Biased predation could promote convergence yet maintain diversity within Müllerian mimicry rings of Oreina leaf beetles

Müllerian mimicry is a classic example of adaptation, yet Müller's original theory does not account for the diversity often observed in mimicry rings. Here, we aimed to assess how well classical Müllerian mimicry can account for the colour polymorphism found in chemically defended Oreina leaf beetles by using field data and laboratory assays of predator behaviour. We also evaluated the hypothesis that thermoregulation can explain diversity between Oreina mimicry rings. We found that frequencies of each colour morph were positively correlated among species, a critical prediction of Müllerian mimicry. Predators learned to associate colour with chemical defences. Learned avoidance of the green morph of one species protected green morphs of another species. Avoidance of blue morphs was completely generalized to green morphs, but surprisingly, avoidance of green morphs was less generalized to blue morphs. This asymmetrical generalization should favour green morphs: indeed, green morphs persist in blue communities, whereas blue morphs are entirely excluded from green communities. We did not find a correlation between elevation and coloration, rejecting thermoregulation as an explanation for diversity between mimicry rings. Biased predation could explain within‐community diversity in warning coloration, providing a solution to a long‐standing puzzle. We propose testable hypotheses for why asymmetric generalization occurs, and how predators maintain the predominance of blue morphs in a community, despite asymmetric generalization.

Lyytinen, & Mappes, 2001). On the other hand, when aposematic prey are common, their per capita mortality will be low, and an established aposematic signal will be very difficult to invade. Indeed, positive frequency dependence can be so strong that individuals of different defended species evolve to resemble one another, in a phenomenon called Müllerian mimicry (Müller, 1879).
Although general evidence for Müllerian mimicry is strong (Ruxton et al., 2018), there are several issues with the theory.
We tested Müller's hypothesis in a system of beetles from temperate latitudes. Oreina leaf beetles are colourful, chemically defended insects with a range centred in the European Alps (Dobler, Mardulyn, Pasteels, & Rowell-Rahier, 1996). The majority of species are polymorphic and glossy, with most morphs having a basal colour of either blue or green (Kippenberg, 1994;Waldron et al., 2017).
Within the Alps, communities of three to six species can be found in patchily distributed locations (Figure 1). They rely heavily on the availability of their host plants- Adenostyles and Petasites (Asteraceae) and Chaerophyllum, Heracleum or Peucedanum (Apiaceae). They also carry chemical defences in specialized exocrine glands (Pasteels, Eggenberger, Rowell-Rahier, Ehmke, & Hartmann, 1992). Borer et al. (2010) found positive frequency-dependent selection on coloration among local populations of Oreina gloriosa where either blue or green morphs predominated. This supports the hypothesis that predators stabilize the most abundant local colour morph in O. gloriosa and that coloration functions as a warning signal in that species. Taken with the results of Waldron et al. (2017), who showed that specular highlights on the dorsum of Oreina enhance predator avoidance learning, this supports the conjecture that multiple Oreina species may form Müllerian mimicry rings across central Europe. Although this genus is common and its chemical ecology has been well studied (Dobler et al., 1996;Dobler & Rowell-Rahier, 1994), curiously there are no quantitative data on local colour morph frequencies.
If Oreina beetles in fact form local Müllerian mimicry rings, Müller's hypothesis predicts that (1) colour morphs in each species should exhibit positive covariance among different local communities, indicating that local frequency-dependent selection drives convergence in coloration. We tested this prediction by analysing the frequencies of Oreina colour morphs across eight communities in the Alps. We also tested the behaviour of predators in response to different Oreina colour morphs and species. Specifically, Müller's hypothesis predicts that (2) predators will be able to learn to avoid either the blue or green morphs; (3) after learning to avoid blue or green morphs, predators will be more willing to attack the alternative colour morph, which would lead to positive frequency-dependent selection; and 4) learned avoidance of a colour morph of one species will be generalized to colour morphs of different species.
Additionally, where these predictions are not met, they have the potential to explain deviations from perfect Müllerian convergence, such as polymorphism within populations.
F I G U R E 1 Six of the most common species represented in typical blue and green morphs. The species are aligned in alphabetical order; (1) Oreina alpestris, (2) Oreina bifrons, (3) Oreina cacaliae, (4) Oreina gloriosa, (5) Oreina speciosissima and (6) Oreina speciosa As thermoregulation may limit the evolution of warning signals in temperate regions (Hegna, Nokelainen, Hegna, & Mappes, 2013;Lindstedt, Lindström, & Mappes, 2009), we tested the additional hypothesis that variation in colour morph among populations of Oreina could be linked to a thermoregulatory advantage of the darker, blue morph. This hypothesis predicted a positive correlation between the frequency of blue morphs in different populations and elevation.

