BIOL 4160

Evolution

Phil Ganter

301 Harned Hall

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Flower of a Bunchberry, a Cornus species (the dogwoods) that is not a tree and grows only inches high

Microevolution: Modelling the Natural Selection of Alleles

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Remember that natural selection is a mechanism of evolution, it is not evolution

Natural Selection can enhance, reduce, or maintain variability (in the last case, natural selection resists evolution!)

  • Natural selection can, under the right conditions, favor polymorphism (two or more alleles or phenotypes in a population) and can result in a Balanced Polymorphism if selection resists change in the allele frequencies
    • more on this later
  • Natural selection can have different effects on a population, which we have divided into three "modes of selection" in the lecture on variation:
    • Disruptive (Diversifying)
      • when the extremes are fittest and intermediates are less fit
      • Can split a population into two phenotypes with few intermediate forms
      • in statistical terms, the mean need not change
    • Stabilizing
      • when the fittest individuals are the average, then those with more extreme (larger and smaller) phenotypes are less fit and NS will act to reduce the number of individuals with extreme phenotypes
      • in statistical terms, the mean of the phenotype is not affected but the standard deviation is (it should decrease)
    • Directional
      • when a new, fitter phenotype originates or arrives through migration, the population will move from the older, less fit phenotype to the newer phenotype over time
      • This will change the mean value of that over time but need not affect the standard deviation

Fitness is the per capita rate of increase of some biological unit (we will see that this can be a locus, an individual, a deme, or even a species)

  • For natural selection to occur, there must be a correlation between phenotype and fitness, so lets look closer at fitness
  • Fitness is the overall success in reproduction that can be ascribed to an individual, gene, or group
    • This has many components:
      • Survival of the individual, the individuals carrying the gene, or the group
      • Speed of development
      • Mating success
      • Production of offspring (number, size, condition)
    • Fitness considerations do not stop when the offspring are born, as a parent is only successful if its offspring are also successful (and their offspring, ad infinitum)

Absolute Fitness

  • So, is there a measure that will combine all components
  • Yes, there is.  It is called r (or, as in the book, R (really R0), a related measure that is easier to explain), the intrinsic rate of natural increase
    • When referring to a gene or lineage (can't apply to individuals, only the lineage to which they belong) the letter "m" is often substituted for "r", especially in the older literature
  • r comes from ecology and we will not develop the theory to use it here, so we will conform to the book's use of R0,  the symbol for the replacement rate
    • For asexuals, is the number of individuals in the next generation for ever  individual in the present generation
      • if R0 is greater than 1, the population is growing
      • if R0 equals 1, the population size is stationary
      • if R0 is less than 1, the population is decreasing
    • We can apply this idea to a portion of the population, say those with the A allele at locus A, so if A has an R = 1.4, then there are 1.4 copies of that allele in the next generation for each copy in the present generation
  • R0 (or r) is a measure of absolute fitness because it literally indicates how many copies of a gene there will be in the next generation
    • Absolute fitness is useful but can be hard to measure and hard to work with when modeling evolution

Relative Fitness

  • Relative fitness is often preferred as a measure of fitness
  • The fittest genotype (in absolute fitness terms) in a generation is the reference fitness
  • All other genotypes will have a fitness less than the reference, and so they will be a fraction between 0 and 1 if we simply divide the absolute fitness of each genotype by the absolute fitness of the reference fitness, the maximum absolute fitness
    • notice that the denominator is always at least as large as the numerator and will usually be larger, giving us the 0-to-1 range of relative fitnesses defined above

Mean relative fitness

  • This is a measure of the difference between the actual population fitness and the theoretical maximum
    • The rate of genetic change in a population due to selection will depend on the magnitude of the difference between actual and maximal fitness
  • calculated by multiplying the relative fitness of each genotype by its frequency in the population, then summing up all of the products
    • If absolute fitness (R0) of A1A1 is 1.6, is 1.36 for A1A2 and 1.2 for A2A2,
    • then the relative fitness (Wi) of A1A1 is 1.0, is 0.85 for A1A2 and 0.75 for A2A2
    • Now suppose that half of the population is A1A1 and the other half is equally split between A1A2 and A2A2
    • Then the mean fitness of the population (W-bar) is
    • (0,5 * 1.0) + (0,85 * 0.85) + (0.25 * 0.75) = 0.5 + 0.2125 + 0.1875  =  0.9

Coefficient of Selection (often s)

  • measures the selective disadvantage of a genotype relative to the most fit genotype
  • calculated as   s =  1.0 - W (using the relative fitness of a particular genotype)

