2. Sweet corn.

It is commonly said that sweet corn "does not grow" in the tropics. However, breeding projects in Porto Rico (Harper, Agric. Amer., 6: 74, 1946) in Cuba (del Valle) and, latterly, in Trinidad have all been successful in producing a fairly vigorous mass‑bred sweet corn. The programmes have been of the obvious kind ‑ crossing an imported sweet corn to locally adapted field corns, selfing or crossing, selection, and mass breeding. At the I.C.T.A., the sweet corn used was one which had been grown at the College Farm for 6 to 8 years and was notably poor in vigour. A museum plot of 30 to 40 plants was grown once or twice a year,, 6 to 8 cobs were selected and the grain was shelled, bulked and stored until the next sowing. In at least one year the population was greatly reduced by bad seed and disease. It is assumed that no su pollen other than that from the plot itself would have been available and this, together with the necessary selection for su su su grains, must have constituted an isolation mechanism (but not necessarily an absolutely rigid one if an occasional Su su plant survived to flower). From this realization it was but a short step to the idea that, perhaps, existence as a small isolated population had led to inbreeding, loss of heterozygosis and consequent loss of vigour.

Loss of heterozygosis under a system of random mating is

1

2N

per generation (Wright, Genetics 16: 97, 1931). If N is the population number, g the number of generations, p_o initial heterozygosis, and pg heterozygosis at generation g,

pg = po (1 ‑	1	)g
	2N

whence table 3 is constructed.

Table 3. Heterozygosis ‑ pg = po (1 ‑	1	)g
	2N

g	N	1	3	5	10	50
1		0.50	0.83	0.90	0.95	0.99
3		0.13	0.58	0.73	0.86	0.97
5		0.03	0.40	0.59	0.77	0.95
7		0.01	0.28	0.48	0.70	0.94
9		0.002	0.19	0.39	0.63	0.92

The problem is to determine the effective population number. It is not simply the number of plants in the plot for only a few of these are ovule parents; nor is it the number of cobs selected, for these represent only ovule parents and not pollen parents. The true value must lie somewhere between the two.

I am indebted to Professor Wright for the solution. In the following equations, N_t = total plants in the plot, N_o = ovule parents, N_f = female parents, N_m = male parents, and N_e = effective population number. Case A assumes that self‑fertilization occurs with the same average frequency as pollination by any other plant; case B assumes that self‑fertilization is excluded; case C assumes separate sexes and has already been treated by Wright.

Case A:	1	=	(	1	+	3	)	-	(	1	+	1	)^2
	2Ne			8No		8Nt				8No		8Nt
Case B:	1	=	(	1	+	3	)	(1 -		1	-	3	)
	2Ne			8No		8Nt				8No		8Nt
Case C:	1	=	(	1	+	1		(1 -		1	-	1	)
	2Ne			8Nm		8Nf				8Nm		8Nf

Case A, it will be noted, is not appreciably different from Case B, itself probably a fair approximation to actual events in the field.

		Ne		Ne
A	No = 6, Nt = 30	15.3	No = 8, Nt = 40	20.2
B	No = 6, Nt = 30	15.5	No = 8, Nt = 40	20.5
C	Nf = 6, Nm = 30	20.5	Nf = 8, Nm = 40	27.2

N_e for sweet corn at the College Farm must have been 15 to 20 and this leads to the expectation that p_g = 0.7p_o, assuming 12 generations. Actually it would be rather lower than this because, as noted above, in a few bad seasons, N_e must have been reduced far below 15 to 20. Probably, then p_g approached 0.5p_o and this is in accord with the general aspect of the material, bearing in mind the appearance of corn once‑selfed, and knowing that quite vigorous sweet types can be bred.

These considerations have general application to small museum or maintenance plots of any outbred plant and it might be suggested that, subject to detailed study and test, the N_e of such populations should not be allowed to fall below 90 (p_g = 0.9p_o, g = 100).

N. W. Simmonds