Evolution Test 3 study guide Lecture 13 Multiple Loci combinations The mathematics of multiple loci is the same as single loci but with more When many loci and alleles affect a trait there will be hidden variation There are so many possible combinations of alleles with multiple loci that variation becomes continuous and is best described statistically Basic principles Two loci in a population are in linkage equilibrium when the genotype of a chromosome at one locus is independent of its genotype at the other locus o Knowing the genotype of the chromosome at one locus is of no use at all in predicting genotype at the other Polygenic variation two or more loci affecting one trait Pleiotropy one locus affecting more than one trait genotype e g A1B1 A2B2 or AB ab Genotype frequencies in a two locus system table should be filled out on handout Hidden variation With 1 locus 2 alleles there are 3 genotypes and up to 3 phenotypes With 2 loci 2 alleles each there are 9 genotypes but if of equal effect only 5 phenotypes There may be more genetic variation possible than is expressed in a population If n loci with 2 alleles genotypes 3n phenotypes 2n 1 Continuous traits and variance When a trait is determined by a small number of genes alleles the phenotypes fall into a small number of discrete categories With a large number of underlying genes the variation becomes continuous Quick review of statistics mean x variance V and regression Variance V 2 population measure not applicable to individuals The variance of a trait is the sum of the variances of underlying causes Genetic variance key measure of evolutionary potential the raw material for selection and drift to act upon look at formulas on handout Selection at two loci that are epistatic for fitness and its effect on linkage disequilibrium o Correcting the model of linkage disequilibrium to account for selection i e for differences in the fitnesses of different haplotypes o If specific interactions between alleles at different loci result in different fitnesses there is epistasis for fitness and selection will affect haplotype frequencies Other effects on linkage disequilibrium o Note that genetic drift can also cause linkage disequilibrium one allele combination may drift to excess or fixation and founder populations are likely to have high D o linked locus under strong selection will often show linkage disequilibrium o Examples of selection and disequilibrium in natural populations o Closely linked genes that contribute to the same character or function often show strong linkage disequilibrium and coadaptation between particular alleles at these different loci may result For example Batesian mimicry Heterostyly Selection on quantitative traits heritability and response to selection Heritability is the fraction of the phenotypic variance that is due to the additive component of genetic variation Lecture 14 Quantitative genetics Quantitative genetics provides a framework to study the evolution of polygenic traits than discrete o Quantitative traits distribution of phenotypes is continuous rather Determined by genotype at different loci and environment Consistent with medelian genetics Influenced by combined effects of the genotype at many loci Phenotypic variation the sum of genetic and environmental variation o The selection differential and the selection gradient are two related ways to measure the strength of selection o The response to selection is the product of the strength of selection and the heritability o Observed rates of evolution and strength of selection can be very high but long term evolution is usually much less o The complex relationship between genotype and phenotype e g pleiotropy results in correlations between characters o Genetic correlations can significantly affect the rate and direction of evolution Why quantitative genetics and genotypes are unknown Includes The large majority of traits are polygenic and the relevant allele frequencies o tools for measuring heritable variation o tools for measuring differences in survival and or reproductive o tools for predicting the evolutionary response to selection Allows us to analyze evolution by natural selection in traits controlled by success many loci o We can detect the presence and location of loci influencing a quantitative trait by crossing parents from populations with fixed differences o Among the grandoffspring we look for associations between phenotype and genotype at marker loci o Analyze an F2 population for statistical associations between genotype at marker loci and phenotype If phenotype is associated with genotype at a particular marker locus evidence that a QTL influencing the trait of interest is located near the marker allows researchers to estimate both the locations of the QTL quantitative trait loci and the strength of their influence on phenotype With certain assumptions quantitative genetics can be applied to many more traits to fossil material and extrapolated over much longer periods of time Variance and Heritability Survey of heritabilities o Our measurement of heritability will be accurate only if we can make sure that there is no correlation between the environments experienced by the parents and those experienced by the offspring o the fraction of the total variation in a trait that is due to variation in genes heritability Broad sense heritability Vg Vp Vg Vg Ve Ex Midoffspring height average height of offspring vs heritability Offspring s trait values on Y axis and parent s trait values on X axis We have 2 parents for every offspring so we use the midvalue offspring value average of both parents use this even if we have more than on offspring per family If the offspring don t resemble their parents the best fit line will be near 0 evidence of variation among individuals in the population due to variation in their environments not variation in their genes If their offspring strongly resemble their parents the slope of the best fit line will be near 1 evidence that variation among individuals in the population is due to variation in their genes and not variation in their environments the slope of most traits in most populations fall somewhere in the middle with offspring showing a moderate resemblance to their parents evidence that variation is partly due from parents and partly due from environment o total variation of a trait phenotypic variation o variation among individuals due to variation in their environments environmental