Population genetics III

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Population Genetics Population Genetics is the study of genetic events at the level of the population, and hence, genetics as it pertains to evolution. In studying population genetics, (one branch of evolutionary genetics), the investigator studies evolution by mathematically modeling changing gene frequencies in populations, and comparing those models to what happens in natural populations.

The Terminology

  • population: all individuals of the same species living in a defined geographic (or smaller, organismal) area.
  • deme – a local, actively interbreeding population that shares a distinct gene pool. (Isolation of a deme fronm other conspecific demes can result in the generation of subspecies (microevolution) or even reproductive isolation (macroevolution/speciation).
  • gene pool: all the genes at all loci in every member of an interbreeding population.
  • evolution: change over time
  • organic evolution: change in living organisms over time
    • microevolution – genetic change within a species
    • macroevolutionreproductive isolation between members of a previously interbreeding population, resulting in two new (daughter/sibling) species (a.k.a. speciation)
  • adaptation – short term changes in physiology, morphology, metabolism, etc. made by an individual organism in response to environmental changes Remember: Individuals adapt. Only populations evolve.
    The goal of the population geneticist is to understand the genetic composition of a population and the forces that determine and change that genetic composition. Understanding these forces at the population level helps us reconstruct the course of evolution and the various interacting forces that drive it.
    How did the tremendous variety of earth’s biodiversity evolve? We can’t go back and watch. But we can observe processes occurring now in natural populations and environments and extrapolate.
    Evolution is not always directional, and it does not have a “goal.” It simply results from interactions of living organisms with each other and their environment. Evolution is not a theory. It is an observable phenomenon supported by a tremendous array of physical evidence, from homologies to fossils. The only thing theoretical about evolution is:
    How does it happen?
    And the quest for the answers to this question lies–at least partly–in the field of population genetics.

    Polymorphism The existence in a population of more than one form of a particular trait or suite of related traits is known as polymorphism. In population genetics, this usually refers to the different phenotypes resulting from different alleles at a particular locus. The simplest description of populational variation at a single locus is relative genotype frequency.
    For example, here are frequencies of MN blood group alleles collected in the 1950s…

    Polymorphism can be seen at various levels:

    • morphological polymorphism – variation in physical characteristics (color, size, pattern, etc.)
    • chromosomal polymorphism – karyotype is usually species specific, but in a population, certain non-lethal anomalies may be common. These include aneuploidies, chromsome number changes, polyploidy, reciprocal translocations, inversions, etc.
  • immunological polymorphism – antigen specificities may vary within and among populations. For example:
    • ABO blood groups in humans
    • HLA cellular antigens
        Two loci are known, each with about 5 alleles. That means 25 different possible gametes 25 different homozygous genotypes and 300 possible heterozygous genotypes. Since these antigens are involved in graft compatibility, this is medically relevant.
    • amino acid sequence polymorphisms – codon change –> protein change. This can be determined via electrophoresis.
    • DNA polymorphisms:
      • restriction site variation – variation in location of a restriction sequences among individuals. As you will recall, these are detectable via the activity of restriction endonucleases.
      • tandem repeats – multiplied repeats of a particular DNA sequence
      • complete sequence variation – different electrophoretically distinguishable classes of genes that differ at a single position (single-nucleotide polymorphism (SNP)). Genes can also vary in their polymorphism at different locations. The less variation there is at a particular area of the gene, the more likely it is that the variation has been restricted because that region is necessary for coding a properly functioning protein. Mutants were weeded out by natural selection, or were lethal. By examining SNP, we also have learned that a silent/synonymous mutation is not always necessarily neutral:
        • Different codons for the same amino acid may not be read with equal speed and accuracy by the cell’s transcription machinery.
        • Although different triplets may encode the same amino acid, the different triplets may not be equally abundant in the form of tRNAs carrying that amino acid. (Result: slower or faster translation, depending on the direction of the change.)
        • Evidence: alternative synonymous triplets for any given amino acid are not used equally, and this is much more pronounced in genes that are transcribed at a very high rate (rare triplets in these must have been the victims of natural selection).

    Predicting Genotype Frequencies: Hardy-Weinberg Equilibrium Genetic variability in a population arises from the existence of multiple alleles at different gene loci. A fundamental measurement useful in studies of population genetics is the frequency with which certain alleles occur at a particular locus in a study population, and, by extension, how frequently each allele occurs in any of the possible diploid combinations at that locus.
    In 1908, Godfrey H. Hardy, a British mathematician, and Wilhelm Weinberg, a German physician.

    independently reported a mathematical rule that describes allele frequencies in a population at any given moment in time.
    It’s an expansion of the binomial equation, (p + q)2
    They noted:
    For a population segregating two alleles at a particular locus in which A is the dominant allele and a is the recessive allele, the total frequency of all alleles, A + a = 1.0.
    The total number of either allele is equal to:
    # of allele (A or a)/total # of alleles in the population
    We abbreviate the frequency of A as p.
    We abbreviate the frequency of a as q.
    Hence, p + q = 1.0
    Hardy and Weinberg independently noted that at any given point in time, the allele frequencies in a idealized, model population would be equal to

    p2 + 2pq + q2
    …in which p2 = frequency of homozygous dominant individuals
    q2 = frequency of homozygous recessive individuals
    2pq = frequency of heterozygous individuals

    This model assumes…

  • relative genotype frequencies are predicted by allele frequencies in the population
  • equilibrium is neutral: small changes in frequency that occur between generations will revert to the original frequency within one generation of random mating, as long as certain requirements (to be enumerated below) are met. If the relative allele frequencies at a particular locus in a study population match the predictions of the HW equation, then the population is said to be in Hardy Weinberg equilibrium: alleles are present in the predicted proportions p2, q2 and 2pq after one generation of mating, and the population is not evolving with respect to that gene locus. A population in Hardy-Weinberg equilibrium is not evolving with respect to that gene locus.
    If allele frequencies are significantly different from the HW prediction, or if they change significantly over generations, then the population is undergoing some sort of evolutionary change at that locus.

    Why do these numbers make sense?

