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What does each of these Hardy-Weinberg assumptions mean?

1. INFINITELY LARGE POPULATION SIZE:

In a large population, a huge number of gametes is possible. However, the offspring of that population reflect only a small subset of those possible gametes--and that sample may not be an accurate subset of the population at large.
The smaller the population, the smaller the subset, and the more likely that changes in allele frequency will occur due to random chance. Such changes are referred to as genetic drift

Genetic Drift

  • The zygotes of every generation are a result of fusion of the gametes from the parent generation. (surprise!)

  • Changes in allelic frequencies from one generation to the next that are due only to "inexact" sampling of alleles (i.e., the alleles are not inherited in the same proportions as they are present in the population) are known as SAMPLING ERRORS. (It's a matter of probability once again: Toss a penny twice, and it may not come up heads and tails in your two tosses. But toss it 100 times, and you're more likely to approach the 50:50 ratio expected due to random chance.)

  • Same thing applies when drawing gametes from a gene pool. The smaller the sample size, the more likely that you will have a skewed sample of gamete genotypes (relative to the population at large).

  • If small population size is the only factor affecting H.W. equilibrium, you will see a phenomenon known as RANDOM GENETIC DRIFT: The fluctuation of allele freuqencies from generation to generation. (Example: An Aa individual will sometimes produce an entire cohort carrying only its A allele or only its a allele, simply due to SAMPLING ERROR. Or maybe some kind of catastrophic event will accidentally/randomly kill off all the aa homozygotes in a given generation--again, due to SAMPLING ERROR.)

  • In either of the above scenarios, the surviving offspring generation will not have the same allele frequencies as the parental population.

  • Eventually, one or the other allele will be fixed in the population, and the other will be lost.

  • Once that happens, no further change in population genotype can occur.

    A special case of genetic drift is Founder Effect in which a small sample of breeding individuals from a large population colonizes a new area. This is exemplified by many species on the Galapagos Islands, such as Darwin's finches, and other unique, ENDEMIC Galapagos species similar to mainland species, from which they evolved.

    Not only have these species changed from the mainland species, but they also have become different on each of the Galapagos islands. This is due to a combination of genetic drift AND natural selective forces which are different on each island.

    The evolution of many different species from a single ancestral species in response to different environmental pressures is known as ADAPTIVE RADIATION.

    Bottleneck Effect: basically the opposite of Founder Effect: a large population is essentially wiped out except for a few lucky individual survivors (due to something like a hurricane, volcanic eruption, pathogen invasion or other catastrophe).

    2. RANDOM MATING:

    This means that the two alleles combine with equal frequency.
    Deviation from this probability may be due to choice or to circumstance.
    Assortative mating: Individuals of a particular phenotype are chosen as mates more or less often than expected due to random chance.

  • As you probably already know, systematic inbreeding between close relatives eventually leads to complete homozygosity of the population. The rate at which homozygosity is achieved depends on the degree of relationship.

    3. NO MUTATION:

    This would introduce additional alleles to the population, and would therefore change allele frequencies at a particular locus.

    Classical Model - Within any population, one allele functions better than the others, and natural selection will drive the population to a higher proportion of this "wild type" allele.
    Most mutations are deleterious, but occasionally one will pop up that provides a selective advantage to those that carry it.
    Over time, the new mutation's frequency will increase until it becomes the new "wild type"

    But this doesn't account for the high degree of heterozygosity and multiple loci seen in so many wild populations. A more complex model is required to explain this phenomenon...

    Balance Model - balancing selection occurs at some loci, preventing one allele from completely displacing all other alleles. This occurs in cases of heterozygote superiority (e.g. sickle cell gene).

    Neutral Mutation Model - mutation and random changes in allele frequencies are tolerated by populations in a fluctuating environment, which is sufficient to explain genetic diversity of wild populations.

  • mutation is the only way new genetic material can arise in a population
  • the larger the population, the more likely mutations will occur
  • mutations that have a high rate of occurrence can change allele frequencies over time
  • when forward and reverse mutations of such a change occur at the same rate, mutational equilibrium is reached.

    4. NO MIGRATION:

    Loss or addition of alleles from immigration or emigration will change the allele frequency in the population under study. (See reasons under #1, above)

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

  • A hybrid zone is an area of secondary contact, where there may be limited hybridization between two separate species that have come into contact after having been separated and been subject to some degree of reproductive isolation.
  • Why do some species which share so many genes remain distinct in appearance, behavior and reproduction, while others that have been separate for millions of years are still able to hybridize? WE DON'T KNOW. It's one of life's little mysteries.

    5. NO NATURAL SELECTION:

    This means that all genotypes have an equal probability of leaving offspring to future generations. With respect to the particular trait you are studying (in our old example, the color of wing covers in beetles), AA, Aa, and aa are all equally adaptive genotypes.

