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

                                       Normal Distribution for Mean 100 10$$

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 in nature,
           Show experimentally that heritable variation has consequences for fitness  <=

       What happens to a normal distribution under Selection?
             Compare distributions before [left] and after [right] selection

Directional Selection
      (I) Fitness function has constant slope:
           Trait mean shifted towards one extreme of phenotype
            trait variance changed
      (II) Fitness function normally distributed
           Fitness function shifts mean; variance unaffected

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

    Clinal variation of B allele in human ABO system

    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.: In AS system, deaths from malaria or sickle-cell are "replaced"
                N continually "topped up" to K

            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:
                   e.g. size cannot increase indefinitely
                  Johanssen bean experiment exhausted genetic variation within lineage
 

(2) Stabilizing Selection (AKA truncation selection)
      Fitness function has "peak"
      Trait variance reduced around constant trait mean: optimal phenotype,
              or tails of distribution eliminated (truncated)
 

      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

        Ex.:  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: can natural selection explain it?
       No single optimal from: trait variance increases

       polymorphic: variation maintained within populations
                Ex.: Genetic variation in corn snakes, tomatoes, bell peppers, snails
                Ex.: shell patterns in Cepaea snails
                       combinations of dark / light, banded / unbanded shells varies with substrate

       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) from production of less fit homozygotes            

      Overdominance: heterozygotes have superior fitness
                  because different alleles favored in different environments
      Examples:
           sickle-cell hemoglobin in Homo ('Contradictory' selection)
           Leucine Aminopeptidase (LAP) affects salinity tolerance in mussels (Mytilus)
      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 overall fitness
           Ex.: correlation between phenotype & H_e: antler points in deer (Odocoileus)
           Ex.: Hybrid vigor: crossbreeding of inbred lines in maize (Zea) improves vigor in F₁

Maintaining polymorphic phenotypes by selection

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

      Frequency-dependent selection:
           apostatic predation: thrush predation on Cepaea
                 'search image' changes when prey type becomes rare

      Sexual Selection (Darwin 1871):
            'Exaggerated' ornamentation disadvantageous to individual as survival phenotype
                but favored in competition for mates (reproductive phenotype)
          Sexual dimorphism in birds & mammals
          Antlers in deer (Cervidae) used in male-male combat

       Runaway sexual selection
                Females choose males on basis of secondary sex 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 selection), but polymorphism 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)
                then this becomes Balancing Selection
        or frequency selection occurs

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

Darwinian natural selection defined as
    differential survival & reproduction of individuals:
      Can selection operate on more inclusive biological units?

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

      Related individuals share alleles: r = coefficient of relationship [derivation]
            offspring & parents 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."
            Humans evolved in kin groups, function today in unrelated groups:
                 do evolved (Primate) behaviors persist?

       Parenting behaviour:
           'Broken wing' display in mother birds
           Mother sacrifices herself for (at least two) offspring
           [See also active defense of offspring] [Warning: language!]

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

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

Text material © 2024 by Steven M. Carr