| Collection
We chose eight locations in the Alps at which to characterize communities of Oreina ( Figure S1). These locations were a minimum distance of 50 km apart, far larger than the territory sizes of any individual avian insectivores. At each location, we sampled multiple sites across early, mid-and late summer, ranging from 3 June to 7 August in 2012 and 2013 ( Figure S2). Sites were distributed over an elevational gradient ranging from 961 to 2,338 m. Due to logistical constraints, we were not able to visit each site every season or year (sites have been consistently dominated by the same colour morpheither blue or green-for over 20 years of visits, SD, pers. obs). Sites measured 5 × 5 m square, and like the locations in which they were nested, were far enough apart that they were unlikely to be shared between any passerine bird territories. We scanned the surface of the vegetation and attempted to collect all of the Oreina that could be found in 10 min of searching. Oreina are long-lived or relatively stationary and tend to be on the visible surfaces of the broad leaves of their host plants, so our methods were unlikely to be biased towards collecting one morph or the other even as their frequencies varied between sites.
In our study location, a total of eight species can be identified according to the most recent key for the genus Oreina and its sister genus Chrysolina (Bourdonné & Douget, 1991;Kippenberg, 1994):

| Statistical analysis
We assigned each beetle to a colour morph category (blue or green).
Intermediate or alternative forms were rare, making morph assignment straightforward. We also assigned them to a taxonomic group: O. cacaliae and "other." We adopted this very simple taxonomic classification because although males of all species can be unambiguously identified by dissection, morphological identification of females is often difficult or impossible. Particularly, O. alpestris and O. speciosa are extremely difficult to tell apart and recent genetic analyses revealed a high amount of gene flow and introgression among them (Triponez et al., 2011). Oreina cacaliae, on the other hand, can be easily recognized by its flat and elongate body shape.
Another reason to consider O. cacaliae separate from other Oreina is that the latter use autogenously produced cardenolides for defence, whereas O. cacaliae uses pyrrolizidine alkaloids sequestered from its host plants (Pasteels et al., 1992;Rowell-Rahier, Pasteels, Alonso-Mejia, & Brower, 1995). The pooling among Oreina spp. and C. coerulans was further justified by our behavioural experiments (see Results). We emphasize that species-level identification was not necessary for testing the predictions of our hypotheses.
We used logistic regression to test the prediction (1) that the most frequent colour morph of one species would be correlated with the most frequent colour morph of other species across sites. We modelled the ratio of blue:green beetles of "other" species at each site, with the proportion of blue O. cacaliae as a predictor, and the location of each site included as a random effect.
In a separate model, we tested the prediction of the thermoregulatory hypothesis for differences in colour between different sites: that colour morph frequency would be correlated with elevation. To test this, we used a logistic regression to model the ratio of blue:green among all beetles at each site, with elevation as a continuous predictor and location (which contained multiple sites) included as a random effect. Latitudinal variation was not included, as a relatively small variation in temperature due to its effect was likely given the spatial distribution of our sites. Both of these analyses were performed using the lme4 package (Bates, Maechler, Bolker, & Walker, 2019)

| Birds
Blue tits (Cyanistes caeruleus) are generalist avian insectivores found at our research station, and also in the Alps where they are sympatric with Oreina. Importantly, however, blue tits from our research station are nonmigratory, making them naive to Oreina. Wild-caught birds were housed in purpose-built aviaries (Lindström, Lyytinen, Mappes, & Ojala, 2006) and were ringed and released at the place of capture after the experiments were complete. In two distinct experiments, we first tested avoidance learning and colour generalization between blue and green morphs of O. cacaliae and, second, generalization between green morphs of O. cacaliae and O. alpestris. Each bird participated in only one of the two experiments.

