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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

  • 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:

  • immunological polymorphism - antigen specificities may vary within and among populations. For example:

    (The segment of this lecture between the double lines should be considered a review, and is here only for those of you who don't remember your HW Equilibrium concepts.)

    Predicting Genotype Frequencies: Hardy-Weinberg Equilibrium Review

    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):
    2pq

    (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:

    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

    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.

    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

  • 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.

  • 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:

  • 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.

    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.

    EXAMPLE:

    In your population of squirrels, a recessive allele of an X-linked locus (R) codes for a white star on the forehead (r).

    The dominant allele occurs in

    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:

    In the recessive homozygous females, q2 = 40/1000 (0.04), so q = 0.2.
    In the hemizygous males, the frequency of q is 200/1000 (0.2).
    The summed frequency of q in the expressing individuals is (0.2 + 0.2 = 0.4).

    Solving for p, the expected frequency of the dominant allele should be 1.0 - 0.4 = 0.6

    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:

    You know from your census that

  • 40 starred females carry 80 r alleles
  • 200 starred males carry 200 r alleles

    ...for a total of 280 of the 450 r alleles in the population. That means the remaining unaccounted 170 r alleles (450 - 280 = 170) must be "hiding" in the heterozygous females. Therefore, 170 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.

    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:

    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:

    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+)

    Where:
    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 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:

  • But others do not. A species unlikely to undergo reproductive isolation (for whatever reason) is said to be cohesive.
  • 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:

  • One generation after the migration, the new frequency of a in the recipient population (deme X) will be the changed by the addition of the A allele from the donor population (deme Y). This can be expressed as:

    pt+1 = (1-m)pt + mP

    in which: The change in p from one generation to the next is equal to:

    pt + 1 - pt

    in which:

    Example
    Let's say we have a two demes of frogs living in adjacent ponds. Deme X has a recessive allele for yellow legs present in 80% of the deme. Deme Y has a dominant allele for red legs present in 60% of the deme. There are 100 frogs in each pond.

    One rainy night, a gang of ten rowdy frogs from deme Y decides to hop over and move in with deme X. It happens to be breeding season, and the newcomers make themselves right at home, wooing the locals and sharing their genes.

    After one generation of breeding, what is the effect of this migration on the frequency of the a allele in deme X? Plug in!

    (1 - 0.09)(0.8) + (0.09)(0.6)
    which reduces to...

    (0.91)(0.8) + (0.09)(0.6) = 0.72 + 0.06 = 0.78

    In plain English: After one generation of input of allele A from the deme Y immigrants, the frequency of allele a in recipient deme X has decreased from 80% to 78%.

    Repeated back and forth migrations will have similar effects on the frequencies of the two alleles in either deme over time, and can have a homogenizing effect. The more migration between the two demes, the more similar the frequencies of their two alleles will become.

    Suggestion for better understanding: Create an example of this type of immigration, using your own numbers, and do a sample calculation. It makes sense.

    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...

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

    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.

    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.

    Systematic inbreeding between close relatives eventually will lead to complete homozygosity of the population.

    The diagram below shows the results of the ultimate inbreeding: self-fertilization by a single, heterozygous individual (Aa). By definition, each allele is present in 0.5 frequency in the starting population (one individual).

    If the individual self-fertilizes, then 1/4 of its offspring will be AA, 1/4 will be aa, and 1/2 will be Aa (use a Punnett Square, if you can't do this in your head!).

    The F1 generation will thus be 50% Aa (only half as much as the original population, which was 100% Aa).

    As the F1 generation again self-fertilizes, the AA individuals will give rise to 100% AA offspring, the aa individuals will give rise to 100% aa offspring, and once again the Aa individuals will give rise to 25% AA, 25% aa, and 50% aa.

    There are relatively fewer heterozygoes in each generation, since the heterozygotes are continually generating more homozygotes with each breeding cycle, while the homozygotes continue to generate more homozygotes (because that's all they can generate, if they are self-fertilizing.

    Eventually, the proportion of heterozygotes will be vanishingly small after several generations, and the population will consist almost entirely of homozygous individuals at either locus.

    If a locus segregates two alleles in an inbreeding population (A and a, for example), then one allele or the other will eventually be lost.

    Remember that the rarer will be found most often in heterozygous individuals, and only very seldom in homozygous (rare allele) condition.

    The Risks of Homozygosity
    What if a recessive allele is not only rare, but deleterious (i.e., maladaptive or harmful to the individual expressing it). Let us describe a rare allele (we'll consider the A1 allele carried by both Jethro and Ellie May of the previous story) that is found only once in every 1000 gametes.

    However, recall that if two mating individuals

    ...then there is a 50% (0.5) chance that both 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:

    As we will soon see, 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.

    Are there advantages to genetic diversity, not only within a species, but within a single organism? Recall the probability of homozygosity in a systematically inbreeding population 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.)

    Reduced resistance to disease is one hallmark of inbred populations, and is a result of inbreeding depression, a measure of loss of evolutionary fitness (to be defined shortly).

    Humans have been artificially selecting domestic plants and animals for thousands of years. Hence, many of the most deleterious (harmful) recessive alleles that might cause inbreeding depression have been removed from the population.

    However, in a large, wild population, individuals that begin to inbreed may suffer from significantly higher inbreeding depression, since the deleterious recessive alleles may not yet have been "weeded out" over thousands of years.

    This is a major problem faced by conservationists who randomly choose a few individuals of a wild population for breeding in captivity: The original breeders may be heterozygous at many loci that will quickly become homozygous after only a few generations, and inbreeding depression will appear.

    Zoos must be very careful about breeding their captive animals to avoid the problems inherent with inbreeding

    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.

    ~~~~~~~~~~~~~~~

    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.
  • 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
  • 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:

    .

    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 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."

    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.

    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.

    Consider:

    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.

    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:

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

    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.

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    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 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:

    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.)

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    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

    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.

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    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.

    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 Polymorphism When 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:

    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:

    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?

    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.

    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.

    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. Why is kin selection not altruism?

    Consider The Marmoset.

    This is a tiny, New World monkey who lives 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.
  • How could this possibly be adaptive for the aunt monkeys? (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)?

    Now consider the Honeybee.

    These are social hymenopteran insects whose populations are haplodiploid.

    The kin selection advantage is even greater in this case.

    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

    The probability of promoting one's own genes' survival provides a genetic explanation for apparently "altruistic" behavior of "self sacrifice".