No abstract

A new statistical method called the phylogenetic regression is proposed that applies multiple regression techniques to cross-species data. It allows continuous and categorical variables to be tested for and controlled for. The new method is valid despite the problem that phylogenetically close species tend to be similar, and is designed to be used when information about the phylogeny is incomplete. Information about the phylogeny of the species is assumed to be available in the form of a working phylogeny, which contains multiple nodes representing ignorance about the order of splitting of taxa. The non-independence between species is divided into that due to recognized phylogeny, that is, to phylogenetic associations represented in the working phylogeny; and that due to unrecognized phylogeny. The new method uses one linear contrast for each higher node in the working phylogeny, thus applying the ‘radiation principle’. For binary phylogenies the method is similar to an existing method. A criterion is suggested in the form of a simulation test for deciding on the acceptability of proposed statistical methods for analysing cross-species data with a continuous y-variable. This criterion is applied to the phylogenetic regression and to some other methods. The phylogenetic regression passes this test; the other methods tested fail it. Arbitrary choices have to be made about the covariance structure of the error in order to implement the method. It is argued that error results from omitted but relevant variables, and the implications for those arbitrary choices are discussed. One conclusion is that the dates of splits between taxa, even supplemented by rates of neutral gene evolution, do not provide the ‘ true ’ covariance structure. A pragmatic approach is adopted. Several analytical results about the phylogenetic regression are given, without proof, in a mathematical appendix. A computer program has been written in GLIM to implement the phylogenetic regression, and readers are informed how to obtain a copy.

No abstract

No abstract

Adaptation is conventionally regarded as occurring at the level of the individual organism. However, in recent years there has been a revival of interest in the possibility for group adaptations and superorganisms. Here, we provide the first formal theory of group adaptation. In particular: (1) we clarify the distinction between group selection and group adaptation, framing the former in terms of gene frequency change and the latter in terms of optimization; (2) we capture the superorganism in the form of a 'group as maximizing agent' analogy that links an optimization program to a model of a group-structured population; (3) we demonstrate that between-group selection can lead to group adaptation, but only in rather special circumstances; (4) we provide formal support for the view that between-group selection is the best definition for 'group selection'; and (5) we reveal that mechanisms of conflict resolution such as policing cannot be regarded as group adaptations.

We present an inclusive fitness model on worker-controlled sex investments in eusocial Hymenoptera which expands the existing theory for random mating populations as formulated by Trivers and Hare (1976) and Benford (1978). We assume that relatedness asymmetry is variable among colonies -owing to multiple mating, worker reproduction and polygyny ~ and that workers are able to assess the relatedness asymmetry in their own colony. A simple marginal value argument shows that "assessing" workers maximize their inclusive fitness by specializing on the production of the sex to which they are relatively more related than the average worker in the population is related to that sex. The model confirms our earlier verbal argument on this matter (Boomsma and Grafen, 1990) and gives further quantitative predictions of the optimal sex ratio of relatedness-asymmetry classes for both infinite and finite, random mating populations.It is shown that in large populations all but one of the relatedness-asymmetry classes should specialize on the production of one sex only. The remaining, balancing class is selected to compensate any bias induced by the other class(es) such that the population sex ratio reflects the relatedness asymmetry of that balancing class. In the absence of worker-reproduction, the sex ratio compensation by the balancing-class is generally close to 100%, unless the population is very small.In the Discussion we address explicitly the likelihood of our relatedness-assessment hypothesis and other assumptions made in the model. The relationship of our model with previous theory on sex allocation in eusocial Hymenoptera is worked out in the Appendix.

No abstract

No abstract