Algebras of genetic self-incompatibility systems

P. Holgate
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引用次数: 1

Abstract

To every system of inheritance there corresponds a genetic algebra, generally non-associative, that describes its structure. The genetic algebras of a large number of breeding systems have been studied, but they have all been non-selective, and mostly random mating. The object of this paper is to investigate the genetic algebras of a number of systems involving a very strong form of differential fertility, where some pairs of individuals cannot produce viable offspring at all. For these, none of the classical properties of genetic algebra hold. In §2, the phenomenon of pollen incompatibility with m alleles is studied. The case m = 3 occurs in nature in Nicotiana alata For this, but not when m > 3, the genetic algebra is found to be Lie admissible, and some detailed relations consequent on this are obtained. Section 3 is devoted to two systems of style height self-incompatibility, Lythrum salicaria and Oxalis rosea. For these, described essentially by 6- and 26- dimensional genetic algebras respectively, the idempotents are listed, and full and outline descriptions respectively are given of the lattices of subalgebras. In the last section a class of algebras is defined corresponding to a multilocus generalization of the Lythrum mechanism. It is shown that this mechanism always leads to an isoplethic equilibrium.
遗传自不相容系统的代数
每一个遗传系统都对应着一个描述其结构的遗传代数,通常是非结合的。人们研究了大量繁殖系统的遗传代数,但它们都是非选择性的,而且大多是随机交配。本文的目的是研究一些系统的遗传代数涉及一个非常强的形式的差异生育,其中一些对个体不能产生可行的后代。对于这些,遗传代数的经典性质都不成立。在§2中,研究了花粉与m个等位基因的不亲和现象。在烟叶中自然存在m = 3的情况,但当m > 3时,发现遗传代数是李可容许的,并由此得到了一些详细的关系式。第3节介绍了两种花柱高度自交不亲和系统:水杨曲和玫瑰草。对于这些主要由6维和26维遗传代数分别描述的子代数,分别列出了幂等函数,并给出了子代数格的完整和概要描述。在最后一节中,定义了一类代数,对应于Lythrum机制的多位点推广。结果表明,这一机制总是导致等厚体平衡。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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