Transcript Population Genetics 1

Population Genetics 1
• Chapter 23 in Purves 7th edition, or more
detail in Chapter 15 of “Genetics” by Hartl
& Jones (in library)
• Evolution is a change in genetic
composition of a population - i.e. change in
the relative frequencies of alleles of genes
• The simplest way to describe a population is
by the allele frequencies of all the genes
Populations and Gene Pools
• A population is a group of potentially
interbreeding organisms of same species
living in a prescribed geographical area
• Populations may have “structure”, i.e. groups
(sub-populations) whose members are more
likely to breed with each other, e.g. because
of geography or culture
• The gene pool is the sum total of all alleles in
the population (Purves fig 23.3)
Basic ideas from Darwin
• Variation: individuals are not all the same (Fig
21.5 in Purves shows how artificial selection
reveals the genetic variation in a population)
• Heredity: offspring resemble parents more than
unrelated individuals
• Selection: if resources are limited, not all
offspring survive - some forms are more likely to
survive and reproduce than others (fitness)
• But there are also other forces that affect genes in
populations
Measurement of Genetic Variation
• Cannot usually look at every single individual in a
population - take a sample (the bigger the sample,
the smaller the error)
• For a gene, the frequency of each allele is between 0
and 1, and the sum of all allele frequencies for the
gene is 1
• Allele frequency is defined as:
Number of copies of allele in population
Sum of all alleles in population*
• * Denominator is 2n for an autosomal gene in a
population of n diploid organisms
Calculating allele frequencies
• For a gene with 2 alleles, A and a:
NAA is the number of AA homozygotes
NAa is the number of heterozygotes
Naa is the number of aa homozygotes
• NAA + NAa + Naa = N, number of individuals in
population
• Let p = frequency of allele A, and q = frequency
of a. Then:
• p = (2NAA + NAa) / 2N
• q = (2Naa + NAa) / 2N
Examples
• Fig 23.6 in Purves
Hardy-Weinberg (1)
• A population that is not changing genetically is in
Hardy-Weinberg equilibrium (after 2 scientists in
1908), if these 5 assumptions are correct:
–
–
–
–
–
Random mating
Large N (population size)
No migration between populations
Negligible mutation
Natural selection does not affect alleles being
considered
Hardy-Weinberg (2)
• If the assumptions are true, it follows that:
• Allele frequencies remain constant from one
generation to the next
• After one (or more) generations of random
mating, the genotype frequencies (for a 2allele gene with allele frequencies p,q) are in
the proportions:
p2 (AA), 2pq (Aa), q2 (aa)
• p2 + 2pq + q2 = (p + q)2 = (1)2 = 1
Hardy-Weinberg (3)
• Purves Fig 23.7 shows why population will be in
H-W equilibrium after one generation of breeding
• This is another example in genetics of
multiplication of probabilities of independent
events, and addition of probabilities where there is
>1 way for something to happen (heterozygotes)
• It also shows why dominant alleles do not “take
over” from recessive ones
Allele and Genotype Frequencies
in H-W equilibrium
p2 (AA)
2pq (Aa)
q2 (aa)
Importance of Hardy-Weinberg
• Without H-W, we could not tell that
evolution is occurring
• The way in which a population deviates
from H-W tells us something about what
types of evolutionary force are operating
• We can test if a population is in H-W
equilibrium with the c2 statistical test (3rd
practical)
The
2
c
test
• Compares the observed frequencies of individuals in
different classes to the expected frequencies, to see if there
is a statistically-significant difference
• For example, p = 0.5, q = 0.5, N = 200
• Expect p2, 2pq, q2 of AA, Aa, aa (50, 100, 50)
• Observe 60, 80 and 60
• c2 = sum over all classes of (Obs-Exp)2/Exp
= (60-50)2/50 + (80-100)2/100 + (60-50)2/50 = 8.0
• This exceeds the value in the c2 table for 1 degree of
freedom, p = 0.05, so we conclude that the probability that
the population is in H-W equilibrium is less than 0.05