In natural populations, individuals often  are distributed more or less discontinuously to form numerous colonies, and  individuals may be exchanged between adjacent or nearby colonies. To analyze  such a situation, one of us proposed a model which he termed “stepping stone  model” of population structure (KIMUR 1953)  

在自然种群中，个体往往分布不连续，从而形成或多或少的聚居点，相邻或邻近的聚居点之间有一定的个体交流。为了分析这种情况，我们提出了一个模型，称这种种群结构为“脚踏石模型”(KIMUR 1953)。

ONE DIMENSIONAL CASE

Let US consider an infinite array of  colonies with their position represented by integers on a line (Figure 1).  The simplest situation for this one dimensional stepping stone model is that  in each generation an individual can migrate at most one step” in either  direction between colonies. In other words, exchange of individuals is  restricted to be between adjacent colonies.

一维脚踏石模型

Kimura, M. (1953). "Stepping Stone" model of  population. Rep. Nat. Inst. Genetics Japan. 3: 62-63.

Kimura, M. and G. H. Weiss (1964). "The Stepping  Stone Model of Population Structure and the Decrease of Genetic Correlation  with Distance." Genetics49(4): 561-576.