Let us now consider quantitative characteristics. These characteristics, recall, depend on the combined effects of a number of genes. While the analysis could be presented at a higher level of generality by supposing arbitrary probability distribution functions defined over quantitative genetic attributes observed in populations, both theory and empirical evidence suggest that many quantitative attributes are distributed normally. Quantitative attributes can be regarded as arising from the approximately additive effects of a large number of individual genes. It is a fundamental principle of genetics—the "law of independent assortment"—that the random combination of genetic attributes is statistically independent (Falconer and Mackay, 1996). Hence, a large number of statistically independent random variables are added together, and the conditions for the central limit theorem are satisfied: The quantitative attribute is normally distributed.5

Returning to Eq. (2), the value of production of a variety of type 0 is 9(0)

Assume that the values of 0 encountered in N trials are independently and identically normally distributed with probability (¡)(6\pi, a2). The distribution of the greatest value of 0 encountered in these N trials is, then, the distribution of the greatest order statistic from N draws. Suppressing the mean and variance arguments of the normal distribution, then, the probability density of this greatest order statistic is where O(0) is the cumulative normal density (David, 1981). Thus, I can write the expectation of welfare resulting from choosing the best among N potential parents as e{w) = J J P(q)dq - c(q(e),e) n<i>(g)o(o)ndO

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