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The evolution of Batesian mimicry is affected by model profitability and the availability of alternative
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prey.
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Running title: The evolution of Batesian mimicry.
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Key words: Imperfect Batesian mimicry, predator, selection, aposematism, colour patterns,
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computer games.
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Submission type: Article
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Submitted elements: Manuscript including eight figures and no tables, plus a supplementary file
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including two figures
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Abstract
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Palatable, undefended Batesian mimics gain protection from predation because of their close
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resemblance to defended and/or unpalatable models. The existence of inaccurate (“imperfect”)
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mimics is puzzling: why has selection by predators not favoured ever more perfect mimicry?
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Theoretical work predicts that selection for mimetic accuracy will be reduced if either a) the model
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species that the mimic resembles is particularly noxious or aversive, or b) there is an abundance of
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alternative prey. Using experiments in which humans foraged for computer-generated prey, we
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tested these predictions. As predicted, we found that increased abundance of alternative prey leads
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to reduced attacks on mimics, slowing down the evolution of mimicry, and that inaccurate mimics
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are better protected in the presence of more unprofitable models. However, in contrast to
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predictions, volunteers did not learn to avoid unprofitable models less well as the abundance of
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alternative prey increased, in spite of a decreased frequency of encounters. Also, the presence of
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particularly unprofitable models caused an unexpected initial acceleration in the evolution of
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mimicry. Nevertheless, the results broadly support the hypotheses that the evolution of Batesian
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mimicry is influenced by the presence of alternative prey, and by the costs to predators of attacking
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unprofitable prey.
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Introduction
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Palatable, undefended Batesian mimics, which gain protection from predation by close resemblance
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of noxious or aversive model species, provide a potent and intuitive example of the consequences of
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evolution by natural selection (Bates 1862; Ruxton et al. 2004). However, the existence of relatively
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inaccurate Batesian mimics, whose approximate resemblance to a putative model appears to be
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relatively ineffective in fooling predators, is an enduring puzzle in evolutionary biology (Cuthill 2014;
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Edmunds 2000; Gilbert 2005; Sherratt 2002). Many hypotheses have been proposed to explain such
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“imperfect” mimicry, and exploration of those hypotheses has provided insights into the
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fundamental processes which determine the evolution of phenotypes. Here, we test two of these
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hypotheses: 1) relatively imperfect mimics are likely to persist if the cost to the predator of
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mistakenly attacking a model is very high (Duncan and Sheppard 1965; Edmunds 2000; Sherratt
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2002), and 2) relatively imperfect mimics are protected if predators have ready access to abundant
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alternative palatable prey which bear no resemblance to the model (Carpenter and Ford 1933).
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Predator behaviour, and its consequences for the evolution of Batesian mimicry, can be modelled
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using the principles of signal detection theory (see Getty 1985; Greenwood 1986), and by making the
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assumption that predators will adopt a threshold level of similarity between a potential prey item
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and a model which is known to be noxious, beyond which attacks will not be made (Sherratt 2002).
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For optimally foraging predators, this threshold occurs when similarity to the model is sufficient that
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the risk of mistakenly attacking a model outweighs the potential benefits of consuming a palatable
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mimic. Modelling suggests that the similarity threshold adopted by predators will be influenced by
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their internal state (in particular, hunger) (Sherratt 2003) and by the costs associated with attacking
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the defended or unpalatable model species (Sherratt 2002). Specifically, it is predicted that hungry
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predators will be more willing to risk attacking prey which resemble a noxious model species
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relatively closely, because of the threat of starvation (Sherratt 2003). One factor determining hunger
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is the availability of alternative, easily-distinguished (and thus risk-free), palatable prey. When such
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prey are plentiful, hunger levels will be low, and the need to risk attacks on prey resembling an
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aversive model is reduced (Kokko et al. 2003). Hence, selection for mimetic accuracy in palatable
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Batesian mimics is predicted to be relaxed when alternative prey are readily available (Sherratt
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2003). Similarly, as the cost of mistakenly attacking a defended species increases (e.g. when models
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are more heavily defended), or the probability of paying the cost increases (e.g. when the relative
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abundance of models is high), the similarity threshold adopted by optimally foraging predators is
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expected to favour relatively less accurate mimics, and selection on mimetic accuracy will be relaxed
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(Sherratt 2002).
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There is clear empirical evidence that an increase in model abundance increases the protection
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afforded to its Batesian mimics (Brower 1960; Mostler 1935). Moreover, experiments with humans
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and birds have shown that an increase in model relative abundance reduces attacks on imperfect
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Batesian mimics (Lindstrom et al. 1997; McGuire et al. 2006). This effect appears to have
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evolutionary consequences: the phenotype of the scarlet king snake (Lampropeltis elapsoides) was
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shown to be more variable in a region of high model abundance than in a region where the model
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was relatively rare (Harper and Pfennig 2007). There is also evidence that the relative palatability or
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profitability of the model affects the survival of different mimetic phenotypes. It has been noted that
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highly defended wasp (Hymenoptera: Vespidae) models seem to support Batesian mimics
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(hoverflies) with a greater range of mimetic quality than bumblebees, which are considered less
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costly to attack (Gilbert 2005). Some experiments with birds (but not all - see Lindstrom et al. 1997)
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show that increasing the cost of attacking the model decreases the level of mimetic accuracy needed
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to gain protection from predation (Alcock 1970; Goodale and Sneddon 1977), although there is no
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direct evidence of the evolutionary consequences of this effect.
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Empirical studies support the idea that a predator’s hunger state influences the probability that it
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will attack a potentially costly prey item (Barnett et al. 2007; Gelperin 1968; Sandre et al. 2010).
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Similarly, predators have been shown to be more likely to attack defended prey when alternatives
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are harder to find (Carle and Rowe 2014). There is also evidence from experiments with captive birds
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that the presence of palatable alternative prey reduces the frequency of attacks on imperfect
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Batesian mimics, implying that when alternative prey are rare there may be increased selection for
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more accurate mimicry (Lindstrom et al. 2004).
