Département de mathématiques et de statistique, Université de Montréal, Montréal, Québec H3C 3J7, Canada.
Department of Biology, The University of Pennsylvania, Philadelphia, PA 19104, USA.
J Theor Biol. 2019 Jul 7;472:77-83. doi: 10.1016/j.jtbi.2019.04.014. Epub 2019 Apr 13.
In a recent paper, Grafen (2018) discussed the left-hand side in the equation stating Fisher's (1930, 1958) "Fundamental Theorem of Natural Selection" (FTNS). Fisher's original statement of the FTNS is, in effect, "The rate of increase in fitness of any organism is equal to its genetic variance in fitness at that time" with the rate of increase in fitness understood as the one "due to all changes in gene ratios" (Fisher, 1930, p. 35). For purposes of exposition, Grafen (2018) considered what is today called the analogous discrete-time model, and restated the FTNS on p. 181 as "The increase in population [mean fitness] due to changes in gene frequencies [is equal to the] additive genetic variance in fitness [divided by the] mean fitness". Allowing for the fact that Grafen's statement of the FTNS relates to a discrete-time model, his statement is in effect a discrete-time version of Fisher's. It has however been widely accepted for many years, ever since Price's (1972) deep analysis of the FTNS, that Fisher's wording does not correctly describe the content of the FTNS. The same is therefore true of Grafen's statement. The confusion caused by these misstatements is unfortunate and adds to a continuing misunderstanding of the FTNS, whose source can also be found in Fisher's (1941) own explanation. Our purpose is to review the detailed analysis of the calculations leading to the FTNS to clarify the points at issue.
在最近的一篇论文中，格拉芬（2018 年）讨论了表述费希尔（1930 年、1958 年）“自然选择基本定理”（FTNS）的方程式中的左侧。费希尔最初对 FTNS 的表述实际上是“任何生物体适应度的增长率等于其当时适应度的遗传方差”，适应度的增长率被理解为“由于所有基因比例的变化”（费希尔，1930 年，第 35 页）。为了阐述的目的，格拉芬（2018 年）考虑了今天被称为类似的离散时间模型，并在第 181 页将 FTNS 重新表述为“由于基因频率的变化而导致的种群[平均适应度]的增加[等于]适应度的加性遗传方差[除以]平均适应度”。考虑到格拉芬对 FTNS 的表述与离散时间模型有关，他的表述实际上是费希尔离散时间版本的表述。然而，自普赖斯（1972 年）对 FTNS 的深入分析以来，多年来人们广泛接受了这一观点，即费希尔的措辞并没有正确描述 FTNS 的内容。因此，格拉芬的表述也是如此。这些错误陈述造成的混淆是不幸的，并且增加了对 FTNS 的持续误解，其来源也可以在费希尔（1941 年）自己的解释中找到。我们的目的是审查导致 FTNS 的计算的详细分析，以澄清争议点。
