Mode Charles J, Gallop Robert J
Department of Mathematics, Drexel University, Philadelphia, PA 19104, USA.
Math Biosci. 2008 Feb;211(2):205-25. doi: 10.1016/j.mbs.2007.05.015. Epub 2007 Nov 28.
A case has made for the use of Monte Carlo simulation methods when the incorporation of mutation and natural selection into Wright-Fisher gametic sampling models renders then intractable from the standpoint of classical mathematical analysis. The paper has been organized around five themes. Among these themes was that of scientific openness and a clear documentation of the mathematics underlying the software so that the results of any Monte Carlo simulation experiment may be duplicated by any interested investigator in a programming language of his choice. A second theme was the disclosure of the random number generator used in the experiments to provide critical insights as to whether the generated uniform random variables met the criterion of independence satisfactorily. A third theme was that of a review of recent literature in genetics on attempts to find signatures of evolutionary processes such as natural selection, among the millions of segments of DNA in the human genome, that may help guide the search for new drugs to treat diseases. A fourth theme involved formalization of Wright-Fisher processes in a simple form that expedited the writing of software to run Monte Carlo simulation experiments. Also included in this theme was the reporting of several illustrative Monte Carlo simulation experiments for the cases of two and three alleles at some autosomal locus, in which attempts were to made to apply the theory of Wright-Fisher models to gain some understanding as to how evolutionary signatures may have developed in the human genome and those of other diploid species. A fifth theme was centered on recommendations that more demographic factors, such as non-constant population size, be included in future attempts to develop computer models dealing with signatures of evolutionary process in genomes of various species. A brief review of literature on the incorporation of demographic factors into genetic evolutionary models was also included to expedite and stimulate further development on this theme.
当将突变和自然选择纳入赖特 - 费希尔配子抽样模型，从经典数学分析的角度来看使其变得难以处理时，有人提出了使用蒙特卡罗模拟方法的理由。本文围绕五个主题展开。这些主题包括科学开放性以及对软件所基于数学原理的清晰记录，以便任何感兴趣的研究人员都可以用他选择的编程语言复制任何蒙特卡罗模拟实验的结果。第二个主题是公开实验中使用的随机数生成器，以提供关于生成的均匀随机变量是否令人满意地满足独立性标准的关键见解。第三个主题是回顾遗传学领域的近期文献，这些文献试图在人类基因组数百万个DNA片段中寻找自然选择等进化过程的特征，这可能有助于指导寻找治疗疾病的新药。第四个主题涉及以一种简单的形式对赖特 - 费希尔过程进行形式化，这加快了运行蒙特卡罗模拟实验的软件编写。这个主题还包括报告一些关于某个常染色体位点两个和三个等位基因情况的说明性蒙特卡罗模拟实验，其中试图应用赖特 - 费希尔模型理论来了解人类基因组以及其他二倍体物种的进化特征可能是如何形成的。第五个主题集中在建议上，即在未来开发处理各种物种基因组进化过程特征的计算机模型时，应纳入更多人口统计学因素，如非恒定种群大小。还包括对将人口统计学因素纳入遗传进化模型的文献的简要回顾，以加快并促进关于这个主题的进一步发展。
