Generation Mean Analysis
Generation mean analysis with three, five and six parameter models, joint scaling test and gene effects.
When to use it
Use when you have generation means from a cross of two parents (P1, P2, F1, F2, BC1, BC2) and want to estimate additive (d), dominance (h), and epistatic (i, j, l) gene effects. The 3-parameter model (m, d, h) assumes no epistasis; the 5- and 6-parameter models add epistatic terms; the Cavalli (1952) joint scaling test compares model fit to identify which parameters are needed.
When NOT to use it
Do not use when generation means come from a multi-parental cross or backcross series outside the classical Mather and Jinks design; the parameterisation no longer matches. Do not use when generations were not all replicated in the same trial; combining historical means inflates error. Do not over-fit the 6-parameter model when degrees of freedom are tight; the 3-parameter model is the parsimonious default.
What you get
Parameter estimates m, d, h, and (depending on model) i, j, l with their SEs and t-tests against zero. Chi-square goodness-of-fit for each model with df. The Cavalli joint scaling test comparing nested models. A model-selection summary recommending the simplest model whose fit is acceptable. Per-generation predicted means against observed.
How to interpret the output
If the 3-parameter model fits (joint chi-square not rejected), additive and dominance gene effects are sufficient and epistasis is not detected. If the 3-parameter fits poorly but the 6-parameter fits, one or more epistatic terms are needed; t-tests on i, j, l identify which. d (additive) is selectable; h (dominance) and l (dominance x dominance) are not directly selectable in self-pollinated crops. Mather and Jinks (1971) is the canonical reference.
Common pitfalls
- Fitting the 6-parameter model when df do not support it (an over-fit will look great by definition).
- Treating the Cavalli chi-square as a hypothesis test on individual parameters (it is a model-fit test).
- Ignoring the per-generation residuals; a poor fit may localise to one generation (data-quality flag).
- Reporting non-additive gene effects without confirming that the variance is heritable (estimable only with replicated trials).
Try it in StatVeda
The Generation Means (3/5/6-parameter + Cavalli JST) engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open Generation Means (3/5/6-parameter + Cavalli JST)References
- Cavalli, L. L. (1952). An analysis of linkage in quantitative inheritance. In Quantitative Inheritance (Reeve, E. C. R. and Waddington, C. H., editors), 135 to 144. HMSO, London.
- Mather, K. and Jinks, J. L. (1971). Biometrical Genetics, 2nd edition. Chapman and Hall, London.
- Hayman, B. I. (1958). The separation of epistatic from additive and dominance variation in generation means. Heredity, 12, 371 to 390.