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In summary then, there is reasonable empirical support for the assumptions made about predator
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behaviour by theoretical studies of the effect of model profitability and the abundance of alternative
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prey on the persistence of imperfect mimicry. By contrast, model predictions about the long-term
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effects of this behaviour for the evolution of Batesian mimicry remain largely untested. No study to
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date has considered how alternative prey affect selection on mimics with different levels of
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accuracy, or investigated the evolutionary consequences of such selection. Similarly, no study has
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examined empirically the dynamic evolutionary consequences for mimics of variation in the costs for
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the predator associated with attacking the model. The shortage of empirical evidence is in part be
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because experimental tests of hypotheses relating to evolutionary processes in real organisms are
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logistically difficult. Studies of mimicry typically give a “snap-shot” of selection pressures at one
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particular time, and discuss the possible evolutionary consequences. However, several studies have
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exploited computer games to measure the long-term effects of selection pressures generated by real
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predators (normally humans) on digital “prey” in an artificial environment (McGuire et al. 2006;
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Sherratt and Beatty 2003; Sherratt et al. 2004). Such studies have great potential to bridge the gap
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between modelling and experimentation.
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In the present study, we ran a series of experiments looking at the effects of human foraging
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behaviour on the survival (within-generation) and evolution (across generations) of computer-
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generated model and mimic “prey”. Our aim was to test the following specific theoretical
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predictions: 1) relatively inaccurate mimics will be attacked less often when their model is less
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profitable or more aversive from the predator’s perspective; 2) in such situations, selection for
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mimetic accuracy will be relaxed, and the evolution of increased accuracy will be slower, and will be
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balanced sooner by other evolutionary forces; 3) a predator is less likely to learn to avoid defended
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model phenotypes when alternative palatable prey are abundant; 4) relatively inaccurate mimics are
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better protected from predation when alternative prey are abundant; 5) mimetic accuracy evolves
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more slowly, and reaches a less accurate end-point, when alternative prey are abundant.
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Methods
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The computer game
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A computer game was written using action script in Adobe® Flash® CS4 Professional, and mounted
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on a website (www.predatorbehaviour.com). Running the game on-line allowed larger sample sizes
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of participants than would otherwise be possible, although it also meant that we could not control
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certain external influences (computer screen type, player motivation, distractions etc.). Players
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foraged for randomly-positioned digital prey (coloured squares, 13 x 13 mm on a 17 inch screen) on
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a white background. Prey were initially hidden beneath white squares of the same dimensions, with
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a narrow black border. Players uncovered hidden prey by clicking on a white square, and could then
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decide whether to attack the prey (click on it with their mouse) or not. They were encouraged to
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forage optimally by awarding points (equivalent to “fitness”) when prey were attacked. Mimics were
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always worth more than their models, in order to simulate the natural situation in which it benefits a
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predator to learn to avoid the signals of an unprofitable prey species. At the onset of each game,
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players were further motivated by a high scores table, displaying the twelve highest scores, and a
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message encouraging them to maximise their score.
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When prey were attacked, four events were triggered: 1) the prey disappeared from the screen; 2) a
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sound file played; 3) the points awarded for the attack appeared in a short-lived graphical “bubble”;
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and 4) the player’s score, which appeared at the bottom of the screen, was adjusted appropriately.
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Attacks on palatable mimics and alternative prey produced a high-pitched “boing” sound, whilst
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attacks on unprofitable models generated a succession of notes with reducing pitch. The sounds
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were included to make the game more engaging, and to reinforce the stimulus of the score awarded
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for that attack. If the player chose to ignore a particular prey item and continued foraging by clicking
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on another white square, the previously uncovered prey was covered by a grey square of the same
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dimensions and became permanently unavailable. Prey encounters were thus sequential rather than
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simultaneous, and each player only encountered a prey individual once, which we considered to
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reflect a natural foraging situation such as when birds hunt for insect prey.
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Players were able to use the colour of the prey to determine whether to attack them. Mimic
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phenotypes could be close enough to those of the models to be indistinguishable, or far enough
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away to be clearly different, allowing a full range of mimetic accuracies to be simulated. The
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phenotype of the prey was determined by two quantitative genetic loci (θ and φ) with values which
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corresponded to longitudinal (between –π and +π radians) and latitudinal (between –π/2 and +π/2
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radians) positions on a sphere in three-dimensional computer (RGB) colour space. A spherical
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phenotypic space was chosen to prevent the inhibition of evolutionary movement by fixed
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boundaries, as would occur on a flat two-dimensional plane (e.g. McGuire et al, 2006). The fact that
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the prey could differ in two phenotypic dimensions made greater variability in phenotypic colour
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possible than would be possible in a one-dimensional space (as in Franks & Noble, 2004; McGuire et
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al, 2006). This made the game more challenging and more interesting for the human players, helping
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to retain their interest. In reality we would expect real mimetic/aposematic patterns to be highly
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multi-dimensional in most cases.
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The position of each prey individual on the surface of the colour sphere, and hence its phenotype,
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was determined using standard spherical geometry. In particular the Haversine equations (Smith,
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2007) was used to compute new phenotypes for mimic offspring, given parental θ and φ, a mutation
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distance, and a bearing along which to travel:
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ℎ𝑎𝑣𝑒𝑟𝑠𝑖𝑛 (𝑅) = ℎ𝑎𝑣𝑒𝑟𝑠𝑖𝑛(𝜑2 − 𝜑1) + cos(𝜑1) cos(𝜑2) ℎ𝑎𝑣𝑒𝑟𝑠𝑖𝑛 (∆𝜆)
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and
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ℎ𝑎𝑣𝑒𝑟𝑠𝑖𝑛 (𝜃) = sin ² (2 ) = 1 − cos (2 ),
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where d is the distance between two points, R is the radius of the sphere, φ1 is the latitude of point
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1, φ2 is the latitude of point 2 and ∆λ is the longitudinal separation between points 1 and 2. The
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Haversine equation was also used to compute the distance between any two points on the surface
𝑑
𝜃
𝜃
Eqn 1
Eqn 2
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of the sphere, which provided a measure of mimetic accuracy. In all experiments, the radius R of the
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colour sphere was set at 125 RGB units, giving a wide range of possible phenotypes across the colour
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spectrum that can be displayed by a standard computer monitor.
