Extend single-locus  multilocus  quantitative models

      p²:2pq:q²                      W₀,W₁,W₂          Mendel & H-W Theorem
                                                                           
 normal distribution       fitness function     Heritability

Quantitative genetics: 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)

           h² : "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
           Norm of Reaction for differential expression within & between environments

Artificial breeding indicates that organismal phenotypic 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
    A continuous variable over range of genotypes, 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 [skewed to right]
      (II) Fitness function normally distributed
           Trait mean shifted: 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 is density-dependent
               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 continuously "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 developmental 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"
          Variance reduced around constant trait mean at 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
              Müllerian mimicry:
                       Ex.: Heliconiusspp. butterflies exchange alleles by hybridization
                          Distasteful models converge on each other,
                          Different combinations evolve in different parts of range            

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
 
      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 multi-locus phenotypes by Natural Selection

      Alternative phenotypes favored in different environments
       Batesian mimicry:
           'Tasty' mimics converge on 'distasteful' models
                     Ex.: Viceroy butterflies (Limenitis) converge on Monarch (Papilio) butterflies
                             Mimic remains rare wrt model
       Müllerian mimicry: 
                Distasteful models converge on each other,
                Different combinations evolve in different parts of range
               Ex.: Heliconius spp. butterflies exchange alleles by hybridization
       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: Turdus thrush predation on Cepaea snails
                 'search image' changes when prey type becomes rare

      Sexual Selection (Darwin 1871):
            'Exaggerated' ornamentation disadvantageous to individual 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?
         Group Selection controversy: cf. Kropotkin (1902) "Mutual Aid"

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 + [2](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 small kin groups, function today in large, ~unrelated groups:
                 do evolved Primate behaviors persist?

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

       Altruistic behavior ( "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
                  [NB: 'Queen' Bee mates with multiple drones: workers related to half-sisters only by 1/2]

Text material © 2025 by Steven M. Carr