Book: The Genetical Theory of Natural Selection

Overview
Ronald A. Fisher's The Genetical Theory of Natural Selection synthesizes Mendelian genetics with Darwinian natural selection through a rigorous mathematical framework. Fisher frames evolution as a process driven by differential reproductive success of genetically determined traits, and develops quantitative measures that link heredity to changes in population composition. The book combines careful theoretical derivations with broad biological arguments about sex, dominance, and adaptation.
Fisher treats populations as ensembles of genotypes whose frequencies change under selection, mutation, migration and mating, and he uses statistical reasoning to extract general principles. His tone is both mathematical and interpretive: equations are used to define and clarify biological concepts such as fitness and genetic variance rather than to produce one-off numerical predictions.

Main contributions
A central result is the Fundamental Theorem of Natural Selection, stated roughly as: the rate of increase in mean fitness of a population is equal to the additive genetic variance in fitness. Fisher formulates this theorem to capture the directional tendency of selection to translate genetic variance into improved average adaptation, while acknowledging that nonselective forces and changes in the environment complicate the simple statement.
Fisher also introduces the concept of genetic load to quantify the cost that deleterious alleles and substitutions impose on a population's mean fitness. He uses this idea to address limits on the pace of evolution and to discuss the implications of mutation rates, inbreeding, and the maintenance of polymorphism.

Key concepts developed
Fitness is formalized as a property linked to reproductive output and gene transmission, and Fisher emphasizes the additive component of genetic variance as the key currency for selection. His treatment of dominance conjectures that dominance relations can evolve through cumulative effects of modifiers, arguing that dominance is not an immutable gene property but the outcome of selection for buffering.
Sexual selection and the evolution of sex receive extended treatment. Fisher provides an elegant account of sex ratios, showing why equal parental investment in males and females tends to be an evolutionarily stable outcome. He also develops the idea that mate choice can generate positive feedbacks between preference and trait expression, leading to exaggerated sexual ornaments, a concept that later became known as Fisherian runaway.
Fisher analyzes inbreeding, assortative mating and the consequences of different mating systems for the transmission of genes and the exposure of recessive deleterious alleles. He treats mutation, selection and the balance that determines polymorphism and the persistence of variation.

Approach and methods
Mathematical analysis is used to isolate general forces and to derive inequalities and identities that constrain evolutionary change. Fisher brings statistical thinking, variance decomposition and likelihood-based intuition, into genetics, laying groundwork for the quantitative genetics tradition. Rather than detailed simulation of particular cases, the book seeks universal relations and conceptual clarity about how selection operates on measurable genetic components.
Fisher's proofs and arguments often invoke idealized assumptions, large populations, random mating, and well-defined measures of fitness, to make the mathematics tractable, while he discusses the implications when those assumptions are relaxed.

Legacy and controversy
The Genetical Theory of Natural Selection became a cornerstone of the modern synthesis, shaping population genetics, quantitative genetics and evolutionary theory. Fisher's formulations of sex ratio, sexual selection and genetic load influenced decades of empirical and theoretical work. The Fundamental Theorem in particular provoked extensive debate; later generations clarified its formal assumptions and limitations, and reconciled it with alternative perspectives offered by Sewall Wright and J.B.S. Haldane.
Some of Fisher's specific claims, most notably his account of the evolution of dominance, provoked sharp critiques and revisions, yet the questions he raised remained central. The book stands as a rigorous, idea-rich statement that transformed evolutionary biology into a quantitatively grounded science.