4.38 Counting carnivores. Ecologists look at data to learn about nature’s patterns. One pattern they have found relates the size of a carnivore (body mass in kilograms) to how many of those carnivores reside in an area. One way to measure “how many” is to count carnivores per 10,000 kilograms of their prey in the area. Table 4.2 gives average data for 25 carnivore species.23 TABLE 4.2 Size and abundance of carnivores Carnivore species Body mass (kg)
Abundance Carnivore species Body mass (kg)
Abundance Least weasel 0.14 1656.49 Eurasian lynx 20.0 0.46 Ermine 0.16 406.66 Wild dog 25.0 1.61 Small Indian mongoose 0.55 514.84 Dhole 25.0 0.81 Pine marten 1.3 31.84 Snow leopard 40.0 1.89 Kit fox 2.02 15.96 Wolf 46.0 0.62 Channel Island fox 2.16 145.94 Leopard 46.5 6.17 Arctic fox 3.19 21.63 Cheetah 50.0 2.29 Red fox 4.6 32.21 Puma 51.9 0.94 Bobcat 10.0 9.75 Spotted hyena 58.6 0.68 Canadian lynx 11.2 4.79 Lion 142.0 3.40 European badger 13.0 7.35 Tiger 181.0 0.33 Coyote 13.0 11.65 Polar bear 310.0 0.60 Ethiopian wolf 14.5 2.70

a. Plot and describe the relationship between carnivore abundance (response variable) and body mass (explanatory variable). Would it be appropriate to conduct a linear regression analysis for the data as is?
Explain your answer.

b. When a relationship is clearly not linear, transforming the data can sometimes help. For each species, compute the logarithm of body mass and the logarithm of abundance. Plot and describe the relationship between the log of abundance and the log of body mass. Is linear regression appropriate for the transformed data?

c. The least-squares regression for the transformed data gives the equation log(abundance)=1.95-[1.05×log(body mass)]
Predict the abundance of a carnivore species whose individuals weigh about 1 kg. Make sure to transform the units both ways (remember that y=10log(y) ).