  • If the dominant allele (A) is present in known frequency (p) in both eggs and sperm, then its likelihood of being inherited from both an egg and sperm by the next generation can be expressed by the Product Rule:
    p x p = p2
  • The same is true for the recessive allele:
    q x q = q2
  • And Product Rule also gives us the expected frequency of heterozygotes in the multiplied frequency of both alleles (p x q)(p x q):
    (Each offspring inherits two alleles for a given locus, and each of these two “inheritance events” will give either A or a. That is: a zygote can inherit either Asperm and aovum or asperm and Aovum, so the probabilitis of each event are multiplied, according to the Product Rule.)
    Hence, given any initial relative starting frequencies of A (p) and a (q), the three genotypes should be present in the predicted relative frequencies in the next generation: p2 : 2pq : q2
    …as long as the following five conditions are met:

    • there is no mutation at the locus in question
    • the population is infinitely large
    • individuals in the population mate randomly
    • no individuals migrate into or out of the population
    • no genotype has a reproductive advantage over another (no natural selection)

    The De Finetti Triangle helps us visualize the expected genotype frequency shifts with varying initial frequencies of the dominant and recessive alleles. The three sides represent the relative frequencies of

    • AA genotype
    • Aa genotype
    • aa genotype
  • Any point within the triangle can be considered a population. (Yes, there’s an infinite number of possible points.)
  • If the triangle is drawn with an arbitrarily chosen altitude of 1.0 (handy, since the allele frequencies together will equal 1.0, or 100% of all alleles), the three perpendiculars drawn from any population show the relative proportions of the three genotypes predicted by the Hardy-Weinberg equation.
    • D = proportion of homozygous dominants (AA)
    • R = proportion of homozygous recessives (aa)
    • H = proportion of heterozygotes (Aa).
  • Populations whose points fall along the blue parabolic line are in Hardy Weinberg equilibrium: their relative frequencies of AA, Aa and aa are the same as what would be predicted by the HW equation at any given starting relative frequencies of A and a. On this diagram, three populations are shown:
    • Population 1 (green point) is not in Hardy Weinberg equilibrium. At its given (known) frequencies of A and a (p is approximately 33.3%, and q is approximately 66.6%), this population has a greater proportion of heterozygotes than predicted by the HW equation.
    • Population 2 (blue point) is in Hardy-Weinberg equilibrium. The proportions of AA, Aa and aa are equal to those predicted by the HW equation at the relative starting frequencies of A and a (in this case, about 80% A (p = 0.8) and 20% a (q = 0.2)).
    • Population 3 (red point) is in Hardy-Weinberg equilibrium. At the very high starting frequency of A (p is about 0.95, and q is about 0.05). With this many A alleles in the population, you’d expect to see mostly AA genotypes, relatively few Aa genotypes, and almost no aa genotypes. And that’s just what the graph shows for this population.)
  • Heterozygote frequency should be greatest when p and q both equal 0.5 (the maximum possible relative frequency in a two-allele system.)
  • As allelic frequency of one allele increases, the relative proportion of [heterozygotes:rarer homozygotes] increases.
  • As an allele becomes more rare, it is more likely to be found in heterozygotes than in homozygous form. Rare alleles are almost never found in homozygous condition if a population is in Hardy-Weinberg equilibrium. For example, an allele found in only one in 1000 gametes will be homozygous in only one out of a million individuals in the population. (apply the Product Rule) The distribution of genotypes in a population in Hardy-Weinberg equilibrium can be graphically expressed in this way:
    The perpendicular lines represent a range of possible relative frequencies of a dominant and recessive allele. Where the perpendicular intersects the three lines (orange for homozygous recessive, blue for homozygous dominant, and green for heterozygous), the horizontal leading to the y axis tells the expected proportion of each genotype at that particular starting frequency of A and a. Examples:
  • When p and q are present in equal frequency (both equal 0.5), then the perpendicular at the 0.5/0.5 frequency mark intersects the orange line at 0.25 (25%), the blue line at 0.25 (25%) and the green line at 0.5 (50%). This means that when p and q are both present in equal frequency (50:50), then the population should contain 25% AA, 50% Aa, and 25% aa if it is not evolving (i.e., in Hardy Weinberg equilibrium).
  • Similarly, if the population is 100% dominant allele at that locus, then there must be 100% AA, and zero Aa or aa.
  • Try it yourself and see!

    Example of a Hardy-Weinberg calculation Species: Sciurus carolinensis (Grey Squirrel)
    Gene Locus: A
    Alleles: A (dominant; wild type agouti fur) and a (recessive; melanistic black fur)

    We are studying a population of 1000 squirrels. Of these, 60 (60/1000, or 0.06) are melanistic.
    If each of these melanistic squirrels carries two recessive alleles, we can use this to calculate the expected frequency of q, since q2 is the frequency of the alleles in the homozygous recessive individuals.
  • The square root of q2 is equal to q. (duh)
    In our example, the square root of 0.06 = .25.
  • Since p + q = 1.0, you can now solve for p
  • 1 – 0.25 = 0.75
  • Our predicted frequencies, based on the assumption that the squirrel population is in HW equilibrium, are p = 0.75 and q = 0.25
  • plug these values into the HW equation to calculate expected relative genotype frequencies:
    0.752 + 2(0.75)(0.25) + 0.252
    This means that if our population of 1000 squirrels is in HW equilibrium, then
    • p2 = 0.56 – (0.56 x 1000, or 560 squirrels should be AA)
    • 2pq = 0.38 – (0.38 x 1000, or 380 squirrels should be Aa)
    • q2 = 0.06 – (0.06 x 1000, or 60 squirrels should be aa)

    Notice that these three frequencies add up to 1.0, 100% of the 1000 squirrels in the population. Predictions of expected relative genotype frequencies can also be made for loci with more than two alleles (as in this example of a three-allele locus handled with an expansion of the trinomial equation), but they rapidly become unwieldy as the number of alleles increases, and are best done with computer software.

    Hardy-Weinberg Equilibrium for X-linked Loci Calculation of allele frequencies for an X-linked locus requires a bit of caution, as males are hemizygous for this locus. But the same rules apply.
    Simply count males as having only one allele for each frequency calculation.
    In your population of squirrels, a recessive allele of an X-linked locus (R) codes for a white star on the forehead (r).


        • XRXR – no star
        • XRXr – no star
        • XrXr – star

      • XRY – no star
      • XrY – star

    The dominant allele occurs in

    • RR females x 2 (since each one carries two alleles)
    • heterozygous females (each of whom carries one R allele)
    • starless males (each of whom carries one R allele)

    The recessive allele occurs in:

  • rr females x 2 (since each one carries two alleles)
  • heterozygous females (each of whom carries one r allele)
  • starred males (each of whom carries one r allele) In our population of 1000 squirrels, there are (conveniently!) 500 females and 500 males.
    But unlike an autosomal trait, which would have 2000 copies in this population, the X-linked trait has only 1500 copies due to the hemizygosity of the males. In our population, we counted:

    • 460 unstarred females (XRX)
    • 40 starred females (XrXr)
    • 300 unstarred males (XRY)
    • 200 starred males (XrY)

    In the recessive homozygous females, q2 = 40/1000 (0.04), so q = 0.2.
    In the hemizygous males, the frequency of q is 100/1000 (0.1).
    The summed frequency of q in the expressing individuals is (0.2 + 0.1 = 0.3). Solving for p, the expected frequency of the dominant allele should be 1.0 – 0.3 = 0.7
    Since the total number of alleles in the population is only 1500, this means that the expected relative frequencies of R and r should be:

    • 1500 x 0.7, or 1050 R alleles
    • 1500 x 0.3, or 450 r alleles

    You know from your census that

  • 40 starred females carry 80 r alleles
  • 200 starred males carry 100 r alleles …for a total of 300 of the 450 r alleles in the population. That means the remaining unaccounted 150 r alleles (450 – 300 = 150) must be “hiding” in the heterozygous females. Therefore, 150 of your 460 unstarred females are expected to be heterozygous for the recessive “starring” allele (r) if the population is in HW equilibrium.