| Prey
We collected green beetles, O. cacaliae and O. alpestris (fomerly known as O. variabilis; Dobler et al., 1996;see Kippenberg, 1994) near Zastler in the Black Forest, Germany (June 2013), and blue O. cacaliae from Tschiertschen, Switzerland (June 2013). Both beetle species release chemical defensive secretions from exocrine glands located laterally on the pronotum and the elytra when they are disturbed or attacked. As the chemical defences of the two species differ, we made sure that the beetles we used of each species contained their maximum supply of chemicals, as well as we could manage given our experimental equipment. We did this by maintaining beetles in environmental chambers (day: night temperature regime of 16:16°C and a light schedule of 16:8 hr) for 15 days with food ad libitum before freezing them at −80°C.
Species-appropriate host plants were gathered at the site of collection and later provided by the Botanical Garden, Universität Hamburg, Germany.

| Aviaries
Experimental aviaries (50 × 65 × 45 cm) were lit to simulate daylight using a 26W, Repti Glo 5.0 Compact UVB light bulb positioned in the centre of the aviary roof. Each aviary had a perch, a water bowl (access ad libitum) and a small mesh-covered observation hole. A vertical metal barrier (ca. 15 cm) was used to obscure prey items during behavioural experiments. A moveable floor tray was used to insert a Petri dish, fitted with green cardboard, to present sunflower seeds and prey during training and experimental trials.

| Pretraining
Pretraining included habituation into the experimental cage and training birds to find food behind the metal barrier, which obscured it from view while they were on their perches. Birds had to hop on top of the barrier to observe the food, giving an obvious point at which to begin recording latency to attack prey items.
For further description, see Rojas et al. (2017). Pretraining took between 1 and 4 hr to complete. All birds completed pretraining successfully.

| General protocol for experimental trials
Both the colour and the species generalization experiments followed the same protocol ( Figure 2a). After pretraining was complete, a two-hour food deprivation period was started, to ensure that all birds were in a similar state of hunger. After two hours, a last instar larva of Tenebrio molitor (mealworm) was offered to check that each bird was hungry and motivated to forage. After eating the larvae, a second, shorter food deprivation period (20 min) began before we offered an adult control beetle of T. molitor. The palatable T. molitor prevented birds from learning to avoid all beetles per se. Two to five minutes after the T. molitor had been consumed, we introduced an Oreina. We began recording attack latency as soon as the bird landed on the metal barrier and could see the beetle. Birds had a maximum of four minutes (240 s) to attack the Oreina before the trial was terminated. If the bird did not attack within this time, the trial was recorded as a nonattack. An attack was recorded if the beetle was touched. Finally, to verify that birds remained motivated to forage throughout the experiment, we offered a final mealworm that concluded the experimental trial.

| Colour morph generalization experiment
This experiment tested prediction (2) that predators could learn to avoid either blue or green colour morphs and prediction (3) that learning to avoid one colour morph would not result in protection for the alternative morph. It consisted of a total of four experimental trials for each bird. First, during avoidance learning, we distributed 76 birds into two treatment groups (Blue and Green) that were exposed to a single colour morph of O. cacaliae (blue or green, respectively) in three trials that were administered on three different days. On the fourth day, we administered a generalization trial to see whether learned avoidance of one colour morph transferred to the alternative colour morph. For the generalization trial, Blue and Green groups were subdivided into two smaller groups, two control (BB and GG) and two treatment groups (BG and GB) (Figure 2b). The first letter indicates the colour morph that birds were trained to avoid, whereas the second letter indicates the colour morph presented to birds during the generalization test (trial 4). Thus, the two control groups (BB and GG) received the same colour morphs for all four days of the experiment. The treatment groups (BG and GB) experienced either blue or green morphs during the three days of avoidance learning before receiving the alternative morph on the fourth day.

