Editing Signalling theory (section)

== Handicap principle ==

{{main|Handicap principle}}

[[File:Curlin in the Final Turn in the 2008 Stephen Foster Handicap (2972085393).jpg|thumb|upright=1.35|The best horses in a [[Handicap (horse racing)|handicap race]] carry the largest weights, so the size of the handicap is a measure of the animal's quality.]]

In 1975, [[Amotz Zahavi]] proposed a verbal model for how signal costs could constrain [[Cheating (biology)|cheating]] and stabilize an "honest" correlation between observed signals and unobservable qualities, based on an analogy to sports [[handicapping]] systems.{{sfn|Zahavi|1975}}{{sfn|Zahavi|1997}} He called this idea the [[handicap principle]]. The purpose of a sports handicapping system is to reduce disparities in performance, making the contest more competitive. In a [[Handicap (horse racing)|handicap race]], intrinsically faster horses are given heavier weights to carry under their saddles. Similarly, in [[Golf handicap|amateur golf]], better golfers have fewer strokes subtracted from their raw scores. This creates correlations between the handicap and unhandicapped performance, if the handicaps work as they are supposed to, between the handicap imposed and the corresponding horse's handicapped performance. If nothing was known about two race horses or two amateur golfers except their handicaps, an observer could infer who is most likely to win: the horse with the bigger weight handicap, and the golfer with the smaller stroke handicap. By analogy, if peacock 'tails' (large [[tail covert]] [[feather]]s) act as a handicapping system, and a peahen knew nothing about two peacocks except the sizes of their tails, she could "infer" that the peacock with the bigger tail has greater unobservable intrinsic quality. Display costs can include extrinsic social costs, in the form of testing and punishment by rivals, as well as intrinsic production costs.{{sfn|Searcy|Nowicki|2005}} Another example given in textbooks is the extinct Irish elk, ''[[Megaloceros giganteus]]''. The male Irish elk's enormous [[antler]]s could perhaps have evolved as displays of ability to overcome handicap, though biologists point out that if the handicap is inherited, its genes ought to be selected against.{{sfn|Feldhamer|2007|p=423}}

[[File:Flickr - lo.tangelini - Tonos (1).jpg|left|thumb|[[Peacock]] signals reproductive fitness with its large colourful tail, possibly because it is a [[handicap principle|handicap]].]]

The essential idea here is intuitive and probably qualifies as [[folk wisdom]]. It was articulated by [[Kurt Vonnegut]] in his 1961 short story ''[[Harrison Bergeron]]''.{{sfn|Vonnegut|1961}} In Vonnegut's futuristic [[dystopia]], the Handicapper General uses a variety of handicapping mechanisms to reduce inequalities in performance. A spectator at a ballet comments: "it was easy to see that she was the strongest and most graceful of all dancers, for her handicap bags were as big as those worn by two hundred pound men." Zahavi interpreted this analogy to mean that higher quality peacocks with bigger tails are signalling their ability to "waste" more of some resource by trading it off for a bigger tail. This resonates with [[Thorstein Veblen]]'s idea that [[conspicuous consumption]] and extravagant [[status symbol]]s can signal wealth.{{sfn|Veblen|1899}}

[[File:Irish Elk Side (white background).jpg|thumb|The enormous [[antler]]s of the extinct Irish elk, ''[[Megaloceros giganteus]]'' may have evolved as displays of ability to overcome handicap.]]
Zahavi's conclusions rest on his verbal interpretation of a metaphor, and initially the handicap principle was not well received by evolutionary biologists.{{sfn|Zahavi|1997}} However, in 1984, Nur and Hasson{{sfn|Nur|Hasson|1984}} used [[life history theory]] to show how differences in signalling costs, in the form of survival-reproduction tradeoffs, could stabilize a signalling system roughly as Zahavi imagined. Genetic models also suggested this was possible.{{sfn|McElreath|Boyd|2007}} In 1990 Alan Grafen showed that a handicap-like signalling system was evolutionarily stable if higher quality signallers paid lower marginal survival costs for their signals.{{sfn|Grafen|1990}}

In 1982, [[W. D. Hamilton]] proposed a specific but widely applicable handicap mechanism, [[parasite]]-mediated [[sexual selection]].{{sfn|Hamilton|Zuk|1982}} He argued that in the never-ending [[co-evolution]]ary race between hosts and their parasites, sexually selected signals indicate health. This idea was tested in 1994 in [[barn swallow]]s, a species where males have long tail streamers. Møller found that the males with longer tails, and their offspring, did have fewer bloodsucking mites, whereas fostered young did not. The effect was therefore genetic, confirming Hamilton's theory.{{sfn|Møller|1994}}

Another example is Lozano's hypothesis that [[carotenoids]] have dual but mutually incompatible roles in [[immune system|immune]] function and signalling. Given that animals cannot synthesize carotenoids ''de novo'', these must be obtained from food. The hypothesis states that animals with carotenoid-depended sexual signals are demonstrating their ability to "waste" carotenoids on sexual signals at the expense of their immune system.{{sfn|Lozano|1994}}{{sfn|McGraw|Ardia|2003}}

