# diallel
## English
### Etymology

From Ancient Greek.

### Adjective

diallel (not comparable)
* (genetics) Involving crosses between several or all possible combinations.
** 1970, David William Burrows, Snap-back and Lodging Studies of a Nine Barley Variety Diallel Cross, page 15:Nine varieties were chosen for a diallel crossing
** 1988, Arnel R. Hallauer, Marcelo J. Carena, J.B. Miranda Filho, Quantitative Genetics in Maize Breeding, second edition, →ISBN, page 119:The main difference with design II is that the same individuals are used as parents for the diallel mating design (individuals are used both as male and female).
** 1990, David E. Harrison, Genetic Effects on Aging, page 73:A series of diallel analyses (cf. Mather and Jinks, 1982) were performed to test for heterogeneity among lines of a given type.
** 2005, Maydica, page 148:The diallel mating design is particularly well suited to characterizing genetic effects of inbred lines and their hybrid combinations .
* (rare) Of lines: Meeting and intersecting; not parallel.
** 1900, Official Proceedings of the Annual Convention of the National Editorial Association, page 99:[…] like conditions and common ends as the ideal and goal of human effort are attained along parallel and not diallel lines in all the diversities of human application and invention.
** 2000, David W. Allan, Jeff Lorbeck, New Gravitational Theory with Experimental Validation, page 2:Fundamental to this new theory is the discovery of diallel, gravitational-field lines. These connect the two bodies — providing a path for the gravitational information to flow. To see the evidence of these diallel lines in nature requires a paradigm shift away from the traditional view of gravitational interaction.
** 2020, Jean de Climont, The Worldwide List of Alternative Theories and Critics, page 63:[…] connecting diallel lines which provide not only particle flow between the bodies, but also the flow of photon and gravitational information as well […]

#### Related terms

* diallage

### Noun

diallel (plural diallels)
* A set of all possible pairs of items from a specified set of items, especially when used for a study of diallel crosses.
** 1978, E. B. Snyder, Gene Namkoong, Inheritance in a Diallel Crossing Experiment with Longleaf Pine, page 2:Pollinations in 1956 and 1957 produced seed for eight replications of all 78 combinations of a complete half diallel, excluding selfs.
** 1991, Rice Genetics II, page 287:However, complex gene action involving nonallelic interaction was found in the original 6×6 diallel.
** 2012, H.K. Jain, M.C. Kharkwal, Plant Breeding: Mendelian to Molecular Approaches, page 526:In a diallel, a set of genotypes are crossed in all possible combinations.
* A form of logical fallacy in which a proposition that is required to prove another proposition can only be proved by means of assuming the truth of the proposition one is trying to prove; circular reasoning.
** 1871, Thomas Woodhouse Levin, Six Lectures Introductory to the Philosophical Writings of Cicero, page 110:Fifth is the diallel (ó διάλληλος τρóπος)—petitio principii—the fallacy of circle, or the method of showing that a proof which is employed to establish the truth of a proposition, can itself only be proved by the proposition in question: as for example, "if anyone should infer the authenticity of a certain history, from its recording such and such facts, the reality of which rests on the evidence of that history."
** 2008, Thomas M. Lennon, The Plain Truth: Descartes, Huet, and Skepticism, page 50:In particular, Huet is said to apply the five tropoi of Agrippa (viz. relativity, diaphonia or disagreement, hypothesis or begging the question, infinite regress, and diallel or circular argument) to the cogito, the criterion of clarity and distinctness, and the proofs of the existence of God.
** 2017, Jannis Kozatsas, Georges Faraklas, Stella Synegianni, Hegel and Scepticism: On Klaus Vieweg's Interpretation, page 47:This reminds us of what Sextus calls a diallel. A diallel is a situation where we need a in order to “prove” b and b in order to “prove” a (PH, I, 169), so that we can’t prove anything.

#### Derived terms

* diallelous