Fisher’s ‘fundamental theorem of natural selection’ is notoriously abstract, and, no less notoriously, many take it to be false. In this paper, I explicate the theorem, examine the role that it played in Fisher’s general project for biology, and analyze why it was so very fundamental for Fisher. I defend Ewens (1989) and Lessard (1997) in the view that the theorem is in fact a true theorem if, as Fisher claimed, ‘the terms employed’ are ‘used strictly as defined’ (1930, p. (...) 38). Finally, I explain the role that projects such as Fisher’s play in the progress of scientific inquiry. (shrink)

The diversity, complexity and adaptation of the biological realm is evident. Until Darwin, the best explanation for these three features of the biological was the conclusion of the “argument from design.” Darwin's theory of natural selection provides an explanation of all three of these features of the biological realm without adverting to some mysterious designing entity. But this explanation's success turns on the meaning of its central explanatory concept, ‘fitness’. Moreover, since Darwinian theory provides the resources for a purely causal (...) account of teleology, wherever it is manifested, its reliance on the concept of ‘fitness’ makes it imperative that conceptual problems threatening the explanatory legitimacy of this notion be solved. (shrink)

Fisher’s ‘fundamental theorem of natural selection’ is notoriously abstract, and, no less notoriously, many take it to be false. In this paper, I explicate the theorem, examine the role that it played in Fisher’s general project for biology, and analyze why it was so very fundamental for Fisher. I defend Ewens and Lessard in the view that the theorem is in fact a true theorem if, as Fisher claimed, ‘the terms employed’ are ‘used strictly as defined’. Finally, I explain the (...) role that projects such as Fisher’s play in the progress of scientific inquiry. (shrink)

Fisher’s ‘fundamental theorem of natural selection’ is notoriously abstract, and, no less notoriously, many take it to be false. In this paper, I explicate the theorem, examine the role that it played in Fisher’s general project for biology, and analyze why it was so very fundamental for Fisher. I defend Ewens and Lessard in the view that the theorem is in fact a true theorem if, as Fisher claimed, ‘the terms employed’ are ‘used strictly as defined’. Finally, I explain the (...) role that projects such as Fisher’s play in the progress of scientific inquiry. (shrink)

The Formal Darwinism Project is an attempt to use mathematical theory to prove the claim that fitness maximization is the outcome of evolution in nature. Grafen’s (2014, p. 12) conclusion from this project is that “….there is a very general expectation of something close to fitness maximisation, which will convert into fitness-maximisation unless there are particular kinds of circumstances—and further, that fitness is the same quantity for all genetic architectures.” Grafen’s claim appears to mean to him that natural populations are (...) expected to contain individuals whose traits are optimal, i.e., any given trait outperforms all reasonable alternatives. I describe why Grafen’s attempt can never provide a meaningful expectation as to the ubiquity of optimal traits in nature. This is so because it is based upon a misconception of the relationship between theory and empirical analysis. Even if one could use theory in the way Grafen proposes, I describe how his theory is causally incomplete. Finally, I describe how Grafen’s conceptual framework is ambiguous. The Formal Darwinism Project has been inspired by “On The Origin of Species” by Darwin. The great lesson of this book was Darwin’s demonstration of the necessary dialog between theory and data, with each influencing and being influenced by the other. Grafen’s Formal Darwinism Project, an attempt to create understanding of nature by removing data from this dialog, reflects a failure to understand Darwin’s great lesson. (shrink)

This paper provides a philosophical analysis of the ongoing controversy surrounding R.A. Fisher's famous ‘fundamental theorem’ of natural selection. The difference between the ‘traditional’ and ‘modern’ interpretations of the theorem is explained. I argue that proponents of the modern interpretation have captured Fisher's intended meaning correctly and shown that the theorem is mathematically correct, pace the traditional consensus. However, whether the theorem has any real biological significance remains an unresolved issue. I argue that the answer depends on whether we accept (...) Fisher's non-standard notion of environmental change, on which the theorem rests; arguments for and against this notion are explored. I suggest that there is a close link between Fisher's fundamental theorem and the modern ‘gene's eye’ view of evolution. Introduction What Does the Fundamental Theorem Say? Key Concepts Explained Alleged Significance of the FTNS Traditional versus Modern Interpretations of the FTNS The Modern Interpretation Illustrated Fisher's Concept of ‘Environmental Change’ Causality and the Modern Interpretation The Significance of the FTNS Re-considered Appendix CiteULike Connotea Del.icio.us What's this? (shrink)

We critically examine a number of aspects of Grafen’s ‘formal Darwinism’ project. We argue that Grafen’s ‘selection-optimality’ links do not quite succeed in vindicating the working assumption made by behavioural ecologists and others—that selection will lead organisms to exhibit adaptive behaviour—since these links hold true even in the presence of strong genetic and developmental constraints. However we suggest that the selection-optimality links can profitably be viewed as constituting an axiomatic theory of fitness. Finally, we compare Grafen’s project with Fisher’s ‘fundamental (...) theorem of natural selection’, and we speculate about whether Grafen’s results can be extended to a game-theoretic setting. (shrink)

