Hardy-Weinberg calculations

Evolution & Homeostasis

2011

When we did computer modelling of beetle populations, for a large population it generally reached a stable state with more oranges than red & yellow

Why?

Why don’t recessive phenotypes disappear from a population over time?

Hardy-Weinberg Equilibrium

Populations that show no phenotypic change over many generations are stable. The frequency of phenotypes is stable.This stability over time was described mathematicallyby:

Hardy: an English mathematicianWeinberg: a German physician

Sharks and horseshoe crabs (Limulus) have remained phenotypically stable over many millions of years.

Hardy-Weinberg equationp2 + 2pq + q2 = 1

p2 is the frequency of RR genotype2pq is the frequency of Rr genotypeq2 is the frequency of rr genotype

DeterminingAllele Frequencies

Each individual has 2 alleles for a single gene A, so there are a total of 16 alleles in the population.

To determine the frequencies of alleles in the population, count up the numbers of dominant and recessive alleles.

No. of dominant alleles

Total no. of allelesX 100

aa

Aa

AA

AA

Aa

Aa

Aa

Aa

Aa

The Hardy-Weinberg principle is based on the stipulation that there will be no change in allele frequency of a population over time- genetic equilibrium.

For this to occur, the following conditions must be present:Random matingNo mutationsLarge population sizeNo migrationNo natural selection

If these conditions aren’t met, the principle doesn’t apply and evolution occurs.

NON-RANDOM MATING The result of non-random mating is

that some individuals have more opportunity to mate than others and thus produce more offspring (and more copies of their genes) than others.

Non random mating includes:

Sexual selectionMating with neighbors rather than with distant members of the population.Choosing mates that are most like themselves.

Assortative mating

Random mating

AA

AAAA

aa

AaAa

Aa

aa

Aa

Aa

AA

AAAA

aa

Aa Aa

Aa

aa

Aaaa

MUTATIONS

When a mutation occurs, the allele frequency is changed.

Mutations add to the genetic variability of populations over time and are thus the ultimate source of variation for evolution.

SMALL POPULATION SIZE

In a large population, it is less likely that random fluctuations will change the allele frequencies (genetic drift).

MIGRATION

Migration – the movement of breeding individuals into or out of isolated populations – results in evolutionary change because alleles move with the individuals.

This individual is entering the population and will add its alleles to the gene pool

This individual is leaving the population, removing its alleles from the gene pool

AA

Aa

Aa

Aa

Aa

Aa

Aa

AA

AAAA

AA

aa

aa

aa

AaAa

Aa

Aa

AA

Aa

Aa

AaAA

AA

Immigration/Emigration

Later, one beetle (AA) joins the gene pool, while another (aa) leaves.

NATURAL SELECTION

Natural selection tends to reduce the genetic variability of populations by decreasing the frequency of some phenotypes and increasing the frequency of others.

Three kinds of selection cause changes in the normal distribution of phenotypes in a population. Stabilizing selection Directional selection Disruptive selection

AA

Aa

Aa

Aa

Aa

Aa

Aaaa

aa

Two pale individuals died and therefore their alleles are removed from the gene pool

AA

AAAA

AA

aa

aa

aa

AaAa

Aa

Aa

AA

Aa

Aa

AaAA

Natural selection

Two pale individuals die due to the poor fitness of their phenotype.

SUMMARY

As long as the conditions are met, the population remains stable.

If the Hardy-Weinberg equation doesn’t apply, then the population is changing and evolution occurs.