Happy Sci-Day, everyone! This week, we are continuing our Crash Course series, and this week's topic will be Hardy-Weinberg equilibrium!
Hardy-Weinberg equilibrium essentially is when the various factors that contribute to biological evolution "balance out". Keep in mind that this equilibrium is only related to the allele of interest - if the allele is in Hardy-Weinberg equilibrium, that simply means that the gene is not undergoing biological evolution (ie allele frequencies not changing significantly in frequency in the population), but it does not mean the SPECIES is not undergoing biological evolution.
Hardy-Weinberg equilibrium is the null hypothesis when investigating population genetics - in other words, it is assumed initially that the population is in HWE with respect to that allele, and the data is collected which may either support or refute that hypothesis. Null hypotheses are critical for any scientific research, as they provide a relatively decent framework for keeping things objective. If the null hypothesis is not supported, then alternative hypotheses are proposed to explain the data.
Anyways, what is important to know about Hardy-Weinberg Equilibrium is that the factors that may cause violations. These include asexual reproduction, non-random mating, small population size, migration (also known as gene flow), mutation, and selection. If any of these are happening to a great enough extent, an allele will not be in Hardy-Weinberg Equilibrium.
The way to test to see if a population is in Hardy-Weinberg equilibrium is relatively straightforward. The first step is to genotype a large sample of animals in the population of interest - for a gene with alleles A and a, you would record how many AA individuals there were, how many Aa individuals there were, and how many aa individuals there were. The next step is to calculate the allele frequencies. To show how this works, let's consider a sample of 500 T. rex, with 300 AA, 75 Aa, and 175aa. To calculate the frequency of A, we add up two times the number of AA homozygotes (600) and the number of heterozygotes (75), and divide that by two times the number of individuals in the entire sample (1000). We multiply the total number by 2 because each individual has two copies of the gene, so the total number of alleles in the population is twice the number of individuals. This is also why we don't multiply the number of heterozygotes by 2 - they only have a single copy of the allele we're looking at. Anyways, the resulting frequency of the A allele is 0.675. Since the frequencies of the two alleles have to add up to 1, we can simply subtract .675 from 1 to get the frequency of a, which is .325.
Now, we have to figure out the EXPECTED genotype frequencies under HWE. This is easy to do. For the expected frequency of AA, simply square the frequency of the A allele. For Aa, it's 2(frequency of A)(frequency of a). For the expected frequency of aa, simply square the frequency of a. Now, we can use this to calculate what the EXPECTED genotype counts would be if the population were in HWE. To do this, we simply multiply the frequency of each genotype by the total number of individuals in the sample. For our example above, the expected counts would be 227.813AA, 219.375Aa, and 52.813aa.
The last step is to test whether these deviations are statistically significant. To do this, we conduct a test called the chi squared test. This, too, is relatively simple math. For each genotype, you do this:
((Observed individuals - expected individuals)^2)/Expected individuals. In our example, doing this with AA would be ((300 - 227.813)^2)/227.813), yielding a value of around 22. In order to get chi squared, you have to do this same calculation for each genotype, and then sum them all up. Once you have a chi squared value, you check it with a table, and see where your chi squared value is mapped according to how likely those results would be based on the expectations. If the probability is less than 0.05, it is considered statistically significant. In our case, the probability is less than 0.001, which is VERY significant!
The important thing about a violation of HWE is that it means there is something that is causing this deviation, which may be selection, migration, etc., which can tell you more about what is happening in the population. While this is not possible to do with prehistoric animals currently, it is possible that Dinosaur Battlegrounds could provide hypothetical simulations to conduct investigations of this sort, that might give some insight into population dynamics in prehistoric creatures.
Well, I hope this has taught you something about Hardy-Weinberg equilibrium! It's a very important concept to understand in evolutionary biology, so make sure you understand it! :)
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