# Evolution Chapter 14 Hints

HINT 14A: The variance in the F1 can be used as an estimate of the environmental variance, because the F1 are genetically identical.

HINT 14B: This question can be answered using “common” logarithms to base 10 or “natural” logarithms to base e. To be consistent with later questions, use base 10.

HINT 14C: It is simplest to find these by plotting mortality against log(dose), and draw a sigmoid curve through the points. The mean is where this curve crosses 0.5, ±1 standard deviation (s.d.) is where the curve crosses 0.16 and 0.84, and ±2 s.d. is where it crosses 0.025 and 0.975.

HINT 14D: See Table 14.2, line 2; we can ignore higher-order components such as VAA, which represent epistasis.

HINT 14E: Remember that these are real data, and so estimates of variance are subject to substantial sampling error.

HINT 14F: The correlation coefficient is defined as cov(x, y)/.

HINT 14G: Think about the different variance components.

HINT 14H: Assume Hardy–Weinberg proportions. See p. 393 and Box 14.1.

HINT 14I: See Box 1.1 for Hardy–Weinberg proportions.

HINT 14J: The normal distribution follows exp(–x2/2)/, where x is measured in standard deviations. Therefore, it has height 0.054, 0.242, 0.399, 0.242, 0.054 at x = –2, –1, ..., 2 standard deviations. These values can be used to make a rough sketch of the bell-shaped distribution.

HINT 14K: This can be similar to Figure 14.18, except that the variance components depend on two allele frequencies, not one. For example, plot them against pA for pB = 0.2, 0.5, 0.8.

HINT 14L: Think about the changes in the effect of variance components over a range of allele frequencies.

HINT 14M: If only one gene were involved, then the parentals would be homozygous for one or other allele, and the F1 would be heterozygous. The distribution in the F2 would have 1:2:1 proportions of the three genotypes.

HINT 14N: The estimated number of genes is Δ2/(8Vg), where Vg is the genetic variance in the F2.

HINT 14O: Think about which chromosomes the markers are located on.

HINT 14P: The sum of the 12 estimated δ for stigma exsertion is Σδ = –2.81; these are defined as the difference between E/E and E/P genotypes at each locus.

HINT 14Q: What happens to markers linked to drug-sensitivity alleles?

HINT 14R: Consider a single marker locus, with alleles MR, MS with a recombination rate c. What are the frequencies of the surviving genotypes?