When a population is in Hardy-Weinberg equilibrium, it is not evolving. Learn how violations of Hardy-Weinberg assumptions lead to evolution.

Key points:

  • When a population is in Hardy-Weinberg equilibrium for a gene, it is not evolving, and allele frequencies will stay the same across generations.
  • There are five basic Hardy-Weinberg assumptions: no mutation, random mating, no gene flow, infinite population size, and no selection.
  • If the assumptions are not met for a gene, the population may evolve for that gene (the gene's allele frequencies may change).
  • Mechanisms of evolution correspond to violations of different Hardy-Weinberg assumptions. They are: mutation, non-random mating, gene flow, finite population size (genetic drift), and natural selection.


In nature, populations are usually evolving. The grass in an open meadow, the wolves in a forest, and even the bacteria in a person's body are all natural populations. And all of these populations are likely to be evolving for at least some of their genes. Evolution is happening right here, right now!
To be clear, that doesn't mean these populations are marching towards some final state of perfection. All evolution means is that a population is changing in its genetic makeup over generations. And the changes may be subtle—for instance, in a wolf population, there might be a shift in the frequency of a gene variant for black rather than gray fur. Sometimes, this type of change is due to natural selection. Other times, it comes from migration of new organisms into the population, or from random events—the evolutionary "luck of the draw."
In this article, we'll examine what it means for a population evolve, see the (rarely met) set of conditions required for a population not to evolve, and explore how failure to meet these conditions does in fact lead to evolution.
If you're new to population genetics, welcome! You may want to start learning with the following videos, which will help you get the most out of this article:

Hardy-Weinberg equilibrium

First, let's see what it looks like when a population is not evolving. If a population is in a state called Hardy-Weinberg equilibrium, the frequencies of alleles, or gene versions, and genotypes, or sets of alleles, in that population will stay the same over generations (and will also satisfy the Hardy-Weinberg equation). Formally, evolution is a change in allele frequencies in a population over time, so a population in Hardy-Weinberg equilibrium is not evolving.
That's a little bit abstract, so let's break it down using an example. Imagine we have a large population of beetles. In fact, just for the heck of it, let's say this population is infinitely large. The beetles of our infinitely large population come in two colors, dark gray and light gray, and their color is determined by the A gene. AA and Aa beetles are dark gray, and aa beetles are light gray.
In our population, let's say that the A allele has a frequency of 0.30.3, while the a allele has a frequency of 0.70.7. If a population is in Hardy-Weinberg equilibrium, allele frequencies will be related to genotype frequencies by a specific mathematical relationship, the Hardy-Weinberg equation. So, we can predict the genotype frequencies we'd expect to see (if the population is in Hardy-Weinberg equilibrium) by plugging in allele frequencies as shown below:
p2^2 + 2pq + q2=1^2 = 1
p = frequency of A, q = frequency of a
Frequency of AA = p2^2 = 0.72^2 = 0.49
Frequency of Aa = 2pq = 2 (0.7)(0.3) = 0.42
Frequency of aa = 0.32^2 = 0.09
Great question! You can learn more in the allele frequency video. Briefly:
  • Allele frequency is the fraction of all the gene copies in a population that a particular allele makes up.
    For instance, to get the frequency of allele A in the population below, we count up all the A alleles. We find 1212 of them (out of the 4040 total alleles in the population). This gives us an allele frequency of 12/40=0.312/40 = 0.3.
  • Genotype frequency is the fraction of individuals in that population that have a particular genotype.
    For instance, to get the frequency of the genotype AA in the population above, we count up all the AA individuals. We find two beetles of this genotype out of 2020 beetles in the population. This gives us a genotype frequency of 2/20=0.12/20 = 0.1.
Let's imagine that these are, in fact, the genotype frequencies we see in our beetle population (9%9\% AA, 42%42\% Aa, 49%49\% aa). Excellent—our beetles appear to be in Hardy-Weinberg equilibrium! Now, let's imagine that the beetles reproduce to make a next generation. What will the allele and genotype frequencies will be in that generation?
To predict this, we need to make a few assumptions:
First, let's assume that none of the genotypes is any better than the others at surviving or getting mates. If this is the case, the frequency of A and a alleles in the pool of gametes (sperm and eggs) that meet to make the next generation will be the same as the overall frequency of each allele in the present generation.
Second, let's assume that the beetles mate randomly (as opposed to, say, black beetles preferring other black beetles). If this is the case, we can think of reproduction as the result of two random events: selection of a sperm from the population's gene pool and selection of an egg from the same gene pool. The probability of getting any offspring genotype is just the probability of getting the egg and sperm combo(s) that produce that genotype.
We can use a modified Punnett square to represent the likelihood of getting different offspring genotypes. Here, we multiply the frequencies of the gametes on the axes to get the probability of the fertilization events in the squares:
As shown above, we'd predict an offspring generation with the exact same genotype frequencies as the parent generation: 9%9\% AA, 42%42\% Aa, and 49%49\% aa. If genotype frequencies have not changed, we also must have the same allele frequencies as in the parent generation: 0.30.3 for A and 0.70.7 for a.
What we've just seen is the essence of Hardy-Weinberg equilibrium. If alleles in the gamete pool exactly mirror those in the parent generation, and if they meet up randomly (in an infinitely large number of events), there is no reason—in fact, no way—for allele and genotype frequencies to change from one generation to the next.
In the absence of other factors, you can imagine this process repeating over and over, generation after generation, keeping allele and genotype frequencies the same. Since evolution is a change in allele frequencies in a population over generations, a population in Hardy-Weinberg equilibrium is, by definition, not evolving.

But is that realistic?

