A fascinating recent paper by Jennifer Hoyal Cuthill et al. (2019) published in Science Advances uses a “deep convolutional neural network” to classify photos of upper and underside of 1234 butterfly specimens, all of them named subspecies of Heliconius erato and H. melpomene, into phenotypic clusters. The researchers worked with Blanca Huertas and Robyn Crowther to photograph specimens from the London Natural History Museum, that has one of the most complete collections of Heliconius worldwide. They compare the “phylogenetic analyses” based on phenotypic classification with those of genes known or thought to be close to sites of colour pattern switch loci, and those of “neutral” genes selected from around the genome. They conclude that the species have converged within each geographic region, due to Müllerian mimicry. They also argue that the results prove that convergence is due to mutual coevolution.

This topic is of particular interest to me because (a) it concerns my favourite organisms, (b) the coevolution conclusion rebuts a paper I wrote arguing that there is little convincing evidence for coevolution in Müllerian mimicry (Mallet 2001). I’ve communicated with Jennifer on the paper, and discussed the difficulty of classifying hybrids between races, and helped to correct her classifications with some of the obvious inter-subspecific hybrids I found in a sample of their photos from the Natural History Museum’s collections of each subspecies. Blanca Huertas also was my PhD student at UCL, so I am somewhat conflicted about this paper.

Firstly how does the algorithm perform? I don’t fully understand how the deep convolutional neural network works, and in fact maybe nobody really does, but the algorithm itself apparently does! It clearly classifies some mimics together. For instance H. erato phyllis is reasonably near H. melpomene nanna and H. melpomene burchelli in Fig. 1A, which is expected because they are usually classified as co-mimics. I assume that the Euclidean “phenotypic distance” referred to in this figure is measured in 64-dimensional space using the algorithm’s classification of each specimen.  But H. erato venustus (https://butterfliesofamerica.com/L/heliconius_erato_venustus.htm) is classified by the algorithm a long way from its common co-mimic in Bolivia H. melpomene penelope (see: http://media.api.aucklandmuseum.com/id/media/v/576002?rendering=original.jpg for a series of the pure subspecies). For some reason penelope is not called a mimic according to the colour coding in Fig. 1, for reasons I don’t understand. And penelope (no. 28) and four other numbered subspecies are completely missed from Table 1, for reasons that are not explained. I am wondering if the Natural History Museum just happens not to have a good collection of pure penelope, and that’s why we have this apparent screw up. It was mentioned in the methods that there was only one “pure” penelope, and maybe it happened to be one of the obvious hybrids in the type series in the Natural History Museum (https://butterfliesofamerica.com/L/t/Heliconius_melpomene_penelope_a.htm). Also, Heliconius melpomene vulcanus is mis-classified to be phenotypically close to H. m. melpomene and H. erato hydara both of which lack a yellow hindwing bar that vulcanus has on the underside, and penelope which is rayed. The authors say that this is because the blue iridescence of H. melpomene vulcanus is reduced compared to the true comimic from Western Colombia, H. erato venus (p. 3). This is true, although this may also be due to the use of photographs taken in artificial light rather than under natural sunlit conditions. Some Heliconius colours, particularly iridescence, are particularly hard to render photographically.

Table 1 itself also shows that penelope groups fairly closely with H. melpomene burchelli and nanna, but that H. erato phyllis is not classified together with these two, but instead with Heliconius erato petiverana from Mexico. In sum, the algorithm, after being trained on 1500 images, does a reasonably good job of classifying the remaining 968 images to subspecies with 86% accuracy. Interestingly, some of the principal component axes (3 and 4) are apparently also able to distinguish H. erato and H. melpomene (Fig. 2F), suggesting that some useful phylogenetic information, as well as mimicry, is detected by the algorithm.

Overall, I’m reasonably impressed with the algorithm’s performance, although it seems only to reach a not-so good taxonomists’ level thus far: a good human taxonomist will still beat it. Deep Convolutional Neural Network (ButterflyNet) is not yet the Deep Blue of taxonomy! But this is the first time I believe that such an extensive classification of this nature has been done by machine learning, and so this represents a considerable achievement for this paper and these authors.

Next, let’s consider the evidence for the authors’ argument for coevolution in Müllerian mimicry. Readers will probably be aware that Müllerian mimicry occurs between species that are both generally rejected by predators, and it is classified as a mutualism because both partners in the mimicry ring benefit. Mimicry evolves because each species benefits from the association due to mortality during predator learning; each species is sharing the costs of educating predators. On the other hand, Batesian mimicry is the case where an edible species evolves to mimic a poisonous species. In this case, the relation is parasitic, because a pleasant experience with an edible mimic may induce a predator to attack the model. The alternative is one-sided “advergent” mimicry (Brower & Brower 1972), whereby a mimic converges to an unpalatable model, but the model does not respond by evolving towards the mimic. Advergent mimicry is expected in parasitic Batesian mimicry, while Müllerian mimicry is a mutualism, and most people imagine that all mutualisms involve coevolution.

