Hardy-Weinberg Equilibrium

A population that is not evolving is said to be at Hardy-Weinberg equilibrium, named for the mathematician and physician who independently worked it out.

Here is a table from your textbook that summarizes the conditions that a population must meet in order to be considered to be at Hardy-Weinberg equilibrium. The right column demonstrates why each condition needs to be met to avoid evolution - essentially it explains how each of those causes evolution when the criterion is not met.

Again, the utility of this is to establish a null hypothesis - one against which we can compare a real population. So the unrealistic nature of these conditions is acceptable for our purposes.

So what exactly are allele frequencies? Alleles are, of course, versions of a gene that code for a protein. Frequencies in science and math refer to how often something appears in a sample or population. Thus, an allele frequency is simple the proportion of one allele compared to all the alleles for that gene in the population.

Remember that in diploid organisms, each individual will have two alleles, so you will need to account for both of the individual's alleles. For example, a heterozygous individual will contribute one dominant allele (A) and one recessive allele (a), whereas a homozygous dominant individual would contribute two dominant alleles (A).

If we do this for the entire population, we can see what the gene pool contains. A gene pool is essentially the genetic makeup of an entire population. Imagine all those alleles just floating around in a big pool. If most of those alleles are one type, that allele frequency is much higher than the other.

To calculate p and q, you have to consider what information you have about the populations. If you are given genotypes for all the individuals, it is easy: count up the alleles! Every homozygous dominant individual will contribute two dominant alleles to the gene pool; every homozygous recessive individual will contribute two recessive alleles; and every heterozygote will contribute one of each allele.

The total number of alleles should be equal to 2 x N, where N is your population size because each individual has two alleles.

p = # dominant alleles / total number of alleles

q = # recessive alleles / total number of alleles

According to the rules of probability, if two independent events need to occur, we multiply their probabilities to find the probability of both occurring.

So the chances of an individual having the homozygous dominant genotype (C^RC^R) are (0.8)(0.8)=64%

Thus, we would expect a population with these allele frequencies to produce 64% homozygous dominant individuals. Remember that these are expectations, so we can compare the observed data to determine if the population is at Hardy-Weinberg equilibrium or not. If the population is NOT at equilibrium, then it is evolving because the genotypes are not meeting expectations and allele frequencies are changing.

Because p refers to the dominant allele and q to the recessive allele, p² pertains to individuals that have received two dominant alleles and q² to homozygous recessive individuals.

However, heterozygotes can be made in two different ways: the sperm can receive the dominant (80% chance) and the egg recessive (20% chance) OR the sperm can receive the recessive (20% chance) and the egg dominant (80% chance). So the probability of each of these is pq= (0.8)(0.2)=0.16

Because either option results in a heterozygote, we can add their probabilities together according to the rules of probability. The probability for either of these scenarios occurring is therefore pq+pq=2pq.

Essentially, Hardy-Weinberg equilibrium is a null hypothesis that states evolution is not occurring. Then a scientist can collect data and compare the actual data to these expectations and accept or reject the null hypothesis.