Alan Grafen

Biological signals as handicaps.

An ESS model of Zahavis handicap principle is constructed. This allows a formal exposition of how the handicap principle works, and shows that its essential elements are strategic. The handicap model is about signalling, and it is proved under fairly general conditions that if the handicap principles conditions are met, then an evolutionarily stable signalling equilibrium exists in a biological signalling system, and that any signalling equilibrium satisfies the conditions of the handicap principle. Zahavis major claims for the handicap principle are thus vindicated. The place of cheating is discussed in view of the honesty that follows from the handicap principle. Parallel signalling models in economics are discussed. Interpretations of the handicap principle are compared. The models are not fully explicit about how females use information about male quality, and, less seriously, have no genetics. A companion paper remedies both defects in a model of the handicap principle at work in sexual selection.

Sexual selection unhandicapped by the Fisher process.

A population genetic model of sexual selection is constructed in which, at equilibrium, males signal their quality by developing costly ornaments, and females pay costs to use the ornaments in mate choice. It is shown that the form of the equilibrium is uninfluenced by the Fisher process, that is, by self-reinforcement of female preferences. This is a working model of the handicap principle applied to sexual selection, and places Zahavis handicap principle on the same logical footing as the Fisher process, in that each can support sexual selection without the presence of the other. A way of measuring the relative importance of the two processes is suggested that can be applied to both theories and facts. A style of modelling that allows simple genetics and complicated biology to be combined is recommended.

Do animals really recognize kin

Abstract Species recognition and group member recognition systems produce an ability to discriminate conspecifics by genetic similarity on first encounter when kin recognition is absent. Experimental evidence of such discrimination is therefore insufficient evidence for kin recognition. The evolution of a true kin recognition system depends on three kinds of loci: matching, detection and using. Matching loci, which affect the traits used to detect kin, will have a higher genetic similarity between interactants than their common ancestry alone suggests. Selection has been erroneously thought to cause individuals to behave according to the higher relatedness implied by this extra similarity. The detection loci and using loci are not expected to be closely linked to the matching loci, implying that individuals will behave according to the relatedness based on their common ancestry. Polymorphism at the matching loci is essential for effective discrimination of kin, and is sustained by the evolution of the kin recognition system in those cases where it is advantageous to interact with kin.

The logic of divisively asymmetric contests: respect for ownership and the desperado effect

It is current orthodoxy in biological game theory that in animal contests with easily recognized asymmetries between the contestants, an asymmetry will be used to settle the dispute. Here it is argued that, if the winning of contests plays a major part in gaining reproductive success, an individual will not be selected to respect an asymmetry which will place it always in the losing role. Asymmetries that create consistent losers of this sort are termed divisive asymmetries. Divisive asymmetries cannot be used to settle important contests in an evolutionarily stable way because the consistent losers will have no incentive to respect them.

Colony-level sex ratio selection in the eusocial Hymenoptera

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.

Capturing the superorganism: a formal theory of group adaptation

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.

BLOCKING FACTORS AND HYPOTHESIS TESTS IN ECOLOGY: IS YOUR STATISTICS TEXT WRONG?

We demonstrate that statistics textbooks differ in their prescription for the analysis of experiments that involve blocking factors. The differences in analysis may lead to differences in conclusions regarding the significance of experimental treatment effects. We outline the two approaches, discuss why they are different, and suggest when each approach may be applicable. We point out that simply following one’s textbook may not be the best course of action for any particular situation.

The hawk-dove game played between relatives

Abstract Maynard Smith (1978) has raised the problem of the hawk-dove game played between relatives. Here, the evolutionarily stable state of the population is found as a function of the average relatedness of a player to his opponents. Surprisingly, the continuous or ‘mixed’ strategy case and the discrete or ‘pure’ strategy case must be treated separately. It is claimed that previous published analyses of the evolutionarily stable state are invalid. The errors committed are discussed, and ascribed to the use of the concept of ‘fitness’, rather than the less confusing notion of gene frequency.

Evolutionarily stable nesting strategy in a digger wasp

Abstract Two alternative “strategies” will not coexist in a population unless on average they are equally successful. The most likely way for such an equilibrium to be maintained is through something equivalent to frequency-dependent selection. Females of the digger wasp Sphex ichneumoneus (Sphecidae) nest in underground burrows. They usually dig and provision these by themselves but occasionally a nest is jointly occupied. The two wasps fight whenever they meet and in the end only one of the two females lays an egg in the shared nest. Two models based on the theory of mixed evolutionarily stable strategies were developed and tested on comprehensive field data from two North American populations of these wasps. The first model proposes two strategies called founding and joining. Founders start burrows alone, but they are more successful when they are joined by a joiner. At equilibrium founders and joiners are equally successful, which amounts to an amicable, sharing relationship. The predictions of this amicable model are decisively rejected by the data. The second model proposes two strategies called digging and entering. Diggers dig their own burrows but they often have to abandon these burrows because of temporary unsuitability. Enterers move in later, thereby exploiting abandoned burrows as a valuable resource. They do not distinguish an adandoned burrow from one that is still occupied. Therefore sharing of burrows arises as an unfortunate by product of selection for entering abandoned burrows, and Model 2 is not an amicable model. Its quantitative predictions are impressively fulfilled in one population, though not in another population. This is one of the only examples yet known of a mixed evolutionarily stable strategy in nature. Yet the word strategy itself can confuse, and this paper tries the experiment of substituting “decision”, defined as a moment at which the animal commits future time to a course of action.

ALTRUISM VIA KIN-SELECTION STRATEGIES THAT RELY ON ARBITRARY TAGS WITH WHICH THEY COEVOLVE

Abstract Hamiltons 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 Hamiltons rule, we demonstrate how altruism can emerge and be sustained in a coevolutionary setting where relatedness depends on an individuals 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.