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We conducted four separate experiments. Experiments 1 and 3 measured attack frequencies on
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different prey types in various ecological scenarios in the absence of evolution. Experiments 2 and 4
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explored the evolution of mimetic phenotypes resulting from the predator selection observed in the
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other two experiments. The game was separated into “generations” in which the predator was
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forced to attack a particular number of prey (k). In the non-evolving games, genotypes and
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corresponding phenotypes (positions on the colour sphere) for each mimic were randomly chosen at
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the start of each generation. In the evolving games, each generation of prey represented the
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“offspring” of the previous generation. In these games, the first generation of prey phenotypes was
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randomly distributed, and subsequently φ and θ for each individual mimic were determined by
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“parent” loci, subject to a small mutation. Every surviving mimic from the previous generation (i.e.
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those that were not “eaten” by the players) reproduced asexually. Every generation had the same
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number of mimics (Dmim). Once all surviving mimics had produced one offspring in the next
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generation, the remaining mimetic phenotypes were determined by randomly selecting a surviving
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parent to produce another offspring. Thus, a single game tracked the evolution of the mimetic
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phenotypes from the first generation, and no successful phenotype was lost in subsequent
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generations unless preyed upon.
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Offspring phenotypes mutated from the parental phenotype by travelling a small distance, randomly
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drawn from a normal distribution with a mean of zero, along a randomly-generated bearing
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(between zero and 2π radians) on the surface of the colour sphere. The mutation rate (µ) was set by
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the standard deviation of the normal distribution. In all games µ was 20 units on a standard
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computer RGB scale, which was approximately 10 % of the average phenotypic distance between
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two randomly chosen mimics within the population in the first generation. Mutations were thus
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small but perceptible to the trained eye.
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Model phenotypes were selected at random at the start of every game, but all models in each game
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were identical. Model abundance (Dmod) was fixed for the whole game. In all experiments, to simplify
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interpretation of the results, and to make it easy for the players to learn which prey were
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unprofitable, the model’s phenotype was constant across generations. This probably approximately
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reflects what happens in nature: it has long been assumed that the model phenotype will evolve at a
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slower rate than that of the mimic owing to the disadvantage of mutations in the warning pattern
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which could render the model’s signals unfamiliar to a predator (Nur, 1970). The game set-up also
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assumed that the predator outlives the prey and therefore carries any leaned behaviour across
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several generations of prey. This assumption reflects the fact that predators (often vertebrates)
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would normally live longer than their prey (often invertebrates), although this is not always the case.
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In contrast, other investigations using humans foraging for virtual prey have assumed that predator
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and prey have similar life expectancies (McGuire et al, 2006).
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Palatable but non-mimetic “alternative prey”, where present, were also uniform and constant in
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abundance (Dalt) and appearance, but were very distinct from models and mimics (open black circles,
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13 mm in diameter on a 17 inch screen). They were always profitable, with an attack yielding the
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same score as that for attacking a mimic. Other studies involving alternative prey often assume they
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are cryptic (e.g. Kokko et al, 2003; Lindström et al, 2004). However, because we were not specifically
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interested in the trade-off between searching for cryptic prey and attacking potentially unprofitable
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prey, we chose a phenotype for alternative prey that was just as conspicuous as those of the models
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and mimics.
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Players attacked k = 7 prey per generation. Once this limit was reached, the screen refreshed and
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the next generation of prey appeared, again initially hidden behind white squares. A generation
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counter was displayed at the bottom of the screen. Each game ran for a predetermined number of
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generations (g) before it ended. Apart from the prey, all other aspects of the foraging environment
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were kept as neutral as possible, using colours from the grey scale. Before starting the game, players
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were told how many generations the game would run for, how many prey they had to eat per
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generation, and the maximum possible score. They were asked their sex, whether they had played
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before and whether they had their sound turned on, and their IP address was recorded. In the
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analysis, data from players who said they had played before, or whose IP address had been logged
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previously, were discarded. Volunteers were solicited by emailing undergraduate students at the
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University of Nottingham, but the website was accessible to anyone with internet access.
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Participants were anonymous; names were not recorded and IP addresses were discarded after
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removal of duplicates. Players were made aware of the general purpose (biological research) of the
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game prior to choosing whether to participate, and could stop playing at any time during a game.
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Experiment 1: The effect of model profitability on mimic survival
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The first experiment tested the effect of the relative cost of attacking the model species on the
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survival of mimics of varying accuracy. From 2nd to 25th November 2010, visitors to the website
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foraged on a mixture of non-evolving profitable mimics of varying phenotypes (Dmim = 30 per
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generation) and less profitable models (Dmod = 15) for g = 10 generations. The score awarded for
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attacking a mimic (Bmim) was always 10 points, whilst the score awarded for attacking a model (Bmod)
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was chosen randomly for each player from a range of scores (8, 5, 2, 0, -5, -10, -15 or -20 points).
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Thus, whilst models sometimes gave a positive score, they were always less profitable than mimics.
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Given the constraint on the number of prey that could be consumed per generation (k = 7), the
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highest score was therefore only attainable by avoiding all attacks on models. In total 175 naïve
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players took part, and 160 control games (with random computer-generated attacks on prey) were
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conducted (20 for each model score treatment).
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Experiment 2: The effect of model profitability on the evolution of mimicry
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The second experiment explored the consequences of the selection measured in Experiment 1 for
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the evolution of mimic phenotypes in the presence of models which vary in profitability. From 25th
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March and the 7th April 2011, visitors to the website foraged on a mixture of evolving profitable
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mimics of varying phenotypes (Dmim = 30 per generation) and non-evolving, less profitable models
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(Dmod = 15). Pilot data suggested that more generations (g = 15) were required than in Experiment 1
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in order to observe the effects of selection on mimic evolution. The score awarded for attacking a
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mimic (Bmim) was always 10 points, whilst the score awarded for attacking a model (Bmod) was chosen
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randomly for each player from a range of scores (8, 6, 4, 2, or 0 points). Possible model scores were
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chosen based on preliminary results from Experiment 1, which suggested that the effect on predator
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behaviour of increasing the cost of attacking the model beyond Bmod = 0 was minimal. In total 316
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naïve players took part and 350 control games were conducted (70 for each model score treatment).
