Chapter 12 18. The males of stalkeyed flies (Cyrtodiopsis dalmanni) have long eye stalks. The females sometimes use the length of these eye stalks to choose mates. (See Example 11.2 for a similar story in a related species.) Is the male’s eyestalk length affected by the quality of its diet? An experiment was carried out in which two groups of male “stalkies” were reared on different foods (David et al. 2000). One group was fed corn (considered a high quality food), while the other was fed cotton wool (a food of substantially lower quality). Each male was raised singly and so represents an independent sampling unit. The eye spans (the distance between the eyes) were recorded in millimeters. The raw data, which are plotted as histograms below, are as follows: Corn diet: 2.15, 2.14, 2.13, 2.13, 2.12, 2.11, 2.1, 2.08, 2.08, 2.08, 2.04, 2.05, 2.03, 2.02, 2.01, 2, 1.99, 1.96, 1.95, 1.93, 1.89. Cotton diet: 2.12, 2.07, 2.01, 1.93, 1.77, 1.68, 1.64, 1.61, 1.59, 1.58, 1.56, 1.55, 1.54, 1.49, 1.45, 1.43, 1.39, 1.34, 1.33, 1.29, 1.26, 1.24, 1.11, 1.05. These data can be summarized as follows, where the cornfed flies represent treatment group 1 and the cottonfed flies represent treatment group 2.
Transcript
Chapter 12
18. The males of stalk-‐eyed flies (Cyrtodiopsis dalmanni) have long eye stalks. The females sometimes use the length of these eye stalks to choose mates. (See Example 11.2 for a similar story in a related species.) Is the male’s eyestalk length affected by the quality of its diet? An experiment was carried out in which two groups of male “stalkies” were reared on different foods (David et al. 2000). One group was fed corn (considered a high quality food), while the other was fed cotton wool (a food of substantially lower quality). Each male was raised singly and so represents an independent sampling unit. The eye spans (the distance between the eyes) were recorded in millimeters. The raw data, which are plotted as histograms below, are as follows: Corn diet: 2.15, 2.14, 2.13, 2.13, 2.12, 2.11, 2.1, 2.08, 2.08, 2.08, 2.04, 2.05, 2.03, 2.02, 2.01, 2, 1.99, 1.96, 1.95, 1.93, 1.89. Cotton diet: 2.12, 2.07, 2.01, 1.93, 1.77, 1.68, 1.64, 1.61, 1.59, 1.58, 1.56, 1.55, 1.54, 1.49, 1.45, 1.43, 1.39, 1.34, 1.33, 1.29, 1.26, 1.24, 1.11, 1.05. These data can be summarized as follows, where the corn-‐fed flies represent treatment group 1 and the cotton-‐fed flies represent treatment group 2.
Mean
(mm) Variance
(mm2)
Sample size, n Corn diet (group 1) 2.047 0.00558 21
Cotton diet (group 2) 1.543 0.08119 24 a. What is the best test to use to compare the means of the two groups? Why? b. Carry out the test identified in part (a), using α = 0.01. 24. Weddell seals live in the Antarctic and feed on fish during long deep dives in freezing water. The seals benefit from these feeding dives, but the food they gain comes at a metabolic cost. The dives are strenuous. A set of researchers wanted to know whether feeding per se was also energetically expensive, over and above the exertion of a regular dive (Williams et al. 2004). They determined the metabolic cost of dives by measuring the oxygen use of seals as they surfaced for air after a dive. They measured the metabolic cost of 10 feeding dives and for each of these also measured a non-‐feeding dive by the same animal that lasted the same amount of time. The data, in (ml O2 kg-‐1), are as follows:
a. Estimate the mean change in oxygen consumption in feeding dives compared with non-‐feeding dives.
b. What is the 99% confidence interval for the mean change calculated in part (a)? c. Test the hypothesis that feeding does not change the metabolic costs of a dive.
Chapter 13
28. The pseudoscorpion Cordylochernes scorpioides lives in tropical forests, where it ride on the backs of harlequin beetles to reach the decaying fig trees in which they live. Females of the species mate with multiple males over their short lifetimes, which is puzzling because mating just once provides all the sperm she needs to fertilize her eggs. A possible advantage is that by mating multiple times a female increases the chances of mating with at least one sperm-‐compatible male, if incompatibilities are present in the population. To investigate, Newcomer et al. (1999) recorded the number of successful broods by female pseudoscorpions randomly assigned to one of two treatments. Females were each mated to two different males (DM treatment), or they were each mated twice to the same male (SM). This design provided the same total amount of sperm to females in both treatments, but DM females received genetically more diverse sperm than SM females. The number of successful broods of offspring for each female is listed below. The data were not normally distributed and to test the null hypothesis of no difference between treatments in the mean number of broods we carried out a permutation test in which the data were randomly reshuffled 10,000 times on the computer. Our test statistic was the difference between groups in the mean number of broods (SM minus DM). The observed value of this difference was -‐0.841. The null distribution from the 10,000 permutations is shown in the upper panel of the accompanying figure. The far left tail of the null distribution is shown in the lower panel. Numbers below each bar give the exact values of the test statistic; numbers above give the frequency of each of the values in 10,000 permutations. Using these values, carry out the permutation test.1 SM treatment: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2,
