From teosinte to maize. III. Allometric genetics 12th theorem - a more involved three point test
--L. E. C. de Miranda and L. T. de Miranda

E. Dempsey, E (MNL45:58-59) presented the sequence, centromere - y - pg11. If p is the y-pg11 distance and q the pg11-K distance we complete these data with the expectations:
 
Coded Pedigree Class frequency Total Expectation of regions
+ - - (0) Y pg11 k 12
- + + (0) y Pg11 K 6 18 p(1-q) a
+ + + (1) Y Pg11 K 10
- - - (1) y pg11 k 6 16 (1-p)(1-q) b
+ - + (2) Y pg11 K 3
- + - (2) y Pg11 k 1 4 pq c
+ + - (3) Y Pg11 k 0 not found
- - + (3) y pg11 K 0 not found (1-p)q d

The plants with crossover phenotypes were purposely selected and even so the last two classes did not appear. So the linkages calculated with these data are stronger than if calculated with a non-skewed sample.

By the additive or Emerson method, which is the same as the maximum likelihood of Fisher, we get p=(b+c):n
    p for y-pg11=57.9±8.0 and q for pg-K=10.5±5.0

By the product moment method, whose theory for backcrosses is demonstrated in MNL61:32, we get

p for y-pg11=57.0±8.0 and q for pg11-K=9.3±4.7

With the expectations shown above we can mount a new maximum likelihood model as:

L = 18 [lnp + ln(1-q)] + 16[ln(1-p) + ln(1-q)] + 4(lnp + lnq)

Derivating in relation to q to calculate pg11 to K distance and following through we have

dL/dq = -q(a + b + c + d) + c + d = 0
and q = (4 + 0) : 38 = 0.105 = 10.5%

Making the same for p we get p = 57.9, the same as by the additive method.

The distance calculated here in the three models as about 57 or 58 is known to be 19. The value obtained is triple the real one. Thus dividing by 3 the results obtained by the product moment method we have 3.0. This would put K in position 41 within our 35-42 positions proposed for tr (krn) in our prior report. The work of Kato (Mass. Agric. Exp. Stn. Bull. 635, 1976) is most illuminating in understanding the process of conversion of wild teosinte to cultivated teosinte, maize.

In five different sympatric races of teosinte and corn, there were the same chromosome knob complexes, and the knobless genome is the "basic chromosome morphology". This is a result of domestication, knobs.

Even today men in the field talking around a bonfire keep tinkering with it. Beadle (Maize Breeding and Genetics, 1978) states that teosinte pops. This explains the polyphyletic origin of maize, in the beginning, all popcorns. 


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