### Abstract

The “cost of begging” is a prominent prediction of costly signalling theory, suggesting that offspring begging has to be costly in order to be honest. Seminal signalling models predict that there is a unique equilibrium cost function for the offspring that results in honest signalling and this cost function must be proportional to parent’s fitness loss. This prediction is only valid if signal cost and offspring condition is assumed to be independent. Here we generalize these models by allowing signal cost to depend on offspring condition. We demonstrate in the generalized model that any signal cost proportional to the fitness gain of the offspring also results in honest signalling. Moreover, we show that any linear combination of the two cost functions (one proportional to parent’s fitness loss, as in previous models, the other to offspring’s fitness gain) also leads to honest signalling in equilibrium, yielding infinitely many solutions. Furthermore, we demonstrate that there exist linear combinations such that the equilibrium cost of signals is negative and the signal is honest. Our results show that costly signalling theory cannot predict a unique equilibrium cost in signalling games of parent-offspring conflicts if signal cost depends on offspring condition. It follows, contrary to previous claims, that the existence of parent-offspring conflict does not imply costly equilibrium signals. As an important consequence, it is meaningless to measure the “cost of begging” as long as the dependence of signal cost on offspring condition is unknown. Any measured equilibrium cost in case of condition-dependent signal cost has to be compared both to the parent’s fitness loss and to the offspring’s fitness gain in order to provide meaningful interpretation.

Original language | English |
---|---|

Article number | e0208443 |

Journal | PLoS One |

Volume | 14 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### ASJC Scopus subject areas

- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)

### Cite this

*PLoS One*,

*14*(1), [e0208443]. https://doi.org/10.1371/journal.pone.0208443

**One problem, too many solutions : How costly is honest signalling of need?** / Számadó, S.; Czégel, Dániel; Zachar, István.

Research output: Contribution to journal › Article

*PLoS One*, vol. 14, no. 1, e0208443. https://doi.org/10.1371/journal.pone.0208443

}

TY - JOUR

T1 - One problem, too many solutions

T2 - How costly is honest signalling of need?

AU - Számadó, S.

AU - Czégel, Dániel

AU - Zachar, István

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The “cost of begging” is a prominent prediction of costly signalling theory, suggesting that offspring begging has to be costly in order to be honest. Seminal signalling models predict that there is a unique equilibrium cost function for the offspring that results in honest signalling and this cost function must be proportional to parent’s fitness loss. This prediction is only valid if signal cost and offspring condition is assumed to be independent. Here we generalize these models by allowing signal cost to depend on offspring condition. We demonstrate in the generalized model that any signal cost proportional to the fitness gain of the offspring also results in honest signalling. Moreover, we show that any linear combination of the two cost functions (one proportional to parent’s fitness loss, as in previous models, the other to offspring’s fitness gain) also leads to honest signalling in equilibrium, yielding infinitely many solutions. Furthermore, we demonstrate that there exist linear combinations such that the equilibrium cost of signals is negative and the signal is honest. Our results show that costly signalling theory cannot predict a unique equilibrium cost in signalling games of parent-offspring conflicts if signal cost depends on offspring condition. It follows, contrary to previous claims, that the existence of parent-offspring conflict does not imply costly equilibrium signals. As an important consequence, it is meaningless to measure the “cost of begging” as long as the dependence of signal cost on offspring condition is unknown. Any measured equilibrium cost in case of condition-dependent signal cost has to be compared both to the parent’s fitness loss and to the offspring’s fitness gain in order to provide meaningful interpretation.

AB - The “cost of begging” is a prominent prediction of costly signalling theory, suggesting that offspring begging has to be costly in order to be honest. Seminal signalling models predict that there is a unique equilibrium cost function for the offspring that results in honest signalling and this cost function must be proportional to parent’s fitness loss. This prediction is only valid if signal cost and offspring condition is assumed to be independent. Here we generalize these models by allowing signal cost to depend on offspring condition. We demonstrate in the generalized model that any signal cost proportional to the fitness gain of the offspring also results in honest signalling. Moreover, we show that any linear combination of the two cost functions (one proportional to parent’s fitness loss, as in previous models, the other to offspring’s fitness gain) also leads to honest signalling in equilibrium, yielding infinitely many solutions. Furthermore, we demonstrate that there exist linear combinations such that the equilibrium cost of signals is negative and the signal is honest. Our results show that costly signalling theory cannot predict a unique equilibrium cost in signalling games of parent-offspring conflicts if signal cost depends on offspring condition. It follows, contrary to previous claims, that the existence of parent-offspring conflict does not imply costly equilibrium signals. As an important consequence, it is meaningless to measure the “cost of begging” as long as the dependence of signal cost on offspring condition is unknown. Any measured equilibrium cost in case of condition-dependent signal cost has to be compared both to the parent’s fitness loss and to the offspring’s fitness gain in order to provide meaningful interpretation.

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U2 - 10.1371/journal.pone.0208443

DO - 10.1371/journal.pone.0208443

M3 - Article

C2 - 30633748

AN - SCOPUS:85059856651

VL - 14

JO - PLoS One

JF - PLoS One

SN - 1932-6203

IS - 1

M1 - e0208443

ER -