What Causes Phenotypic Variation Among Individuals by dffhrtcv3

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									            Quantitative Genetics
• Up until now, we have dealt with characters (actually
  genotypes) controlled by a single locus, with only two
  alleles:




                                           Discrete Variation
            Many Traits are Polygenic


                                           Quantitative Variation
                                           or Continuous variation




• continuous and quantitative refer to variation, polygenic
  refers to the mode of inheritance, ("many genes")
         Studying Quantitative Traits
• It would be impossibly difficult to use the same approach
  as population genetics to consider inheritance at many
  many loci, especially if the number of loci is unknown



• We need to look at DISTRIBUTIONS of characters rather
  than frequencies of alleles
Characterizing a Quantitative Trait


                                 Mean (average)    z

                                 Variance in Phenotype (VP)
# of individuals




                                 (mean squared deviation from mean)

                                                      zi  z 
                                                                   2

                                                  
                                                          N


                        Z
                   (Phenotype)
                   What Causes Phenotypic Variation
                          Among Individuals
                                         Genetics?
# of individuals




                                         Environment?

                                         Both?
                           Z


                      VP  VG  VE  VG x E
 Partitioning Variance

VP  VG  VE  VG x E

 Total Phenotypic Variance (VP)




VG                     VE         VG x E
Fig 8.26




Unspecified
source
population
                 Partitioning Variance
                 Total Phenotypic Variance (VP)




               VG                            VE             VG x E

                                        Genetic Variance can be subdivided:

      VADD      VDOM      VEPI          VADD= phenotypic variation due to
                                        the additive effects of alleles
VEPI = phenotypic variation due to      VDOM = phenotypic variation due to
epistatic effects (when the effect of   dominance effects (when the effect of
the allele depends on the identity      the allele depends on the identity of
of alleles at different loci)           the other allele at that locus)
       Dominance and Epistasis




BBEE                             BBee
BBEe                             Bbee
                                 bbee
BbEE
BbEe

                  bbEE
                  bbEe
             Additive Genetic Variation
 VADD= phenotypic variation due to the additive effects of alleles


 Consider a gene with 2 alleles, A1 and A2:

                        A1 A1    A1 A2    A2 A2     a     d
     Additive effects
                        10       8        6
     only

     W/ dominance       10       10       6

How much does each additional copy of A1 add to phenotype?

Which of these can be passed on to offspring?
                   Partitioning Variance
                    Total Phenotypic Variance (VP)




                  VG                       VE              VG x E

Environmental Variance can be
subdivided:
                                         VENV VCOM VMAT
VEN V= phenotypic variation due to
random environmental influences

VCOM = phenotypic variation due to   VMAT = phenotypic variation due to
common family influences             maternal influences
                            Maternal Environment Effect in
                                Guppy Offspring Size
                      Food stressed mothers produce larger offspring
                      1.4

                      1.3
Offspring Size (mg)




                      1.2

                      1.1

                       1

                      0.9
                               Low              High
                                Maternal Food Level

                                                       Reznick and Yang 1993
     Breaking the Stick of Variation
• By breaking the stick of variation, we can determine
  how much of the phenotypic variation is due to each
  component.
• Selection acts on phenotypic variation, but can only
  cause evolution if the variation is heritable

• Broad-sense heritability: H2 = VG/VP

• Narrow-sense heritability: h2 = VA/VP
              Partitioning Variance
              Total Phenotypic Variance (VP)




            VG                               VE                 VG x E



  VADD       VDOM       VEPI      VENV VCOM VMAT                VG x E

heritability (h2) = the proportion of phenotypic variation that is due to
the additive effects of alleles [how much of VP is made up by VADD]

   VADD          Total Phenotypic Variance (VP)
   Why only Additive Genetic Variance?
  The additive effects of alleles are responsible for the
    degree of similarity between parents and offspring
               Additive effects                            Dominant A2




a = the effect of substituting an A1 or A2
                                                      A2A2 A1A2 A1A1 a   d
allele
                                             ADD only 10    8    6   2   0
                                             w/ DOM 10     10    6   2   2
Why is there spread around the
phenotypic values of 6, 8, and 10 for
each genotype?
          VE
     Why only Additive Genetic Variance?
    The additive effects of alleles are responsible for the
      degree of similarity between parents and offspring
              Additive effects                         Dominant A2




                                 A1A2 x A1A2
          Parents = 8                                Parents = 10
Offspring = .25(6)+.5(8)+.25(10) = 8    Offspring = .25(6)+.5(10)+.25(10) = 9
 Dominance causes offspring phenotype to deviate from parental phenotype!
           So, What is Heritability?
Heritability describes the proportion of variation in trait
  that can respond to selection

Broad-sense Heritability (H2 = h2B = VG/VP)
   – could include dominance and epistatic variation

Narrow-sense Heritability (h2= VA/VP)
   – proportion of phenotypic variance that is due to
     additive genetic causes
                                           Measuring Heritability
Heritability is the slope of the regression between offspring and
  mid-parent phenotype
Offspring phenotypic trait value




                                                                       covariance between parent & offspring
                                                          slope =               variance of parents
                                   h2= 0.89
                                   Slope = 0.89




                                                                       Can look at other relatives too!

                                                                           Slope(mom,daughter) = ½ h2
                                   Mid-parent phenotypic trait value
                                                                             Slope(half-sibs) = ¼ h2
           Meaning of Heritability




• Evolution by natural selection can only occur in pops A
  &B
• h2=0 in pop C--> none of the variation is due to VA
• h2 is undefined, there is no variation
                     Notes about h2
1) Heritability is NOT THE PROBABILITY A TRAIT IS
   INHERITED OR THE PROBABILITY A TRAIT HAS A
   GENETIC BASIS
2) Estimates of heritability are specific to the population in
   which they are measured.
3) heritabilities are statements about variance, not means (e.g.,
   the number of eyes in humans has a 0 heritability, but this
   doesn't mean that eye number is not under genetic control)
4) high heritability doesn't mean environment doesn't matter or,
   vice versa, low heritability doesn't mean genes aren't important.


      VADD       Total Phenotypic Variance (VP)



      VADD        Total Phenotypic Variance (VP)

								
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