    Note that any heritable trait may be:

    The bottom line of evolution by natural selection is that the individuals in a population that leave the most offspring are, by definition, the most "EVOLUTIONARILY FIT." And that term may not be what you've been told it is.

    The Darwinian Revolution:
    On the Origin of Species by Means of Natural Selection

    First, let's discuss Darwin's revolutionary theory: Evolution by means of Natural Selection.

    This type of evolution cannot truly be considered random change. It is, in a sense, "directed" change in gene frequencies due to the interaction of individuals in a population with their environment. Those individuals best suited to exploiting the various factors of the environment will, by definition, leave more genes to succeeding generations than their conspecifics (i.e., members of the same species).

    NOTE THAT THIS DOES NOT MEAN THAT EVOLUTION HAS A "GOAL" OR THAT THERE IS A "MOST HIGHLY EVOLVED SPECIES." Evolution is not directional, nor does it have a value system.

    Bottom line: in the game of natural selection, organisms do not compete against their predators or parasites or pathogens. They compete against EACH OTHER. (Recall the story of the bear!) And the organisms best suited to leave the most offspring in a given environment are the "winners" of that round of natural selection.

    Darwin's four tenets of natural selection can be distilled down into FOUR MAIN IDEAS PERTINENT TO THE POPULATION GENETICIST...

    Evolution via natural selection can occur only if there is variation in the population to begin with.

    NATURAL SELECTION IS PROBABLY THE DOMINANT FORCE IN THE EVOLUTION OF SPECIES. IT IS NOT DIRECTIONAL, AND IT IS NOT AN INEXORABLE MARCH TO AN "IDEAL PINNACLE SPECIES" (which is most often defined as Homo sapiens by people who haven't a clue about biological realities...)


    An individual's DARWINIAN (EVOLUTIONARY) FITNESS is a measure of the proportion of genes it contributes to succeeding generations. Nothing more, nothing less. Evolutionary fitness is defined by the environment. A phenotype which confers great fitness today in a particular environment could be a real liability if the environment changes tomorrow!

  • Fitness = W (= adaptive value of a particular genotype)
  • The genotype that produces the most offspring in a given population is said to have a fitness of 1.0. All other genotypes' W value is measured relative to the most successful genotype's W.
  • If you have three genotypes, AA, AA' and A'A' and over their lifetimes, AA genotypes produce an average of 10 offspring, AA' genotypes produce an average of 5 offspring and A'A' genotypes produce an average of 2 offspring, then...
    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!

    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:
    AA: s = 1 - 1 = 0
    AA': s = 1 - 0.5 = 0.5
    A'A': s = 1 - 0.2 = 0.8
    Selection pressure is highest against the A'A' genotype, relative to the others.

    COMPONENTS OF EVOLUTIONARY FITNESS

    Natural selection can operate at any stage of an organism's life cycle, but usually in one of four ways...

  • zygotic selection (a.k.a. viability selection) - differential survival of genotypes, whether at the prenatal, juvenile or adult stage.
  • gametic selection (a.k.a. segregation distortion or meiotic drive) - the gametes of a heterozygote have differential success because of their genotypes. That is, one allele becomes part of a successful fertilization than the other allele.
  • sexual selection - organisms of a particular genotype mate more often than those of a different genotype (this usually occurs where there is competition for mates; you can no doubt think of plenty of examples.).
  • fecundity selection - one genotype is more fertile than other genotypes.

    EFFECTS OF NATURAL SELECTION

    At the start of a "selection cycle" the population is usually made up of individuals which express 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 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, the resource is food.)

    There are considered to be THREE GENERAL MECHANISMS FOR SPECIATION

  • allopatric speciation
  • parapatric speciation
  • sympatric speciation

    Which can be diagrammed for ease of understanding like SO.

    Now that we've considered all of this, remember that...

  • Genetic variability in a population arises from many alleles at many different loci.

  • Evolution may be occuring with respect to one gene, and not others. And that's how populations change.

  • Ultimately, small changes in allele frequencies over time and non-lethal mutations may accumulate and result in reproductive isolation, and a new species is born!

    THEORIES OF EVOLUTION

    Traditional, classical view: GRADUALISM - Large changes (reproductive isolation and morphological differentiation) occur due to the gradual accumulation of many genetic changes.

    New hypothesis was put forth in 1972 by N. Eldredge and Stephen J. Gould: PUNCTUATED EQULIBRIUM.
    They suggested that major changes occur very suddenly, and are "punctuated" by periods of relatively little change. (examples include polyploidy in plants and Founder Effect in various species). (NOTE: "very suddenly" is a relative term, geologically speaking. This can mean over thousands of generations instead of over millions!)
    Eldredge and Gould suggest that this could explain how "awkward" intermediate forms such as the reptile-->flying bird and the terrestrial tetrapod-->swimming cetacean could have been "skipped".

