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Population and Community
Dynamics
The Hardy-Weinberg
Principle
Key Terms
● Population: same species, same place, same time
● Gene: unit of heredity. Controls the expression of a
trait. Can be passed to offspring.
● Allele: different forms of a gene
● Gene pool: sum of all alleles for all the genes in a
population (sum of all the genetic variation)
Gene Pools Evolve
● All individuals of same species have common genome
(except sex chromosomes)
- different genotypes and environmental influences result in
different phenotypes that are acted on by natural selection
● Larger genomes = greater potential genetic diversity
● Greater number of different alleles = greater genetic
diversity
- sexual reproduction: recombination of parent alleles
● Gene Pool: all genes that occur in a population
- maintains continuity of traits from generation to
generation
- some gene frequencies remain the same over time, but
others can change
Frequencies
1. Genotype Frequency
● Proportion of population with a particular genotype
● Decimal (or percentage)
● Ex. 37/55 goldfish have GG colour genotype.
Genotype frequency of GG = 0.67
2. Phenotype Frequency
● Proportion of a population with a particular phenotype
● Decimal (or percentage)
● Ex. 50/55 goldfish are gold colour
Phenotype frequency of gold = 0.91
3. Allele Frequency
● Rate a particular allele occurs in a population
● Total number of alleles in a population is twice the
number of individuals (each individual has 2 copies of
a gene)
● Ex. 37GG, 13Gg, 5gg
Allele frequency of g =
13 + 5 + 5 = 23/100 = 0.23
By combining Darwin’s theory of evolution with
Mendel’s understanding of inheritance, scientists were
able to determine that evolution occurs when there are
genetic changes in a population over time.
Gene Pools Evolve
● Evolution: sum total of the genetically
inherited changes in the individuals who
are members of a population’s gene pool
- felt by individuals, but whole population
evolves
● Example: trait that is determined by the
inheritance of a gene with 2 alleles, B and
b
- if parent generation has 92% B and 8%
b, and their offspring collectively have
90% B and 10% b.....
- entire population’s gene pool has
evolved
- higher b allele frequency
Hardy-Weinberg Principle
● Quantify a gene pool: measure each allele frequency
● Changes can be measured by looking for changes in allele
frequencies
● Only one allele? Fixed frequency of 100%
● Questions of allele frequencies being constant or
changing....
- Reginald Punnett posed these questions to
mathematician Godfrey Hardy in 1908, wrote solution on
a napkin
- Wilhelm Weinberg, German physician independently
came to same results
● Hardy-Weinberg Principle: mathematical relationship
showing that allele frequencies will not change from
generation to generation as long as certain conditions are
met
Conditions of Hardy-Weinberg Principle
● Allele frequencies in a population will not change from
generation to generation IF
1.
2.
3.
4.
5.
population is infinitely large (chance events don’t alter
allele frequencies)
no migration in or out of population
no mutations occur
no natural selection occurs
mating is random
● Basically: No mechanisms of evolution are acting on the
population
● Highly unlikely that any of these conditions will happen in
the real world – evolution inevitable result
Hardy-Weinberg Principle
● For gene with only 2 alleles:
● If p = frequency of dominant allele and q = frequency of
recessive, then
●
●
●
●
p+q=1
p2 = frequency of genotype AA
2pq = frequency of genotype Aa
q2 = frequency of genotype aa
Equation gives expected genotype frequencies of the
population, when all conditions are met
p2 + 2pq +q2 = 1
Frequency of: Homozygous + heterozygous + homozygous = all individuals
dominant
recessive
Applying the Principle
● Moth Population: If mating is random, 80% gametes
●
●
●
bear A allele, 20% gametes bear a allele
Next generation.....
(0.80)2 + 2(0.80)(0.20) + (0.20)2 = 1
0.64 + 0.32 + 0.04 = 1
Frequency of AA is 0.64, Aa is 0.32, aa is 0.04
- same as PARENTS
If random mating continues, allele frequencies are
likely to remain constant from generation to generation
Example 1
● Consider a situation in which one gene has two alleles, A and a.
The possible genotypes that could be found in a large
population will be AA, Aa and aa. The dominant allele A has
a frequency of 0.7.
a) What is the frequency of the recessive allele, a?
b)
Use a Punnett square to determine the expected frequencies
of the 3 possible genotypes.
Example 1 Cont.
Now use the Hardy-Weinberg Principle to determine the
expected frequencies of the 3 possible genotypes.
c)
d)
Given the distribution of the genotypes, predict the
frequency of the A and a alleles in the population.
Example 1 Cont.
● Because the allele frequencies are the same in the original
gametes, identical results will be obtained generation after
generation.
● However, in nature, a population rarely meets the ideal
conditions for genetic equilibrium, but the principle allows
us to make predictions about populations that are NOT
EVOLVING.
Example 2
● Suppose a recessive genetic disorder occurs in 9% of the
population. Determine what percentage of the population is
heterozygous, or “carriers” of the allele for the disorder, but
do not have the disorder.
Make sure you check your solution –
is it logical? Does everything add up
to 1?
Genetic Equilibrium
● Aka Hardy-Weinberg Equilibrium
● Allele frequencies stay constant over time – the
population is not evolving
● Microevolution is the gradual change in allele
frequencies in a population ex. DDT resistant
mosquitoes
● We can use the HW Equation to study co-dominant
alleles, incomplete dominant alleles, and multiple
alleles. The total of all alleles is always 1.
● Sometimes, we will take DNA samples from individuals
to determine allele frequencies and then apply the
sample data to the population.