Discrete conventional signalling of a continuous variable

Abstract
In aggressive interactions, animals often use a discrete set of signals, while the properties being signalled are likely to be continuous, for example fighting ability or value of victory. Here we investigate a particular model of fighting which allows for conventional signalling of subjective resource value to occur. The result shows that neither perfect nor no signalling are evolutionarily stable strategies (ESSs) in the model. Instead, we find ESSs in which partial information is communicated, with discrete displays signalling a range of values rather than a precise one. The result also indicates that communication should be more precise in conflicts over small resources. Signalling strategies can exist in fighting because of the common interest in avoiding injuries, but communication is likely to be limited because of the fundamental conflict over the resource. Our results reflect a compromise between these two factors. Data allowing for a thorough test of the model are lacking; however, existing data seem consistent with the obtained theoretical results
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