Click HERE for your print-friendly copy of the notes. Don't print the big font pages!

The Five Criteria for Hardy-Weinberg Equilibrium

What does each of the five HW assumptions mean? Let's consider each in turn.

Criterion 1. No Mutation

If a gene locus segregating only two alleles undergoes a mutation that's passed on to an individual in the population, the relative allele frequencies in that population have, obviously, changed. (A new one has been added.)

Whether the mutant allele remains in the population depends on many things, including random sampling error (genetic drift) and natural selection. But mutation is the raw material of evolution. Without it, there is no genetic variability upon which other forces of evolution can act.

Several models have been proposed to explain how new mutations might take up residence in a population.

The Classical Model states that within any population, one allele functions better than the others, and natural selection will drive the population to a higher proportion of this allele.

  • Mutant forms of each of these wild types exist, and may or may not confer a selective advantage in wild populations, depending on circumstances.
  • Tigers: white, not to be confused with albino
  • Leopards: wild type and melanistic (The fabled "black panther" is nothing more than a melanistic leopard or jaguar.) ...and more than we have time to look at here.

  • Mutation is the only way new genetic material can arise in a population
  • Mutation of a wild type allele to a mutant form is known as a forward mutation.
  • Mutations also can change back to wild type from one generation to the next. This is known as a reverse mutation or reversion mutation.
  • The larger the population, the more likely it is that mutations will occur.
  • Non-lethal mutations that have a high rate of occurrence can change allele frequencies over time.
  • When forward and reverse mutations (at a particular locus) occur at the same rate, mutational equilibrium has been reached at that locus.

    Mutations may cause phenotypic traits that may be adaptive, maladaptive, or neutral in the particular environment in which they occur. No one really knows for sure yet just how often mutations fall into any of those three categories. It depends on environmental (and organismal) context. Once in a while, though, a new allele can confer a selective advantage to those that carry it.
    In this case, the new phenotype's genetic representation may increase until it becomes the new wild type.

    The Classical Model alone does not explain the high degree of heterozygosity and multiple loci seen in so many wild populations. Additional models flesh out the story.

  • The Balance Model (first proposed by Theodosius Dobzhansky in 1970 in Genetics of the Evolutionary Process) states that balancing selection may occur in some cases, preventing one allele from completely displacing all other alleles.

    Balancing selection can result in balanced polymorphism, the maintenance of stable frequencies of two or more phenotypic forms in a single population. Two of the best known mechanisms by which Balancing Selection operates are

  • The Neutral Mutation Model was first proposed by Mootoo Kimura in 1968.

    The author noted that changes in hemoglobin sequences proceeded at a regular rate, and might not have had any consequences with respect to natural selection. These neutral mutations simply "went along for the ride" as other forces shaped the organism at other loci.

    This was the first time that anyone had proposed that evolution proceeds largely via the accumulation of neutral mutations and random changes in allele frequencies. In natural populations, fluctuating environmental conditions may eventually change the nature of a neutral mutation, making it adaptive or maladaptive.

    Criterion 2. Infinitely Large Population Size

  • An infinitely large population can produce an infinite number of genetically unique gametes.

  • In reality, an infinitely large population is extremely rare to non-existent. This means that in natural populations, this criterion is almost never met, and such populations may undergo evolution due to random sampling error. (i.e., the gametes that are passed on to the next generation may not carry the same proportions of alleles found in the entire population.)

  • Changes in relative allele frequency that are due only to random sampling error are known as genetic drift.

  • The smaller the population, the smaller the subset of potentially successful gametes, and the more likely that genetic drift will occur.

  • Genetic drift can happen in two ways:

    Here's an overview of genetic drift and its consequences. Be sure to read the links about

    for greater understanding of this phenomenon, a major source of the genetic change leading to microevolution and, ultimately, macroevolution.

    Criterion 3. Random Mating

    This means that the alleles at a given gene locus combine with the frequency predicted by their relative frequency in the population.

    The probability of two genotypes mating is the product of the frequencies of the genotypes in the population.

    Let's create an imaginary population in which a dominant allele (A) represents 60% (0.6) of the alleles and a recessive allele makes up the remaining 40% (0.6) at a given gene locus.

    There are two types of assortative mating: Example of non-random mating: Inbreeding vs. Outbreeding

  • inbreeding occurs in a population when matings between closely related individuals occurs more frequently than would be predicted by their relative frequency in the population. That is, individuals preferentially mate with relatives.

  • outbreeding occurs in a population when matings between unrelated individuals occurs more frequently than would be predicted by their relative frequencies in the population. That is, individuals preferentially mate with non-relatives.

    Inbreeding can change allele frequencies, as can be seen in this diagram of a brother/sister mating

    .

  • The gene in question is Gene A, and it has four alleles (A1, A2, A3 and A4)
  • In the diagram, the top generation represents unrelated parents (Bob and Alice) who are both heterozygous for Gene A. Bob is A1A2, and Alice is A3A4.
  • Since Bob has two alleles, the chance he will contribute the A1 to his offspring is 1/2 (0.5).
  • The chance that Alice will contribute either of her alleles to her offspring is also 1/2 (0.5).
  • In this particular example, Bob has contributed the A1 allele to both his offspring, Jethro and Ellie May. The likelihood of this occurrence can be calculated with the Product Rule (The combined probability of any two independent events occurring together is equal to the product of their individual probabilities.)

