Department of Mathematics and Statistics, Queen's University, Jeffery Hall, Kingston, Ontario, Canada.
J R Soc Interface. 2012 Mar 7;9(68):511-7. doi: 10.1098/rsif.2011.0429. Epub 2011 Aug 17.
When investigating evolution in structured populations, it is often convenient to consider the population as an evolutionary graph-individuals as nodes, and whom they may act with as edges. There has, in recent years, been a surge of interest in evolutionary graphs, especially in the study of the evolution of social behaviours. An inclusive fitness framework is best suited for this type of study. A central requirement for an inclusive fitness analysis is an expression for the genetic similarity between individuals residing on the graph. This has been a major hindrance for work in this area as highly technical mathematics are often required. Here, I derive a result that links genetic relatedness between haploid individuals on an evolutionary graph to the resistance between vertices on a corresponding electrical network. An example that demonstrates the potential computational advantage of this result over contemporary approaches is provided. This result offers more, however, to the study of population genetics than strictly computationally efficient methods. By establishing a link between gene transfer and electric circuit theory, conceptualizations of the latter can enhance understanding of the former.
在研究结构种群中的进化时，将种群视为进化图——个体为节点，以及他们可能与之相互作用的节点为边，通常是很方便的。近年来，人们对进化图的兴趣激增，特别是在研究社会行为的进化方面。适合这种类型研究的是适合度综合模型。适合度综合分析的一个核心要求是表示图上个体之间的遗传相似性。这一直是该领域工作的主要障碍，因为通常需要高度技术性的数学。在这里，我推导出一个结果，将进化图上的单倍体个体之间的遗传相关性与相应的电网络上的顶点之间的电阻联系起来。提供了一个示例，演示了与当代方法相比，该结果在计算上的潜在优势。然而，这个结果为群体遗传学的研究提供的不仅仅是更严格的计算效率方法。通过在基因转移和电路理论之间建立联系，可以增强对后者的理解，从而增强对前者的理解。