    Heterozygosity The raw material of evolution is genetic variability. Phenotypic variability of a particular trait (or suite of related traits) in a population, known as polymorphism, may range from the sublime (variation in mRNA sequence) to the obvious (crop yield, size, body shape, metabolic rate, behavior, color, etc.). Any of these traits may be monitored for variation in a population, and the relationship between genotype and phenotype is not always simple.
    Heterozygosity (i.e., the proportion of gene loci in a population that exist as a heterozygous genotype) is one measure of genetic variability within a population, the heterozygosity of one particular locus of interest is a common value used by population geneticists to monitor overall population heterozygosity.

    • Heterozygosity is greatest when all alleles are present in equal frequency.
    • The more alleles there are for a particular locus, the greater the expected heterozygosity at that locus.
    • If more than one locus is being considered, then overall heterozygosity can be examined by
          1. measuring the heterozygosity of each separate locus
          2. examining the diversity of gamete genotypes 3. examining the combination of alleles of different genes on the same chromosomal homolog (



          The term “haplotype” derives from “half of a genotype”. It is the set of alleles on a single chromosome, or on all the single chromosomes passed from a parent to an offspring, or on a localized region of a single chromosome.

    Changes in Allele Frequencies: Microevolution With respect to a particular gene locus in which a dominant and recessive allele are present in given relative proportions, changes in those relative frequencies will not change, as long as the five aforementioned criteria are met:

    • No mutation (at the locus in question)
    • No migration (to other demes or from other demes)
    • Random mating (individuals of any genotype at this locus have an equal chance of mating with an individual of any genotype at this locus)
    • Infinitely large population (not gonna happen)
    • No natural selection

    If all of these things are true of the population in question, then the population is not evolving with respect to allele frequencies at the locus under study. But when one or more HW criterion is not met, that’s when things get interesting. (For a great tutorial about the mechanisms of evolution, visit Understanding Evolution hosted by the UC Berkeley Museum of Paleontology.)
    What does each of these HW assumptions mean?

    Sources of Genetic Variation
    Three things can alter the genetic composition of a population:

    • mutation
    • recombination
    • immigration/emigration of genes

    1. Mutation

  • Recall that the phenotype–for a particular trait–most common in a particular wild population is known as the wild type.
  • Also recall that wild type is often designated–rather than with letters–as “+”.
  • Any allele other than the wild type is said to be mutant.
  • Examples of “wild type” traits in various species:
  • Mutant forms of each of these wild types exist, and may or may not confer a selective advantage in wild populations.
  • Tigers: white, not to be confused with albino
  • Leopards: wild type and melanistic
  • Mutation is the only way new genetic material can arise in a population
  • A wild type allele can mutate via a forward mutation.
  • A mutation that changes a mutant form back to wild type is a reverse mutation.
  • When forward and reverse mutations at a particular locus occur at the same rate, mutational equilibrium is reached.
  • The larger the population, the more likely mutations will occur Mutations may result in phenotypic traits that may be adaptive, maladaptive, or neutral in, depending on the particular environment in which they occur. In some cases, a mutant form will confer a selective advantage, and could eventually become a new wild type.
    A population’s mutation rate is the probability that a given allele will change in form in one generation. All else being equal (i.e., none of the other HW factors are acting here), the increase in frequency of a mutant allele is equal to:
    (mr) x (ν+)

    mr = mutation rate
    ν+ = frequency of the wild type allele Example: If a population is completely homozygous at locus A, but a mutation occurs once in every 1000 gametes to change A into a, then in one generation:

    0.001 x 1.0 = 0.001
    Meaning that after one generation, 0.999 of the alleles will be A, and 0.001 will be a.
    In two generations, the increase in frequency of a will be:

    0.001 x 0.999 = 0.000999
    and the frequency of A will be

    0.999 – 0.000999 = 0.998001
    …and so on. As the new mutant alleles increase in frequency, the wild type alleles decrease. So as the generations proceed, the actual mutation rate decreases, compared to the initial rate when it first began happening.

    Our example of a mutation rate of 1/1000 is, in almost any case, an unrealistically high rate. In natural populations, mutation rates are quite low at any given locus. So something more than simple random mutation is almost always at work in an evolving population.
    1a. Recombination
    Without recombination, a new mutant allele would always be inherited along with the allelic forms of other loci on the same chromosome or chromosome set. Haplotypes in the population would not change. But because of recombination and crossing over, there is a shuffling of allelic combinations of loci between generations.
    If two loci are completely unlinked, then the probability of their being inherited together is calculated with the Product Rule. If our new mutant allele a has now reached a frequency of 10% (0.1), and a second locus “B” has two alleles with relative frequencies of 60% (B) and 40% (b), then the likelihood of an aB gamete is

    (0.1)(0.6) = 0.06
    and the likelihood of an ab gamete is

    (0.1)(0.4) = 0.04
    The randomized recombinations reflect linkage equilibrium that is not exhibited by loci linked on the same chromosomes. It may take several generations for linked loci to undergo crossing over and some degree of independent inheritance.
    Linked chromosomes, not playing by Mendelian rules, exhibit linkage disequilibrium, which slowly decays as crossing over during meiosis gradually separates initially linked allelic forms on the same chromosome at the rate at which crossing over takes place between two linked loci.
    Depending on the map distance between two loci, their linkage disequilibrium can break down relatively quickly. In general, this results in populational variation far more quickly than mutation, once there is more than one allele at any given locus.

    2. Migration
    The process by which movement of genes takes place between populations or demes via movement of their members is known as gene flow, which

    • spreads novel alleles that have arisen via mutation
    • has a homogenizing effect if a recipient population is small relative to a donor population.
    • increases the effective size of a population.

    Lack of gene flow may eventually lead to speciation, but the rate at which this occurs depends on the species and other factors.

  • Some species undergo reproductive isolation very readily:
        e.g. –


      spp. in Hawaii vary tremendously in appearance and behavior, and many are reproductively isolated from one another. However, they are genetically almost indistinguishable.
  • But others do not. A species unlikely to undergo reproductive isolation (for whatever reason) is said to be cohesive.
        e.g. – Red-winged Blackbird (

    Agelaius phoeniceus

        ) has populations in California and Florida which are physically indistinguishable, yet there is no gene flow between them. They have not speciated, despite lack of gene flow. e.g. – Coyote (

    Canis latrans

        ) and Timber Wolf (

    Canis lupus

        ) occasionally hybridize, producing fertile offspring–yet their lineages have remained separate for two million years. (The Tale of the

    Red Wolf

        e.g. – Black Cottonwood (

    Populus trichocarpa

        ) and Balsam Poplar (

    Populus balsamifera

      ) are separate species, physically distinguishable. They have existed as such for 12 million years, according to the fossil record. Yet they occasionally hybridize to produce fertile offspring.

