in plant and animal breeding because it can be used to predict the magnitude and speed of population improvement 15

Heritability: Twin Studies • Twin studies are often used to assess genetic effects on variation in a trait • Identical twins arise from the splitting of a single fertilized egg = genetically identical • Fraternal twins arise from two fertilized eggs = only half of the genes are identical • Theoretically, the variance between identical twins would be equivalent to e 2 , and between fraternal twins - g 2/2 + e 2 16

Heritability: Twin Studies Potential sources of error in twin studies of heritability: – Genotype-environment interaction increases the variance in fraternal twins but not identical twins – Frequent sharing of embryonic membranes by identical twins creates similar intrauterine environment – Greater similarity in treatment of identical twins results in decreased environmental variance – Different sexes can occur in fraternal but not identical twins 17

Narrow-Sense Heritability • Narrow-sense heritability (h 2) = proportion of the variance in phenotype that is transmissible from parents to offspring. The genetic variance can be split into both additive and dominant alleles. h 2 = g 2 / p 2 = g 2 / a 2 + d 2 + e 2 • Narrow-sense heritability can be used to predict changes in the population mean in with individual selection h 2 = (M’ - M)/(M* - M) • In general, h 2 < H 2. They are equal only when the alleles affecting the trait are additive in their effects = heterozygous phenotype is exactly intermediate between homozygous dominant and recessive 18

Artificial Selection • Artificial selection =“managed evolution” = the practice of selecting a group of organisms from a population to become the parents of the next generation • h 2 is usually the most important in artificial selection • Individual selection = each member of the population to be selected is evaluated according to its individual phenotype • Truncation point = arbitrary level of phenotype that determines which individuals will be used for breeding purposes 19

Artificial Selection There are limits to the improvement that can be achieved by artificial selection: • Selection limit at which successive generations show no further improvement can be reached because natural selection counteracts artificial selection due to indirect harmful effects of selected traits (weight at birth versus viability) • Correlated response = effect of selection for one trait on a non-selected trait (number of eggs and their size) 20

Inbreeding • Inbreeding can have harmful effects • Inbreeding depression = decrease in fitness due to harmful recessive alleles which become homozygous • Heterosis = hybrid vigor refers to superior fitness of heterozygote; often used in agricultural crop production Fig. 15. 14 21

Correlation Between Relatives • Genetic variation is revealed by correlations between relatives • Covariance (Cov), the tendency for traits to vary together, is Cov(x, y)=∑fi(xi - x )(yi - y )/N-1 • Correlation coefficient (r) = statistical evaluation of paired data (pairs of parents, twins, parent and offspring) r =Cov(x, y)/sxsy • Covariance and correlation coefficient are important in heritability estimates 22

Correlation Between Relatives • Correlation coefficient of a trait between relatives is related to the narrow- or broad -sense heritability 23

Threshold Traits: Heritability • Liability = quantitative trait that presents a genetic risk for a threshold trait • Individuals with a liability above threshold develop the trait • The risk of manifesting a threshold trait has H 2 and h 2 that cannot be estimated directly, but can be inferred from the incidents of the trait among individuals and their relatives 24

Threshold Traits: Heritability • Many congenital abnormalities are inherited as threshold traits • Heritability analyses can be used to determine recurrence risks • Theoretical curves show incidence, type of inheritance and risk among first-degree relatives of an affected individual 25

Multifactorial Disorders • Most common disorders in human families are multifactorial • Pedigree studies of genetic polymorphisms are used to map loci for quantitative traits • Quantitative trait locus (QTL) = gene that affects a quantitative trait • Simple tandem repeat polymorphisms (STRPs) are used to locate QTLs • Candidate gene = gene for which there is some a priori basis for suspecting that it affects the trait 26