Theory and analysis of partial diallel crosses

Genetic control of agronomically important traits of pepper fruits analyzed by Hayman's partial diallel cross scheme

Pepper species of the genus Capsicum have been cultivated over centuries, producing both pungent and sweet fruit; the pungency is caused by alkaloids called capsaicinoids. Among the five cultivated species, Capsicum chinense is one of the most popular, being native to the Amazon basin. This species is characterized by a wide variety of fruit sizes, shapes and colors, with different capsaicinoid content. In addition, fruits are rich in vitamins A and C. Despite the importance of this plant as a spice and its medicinal uses, research on its genetic variability and potential for breeding programs is still incipient. We investigated the genetic control of some traits through diallel analysis with the objective of introgressing these traits into cultivated varieties. For the diallel analysis, the progeny of crosses between peppers with pungent and sweet fruits, together with the parents, were grown in pots under greenhouse conditions. The fruits were harvested and analyzed for the traits total fresh fruit mass, total dry fruit mass, percentage dry matter, total soluble solids, vitamin C content, fruit pungency, and number of seeds per fruit. Genetic variability was detected for all traits. In the diallel analysis, the additive-dominant model was considered to be adequate for total fresh fruit mass, percentage dry matter, total soluble solids, and vitamin C content. Additive genetic effects and dominance were found for all traits; consequently, breeding for improvement of these fruit traits would be viable.

Using mating designs to uncover QTL and the genetic architecture of complex traits

Analysis of quantitative trait loci (QTL) affecting complex traits is often pursued in single-cross experiments. For most purposes, including breeding, some assessment is desired of the generalizability of the QTL findings and of the overall genetic architecture of the trait. Single-cross experiments provide a poor basis for these purposes, as comparison across experiments is hampered by segregation of different allelic combinations among different parents and by context-dependent effects of QTL. To overcome this problem, we combined the benefits of QTL analysis (to identify genomic regions affecting trait variation) and classic diallel analysis (to obtain insight into the general inheritance of the trait) by analyzing multiple mapping families that are connected via shared parents. We first provide a theoretical derivation of main (general combining ability (GCA)) and interaction (specific combining ability (SCA)) effects on F(2) family means relative to variance components in a randomly mating reference population. Then, using computer simulations to generate F(2) families derived from 10 inbred parents in different partial-diallel designs, we show that QTL can be detected and that the residual among-family variance can be analyzed. Standard diallel analysis methods are applied in order to reveal the presence and mode of action (in terms of GCA and SCA) of undetected polygenes. Given a fixed experiment size (total number of individuals), we demonstrate that QTL detection and estimation of the genetic architecture of polygenic effects are competing goals, which should be explicitly accounted for in the experimental design. Our approach provides a general strategy for exploring the genetic architecture, as well as the QTL underlying variation in quantitative traits.

Analysis of variance of partial diallel tables

The theory of variance analysis of partial diallel tables, following Hayman's proposal of 1954, is presented. As several statistical tests yield similar inferences, the present analysis mainly proposes to assess genetic variability in two groups of parents and to study specific, varietal and mean heteroses. Testing the nullity of specific heteroses equals testing absence of dominance. Testing equality of varietal heteroses of the parents of a group is equivalent to testing the hypothesis that in the other group allelic genes have the same frequency. Rejection of the hypothesis that the mean heterosis is null indicates dominance. The information obtained complements that provided by diallel analysis involving parents and their F1 hybrids or F2 generations. An example with the common bean is included.