  • 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. One example is the relatively recent hybrid zone found in the northern U.S., where Mule Deer (Odocoileus hemionus) and White-tailed Deer (Odocoileus virginianus) sometimes hybridize. This could cause some problems for Bambi.
  • 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?
    It’s one of life’s little mysteries. But we can examine what happens when there is sharing of genes between demes.

    Effects of Migration on Allele Frequencies
    If two demes have different allele frequencies at a particular locus, then migration between the two demes can change the genetic composition of the populations at that locus.
    Let’s say…

  • For a given gene locus, deme X has allele a with the frequency p in generation t
  • and deme Y has allele A with frequency P.
  • Individuals from deme Y migrate into the terrirory of deme X.
  • The proportion of the post-immigration population made up of individuals from deme Y is m.
  • In the next generation (after migration), the frequency of the recipient population’s original allele (pt + 1) is the result of mixing (1-m) genes from the recipient population with m genes from the donor population:
    pt+1 = (1-m)p + mP = pt + 1 + m(P – pt)
    The change in p is equal to:
    pt + 1 – pt
    which is equal to
    m(P – pt)
    Your assignment: Make up an example of this type of immigration, using your own numbers, and do a sample calculation.

    3. Non-random Mating
    This can lead to disproportionate survival of recessive alleles.
    In a population segregating a dominant and a recessive allele at a particular locus…

    • If mating is random, then the two alleles of that locus should combine with frequency proportional to their frequencies in the population.
    • The probability of two genotypes mating is the product of the frequencies of the genotypes in the population (Product Rule).

    We’ll use our agouti/melanistic 1000 squirrel population again, in which

    • p2 = 0.56 (560 squirrels should be AA)
    • 2pq = 0.38 – (380 squirrels should be Aa)
    • q2 = 0.06 – (60 squirrels should be aa)

    The probability of an AA squirrel mating with an Aa squirrel is (.56)(.38), or 0.21.

  • Significant deviation from this probability may be due to choice or to circumstance. Forms of Non-Random Mating
  • assortative mating: Individuals of a particular genotype (and hence–often–phenotype) mate with a frequency different from that predicted by the population’s relative genotype frequencies.
    • positive assortative mating: individuals of similar genotype/phenotype mate together more often than predicted by random chance.
    • negative assortative mating: individuals of dissimilar genotype/phenotype mate together more often than predicted by random chance.
    • inbreeding occurs when matings are more frequent between related individuals than between partners chosen at random
    • outbreeding occurs when matings are less frequent between related individuals than between partners chosen at random

    NOTE: Assortative mating occurs with respect to a particular trait, as in height or skin color in humans.
    Inbreeding occurs with respect to the entire genome–not just one trait.

    Inbreeding (and positive assortative mating in general) can result in increased homozygosity at multiple loci at a greater rate than expected due to random chance. This can be expressed with the inbreeding coefficient (F). The Inbreeding Coefficient is a measure of the probability of autozygosity: homozygosity in which the two alleles are identical by descent (i.e., they are exact copies of an ancestral gene inherited due to some degree of relatedness of the parents.)

    F = (2pq – H)/2pq
    In which H is the observed proportion of heterozygotes in a population, and 2pq is the expected proportion of heterozygotes, based on the Hardy-Weingerg prediction.
    Note that when H = 2pq, F is equal to zero, heterozygosity is no greater and no less than predicted, and that no more matings between close relatives are occurring than would be predicted by random chance.
    When there are no heterozygotes, F = 1, the population may be completely inbred, as in a self-fertilizing plant species.
    Inbreeding can change allele frequencies:

  • The top generation represents unrelated parents giving rise rise to two siblings (Jethro and Ellie May, on line two).
  • If the two siblings both happen to have inherited the same allele for gene “A” (in this case, a relatively rare allele, A1), then each has a 50% (0.5) chance of passing it on to their offspring.
  • If the siblings breed together, the chance of each of them passing the A1 allele to their offspring is 0.5 x 0.5, or one chance in four. (Product Rule again)
  • This event occurred in the third line of the diagram. (Lil’ Twelve Toes).
  • Note that the offspring of the two siblings also could have inherited dissimilar alleles from each parent. There’s a 50% chance of each parent contributing the allele other than A1, too. But the issue is the difference in probability if two siblings mate together preferentially compared to the likelihood of the (relatively rare) A1 allele being contributed by both parents if they are not closely related. If the A1 allele happened to be deleterious…well…you can see why there are taboos in human society against inbreeding.

    Over several generations, relative genotype frequencies may or may not shift:

    If population size is infinite, genotype frequencies may shift with non-random mating, although allele frequencies should remain constant.
    However, there’s really no such thing as an infinitely large population in the real world. In real populations, the loss of heterozygosity can be predicted and measured.

    4. Genetic Drift
    Tracking Allele Frequency Changes Over Generations

  • mathematical models are created to predict changes
  • data are collected to test predictions made by the models In a large, genetically diverse population, a huge number of genetically different of gametes is possible. However, the offspring of that population reflect only a small subset of those possible gametes–and that sample may not always be an accurate subset of the population at large.
  • The zygotes of every generation are a result of fusion of the gametes from the parent generation.
  • 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.
  • This is a simple matter of probability: Toss a penny twice, and it may not come up heads once and tails once in your two tosses, even though this is the most likely result. But toss it 100 times, and you’re more likely to approach the 50:50 ratio expected due to random chance.
  • Drawing gametes from a gene pool is similar. The smaller the sample size (the fewer the successful gametes), the more likely that there will be a skewed sample of gamete genotypes, relative to the population at large.
  • If small population size is the only factor affecting H.W. equilibrium, random genetic drift is said to occur. This is the fluctuation of allele freuqencies from generation to generation due to random chance.
    • For 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 perhaps a catastrophic event (hurricane; volcanic eruption, etc.) accidentally/randomly kills a disproportionate number of the aa homozygotes in a given generation. The resulting change in allele frequency in the next generation is another example of sampling errordue to random chance.
  • The smaller the population, the smaller the gamete subset, and the more likely that changes in allele frequency will occur due to genetic drift.
  • This will occur in any population that is not infinite in size.
    Two special categories of genetic drift include

