1 Equal Gene Frequencies

Genotype | Effect | Frequency | ||||||

Pair | MZ | DZ | U | |||||

- | ||||||||

- | ||||||||

- | ||||||||

- | ||||||||

- | ||||||||

- | ||||||||

in all cases; genetic covariance = |

The products in column 6, weighted by the frequencies for the three sibling types, yield the degree of genetic resemblance between siblings. In the case of MZ twins, the covariance equals

(11) |

which is simply expression 3.2, the total genetic variance in the population. If we sum over loci, as we did in expression 3.4, we obtain , the additive and dominance variance, as we would intuitively expect since identical twins share all genetic variance. The calculation for DZ twins, with terms in , , and initially separated for convenience, and collected together at the end, is

(12) |

When summed over all loci, this expression gives . The calculation for unrelated pairs of individuals yields a zero value as expected, since, on average, unrelated siblings have no genetic variation in common at all:

(13) |

It is the fixed coefficients in front of and , 1.0 and 1.0 in the case of MZ twins and and , respectively, for DZ twins that allow us to specify the Mx model and estimate and , as will be explained in subsequent chapters. These coefficients are the correlations between additive and dominance deviations for the specified twin types. This may be seen easily in the case where we assume that dominance is absent. Then, MZ and DZ genetic covariances are simply and , respectively. The variance of twin 1 and twin 2 in each case, however, is the population variance, . For example, the DZ genetic correlation is derived as