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Fig. 4 | BMC Biology

Fig. 4

From: Honesty in signalling games is maintained by trade-offs rather than costs

Fig. 4

The effect of different trade-off functions on the fitness of the signaller in case of Godfray’s additive model of parent-offspring conflict [15]. a The signaller’s benefit function B (without trade-off; dependent on its quality q and the received amount of resource z) defines its optimum strategy for any q (dark green curve; optimum curves are also projected onto the q − z baseplane for all surfaces). b The receiver’s fitness function wR defines its optimum strategy for any signaller quality and resource shared (yellow curve). c At the honest equilibrium, the trade-off function T ensures that the signaller’s optimum coincides with the receiver’s optimum (for the derivation of the terms of T, see Fig. 3). d An arbitrary set of equilibrium signal trade-off functions D(q) is selected (green curves) from left to right: \(\left\{{D}_1(q)=0,{D}_2(q)=B\left(q,\hat{z}\right),{D}_3(q)=-B\left(q,\hat{z}\right),{D}_4(q)=\sin (3q)/2\right\}\), where \(\hat{z}\) is the optimum transfer of the receiver for the given quality q. e For any Di(q), a trade-off function Ti is generated (red surfaces), describing the cost value of signals in and out of equilibrium. f The trade-off function T transforms the benefit function B of the signaller to the fitness function wS (blue surfaces) such that its optimum strategy coincides with the receiver’s optimum strategy (yellow surfaces replicate the receiver’s fitness wR as of panel b; note different scaling). Projected optima of wS and wR entirely overlap at the q − z baseplane. Parameters are {ψ = 1/2, γ = 1/2, G = 0.08, U = 1, Z = 10, ε = 1}, for details, see Appendix 2 and 4

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