1. Measuring Evolution of Populations

2. 5 Agents of evolutionary change
Mutation
Gene Flow
Non-random mating
Genetic Drift
Selection

3. 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

4. Evolution of populations
Evolution = change in allele frequencies in a population
hypothetical: what conditions would cause allele frequencies to not change?
non-evolving population
REMOVE all agents of evolutionary change
very large population size (no genetic drift)
no migration (no gene flow in or out)
no mutation (no genetic change)
random mating (no sexual selection)
no natural selection (everyone is equally fit)

5. Hardy-Weinberg Principle
original proportions of genotypes in a population will remain constant from generation to generation
Sexual reproduction (meiosis and fertilization) alone will not change allelic (genotypic) proportions.

6. Hardy-Weinberg equilibrium
Hypothetical, non-evolving population
preserves allele frequencies
Serves as a model (null hypothesis)
natural populations rarely in H-W equilibrium
useful model to measure if forces are acting on a population
measuring evolutionary change
G.H. Hardy
Mathematician
( )
W. Weinberg
Physician
( )

7. Hardy-Weinberg Principle
Necessary assumptions
Allelic frequencies would remain constant if…
population size is very large
random mating
no mutation
no gene input from external sources
no selection occurring

8. Hardy-Weinberg theorem
Counting Alleles
assume 2 alleles = B, b
frequency of dominant allele (B) = p
frequency of recessive allele (b) = q
frequencies must add to 1 (100%), so:
p + q = 1 BB Bb bb

9. Hardy-Weinberg theorem
Counting Individuals
frequency of homozygous dominant: p x p = p2
frequency of homozygous recessive: q x q = q2
frequency of heterozygotes: (p x q) + (q x p) = 2pq
frequencies of all individuals must add to 1 (100%), so:
p2 + 2pq + q2 = 1 BB Bb bb

10. Hardy-Weinberg Principle
Calculate genotype frequencies with a binomial expansion
(p+q)2 = p2 + 2pq + q2
p2 = individuals homozygous for first allele
2pq = individuals heterozygous for alleles
q2 = individuals homozygous for second allele

11. H-W formulas Alleles: p + q = 1 Individuals: p2 + 2pq + q2 = 1 B b BB

12. Hardy-Weinberg Principle
Problem: 100 cats 16 are white 84 are black. What is the frequency of black and white allele in the population?
p2 + 2pq + q2
and
p+q = 1 (always two alleles)
16 cats white = 16bb then (q2 = 0.16)
This we know we can see and count!!!!!
If p + q = 1 then we can calculate p from q2
q = square root of q2 = q = √ q = 0.4
p + q = 1 then p = .6 ( = 1)
P2 = .36
All we need now are those that are heterozygous (2pq) (2 x .6 x .4)=0.48

13. Using Hardy-Weinberg equation
population: 100 cats
84 black, 16 white
How many of each genotype?
q2 (bb): 16/100 = .16
q (b): √.16 = 0.4
p (B): = 0.6
p2=.36
2pq=.48
q2=.16 BB Bb bb
Must assume population is in H-W equilibrium!
What are the genotype frequencies?

14. HARDY-WEINBERG & EVOLUTION
ANOTHER PROBLEM
Fraggles are mythical, mouselike creatures that live beneath flower gardens.
Of the 100 fraggles in a population, 91 have green hair(F) and 9 have grey hair(f).
Assuming genetic equilibrium:
What are the gene frequencies of F and f?
What are the genotypic frequencies?

15. ANSWERS TO PROBLEM Gene frequencies: F = 0.7 and f = 0.3
Genotypic frequencies
FF = 49% or 0.49
Ff = 42% or 0.42
f f = 9% or .09

16. Hardy Weinberg Illustration