One additional and important advantage of using relative fitnesses

  • The rate of genetic change under selection depends not on the absolute fitnesses but on the relative fitnesses
    • So, it doesn't matter if the R0's are 1.6, 1.36, and 1.2 or 8, 6.8 and 6 or 0.5, 0.425, and 0.375 (this last for a declining population), evolution will proceed in the same manner and speed because the relative fitness of all three scenarios is 1.0, 0.85, and 0.75.
  • Note that it does not matter if the population is growing or not, evolution will proceed as expected

A Model of Selection

  • Since the purpose of this model is to understand how selection will effect evolution, we will ignore genetic drift (and mutation, migration, and mating)
    • this is only a simplification and more realistic models incorporate both
  • We will also simplify by focusing on a single locus with only two alleles present in the population
  • From the Hardy-Weinberg equation, we will borrow p and q (the frequency of the A and A alleles, respectively) and the starting point for our population
Genotypes
A1A1
A1A2
A2A2
Frequency of Genotypes at Birth
p2
2pq
q2
Fitness of Genotypes
w11
w12
w22
  • The model predicts what the allele frequencies will be after selection operates on this population
  • Since we know the initial frequencies of each genotype and their fitnesses, we can calculate the mean population fitness at birth as (this is useful later):

  • We will use the change in allele frequency as our measure of the effect of selection and, for consistency, we will always predict the change in p, the frequency of allele A1

  • Logically, if p increases, then q, the frequency of the A2 allele, must go down

  • The general solution is (see book for derivation):

  • But this equation can be simplified if we make some assumptions about dominance and the fitnesses

A1 dominant and advantageous (A2 disadvantageous)

  • First, and for all of the equations below, we will express the relative fitnesses in terms of selection coefficients and then present the algebraic simplification that results from substituting them into the general equation above (all five cases are simplifications to predict the outcome in specific situations)
 
w11
w12
w22
Fitness
1
1
1-s

  • This says that p will increase (the right side of the equation is positive and so delta-p is positive), which makes sense as A1 is the most fit of the two alleles

A1 dominant but A2 selectively advantageous

 
w11
w12
w22
Fitness
1-s
1-s
1

  • Here delta-p is negative (look at the right side) and so A1 is being lost from the population, as is should if A2 is more fit than A1

Incomplete Dominance with the heterozygote fitness between the advantageous dominant homozygote and the disadvantageous recessive heterozygote

  • In this case, the heterozygote must have a higher fitness than the homozygous recessive genotype and one way to do that is to multiply s by a second fraction, h
  • h will increase w because, as h is between 0 and 1, the product of h and s will be smaller than s and this smaller product is subtracted from 1
 
w11
w12
w22
Fitness
1
1-hs
1-s

  • This equation predicts that the change in p is always positive, so the endpoint arrives when A1 is fixed in the population
  • Note that this equation differs from the text's equation (equation A3 on page 274).  I could not derive the equation presented in the text but, when I graphed the equation, it did not behave as described there.  So, I am presenting my derivation, which does behave as predicted (and as makes sense because w11 is the fittest genotype and should move A1 to fixation)

Incomplete Dominance with Heterozygote advantage

  • The heterozygote has the fittest genotype but we will allow each of the homozygotes their own selection coefficient
 
w11
w12
w22
Fitness
1-s
1
1-t

  • The change in p will depend on its frequency: it will be positive below a particular value of p and negative when p is over that value (change = 0 when p is at that value)
  • This scenario produces a Balanced Polymorphism, a stable equilibrium (stable because when not at the equilibrium point the value of p moves toward equilibrium so that the system returns to equilibrium)
  • This situation is called Heterosis

Incomplete Dominance with Heterozygote disadvantage

 
w11
w12
w22
Fitness
1+s
1
1+t

  • The outcome here is also an equilibrium but an unstable equilibrium
  • When the value of p is not at the equilibrium point the change in p will not move it toward the equilibrium point but away from it (toward either fixation or loss of the A1 allele, depending on the value of p)

A special case - A1 is dominant and A2 is a recessive that is lethal when homozygous (harmless when heterozygous due to the dominance effect)

  • In this case, we see that dominance can protect the heterozygote but every generation, the homozygous recessive individuals are lost before they can reproduce (or even before they can develop)
 
w11
w12
w22
Fitness
1
1
0

  • Notice something about the equation above
    • As q, the frequency of the lethal allele (A2) decreases, as it should (after all, its lethal in the homozygous condition), the rate of change for p is smaller and smaller (it depends on q2, which is a smaller and smaller numerator)
    • Thus, the rate of loss of the lethal slows to a trickle and it persists in the population for many generations
  • This makes sense because, when there are very few A alleles present, the chance of an individual carrying A mating with another rare carrier of A is very small and that is the only way to get homozygous individuals that will be lost