| Species generalization experiment
Prediction (4)  Due to a low number of blue tits captured and a restricted number of green O. cacaliae, data for treatment CC, where the birds experienced green O. cacaliae throughout the experiment, were taken from a previous experiment (Waldron et al., 2017). Despite minor differences in the beetle preparations before they were offered to the birds, this produced no differences in initial latency to attack or in learning (see Supporting information).

| Statistical analysis
For the colour generalization experiment using O. cacaliae, we analysed birds' willingness to attack during the first encounter using Cox proportional hazard regression. The attack risk per unit time was modelled as a function of colour. Then, we analysed how birds learned to avoid blue and green colour morphs across trials 2-3. We used a mixed-effects Cox proportional hazard model with attack latency as the dependent variable; colour, trial and their interaction as predictors; and bird identity as a random effect (package "coxme"; Therneau, 2019). Finally, we compared attack latency between treatment and control groups using Cox proportional hazard models in trial 4 (generalization).
We used an identical analysis for the species generalization experiment between O. cacaliae and O. alpestris, except that wherever colour was used as a predictor variable, we substituted species. In addition, we analysed learning across trials 1-3 instead of trials 2-3, as most learning took place between trials 1 and 2 (see Results).
All analyses were performed in R 3.4.4 (R Core Team, 2019).

F I G U R E 2 (a)
Experimental protocol for all trials. The sequence was as follows: foraging control (Tenebrio molitor larva), beetle control (T. molitor adult), experimental beetle (Oreina) and motivation control (T. molitor larvae). (b) Design of colour generalization experiment. From left to right, each row represents one treatment and each column represents one trial. All beetles used were Oreina cacaliae. First, birds learned to avoid either blue or green beetles across trials 1-3. Birds were then split into four groups for the generalization test (trial 4): BB and GG, which received beetles of the same colour as in avoidance learning, and BG and GB, which received beetles of the alternative colour morph. The dark grey scale line is 10 mm. (c) Design of species generalization experiment. All beetles used in this experiment were green Oreina cacaliae or Oreina alpestris. During avoidance learning, birds were divided into two groups that received three trials with either O. cacaliae or O. alpestris. For the generalization test (trial 4), birds were divided into four groups: CC and AA received the same species of beetles for all four trials, whereas CA and AC received the alternative species of beetle in the generalization test. The grey scale line is 10 mm

| Colour morph generalization
Cox proportional hazards regression revealed that birds initially hesitated ~50 s longer in trial 1 to attack green beetles than blue beetles (Table 1a, Figure 5). During learning (trials 2-3), the effect of colour was nonsignificant (Table 1b, Figure 5), but the effect of trial was significant (Table 1c). The colour:trial interaction was nonsignificant (Table 1d). Therefore, birds learned to avoid both colour morphs at the same rate. This confirmed prediction 2 that birds should learn to avoid both Oreina colour morphs.
In trial 4, we tested to see whether birds generalized their learned avoidance of one colour onto the other. Birds did not entirely generalize their learned avoidance of green beetles onto blue beetles (treatment GG versus GB; Table 1e, Figure 5). This agreed with prediction 3 that the colour morph that birds have learned to avoid should receive more protection. However, we found that birds strongly generalized learned avoidance of blue beetles onto green beetles, such that there was no difference in their attack rates (treatment BB versus BG; Table 1f, Figure 5). Thus, prediction 3 was rejected for birds that learned to avoid blue.