The broader context for the formal darwinism project established by two of the commentators, in terms of reconciling the Modern Synthesis with Darwinian arguments over design and in terms of links to other types of selection and design, is discussed and welcomed. Some overselling of the project is admitted, in particular of whether it claims to consider all organic design. One important fundamental question raised in two commentaries is flagged but not answered of whether design is rightly represented by an (...) optimisation program, and another from one commentary of whether the coreplicon dissolves in the face of multi-generational imprinting. Calls for the project to be extended to design at levels above and below the individual are considered sympathetically, but judged impractical at the high level of abstraction of the project. All claims of substantive technical error are emphatically rejected. Close technical readings are welcomed that, among other things, represent the project as 'axiomatizing fitness'. The prospects for the project are set out in the light of this highly varied set of commentaries. (shrink)

The broader context for the formal darwinism project established by two of the commentators, in terms of reconciling the Modern Synthesis with Darwinian arguments over design and in terms of links to other types of selection and design, is discussed and welcomed. Some overselling of the project is admitted, in particular of whether it claims to consider all organic design. One important fundamental question raised in two commentaries is flagged but not answered of whether design is rightly represented by an (...) optimisation program, and another from one commentary of whether the coreplicon dissolves in the face of multi-generational imprinting. Calls for the project to be extended to design at levels above and below the individual are considered sympathetically, but judged impractical at the high level of abstraction of the project. All claims of substantive technical error are emphatically rejected. Close technical readings are welcomed that, among other things, represent the project as 'axiomatizing fitness'. The prospects for the project are set out in the light of this highly varied set of commentaries. (shrink)

The aim of this paper is to offer a new biological interpretation of Fisher’s ‘Fundamental Theorem of Natural Selection’ and from this to consider optimality properties of gene frequency changes. These matters are of continuing interest to biologists and philosophers alike. In particular, the extent to which biological evolution can be calculated from the ‘gene’s-eye’ point of view is also discussed. In this sense, the paper bears indirectly on the concepts of the unit of selection and of the ‘selfish gene’. (...) A new biological significance for the Fundamental Theorem, not previously found in the literature, is offered, together with an optimality principle connected with this theorem. (shrink)

This paper is a commentary on the focal article by Grafen and on earlier papers of his on which many of the results of this focal paper depend. Thus it is in effect a commentary on the “formal Darwinian project”, the focus of this sequence of papers. Several problems with this sequence are raised and discussed. The first of these concerns fitness maximization. It is often claimed in these papers that natural selection leads to a maximization of fitness and that (...) this view is claimed in Fisher’s “fundamental theorem of natural selection”. These claims are refuted, and various incorrect statements about the meaning and interpretation of the fundamental theorem of natural selection, in this sequence and in other papers by other authors, are discussed. Next, much of the work in this sequence rests on the first Price equation. In the deterministic (infinite population) case this equation is no more than the standard classical equation relating to changes in gene frequencies. In the stochastic case the equation gives the change in gene frequencies as the sum of two terms (the second of which vanishes in the deterministic case). These two terms are of essentially equal importance in the situation considered in the focal article, yet one of Grafen’s results ignores the second term in the stochastic analysis. This is associated with a wavering between deterministic and stochastic analyses and the use of the Price fitness concept and the classical fitness concept. These comments cast doubts on Grafen’s optimization theory. (shrink)

The debate over the relative importance of natural selection as compared to other forces affecting the evolution of organisms is a long-standing and central controversy in evolutionary biology. The theory of adaptationism argues that natural selection contains sufficient explanatory power in itself to account for all evolution. However, there are differing views about the efficiency of the adaptation model of explanation. If the adaptationism theory is applied, are energy and resources being used to their optimum? This book presents an up-to-date (...) view of this controversy and reflects the dramatic changes in our understanding of evolution that have occurred in the last twenty years. The volume combines contributions from biologists and philosophers, and offers a systematic treatment of foundational, conceptual, and methodological issues surrounding the theory of adaptationism. The essays examine recent developments in topics such as phylogenetic analysis, the theory of optimality and ess models, and methods of testing models. (shrink)

We consider the question: under what circumstances can the concept of adaptation be applied to groups, rather than individuals? Gardner and Grafen (2009, J. Evol. Biol.22: 659–671) develop a novel approach to this question, building on Grafen's ‘formal Darwinism’ project, which defines adaptation in terms of links between evolutionary dynamics and optimization. They conclude that only clonal groups, and to a lesser extent groups in which reproductive competition is repressed, can be considered as adaptive units. We re-examine the conditions under (...) which the selection–optimization links hold at the group level. We focus on an important distinction between two ways of understanding the links, which have different implications regarding group adaptationism. We show how the formal Darwinism approach can be reconciled with G.C. Williams’ famous analysis of group adaptation, and we consider the relationships between group adaptation, the Price equation approach to multi-level selection, and the alternative approach based on contextual analysis. (shrink)