Lange K, Risch N
J Math Biol. 1977 Dec 27;5(1):55-9. doi: 10.1007/BF00275806.
Assuming a four strand model and no chromatid interference, lack of chiasma interference is known to be equivalent to the assumption that the formation of chiasmata follows a Poisson process. We prove the lack of chiasma interference is also equivalent to the assumption that a random gamete shows recombination on any given interval of a chromosome independently of recombination on all disjoint intervals. Both assumptions are sufficient, but not necessary, for Haldane's formula relating recombination to map distance to be true, as we demonstrate by specific counterexamples. These issues are discussed in the context of the theory of stochastic point processes.
假设为四线模型且不存在染色单体干涉，已知不存在交叉干涉等同于假设交叉的形成遵循泊松过程。我们证明不存在交叉干涉也等同于假设一个随机配子在染色体的任何给定区间上发生重组，且与所有不相交区间上的重组相互独立。正如我们通过具体反例所证明的，这两个假设对于将重组与图距相关联的霍尔丹公式成立而言都是充分的，但并非必要条件。这些问题将在随机点过程理论的背景下进行讨论。
