The paper “The Shelf Life of Bird Eggs: Testing Egg Viability Using a Tropical Climate Gradient”

(Ecology [2005]: 2164–2175) investigated the effect of altitude and length of exposure on the hatch rate of thrasher eggs. Data consistent with the estimated probabilities of hatching after a number of days of exposure given in the paper are shown here.

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Probability of Hatching Exposure (days) 1 2 3 4 5 6 7 8 Proportion 0.81 0.83 0.68 0.42 0.13 0.07 0.04 0.02 (lowland) Proportion 0.73 0.49 0.24 0.14 0.037 0.040 0.024 0.030 (mid-elevation) Proportion 0.75 0.67 0.36 0.31 0.14 0.09 0.06 0.07 (cloud forest) a. Plot the data for the low- and mid-elevation experi- mental treatments versus exposure. Are the plots generally the shape you would expect from "logistic" plots? b. Using the techniques introduced in this section, for each of the exposure calculate y' = In times in the cloud forest and fit the line y=a+b(Days). What is the significance of a negative slope to this line? c. Using your best-fit line from Part (b), what would you estimate the proportion of eggs that would, on average, hatch if they were exposed to cloud forest conditions for 3 days? 5 days? d. At what point in time does the estimated proportion of hatching for cloud forest conditions seem to cross from greater than 0.5 to less than 0.5?