Maintaining Allelic Variation

  • Many of the predicted outcomes from selection predict the loss of less fit alleles, which should decrease genetic variation
  • In the face of loss of alleles through selection (and genetic drift), what maintains genetic variation
    • Migration can re-supply alleles
    • Mutation can re-supply alleles
      • This is only true for mutations that recur (i. e. that are not unique events) like point mutations (and, to a lesser extent, indels)
      • Mutation pressure produces an equilibrium that depends on the ratio of the mutation rate to the selection coefficient

    • Balancing Selection
      • I disagree with the book on the equivalence of the terms "Heterozygote Advantage" and "Overdominance"
        • Heterozygote advantage is measured in terms of fitness (heterozygotes have the greatest fitness)
        • Overdominance refers to the phenotype of the heterozygote
          • when the phenotype of the heterozygote lies outside of the range between the two homozygotes
      • Why is this confounded in the book (and by many)?
        • If you consider fitness a phenotypic measure, then it is a case of overdominance
        • however, an overdominant phenotype need not be the most fit (which seems to imply that fitness is not, in actuality, a phenotype but a measure of success linked to a phenotype)
    • Antagonistic Selection
      • when a phenotype affects more than one fitness component, selection of one component may oppose selection of another component
      • Malaria-linked anemias
        • heterozygotes experience lowered viability and homozygotes often have very low viability, which selects against the recessive (anemia-producing) allele
        • when malaria is present, heterozygotes do not support the parasite as well as homozygous dominant, giving the heterozygote the greatest fitness
      • so the anemia-producing alleles are not favored unless malaria is present
    • Selection that varies over Time or Space (Multiple-Niche Polymorphisms)
      • polymorphism can result:
        • if one allele is favored part of the time and the other allele is favored the rest of the time  OR
        • if one allele is favored over part of the habitat and the other allele is favored in the rest of the habitat
      • often detected when older individuals' phenotypes are distributed bimodally but not so at birth
      • Chiricauhua chromosome in Drosophila pseudoobscura (favored part of the year, disadvantageous the rest of the year)
    • Frequency-Dependent Selection
      • Inverse frequency-dependence
      • selection advantage is inverse to allele frequency
      • produces a stable polymorphism
      • Sex-Ratio is an example of inverse-frequency dependence

Multiple Outcomes

  • Some situations are unstable equilibria
  • here, both fixation of an allele and its elimination are both possible
  • Adaptive Landscapes
    • Here, the average fitness of a population is mapped
    • The length and width represent phenotypes
    • The vertical dimension is fitness, so going up a hill means increasing fitness and down decreases fitness
    • Top of each hill is an Adaptive Peak
    • populations cannot leave as all directions are down
    • multiple hills (peaks) represent multiple stable outcomes

Detecting Selection in the Gene

Background:

  • Recombination:
    • All nucleotide positions along a gene are subject to point mutations
      • Each position is a separate "locus" and recombination can occur within the sequence of a gene
    • However, the probability of recombination between any two points along a chromosome depends on the distance between those points
    • Since no gene is that large, the distances between any two nucleotides is very small and so is the chance of recombination
      • Even with such tight linkage between positions within a gene, over sufficient time recombination should occur
      • Recombination "breaks" linkage between sites along a chromosome
  • Selection and Hitchhiking within the Gene
    • When a mutation occurs a particular site, it has a chance of becoming fixed
      • For neutral mutations, the probability of fixation and time until fixation depend on the population size
      • For advantageous (in terms of selection) mutations, the mutation will become fixed and the time until fixation will depend on the selection coefficient
      • Advantageous mutations should be fixed in less time than neutral mutations in large populations (in small populations, there may be no great advantage when the selection coefficient is not very large)
    • Due to tight linkage, when an advantageous mutation is fixed, so are most (if not all) of the neutral mutations that happened to be near the mutant position on the particular gene sequence bearing the advantageous mutation (another case of hitchhiking)
      • Selective Sweep
        • The fixation of an advantageous point mutation carries a set of neutral mutations to fixation as well, "sweeping away" the variation that was present in the population at each of the proximal nucleotide sites along the gene
      • Balanced Polymorphism
        • Once a balanced polymorphism hits the equilibrium frequency for each allele, each lineage is preserved (will not become fixed due to genetic drift) if the population is large
        • This prevents "selective sweeps" affecting variation within that gene

Consequences:

  • When we sequence genes, we can sequence many examples of the gene from different individuals in the population
  • If we count the number of variable sites along the gene by comparing all of the sequences, we can get an estimate of the time since the previous "selective sweep"
  • We can detect selection by looking for regions with exceptionally little variation (directional selection causing selective sweeps) and exceptionally great variation (balancing selection preserving particular alleles)

 

Last updated March 24, 2010