A rather critical examination has been completed of the relationships existing among the three variables, yield of tomatoes, and components of yield, total number of fruits per plant, and fruit weight.
The resolution of a complex variable into component parts allows at least two objectives: (1) an examination of the relationships existing among the components; a determination of the reletive importance of these components and how they fit together into different patterns in the synthesis of the more complex variable such as yield, and, (2) a clarification of the genetic system in which gene models may be developed for the components and then combined to give a gene model for yield.
The experimental material involves six inbred lines and all possible F1's from these lines. The parents collectively exhibited tremendous ranges of expression for all characteristics. At the two extremes were the Parents, L. pimpinellifolium having an average of 1287 fruits of .5 gms each, and, Matchless, a variety of L. esculentum, with an average of 16 fruits each of 142.6 gms.
The first problem was that of describing as exactly as possible in linear form the relationships existing between the three variables. Beginning with the arithmetic data which exhibited curvilinear, non-distinct relationships, the first improvement was made by choosing a scale of measurement by which the relationships were linear. Various scales were tried including forms of the logit, but the simple logarithmic scale gave the best results. Linear relationships were obtained with this scale between all variables and involving all parental and F1 data grouped together.
The next step was to organize the experimental material into more homogeneous sub-groups. The first grouping isolated the parents as one set, and all the F1's as another. This accomplished two objectives. First it allowed the exact relationships of the parents to become evident. The exceedingly high correlations coefficients of r\l2\ = -.989, r\13\ = +.994, and r\23\ = -.999 demonstrated how accurately a linear description was possible with the logarithmic transformation. These statistics also demonstrated that for these lines the log(fruit weight) is relatively more important in determining log(yield) than log(number of fruits). The second objective was that it allowed a contrast of the F1 relationships with those of the parents. The differences found were obviously due to non-additively genetic effects generated by the heterozygous F1 condition. The partitioning of the F1 values into additively and nonadditively genetic components was accomplished and it was possible to demonstrate exacctly the relative contribution of these two different types of genetic effects to the F1 phenotypic statistics.
The last step in attempting to obtain as exact relationships on the F1's as possible was to group the F1's into constant parent groups(all F1's having one parent in common were put into a group labeled by the particular constant parent). With this procedure distinct relationships among the F1's were found which approached the exactness found among the parents. In these analyses it was discovered that each constant parent group of F1's yielded statistics different from those of the parents, and, again, these differences were due to the non-additively genetic effects. For example, the relative importance of log(fruit weight) in determining log(yield) changed radically but consistently through all constant parent groups from constant parent group (1) to (6). (Where c.p.g. (1) had the smallest fruited parent as common parent and c.p.g. (6) had the largest fruited parent as common parent).
By the above techniques yield in tomatoes was broken down into two, simpler components, and the relitionships leading to an integrated gene system were developed. Much of the puzzling behivior of non-additively genetic effects, whose relationships were quite different from those of the additively genetic effects, was clarified and made interpretable with the gene models which were developed in connection with the problem of describing the relationships existing among the variables.