| Species generalization
Birds hesitated longer to attack O. cacaliae than O. alpestris in trial 1 (Table 2a, Figure 6). This hesitation carried over into our analysis of learning across trials 1-3: species significantly affected attack latency (Table 2b). However, birds learned to avoid both species across the learning trials (Table 2c), and there was no difference in learning rate for O. cacaliae or O. alpestris (Table 2d). In trial 4, there were no differences between the control and treatment groups (Table 2e,f), indicating that birds completely generalized their learned avoidance of one species onto the other. This result confirmed prediction 4 that predators should not distinguish between species after learning.

| D ISCUSS I ON
We tested the predictions of the hypothesis that Oreina leaf beetles are classical Müllerian mimics (Müller, 1879). Field data confirmed the prediction that the ratio of blue:green morphs in different species should covary across different local communities. Behavioural experiments confirmed two additional predictions: birds learned to avoid either blue or green beetles, and they generalized their learned avoidance of green morphs of one species to green morphs of another, quite different species. The prediction that avoidance of one colour should not be generalized to another colour, which would produce positive frequencydependent selection, was not entirely true, however. Avoidance of green was not well generalized to blue, but avoidance of blue was entirely generalized to green. Therefore, green communities of Oreina meet all the criteria for Müllerian mimicry, but the evidence in blue communities is more equivocal. If green morphs The persistence of blue morphs could be explained if they were favoured in environments with cooler temperatures where their coloration might let them become active more quickly than green morphs (Hegna et al., 2013;Lindstedt et al., 2009). This hypothesis predicts a positive relationship between the frequency of blue morphs in local communities and elevation (higher elevations are of course on average cooler). We did not find such a pattern, rejecting the simple hypothesis that blue beetles are favoured at cooler temperatures, although other, more complex interactions between beetle colour and environment are possible.
A more plausible explanation lies in predator behaviour. In the wild, the positive frequency-dependent selection that characterizes Müllerian mimicry may be more evident in blue Oreina communities than our data imply. Borer et al. (2010) found that 65% of wild populations of O. gloriosa experience positive frequency-dependent selection on colour, in both green and in blue populations.
This suggests that at their naturally occurring frequencies, both colour morphs experience an advantage when they are most abundant. Therefore, although our bird experiments show an advantage to green morphs under our laboratory conditions, a change in bird behaviour with frequency might help explain why blue morphs are not driven to extinction. This raises the additional question of how an advantage to green morphs gives way to an advantage to blue ones.
Our data on morph frequencies in the field show an asymmetry. In green communities, blue morphs are not present among any species (Figure 3, top row). In contrast, in blue communities, green morphs are often a noticeable minority of individuals (Figure 3, bottom row). Green morphs may have an advantage when they are rare that stems from asymmetric predator generalization. This may allow green to spread until it achieves a noticeable frequency, which would produce the pattern in the bottom row of Figure 3.
We hypothesize that above a certain threshold of rarity, but before they become more common than blue morphs, predators may begin to recognize green beetles as a distinct category of prey and start to sample them (i.e. overcoming neophobia; Sherratt, 2011).
This would allow blue communities to resist invasion by green morphs, yet at the same time explain the persistence of green morphs in blue communities. To visualize the scenario that we describe in terms of a selective surface, see Figure 7, which depicts both negative frequency-dependent selection at low frequencies and positive frequency-dependent selection at high frequencies.
