Problem Set I Answers, Fall 2008

1)  This is one possible answer.  Other answers are possible as long as they have no more than 3 changes.

2)  The gene controlling web building is on the X chromosome, with colonial web building (A) dominant to solitary web building (B).

      Offspring from a cross between an A female and a B male: females are AB (on Xs) and males have only A (on lone X). Offspring from a B female and an A male: females are AB (on Xs) while males have only B (on lone X)

3)  You are related to your mother by 1/2 and she is related to her mother by 1/2, so you are related to your grandmother by 1/4.

4)  To answer this question correctly you have to trace the path to your mom's neice through both your grandmother and grandfather (closest common ancestors of your mom and her brother).

        Through grandmother - 1/2 * 1/2 * 1/2 * 1/2 = 1/16

        Through grandfather - 1/2 * 1/2 * 1/2 * 1/2 = 1/16

        1/16 + 1/16 = 1/8

5)  Either the F1 or Parental generation would be best to measure environmental variability because all individuals within an inbred strain or among F1 individuals should be genetically identical and, therefore, any differences in phenotype can be attributed to environmental variation.  In contrast, variation among F2 individuals includes both environmental differences and genotypic differences.

6)  This question used the relationship b or t = rh2 

      h2 estimated from avg parent-avg offspring regression = 0.9

      h2 estimated from full-sibling correlation: 0.3 = 0.5(h2); h2 = 0.6

      You need to propose a mechanism that would cause parent-offspring similarity to be higher than sibling similarity.  Since the example is about song and song is known to be acquired by learning, a simple and plausible answer is that nestlings learn their song from their parents, which causes them to be more similar to their parents than to their siblings. 

7)   The selection differential for a trait equals the covariance between lifetime reproductive success and the trait, i.e. S = Cov(LRS, trait). But if the trait is expressed only in one sex, then selection can only act on the trait through that one sex, and S must be divided by 2.

    To answer this problem you use the breeder's equation: R = h^2 * S

    So: S = 20 / 2 = 10
    R = 105 - 100 = 5

    and h2 = 5 / 10 = 0.5

8)  To answer this question you need to apply the breeder's equation again where

      R (Response to selection) = mean of offspring pop - mean of parental pop

      S (Selection differential) = mean after selection - mean before selection

      h2 = heritability = regression coefficient for regression of average parent on average offspring    

      Then, given that

      h2 = 0.8

      mean of parental pop = 75

      mean of selected parents = 50

      mean of offspring pop -75 = 0.8(50-75) 

    Therefore,
    S = 9 / 2 = 4.5
    h2 = 0.2 * 4 = 0.8
    R = h2 x S = 4.5 x 0.8 = 3.6

    and the expected mean in the next generation = R + mean previous generation = 25 + 3.6 = 28.6