1.  Hardy-Weinberg Equilibrium Review By Sean McGrath

2. Hardy-Weinberg Theorem  Laid out in 1908 by the two scientists who independently discovered it  States that frequencies of alleles within a population that is not evolving will remain constant from generation from generation  Certain improbable conditions must be fulfilled in order for this Theorem to apply

3. Conditions of the Theorem  Extremely Large Population Size: As population size decreases, there are greater chance fluctuations in allele frequencies (genetic drift)  No Gene Flow: Transfer of alleles between populations cannot occur  No Mutations: Introducing or removing genes form chromosomes will modify gene pool  Random Mating: Preferential mating based on certain genotypes will not allow random mixing of gametes  No Natural Selection!: Differential survival and reproductive success alters allele frequencies

4. Hardy-Weinberg Equilibrium  The Theorem can be used to calculate expected Genotype frequencies, based on Allele frequencies within the population, and vice versa  When ‘p’ represents the dominant allele’s frequency, and ‘q’ represents the recessive allele’s frequency, then p+q=1  When two haploid gametophytes merge, each with one copy of gene, the resulting genotype frequencies can be calculated based on (p+q) 2 =1 2, or p 2 +2pq+q 2 =1  Thus p 2 =Homozygous Dominant Individuals, 2pq=Heterozygous Individuals, and q 2 =Homozygous Recessive Individuals.

5. Example 1  A population of velociraptors has two alleles for color, the dominant allele is for purple scales, while the recessive allele is for green scales.  If the purple allele has a frequency of.3, what is the frequency of the green scale allele?  p+q=1p=.3.3+q=1 q=1-.3 q=.7  Thus, the frequency of the green allele is.7

6. Example 2  In a population of sweaters, one allele codes for stripes, while the other allele codes for a plaid pattern.  The plaid allele is dominant, with a frequency of.8  What is the frequency of the recessive genotype? (striped sweaters)  If p=.8, then q=.2  The frequency of the Recessive Genotype=q 2 .2 2 =.04, thus the frequency of the recessive genotype is.04

7. Example 3  In a population of horses, there are brown horses and black horses. If the brown allele is recessive with an allelic frequency of.7, what is the frequency of the black phenotype?  If q=.7, then we can calculate that p=.3  ‘p 2 ’ gives us the Homozygous Dominant genotype and Dominant phenotype, but ‘2pq’ also displays the Dominant genotype despite being Heterozygous.  p 2 =.3 3 =.092pq=2×.3×.7=.42  p 2 +2pq=.09+.42=.51  Black Colored Phenotype

8. Switching it Up  So far, the examples have been used to calculate genotype frequencies based on allele frequencies.  In real life scenarios, often only the phenotypes may be observed, and we can work backwards to calculate allelic frequencies  These methods are often used to estimate percentages of the population carrying alleles for inherited diseases

9. Example 4  In a population of cats, brown eyes are dominant and blue are recessive. 36% of the cats in the population display blue eyes  What are the allelic frequencies within the population?  36% (.36) represents the Homozygous Recessive frequency or q 2. To find q, we take the square root of.36  √.36 =.6 if q (recessive frequency)=.6, then p must =.4 (remember, p+q=1

10. Example 5  In a population of lab mice, brown fur is dominant, while white is recessive. 57.75% of the mice are brown.  What are the allelic frequencies within the population?  If.5775 = the frequency of the dominant phenotype (p 2 +2pq) then we can substitute this into the genotypic frequency equation, resulting in.5775+q 2 =1  Subtracting, we find q 2 =.4225  √q 2 =√.4225, q=.65  The allelic frequency of white fur is.65, thus the frequency of the allele for brown fur is.35

11. You’re Now a Hardy-Weinberg Expert  Remember…the Hardy-Weinberg Theorem describes a hypothetical population that is not evolving, while in real populations allele and genotype frequencies change over time  Departure from the strict Hardy-Weinberg conditions often causes evolution  However, many populations evolve so slowly that for the most part they display near-equilibrium. In these cases, the Theorem may be applied.