PAIN IN TORUS - SOME DIFFICULTIES WITH MODELS OF ISOLATION BY DISTANCE
PAIN IN TORUS - SOME DIFFICULTIES WITH MODELS OF ISOLATION BY DISTANCE
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DOI：
10.1086/283003
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发表时间：
1975-01-01
影响因子：
2.9
通讯作者：
FELSENSTEIN, J
中科院分区：
文献类型：
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作者：
FELSENSTEIN, J
Malecot的距离隔离模型似乎假设了空间上的随机分布、后代数量的泊松分布和个体的独立迁移。这些假设是不一致的。通过计算在距离x处两个位置共同占据的概率，表明体现后两个假设的单倍体模型违背了第一个假设，形成越来越大的个体团块，它们之间的距离越来越大。因此，这个模型在生物学上是不相关的，尽管可以用它来计算不同距离上基因同一性的概率。通过计算机模拟验证了这些团块的形成。同样的现象也出现在二维和三维模型中。在有限区域（圆形或环面）的模型中，团块的形成以每个区域内生物最终局部灭绝的确定性形式出现。如果我们保持圆或环面上的个体数不变，则不会发生这种情况，但仍然会导致与随机分布的相当大的偏离。对于人口密度有限的地理结构人口，目前看来，垫脚石模型是唯一定义良好的模型。
Malecot's models of isolation by distance seem to assume random distribution in space, Poisson distribution of offspring number, and independent migration of individuals. These assumptions are inconsistent. By calculating the probability of joint occupancy of two locations at a distance x, it is shown that a haploid model embodying the latter two assumptions violates the first, forming larger and larger clumps of individuals separated by greater and greater distances. Thus the model is biologically irrelevant, even though it is possible to use it to calculate probabilities of genetic identity at different distances. The formation of these clumps is verified by computer simulation. The same phenomenon occurs in two- and three-dimensional models. In models of finite regions (a circle or a torus), the formation of clumps takes the form of the certainty of ultimate local extinction of the organism in each region. This does not occur if we hold the number of individuals on the circle or torus constant, but considerable departure from random distribution still results. The stepping-stone models appear for the present to be the only well-defined models of geographically structured populations with finite population density.