Traditionally, negative frequency-dependent selection and positive frequency-dependent selection are considered separately,   If the hypothesis that we describe above is correct, it would be a psychological twist on the evolution of Müllerian mimicry. It is well understood that the simple mathematical model proposed in 1879 by Fritz Müller does not accurately describe predator behaviour (Rowland et al., 2007;Sherratt, 2008). Müller assumed that predators had to sample a fixed number n of prey with a given phenotype to learn avoidance. This assumption has been shown to be false by a number of experimental studies, which instead find that as the abundance of defended prey increases, they are increasingly likely to be sampled (Beatty, Beirinckx, & Sherratt, 2004;Lindström et al., 2001;Rowland, Hoogesteger, Ruxton, Speed, & Mappes, 2010;Rowland, Wiley, Ruxton, Mappes, & Speed, 2010). Indeed, predators should display this behaviour if they learn about prey optimally (Sherratt, 2011). Optimal learning by predators also leads to neophobia, which can allow diversity to persist in Müllerian mimicry rings (Aubier & Sherratt, 2015). In a Müllerian mimicry ring, neophobia permits rare morphs to persist at low frequencies. When they increase above a certain threshold, however, they become worthwhile for predators to sample, which depresses their numbers.
Only if they rise to become the predominant morph in a community through some demographic accident does positive frequency-dependent selection work in their favour (Aubier & Sherratt, 2015).
Generalized avoidance of green morphs from learned avoidance of blue morphs could have a similar effect to neophobia, maintaining green morphs at low frequencies in blue communities, if it attenuates as predators encounter more and more green morphs ( Figure 7). This scenario is entirely consistent with results from this study and Borer et al. (2010), and implies that predator biases may play a role in maintaining diversity in warning coloration within mimicry rings. A rigorous test of this hypothesis would require measuring the fitness of green morphs over a range of frequencies and would be an important addition to our understanding of frequency-dependent selection on invertebrate coloration (Ajuria Ibarra & Reader, 2013). To illustrate mechanism, it would also be necessary to show that as more green beetles are encountered by predators, predators become more likely to sample them. Furthermore, this hypothesis does not explain why there is an asymmetry in predator generalization between blue and green morphs in the first place.
It is also too simplistic for systems where trait variation between morphs is more continuous.
Supernormal stimuli occur within the same dimension as a stimulus that an animal has been conditioned to, but at a greater intensity, eliciting a correspondingly greater response (Baddeley, Osorio, & Jones, 2007;Ghirlanda & Enquist, 2003). If the green coloration of Oreina is indeed a more intense stimulus than blue along a single dimension of predator perception (e.g., hue), it should be possible to predict predator responses to more and less intense stimuli along the same dimension. Whether either of the hypotheses for asymmetric generalization is true, it is worth noting that some generalization occurs in the opposite direction; that is, learned avoidance of green provides some degree of protection to blue. This is shown by the increased latency to attack blue beetles in the test trial of the GB group compared to birds' initial latency to attack blue beetles ( Figure 5 (Doktorovová et al., 2019;Exnerová, Svádová, Fucíková, Drent, & Stys, 2010;Rowe, Lindström, & Lyytinen, 2004;Ruxton et al., 2018; but see Ihalainen, Lindström, Mappes, & Puolakkainen, 2008).
In sum, we found that simple assumptions about predator behaviour could only explain Müllerian mimicry among green morphs of Oreina. More nuanced predator behaviour may explain the persistence of Müllerian mimicry among blue Oreina morphs. Due to its simple basis in a binary colour polymorphism that diverges in frequency among populations, Oreina mimicry rings may also be ideal to test evolutionary hypotheses about mimicry in the field. Oreina adds to our knowledge of warning signals at temperate latitudes, showing that even in comparatively species-poor communities such as alpine meadows, warning signals experience complex selective pressures.

ACK N OWLED G M ENTS
We thank staff at Konnevesi research station for logistical support and Jimi Kirvesoja for help with collecting beetle spectra.
We thank members of Mappes lab and Tom Reader for feedback F I G U R E 7 A hypothetical selective surface where green morphs can spread up to a certain frequency due to asymmetric predator generalization from blue to green, favouring green when it is rare (green area). When green morphs become more abundant, however, predators begin to sample them, which decrease their fitness relative to the more common blue morph (i.e. positive frequency-dependent selection). This would maintain a low frequency of green morphs within blue populations. Compare with Aubier and Sherratt (2015)

DATA AVA I L A B I L I T Y S TAT E M E N T
The data sets of the article are available in dryad https://doi.