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Experiment 3: The effect of alternative prey on mimic survival
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The third experiment tested the effect of the availability of palatable alternative prey on the survival
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of mimics of varying accuracy. From 13th to 20th January 2011, visitors to the website foraged on a
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mixture of non-evolving profitable mimics of varying phenotypes (Dmim = 20 per generation; Bmim =
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10), non-evolving, less profitable models (Dmod = 12; Bmod = 0) and non-evolving profitable (Balt = 10)
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alternative prey for g = 10 generations. The abundance of alternative prey in the population (Dalt)
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was chosen at random for each player from a range of values (0, 3, 6, 9, or 12 per generation). Thus,
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the relative frequency and absolute abundance of the alternative prey varied simultaneously. The
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numbers of alternative prey were chosen to range from zero to well above the upper limit on attacks
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per generation (k = 7), meaning that a player could forage solely on alternative prey in some
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treatments. In total 91 naïve players took part and 200 control games were conducted (40 for each
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alternative prey treatment).
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Experiment 4: The effect of alternative prey on the evolution of mimicry
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The final experiment tested the effect of the availability of alternative prey on the evolution of
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mimetic phenotypes. The experimental set-up and treatments were identical to those in Experiment
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3, except that mimics were allowed to evolve over time (as in Experiment 2), and games lasted for g
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= 15 generations. In total 72 naïve players took part between 12th and 30th April 2011, and 400
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control games were conducted (80 for each alternative prey treatment).
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Statistical Analysis
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Attack probabilities and mimetic accuracy were analysed using Generalised Linear Mixed Effects
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Models (GLMMs) in R Version 2.12.1 with the appropriate error structures (binomial or Gaussian,
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respectively). Player was a random factor, and treatment, prey type, mimic accuracy (distance to the
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model in colour-space) and generation, and relevant interactions, were fitted as fixed effects. Where
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there was evidence of a nonlinear change in attack rates or mimic phenotypes over time, we
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explored this change in one of two ways. In some cases, we discriminated between data from the
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first four generations, during which players were learning to avoid unprofitable models, and later
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generations, in which the effects of that learning process were typically fully realised. In other cases,
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we fitted quadratic (and in one case cubic) terms to model the temporal trends. The choice of
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modelling approach was determined by visual inspection of the data, and AIC scores from
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preliminary analyses. In all cases, model terms were removed in a backwards step-wise manner from
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a saturated model, and the effect of removal tested using likelihood ratio tests (Zuur et al. 2009).
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Preliminary analysis revealed large, significant and predictable differences in key response variables
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between the games played by humans and control games in all experiments. Observed patterns of
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mortality and evolution in the prey were almost always clearly non-random in games with human
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predators. Therefore, to simplify the presentation of the results, and to allow us to focus on the
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most interesting main effects and interactions, most analyses presented below exclude control data,
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except where human attacks on prey were not clearly distinguishable from random. The control data
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are, however, plotted alongside the experimental data in figures for comparison. Finally, preliminary
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analysis of data from Experiment 1 showed that once the score awarded to the player on attacking
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the model (Bmod) reached zero, any further decrease in the score had little effect on the protection
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received by mimics (see Figures S1 and S2). Thus, data from treatments where the model score was
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zero or below were pooled for further analysis of this experiment.
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Results
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Experiment 1: The effect of model profitability on non-evolving mimics
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Overall, models were attacked more often by players when they were less costly to attack (binomial
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GLMM: LR = 26.547, df = 7, p < 0.001; see Figure 1). As the game progressed, the frequency of
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attacks on the models decreased (LR = 131.43; df = 1, p < 0.001), an effect which was greater as the
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cost of the model increased (interaction between Bmod and generation: LR = 16.232, df = 7, p =
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0.023). This is presumably because the players learned to avoid the models more readily when the
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model was more costly to attack. For the most unprofitable models, the learning phase seemed to
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last for only about four generations, after which point attack rates on the model were stable.
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Considering only the latter generations (5 – 10), after players had learned that models were costly,
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the results of Experiment 1 clearly show the benefits of mimicry. The more the mimics resembled
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the models, the less frequently they were attacked (LR = 366.76, df = 1, p < 0.001; Figure 2). There
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was a significant negative main effect of model profitability (Bmod) on the probability that a mimic
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was attacked (LR = 18.210, df = 7, p = 0.011), mirroring the increase in attack frequency on models
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described above. Importantly, there was a significant interaction between model profitability and
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mimetic accuracy: as the cost of attacking the model increased, less accurate mimics gained
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relatively more protection from predation (LR = 19.087, df = 7, p = 0.001). Players which
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encountered the least costly model attacked the mimics in a manner similar to the random pattern
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seen in the control games.
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Experiment 2: The effect of model profitability on evolving mimics
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When mimics were allowed to evolve, players were also less likely to attack models as the
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generations progressed (binomial GLMM: LR = 180.90, df = 1, p < 0.001; Figure 3). This effect was
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less important in later generations: there was a significant positive quadratic effect of generation on
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the probability of attacks on models (LR = 98.933, df = 1, p < 0.001). The more costly the models, the
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less likely players were to attack them (LR = 10.229, df = 4, p = 0.037), the steeper the initial decline
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in the attack frequencies on models across generations (interaction between Bmod and the linear
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effect of generations: LR = 12.598, df = 4, p = 0.013), and the less marked the decline in later
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generations (interaction between Bmod and the quadratic effect of generations: LR = 15.462, df = 4, p
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= 0.004). This suggests that players learned to avoid models more rapidly when attacks on them
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were more costly.
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Overall, the mean mimic phenotype evolved closer to the model over the generations (Gaussian
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GLMM: LR = 5.646, df = 1, p = 0.018; Figure 4), typically in a decelerating fashion (quadratic effect of
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generation: LR = 6.197, df = 1, p = 0.013; cubic effect of generation: LR = 7.209, df = 1, p = 0.007).
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Although there was no main effect of model profitability on mimic phenotype (LR = 2.046, df = 4, p =
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0.727), the shape of the trend in the mean mimic phenotype over time varied subtly among
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treatments: the effect of model score interacted significantly with the linear (LR = 68.816, df = 4, p <
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0.001) and cubic effects (LR = 49.853, df = 4, p < 0.001) of generation, but not with the quadratic
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effect of generation (LR = 5.691, df = 4, p = 0.223). When attacking the model was relatively costly
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(Bmod = 0), mimics initially evolved rapidly towards the model, but then appeared to stop evolving in
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later generations. In contrast, mimicry of less costly models (most notably when Bmod = 8) evolved
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more slowly at first, but continued right throughout the 15 generations studied.
