Inheritance of Rest Period of Seeds in the Peanut
These formulae are apparently correct mathematically. They
work perfectly with hypothetical cases when no deviations from
expected values are allowed. Deviations in any one of the ratios,
a, b, or c, which have 50 percent probability with samples of
500 to 1,000 throw the results entirely out of line. The formulae
are of very limited utility, presumably because of enormous size
of their sampling variances. Similar formulae might be cal-
culated from the ratios of segregating to total progeny, or to
true breeding progeny, or from any set of three independent
equations involving the three unknowns. None of these other
possibilities has been investigated fully as yet, but the prob-
ability of finding a more valuable set of formulae appears to
be very small.
Estimates of q, q', and w were obtained by calculating maxi-
mum and minimum w in the dihybrid F2 and the monohybrid
F4 families of cross 1 x 14 by the formulae given above. For
the F2 maximum w is 0.82 and minimum w is 0.79 while for
the monohybrid F4 families maximum w is 0.76 and minimum
w is 0.73. In either case, for maximum w, q = 1.00, q' 0.66;
while for minimum w, q = q' = 0.83. The corrected ratios in
Table 10 have been based on an hypothesis of q = q' = 0.83,
and w = 0.75. There is, unfortunately, no evidence for or
against equality of q and q'. The ratios of F2 seedlings, F2
families, F4 families, and F5 seedlings were used to build the
hypothesis and are not entirely independent of it. Tests of the
hypothesis lie in the ratios of F3 seedlings, F3 families, and F4
seedlings, which data were not used to calculate q, q', and w.
Theoretical ratios for later generations were also corrected
for random deviations and differential productivity in earlier
generations. The ratio of F3 families was, in addition, cor-
rected for the proportion of dihybrid families expected to pro-
duce no recessive progeny and apparently breed true because
of few progenies tested. Contributions of these factors to X2
must of course be eliminated if a fair test of the hypothetical
values of q, q', and w is to be obtained.
It was possible to make the above corrections on the theo-
retical F3 ratio with reasonable assurance. This ratio is pre-
sented in Table 11 for the entire population and for the progenies
of dihybrid and monohybrid F2 plants separately. Good fits
were obtained in all cases. The ratios of F3 families and F4
seedlings could not be corrected so accurately and the fits obtained
were hardly within the limits of random sampling. However,