Coping with Danger and Deception: Lessons from Signal Detection Theory.

AbstractSignal detection theory (SDT) has been used to model optimal stimulus discrimination for more than four decades in 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 an 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.

Reciprocal mimicry: kin selection can drive defended prey to resemble their Batesian mimics.

Established mimicry theory predicts that Batesian mimics are selected to resemble their defended models, while models are selected to become dissimilar from their mimics. However, this theory has mainly considered individual selection acting on solitary organisms such as adult butterflies. Although Batesian mimicry of social insects is common, the few existing applications of kin selection theory to mimicry have emphasized relatedness among mimics rather than among models. Here, we present a signal detection model of Batesian mimicry in which the population of defended model prey is kin structured. Our analysis shows for most of parameter space that increased average dissimilarity from mimics has a twofold group-level cost for the model prey: it attracts more predators and these adopt more aggressive attack strategies. When mimetic resemblance and local relatedness are sufficiently high, such costs acting in the local neighbourhood may outweigh the individual benefits of dissimilarity, causing kin selection to drive the models to resemble their mimics. This requires model prey to be more common than mimics and/or well-defended, the conditions under which Batesian mimicry is thought most successful. Local relatedness makes defended prey easier targets for Batesian mimicry and is likely to stabilize the mimetic relationship over time.

Disentangling taste and toxicity in aposematic prey.

Many predators quickly learn to avoid attacking aposematic prey. If the prey vary in toxicity, the predators may alternatively learn to capture and taste-sample prey carefully before ingesting or rejecting them (go-slow behaviour). An increase in prey toxicity is generally thought to decrease predation on prey populations. However, while prey with a higher toxin load are more harmful to ingest, they may also be easier to recognize and reject owing to greater distastefulness, which can facilitate a taste-sampling foraging strategy. Here, the classic diet model is used to study the separate effects of taste and toxicity on predator preferences. The taste-sampling process is modelled using signal detection theory. The model is applicable to automimicry and batesian mimicry. It shows that when the defensive toxin is sufficiently distasteful, a mimicry complex may be less profitable to the predator and better protected against predation if the models are moderately toxic than if they are highly toxic. Moreover, taste mimicry can reduce the profitability of the mimicry complex and increase protection against predation. The results are discussed in relation to the selection pressures acting on prey defences and the evolution of mimicry.

Aposematism and the handicap principle.

Aposematic prey use conspicuous warning signals to advertise their defenses to predators. It has long been recognized that the efficiency of a warning signal may be reduced if poorly defended prey (automimics) are present in the population. The handicap principle suggests that the use of warning signals by poorly defended prey may be kept in check if signaling is costly. Three mechanisms that involve signal costs have been proposed to facilitate honest warning signals in prey: go-slow behavior in predators, resource allocation trade-offs, and costs of detection alone. We study all three in a unified game-theoretical framework. We find that the go-slow mechanism and the resource allocation mechanism can introduce differential benefits and differential costs of signaling, respectively, and can support honest signaling in accordance with the handicap principle. When honest signaling is maintained by the go-slow mechanism, conspicuous prey will necessarily suffer more attacks on average than cryptic prey. In contrast, when honest signaling is maintained by the resource allocation mechanism, cryptic prey will suffer more attacks. The detection cost mechanism lacks differential costs and benefits, and its potential for maintaining honest signaling equilibria is limited. We relate our results to intra- and interspecific correlations between conspicuousness and defense.

Inducible defenses: continuous reaction norms or threshold traits?

Phenotypically plastic traits can be expressed as continuous reaction norms or as threshold traits, but little is known about the selective conditions that favor one over the other. We study this question using a model of prey defenses in which prey can induce any level of defense conditional on cues that are informative of local predator density. The model incorporates a trade-off between defense expression and fecundity and feedback between the defense level of prey and predator attack rates. Both continuous reaction norms and threshold traits can emerge as evolutionarily stable solutions of defense induction, and we show that the shape of the trade-off curve plays a key role in determining the outcome. Threshold traits are favored when selection is disruptive. Ecological conditions that favor defense dimorphisms in the absence of cues will favor threshold traits in the presence of slightly informative cues. We caution that continuous reaction norms and threshold traits may result in similar patterns of defense expression at the population level, and we discuss potential pitfalls of inferring reaction norm type from observational data.

