Hardy Weinberg Population Genetics Hardy Weinberg Population Genetics
Hardy Weinberg Population Genetics
Hardy Weinberg: Population Genetics Using mathematical approaches to calculate changes in allele frequencies…this is evidence of evolution.
Hardy-Weinberg equilibrium § Hypothetical, non-evolving population upreserves allele frequencies § natural populations rarely in H-W equilibrium uuseful model to measure if forces are acting on a population § measuring evolutionary change G. H. Hardy mathematician W. Weinberg physician
Evolution of populations § Evolution = change in allele frequencies in a population u hypothetical: what conditions would cause allele frequencies to not change? 1. very large population size (no genetic drift) 2. no migration (no gene flow in or out) 3. no mutation (no genetic change) 4. random mating (no sexual selection) 5. no natural selection (everyone is equally fit) H-W occurs ONLY in non-evolving populations!
Populations & gene pools § Concepts a population is a localized group of interbreeding individuals gene pool is collection of alleles in the population *remember difference between alleles & genes! allele frequency is how common is that allele in the population *how many A vs. a in whole population
H-W formulas § Alleles: p+q=1 B § Individuals: b p 2 + 2 pq + q 2 = 1 BB BB Bb Bb bb bb
My Trick (because my memory is terrible!) • p = POWERFUL (dominant trait) • q = quiet (recessive trait)
Origin of the Equation • Assuming that a trait is recessive or dominant • Allele pairs AA, Aa, aa would exist in a population • p+q=1 • The probability that an individual would contribute an A is called p • The probability that an individual would contribute an a is called q • Because only A and a are present in the population the probability that an individual would donate one or the other is 100% • p 2 + 2 pq + q 2 Male Gametes A(p) Male Gametes a(q) Female gametes A(p) AA p 2 Aa pq Female Gametes a(q) Aa pq aa q 2
Hardy-Weinberg theorem § Counting Alleles uassume 2 alleles = B, b ufrequency of dominant allele (B) = p ufrequency of recessive allele (b) = q Frequencies are usually written as decimals! § frequencies must add to 1 (100%), so: p+q=1 BB Bb bb
Hardy-Weinberg theorem § Counting Individuals ufrequency of homozygous dominant: p x p = p 2 ufrequency of homozygous recessive: q x q = q 2 ufrequency of heterozygotes: (p x q) + (q x p) = 2 pq § frequencies of all individuals must add to 1 (100%), so: p 2 + 2 pq + q 2 = 1 BB Bb bb
Practice Problem: § In a population of 100 cats, there are 16 white ones. White fur is recessive to black. § What are the frequencies of the genotypes?
Use Hardy-Weinberg equation! q 2 (bb): 16/100 =. 16 q (b): √. 16 = 0. 4 p (B): 1 - 0. 4 = 0. 6 p 2=. 36 BB 2 pq=. 48 Bb q 2=. 16 bb Must. What assume are population the genotype is in frequencies? H-W equilibrium!
Answers: p 2=. 36 Assuming H-W equilibrium: Expected data Observed data How do you explain the data? 2 pq=. 48 q 2=. 16 BB Bb bb p 2=. 20 =. 74 BB 2 pq=. 64 2 pq=. 10 Bb q 2=. 16 bb
Tips for Solving HW Problems: • Solve for q first. • Then solve for p. • Don’t assume you can just solve for p 2 if only given dominant phenotypic frequency. • READ carefully!!! HW Math is fun
Hardy Weinberg Lab - Grebe-Grebe • Each person must fill out their own lab and complete the practice problems. This is a lab grade. Due next time. • Listen carefully to the directions and follow them exactly. • We will record data on the board for each simulation.
- Slides: 15