Extend single-locus  multilocus  quantitative models

      p²:2pq:q²                 W₀,W₁,W₂          Mendel's Laws & H-W Theorem
                                                                                                
 normal distribution     fitness function              high heritability

Variation can be quantified

       mean  standard deviation: 
      variance: ²

      Quantitative variation follows "normal distribution" (bell-curve) iff [read: "if and only if"]
              Multiple loci involved
              Each locus contributes equally (variance is additive)
              Each locus acts independently:
                    interaction variance ( σ²_GxE ) minimal$σ$

Phenotypic variation has two sources: genetic (σ²_G) & environmental (σ²_E$$) variance$$$$$$$$

      phenotypic variance     σ²_P = σ²_G + σ²_E + σ²_GxE
      additive variance           σ²_A = σ²_G + σ²_E
      heritability                      h²  = σ²_G$$/ σ²_A  = σ²_G / (σ²_G + σ²_E)

          "Heritability in the narrow sense": ignores _GxE²  =  interaction variance:
           Identical genotypes produce different phenotypes in different environments.
               Ex.: same breed of cows produces different milk yield on different feed
              Contra: Norm of Reaction for differential expression within & between environments

Artificial breeding indicates that organismal variation is highly heritable
      ex.: Darwin's pigeon breeding experiments
             Artificial selection on agricultural species
                  Commercially useful traits improved by selective breeding
             IQ scores in Homo: h²  ~ 0.7
                   But: IQ scores improve with education: σ²_GxE$$ is large
            Offspring / Mid-parent correlation

Fitness function expresses relationship between genotype & fitness
    Function is a continuous variable, rather than discrete values for W₀, W₁, & W₂

=> Most traits variable & heritable
          Many traits do respond to 'artificial' selection (h²  = 0.5 ~ 0.9)
          Many traits should respond to 'natural' selection

=> To demonstrate & measure Natural Selection,
           Show experimentally that heritable variation has consequences for fitness  <=

 Quantitative traits can be described as a bell curve with a mean & variance

       What happens to this distribution under Selection?

(1) Directional Selection

      Fitness function has constant slope:
      Trait mean shifted towards favored phenotype
            trait variance unaffected

     In single-locus models, limit of selection is
      Elimination of variation by fixation of favored allele

    In quantitative models, rate limited by
       substitutional genetic load:
            Fitness "cost" (lost reproductive potential) to replace disadvantageous allele

        Substitutional Load = cumulative N over time as q 0

   "Soft" selection
          Mortality density-dependent
          In 'real' populations  N_(after)  ~ N_(before)

          Survivorship proportional to fitness up to K: more realistic
              Selection affects recruitment to next generation
         Ex.: Deaths from malaria are "replaced"
                 More births such that N continually "topped up" to K

            Gecko lizards (Aristelliger) have "suction pad" feet:
               lamellar scale counts increase with age

            Darwin's Finch (Geospiza fortis) adapts to drought:
                larger birds survive because of changes in seed size & hardness

      Developmental canalization limits extent of directional selection
              Systems are controlled by multiple epistatic loci:
                    difficult to select on all loci simultaneously
              Organisms have mechanical limits:
                   size cannot increase indefinitely
              Johanssen bean experiment exhausted genetic variation within lineage
              But: Eozostrodon-like Triassic mammal evolved into whales & bats between lineages
 

(2) Stabilizing Selection (AKA truncation selection)
      Fitness function has "peak"
      Trait variance reduced around (existing) trait mean: optimal phenotype,
 

      Limits: elimination of  variant alleles
              or, 'weeding out' of disadvantageous variants
              homozygosity at multiple loci:
                    difficult iff variance due to recessive alleles
             inbreeding depression: loss of 'somatic vigor' in inbred lines

      Examples:

        Cold shock in House Sparrows (Passer) [Bumpus 1898] 
                Animals that die occur in extreme tails of distribution

       Birth weight in Homo
                Modal birth weight has optimum survival
                Implications for future human evolution ?

(3) Diversifying Selection (two kinds)
      There is a lot of variation: does selection explain it?

    (A) Balancing Selection:
      Fitness function has more than one peak (multi-modal)

      Trait variance increases
       polymorphic: variation maintained within populations
                Ex.: corn snakes, tomatoes, bell peppers, snails

       polytypic: variation distributed among populations
                Ex.: Clinal variation in Cepaea snails
                        patterns of banded / unbanded shells vary over short distances

Limits:
      segregational genetic load:
          Fitness "cost" (loss of reproductive potential) due to production of less fit homozygotes            

      Overdominance: heterozygotes have superior fitness
                  because different alleles favoured in different environments
      Examples:
           sickle-cell hemoglobin in Homo ('Contradictory' selection)
            Leucine Aminopeptidase (LAP) & salinity tolerance in Mytilus mussels
       heterodimers:
                  multimeric enzymes with polypeptides from different alleles
                     often show wider substrate specificity, kinetic properties (V_max & K_M)
           myoglobin in diving mammals

      Heterosis: heterozygosity at multiple loci correlated with general fitness
           Ex.: correlation between phenotype & H_e: antler points in Odocoileus deer
 
      Hybrid vigor: crossbreeding of inbred lines improves fitness in F₁

Maintaining polymorphic phenotypes by selection

      Alternative phenotypes favored in different environments
       Batesian mimicry:
           'Tasty' mimics converge on 'distasteful' models
                     Viceroy butterflies (Limenitis) converge on Monarch (Papilio)  butterflies
       Müllerian mimicry: 
                Distasteful models converge on each other,
                different combinations evolve in different parts of range
               Heliconius butterflies [S&R 2.20]
       Mertensian mimicry:
                aposematic (warning) colouration discourages predators
                   Ex.: non-venomous scarlet king snakes mimic
                          venomous coral snakes with black / red / yellow pattern

