Modern Evolutionary Biology I. Population Genetics A. Overview Sources of Variation Agents of Change Mutation N.S. Recombination mutation (polyploidy) - crossing over - independent assortment VARIATION

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population G. Hardy and W. Weinberg 1. Definitions - Evolution: a change in the genetic structure of a population - Population: a group of interbreeding organisms that share a common gene pool; spatiotemporally and genetically defined - Gene Pool: sum total of alleles held by individuals in a population - Genetic structure: Gene array and Genotypic array - Gene/Allele Frequency: % of alleles at a locus of a particular type - Gene Array: % of all alleles at a locus: must sum to 1. - Genotypic Frequency: % of individuals with a particular genotype - Genotypic Array: % of all genotypes for loci considered; must = 1.

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population 1. Definitions 2. Basic Computations AA Aa aa Individuals 70 80 50 (200)

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population 1. Definitions 2. Basic Computations AA Aa aa Individuals 70 80 50 (200) Genotypic Array 70/200 = 0.35 80/200 = .40 50/200 = 0.25 = 1

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population 1. Definitions 2. Basic Computations AA Aa aa Individuals 70 80 50 (200) Genotypic Array 70/200 = 0.35 80/200 = .40 50/200 = 0.25 = 1 ''A' alleles 140 220/400 = 0.55

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population 1. Definitions 2. Basic Computations AA Aa aa Individuals 70 80 50 (200) Genotypic Array 70/200 = 0.35 80/200 = .40 50/200 = 0.25 = 1 ''A' alleles 140 220/400 = 0.55 'a' alleles 100 180/400 = 0.45

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population 1. Definitions 2. Basic Computations - Determining the Gene Array from the Genotypic Array a. f(A) = f(AA) + f(Aa)/2 = .35 + .4/2 = .35 + .2 = .55 b. f(a) = f(aa) + f(Aa)/2 = .25 + .4/2 = .25 + .2 = .45 KEY: The Gene Array CAN ALWAYS be computed from the genotypic array; the process just counts alleles instead of genotypes. No assumptions are made when you do this.

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 1. Goal: Describe what the genetic structure of the population would be if there were NO evolutionary change – if the population was in equilibrium.

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 1. Goal: Describe what the genetic structure of the population would be if there were NO evolutionary change – if the population was in equilibrium. For a population’s genetic structure to remain static, the following must be true: - random mating - no selection - no mutation - no migration - the population must be infinitely large

Initial genotypic freq. Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 2.Example: AA Aa aa Initial genotypic freq. 0.4 0.2 1.0 Gene freq. Genotypes, F1 Gene Freq's Genotypes, F2

Initial genotypic freq. Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 2.Example: AA Aa aa Initial genotypic freq. 0.4 0.2 1.0 Gene freq. f(A) = p = .4 + .4/2 = 0.6 f(a) = q = .2 + .4/2 = 0.4 Genotypes, F1 Gene Freq's Genotypes, F2

Initial genotypic freq. Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 2.Example: AA Aa aa Initial genotypic freq. 0.4 0.2 1.0 Gene freq. f(A) = p = .4 + .4/2 = 0.6 f(a) = q = .2 + .4/2 = 0.4 Genotypes, F1 p2 = .36 2pq = .48 q2 = .16 = 1.00 Gene Freq's Genotypes, F2

Initial genotypic freq. Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 2.Example: AA Aa aa Initial genotypic freq. 0.4 0.2 1.0 Gene freq. f(A) = p = .4 + .4/2 = 0.6 f(a) = q = .2 + .4/2 = 0.4 Genotypes, F1 p2 = .36 2pq = .48 q2 = .16 = 1.00 Gene Freq's f(A) = p = .36 + .48/2 = 0.6 f(a) = q = .16 + .48/2 = 0.4 Genotypes, F2 After one generation with these conditions, the population equilibrates

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 2.Example 3. Utility: If no populations meets these conditions explicitly, how can it be useful?

Initial genotypic freq. Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 2.Example 3. Utility: If no populations meets these conditions explicitly, how can it be useful? For comparison, like a “perfectly balanced coin” AA Aa aa Initial genotypic freq. 50 20 30 100 Is this population in HWE, or is it evolving?

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model 3. Utility: - if a population is NOT in HWE, then one of the assumptions must be violated. Sources of Variation Agents of Change Mutation N.S. Recombination Drift - crossing over Migration - independent assortment Mutation Non-random Mating VARIATION So, if NO AGENTS are acting on a population, then it will be in equilibrium and WON'T change.

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model D. Deviations from HWE 1. mutation 1. Consider a population with: f(A) = p = 0.6 f(a) = q = 0.4 2. Suppose 'a' mutates to 'A' at a realistic rate of: μ = 1 x 10-5 3. Well, what fraction of alleles will change? 'a' will decline by: qm = .4 x 0.00001 = 0.000004 'A' will increase by the same amount. f(A) = p1 = 0.600004 f(a1) = q = 0.399996

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model D. Deviations from HWE 1. mutation 2. migration p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population

Modern Evolutionary Biology I. Population Genetics A. Overview B. The Genetic Structure of a Population C. The Hardy-Weinberg Equilibrium Model D. Deviations from HWE 1. mutation 2. migration p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 M = 10% p(new) = p1(1-m) + p2(m) = 0.2(0.9) + 0.7(0.1) = 0.18 + 0.07 = 0.25

a. Positive Assortative Mating – “Like mates with Like” D. Deviations from HWE 1. mutation 2. migration 3. Non-random Mating a. Positive Assortative Mating – “Like mates with Like” AA Aa aa 0.2 0.6 offspring F1

a. Positive Assortative Mating – “Like mates with Like” D. Deviations from HWE 1. mutation 2. migration 3. Non-random Mating a. Positive Assortative Mating – “Like mates with Like” AA Aa aa 0.2 0.6 offspring ALL AA 1/4AA:1/2Aa:1/4aa ALL aa F1

a. Positive Assortative Mating – “Like mates with Like” D. Deviations from HWE 1. mutation 2. migration 3. Non-random Mating a. Positive Assortative Mating – “Like mates with Like” AA Aa aa 0.2 0.6 offspring ALL AA 1/4AA:1/2Aa:1/4aa ALL aa 0.15 + 0.3 + 0.15 F1 0.35 0.3

D. Deviations from HWE 1. mutation 2. migration 3. Non-random Mating a. Positive Assortative Mating – “Like mates with Like” b. Inbreeding: Mating with Relatives Decreases heterozygosity across the genome, at a rate dependent on the degree of relatedness among mates.