In MNL 61:32-34 we presented an universal mathematical solution for
the calculus of p, recombination value, and** **a and b, the allometric
coefficients of the effects of genes *A* and *B*. The p variance
was also calculated. The purpose of this report is to obtain the variance
of a and b.

Only the signs of the 3rd and 4th terms change. Deriving again, these same terms change sign again and we are at a loss to decide which means which, on the inequality. A solution is found for a similar problem by R.A. Fisher (Ann. Eug. 9:50, 1939), and we reproduce his work with the adaptations required for our case.

That is, the variance of a or b is the square root of the total sum
of the inverse each squared first, four terms. It is another inequality
to extend the Cramer-Rao one. Note in Table
1 that by allometry the value is usually a little smaller. The discrepancies
are mostly with the markers *B*, *Su*, and *Pl* due to values
of p > 0.5 which is not congruent with the mathematical models. Comparing
with p measures several-fold bigger populations are needed to measure effects
of a and b.

Only the *Ts5 Tr* a effect approaches significance. It becomes
more clear that the expression of *pd* and *tr* is due to a much
more complex system of epistatic effects, since with so many duplicated
genes it expresses itself as being always a single pair of recessive alleles
with disturbed segregation, which once attained, blocks the effects of
the other loci, because we always have a little less than one fourth *tr*
or *pd* in F2 segregation. Within cultivated maize, these numerous
genes at different loci act in a more quantitative way, the dominants adding
their effects to achieve higher kernel row numbers.

Luiz Torres de Miranda, Luiz Eugenio Coelho de Miranda and Toshio Igue

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