Biomedical subjects

Alan Grafen

Publications and source records attributed to Alan Grafen.

6 recordsLinked to original sources

PubMed2006

A theory of Fisher's reproductive value.

The formal Darwinism project aims to provide a mathematically rigorous basis for optimisation thinking in relation to natural selection. This paper deals with the situation in which individuals in a population belong to classes, such as sexes, or size and/or age classes. Fisher introduced the concept of reproductive value into biology to help analyse evolutionary processes of populations divided into classes. Here a rigorously defined and very general structure justifies, and shows the unity of concept behind, Fisher's uses of reproductive value as measuring the significance for evolutionary processes of (i) an individual and (ii) a class; (iii) recursively, as calculable for a parent as a sum of its shares in the reproductive values of its offspring; and (iv) as an evolutionary maximand under natural selection. The maximand is the same for all parental classes, and is a weighted sum of offspring numbers, which implies that a tradeoff in one aspect of the phenotype can legitimately be studied separately from other aspects. The Price equation, measure theory, Markov theory and positive operators contribute to the framework, which is then applied to a number of examples, including a new and fully rigorous version of Fisher's sex ratio argument. Classes may be discrete (e.g. sex), continuous (e.g. weight at fledging) or multidimensional with discrete and continuous components (e.g. sex and weight at fledging and adult tarsus length).

Animals↗

PubMed2005

The illusion of invariant quantities in life histories.

Life-history theory attempts to provide evolutionary explanations for variations in the ways in which animal species live their lives. Recent analyses have suggested that the dimensionless ratios of several key life-history parameters are the same for different species, even across distant taxa. However, we show here that previous analyses may have given a false picture and created an illusion of invariants, which do not necessarily exist; essentially, this is because life-history variables have been regressed against themselves. The following question arises from our analysis: How do we identify an invariant?

Analysis of Variance↗

PubMed2005

Optimization of inclusive fitness.

The first fully explicit argument is given that broadly supports a widespread belief among whole-organism biologists that natural selection tends to lead to organisms acting as if maximizing their inclusive fitness. The use of optimization programs permits a clear statement of what this belief should be understood to mean, in contradistinction to the common mathematical presumption that it should be formalized as some kind of Lyapunov or even potential function. The argument reveals new details and uncovers latent assumptions. A very general genetic architecture is allowed, and there is arbitrary uncertainty. However, frequency dependence of fitnesses is not permitted. The logic of inclusive fitness immediately draws together various kinds of intra-genomic conflict, and the concept of 'p-family' is introduced. Inclusive fitness is thus incorporated into the formal Darwinism project, which aims to link the mathematics of motion (difference and differential equations) used to describe gene frequency trajectories with the mathematics of optimization used to describe purpose and design. Important questions remain to be answered in the fundamental theory of inclusive fitness.

Adaptation, Biological↗

PubMed2004

Testosterone in tropical birds: effects of environmental and social factors.

Previous investigations suggest that male tropical birds have lower plasma testosterone concentrations than northern latitude species. To test whether this generalization is valid, we analyzed all currently available plasma testosterone data of tropical birds. We focused on peak breeding testosterone levels using phylogenetic and conventional statistics. Explanatory variables considered were social mating system, type of territoriality, breeding season length, and altitude. On average, tropical birds had lower mean peak testosterone levels than northern temperate birds. However, in several tropical species, testosterone levels were well within the range of northern latitude birds. Without controlling for phylogeny, breeding season length, type of territoriality, and altitude explained a significant proportion of the variance in testosterone levels. The shorter the breeding season, the higher the testosterone levels. Tropical birds that defend a breeding season territory had higher testosterone levels than birds that were year-round territorial or colonial, and testosterone levels were positively correlated with altitude. When controlling for phylogeny, only breeding season length predicted testosterone levels. In conclusion, we propose to refine previous notions of low plasma testosterone levels in tropical birds: short breeding seasons and perhaps environmental conditions at high altitudes precipitate conditions under which high testosterone levels are beneficial in the tropics.

Animals↗

PubMed2004

Altruism via kin-selection strategies that rely on arbitrary tags with which they coevolve.

Hamilton's rule explains when natural selection will favor altruism between conspecifics, given their degree of relatedness. In practice, indicators of relatedness (such as scent) coevolve with strategies based on these indicators, a fact not included in previous theories of kin recognition. Using a combination of simulation modeling and mathematical extension of Hamilton's rule, we demonstrate how altruism can emerge and be sustained in a coevolutionary setting where relatedness depends on an individual's social environment and varies from one locus to another. The results support a very general expectation of widespread, and not necessarily weak, conditional altruism in nature.

Altruism↗

PubMed2002

A first formal link between the price equation and an optimization program.

The Darwin unification project is pursued. A meta-model encompassing an important class of population genetic models is formed by adding an abstract model of the number of successful gametes to the Price equation under uncertainty. A class of optimization programs are defined to represent the "individual-as-maximizing-agent analogy" in a general way. It is then shown that for each population genetic model there is a corresponding optimization program with which formal links can be established. These links provide a secure logical foundation for the commonplace biological principle that natural selection leads organisms to act as if maximizing their "fitness", provides a definition of "fitness", and clarifies the limitations of that principle. The situations covered do not include frequency dependence or social behaviour, but the approach is capable of extension.

Adaptation, Biological↗