    • founder effect in which a small sample of breeding individuals from a large population colonizes a new area, and the new individuals do not carry a representative sample of the original population’s allele frequencies at various loci. (e.g. – Galapagos Islands species).
    • bottleneck effect: A large population is essentially wiped out except for a few lucky individual survivors who do not represent the same allele proportions as the original poulation.
  • In either of the above scenarios, the surviving offspring generation are not likely to have exactly the same allele frequencies as the original parental population. Measuring Genetic Drift: Loss of Heterozygosity in Island Populations
    Small population size, as we saw above in our examples concerning Genetic Drift, can lead to Non-random Mating due to inbreeding.
    Small, isolated populations eventually will consist of members that are related to one another, sharing most of their alleles. This can lead to fixation of a single allele in the population, as we saw above in our hypothetical island populations.
    It’s simply a matter of increased probability of inheritance of a given allele (since there are more of a particular allele available after repeated generations of inbreeding) in each successive mating, as you will recall from our previous happy family:

        Remember that the rarer the allele, the more often it will appear in heterozygous condition (and less often in homozygous condition) in a population if mating is random. We already have decided that the A1 allele we’ve been tracking above is rare, but let us now also decide that it is


        (i.e., maladaptive in some way). In our population, it’s found only once in every 1000 gametes.
          • The probability of a zygote receiving two copies of the rare allele can be calculated with the Product Rule: 1/1000 x 1/1000 = 1/1,000,000
          • Only one in a million zygotes are expected to be homozygous for A1 if mating is random.

    However, recall that if two mating individuals

          • are brother and sister (as are Jethro and Ellie May)
          • and one of their (common) parents happens to be a carrier of A1 (as their dad was).

    …then there is a 50% (0.5) chance that


        siblings may have received A1 and thus, a 25% (0.25) chance that any of their offspring will receive two copies (one from each parent).
        Bottom line:
      • If mating is random, then the risk of inheriting two copies of the rare deleterious A1 allele floating around in the population is one in a million.
      • Inbreeding increases that risk to one in four, and on an island in which a very small founder population has started to breed, soon all individuals on the island will be related.
      • The rarer the allele in a population, the greater the relative risk of homozygous recessive offspring if inbreeding does occur.

    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.

    Now that we’ve said all that, note that there are exceptions to every rule. Regular inbreeding in some wild populations has been recorded, and may be tolerated in a relatively stable environment.

  • In a small population, such as that on an island, it is more likely that one or the other allele (of a two-allele locus) can become be fixed in the population, with the other being permanently lost.
  • Once that happens, no further change in population genotype can occur.
  • Consider these ten hypothetical populations. All these changes (in these populations, fixation of the a allele) are due to sampling error. This phenomenon can be simulated mathematically:
  • Let’s start with 1000 hypothetical populations, each consisting of 100 individuals. (This is a small population number for any species, and as such, is conducive to relatively rapid genetic drift compared to the idealized “infinitely large” population.)
    • In all 1000 of our simulated populations, the frequency of A and a are each 0.5. (i.e., p = 0.5 and q = 0.5)
    • We will measure time (t) in terms of generations…
    • …as a function of population size (N)
    • That means that t = N is generation 100; t = N/5 is generation 20, t = 3N is generation 300, etc.
    • A computer simulation using the Fokker-Planck Equation (the same one physicists use to describe diffusion processes such as Brownian motion, another random process), generates a series of curves showing the reduction in heterozygosity and increase in homozygosity in the 1000 populations.
    • In which…
      • Ht = the proportion of heterozygotes at time “t”
      • H0 = the proportion of heterozygotes at time O (start)
      • N = number of diploid individuals in the population

      Ht = H0(1 – 1/2N)t = H0e-t/2N

    In each of our our 1000 populations, heterozygosity will decrease, with the locus becoming fixed (at random) at either the dominant or recessive allele as shown HERE.

    The degree of allelic variance in a population (P) due to genetic drift is expressed as:

    [s2]P = pq/2Ne
    The standard deviation of the population’s allelic frequency can be used to establish the 95% confidence limit with which either allele is expected to occur in the population due to random chance. (For the dominant allele, for example, this is approximately equal to p + 2[standard deviation])
    Let’s return to a population of wild type and melanistic squirrels This time let’s consider a population of 500 agouti and melanistic squirrels (250 males and 250 females) in which the dominant allele is present at a frequency of 0.75 and the recessive allele at a frequency of 0.25. With this information, we can set up confidence limits for a two-tailed null hypothesis stating “In populations of 500 squirrels in which p = 0.75 and q = 0.25, the dominant allele frequency should not differ significantly from (p = 0.75) if only genetic drift is operating to change relative allele frequencies.”

    • the frequency of the dominant allele is 0.75 (p = 0.75)
    • the frequency of the recessive allele is 0.25 (q = 0.25)
    • because the males and females were both present in equal proportion, Ne = 500. The effective population size is
      4 x [(250 x 250)/(250 + 250)] = 500 (as expected)
    • the variance of allelic frequency is (.75)(.25)/2(500) = .0002
    • the standard deviation is the square root of .0002, or 0.014
    • the 95% confidence limits for a two-tailed hypothesis are thus
      • plus [p + 2(standard error)] on one tail
      • minus [p + 2(standard error)] on the other tail
    • Hence, the confidence limits for this example are:
      [0.75 – (2 x .014)] < p < [0.75 + (2 x .014)] or
      0.72 < p < 0.78
    • In prose, this means that in 100 populations with the same genetic/allelic makeup as the melanistic squirrel population we examined, that 95 of those populations would have a dominant allele frequency (p) between 0.72 and 0.78 if only genetic drift is operating to change allele frequencies.
    • A single population with a dominant allele frequency (p) of say, 0.38 might have some other factor besides genetic drift contributing to its deviation from the 0.72 – 0.78 range,
    • but if fewer than 5 of the 100 populations deviate from the expected, you cannot reject the null to say that there is some factor other than random chance that has caused this small proportion of the sample to deviate from the expected.
    • Only if more than 5 (on either tail) of the 100 populations deviate from the confidence intervals can you say that something other than genetic drift is likely contributing to the observed deviation from the expected relative allele frequency.

    Side Note In real populations, demographers link generation time to age of reproducing females and probability of survival in each age group.
    To avoid the complexities inherent in including these factors (which you must do if you’re a demographer), we’ve been using discrete generations. That means that when we sample, we don’t overlap generations: each time we measure a population (for change in allele frequency), we will assume that all measured individuals are from the same generation, and that there are no individuals from a previous generation included.

    Sex Ratio and Genetic Drift What happens if the sex ratio is not 50:50?The effective population is the equivalent number of adults contribuing gametes to the succeeding generation. If the number of males and females is equal, and each has an equal probability of leaving offspring, then the effective population size is equal to the number of breeding adults.
    However, if the sexes are not present in equal numbers, genetic drift is expected to occur at a greater rate than if the sexes are equal in number.

