## Problem box answers

Problem box 8.1 answer

For the wheat-maize divergence 60 million years ago divergence rates are

0.0504 substitutions per site coxl ------= 0.00042 substitutions per site per million years

2(60 million years)

0.1374 substitutions per site atp9 ---= 0.001145 substitutions per site per million years

2(60 million years)

0.0381 substitutions per site nad4 ------= 0.000318 substitutions per site per million years

2(60 million years)

Using these absolute divergence rates, the divergence time of the monocot-dicot split is estimated as

0.2060 substitutions per site coxl ---= 245.2 million years

(2)0.00042 substitutions per site per million years

0.4439 substitutions per site atp9 —:—:—:-r--^-= 193.8 million years

(2)0.001145 substitutions per site per million years

0.1101 substitutions per site nad4 ---= 173.1 million years

(2)0.000318 substitutions per site per million years

In both cases there is a factor of 2 in the denominator because there are two lineages accumulating substitutions independently during divergence. The estimated divergence time clearly depends on the locus used since the molecular clock ticks at slightly different rates per million years for each locus. The average divergence time of 204 million years ago for these three loci matches the average of about 200 million years based on all available data (Laroche & Bousquet 1995).

Problem box 8.2 answer

The Mayotte and Europe populations both contain a sample of 15 sequences for the runt locus so that n = 15

a = \ - = \ _ + _ + _ + _ + _ + _ + _ + _ + _ + — + — + — + — + —

v12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 + 92 + 102 + 112 + 122 + 132 + 142y and

c = ^^-zr-t---+ "4 = L.w,. J - ~ +______ = 0.04813

9n(n -1) an a2 9(15)(15 -1) (3.2516)(15) (3.2516)2 so that e2 = = 0 024813 = 0.00396

In the European population there are 17 segregating sites out of a total of 556 sites so that

whereas in the Mayotte population there are 34 segregating sites out of a total of 538 sites so that

Tajima's D for the European population is

yje1ps + e2ps(ps - 1) ^(0 0226)0.0306 + (0.00396)(0.0306)(0.0306 -1) = 0.0030/0.02393 = 0.1254

whereas Tajima's D for the Mayotte population is

yje1ps + e2ps(ps - 1) V(0 0226)(0.0632) + (0.00396)(0.0632)(0.0632 - 1) = -0.0059/0.0345 = -0.0171.

Neither population has patterns of DNA sequence polymorphism that deviate from those expected under the standard neutral model.

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