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Transcript
Population Genetics 1 • Chapter 23 in Purves 7th 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 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) 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 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 Calculating allele frequencies • For a gene with 2 alleles, A and a: NAA is the number of AA homozygotes NAa is the number of heterozygotes Naa is the number of aa homozygotes • NAA + NAa + Naa = N, number of individuals in population • Let p = frequency of allele A, and q = frequency of a. Then: • p = (2NAA + NAa) / 2N • q = (2Naa + NAa) / 2N Examples • Fig 23.6 in Purves 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 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 2allele gene with allele frequencies p,q) are in the proportions: p2 (AA), 2pq (Aa), q2 (aa) • p2 + 2pq + q2 = (p + q)2 = (1)2 = 1 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 Allele and Genotype Frequencies in H-W equilibrium p2 (AA) 2pq (Aa) q2 (aa) 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 c2 statistical test (3rd practical) The 2 c 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 p2, 2pq, q2 of AA, Aa, aa (50, 100, 50) • Observe 60, 80 and 60 • c2 = 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 c2 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