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Population Genetics 1 Chapter 23 in Purves 7 th edition, or more detail in Chapter 15 of Genetics by Hartl & Jones (in library) Evolution is a change in genetic composition of a population - i.e. change in the relative frequencies of alleles of genes The simplest way to describe a population is by the allele frequencies of all the genes

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Populations and Gene Pools A population is a group of potentially interbreeding organisms of same species living in a prescribed geographical area Populations may have structure, i.e. groups (sub-populations) whose members are more likely to breed with each other, e.g. because of geography or culture The gene pool is the sum total of all alleles in the population (Purves fig 23.3)

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Basic ideas from Darwin Variation: individuals are not all the same (Fig 21.5 in Purves shows how artificial selection reveals the genetic variation in a population) Heredity: offspring resemble parents more than unrelated individuals Selection: if resources are limited, not all offspring survive - some forms are more likely to survive and reproduce than others (fitness) But there are also other forces that affect genes in populations

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Measurement of Genetic Variation Cannot usually look at every single individual in a population - take a sample (the bigger the sample, the smaller the error) For a gene, the frequency of each allele is between 0 and 1, and the sum of all allele frequencies for the gene is 1 Allele frequency is defined as: Number of copies of allele in population Sum of all alleles in population* * Denominator is 2n for an autosomal gene in a population of n diploid organisms

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Calculating allele frequencies For a gene with 2 alleles, A and a: N AA is the number of AA homozygotes N Aa is the number of heterozygotes N aa is the number of aa homozygotes N AA + N Aa + N aa = N, number of individuals in population Let p = frequency of allele A, and q = frequency of a. Then: p = (2N AA + N Aa ) / 2N q = (2N aa + N Aa ) / 2N

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Examples Fig 23.6 in Purves

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Hardy-Weinberg (1) A population that is not changing genetically is in Hardy-Weinberg equilibrium (after 2 scientists in 1908), if these 5 assumptions are correct: –Random mating –Large N (population size) –No migration between populations –Negligible mutation –Natural selection does not affect alleles being considered

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Hardy-Weinberg (2) If the assumptions are true, it follows that: Allele frequencies remain constant from one generation to the next After one (or more) generations of random mating, the genotype frequencies (for a 2- allele gene with allele frequencies p,q) are in the proportions: p 2 (AA), 2pq (Aa), q 2 (aa) p 2 + 2pq + q 2 = (p + q) 2 = (1) 2 = 1

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Hardy-Weinberg (3) Purves Fig 23.7 shows why population will be in H-W equilibrium after one generation of breeding This is another example in genetics of multiplication of probabilities of independent events, and addition of probabilities where there is >1 way for something to happen (heterozygotes) It also shows why dominant alleles do not take over from recessive ones

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Allele and Genotype Frequencies in H-W equilibrium p 2 (AA) 2pq (Aa) q 2 (aa)

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Importance of Hardy-Weinberg Without H-W, we could not tell that evolution is occurring The way in which a population deviates from H-W tells us something about what types of evolutionary force are operating We can test if a population is in H-W equilibrium with the 2 statistical test (3rd practical)

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The 2 test Compares the observed frequencies of individuals in different classes to the expected frequencies, to see if there is a statistically-significant difference For example, p = 0.5, q = 0.5, N = 200 Expect p 2, 2pq, q 2 of AA, Aa, aa (50, 100, 50) Observe 60, 80 and 60 2 = sum over all classes of (Obs-Exp) 2 /Exp = (60-50) 2 /50 + (80-100) 2 /100 + (60-50) 2 /50 = 8.0 This exceeds the value in the 2 table for 1 degree of freedom, p = 0.05, so we conclude that the probability that the population is in H-W equilibrium is less than 0.05

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