    • males contribute 50% of their genes to each generation
    • females contribute 50% of their genes to each generation.
    • if the sexes are unequally represented, individuals belonging to the scarcer sex will leave a disproportionate number of genes to succeeding generations.
    • The genetic contribution of each male or female of a population is equal to 1/2 x 1/number of individuals of their sex.
    • All other HW factors being met, in a population of 20 males and 20 females:
      • each male will provide 1/2 x 1/20 = 0.025 of the genes in the next generation
      • each female will provide 1/2 x 1/20 = 0.025 of the genes in the next generation.
      • To check this, multiply 0.025 by the # of individuals of each sex, add the two quantities together, and you should get 1.0–100% of the genes of the next generation.
    • In a population of 20 males and 100 females
      • each male will contribute 1/2 x 1/20 (= 0.025) to the next generation
      • each female will contribute only 1/2 x 1/100 (0.005) to the next generation
      • To check this, multiply 0.005 x 100 = 0.5 (females) and 0.025 x 20 = 50% (males); each contributes 50% of the next generation).
    • To calculate the effective population size (Ne):
      Ne = 4 x [(Nf x Nm)/(Nf + Nm)]
      In which…
    • Nf = number of breeding females
    • Nm = number of breeding males In our 20 male/100 female population, the effective population size would be:
      4 x [(100 x 20)/(100 + 20)] = 66.6

    This means that genetic drift will occur at the same rate with these 120 individuals as if there were only 67 individuals. This will result in genetic drift occurring more rapidly than in a population with an equal number of males and females.The more skewed the sex ratio, the more rapid the expected genetic drift due to reduced effective population size.
    Genetic Drift may be one of the most important factors driving evolution, even though natural selection gets all the press.

    5. Natural Selection Without initial polymorphism at a given locus, there can be no evolution. And in the best known mechanism of evolution, changes in relative allele and genotype frequencies are due to interactions between individuals within and between populations, as well as with the environment itself. This is known as natural selection.

    • human wisdom teeth
    • human little toes
    • other “vestigial” structures

    Some have asked, “Why don’t these things just “evolve away” if we don’t need them?” Polymorphism of an apparently “useless” trait is one example of the diversity of gene expression in a population that may occur, in this case when the trait in question is neither a benefit nor a liability to the organism expressing it.
    Are there advantages to genetic diversity, not only within a species, but within a single organism? Recall the genetic risks of inbreeding, and consider the following…

    This trend is seen not only with AIDS patients, but also for other pathogenic diseases and other species.
    (For example parvo virus in captive populations of Panthera spp. and Acionyx jubatus.)

    One of the criteria that must be met in order for a population to remain in Hardy-Weinberg equilibrium is that no genotype confers a reproductive advantage over another. If a particular environment or interactions between conspecifics results in one genotype (of a particular locus) having greater reproductive success than another genotype, then natural selection is at work. This mechanism of evolution cannot 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, theoretically, leave more genes to succeeding generations than their conspecifics. Eventually, this will cause a shift in the allelic composition of that locus in the population undergoing natural selection.
    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 tenets:

    • Principle of overproduction
        Organisms are capable of producing huge numbers of offspring
    • Principle of variation
        Those offspring exhibit (heritable) variation
    • Principle of competition
        Those offspring must compete for limited resources
    • Principle of differential reproduction
        Those whose phenotypic characters allow them to best exploit those limited resources will leave the most genes to succeeding populations.

    Evolution via natural selection can occur only if there is genetic variation in the population. Any genetically encoded trait may be

    • adaptive (increasing an individual’s likelihood of leaving offspring)
    • maladaptive (decreasing an individual’s likelihood of leaving offspring)
    • neutral (not affecting an individual’s likelihood of leaving offspring)

    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 that confers fitness in a particular environment could be a liability if the environment changes.

    Fitness and Selection
  • Fitness can be assigned a variable, 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 that of the most successful genotype.
  • If there are three genotypes in a population (AA, Aa and aa) and over their lifetimes, AA genotypes produce an average of 10 offspring, Aa genotypes produce an average of 5 offspring and aa genotypes produce an average of 2 offspring, then
        relative fitness of AA = 1.0 (W


        relative fitness of Aa = 5/10 = 0.5 (W


        relative fitness of aa = 2/10 = 0.2 (W



    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
      aa: s = 1 – 0.2 = 0.8

    Selection pressure is highest against the aa genotype, relative to the others. These values can be used to calculated the expected frequencies of each genotype in successive generations after selection has occured.

    (If we have time, we’ll cover selection against a recessive homozygote.)

    Frequency Dependent vs. Frequency Independent Selection
    In most natural situations, individuals of the same species are competing for resources or to avoid being captured by a predator. In such populations, if there are different genotypes at a locus that affects such competition, then the relative fitness of each genotype will soon be reflected in a shift in genotype and/or allele frequency. This depends in large part on the relative abundances of the different genotypes, and the fitness of each genotype is frequency dependent


    Mullerian mimicry

        Several species of

    toxic, distasteful butterflies (Heliconius spp.)

        have converged on a single color pattern in northeastern Peru. Bird predators recognize this color pattern after one bad experience, and avoid that color pattern from that point on. In the original, ancestral butterly population, there may have been a variety of color patterns. But if one particular pattern was rare, then birds would be more likely to go ahead and attack it because they are unlikely to have had prior experience with this particular color. Thus, there was selection pressure against individuals who did not resemble other individuals, and eventually the populations converged on a single, recognizable pattern of warning or



    In other cases, a genetically encoded trait does not depend on the relative abundance of each phenotype in the population. In this case, each genotype has fitness that is frequency independent.

      Example: If a frog population includes individuals that have variably immune systems, and some are better at fighting off a particular pathogen than others, then those individuals should leave more offspring, no matter what the abundance of each genotype is.

    Components of 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 each should be considered.

    • 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.
    • zygotic selection (a.k.a. viability selection) – differential survival of genotypes at the zygote stage
    • fecundity selection – one genotype is more fertile than other genotypes.
    • sexual selection – This is a special case of natural selection based upon an individual’s relative ability to attract and mate with members of the opposite sex. Individuals exhibiting characters that make them more attractive to the opposite sex may have an advantage.
      • Some characters are preferred by both sexes, and hence are sexually selected (e.g., blonde hair in many human populations)
      • Some characters confer an advantage over some members of one sex over members of the same sex. This can operate in two ways:
        • Members of one sex compete against each other for mates, thereby creating a reproductive differential among themselves. If those members of the population having heritable characteristics that contribute to their winning more mates reproduce more than those lacking those traits, then natural (sexual) selection is occurring.
          (e.g., male lion mane; larger size of males in some species)
        • Members of one sex prefer a particular trait in the members of the opposite sex, creating a reproductive differential in the other sex. If members of the population having a heritable trait that makes them more attractive to the opposite sex than those lacking the trait, they will out-reproduce them. Natural selection (of the sexual kind) is occuring.
          (e.g., colorful plumage in male birds; various secondary sex characters in humans; male courtship behaviors in many birds and insects)

    The expected frequencies of genotypes over generations from fecundity and sexual selection require much more complex calculations than simple selection at the level of zygote survival. We won’t do them here.

