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Comparison of Genetic Models for Inbreeding in Autotetraploids Using Maize Data¹

In an attempt to clarify inbreeding depression in autotetraploids, three models for inbreeding depression were compared using data from autotetraploid maize (Zea mays L.). Generations included were S₁ through S₄ and full-sib generations 1 through 6. The first genetic model was µ₁ = µ + 6Fß_ii + (4P₀ + P₁)_iii + P_0iii + P_2iijj (Gallais). The second model (Hill's) was µ₁ = µ + pq(D + 2pT + p^2,Q) + Pq(q - P) (T + pQ) + pQ) + p²q²Q. Hill's model can be applied with or without assumptions about the origin of the parents for the inbreds. It was fit with the assumption of a source population in random mating equilibrium in this study except for a comparison involving four selfed generations. The third model fit the first four powers of F (coefficient of inbreeding). Deviations from fitting powers of F were significant in 10 of 20 cases while deviations from the other models were significant in only four. Thus, the F model was considered unsatisfactory. Comparison of Hill's model with no assumption of equilibrium with Gallais' model and Hill's model with assumption of equilibrium revealed no significant differences. Although no clear evidence from fits to data favored either model, it appears reasonable to conclude that Gallais' model or Hill's model assuming equilibrium is more appropriate when the source population was at equilibrium and that Hill's model without assumptions may be more appropriate when the equilibrium assumption is not possible.

Key Words: Generation means • Full-sib mating • Gene interactions • Zea mays L.

² Associate professor, Dep. of Agronomy and Soils, Clemson Univ., Clemson, SC 29631 and professor of plant genetics, Dep. of Agronomy, Univ. of Illinois, Urbana 61801.

Received for publication December 6, 1982.