Estimating single gene effects on quantitative traits : 2. Statistical properties of five experimental methods

Estimating effects of a single gene and polygenes on quantitative traits from a diallel design

A genetic model is developed with additive and dominance effects of a single gene and polygenes as well as general and specific reciprocal effects for the progeny from a diallel mating design. The methods of ANOVA, minimum norm quadratic unbiased estimation (MINQUE), restricted maximum likelihood estimation (REML), and maximum likelihood estimation (ML) are suggested for estimating variance components, and the methods of generalized least squares (GLS) and ordinary least squares (OLS) for fixed effects, while best linear unbiased prediction, linear unbiased prediction (LUP), and adjusted unbiased prediction are suggested for analyzing random effects. Monte Carlo simulations were conducted to evaluate the unbiasedness and efficiency of statistical methods involving two diallel designs with commonly used sample sizes, 6 and 8 parents, with no and missing crosses, respectively. Simulation results show that GLS and OLS are almost equally efficient for estimation of fixed effects, while MINQUE (1) and REML are better estimators of the variance components and LUP is most practical method for prediction of random effects. Data from a Drosophila melanogaster experiment (Gilbert 1985a, Theor appl Genet 69:625-629) were used as a working example to demonstrate the statistical analysis. The new methodology is also applicable to screening candidate gene(s) and to other mating designs with multiple parents, such as nested (NC Design I) and factorial (NC Design II) designs. Moreover, this methodology can serve as a guide to develop new methods for detecting indiscernible major genes and mapping quantitative trait loci based on mixture distribution theory. The computer program for the methods suggested in this article is freely available from the authors.

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.

An additive-dominance model to determine chromosomal effects in chromosome substitution lines and other gemplasms

When using chromosome substitution (CS) lines in a crop breeding improvement program, one needs to separate the effects of the substituted chromosome from the remaining chromosomes. This cannot be done with the traditional additive-dominance (AD) model where CS lines, recurrent parent, and their hybrids are used. In this study, we develop a new genetic model and software, called a modified AD model with genotype x environment interactions, which can predict additive and dominance genetic effects attributed to a substituted alien chromosome in a CS line as well as the overall genetic effects of the non-substituted chromosomes. In addition, this model will predict the additive and dominance effects of the same chromosome of interest (i.e. chromosome 25 of cotton in this study) in an inbred line, as well as the effects of the remaining chromosomes in the inbred line. The model requires a CS line, its recurrent parent and their F(1) and/or F(2) hybrids between the substitution lines and several inbred lines. Monte Carlo simulation results showed that genetic variance components were estimated with no or slight bias when we considered this modified AD model as random. The correlation coefficient between predicted effects and true effects due to the chromosomes of interest varied from zero to greater than 0.90 and it was positively relative to the difference between the CS line and the recurrent line. To illustrate the use of this new genetic model, an upland cotton, Gossypium hirsusum L, CS line (CS-B25), TM-1 (the recurrent parent), five elite cultivars, and the F(2) hybrids from test-crossing these two lines with the five elite cultivars were grown in two environments in Mississippi. Agronomic and fiber data were collected and analyzed. The results showed that the CS line, CS-B25, which has chromosome 25 from line 3 to 79, Gossypium barbadense substituted into TM-1, had positive genetic associations with several fiber traits. We also determined that Chromosome 25 from FiberMax 966 had significantly positive associations with fiber length and strength; whereas, chromosome 25 from TM-1 and SureGrow 747 had detectable negative genetic effects on fiber strength. The new model will be useful to determine effects of the chromosomes of interest in various inbred lines in any diploid or amphidiploid crop for which CS lines are available.

A mixed model for the effects of single gene, polygenes and their interaction on quantitative traits : 1. The model and experimental design

A model for the effects of single gene (SG), polygenes (PG) and their interaction on quantitative traits was developed. It is a mixed model where the SG is a fixed effect and the PG is a random effect. A two-way factorial experiment, in which the SG and the PG are the main effects, is proposed. The experimental material is comprised of F3 families derived from F2 plants heterozygous for the SG. For this experiment an ANOVA table with expected mean square is proposed, which facilitates estimation of the components of the model and testing of their significance. A detailed method for the interpretation of results from such an experiment is proposed, with emphasis on the analysis of the SG × PG interaction. Theoretical and applied aspects of SG × PG interaction is discussed.

Estimating single gene effects on quantitative traits 1. A diallel method applied to Est 6 in D. melanogaster

A modified diallel cross is used to estimate effects of alleles at the esterase 6 locus, relative to strain and environmental variance, in Drosophila melanogaster. Three strains homozygous for Est 6 (s) and three homozygous for Est 6 (F) were crossed in all 36 combinations. Male progeny were scored for mating speed, copula duration and esterase 6 enzyme activity, and all progeny for developmental time. These alleles show a significant additive effect on mating speed, but not on the other traits. Copula duration, developmental time and enzyme activity show additive strain genetic variance. Enzyme activity and developmental time also have maternal or X-chromosome strain variance, and these two traits are significantly correlated. This modified diallel method is generally useful because it permits the partition of trait variance into additive and dominant locus, background genetic and environmental components.