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Experiment 3: The effect of alternative prey on non-evolving mimics
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In the presence of alternative prey, as in Experiment 1, the frequency with which models were
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attacked declined sharply in the first four generations (effect of generation in binomial GLMM for
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first four generations: LR = 74.873, df = 1, p < 0.001; Figure 5), but stabilized thereafter (effect of
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generation in generations 5 – 10: LR = 0.633, df = 1, p = 0.426). The abundance of alternative prey
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present did not affect the frequency of attacks on models in either the learning period (LR = 0.088,
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df = 1, p = 0.767) or in later generations (LR = 0.005, df = 1, p = 0.943). Furthermore there was no
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effect of the abundance of alternative palatable prey on the rate that the players learned to avoid
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the models: there was no significant interaction between generation and the number of alternative
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prey either during the learning period (LR = 0.088, df = 1, p = 0.767) or later (LR = 0.428, df = 1, p =
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0.513).
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Alternative prey were generally less likely to be attacked than mimics in Experiment 3 (see Figure 5),
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despite the fact that the two prey types were equally “palatable”, and in two treatments (Dalt = 9 and
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12) players could forage exclusively on alternative prey. In fact, overall, players did not attack the
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alternative prey any more or less than random: there was no difference in the attack rate on
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alternative prey between experimental and control games, either in the first four generations
347
(binomial GLMM: LR = 0.406, df = 1, p = 0.524), or later (LR = 0.223, df = 1, p = 0.637). In the first four
348
generations, the probability that alternative prey were attacked increased somewhat (LR = 6.931, df
349
= 1, p = 0.008; Figure 5), as attacks on models became less frequent (see above), and then stabilised
350
in later generations (LR = 0.019, df = 1, p = 0.890). This trend in early generations was relatively
351
weak, and the interaction between generation and whether the data were from experimental or
352
control games was not significant, either early in games (LR = 1.658, df = 1, p = 0.199) or later (LR =
353
0.019, df = 1, p = 0.890). In the first four generations, there were no significant main effects of the
354
abundance of alternative prey on the probability that they were attacked, and no significant
355
interactions between treatment and the other fixed effects we considered (p < 0.05 in all cases). In
356
later generations, alternative prey were slightly less likely to be attacked when they were more
357
abundant (LR = 4.819, df = 1, p = 0.028), but this main effect of treatment did not interact with the
358
other effects considered (p < 0.05 in all cases).
359
To explore the effects of the abundance of alternative prey on the frequencies of attacks on mimics
360
with varying levels of accuracy, we analysed data from the last six generations, by which time players
361
had learned to avoid models. As expected, less accurate mimics were more likely to be attacked (LR
362
= 308.58, df = 1, p < 0.001; Figure 6). Overall, the probability that a mimic was attacked decreased
363
with increasing numbers of alternative prey (LR = 110.92, df = 1, p < 0.001). However, there was no
364
significant interaction between the distance from the model and the number of available alternative
365
prey (LR = 0.830, df = 1, p = 0.362); this contrasts with the theoretical prediction that the presence of
366
alternative prey should give less accurate mimics more protection.
367
Experiment 4: The effect of alternative prey on evolving mimics
368
In games with alternative prey in which mimics were allowed to evolve, the attack rate on the model
369
declined rapidly over the first four generations, as in the other experiments (binomial GLMM: LR =
370
51.086, df = 1, p < 0.001; Figure 7), before stabilising in later generations (LR = 1.265, df = 1, p =
371
0.261). The abundance of alternative prey had no overall effect on the probability that models were
372
attacked in the first four generations (LR = 2.9832, df = 1, p = 0.084), but experienced players
373
attacked fewer models when alternative prey were relatively abundant (LR = 7.595, df = 1, p =
374
0.006). There was no indication that the abundance of alternative prey affected the rate at which
375
players learned to avoid models: there was no significant interaction between treatment and
376
generation either early in the game (LR = 0.1466, df = 1, p = 0.702) or later (LR = 0.118, df = 1, p =
377
0.731).
378
In contrast to the equivalent non-evolving game (Experiment 3), alternative prey in Experiment 4
379
were generally more likely to be attacked by humans than mimics, especially in later generations
380
(Figure 7). During the first four generations, while players learned to avoid models, the frequency of
381
attacks on alternative prey increased (LR = 8.068, df = 1, p = 0.006), before stabilising in later
382
generations (LR = 0.114, df = 1, p = 0.736). The abundance of alternative prey did not have a
383
significant effect on the probability that they were attacked in either the first four generations (LR =
384
1.324, df = 1, p = 0.250), or later (LR = 2.980, df = 1, p = 0.084). Similarly, there was no significant
385
interaction between the effects of generation and the abundance of alternative prey on the
386
probability that they were attacked, either in the first four generations (LR = 0.106, df = 1, p = 0.745),
387
or later (LR = 1.914, df = 1, p = 0.167).
388
Under selection from human predators, mimics evolved towards the model in phenotypic space over
389
15 generations, in a decelerating fashion (Gaussian GLMM; linear effect of generation: LR = 161.56,
390
df = 1, p < 0.001; quadratic effect of generation: LR = 17.442, df = 1, p < 0.001; Figure 8). The
391
abundance of alternative prey had no overall effect on mean mimetic accuracy (LR = 1.987, df = 1, p
392
= 0.159). Importantly, however, mimics evolved towards the model more slowly when alternative
393
prey were more abundant: the interaction between linear effect of generation and the abundance of
394
alternative prey was significant (LR = 52.734, df = 1, p < 0.001). The deceleration in the evolution of
395
mimicry, as captured by a quadratic term in the model, was not significantly affected by the
396
abundance of alternative prey (LR = 2.918, df = 1, p = 0.088). Nevertheless, it is interesting to note
397
that when alternative prey were at their most abundant, the mean mimic phenotype was relatively
398
constant in the last four generations, implying that evolution of mimetic accuracy had halted in this
399
treatment.
400
401
402
403
404
Discussion
405
Our experiments demonstrate that humans can rapidly learn to avoid unprofitable artificial prey
406
(models), even when the costs associated with attacks on those prey are small. The resultant
407
selection favours the evolution of relatively accurate Batesian mimicry in more profitable prey, but
408
this process is influenced significantly by the exact magnitude of the costs associated with attacks on
409
models, and by the availability of alternative palatable non-mimetic prey. Broadly, these findings
410
support the predictions of theoretical work which has sought to understand the factors affecting the
411
evolution of relatively inaccurate or imperfect Batesian mimicry. Some of the details of our results,
412
however, suggest that not all the assumptions made in such theoretical work are entirely
413
appropriate.
414
Model profitability and the evolution of Batesian mimicry
415
Our experiments demonstrate that the higher the cost of attacking a model, the less accurate a
416
mimic needs to be to gain a degree of protection from predation. This intuitive finding supports the
417
predications of Signal Detection Theory (Sherratt 2002), and is consistent with other studies of the
418
effects of model palatability on the survival of different mimic phenotypes (Alcock 1970; Goodale
419
and Sneddon 1977). It is hypothesised that particularly well-defended model species can protect a
420
wider range of mimetic phenotypes from predation, because predators will generalise more widely
421
when the costs of mistakenly attacking a model are greater (Darst and Cummings 2006). Our results
422
suggest that this effect is not linear: after a certain point, further increases in model costliness have
423
a neutral effect predator behaviour (for more detail, see Figures S1 and S2). This suggests that, at
424
least in our study system, there is a threshold cost at which predator aversion is maximised. Such a
425
threshold could account for the fact that some studies have failed to find an effect of model
426
profitability on mimic survival (Lindstrom et al. 1997). It is reasonable to expect that the optimal
427
position of such a threshold would be contingent on predator motivation, and if so, we would expect
428
the effects of model profitability and the availability of alternative prey to interact. This could easily
429
be tested by extensions of the experiments we present in this paper.
430
It has been suggested that an increase in the cost associated with an attack on a model will decrease
431
the time needed for avoidance learning by a predator (e.g. Leimar et al. 1986). Our results support
432
this suggestion: players faced with the least profitable models reduced their attack rate on them
433
more rapidly than in other treatments. This is presumably explained by the fact that the incentive to
434
learn to avoid the model was small when the relative cost of accidently attacking a model prey item
435
was low. This in turn implies that learning is costly in its own right, as otherwise any incentive, no
436
matter how small, should be sufficient to promote learning. We did not impose an explicit cost on
437
learning – there was no time limit on games, for example – but players could have been using a rule
438
of thumb that may have evolved to suit a wide range of foraging situations. Interestingly, the results
439
from the evolving games (Experiment 2) imply that, given enough time, less costly models will be
440
avoided to the same extent as more costly models. This supports the theory that predators take
441
longer to learn to avoid a less costly model, but that they will eventually learn to avoid even weakly-
442
defended prey (Ihalainen et al. 2007).
443
Players clearly recognised mimetic inaccuracy. Once experienced, they selected prey according to
444
the phenotypic distance from the model, with more accurate mimics receiving the best protection.
445
As predicted, selection on mimetic accuracy was relaxed when models were relatively costly to
446
attack. This relaxed selection might be expected to slow the rate of evolution towards mimetic
447
perfection, but our data (Experiment 2) do not entirely support this idea: at least initially, the rate of
448
evolution of mimetic accuracy increased in presence of particularly costly models. This may be a
449
result of the increased pressure on the predator to learn to discriminate between the model and
450
palatable prey when the costs of mistaken identity are high. Alternatively, it could be a consequence
451
of an increase in the number of models attacked per generation when models were less costly;
452
because we limited the total number of attacks per generation, an increase in the proportion of
453
models in the predator’s “diet” led to a corresponding decrease in the proportion of mimics
454
attacked, which could in turn reduce selection on mimetic accuracy.
455
Following an initial rapid evolution of mimetic accuracy in the presence of the most costly models
456
(Bmod = 0 in Figure 4), the results suggest that eventually a very unprofitable model could support a
457
wider range of mimetic phenotypes than a less costly model (cf. Bmod = 2 to Bmod = 6 in Figure 4). It
458
has been argued that there may be a threshold level of accuracy at which predation reaches a
459
minimum, beyond which improvements are selectively neutral, and that this threshold may be
460
reached at lower levels of accuracy when models are particularly unprofitable (Sherratt 2002; Speed
461
and Ruxton 2010). Our results weakly support this supposition, but further investigation is required
462
in which prey are subject to longer periods of selection by predators than were investigated here.
463
Such investigations may need to utilise different study systems, or at least a different experimental
464
design, because in our experience the interest of human volunteers can only be maintained for so
465
long!
466
Alternative prey and the evolution of Batesian mimicry
467
In non-evolutionary games, the availability of alternative prey had modest effects on the protection
468
afforded to palatable but mimetic prey (Experiment 3). As predicted (e.g. Nonacs 1985; Sherratt
469
2003), the abundance of palatable alternative prey was negatively related to attack rates on mimics.
470
Interestingly, however, the availability of alternative prey did not affect the level of mimetic
471
accuracy required to gain protection. The propensity of players to distinguish between model and
472
mimics was consistent across treatments. This contrasts with Lindström et al. (2004), who found that
473
great tits (Parus major) learned to avoid artificial model prey faster in the presence of more
474
abundant alternative prey.
475
Lindström et al (2004) also found that the presence of alternative prey had no overall effect on the
476
proportion of models attacked, and this does accord with our results. It has been suggested that if
477
the frequency of alternative prey is particularly high, the predator may not encounter the model
478
often enough to establish avoidance behaviour (Kokko et al. 2003). For example, Rowland et al.
479
(2010) found that increasing the number of alternative palatable prey increased the relative
480
predation risk for defended prey species, perhaps because the longer time period between each
481
encounter with a model resulted in the predator taking longer to learn to avoid the costly prey.
482
Indeed Signal Detection Theory predicts that as the chances of incurring a cost decreases, the
483
predator should behave less cautiously, more readily attacking potentially defended prey (Sherratt
484
2002). Our results failed to support this prediction, suggesting that a player’s ability to learn to
485
associate the model’s phenotype with a cost was unaffected by the availability of alternative prey.
