Answers to Analyzing Data 10.1 Questions

1. For years 2-6 (respectively), the five missing values for the table are 1.22, 0.87, 1.17, 1.02, and 1.13.

2. If λ remained constant and equal to 1.02, when N₀ = 1,000 the population size at year 7 would be: N₇ = N₀ (1.02)⁷ = 1,149.

3. The geometric mean of the yearly population growth rates equals 1.00945.

4. Using the geometric mean calculated in Question 2 as our estimate of λ, we have: N₇ = N₀ (1.000945)⁷ = 1,068. This value is lower than that calculated in Question 1 (1,149) and almost identical to the value in the table (1,069).

5. When environmental conditions vary, it is likely that the growth rate of a population will also vary over time. The results in Questions 1-3 suggest that using the arithmetic mean of such variable population growth rates will over-estimate the population size, whereas using the geometric mean would be more accurate. Because the arithmetic mean is known to overestimate actual population sizes, in that sense it would be wrong to use the arithmetic mean to describe the growth of a population in a variable environment.