I.  Quantitative trait characteristics

    A.  Phenotypes continuously distributed, not discrete

    B.  Usually controled by several to many genes

            1.  ideal (completely additive case)
            2.  complications--dominance and epistasis, different magnitude of effects on trait

II.  Example of quantitative traits: floral morphology in Mimulus
                (from Fishman, Kelly, and Willis, 2002, Evolution 2138-2155)

            1.  Two species:  Mimulus guttatus and M. nasutus
          2.  The two species differ in lengths of several characters:
 

            2.  How many loci contribute to this difference?

                    a.  QTL (Quantitative Trait Locus) analysis

                    b.  Results of QTL analysis

                            i.  QTL's on Linkage Group 8
 

                    b.  QTL's on all 14 Linkage Groups (2n=28)

                    c.  Each trait represented by many QTL's, each QTL with relatively small effect.
 

III.  Approach to modeling evolution of quantitative trait

    A.  Cannot model change in allele frequences at all loci involved

    B.  Instead, model how evolutionary change in mean value of trait is expected to occur based on knowledge
            of small number of measurable parameters:

            1.  Additive genetic variance, V_a

            2.  Phenotypic variance, V_p

            3.  heritability:  h2 = V_a / V_p

    C.  Experimental methods for estimating these parameters