Learning Objectives
- Recognize five key assumptions of the Hardy-Weinberg principle, and explain why they are necessary to maintain equilibrium
- Use the gene pool concept and the Hardy-Weinberg principle to determine whether a population is evolving at a locus of interest
- Recognize which mathematical components of the Hardy-Weinberg equations are relevant to determine whether a population is evolving
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 evolution to detect evolution happening in real populations? To do that we’d need a null expectation or a baseline against which to measure change, a baseline in which no evolution at all can occur. 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 in a sexually reproducing population, each individual is a diploid, carrying two copies (alleles) of each gene. Let’s imagine a population of pea plants. Assume that the entire population only has two variants, or alleles, for a gene for yellow or green 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 other words, yellow plants can have genotypes YY or Yy, while green plants have genotype yy. In the figure below, the frequency of the y allele is q, and the frequency of the Y allele is p. Because there are only Y and y alleles, p and q represent the entire population, and p and q sum to 1 (p + q = 1).
The Hardy-Weinberg analysis in the next 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 = p2
- frequency of Yy = 2pq
- frequency of yy = q2
In the Hardy-Weinberg math, there are several places where frequencies sum to 1. For example, p + q = 1 and p2 + 2pq + q2 = 1 as well. These are mathematical realities when you have two or three types of things that represent an entire set. In fact, checking that your frequencies sum to 1 is an important and helpful step to make sure you are working the math correctly when solving these equations.
To use the outcome of these equations to determine if a population is in Hardy-Weinberg equilibrium, two things will be true:
- allele frequencies will not change from one generation to the next (recall our definition of biological evolution), and
- 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 proportions of YY, Yy, and yy observed genotypes given in the parental generation match the H-W predictions of p2, 2pq, and q2, respectively, in the predicted offspring generation.
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? We will work an example in class. Importantly, how would you decide if the frequencies differed in a meaningful way? If the homozygous YY observed frequency was 0.49 and the expected frequencies was 0.47, is that different enough to say the population shows evidence of evolution? You will need a margin of error to make that judgement call. With a less than 2% margin of error, it would be fair to indicate that 0.49 and 0.47 are significantly different. However, given a 2 or 3% margin of error, this population cannot be said to be changing over time. The actual and predicted genotype frequencies are still too similar.
Below is a Crash Course Biology video on Population Genetics that explains Hardy-Weinberg equilibrium dynamically…using the ear wax phenotype in humans.
Recommended Readings
Grant and Grant. 2002. Unpredictable Evolution in a 30-Year Study of Darwin’s Finches. Science 296: 707-711.
UN Sustainable Development Goal
SDG 13: Climate Action – Studying the genetic diversity of organisms can help in identifying species that are resilient to climate change and developing strategies for conservation and management. The application of the Hardy-Weinberg principle to determine whether a population is evolving can be used to study the effects of environmental changes on populations and their genetic diversity, including the resiliency or vulnerability of populations to environmental changes that outpace evolutionary responses.
Hank Green’s videos are always entertaining, but the reason he gives for squaring the equation: p + q = 1 makes no sense to me. Instead, random mating of sexually reproducing individuals should produce homozygotes at frequencies of p^2 and q^2, and heterozygotes at frequencies of 2pq. The sum of these three genotype frequencies should be 1, as shown in the figure table on Hardy-Weinberg analysis.
Text in dark red are edits to match the description to the figure below and to clarify that H-W equilibrium leads to predictions of genotype frequencies that correspond to p^2, 2pq and q^2.