The Evolution of Populations HARDY WEINBERG EQUATIONS Ms. Day AP Biology www.campbellbiology.com (Ch 23 Bioflix)
Population genetics- Vocab Population genetics is the study of how populations change genetically over time Population: Group of the same species living in the same area that can interbred Species: a group of populations whose individuals have the potential to interbreed and produce fertile offspring Gene pool: the total combination of genes (alleles) in a population at any one time
“Individuals are selected for/against, but populations adapt and evolve.”
Microevolution The change in the frequency of ALLELES (or how often a certain allele appears) in a population over time The change in a population’s gene pool over time
Allele Frequencies Each allele has a frequency in a population’s gene pool a # of times it appears in a population A a A a a A
Allele Frequencies- EXAMPLE In a population of wildflowers, the Red allele is A and white allele is a. 500 total plants in the population, 20 are white (aa), 320 are red (AA), 160 are pink (Aa) How many total alleles for flower color are there in this population? 1000 (500 plants with 2 alleles EACH) a= 20 + 20 + 160 = 200 alleles A = 320 + 320 + 160 = 800 alleles
Allele Frequencies- EXAMPLE (Con’t) What is the frequency of “A” allele and “a” allele? Always use a decimal for frequency! 800/1000 A = 0.8 200/1000 a = 0.2
How do we KNOW if a population is evolving? Use the Hardy-Weinberg theorem (or equilibrium) It is used to describe a population that is NOT evolving Conditions in the population are completely RANDOM (null hypothesis)
Hardy Weinberg Theorem Conditions for non-evolving (NOT CHANGING) population: Very large population size No migration No mutations Random mating No natural selection Since all is RANDOM, the null hypothesis is that the population is not evolving. RARELY MET IN NATURE
2 equations are used in the Hardy Weinberg Theorem p + q = 1 (1 means 100% of all alleles) This means that there are only 2 possible alleles p and q p = dominant allele frequency q = recessive allele frequency The equation that corresponds to the frequency of individuals regarding these 2 alleles: p2 + 2pq + q2 = 1
(frequency of Aa plus aA genotype) p2 + 2pq + q2 = 1 p2 = frequency of homozygous dominant individuals 2pq = frequency of heterozygous individuals (frequency of Aa plus aA genotype) q2 = frequency of homozygous recessive individuals EXAMPLE Round head is dominant to cone heads, 51% of the individuals in the population have round heads. What portion of this 51% are homozygous? 0.49 = q2 (recessive), Therefore q = 0.7, so p = 0.3 p2 is the frequency of homozygous dominant individuals = 0.09 or 9%
Hardy-Weinberg Theorem States that… the frequencies of alleles and genotypes will stay CONSTANT over generations UNLESS acted upon by agents or It describes a population where allele frequencies do NOT change p and q do NOT change over generations
Hardy-Weinberg Equation When using this equation, we assume fertilization is RANDOM and all male/female combinations are likely
Conditions for Hardy-Weinberg Equilibrium The Hardy-Weinberg theorem describes a hypothetical (IDEAL) population All FIVE conditions are being met Allele frequencies do NOT change over time Genotype frequencies do NOT change over time So…p and q values CAN be used (connected to) p2 + 2pq + q2 = 1 http://www.hippocampus.org/Biology;jsessionid=6E6D9D7721EBDBFE9BD00616517846DD
HOWEVER…p2 + 2pq + q2 and p + q will ALWAYS equal 1 (100%). Real Life Populations In real populations, allele and genotype frequencies DO change over time All FIVE conditions are rarely met together! So…p and q values can NOT be used (connected to) p2 + 2pq + q2 = 1 HOWEVER…p2 + 2pq + q2 and p + q will ALWAYS equal 1 (100%).