DiallelAnalysisR: Diallel Analysis, Heterosis and Related Mating Designs
Source:R/DiallelAnalysisR-package.R
DiallelAnalysisR-package.RdDiallelAnalysisR analyses diallel crosses of plant-breeding experiments laid out in randomized complete blocks: Griffing's (1956) four methods and two models, Hayman's (1954) analysis with the \(W_r\)-\(V_r\) graph and the components of variation, the partial diallel between two groups of parents, heterosis, Gardner and Eberhart's models, line by tester and North Carolina designs, diallels over environments, simulation and planning, tables for papers and an interactive application.
Details
Functions.
Griffing: combining-ability analysis by Griffing's Methods 1 to 4 and Models 1 (fixed) and 2 (random): analysis of variance, gca, sca and reciprocal effects with standard errors, variance components.Hayman: Hayman's analysis of variance, the \(W_r\)-\(V_r\) analysis and graph, the components \(D\), \(H_1\), \(H_2\), \(F\), \(h^2\), \(E\), genetic ratios and tests of the additive-dominance model.PartialDiallel: crosses between two groups of parents: gca of each group, sca, variance components.GriffingMeans: Griffing's analysis of a table of cross means;GriffingEnv: over several environments.Heterosis: mid-parent, better-parent and standard heterosis with \(t\) tests.GardnerEberhart: Gardner and Eberhart's Analyses II and III.LineTester,NCDesign: line by tester analysis; North Carolina designs I to III.DiallelSim,DiallelPower: simulated diallels and the power of the tests.da_export: the main tables in Word, LaTeX, HTML, Markdown or CSV;DiallelApp: the interactive application.
Every analysis returns the named list documented on its help page, with a class and the methods print,
summary, plot and as.data.table; see da-methods. Utilities:
da_theme, da_save, da_notation, da_reference.
Data. GriffingData1 (complete diallel of eight parents), its subsets
GriffingData2, GriffingData3, GriffingData4 for Methods 2 to 4,
HaymanData, PartialDiallelData (ten by four parents), Griffing56
(Griffing's 1956 maize example), LineTesterData and NCData.
Vignettes. Start with vignette("DiallelAnalysisR_01_getting_started", package =
"DiallelAnalysisR"); browseVignettes("DiallelAnalysisR") lists all of them, each as HTML and as PDF.
Notation
Scalars are upper-case letters in normal face, indices lower-case italic, vectors lower-case bold and matrices
upper-case bold; elements of vectors and matrices keep their letter in normal face. The full table is
da_notation().
| \(P\), \(B\) | number of parents, number of replicates (blocks) |
| \(i\), \(j\) | female and male parent of a cross |
| \(\mathbf{Y}\), \(Y_{ij}\) | matrix of cell means, mean of cross \(i \times j\) |
| \(\mathbf{g}\), \(g_i\) | vector of gca effects, gca effect of parent \(i\) |
| \(\mathbf{S}\), \(\mathbf{R}\) | matrices of sca and reciprocal effects |
| \(\sigma^2_g\), \(\sigma^2_s\), \(\sigma^2_r\) | variances of gca, sca and reciprocal effects (random model) |
| \(MS_E\), \(\sigma^2_m\) | error mean square, error variance of a cell mean |
| \(V_r\), \(W_r\) | variance of array \(r\), its covariance with the parents |
| \(D\), \(H_1\), \(H_2\), \(F\) | Hayman's components of variation |
References
Griffing, B. (1956). Concept of general and specific combining ability in relation to diallel crossing systems. Australian Journal of Biological Sciences, 9(4), 463–493. doi:10.1071/BI9560463
Hayman, B. I. (1954). The theory and analysis of diallel crosses. Genetics, 39(6), 789–809. doi:10.1093/genetics/39.6.789
Hayman, B. I. (1954). The analysis of variance of diallel tables. Biometrics, 10(2), 235–244. doi:10.2307/3001877
Kempthorne, O. and Curnow, R. N. (1961). The partial diallel cross. Biometrics, 17(2), 229–250. doi:10.2307/2527989
Singh, R. K. and Chaudhary, B. D. (2004). Biometrical Methods in Quantitative Genetic Analysis. Kalyani Publishers, New Delhi.
Author
Muhammad Yaseen (myaseen208@gmail.com), ORCID 0000-0002-5923-1714; Kent M. Eskridge; Pedro A. M. Barbosa; Yuhang Guo.