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所谓拓扑空间的最大(小)值定理是指下面的: 定理1 紧致拓扑空间X中的任一连续函数能在X的点处达到它的最大值与最小值 本文主要讨论上述定理在遗传理论、畜牧水产养殖业以及在时间生物学中应用。 1.在遗传理论上应用 我们把定理1用到数量遗传学上,可以得到下面意义深刻的: 定理2 对于一个随机交配的群体,任一个经济性状W,当它受到某些微效加性多基因控制时,则这些多基因一定有一种最佳的搭配(包括搭配方式及相应的频率),使得群体的W性状的平均基因型值为最优。特别当这个群体是一个大的随机交配的群体,且在世代相传过程中不发生迁移、突变与选择时,则上述那个最佳搭配将世世代代保持下去。 证 设W受N个位点上的基因控制,为讨论方便起见,不妨设每个位点上有两个等位基因,且用A_i,B_i表示第i个(i=1,2,…,N)位点上的等位基因;用x_i表示A_i(在群
The maximum (small) value theorem of so-called topological space refers to the following: Theorem 1 The maximum and minimum of any continuous function in compact topological space X can reach its point at X. This paper mainly discusses the above theorems in the theory of genetics , Livestock husbandry and aquaculture as well as in time biology. Applying Theorem 1 to Quantum Genetics, we can obtain the following profound meanings: Theorem 2 For a random mating population, any economic trait W, when it is subjected to some micro-additive polygenes When controlling, then there must be an optimal mix of these multiple genes (including how and how often) so that the average genotype of the W trait is optimal. Especially when this group is a large, random-coping group and there is no migration, mutation or choice from generation to generation, the best match above will be maintained for generations to come. It is assumed that W is controlled by the genes at N loci. For convenience of discussion, let’s assume that there are two alleles at each locus, and the i-th is denoted by A_i and B_i (i = 1, 2, N) alleles; with x_i said A_i (in the group