 Read Chapter 6 of text

 Brachydachtyly displays the classic 3:1 pattern of inheritance (for a cross between heterozygotes) that mendel described.

 In the early 1900’s there was confusion about how such simple patterns of inheritance affected populations.  Why, aren’t 3 of every 4 people brachdactylyous?  Why don’t dominant alleles replace recessive alleles?

 Problem stems from confusing what happens at the individual level with what occurs at the population level.  Individual-level thinking enables us to figure out the result of particular crosses.

 Population level thinking is used to figure out how the genetic characteristics of populations change quantitatively over time.

 Population genetics is the study of the frequency distribution of alleles and genotypes in populations and the causes of allele frequency changes

 Diploid individuals carry two alleles at every locus › Homozygous: alleles are the same › Heterozygous: alleles are different

 Hardy-Weinberg equilibrium model serves as the fundamental null model in population genetics

 The Hardy-Weinberg model examines a situation in which there is one gene with two alleles A 1 and A 2.  There are three possible genotypes A 1 A 1, A 2 A 2,and A 1 A 2

 Hardy and Weinberg used their model to predict what would happen to allele frequencies and genotype frequencies in a population in the absence of any evolutionary forces acting on the population.  Their model produced three important conclusions

 In the absence of evolutionary processes acting on them:  1. The frequencies of the alleles A 1 and A 2 do not change over time.  2. If we know the allele frequencies in a population we can predict the equilibrium genotype frequencies (frequencies of A 1 A 1, A 2 A 2,and A 1 A 2 ).

 3. A gene not initially at H-W equilibrium will reach H-W equilibrium in one generation.

 1. No selection. › If individuals with certain genotypes survived better than others, allele frequencies would change from one generation to the next.

 2. No mutation › If new alleles were produced by mutation or alleles mutated at different rates, allele frequencies would change from one generation to the next.

 3. No migration › Movement of individuals in or out of a population would alter allele and genotype frequencies.

 4. Large population size. › Population is large enough that chance does not affect allele frequencies. › If assumption is violated and by chance some individuals contributed more alleles than others to next generation allele frequencies might change. This mechanism of allele frequency change is called Genetic Drift.

 5. Individuals select mates at random. › Individuals do not prefer to mate with individuals of a certain genotype. › If this assumption is violated allele frequencies will not change, but genotype frequencies might.

 Assume two alleles A 1 and A 2 with known frequencies (e.g. A 1 = 0.6, A 2 = 0.4.)  Only two alleles in population so their allele frequencies add up to 1.

 Can predict frequencies of genotypes in next generation using allele frequencies.  Possible genotypes: A 1 A 1, A 1 A 2 and A 2 A 2

 Assume alleles A 1 and A 2 enter eggs and sperm in proportion to their frequency in population (i.e. 0.6 and 0.4)  Assume sperm and eggs meet at random (one big gene pool).

 Then we can calculate genotype frequencies.  A 1 A 1 : To produce an A 1 A 1 individual, egg and sperm must each contain an A 1 allele.  This probability is 0.6 x 0.6 or 0.36 (probability sperm contains A 1 times probability egg contains A 1 ).

 Similarly, we can calculate frequency of A 2 A 2.  0.4 x 04 = 0.16.

 Probability of A 1 A 2 is given by probability sperm contains A 1 (0.6) times probability egg contains A 2 (0.4). 0.6 x 04 = 0.24.

 But, there’s a second way to produce an A 1 A 2 individual (egg contains A 1 and sperm contains A 2 ). Same probability as before: 0.6 x 0.4=  Overall probability of A 1 A 2 = = 0.48.

 Genotypes in next generation:  A 1 A 1 = 0.36  A 1 A 2 = 0.48  A 2 A 2 = 0.16  Adds up to one.

 General formula for Hardy-Weinberg.  Let p= frequency of allele A 1 and q = frequency of allele A 2.  p 2 + 2pq + q 2 = 1.

 If three alleles with frequencies P 1, P 2 and P 3 such that P 1 + P 2 + P 3 = 1  Then genotype frequencies given by:  P P P P 1 P 2 + 2P 1 P 3 + 2P 2 P 3

 1. Allele frequencies in a population will not change from one generation to the next just as a result of assortment of alleles and zygote formation.

 2. If the allele frequencies in a gene pool with two alleles are given by p and q, the genotype frequencies will be given by p 2, 2pq, and q 2.

 3. The frequencies of the different genotypes are a function of the frequencies of the underlying alleles.  The closer the allele frequencies are to 0.5, the greater the frequency of heterozygotes.

 You need to be able to work with the Hardy-Weinberg equation.  For example, if 9 of 100 individuals in a population suffer from a homozygous recessive disorder can you calculate the frequency of the disease causing allele? Can you calculate how many heterozygotes are in the population?

 p 2 + 2pq + q 2 = 1. The terms in the equation represent the frequencies of individual genotypes.  P and q are allele frequencies. It is vital that you understand this difference.

 9 of 100 (frequency = 0.09) of individuals are homozygotes. What term in the H-W equation is that equal to?

 It’s q 2.  If q 2 = 0.09, what’s q? Get square root of q 2, which is 0.3.  If q=0.3 then p=0.7. Now plug p and q into equation to calculate frequencies of other genotypes.

 p 2 = (0.7)(0.7) = 0.49  2pq = 2 (0.3)(0.7) = 0.42  Number of heterozygotes = 0.42 times population size = (0.42)(100) = 42.

 There are three alleles in a population A 1, A 2 and A 3 whose frequencies respectively are 0.2, 0.2 and 0.6 and there are 100 individuals in the population.  How many A 1 A 2 heterozygotes will there be in the population?

 Just use the formulae P 1 + P 2 + P 3 = 1 and P P P P 1 P 2 + 2P 1 P 3 + 2P 2 P 3 = 1 Then substitute in the appropriate values for the appropriate term 2P 1 P 2 = 2(0.2)(0.2) = 0.08 or 8 people out of 100.

 Hardy Weinberg equilibrium principle identifies the forces that can cause evolution.  If a population is not in H-W equilibrium then one or more of the five assumptions is being violated.