The Hardy-Weinberg Equation
- p2 (
AA ) + 2pq (
Aa ) + q2 (
aa ) = 1
is incredibly useful because it describes mathematically the genetic product of a population in which all individuals are equally likely to survive and to produce surviving offspring. Specifically, it calculates the genotype frequencies that will be observed in a population that is not evolving. This information functions as a null hypothesis or standard against which we can judge if a population is evolving.
Summarizing the concepts on which hardy-weinberg is based
To understand how Hardy-Weinberg enables this, let’s review what we have learned:
- When agents of evolution favor the survival and/or reproduction of some individuals (and their alleles) over others, the population’s allele frequencies change over time and the population is said to evolve.
- When all individuals are equally likely to survive and to produce offspring that survive, allele frequencies do not change from one generation to the next because alleles end up in fertilization events, and thus the offspring generation, in proportion to their relative commonness (frequency) in the parental generation.
- When alleles end up in fertilization events (and the offspring generation) in proportion to their relative commonness in the parental generation,
genotype frequencies of the offspring generation can be determined from the
allele frequencies of the parental generation using simple rules for calculating the probability of an event composed to two independent events.
- Specifically, these rules say that, if we let p equal the frequency of the
A allele and q the frequency of the
a allele in the parental generation, and thus p equals the probability of picking an
A allele and q an
a allele from the parental generation, the:
- frequency of the
AA genotype in the offspring generation is equal to the probability of picking two
A alleles from the parent generation or p x p = p2
- frequency of the
aa genotype in the offspring generation is equal to the probability of picking two
a alleles from the parent generation or q x q = q2
- frequency of the
Aa genotype in the offspring generation is equal to two times the probability of picking an
A and
a allele from the parent generation or 2 x (p x q) = 2pq
- This relationship, which is often written as p2 (
AA ) + 2pq (
Aa ) + q2 (
aa ) = 1, is known as the Hardy-Weinberg equation. It tells us what genotype frequencies (p2, 2pq, q2) we will see in a population that is not evolving based on parental allele frequencies, p and q.
Finally, please recall that the Hardy-Weinberg equation only applies to a locus for which there are two alleles in a population. And that, although some individuals in the population will die or fail to reproduce, population allele frequencies will be maintained because these losses will remove alleles in proportion to their commonness in the population.
So what is the power of these concepts?
Notice that these principles apply to the production of a
single generation. Thus, if an offspring generation is the product of a parental generation that was not subject to an agent of evolution, then the offspring generation must have the following two properties.