The tabulated the body masses of 17 male White Rock chickens and the means of their male progeny were presented.  Individuals were weighed to nearest gram at 8 weeks of age.  When mature, 17 males were randomly mated and their male progeny weighed when 8 weeks old. 

1.  Estimate the heritability of body mass in the population of chickens from which this sample was obtained.

See attached spreadsheet. 
Heritability = h2 = 0.43, indicating that 43% of the phenotypic variance in the population is heritable.  

2.  What can you say about the environments of fathers and their offspring?

The mean of the offspring is greater than the mean of the fathers.  Assuming that there was no selection, this difference indicates that the progeny’s environment led to greater body mass.

You were provided the number of leaves per plant in 25 F1 and 25 F2 plants from a cross of two cultivated varieties of tobacco, which had mean leaf numbers of 15.0 and 17.9, respectively.

3.  Tabulate and plot the frequency distributions of the F1 and F2 generations. 

See attached spreadsheet.

4.  From each distribution calculate the mean, the variance, and the standard error of the mean.

F1:  mean + S. E. = 15.72 + 0.24, V = 1.46
F2:  mean + S. E. = 15.84 + 0.49, V = 5.97

5.  What are the main differences between the two distributions?

F2 is more variable and has a greater range.

6.  Estimate the degree of genetic determinism in the F2 generation.  What assumptions must you make to do this?

Assume that the varieties crossed were homozygous at all loci.  Tobacco is normally self-pollinating, so this is likely to be true.  If so, the F1 progeny are all genetically identical heterozygoes and their variance is wholly environmental in origin.  The variance of the F2 includes both environmental and genetic components. 

The second assumption is that the environmental variance in the F2 is the same as that in the F1.  With this assumption, the genetic variance is obtained by subtraction.

Population

components

 

variance

 

F2

VG

VE

5.97

F1

 

VE

1.46

, or, 76%.

difference

VG

 

4.51

 

7.  You were presented data from a study of the adult height of people in two West African villages.  Female heights were adjusted to male equivalents so that the means were the same in males and females.  Derive what you regard as the most reliable estimate of the heritability.  (Data from Roberts, D. F. et al. (1978) Ann. Hum. Gen. 42:15-24.)

Because , the heritabilities are obtained by doubling the regression coefficients:

 

Offspring-parent regressions

 

 

Father

Mother

Sons

0.646

0.908

Daughters

0.582

0.840

Mean

0.614

0.874

Standard deviations (inches):  Males 2.5; Females 2.3

 

 

The heritabilities obtained from the regressions on the mother are substantially higher than those from fathers, which can be attributed to a maternal effect.  The regressions on fathers consequently provide the most reliable estimates of heritability.  Because the heights were corrected for the sex differences, there are no reasons to prefer the daughters or the sons, so we take the mean as h2 = 0.614. 

It is interesting to note that the maternal effect can be obtained from the difference between the regressions on mothers and fathers: