## Problem box answer

This captive population has experienced a reduction in population size due to three factors. This case can be thought of as a triple bottleneck. First, the breeding sex ratio became unequal. The effective size based on the number of males (10) and females (15) is:

from equation 3.44. The mean family size among the 15 females was four, returning the population back to a census size of 60. However, the variance in family size was 6.5 and thus greater than expected for a Poisson distribution. The effective population size based on the variance in family size is:

from equation 3.46. Notice that the effective population size used in the numerator is 24, as determined for the unequal sex ratio. In total, the population has fluctuated from N e = 60 before the fire, to census sizes of 25, and then 60 over three generations. The effective size in generation two was 24 due to unequal sex ratio. The effective size in generation three was five (after rounding) due to a growing population with high variance in family size. Therefore, the effective population size over three generations is:

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