The evolutionary stability of automimicry.

Internal defences such as toxins cannot be detected from a distance by a predator, and are likely to be costly to produce and maintain. Populations of well-defended prey may therefore be vulnerable to invasion from rare 'cheater' mutants that do not produce the toxin themselves but obtain some protection from their resemblance to their better defended conspecifics (automimicry). Although it is well established that well-defended and weakly defended morphs may coexist stably in protected dimorphisms, recent theoretical work suggests that such dimorphisms would not be resistant to invasion by novel mutants with defence levels intermediate to those present. Given that most defences (including toxins) are likely to be continuous traits, this implies that automimicry may tend to be a transitory phenomenon, and thus less likely to explain variation in defence levels in nature. In contrast to this, we show that automimicry can also be evolutionarily stable for continuous traits, and that it may evolve under a wide range of conditions. A recently developed geometric method allows us to determine directly from a trade-off curve whether an evolutionarily stable defence dimorphism is at all possible, and to make some qualitative inferences about the ecological conditions that may favour it.

Context-dependent discrimination and the evolution of mimicry.

Many mimetic organisms have evolved a close resemblance to their models, making it difficult to discriminate between them on the basis of appearance alone. However, if mimics and models differ slightly in their activity patterns, behavior, or use of microhabitats, the exact circumstances under which a signaler is encountered may provide additional clues to its identity. We employ an optimality model of mimetic discrimination in which signal receivers obtain information about the relative risk of encountering mimics and models by observing an external background cue and flexibly adjust their response thresholds. Although such flexibility on the part of signal receivers has been predicted by theory and is supported by empirical evidence in a range of biological settings, little is known about the effects it has on signalers. We show that the presence of external cues that partly reveal signaler identity may benefit models and harm mimics, harm both, or even benefit both, depending on ecological circumstances. Moreover, if mimetic traits are costly to express, or mimics are related to their neighbors, context-dependent discrimination can dramatically alter the outcome of mimetic evolution. We discuss context-dependent discrimination among signal receivers in relation to small-scale synchrony in model and mimic activity patterns.

The evolution of mimicry under constraints.

The resemblance between mimetic organisms and their models varies from near perfect to very crude. One possible explanation, which has received surprisingly little attention, is that evolution can improve mimicry only at some cost to the mimetic organism. In this article, an evolutionary game theory model of mimicry is presented that incorporates such constraints. The model generates novel and testable predictions. First, Batesian mimics that are very common and/or mimic very weakly defended models should evolve either inaccurate mimicry (by stabilizing selection) or mimetic polymorphism. Second, Batesian mimics that are very common and/or mimic very weakly defended models are more likely to evolve mimetic polymorphism if they encounter predators at high rates and/or are bad at evading predator attacks. The model also examines how cognitive constraints acting on signal receivers may help determine evolutionarily stable levels of mimicry. Surprisingly, improved discrimination abilities among signal receivers may sometimes select for less accurate mimicry.

Avian brood parasitism: information use and variation in egg-rejection behavior.

Hosts of avian brood parasites often vary in their response to parasitized clutches: they may eject one or several eggs, desert the nest, or accept all the eggs. Focusing on hosts exposed to single-egg parasitism by an evicting brood parasite, we construct an optimality model that includes all these behavioral options and use it to explore variation in rejection behavior. We particularly consider the influence of egg mimicry and external cues (observations of adult parasites near the nest) on optimal choice of rejection behavior. We find that several rejection responses will be present in a host population under a wide range of conditions. Ejection of multiple eggs tends to be adaptive when egg mimicry is fairly accurate, external cues provide reliable information of the risk of parasitism, and the expected success of renesting is low. If the perceived risk of parasitism is high, ejection of one or a few eggs may be the optimal rejection response even in cases in which hosts cannot discriminate between eggs. This may have consequences for the long-term outcome of the coevolutionary chase between hosts and parasites. We propose an alternative evolutionary pathway by which egg ejection may first arise as a defense against brood parasitism.