    Balanced PolymorphismWhen the heterozygous condition confers greater fitness than either homozygous condition, this condition is known as overdominance in fitness.
    Example: Sickle Cell anemia: Heterozygotes have a reproductive advantage over either type of homozygote.
    When the heterozygous condition confers lower fitness than either homozygous condition, this condition is known as underdominance in fitness. Example:
    Such cases can help explain why an allele that might be expected to be “weeded out” of a population is retained, despite a selective disadvantage in certain allelic combinations. This leads to a population exhibiting a degree of balanced polymorphism with respect to this locus.

    Results 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 favor greatest reproduction by individuals exhibiting the average state of a particular character. In this instance, the phenotypic composition of the population does not 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:

        1. stripping bark to expose insects (deep, strong bill) 2. cracking cactus seeds (large, heavy bill)
        3. extracting cactus seeds & eating attached fruit (very long bill)
      4. tearing open cactus pads to reach insects (very long bill)

    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 sympatric species (i.e, living in a single geographic area) due to competition for a resource. In this case, the resource is food.)

    Summing up…
    Organic Evolution is change in the genetic composition of a population due to genetic drift, non-random mating, mutation, gene flow, 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 even now:

    • antibiotic resistant bacteria
    • pesticide resistant insects (and other competitors of Homo sapiens)

    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?
    1. Generation Time

        The shorter the cycle time between generations, the more opportunities there are for genetic change and mutations to be incorporated into a population. (Vertebrates have very long generation time in comparison to bacteria.)

    2. Exaptation

        Populations cannot simply evolve a character because they “need” it. The genetic machinery to create a phenotypically beneficial trait (in a particular environment) must already exist in the gene pool in order to be selected. Such a pre-existing trait which may confer a selective advantage under certain circumstances is known as an


      . But if an exaptation that would make the difference between survival and extinction doesn’t exist in a species’ genetic makeup–then that species will go extinct.

    Macroevolution: The Genesis of Reproductively Isolated Populations
    Over generations, a population can undergo a great deal of change from its original state. But all members of that population are still members of the same species unless some members become reproductively isolated from one another. Speciation is the separation of two previously interbreeding populations into two populations that can no longer mate to produce fertile, viable offpring.
    Modes of Speciation

  • allopatric speciation – a single population is divided into two by a geographic barrier.
  • peripatric – a new species arises at the edge of the range of the orignal population.
  • parapatric speciation – a “gradient” of genetic (and possibly phenotypic) difference develops across a species’ range.
  • sympatric speciation – speciation occurs without physical separation, within the range of the ancestral population. Let’s have a LOOK.

    The Pace of Evolution How fast does evolution proceed? It depends.
    Phyletic Gradualism
    This is the classical, traditional view stating that large changes (reproductive isolation and morphological differentiation) occur due to the gradual accumulation of many genetic changes. The classic example put forth in many natural history museums in the form of a nice display is that of the evolution of the modern horse from the “Dawn Horse”:

    Punctuated Equilibrium
    This hypothesis was proposed in 1972 by Niles Eldredge and Stephen J. Gould.
    They suggested that major changes can occur relatively suddenly, and that they “punctuate” long periods of relatively little change. Let’s have a LOOK.
    Remember: “suddenly” is a relative term, geologically speaking, and can mean over thousands of generations (quick!) instead of over millions (not so quick!)
    Eldredge and Gould suggested that this could explain how “awkward” intermediate forms such as the reptile–>flying bird and the terrestrial tetrapod–>swimming cetacean might have been “skipped”. A major genetic event could have produced a phenotype that was drastically different from the original, and that this trait could become modified and fixed in the population over relatively few generations.
    Known examples:

    • transition from tetrapod ancestor to aquatic cetacean (whale)
    • polyploidy resulting in relatively sudden reproductive isolation (many annual “wildflowers”)

    How Do Ancestral Species Give Rise to Descendant Species? 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. Species that are on the verge of becoming separated are known as incipient species.
    Competing hypotheses:

        (= phyletic evolution) – the conversion of an entire population, over tiem, to a new form so different from the original that the classical evolutionary taxonomist would consider it a new species. (No net increase in species diversity).


      (= diversifying evolution) – the creation of two new species from a single ancestral species. (Net increase in species diversity).

    Let’s return to the museum for a more critical look at the Evolution of Equus.
    An ancestral species which gives rise to a variety of diverse species through repeated cladogenesis is said to have undergone adaptive radiation. The diversification is a result of any of the factors, discussed above, which can alter allele frequencies and shift Hardy Weinberg equilibrium.
    The biosystematist using cladistic methods will often use various characteristics to construct a cladogram (such as this one for Beta-globin in vertebrates) based upon synapomorphies.

    What Does Phenotype Tell Us about Evolution? Phenotype (at many levels, including the molecular) provides the the biologist with the most basic information s/he needs in trying to accurately reconstruct evolutionary relationships.
    The goal of the modern biosystematist (i.e., a biologist who studies the evolutionary relationships between organisms) is to construct taxa (classification groups) that are monophyletic – derived from a single common ancestor.
    In so doing, the biosystematist considers homologies, analogies, primitive and derived characters in the taxa under study at the level of morphology, ontogeny, and the biological macromolecules (DNA, RNA, proteins) themselves.
    Multiple hypothetical phylogenetic trees can be generated by considering different characteristics (morphological traits, allozymes, nucleic acid sequences, etc.), and then input into a computer program that can create consensus trees. These phylogenetic trees show which hypothetical ancestral relationships are supported by all the data.
    The biosystematist generally chooses the most parsimonious tree as a working hypothesis.

    The Molecular Clock As we already know, any change in the DNA may be

    • adaptive
    • maladaptive
    • neutral

    Of these latter types, there is a difference between

    • effectively neutral
    • selectively neutral

    While some mutations may have no effect on fitness, others may have a very small effect that becomes negligible because their fitness effects are less than the reciprocal of population size. These are effectively neutral. The Molecular Clock is relevant to the biologist interested in distinguishing how much of evolution is due to

        1. the appearance and selection of novel, beneficial genes
      2. the simple accumulation of randomly fixed, effectively neutral mutations

    If a mutation is effectively neutral, then the probability that it will replace another allele at that locus (simply due to random genetic drift) is equal to:

    …in which N is population size.
  • If “μ” is the rate at which new, effectively neutral mutations appear at a particular locus per generation, then
  • The the number of new mutational copies that will appear in a population of N diploid individuals can be calculated as:
  • Since each of these new copies has a likelihood of replacing the old allele of 1/2N, then the absolute rate of replacement of alleles by effectively neutral alleles (due to genetic drift) is equal to:
    2N&mu x 1/2N = μ
    Stated simply, this means that the rate at which random genetic drift will replace alleles simply because of random, neutral mutations is equal to the mutation rate of the mutating locus (μ).
    Since the rate of substitution should remain constant, the “molecular clock” that “ticks” at the rate of μ should be able to give information regarding the time since divergence of two related populations.
    If this is the case, then one would predict that nonsynonymous mutations would occur at a much slower rate than synonymous ones, since many of the nonsynonymous ones will be deleterious, and not result in permanent change.
    This is what we observe in several different types of genes, such as sites within the Hemoglobin Gene as well as several other classes of proteins.
    CAUTION: Though this may hold true for some proteins, there is evidence that not all sites are subject to equal rates of neutral mutations.
    For a nice overview of the “message” of the molecular clock concept, click HERE.

