Editing Handicap principle (section)

=== Grafen's signaling game model ===

{{further|Signaling game}}

[[File:Handicap-signal-of-quality.png|thumb|upright=1.5|Graph based on Johnstone's 1997 graphical representation of a Zahavian handicap. Where <math>C_L</math> is cost to a low-quality signaller and <math>C_H</math> is cost to a high-quality signaller. Optimal signalling levels are <math>S^*_L</math> for a low-quality signaller, and <math>S^*_H</math> for a high-quality signaller.<ref name="Johnstone97"/>|alt=Graph showing mathematically how a handicap would in theory work]]

The handicap principle was initially controversial,<ref name="Davis 1976">{{cite journal |last1=Davis |first1=J. W. F. |last2=O'Donald |first2=P. |year=1976 |title=Sexual selection for a handicap: A critical analysis of Zahavi's model |journal=Journal of Theoretical Biology |volume=57 |issue=2 |pages=345–354 |doi=10.1016/0022-5193(76)90006-0 |pmid=957664 |bibcode=1976JThBi..57..345D }}</ref><ref name="Eshel 1978">{{cite journal |last=Eshel |first=I. |year=1978 |title=On the Handicap Principle—A Critical Defence |journal=Journal of Theoretical Biology |volume=70 |issue=2 |pages=245–250 |doi=10.1016/0022-5193(78)90350-8 |pmid=633919 |bibcode=1978JThBi..70..245E }}</ref><ref name="Kirkpatrick 1986">{{cite journal |last=Kirkpatrick |first=M. |year=1986 |title=The handicap mechanism of sexual selection does not work |journal=[[American Naturalist]] |volume=127 |issue=2 |pages=222–240 |doi=10.1086/284480|jstor=2461351 |s2cid=83984463 }}</ref><ref name="Pomiankowski 1987">{{cite journal |last=Pomiankowski |first=A. |year=1987 |title=Sexual selection: The handicap principle does work sometimes |journal=[[Proceedings of the Royal Society B]] |volume=231 |issue=1262 |pages=123–145 |doi=10.1098/rspb.1987.0038 |bibcode=1987RSPSB.231..123P |s2cid=144837163 }}</ref> with the British biologist [[John Maynard Smith]] a notable early critic of Zahavi's ideas.<ref name="Maynard Smith 1976">{{cite journal |last=Maynard Smith |first=John |author-link=John Maynard Smith |year=1976 |title=Sexual selection and the handicap principle |journal=Journal of Theoretical Biology |volume=57 |issue=1 |pages=239–242 |doi=10.1016/S0022-5193(76)80016-1 |pmid=957656 |bibcode=1976JThBi..57..239S }}</ref><ref>{{cite journal |last=Maynard Smith |first=John |author-link=John Maynard Smith |year=1978 |title=The Handicap Principle—A Comment |journal=Journal of Theoretical Biology |volume=70 |issue=2 |pages=251–252 |doi=10.1016/0022-5193(78)90351-X |pmid=633920 |bibcode=1978JThBi..70..251S }}</ref><ref>{{cite journal |last=Maynard Smith |first=John |author-link=John Maynard Smith |year=1985 |title=Mini Review: Sexual Selection, Handicaps and True Fitness |journal=Journal of Theoretical Biology |volume=115 |issue=1 |pages=1–8 |doi=10.1016/S0022-5193(85)80003-5 |pmid=4033159 }}</ref> However, the handicap principle gained wider acceptance because it is supported by [[game theory]] models, most notably the Scottish biologist [[Alan Grafen]]'s 1990 [[signalling game]] model.<ref name="Grafen 1990">{{cite journal |last=Grafen |first=A. |year=1990 |title=Biological signals as handicaps |journal=Journal of Theoretical Biology |volume=144 |issue=4 |pages=517–546 |doi=10.1016/S0022-5193(05)80088-8 |pmid=2402153|bibcode=1990JThBi.144..517G }}</ref> This was essentially a rediscovery of the Canadian-American economist [[Michael Spence]]'s [[Signaling (economics)|job market signalling model]],<ref>{{cite journal |last=Spence |first=A. M. |year=1973 |title=Job Market Signaling |journal=[[Quarterly Journal of Economics]] |volume=87 |issue=3 |pages=355–374 |doi=10.2307/1882010 |jstor=1882010 }}</ref> where the job applicant signals their quality by declaring a costly education. In Grafen's model, the courting male's quality is signalled by investment in an extravagant trait—similar to the [[peacock]]'s tail. The signal is reliable if the cost to the signaller of producing it is proportionately lower for higher-quality signallers than for lower-quality ones.<ref name="Grafen 1990"/>

