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Population and Community Dynamics The Hardy-Weinberg Principle Key Terms ● Population: same species, same place, same time ● Gene: unit of heredity. Controls the expression of a trait. Can be passed to offspring. ● Allele: different forms of a gene ● Gene pool: sum of all alleles for all the genes in a population (sum of all the genetic variation) Gene Pools Evolve ● All individuals of same species have common genome (except sex chromosomes) - different genotypes and environmental influences result in different phenotypes that are acted on by natural selection ● Larger genomes = greater potential genetic diversity ● Greater number of different alleles = greater genetic diversity - sexual reproduction: recombination of parent alleles ● Gene Pool: all genes that occur in a population - maintains continuity of traits from generation to generation - some gene frequencies remain the same over time, but others can change Frequencies 1. Genotype Frequency ● Proportion of population with a particular genotype ● Decimal (or percentage) ● Ex. 37/55 goldfish have GG colour genotype. Genotype frequency of GG = 0.67 2. Phenotype Frequency ● Proportion of a population with a particular phenotype ● Decimal (or percentage) ● Ex. 50/55 goldfish are gold colour Phenotype frequency of gold = 0.91 3. Allele Frequency ● Rate a particular allele occurs in a population ● Total number of alleles in a population is twice the number of individuals (each individual has 2 copies of a gene) ● Ex. 37GG, 13Gg, 5gg Allele frequency of g = 13 + 5 + 5 = 23/100 = 0.23 By combining Darwin’s theory of evolution with Mendel’s understanding of inheritance, scientists were able to determine that evolution occurs when there are genetic changes in a population over time. Gene Pools Evolve ● Evolution: sum total of the genetically inherited changes in the individuals who are members of a population’s gene pool - felt by individuals, but whole population evolves ● Example: trait that is determined by the inheritance of a gene with 2 alleles, B and b - if parent generation has 92% B and 8% b, and their offspring collectively have 90% B and 10% b..... - entire population’s gene pool has evolved - higher b allele frequency Hardy-Weinberg Principle ● Quantify a gene pool: measure each allele frequency ● Changes can be measured by looking for changes in allele frequencies ● Only one allele? Fixed frequency of 100% ● Questions of allele frequencies being constant or changing.... - Reginald Punnett posed these questions to mathematician Godfrey Hardy in 1908, wrote solution on a napkin - Wilhelm Weinberg, German physician independently came to same results ● Hardy-Weinberg Principle: mathematical relationship showing that allele frequencies will not change from generation to generation as long as certain conditions are met Conditions of Hardy-Weinberg Principle ● Allele frequencies in a population will not change from generation to generation IF 1. 2. 3. 4. 5. population is infinitely large (chance events don’t alter allele frequencies) no migration in or out of population no mutations occur no natural selection occurs mating is random ● Basically: No mechanisms of evolution are acting on the population ● Highly unlikely that any of these conditions will happen in the real world – evolution inevitable result Hardy-Weinberg Principle ● For gene with only 2 alleles: ● If p = frequency of dominant allele and q = frequency of recessive, then ● ● ● ● p+q=1 p2 = frequency of genotype AA 2pq = frequency of genotype Aa q2 = frequency of genotype aa Equation gives expected genotype frequencies of the population, when all conditions are met p2 + 2pq +q2 = 1 Frequency of: Homozygous + heterozygous + homozygous = all individuals dominant recessive Applying the Principle ● Moth Population: If mating is random, 80% gametes ● ● ● bear A allele, 20% gametes bear a allele Next generation..... (0.80)2 + 2(0.80)(0.20) + (0.20)2 = 1 0.64 + 0.32 + 0.04 = 1 Frequency of AA is 0.64, Aa is 0.32, aa is 0.04 - same as PARENTS If random mating continues, allele frequencies are likely to remain constant from generation to generation Example 1 ● Consider a situation in which one gene has two alleles, A and a. The possible genotypes that could be found in a large population will be AA, Aa and aa. The dominant allele A has a frequency of 0.7. a) What is the frequency of the recessive allele, a? b) Use a Punnett square to determine the expected frequencies of the 3 possible genotypes. Example 1 Cont. Now use the Hardy-Weinberg Principle to determine the expected frequencies of the 3 possible genotypes. c) d) Given the distribution of the genotypes, predict the frequency of the A and a alleles in the population. Example 1 Cont. ● Because the allele frequencies are the same in the original gametes, identical results will be obtained generation after generation. ● However, in nature, a population rarely meets the ideal conditions for genetic equilibrium, but the principle allows us to make predictions about populations that are NOT EVOLVING. Example 2 ● Suppose a recessive genetic disorder occurs in 9% of the population. Determine what percentage of the population is heterozygous, or “carriers” of the allele for the disorder, but do not have the disorder. Make sure you check your solution – is it logical? Does everything add up to 1? Genetic Equilibrium ● Aka Hardy-Weinberg Equilibrium ● Allele frequencies stay constant over time – the population is not evolving ● Microevolution is the gradual change in allele frequencies in a population ex. DDT resistant mosquitoes ● We can use the HW Equation to study co-dominant alleles, incomplete dominant alleles, and multiple alleles. The total of all alleles is always 1. ● Sometimes, we will take DNA samples from individuals to determine allele frequencies and then apply the sample data to the population.