As we mentioned at the beginning of the article, populations are usually not in Hardy-Weinberg equilibrium (at least, not for all of the genes in their genome). Instead, populations tend to evolve: the allele frequencies of at least some of their genes change from one generation to the next.
In fact, population geneticists often check to see if a population is in Hardy-Weinberg equilibrium because they suspect other forces may be at work. If the population’s allele and genotype frequencies are changing over generations (or if the allele and genotype frequencies don't match the predictions of the Hardy-Weinberg equation), the race is on to find out why.

Hardy-Weinberg assumptions and evolution

What causes populations to evolve? In order for a population to be in Hardy-Weinberg equilibrium, or a non-evolving state, it must meet five major assumptions:
  1. No mutation. No new alleles are generated by mutation, nor are genes duplicated or deleted.
  2. Random mating. Organisms mate randomly with each other, with no preference for particular genotypes.
  3. No gene flow. Neither individuals nor their gametes (e.g., windborne pollen) enter or exit the population.
  4. Very large population size. The population should be effectively infinite in size.
  5. No natural selection. All alleles confer equal fitness (make organisms equally likely to survive and reproduce).
    The "big five" assumptions are the ones listed in the main text. However, the basic formulation of Hardy-Weinberg equilibrium also relies on a few other assumptions1^1:
    • Organisms are diploid (have two copies of each gene). Humans and many other animals are diploid, but bacteria, for example, are not. Some plants are diploid, but others are polyploid (have more than two copies of each gene).
    • Organisms reproduce sexually. Bacteria, which divide by binary fission to make clones of themselves, don't fit this criteria. Neither do plants that reproduce clonally (e.g., by dropping chunks of themselves, which take root and develop into new individuals).
    • Populations have non-overlapping generations. That is, generations are cleanly separated in time, and we don't get a population that is part parents and part offspring.
    • Allele and genotype frequencies don't differ between males and females. That is, the basic form of Hardy-Weinberg does not cover sex-linked genes.
    There are modified forms of the Hardy-Weinberg equation to deal with overlapping generations, polyploid organisms, and sex linkage.
    Hardy-Weinberg equilibrium per se doesn't apply to haploid or asexually reproducing organisms, but we can predict that the allele and genotype frequencies in the populations of these organisms would tend to remain stable in the absence of outside forces (since each organism would simply make a genetically identical copy of itself during reproduction).
If any one of these assumptions is not met, the population will not be in Hardy-Weinberg equilibrium. Instead, it may evolve: allele frequencies may change from one generation to the next. Allele and genotype frequencies within a single generation may also fail to satisfy the Hardy-Weinberg equation.

Some genes may satisfy Hardy-Weinberg, while others do not

Note that we can think about Hardy-Weinberg equilibrium in two ways: for just one gene, or for all the genes in the genome.
  • If we look at just one gene, we check whether the above criteria are true for that one gene. For example, we would ask if there were mutations in that gene, or if organisms mated randomly with regards to their genotype for that gene.
  • If we look at all the genes in the genome, the conditions have to be met for every single gene.
While it’s possible that the conditions will be more or less met for a single gene under certain circumstances, it’s very unlikely that they would be met for all the genes in the genome. So, while a population may be in Hardy-Weinberg equilibrium for some genes (not evolving for those genes), it’s unlikely to be in Hardy-Weinberg equilibrium for all of its genes (not evolving at all).

Mechanisms of evolution

Different Hardy-Weinberg assumptions, when violated, correspond to different mechanisms of evolution.
  • Mutation. Although mutation is the original source of all genetic variation, mutation rate for most organisms is pretty low. So, the impact of brand-new mutations on allele frequencies from one generation to the next is usually not large. (However, natural selection acting on the results of a mutation can be a powerful mechanism of evolution!)
  • Non-random mating. In non-random mating, organisms may prefer to mate with others of the same genotype or of different genotypes. Non-random mating won't make allele frequencies in the population change by itself, though it can alter genotype frequencies. This keeps the population from being in Hardy-Weinberg equilibrium, but it’s debatable whether it counts as evolution, since the allele frequencies are staying the same.
  • Gene flow. Gene flow involves the movement of genes into or out of a population, due to either the movement of individual organisms or their gametes (eggs and sperm, e.g., through pollen dispersal by a plant). Organisms and gametes that enter a population may have new alleles, or may bring in existing alleles but in different proportions than those already in the population. Gene flow can be a strong agent of evolution.
  • Non-infinite population size (genetic drift). Genetic drift involves changes in allele frequency due to chance events – literally, "sampling error" in selecting alleles for the next generation. Drift can occur in any population of non-infinite size, but it has a stronger effect on small populations. We will look in detail at genetic drift and the effects of population size.
  • Natural selection. Finally, the most famous mechanism of evolution! Natural selection occurs when one allele (or combination of alleles of different genes) makes an organism more or less fit, that is, able to survive and reproduce in a given environment. If an allele reduces fitness, its frequency will tend to drop from one generation to the next. We will look in detail at different forms of natural selection that occur in populations.
All five of the above mechanisms of evolution may act to some extent in any natural population. In fact, the evolutionary trajectory of a given gene (that is, how its alleles change in frequency in the population across generations) may result from several evolutionary mechanisms acting at once. For instance, one gene’s allele frequencies might be modified by both gene flow and genetic drift. For another gene, mutation may produce a new allele, which is then favored (or disfavored) by natural selection.
This article is licensed under a CC BY-NC-SA 4.0 license.

Works cited:

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  2. McDonald, D. (n.d.). Introduction to population genetics. In Genetic markers. Retrieved from http://www.uwyo.edu/dbmcd/molmark/lect03/lect3.html.


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