The handicap principle has proven hard to test empirically, partly because of inconsistent interpretations of Zahavi's metaphor and Grafen's marginal fitness model, and partly because of conflicting empirical results: in some studies individuals with bigger signals seem to pay higher costs, in other studies they seem to be paying lower costs.{{sfn|Kotiaho|2001}} A possible explanation for the inconsistent empirical results is given in a series of papers by Getty,{{sfn|Getty|1998a}}{{sfn|Getty|1998b}}{{sfn|Getty|2002}}{{sfn|Getty|2006}} who shows that Grafen's proof of the handicap principle is based on the critical simplifying assumption that signallers trade off costs for benefits in an additive fashion, the way humans invest money to increase income in the same currency.{{efn|Grafen's proof is formally similar to a classic monograph on economic market signalling by Nobel laureate [[Michael Spence]].{{sfn|Spence|1974}}}} But the assumption that costs and benefits trade off in an additive fashion is true only on a logarithmic scale;{{sfn|Tazzyman|Iwasa|Pomiankowski|2014}} for the survival cost – reproduction benefit tradeoff is assumed to mediate the evolution of sexually selected signals. Fitness depends on producing offspring, which is a multiplicative function of reproductive success given an individual is still alive times the probability of still being alive, given investment in signals.{{sfn|Nur|Hasson|1984}}

Later models have shown that the popularity of handicap principle relies on the critical misinterpretation of Grafen's model{{sfn|Grafen|1990}} by Grafen himself.<ref name=":0">{{Cite journal |last1=Penn |first1=Dustin J. |last2=Számadó |first2=Szabolcs |date=February 2020 |title=The Handicap Principle: how an erroneous hypothesis became a scientific principle |journal=Biological Reviews |language=en |volume=95 |issue=1 |pages=267–290 |doi=10.1111/brv.12563 |issn=1464-7931 |pmc=7004190 |pmid=31642592}}</ref> Contrary to his claims, his model is not a model of handicap signalling. Grafen's key equations show the necessity of marginal cost and differential marginal cost, nowhere in his paper was Grafen able to show the necessity of wasteful equilibrium cost (a.k.a. handicap). Grafen's model is a model of condition dependent signalling that builds on a traditional life-history trade-off between reproduction and survival. In general, later models have shown that the key condition of honest signalling is the existence of such condition-dependent trade-off and that the cost of signals can be anything at the equilibrium for honest individuals, including zero or even negative.<ref>{{Cite journal |last=Hurd |first=Peter L. |date=1995-05-21 |title=Communication in discrete action-response games |url=https://www.sciencedirect.com/science/article/pii/S0022519385700938 |journal=Journal of Theoretical Biology |language=en |volume=174 |issue=2 |pages=217–222 |doi=10.1006/jtbi.1995.0093 |bibcode=1995JThBi.174..217H |issn=0022-5193|url-access=subscription }}</ref><ref>{{Cite journal |last=Számadó |first=Szabolcs |date=1999-06-21 |title=The Validity of the Handicap Principle in Discrete Action–Response Games |url=https://www.sciencedirect.com/science/article/pii/S0022519399909359 |journal=Journal of Theoretical Biology |language=en |volume=198 |issue=4 |pages=593–602 |doi=10.1006/jtbi.1999.0935 |pmid=10373357 |bibcode=1999JThBi.198..593S |issn=0022-5193|url-access=subscription }}</ref><ref>{{Cite journal |last=Getty |first=THOMAS |date=1998-07-01 |title=Reliable signalling need not be a handicap |url=https://www.sciencedirect.com/science/article/pii/S0003347298907485 |journal=Animal Behaviour |language=en |volume=56 |issue=1 |pages=253–255 |doi=10.1006/anbe.1998.0748 |pmid=9710484 |s2cid=34066689 |issn=0003-3472|url-access=subscription }}</ref><ref>{{Cite journal |last1=Lachmann |first1=Michael |last2=Számadó |first2=Szabolcs |last3=Bergstrom |first3=Carl T. |date=2001-11-06 |title=Cost and conflict in animal signals and human language |journal=Proceedings of the National Academy of Sciences |language=en |volume=98 |issue=23 |pages=13189–13194 |doi=10.1073/pnas.231216498 |issn=0027-8424 |pmc=60846 |pmid=11687618|bibcode=2001PNAS...9813189L |doi-access=free }}</ref><ref>{{Cite journal |last1=Johnstone |first1=R. A. |last2=Dall |first2=S. R. X. |last3=Bergstrom |first3=Carl T. |last4=Számadó |first4=Szabolcs |last5=Lachmann |first5=Michael |date=2002-11-29 |title=Separating equilibria in continuous signalling games |journal=Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences |volume=357 |issue=1427 |pages=1595–1606 |doi=10.1098/rstb.2002.1068 |pmc=1693066 |pmid=12495516}}</ref><ref name=Szamado>{{Cite journal |last1=Számadó |first1=Szabolcs |last2=Czégel |first2=Dániel |last3=Zachar |first3=István |date=2019-01-11 |title=One problem, too many solutions: How costly is honest signalling of need? |journal=PLOS ONE |language=en |volume=14 |issue=1 |pages=e0208443 |doi=10.1371/journal.pone.0208443|biorxiv=10.1101/240440 |issn=1932-6203 |pmc=6329501 |pmid=30633748|bibcode=2019PLoSO..1408443S |doi-access=free }}</ref><ref name=":1">{{Cite journal |last1=Számadó |first1=Szabolcs |last2=Zachar |first2=István |last3=Czégel |first3=Dániel |last4=Penn |first4=Dustin J. |date=2023-01-08 |title=Honesty in signalling games is maintained by trade-offs rather than costs |journal=BMC Biology |volume=21 |issue=1 |pages=4 |doi=10.1186/s12915-022-01496-9 |issn=1741-7007 |pmc=9827650 |pmid=36617556 |doi-access=free }}</ref> The reason is that deception is prevented by the potential cost of cheating and not by the cost paid by the honest individuals.  This potential cost of cheating (marginal cost) has to be larger than the potential (marginal) benefits for potential cheaters.  In turn this implies that the honest peacock or deer need not be wasteful, it will be efficient. It is the potential cheater that needs to be less efficient.<ref name=":0" /><ref name=":1" /> Signal selection is not a selection for waste, as claimed by Zahavi, it is guided by the same mechanism - natural selection - as any other trait in nature.