American Society of Naturalists

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“Coping with danger and deception: lessons from signal detection theory”

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Øistein Haugsten Holen and Thomas N. Sherratt (Feb 2021)

Many signal detection models of repeated encounters share fundamental similarities and counterintuitive predictions

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Coping with danger and deception: lessons from signal detection theory

The Eurasian Bee Beetle, <i>Trichius fasciatus</i>, a Batesian mimic of bumble bees. <br />(Photo © Øistein Haugsten Holen)
The Eurasian Bee Beetle, Trichius fasciatus, a Batesian mimic of bumble bees.
(Photo © Øistein Haugsten Holen)

Evolutionary ecologists often use signal detection theory to model how animals discriminate between desirable and undesirable events or items. The standard model has the limitation that it assumes that signal receivers behave so as to maximize payoff for a single encounter, and that undesirability is a fixed, absolute property of the items themselves. The standard model therefore cannot represent many common ecological scenarios in which the signal receivers benefit from rejecting low-quality items (e.g. mates, food items, resources) if high-quality alternatives are common but yet benefit from accepting them if high-quality alternatives are rare (in this case making the best of a bad situation).

In this study, Øistein Holen (researcher at the University of Oslo, Norway) and Tom Sherratt (professor at Carleton University, Canada) have reviewed and reanalyzed a number of previously published signal detection models that were originally constructed to study prey choice, mimicry, mate search, and the aiding of kin. These signal detection models feature repeated encounters and have earlier been studied on a case-by-case basis. Holen and Sherratt show that they have a common mathematical form that allow them to be analyzed in a unified framework.

This repeated-encounter framework provides a convenient and versatile alternative to the standard signal detection model: It is flexible enough to allow the undesirability of an item (e.g. a low-quality mate or food item) to be relative and dependent on the availability of better alternatives. In such cases, the repeated-encounter framework makes different predictions than the standard model. For example, the standard signal detection model has frequently been used to model Batesian mimicry, in which harmless prey gain protection from predators by resembling undesirable model prey. The authors show that if model prey are protected by low profitability rather than by harmful defense, counter-intuitive forms of Batesian mimicry may exist in which the predator is less likely to attack model prey upon encounter if the Batesian mimics are more abundant or more profitable. Two recent signal detection models of the building up of reserves under predation risk found that prey should sometimes respond to an increased probability of danger by being bolder and more willing to risk predation. Holen and Sherratt show that similar counter-intuitive predictions are common in the repeated-encounter models they review: If undesirable events are undesirable in a relative rather than an absolute sense, an increased probability of events being undesirable may lead to increased acceptance rates. Holen and Sherratt also identify ecological conditions under which the standard signal detection model remains a reasonable model of stimulus discrimination.


Abstract

Signal detection theory (SDT) has been used to model optimal stimulus discrimination for over four decades within evolutionary ecology. A popular standard model that maximizes payoff per encounter was recently criticized for being too simplistic, leading to erroneous predictions. We review a number of SDT models that have received less attention but have explicitly taken repeated encounters into account, focusing on prey choice, mate search, aggressive mimicry, and the aiding of kin. We show how these models can be seen as variants of a second standard model that can be analyzed in a unified framework. In contrast to the simpler model, in this second model a higher probability of an undesirable or dangerous event occurring may either decrease or increase the receiver's acceptance rates. In each instance, the latter outcome requires undesirable events to be undesirable in a relative rather than absolute sense. Increasing the abundance of desirable signalers or the payoff from accepting them may also either raise or reduce acceptance rates. Our synthesis highlights fundamental similarities among models previously studied on a case-by-case basis, and challenges some long-held beliefs. For example, some classic predictions of Batesian mimicry can be reversed when model prey are protected by low profitability rather than harmful defense.