    Hence, the chance that both Jethro and Ellie May could both inherit the A1 allele from Bob is 0.5 x 0.5, or 0.25 (25%).

  • If Jethro and Ellie May have both inherited the A1 allele, then the chance of their passing it on to an offspring is again the combined probability of their having inherited the A1 allele...

    0.25 x 0.25

    or 6.25%.

  • If this is a relatively rare allele, that occurs in, say, only 1/1000 of the members of the population, then the likelihood of a Jethro or Ellie May offspring inheriting two copies of A1 if either mated with a non-relative would be

    0.25 x 0.001

    or a mere 0.025%.

    You can see that there is a much greater likelihood of the A1 allele showing up in homozygous form if there is inbreeding. If the allele happens to be deleterious...well...you can see why there are taboos in human society against marrying your first cousin.

    The inbreeding coefficient (F) is the probability that an individual homozygous for a particular gene locus has inherited both alleles from the same ancestor. You'll learn more about this when you take Genetics.

    Note that small, isolated populations will much more quickly come to consist of members who are related to one another than a very large population. Small populations are much more likely to become fixed at only one allele for a given locus, losing the other(s) simply due to random sampling error.

    Small populations and inbreeding can greatly increase the rate of evolution at any given gene locus.

    Criterion 4. No Migration

    Loss or addition of alleles from immigration or emigration will change the allele frequency in the population under study.

    Gene Flow is the process by which movement of genes takes place between populations or demes.

    Hybrids: Evolution in Flux
  • A hybrid zone is an area of secondary contact, where there may be limited hybridization between two closely related species that have come into contact after having been separated and subject to some degree of reproductive isolation.
  • Introgression is the introduction of alleles from one species' gene pool into another (closely related) species, due to limited hybridization.

    Which brings us to The Tale of Bambi and That Other Guy:

    Why do some species that share many genes remain distinct in appearance, behavior and reproduction, whereas others that have been separate for millions of years are still able to hybridize? It's one of life's little mysteries.

    Criterion 5. No Natural Selection

    No genotype confers a reproductive advantage over another genotype. This includes several "subsets" of natural selection, such as sexual selection.

    Recall the tenets of Evolution by Natural Selection:

    Evolutionary fitness is defined by the environment. A phenotype conferring fitness in a particular environment could be a liability if the environment changes.

    Comparative Evolutionary Fitness between two competing genotypes can be quantified.

    Conversely, the selection coefficient (s) is a measure of selective pressure against a particular genotype, relative to the other genotypes in the population. It is calculated as 1 - W.

    In our example, for each of our genotypes:

    Components of Fitness: Selection at Different Levels

    Care must be taken to carefully assign "fitness". An organism that produces the most eggs won't necessarily have the most offspring reared to reproductive maturity.

    Natural selection can operate at any stage of an organism's life cycle, and there are ways to assess fitness at those different stages.

    The Effects of Natural Selection

    At the start of a "selection cycle" the population is usually made up of individuals expressing a particular trait along a continuum, which can be expressed as a bell-shaped curve

    stabilizing selection: selective forces at work on a population favor greatest reproduction by individuals exhibiting the average state of a particular character. In this instance, the composition of the population doesn't change.

    directional selection: the individuals at one extreme or the other of the bell shaped curve have a reproductive advantage over the rest.

    (e.g., in drought years in the Galapagos, insects become scarce and seeds relatively abundant. Finches with deep, thick bills have an advantage in that they can more effectively crack seeds. The narrow-billed birds die out or have lower reproductive success because of the scarcity of food.)

    disruptive (= diversifying) selection: individuals at the average point on the curve are at a selective disadvantage; individuals with either extreme have a reproductive advantage.

    Example: Geospiza conirostris (Galapagos Cactus Finch)

    In drought periods, the birds don't have a wide variety of foods, and must resort to one of several feeding modes:

    In wet years, there's plenty of food everywhere, and birds with intermediate bill sizes can survive. But in drought, only the birds with one of the three bill sizes above can feed effectively. Disruptive selection ensues, and the population eventually is composed of individuals with

    1. deep, strong bills
    2. large, heavy bills
    3. very long bills.
    This production of distinct phenotypes in a population due to selective pressure is known as character displacement, a divergence of an equivalent character in a sympatric species (i.e, living in a single geographic area) due to competition for a resource (in this case, food.).

    Summing up...

    Organic Evolution is change in the genetic composition of a population due to genetic drift, non-random mating, mutation, and natural selection.

    microevolution: genetic change in a species over time without speciation

    macroevolution: the genesis of two reproductively isolated taxa from a single ancestral taxon.

    Some economically important examples of microevolution (many due to anthropogenic factors) are occurring all around us, as we speak

    So...you might ask, why can't larger organisms evolve resistance to poisons and other selective factors. (Why couldn't birds, say, "evolve" an immunity to DDT, which causes them to lay dangerously thin-shelled eggs?