# Population Genetics: the Hardy-Weinberg Principle

### Learning Objectives

1. Know and recognize the five assumptions of the Hardy-Weinberg principle
2. Use the gene pool concept and the Hardy-Weinberg principle to determine whether a population is evolving at a locus of interest

### Measuring Evolutionary Change: the Hardy-Weinberg Equilibrium Principle

How would a researcher know if selection or drift or even mutation were altering the allele frequencies for population? In other words, can we use the mechanisms of to detect evolution happening in real populations? To do that we’d need a null expectation or a baseline against which to measure change. We call that baseline the Hardy-Weinberg equilibrium (HWE). Remember that the modern definition of evolution is a change in the allele frequencies in a population. To calculate what the alleles frequencies (p and q in the example below) should be in the absence of any evolution, we need to assume that the population is undergoing no selection, no mutation, no drift, no gene flow, and that individuals are selecting mates at random.
Also recall that each individual is a diploid, carrying two copies (alleles) of each gene. Assume that the entire population only has two variants, or alleles, for a gene for pea color. Individuals that carry at least one Y allele have yellow coloration, while those who carry two copies of the y allele are green. In the figure below, the frequency of the y allele is q, and the frequency of the Y allele is p, and p + q = 1. The Hardy-Weinberg analysis in the lower half of the figure models the result of random mating in the absence of selection, drift, mutation or migration (eg, in the absence of evolution). The progeny generation will have genotype frequencies in the following proportions:

• frequency of YY = p^2
• frequency of Yy = 2pq
• frequency of yy = q^2

If the population is in Hardy-Weinberg equilibrium, two things will be true:

1. allele frequencies will not change from one generation to the next (recall our definition of biological evolution), and
2. the actual genotype frequencies observed in the population will match the above predicted genotypes based on the Hardy-Weinberg Principle.

We can see that this population of pea plants appears to be in H-W equilibrium, because the proportion of YY, Yy, and yy genotypes match the H-W predictions of p^2, 2pq, and q^2, respectively. When populations are in the Hardy-Weinberg equilibrium, the allelic frequency is stable from generation to generation and the genotype frequencies match the Hardy-Weinberg proportions. If the allelic frequency measured in the field differs from the predicted value, scientists can make inferences about what evolutionary forces are at play. (Source: OpenStax Biology)

What about another population of pea plants, composed of 300 YY plants, 100 Yy plants, and 100 yy plants? Is this second population in H-W equilibrium?
Below is a Crash Course Biology video on Population Genetics that explains Hardy-Weinberg equilibrium dynamically…using ear wax phenotype in humans.