    In 1975, Edward O. Wilson published Sociobiology: The New Synthesis. The controversy generated by one idea in his book spread from biology to many other disciplines, including those in the humanities and the social sciences.
    Wilson’s main tenet:

    Social behavior is at least partly under genetic control.
    The book consists of 26 chapters, but the only one that caused a ruckus is the one that applies the hypothesis to Our Favorite Ape: Homo sapiens. While it’s no doubt true (as some critics have suggested) that one cannot apply the biology of social insects to the biology of humans, it is also quite likely that a great deal of human behavior is at least partly under the control of our genes, and hence, subject to natural selection and other evolutionary forces. (Thought it’s a bit harder to study the connection in our species, due to ethical constraints!)

    In 1962, British zoologist Verno Copner 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. defined as risking the loss of one’s own fitness via an act that could improve the fitness of another individual.
    For example, Wynne-Edwards noted that under crowded conditions, many animals’ reproduction is severely reduced or ceased altogether. He interpreted this behavior as “altruism” that was for the “good for the group.” He hypothesized that a group that restrained its reproductive output and did not “overeat” its food supply would be more likely to survive than a group that reproduced without restraint, to the point of destroying its food supply and then starving.
    Wynne-Edwards believed that behaviors that improved the survival of some of a group’s members would give that entire group an adaptive advantage over groups that did not have altruistic members.
    The idea of “group selection” was subject to severe criticism for many reasons.

    • Genetic variation is much higher between individuals than it is between groups, especially big groups. Alleles will likely be maintained in a population even if some individuals are removed.
    • Many behaviors are not all that heritable, or show complex patterns of inheritance.
    • Behavioral phenotypes are not usually controlled by a single gene. Selection for a behavior (or against it) would have to select for all the genes involved in its development.
    • At the individual level, reproductive restraint is maladaptive (A genetic tendency towards martyrdom is likely to get you kicked out of the gene pool.)
    • A few experiments (e.g., with populations of flour beetles) seemed to indicate that group selection could be possible. However, the results of those experiments could better be explained by another phenomenon (which we’re about to discuss).

    So how can such phenomena as

    • reproductive “restraint” in response to crowding or other stimuli
    • alarm calls (which might draw attention to the caller while allowing its conspecifics to silently escape)
    • sterility in social insects (worker hymenopterans (ants, bees, etc.) never reproduce, but live their entire lives supporting the queen who gave birth to them and who continues to produce more sterile workers

    …be explained without invoking altruism? 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 increasing the likelihood that some of your alleles will be passed on to future generations.
    (Those interested in human medicine might take note that W.D. Hamilton was also well known for his support of the hypothesis that the AIDS pandemic in Africa might have involved a polio vaccine campaign. The idea has been dismissed by many as having been well refuted, but it persists in some circles.)

    Inclusive Fitness, Individual Fitness and Kin Selection, oh my.
    We already know that the Darwinian fitness of a particular phenotype/genotype is its reproductive contribution to subsequent generations relative to an alternative phenotype/genotype.

    • individual fitness – the production of offspring by an individual
    • kin selection – assisting relatives in rearing their offspring, which may share some of the assisting organism’s genes.
    • inclusive fitness – individual fitness PLUS fitness gained via kin selection activity.

    An individual’s inclusive fitness may have a greater contribution from individual fitness or from kin selection, depending on the species’ natural history, depending to a great degree on whether a species is solitary or social.

    • Solitary species tend to have a greater individual fitness component.
    • Social species tend to have input from kin selection.

    Why is kin selection not altruism? Consider The Marmoset.

    This is a tiny, New World monkey who lives in social groups consisting of

    • A Queen: reproductive female
    • A King: reproductive male
    • Immature males
    • Adult females who serve as “aunts” and help their Queen Mum raise the babies.
  • 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.
  • How could this possibly be adaptive for the aunt monkeys?
    • New sibling baby monkeys get 50% of the queen’s genes
    • and 50% of king’s genes
    • On the average, all sisters share 25% of queen genes and 25% of dad genes. It’s not a total genetic loss.

    (Of course, the monkeys aren’t aware of the math. Genes that foster kin selection promote their own passage to future generations simply by fostering the 50% likelihood that they’ll be passed along in any given individual.) Why should an “aunt” not take the chance to contribute all of her genes to future generations (In the form of multiple offspring, as the queen does)?

    • Eventually, the queen may die, and one of the aunts will become the new queen. It’s a “waiting game” and a gamble. But in the meantime, you are ensuring a greater rate of survival for at least some of your genes by helping to rear your own relatives.
    • Staying with the group ensures a better chance of survival. A lone monkey would be monkey meatloaf very shortly after leaving the group, if it couldn’t join a new group. That means it can no longer contribute to its own fitness even via kin selection.

    Now consider the Honeybee.

    These are social hymenopteran insects whose populations are haplodiploid.
    The kin selection advantage is even greater in this case.

    • Females (queen and workers) are diploid.
    • Gametes produced by the queen share 50% of her genes.
    • Males (drones) are haploid. (they produce sperm via mitosis)
    • Gametes produced by a drone contain 100% of his genes.
    • All the daughters of a single drone and queen get 50% of their alleles from dad and 50% from mom (queen).
    • Because the drone is haploid, this means that (full sister) worker bees share 100% of their father’s genes and (on average) 50% of their mother’s genes
    • Hence, a worker bee shares 75% of her alleles with her full sisters.
    • A fertile worker would share only 50% of her genes with each of her offspring.
    • Worker bees are actually more closely related to each other than they would be to their own offspring.
    • Heritable behaviors and physiological modifications that promote helping the queen to produce more 75% related sisters are (mathematically) more adaptive than any that would promote behavior fostering producing offspring that are only 50% related to a worker.

    Granted, the above scenarios make some rather arguable assumptions:

  • The behaviors that foster these genetic events are heritable
  • The worker bees all have the same drone father But the probability of promoting one’s own genes’ survival is a much more logical explanation for apparently “altruistic” behaviors than Wynne-Edwards’s idea of group selection.

    Like physical traits, heritable behavioral traits (and if you believe E.O. Wilson and many others, all animal–including human–behaviors have at least some genetic component at their root) may be either

    • adaptive
    • maladaptive
    • neutral

    And recall that neutral traits may becoem adaptive or maladaptive if the organism’s environment changes.

    Big thanks to http://www.bio.miami.edu/dana/250/25009_16print.html.