      Frequency-dependent selection:
            Fitness value of phenotype varies with frequency

       apostatic predation: thrush predation on Cepaea
                 'search image' changes when prey type becomes rare

       'rare male' effect: females prefer "different" male
                Male zebra finches with artificial crest get more copulations

      Sexual Selection (Darwin 1871):
            'exaggerated' ornamentation disadvantageous somatically
                but favoured in competition for mates [S&R 4.17]
          Sexual dimorphism in birds & mammals
          Antlers in Cervidae used in male-male combat

       Runaway sexual selection
                Females choose males on basis of secondary ornamentation
                  Offspring have exaggerated trait (males) & preference for trait (females)
                     selection reinforces trait & preference for trait simultaneously
                            New phenotype spreads rapidly in population

(B) Disruptive selection
      Fitness function is a valley
            Trait variance increases (like balancing), BUT polymorphism is unstable

      Polymorphism can usually be maintained only temporarily:
            One of the phenotypes will out-compete the other
       unless different phenotypes choose different niches (Ludwig Effect)
                [and then this becomes Balancing Selection]

      Scutellar bristles in Drosophila 
            Selection for 'high #' versus 'low #' lines
                  => 'pseudo-populations' with reduced inter-fertility
          Might disruptive selection contribute to speciation?

Natural selection is ordinarily defined as
    differential survival & reproduction of individuals:
      Can selection operate on other biological units?
      Can such selection 'oppose' individual selection?

Genic (Gametic) Selection
           Differential survival & 'reproduction' of alleles

      Meiotic Drive: t-alleles in Mus
       tt is sterile (W = 0)
       Tt is 'tail-less' (cf. Manx cats) (W < 1)
           t alleles preferentially segregated into gametes (80~90%)
                  => f(t) is high in natural populations (40~70%)
                       even though it is deleterious to individuals

Kin (Interdemic) Selection
           Differential survival & reproduction of related (kin) groups (families)

      Related individuals share alleles: r = coefficient of relationship [derivation]
            offspring & parents are related by   r = 0.50   [They share half their alleles]
            full-sibs                 "    "                     r = 0.50
            half-sibs                "    "                     r = 0.25
            first-cousins           "    "                    r = 0.125

     Inclusive fitness (W_i) of phenotype for individual i
            = direct fitness of i + indirect fitness of relatives j,k,l,...

       W_i = a_i + (r_ij)(b_ij)   summed over all relatives j,k,l,...

            where: a_i    = fitness of i due to own phenotype
                        b_ij  = fitness of j due to i's phenotype
                        r_ij   = coefficient of relationship of i & j

              If i & j are unrelated
                   warn:          W_individual = 0.0 + (0.0)(1.0) = 0.0
                   don't warn: W_individual = 1.0 + (0.0)(0.0) = 1.0
                Such behaviors should not evolve among unrelated individuals

            What is the fitness value in a kin group?
                   W_brothers       = 0.0 + [(0.5)(1.0) + (0.5)(1.0)] = 1.0
                   W_cousins       = 0.0 + [8][(0.125)(1.0)] = 1.0
                Such behaviors can evolve among related individuals in (extended) family groups

       JBS Haldane (1892-1964):
            "I would lay down my life for two brothers or eight cousins."

       Parenting behaviour:
           'Broken wing' display in mother birds
           Mother sacrifices herself for (at least two) offspring

       Altruistic behaviour ( "unselfish concern for others")
           Alarm calls in ground squirrels (Spermophilus)
                        females warn more in related groups
                  Can behaviour to help unrelated individuals evolve?

       Eusocial insects (Hymenoptera, Isoptera)
           Haplodiploidy: females diploid, male drones haploid
                        Females workers are sterile (W_i = 0): what selective advantage?
                            related to queen or offspring by 1/2
                            related to sisters by 3/4
                  Care for sisters, don't have offspring

Natural Selection may be the most misunderstood concept in biology.
    It is ...

(1) Not "Survival of the Fittest"
      H Spencer (1820 - 1903) & others invent "Social Darwinism"
            "naturalistic fallacy": 'is'  = 'ought'
            Darwinian theory accepted in part because
              it could be read to support British imperial ambition

      not phenotype-specific mortality
      not predation (nor inter-species competition, usually)
      not "Nature red in tooth and claw"
              Darwin: plants in desert 'struggle' for water
      not equivalent to population growth:
           Ex.: population N declined in semelparous example

(2) Not equivalent to evolution

      Natural Selection may conserve existing types (stabilizing selection).
      Evolutionary change ultimately requires new variation (mutation).
      Migration, population structure, genetic drift important.

(3) Not a tautology (a self-evident statement; a circular argument)

      "Why do they survive? Because they're fit.
            How do you know they're fit? Because they survive..."etc.

      Darwin phrased syllogism (an if / then statement; a logical consequence):
            (² & W  &  h²) => q
            cf. physics:  F = M A  depending on how Force, Mass, & Acceleration defined
                 arithmetic:  1 + 2 = 3  because I and II make III

(4) Not "Mother Nature"

      not a force, not thing that acts
           [We don't say, "Arithmetic causes one plus two to equal three."
            We might say, "One plus two equals three. That's arithmetic.]
      not good or bad (amoral)

      no noun / verb / object distinctions
            In SVO languages, "nouns verb objects"
                i.e., objects act on other objects. Not.

(5) Not teleological (goal-directed):

      Evolution does not have "goal", "direction", or "purpose"
            Homo sapiens are not the endpoint of evolution!

      Avoid such phrases as "Natural Selection acts ..."
       "in order to ...",
           "for the purpose of ...",
           "so that ...",
           "because its trying to ..."

Text material © 2020 by Steven M. Carr