486
However it is possible that the number of available alternative prey was not high enough to reduce
487
the frequency of encountering the model sufficiently to produce the predicted effect. Further
488
empirical work should focus on the importance of rare encounters on predator behaviour towards
489
defended models and mimetic prey.
490
Despite the fact that in two of the treatments in Experiments 3 the players had the opportunity to
491
“feed” exclusively on alternative prey, in general the players still preferred to attack the Batesian
492
mimics. It is possible that this is a product of the frequency-dependent nature of predatory
493
responses (Huheey 1980): the coloured squares (models and potential mimics) always outnumbered
494
the palatable alternatives (open circles), and perhaps this encouraged players to focus their
495
attention on the former rather than the latter prey type. Furthermore, the average frequency of
496
attacks on models was never zero, even when players were experienced. Although predation
497
pressure on models was greatly reduced in generations five to ten, players continued to sample
498
models in spite of the availability of inaccurate mimics and distinctive, palatable alternative prey.
499
Similarly, Nonacs (1985) found that unpalatable dough balls were repeatedly bitten by chipmunks
500
(Eutamias quadrimaculatus), even when distinguishable, risk-free alternative food was readily
501
available. Perhaps occasional sampling of the most abundant prey type in the environment is
502
generally adaptive, even when previous experience suggests those prey are unprofitable, because it
503
allows predators to evaluate any changes in profitability; alternatively, it might simply occur because
504
predators forget.
505
The evolutionary consequence (Experiment 4) of the reduced predation on mimics in the presence
506
of abundant alternative prey was that mimic phenotypes moved more slowly in the direction of
507
mimetic perfection. This is consistent with the predictions of Signal Detection Theory (Sherratt
508
2003), and generally highlights the importance of considering the availability of alternative prey in
509
the evolution of Batesian mimicry.
510
Evolutionary dynamics produced some noticeable differences in predator behaviour, in comparison
511
with the non-evolutionary Experiment 3. In particular, the probability of alternative prey being
512
attacked increased in the early generations of Experiment 4, and was greater than expected if the
513
players were foraging at random. This suggests that there was more incentive for the players to
514
utilise the palatable alternatives when accurate mimicry was allowed to evolve, presumably because
515
mimics were increasingly hard to distinguish from the model. As the potential risk of attacking a
516
costly model increased, the pay-off for attacking a visually consistent, highly distinguishable
517
palatable alternative will have increased. It has previously been suggested that the accuracy of the
518
mean mimetic phenotype will have a large impact on the decisions of the predator and consequent
519
selection on the mimics (McGuire et al, 2006). Furthermore Signal Detection Theory predicts that as
520
the chances of making a mistake increase, the predator should adopt a more cautious foraging
521
response (Sherratt 2002). Our results are consistent with this prediction, and highlight the
522
importance of the dynamic interplay between predator behaviour and phenotypic evolution in
523
systems like this: static “snap shots” of predator behaviour from laboratory or field trials are clearly
524
constrained in the extent to which they can provide insights into the evolution of phenotypes when
525
there is feedback between the appearance of the phenotype and the nature of selection.
526
Increasing the number of alternative prey in Experiment 4 significantly reduced the overall
527
frequency of attacks on the model. This is consistent with a density-dependent “dilution” effect,
528
which was thought by Rowland et al (2010) to account for the fact that increasing the availability of
529
alternative prey reduced the probability that chicks (Gallus gallus domesticus) would attack highly
530
defended models. Alternatively, decreased risk to aposematic prey in the presence of palatable
531
alternatives may result from the fact that the predators can afford to forage more cautiously when
532
they are less hungry (Sherratt 2003).
533
Sherratt (2003) suggested that a high frequency of alternative prey could allow less accurate
534
Batesian mimics to persist in the long term. After 15 generations of the evolving game, the mimetic
535
phenotypes were still evolving towards the model in phenotypic space, except perhaps when
536
alternative prey were at their most abundant (Figure 8). We would need to extent the duration of
537
our experiments to test Sherratt’s prediction properly, since at present it is not clear if the
538
abundance of alternative prey merely affects the rate at which evolution towards perfection
539
progresses, rather than the evolutionary end-point.
540
The design of Experiments 3 and 4 meant that as the abundance of alternative prey increased, so too
541
did the total prey density on screen. We cannot therefore rule out the possibility that the observed
542
effects of alternative prey availability resulted from a more general effect of prey density. Prey
543
density is known to influence the foraging behaviour of predators, for example by increasing the
544
time they spend foraging in a patch (Wellenreuther and Connell 2002), increasing the success rate of
545
attacks (Draulans 1987), or increasing the conspicuousness of the prey and the spatial error of
546
predator attacks (Ioannou et al. 2009). However most of these effects are unlikely to be important in
547
the present study. First, the players were unaware of the identity (model, mimic or alternative) of
548
each individual prey until they clicked upon the covering square. Second, the players were not
549
restricted by time or challenged by moving prey. Furthermore, the effect of prey density appears to
550
be particularly relevant when it can be contrasted with other experiences (Wellenreuther and
551
Connell 2002), but in our study each player only encountered prey at one particular density. Finally,
552
the players of our game had to attack a fixed number of prey per generation, and an effect of
553
density on the general incentive of players to attack prey was not therefore likely to be important.
554
Conclusion
555
We used computer games to simulate the evolution of Batesian mimicry under selection by human
556
“predators”. This approach helps to bridge the gap between theoretical predictions about the long-
557
term consequences of factors such as model profitability and the availability of alternative prey on
558
the evolution of mimicry, and short-term empirical work with real predators and prey. Human
559
volunteers are a good replacement for the rigid and perhaps oversimplified predation algorithms
560
used in simulation models, because they demonstrate similar behavioural and physiological
561
limitations and complexities to those seen in real predators in natural situations. Of course, the
562
degree of realism offered by evolutionary experiments in virtual environments is limited by the
563
algorithms used to predict the outcome of selection, but computer simulations like ours offer a
564
unique opportunity to study the importance of dynamic feedbacks between phenotypes and
565
behaviour which would not be possible in more naturalistic experiments.
566
Overall, the results of our experiments are broadly consistent with theoretical predictions and
567
previous empirical evidence about the importance of model profitability and alternative prey, and
568
hence they help to confirm some assumptions about how and why Batesian mimicry evolves.
