Biomedical subjects
A Grafen
Publications and source records attributed to A Grafen.
Error-prone signalling.
The handicap principle of Zahavi is potentially of great importance to the study of biological communication. Existing models of the handicap principle, however, make the unrealistic assumption that communication is error free. It seems possible, therefore, that Zahavi's arguments do not apply to real signalling systems, in which some degree of error is inevitable. Here, we present a general evolutionarily stable strategy (ESS) model of the handicap principle which incorporates perceptual error. We show that, for a wide range of error functions, error-prone signalling systems must be honest at equilibrium. Perceptual error is thus unlikely to threaten the validity of the handicap principle. Our model represents a step towards greater realism, and also opens up new possibilities for biological signalling theory. Concurrent displays, direct perception of quality, and the evolution of 'amplifiers' and 'attenuators' are all probable features of real signalling systems, yet handicap models based on the assumption of error-free communication cannot accommodate these possibilities.
The continuous Sir Philip Sidney game: a simple model of biological signalling.
An analysis of Maynard Smith's two-player, ESS model of biological signalling, the "Sir Philip Sidney game", is presented. The stable strategies of the players in this game are shown to satisfy the conditions of Zahavi's handicap principle. At equilibrium, signals are honest, costly, and costly in a way that is related to the true quality revealed. Further analysis reveals that the level of cost required to maintain stability is inversely related to the degree of relatedness between the players. It therefore seems likely that stable biological signalling systems will feature lower signalling costs when communication occurs between relatives. A three-player, extended version of the model is investigated, in which signals are passed via an intermediate, or "messenger". It is shown that this destabilizes the signalling system, and leads to increased signalling costs. This result suggests that "kin conflict" theories of the evolution of the endosperm in flowering plants require further refinement. The introduction of a novel resource acquisition tissue, which mediates parent-offspring interaction during development, cannot be assumed to limit parent-offspring conflict simply because it carries an extra copy of the maternally inherited genes. The ability to add such complications to the Sir Philip Sidney game and still obtain solutions makes it a very useful modelling tool.
Genetic scrambling as a defence against meiotic drive.
Genetic recombination has important consequences, including the familiar rules of Mendelian genetics. Here we present a new argument for the evolutionary function of recombination based on the hypothesis that meiotic drive systems continually arise to threaten the fairness of meiosis. These drive systems act at the expense of the fitness of the organism as a whole for the benefit of the genes involved. We show that genes increasing crossing over are favoured, in the process of breaking up drive systems and reducing the fitness loss to organisms.
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 Zahavi's 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.
Biological signals as handicaps.
An ESS model of Zahavi's 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 principle's 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. Zahavi's 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.
A centrosomal theory of the short term evolutionary maintenance of sexual reproduction.
A new mode of inheritance is postulated in which a sexual offspring receives a contribution from each parent and selects the better to pass on to its own offspring. This could provide a simple advantage to sex over a sex whose magnitude is shown to be of the order of a doubling of fitness in each generation, large enough to cancel the twofold cost of sex. This possible advantage to sex can be realized only if a cell component is in fact inherited in this selectively ambiguous way. No such component is known of, but the eukaryotic centrosome is a possible candidate. The possibility is discussed that the centrosome contains an obligatorily non-digital replicator which has an essential function in the initiation of microtubules. If this theory is true, it has the capacity to apply as widely as sex is found, and it would rescue theories of the long-term maintenance of sex from the necessity to provide a twofold advantage in each generation. If false, the theory will soon be disproved.
Evolutionarily stable nesting strategy in a digger wasp.
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