    Speciation is a temporal process. Populations exist in various stages of this process at any given time, and present day populations are even now undergoing microevolutionary processes which may eventually give rise to macroevolution.

    SOCIOBIOLOGY: What's Genetics Got to Do with It?

    You all owe yourselves the enrichment of reading E. O. Wilson's works. In 1975 he published Sociobiology: The New Synthesis. Now E.O. is nothing if not controversial. And this book has been the center of a great deal of controversy that has spread from biology to many other disciplines, including those in the Humanities and the Social Sciences.

    What could cause such a ruckus? E.O. Wilson has said the unthinkable! The politically incorrect. To wit,

    SOCIAL BEHAVIOR IS UNDER GENETIC CONTROL.

    Now it's amazing that although the book consists of 26 chapters, the only one that makes people blink is the one that applies the theory to Our Favorite Ape: Homo sapiens.

    Back in 1962, V.C. Wynne-Edwards published Animal Dispersion in Relation to Social Behavior, in which he suggested that animals regulated their own population density via behavior called ALTRUISM.

    Altruism - risking the loss of fitness in an act that could improve the fitness of another individual.

    Example: Under crowded conditions, many animals (birds, mammals, etc.) cease to reproduce. Wynne-Edwards interpreted this behavior as altruism: as "good for the species." He suggested a term called "GROUP SELECTION," saying that groups in which individuals exhibited altruistic behaviors that improved the survival of some of its members would have a survival advantage over groups that did NOT have altruistic members.

    This, of course, is hogwash. An individual that gave up its own fitness, martyring itself to the group, would be selected against. And if that "altruistic behavior" were genetically based, it, too, would be a HUGE selective disadvantage to have.

    So how do we explain such phenomena as alarm calls (which call attention to the caller and allow its conspecifics to silently escape) or sterile worker hymenoptera (which never reproduce, but live their entire lives supporting the queen who gave birth to them and who continues to produce more sterile workers)?

    W.D. Hamilton was the first (in 1964) to develop ideas that explained apparently altruistic acts without resorting to the illogical "group selection" idea. Perhaps his most profound concept was that natural selection would favor an allele that promoted altruistic behavior toward relatives, since relatives share the alleles of the altruistic organism. By being altruistic to a relative, you are actually promoting some of your alleles' being passed on to future generations.

    INCLUSIVE FITNESS, INDIVIDUAL FITNESS AND KIN SELECTION, OH MY.

    We already know that the FITNESS of a particular phenotype/genotype is its reproductive contribution to subsequent generations relative to an alternative phenotype/genotype.

    An individual's inclusive fitness may be comprised more of individual fitness or kin selection, depending on the species natural history/behavior.

    The degree to which each of these two factors contributes to inclusive fitness depends to a great degree on whether a species is SOLITARY or SOCIAL.

    Why is kin selection not altruism?

    An example...Marmosets. Tiny, New World monkeys who live in social groups consisting of...

  • Group living is critical to the survival of these monkeys.
  • Queen supresses ovulation in her daughters by behavioral bullying/stress.
  • Aunts help rear their siblings.
  • What is the use to the aunt monkeys? (Of course, the monkeys don't know this! The idea is that genes that foster kin selection promote their own passing on to future generations simply by fostering the 50% likelihood that they'll be passed along in any given individual.)

    Why not take the chance to contribute all of your genes to future generations (In the form of multiple offspring, as the queen does)?

    Honeybees: A Social Hymenopteran Insect with HAPLODIPLOID populations.

    The kin selection advantage is even greater in this case.

  • Females (queen and workers) are diploid.

  • Males (drones) are haploid. (produce sperm via mitosis)

  • So gametes produced by the queen share 50% of her genes.

  • Gametes produced by a drone contain 100% of his genes.

  • Each female bee gets 50% of her alleles from dad and 50% from mom (queen).

  • This means that all sister (worker) bees have 100% of their drone parent's genes in common, and 50% of their queen parent's genes (Each gets 50% of queen's; on average, they'll be 50% different each time, due to crossing over.) in common.

  • Thus, sister worker bees share 75% of their alleles! The are more closely related to each other than they would be to their own offspring, who would share only 50% of their alleles.

    It is to each worker's genes' advantage to encode helping behaviors that allow the queen produce more workers (who are 75% genetically the same as the worker), rather than to produce her own offspring (which would be only 50% related to her)!

    The above scenarios make some rather big assumpitons, which are arguable:

  • The behaviors that foster these genetic events are heritable
  • The worker bees all have the same drone father

    Do the monkeys and the bees make this choice consciously? What do YOU think?

    Remember the Bottom Line: Behaviors that are genetically based (and if you believe E.O. Wilson and many others, all animal--including human--behaviors have at least some genetic component at their root) are either

    It's those interesting neutral ones that might some day become one or the other, depending on what happens in the environment of the organisms carrying the genes for that trait.