Diallel Analysis, Heterosis and Related Mating Designs

Analysis of diallel crosses and related mating designs in plant breeding, from the plot data of randomized complete block experiments: Griffing's four methods and two models (Griffing, 1956 ), from plot data, from a published table of means or over several environments, with gca by environment and sca by environment interactions and a split of reciprocal effects into maternal and non-maternal parts (Cockerham and Weir, 1977); Hayman's analysis with the Wr-Vr graph and the components of variation (Hayman, 1954 ); mid-parent, better-parent and standard heterosis with t tests; Gardner and Eberhart's (1966) Analyses II and III; the partial diallel (Kempthorne and Curnow, 1961 ); line by tester analysis with proportional contributions; and the North Carolina designs I, II and III (Comstock and Robinson, 1948). Missing plots are handled by least-squares means. Results include analyses of variance, effects with standard errors, variance components and genetic ratios, plots of the effects and a biplot of the crosses, tables for papers in Word, LaTeX, HTML or Markdown, simulation of diallel data and the power of the tests for planning the number of replicates, and an interactive 'shiny' application.

DiallelAnalysisR: Diallel Analysis, Heterosis and Related Mating

Designs

Overview

DiallelAnalysisR analyses diallel crosses of plant-breeding experiments laid out in randomized complete blocks:

Griffing(): Griffing’s (1956) Methods 1 to 4 with fixed or random effects: the analysis of variance of general and specific combining ability and reciprocal effects, the effects with their standard errors, and the variance components;
Hayman(): Hayman’s (1954) analysis of variance, the Wr-Vr analysis and graph, the components of variation D, H1, H2, F, h2 and E, genetic ratios and tests of the additive-dominance model;
PartialDiallel(): crosses between two groups of parents: combining ability of each group and of the crosses;
GriffingMeans(): Griffing’s analysis of a published table of cross means, with the error from the paper;
Heterosis(): mid-parent, better-parent and standard heterosis with t tests;
Griffing(..., Reciprocal = "split"): Cockerham and Weir’s maternal and non-maternal reciprocal effects;
GardnerEberhart(): Gardner and Eberhart’s (1966) Analyses II and III;
LineTester() and NCDesign(): line by tester analysis with proportional contributions, and North Carolina designs I, II and III;
GriffingEnv(): a diallel over several environments, with gca by environment and sca by environment;
plot(fit, which = "biplot"): a biplot of the cross means showing the best combiners and crosses;
DiallelSim() and DiallelPower(): simulated diallels for teaching and power for planning the replicates;
da_export(): the main tables in Word, LaTeX, HTML, Markdown or CSV for papers;
DiallelApp(): all of the above in a web browser, without code.

The package has been on CRAN since 2016 (version 0.1.1, 2016-04-09). Version 1.0.0 keeps every function name, argument and result component of earlier versions, so existing scripts run unchanged. It corrects the standard errors of Griffing’s analysis and several results of Hayman() and PartialDiallel() (see NEWS), adds plots and methods to every result, the analyses above, complete help pages with the formulas, fifteen vignettes in HTML and PDF, a comparison with the published values of Griffing (1956), and is many times faster for larger diallels.

Installation

install.packages("DiallelAnalysisR")
# development version
# install.packages("remotes")
remotes::install_github("myaseen208/DiallelAnalysisR")

Quick start

library(DiallelAnalysisR)
fit <-
  Griffing(
      y          = Yield
    , Rep        = Rep
    , Cross1     = Cross1
    , Cross2     = Cross2
    , data       = GriffingData1
    , Method     = 1
    , Model      = 1
    , Reciprocal = c("combined", "split")[1]
    )
fit$ANOVA

             Df  Sum Sq Mean Sq F value Pr(>F)    
gca           7  3804.6  543.52 18.8868 <2e-16 ***
sca          28 22060.8  787.89 27.3783 <2e-16 ***
reciprocals  28   365.5   13.05  0.4536 0.9923    
Error       189  5439.0   28.78                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

round(x = fit$GCA, digits = 2)

    1     2     3     4     5     6     7     8 
 0.06  0.47  9.03 -3.44 -2.33 -1.93  7.24 -9.10

plot(fit)

Learn more

Vignettes: browseVignettes("DiallelAnalysisR"), starting with DiallelAnalysisR_01_getting_started; each is available as HTML and as PDF.
Site: https://myaseen208.com/DiallelAnalysisR/
Notation: da_notation()
Shiny application: DiallelApp()

Citation

Yaseen M, Eskridge K, Barbosa P, Guo Y (2026). _DiallelAnalysisR:
Diallel Analysis, Heterosis and Related Mating Designs_. R package
version 1.0.0 (first released 2016),
<https://CRAN.R-project.org/package=DiallelAnalysisR>.

BibTeX:

@Manual{DiallelAnalysisR,
  title = {{DiallelAnalysisR}: Diallel Analysis, Heterosis and Related Mating Designs},
  author = {Muhammad Yaseen and Kent Eskridge and Pedro Barbosa and Yuhang Guo},
  year = {2026},
  note = {R package version 1.0.0 (first released 2016)},
  url = {https://CRAN.R-project.org/package=DiallelAnalysisR},
}