A series of papers by the American biologist Thomas Getty showed that Grafen's proof of the handicap principle depends on the critical, simplifying assumption that signallers trade off costs for benefits in an additive fashion, analogous to the way humans invest money to increase income in the same currency.<ref>{{cite journal |last=Getty |first=T. |year=1998a |title=Handicap signalling: when fecundity and viability do not add up |journal=[[Animal Behaviour (journal)|Animal Behaviour]] |volume=56 |issue=1 |pages=127–130 |doi=10.1006/anbe.1998.0744 |pmid=9710469|s2cid=36731320 }}</ref><ref>{{cite journal |last=Getty |first=T. |year=1998b |title=Reliable signalling need not be a handicap |journal=Anim. Behav. |volume=56 |issue=1 |pages=253–255 |doi=10.1006/anbe.1998.0748 |pmid=9710484 |s2cid=34066689 }}</ref><ref>{{cite journal |last=Getty |first=Thomas |year=2002 |title=Signaling health versus parasites |journal=[[American Naturalist]] |volume=159 |issue=4 |pages=363–371 |doi=10.1086/338992 |jstor=338992 |pmid=18707421 |s2cid=12598696 }}</ref><ref name="Getty 2006">{{cite journal |last=Getty |first=T. |year=2006 |title=Sexually selected signals are not similar to sports handicaps |journal=[[Trends in Ecology & Evolution]] |volume=21 |issue=2 |pages=83–88 |doi=10.1016/j.tree.2005.10.016 |pmid=16701479 }}</ref> This is illustrated in the figures from Johnstone 1997, which show that the optimum signalling levels are different for low- and high-quality signallers.<ref name="Johnstone97"/> The validity of the assumption that costs and benefits are additive has been contested, in its application to the evolution of [[signalling theory|sexually selected signals]]. It can be reasoned that since fitness depends on the production of offspring, this is a multiplicative rather than additive function of reproductive success.<ref>{{cite journal |last1=Nur |first1=N. |last2=Hasson |first2=O. |year=1984 |title=Phenotypic plasticity and the handicap principle |journal=J. Theor. Biol. |volume=110 |issue=2 |pages=275–297 |doi=10.1016/S0022-5193(84)80059-4 |bibcode=1984JThBi.110..275N }}</ref>

Further game theoretical models demonstrated the [[Evolutionarily stable strategy|evolutionary stability]] of handicapped signals in nestlings' begging calls,<ref name="Godfray 1991">{{cite journal |last=Godfray |first=H. C. J. |year=1991 |title=Signalling of need by offspring to their parents |journal=[[Nature (journal)|Nature]] |volume=352 |issue=6333 |pages=328–330 |doi=10.1038/352328a0 |bibcode=1991Natur.352..328G |s2cid=4288527 }}</ref> in predator-deterrent signals<ref>{{cite journal |last=Yachi |first=S. |year=1995 |title=How can honest signalling evolve? The role of the handicap principle |journal=[[Proceedings of the Royal Society B]] |volume=262 |issue=1365 |pages=283–288 |doi=10.1098/rspb.1995.0207 |s2cid=85339637 }}</ref> and in threat-displays.<ref>{{cite journal |last1=Adams |first1=E. S. |last2=Mesterton-Gibbons |first2=M. |year=1995 |title=The cost of threat displays and the stability of deceptive communication |journal=Journal of Theoretical Biology |volume=175 |issue=4 |pages=405–421 |doi=10.1006/jtbi.1995.0151 |bibcode=1995JThBi.175..405A |doi-access=free }}</ref><ref>{{cite journal |last=Kim |first=Y-G. |year=1995 |title=Status signalling games in animal contests |journal=Journal of Theoretical Biology |volume=176 |issue=2 |pages=221–231 |doi=10.1006/jtbi.1995.0193 |pmid=7475112 |bibcode=1995JThBi.176..221K }}</ref> In the classic handicap models of begging in game theory, all players are assumed to pay the same amount to produce a signal of a given level of intensity, but differ in the relative value of eliciting the desired response (donation) from the receiver. The hungrier the baby bird, the more food is of value to it, and the higher the optimal signalling level (the louder its chirping).<ref name="Godfray 1991"/>