Principles of Life
Hillis • Sadava • Heller • Price
Answers to the Analyze the Data, Apply the Concept, and
Working with Data Questions
Chapter 15: Mechanisms of Evolution
Analyze the Data
Figure 15.19 A Heterozygote Mating Advantage
A. For C. philodice, 43.2% of all viable males are heterozygous, so 56.8% must be
homozygous. To get expected numbers of heterozygous and homozygous mating males,
we multiple the expected proportions (from all viable males) by the total number of
mating males sampled. Therefore, we expect to see (0.432)(50) = 21.6 heterozygous
mating males, and (0.568)(50) = 28.4 homozygous mating males.
If we repeat the same calculations for C. eurytheme, we expect (under the given
assumption) to see (0.478)(59) = 28.2 heterozygous mating males, and (0.522)(50) = 30.8
homozygous mating males.
B.
Chi-square calculations for C. philodice:
Genotype
Expected (E) Observed (O) O – E
(O – E)2
(O – E)2/E
Heterozygotes 21.6
31
9.4
88.36
4.091
Homozygotes 28.4
19
9.4
88.36
3.111
The sum of the last column gives the chi-square test statistic: 7.302. Since this value is
greater than the critical value (P = 0.05) of 3.841, the observed results are significantly
different from the expectations at P < 0.05. In other words, we can reject the null
hypothesis and conclude that the proportions of each genotype (heterozygotes and
homozygotes) of mating males are significantly different from the proportions of these
genotypes seen among all viable males in C. philodice.
Chi-square calculations for C. eurytheme:
Genotype
Expected (E) Observed (O) O – E
(O – E)2
(O – E)2/E
Heterozygotes 28.2
45
16.8
282.17
10.005
Homozygotes 30.8
14
16.8
282.17
9.162
The sum of the last column gives the chi-square test statistic: 19.167. Since this value is
greater than the critical value (P = 0.05) of 3.841, the observed results are significantly
different from the expectations at P < 0.05. In other words, we can reject the null
hypothesis and conclude that the proportions of each genotype (heterozygotes and
homozygotes) of mating males are significantly different from the proportions of these
genotypes seen among all viable males in C. eurytheme.
© 2011 Sinauer Associates, Inc.
1
Apply the Concept
Concept 15.1 Evolution Can Be Measured by Changes in Allele
Frequencies, p. 299
1. Observed allele frequencies:
Frequency of a = p = 0.5; frequency of A = q = 0.5
Observed genotype frequencies:
Frequency aa = 0.4
Frequency Aa = 0.2
Frequency AA = 0.4
2. The population is not in Hardy–Weinberg equilibrium. There are more homozygotes,
and thus fewer heterozygotes, than expected under Hardy–Weinberg equilibrium. Since p
= 0.5 and q = 0.5, we would expect heterozygotes to be present at a frequency of 2pq =
0.5 at Hardy–Weinberg equilibrium. The population is likely from two or more different
source populations (one with a higher frequency of a, and the other with a higher
frequency of A).
3. Allele frequencies:
p = 0.5, q = 0.5 (unchanged)
Genotype frequencies:
Frequency of aa = p2 = 0.25
Frequency of Aa = 2pq = 0.5
Frequency of AA = q2 = 0.25
4. Several of the assumptions of Hardy–Weinberg equilibrium are violated in this
example, any one of which could lead to deviations in Hardy–Weinberg expectations. For
instance, the population size is not infinite, and in fact it is quite small. Thus, it is subject
to random deviations due to chance events. Also, random mating is not possible,
especially since the six males can only mate with four possible females. Since the
genotype frequencies within each sex differ from the genotype frequencies of the
population as a whole, this will have a large effect on the resulting offspring. Further,
given that gene flow has occurred in the past (that is how the population was founded), it
is likely to occur again in the future. Any gene flow from other populations will affect the
allele and genotype frequencies. Finally, the effects from the violated assumptions noted
above will be quite large, and the effects of mutation and selection will probably be very
small by comparison (at least over just one generation). However, over time new
mutations and selection may also influence allele and genotype frequencies in this
population.
© 2011 Sinauer Associates, Inc.
2
Concept 15.2 Genomes Reveal both Neutral and Selective Processes of
Evolution, p. 305
1. Codon numbers 12, 15, and 61 are likely to be evolving under positive selection for
change because these three codons have each experienced a large number of
nonsynonymous substitutions (which give rise to amino acid replacements), but relatively
few synonymous substitutions.
2. Codon number 165 is the most likely of these codons to be drifting neutrally among
states, as it has experienced similar rates of synonymous and nonsynonomous
substitution.
3. Codon numbers 80, 137, 156, and 226 are likely evolving under purifying selection, as
the vast majority of changes at these codons are synonymous substitutions, which do not
result in amino acid replacements. Substitutions that result in amino acid changes
(nonsynonymous substitutions) undoubtedly occur, but are usually selected against in the
population.
Working with Data
15.1 Testing for Significant Differences (Figure 15.9)
1. A. The details of this answer will depend on your specific randomization trials. If you
conduct enough randomization replications, you should expect to see group differences as
large as those seen in this experiment less than 5% of the time.
B. P < 0.05
2. A. Large sample sizes provide greater power to discriminate between group means, if
the groups are actually different. If the actual difference between group means is small,
the experiment will require larger sample sizes to detect the difference. Thus, the power
of the experiment to detect group differences increases with increasing sample size.
B. Try replicating the randomization test above, but increase the sample size by a factor
of two.
C. Assume that the new data are similar to the first set of data collected, and write out two
cards for each observation. Even though the difference in group means is identical, you
should see that it is easier to detect the differences with a larger sample size.
© 2011 Sinauer Associates, Inc.
3
15.2 Determining the Paternity of Butterfly Larvae (Figure 15.19)
1. (0.75)16 is approximately 0.01002. Therefore, the investigators would need to analyze
at least 16 larvae from each batch of eggs to judge the genotype of the father with 99
percent certainty. An easy way to find this answer is to multiply 0.75  0.75, and then
multiply the answer by 0.75, and continue until the result is approximately 0.01. Keep
track of the number of times you multiply by 0.75 to find the appropriate sample size.
2. (See Analyze the Data for Figure 15.19 above.)
3. Alternative explanations are directly from Question 4:
A possible alternative hypothesis to explain why heterozygous males disproportionately
father offspring is that females that mate with those males are more likely to lay eggs
than females that mate with homozygous males. The investigators rejected that
hypothesis because nearly all females laid fertilized eggs in captivity.
Another alternative is that fitness differences were not due to alleles at the PGI locus but
were due to genes at other loci on the same chromosome.
A third possibility is that heterozygote males, being more vigorous flyers, are more
difficult to capture. If so, the investigators might have underestimated the frequency of
heterozygotes in the wild.
4. As already noted, the first hypothesis was rejected because nearly all the females laid
fertilized eggs in captivity. The second hypothesis received no support because the
observed differences in flight performance were consistent (could be accounted for) by
the laboratory-measured differences among the PGI alleles. Thus, although additional
loci on the same chromosome could contribute to flight performance, the observed
variation of PGI alleles is sufficient to explain the observed results. To avoid the third
possibility (a sampling bias against heterozygotes), the investigators did not capture
butterflies while they were attempting to escape (which could have led to a bias against
sampling the better fliers). Instead, they captured unaware individuals as they fed on
flowers, searched for mates, oviposited, or interacted with one another. This ensured that
the likelihood of capture was unrelated to flying ability of the butterflies.
© 2011 Sinauer Associates, Inc.
4