569
However, our data suggest patterns of feedback during the evolutionary process which may not
570
have been fully captured in previous studies of mimicry. We believe that further studies which
571
attempt to observe the evolutionary process in action will shed important light on the origins of
572
phenotypic traits which impact on predator selection, such as mimicry, aposematism and crypsis.
573
574
575
576
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653
Figure 1. The effect of model profitability (Bmod; values shown in panel headings) on the probability
654
that models and mimics were attacked by humans over ten generations in games without evolution,
655
compared with data from control simulations with random predation.
656
Figure 2. The effect of model profitability (Bmod; values shown in panel headings), and similarity to
657
the model (distance in standard computer RBG colour space), on the probability of a mimic being
658
attacked by humans in games without evolution, compared with data from control simulations with
659
random predation. Data shown are pooled across generations, excluding the first four generations,
660
during which players were learning to identify models.
661
Figure 3. The effect of model profitability (Bmod; values shown in panel headings) on the probability
662
that models and mimics were attacked by humans over 15 generations in games with evolution,
663
compared with data from control simulations with random predation.
664
Figure 4. The effect of model profitability (Bmod; values shown in panel headings) on mean mimetic
665
accuracy over 15 generations in games with evolution, compared with data from control simulations
666
with random predation. Mimetic accuracy is expressed as mean distance to the model in standard
667
computer RBG colour space.
668
Figure 5. The effect of the number of available alternative palatable prey (Dalt; shown in panel
669
headings) on the probability that models, mimics and alternative prey were attacked by humans
670
over ten generations in games without evolution, compared with data from control simulations with
671
random predation.
672
Figure 6. The effect of the number of available alternative palatable prey (Dalt; shown in panel
673
headings) and similarity to the model (distance in standard computer RGB colour space) on the
674
probability of mimics with different levels of accuracy being attacked by humans in games without
675
evolution, compared with data from control simulations with random predation. Data shown are
676
pooled across generations, excluding the first four generations, during which players were learning
677
to identify models.
678
Figure 7. The effect of the number of available alternative palatable prey (Dalt; values shown in panel
679
headings) on the probability that models, mimics and alternative prey were attacked by humans
680
over 15 generations in games with evolution, compared with data from control simulations with
681
random predation.
682
Figure 8. The effect of the number of available alternative palatable prey (Dalt; values shown in panel
683
headings) on mean mimetic accuracy over 15 generations in games with evolution, compared with
684
data from control simulations with random predation. Mimetic accuracy is expressed as mean
685
distance to the model in standard computer RBG colour space.
686
<2
2
0.20
0.15
Proportion attacked
0.10
Species
0.05
Mimic
Model
5
8
Treatment
Control
0.20
Human
0.15
0.10
0.05
1
689
7
10
1
Generations
687
688
4
Figure 1
4
7
10
<2
2
0.3
0.2
Proportion attacked
0.1
0.0
Treatment
5
Control
8
0.3
Human
0.2
0.1
0.0
0
692
200
300
0
Distance
690
691
100
Figure 2
100
200
300
0
2
4
0.3
0.2
Proportion attacked
0.1
Species
Mimic
Model
6
8
Treatment
0.3
Control
Human
0.2
0.1
4
695
12
4
8
12
Generations
693
694
8
Figure 3
0
2
4
200
Mean mimetic accuracy
180
160
Treatment
6
Control
8
Human
200
180
160
1
698
7
10
13
1
4
7
10
Generation
696
697
4
Figure 4
13
699
0
3
6
0.3
0.2
Proportion attacked
0.1
Treatment
Control
Human
0.0
9
12
Species
Alternative
Mimic
Model
0.3
0.2
0.1
0.0
1
7
10 1
4
7
Generations
700
701
4
Figure 5
10
0
3
6
0.4
0.3
0.2
Proportion attacked
0.1
0.0
Treatment
9
12
Human
0.4
0.3
0.2
0.1
0.0
0
100 200 300 400
0
100 200 300 400
Distance
702
703
Control
Figure 6
0
3
6
0.4
0.3
0.2
Treatment
Proportion attacked
0.1
Control
Human
0.0
9
12
Species
Alternative
Mimic
0.4
Model
0.3
0.2
0.1
0.0
1
704
705
4
7
10
13
1
4
7
10
Generation
Figure 7
13
0
3
6
200
175
150
Distance
125
Treatment
9
Control
12
Human
200
175
150
125
1
706
707
708
4
7
10
13
1
4
7
10
Generation
Figure 8
13
709
Online Appendix A
710
These two figures illustrate the threshold observed in the effect of model profitability on predator
711
behaviour in Experiment 1. The behaviour of volunteer towards different prey types was consistent
712
for all values of Bmod below 2. In the main manuscript, data were pooled where Bmod < 2 (see Figures
713
1 and 2 in the main manuscript).
714
Figure S1. The effect of model profitability (Bmod; values shown in panel headings) on the probability
715
that models and mimics were attacked by humans over ten generations in games without evolution,
716
compared with data from control simulations with random predation. All values of Bmod explored in
717
the experiment are shown (analysis and figures in main manuscript pool data where Bmod < 2).
718
Figure S2. The effect of model profitability (Bmod; values shown in panel headings), and similarity to
719
the model (distance in standard computer RBG colour space), on the probability of a mimic being
720
attacked by humans in games without evolution, compared with data from control simulations with
721
random predation. All values of Bmod explored in the experiment are shown (analysis and figures in
722
main manuscript pool data where Bmod < 2). Data shown are pooled across generations, excluding
723
the first four generations, during which players were learning to identify models.
724
-20
-15
-10
-5
0
2
0.20
0.15
0.10
Proportion attacked
0.05
Species
0.20
Mimic
0.15
Model
Treatment
0.10
Control
0.05
Human
5
8
0.20
0.15
0.10
0.05
1
7
10 1
4
7
Generation
725
726
4
Figure S1
10
-20
-15
-10
-5
0
2
0.3
0.2
0.1
0.0
Proportion attacked
0.3
0.2
Treatment
Control
Human
0.1
0.0
5
8
0.3
0.2
0.1
0.0
0
727
728
100
200
300 0
100
200
Distance
Figure S2
300