Population Genetics Problem #4

Salamanders in the genus Batrachoseps show a gradient in the number of trunk vertebrae along a gradient from coastal to inland California. Elizabeth Jockusch [1] raised families from 10 populations of four species within the genus to determine whether the difference could be accounted for by differences in developmental temperature. The data provided in the file attenuatus.txt at http://darwin.eeb.uconn.edu/eeb348/supplements-2004/attenuatus.txt is a portion of the data she used in her study.

The data is arranged in columns, and the heading of each column corresponds to the variable name.¹ Each row of the data set corresponds to information about one individual. dam[] is a variable identifying the the mother of the individual, trunkv[] the number of trunk vertebrae, temp[] the developmental temperature, and age[] the age of the individual when measured.²

In analyzing these data, we're going to assume that all of the offspring are half sibs, even though we don't have any direct evidence that this assumption is true. Using these data answer the following questions:

1. What is the value of the phenotypic variance in number of trunk vertebrae, $V_p$, in this population?

2. What is the value of the additive genetic variance in number of trunk vertebrae, $V_a$, in this population?

3. What is the heritability of number of trunk vertebrae in this population?

4. Is there evidence that developmental temperature influences the number of trunk vertebrae in this population?

5. Is there evidence that the number of trunk vertebrae depends on the age at which an individual is measured?

6. Warning: This one's hard. Your analysis assumed that all offspring were half-sibs, i.e., that they all had different fathers. Would your estimates of $V_a$ and $h^2_N$ be larger, smaller, or unchanged if some of the offspring were full sibs? Why?