Alan Grafen
Alan Grafen wrote the 1990 paper Biological signals as handicaps, which built a formal model of Amotz Zahavi's handicap principle and reported the conditions under which an honest signal is stable.
Who they are
Grafen is a theoretical biologist who published the model in the Journal of Theoretical Biology in 1990 (volume 144, issue 4, 517-546). His paper is the formal statement of the handicap principle that later literature on costly signalling cites.
Key papers
Grafen (1990), Biological signals as handicaps, Journal of Theoretical Biology, 144(4), 517-546.
Key ideas
The paper builds an evolutionarily stable strategy model in which signallers differ in quality. Its abstract reports that a stable signalling equilibrium exists under fairly general conditions when the conditions of the handicap principle are met, and that every signalling equilibrium satisfies them.
Three conditions carry the result. Receivers correctly infer a signaller's quality from its level of advertising. Advertising lowers the signaller's fitness. The marginal cost of advertising is lower for the better signaller. If advertising were free, or cost good and poor signallers alike, it could not work as a handicap. The paper also discusses economic signalling models, cheating and the limitations of the model.
Penn and Számadó's 2020 review reads the same models differently, as support for a trade-off account proposed by Zahavi in 1977.
Sources
- Grafen, A. (1990). Biological signals as handicaps. Journal of Theoretical Biology, 144(4), 517-546. doi:10.1016/S0022-5193(05)80088-8 https://doi.org/10.1016/S0022-5193(05)80088-8
- Zahavi, A. (1975). Mate selection: A selection for a handicap. Journal of Theoretical Biology, 53(1), 205-214. doi:10.1016/0022-5193(75)90111-3 https://doi.org/10.1016/0022-5193(75)90111-3
- Penn, D. J., & Számadó, S. (2020). The Handicap Principle: how an erroneous hypothesis became a scientific principle. Biological Reviews, 95(1), 267-290. doi:10.1111/brv.12563 https://doi.org/10.1111/brv.12563