Formal Darwinism, the individual–as–maximizing–agent analogy and bet–hedging

Abstract

The central argument of The origin of species was that mechanical processes (inheritance of features and the di¡erential reproduction they cause) can give rise to the appearance of design. The`mechanical processes' are now mathematically represented by the dynamic systems of population genetics, and the appearance of design by optimization and game theory in which the individual plays the part of the maximizing agent. Establishing a precise individual-as-maximizing-agent (IMA) analogy for a population genetics system justi¢es optimization approaches, and so provides a modern formal representation of the core of Darwinism. It is a hitherto unnoticed implication of recent population-genetics models that, contrary to a decades-long consensus, an IMA analogy can be found in models with stochastic environments (subject to a convexity assumption), in which individuals maximize expected reproductive value. The key is that the total reproductive value of a species must be considered as constant, so therefore reproductive value should always be calculated in relative terms. This result removes a major obstacle from the theoretical challenge to ¢nd a unifying framework which establishes the IMA analogy for all of Darwinian biology, including as special cases inclusive ¢tness, evolutionarily stable strategies, evolutionary life-history theory, age-structured models and sex ratio theory. This would provide a formal, mathematical justi¢cation of fruitful and widespread but`intentional' terms in evolutionary biology, such as`sel¢sh',`altruism' and con£ict'.

The Evolutionary Foundations of Preferences

“…Grafen [63] offers a resolution of the apparent altruism puzzle raised by Cooper and Kaplan. Consider a continuum of agents of size 1.…”

“…Similarly an A mutant in a B population would die out, despite the ultimate advantage of getting to the all-A configuration. Alternatively, 63 See Sober and Wilson [146] for a forcefully argued alternative view.…”

“…63 The requirements of a large number of groups, sufficient isolation of groups, barriers to migration and mutation, and differential group success rates, all combine to limit the applicability of group selection. Intuitively, a loose description of the problem with group selection is that it relies too heavily upon the assumption that a bad choice will lead to group extinction.…”

Formalizing Darwinism and inclusive fitness theory

“…If we can prove strong enough links, including defining the maximand, then that will show how natural selection relates to fitness maximization. That, in essence, is the logic of my formal Darwinism project, which currently consists of five core papers (Grafen 1999(Grafen , 2000(Grafen , 2002(Grafen , 2006a, a bunch of applications (Grafen 2007a,c;Grafen & Archetti 2008;Gardner & Grafen 2009) and two introductory and expository papers, one non-mathematical (Grafen 2007b) and one mathematical (Grafen 2008).…”

Predictive ecology: systems approaches

“…Including evolution will add a level of complexity, but work in evolutionary ecology provides us with tools to start addressing these issues. For example, if we know that organisms act so as to maximize relative fitness [25,26], then we have a conceptual basis for modelling life-history decisions of organisms, even when we have sparse information about their biology. Including evolution may make modelling with limited data more straightforward.…”