First we need some history. Müllerian mimicry has two special features.

First, Müller’s paper was indeed “evolution’s oldest mathematical model” (Müller 1879). Müller was a maths teacher at the college at Desterro, Brazil as well as a correspondent of Darwin and a major naturalist who documented the local fauna and flora. Müller suggested that predators probably learned to avoid unplatable species after killing a certain number of these per year. If two unpalatable prey species shared the same colour pattern so that they were indistinguishable to the predators, then they would each lose fewer individuals killed during the process of learning, making this a mutualism. We expect the rarer species to gain most of the association. Müller showed that each species gains a proportional advantage by becoming an indistinguishable mimic given by the inverse square of the relative abundance. For example, if a species has a tenth of the abundance of its comimic, it gains 100x the fitness benefit from the mimicry. The same will apply to the degree of unpalatability; measured as the reduction in the number killed, unpalatability and abundance combine to reduce predation in the same way (Mallet 2001). Thus, the benefits of Müllerian mimicry will typically be very one-sided unless abundance and unpalatability are closely balanced.

Second, there’s another wrinkle. John R.G. Turner (1977, 1988), citing a 1927 paper by A.J. Nicholson, pointed out that an abundant unpalatable species would typically not gain by mimicking a rarer unpalatable species, because local predators will be better trained by the most abundant (and/or most unpalatable) species. Therefore, a common or very unpalatable mimic has very little interest in converging on a rarer or less unpalatable species, even though, once it did occur, it would ultimately be beneficial for both species (albeit much reduced by the Müller inverse square law for the common species). Turner argued that most Müllerian mimicry would occur with rarer species approaching commoner species and gaining the evolutionary benefits of mimicry. In his “two-step” model, however, Turner did also propose a subsequent truly coevolutionary mechanism for Müllerian mimicry. Once the proto-mimic species overlapped the model species due to advergence in the first step of mimicry, and became somewhat indistinguishable in the perceptual consideration of the predators, then the second step, mutual convergence, became possible (Turner 1977, 1984, 1988).

Thus these two considerations argue that coevolution will occur perhaps rarely between Müllerian mimics, unless some lucky combination of density fluctuations or palatability details are met, at least until after the two species become so close as to be within a tight domain of protection by the most common species.

What is the evidence for coevolution among Heliconius co-mimics in nature? My own PhD supervisor, Larry Gilbert, had suggested that it was clear that normally, H. melpomene adverged to H. erato, but he argued that some evidence suggested that the reverse could also be true. In Central America, H. melpomene rosina has a broad yellow hindwing band. In contrast, H. erato petiverana from Mexico, and H. erato forms southward to northeastern Costa Rica also have narrow yellow hindwing bands. Heliconius melpomene is a southern species in Central America, and enters Nicaragua but is not known from further north. Gilbert suggested that although the prevailing direction of mimicry was melpomene -> erato, nevertheless in the case of the hindwing bars, the broadening of the yellow hindwing bar to the south of the H. erato distribution is due to convergent mimicry with the broader bands of H. melpomene (Gilbert 1983). I disputed that. Heliconius erato may have diverged in northern populations to produce narrow yellow bars, but since it did not occur there, H. melpomene would not have been able to follow this trend in the north. In contrast, the main mimicry force on H. melpomene in the south would be to adopt the broader hindwing bars of the local H. erato. Thus the apparent spatial coincidence of H. melpomene rosina and H. erato forms with broad yellow hindwing bars is readily explained by mimicry, but not necessarily by means of coevolution and mutual convergence.

In my own paper I concluded that the null hypothesis for coevolution had not been effectively rejected, and that most indications suggested H. melpomene was largely an advergent mimic of H. erato rather than the other way round. This was evidenced by the generally greater abundance, more widespread geographic distribution, and neater colour patterns of the latter – H. melpomene, although often an extremely accurate mimic, tends to have fuzzier or more variable colour patterns and, together with close sister species H. cydno and H. timareta, mimics a variety of other species or subspecies in the Heliconius erato-sara group of species.

In the new paper, Hoyal Cuthill et al. (2019) follow on from previous attempts (Hoyal Cuthill & Charleston 2012, 2015) to prove that coevolution did in fact occur between H. erato and H. melpomene. Some of their arguments are: (1) based on molecular dating, the subspecies of the two species are roughly the same age, as would be expected if they had co-diverged in different geographic localities, (2) that genealogical topologies of colour pattern genes are more similar to those of co-mimics than are genealogies based on a set of comparator genes more distantly linked to colour pattern genes, and (3) arguments similar to those of Gilbert (1983) about divergence of races of H. erato in the absence of H. melpomene. For instance, Hoyal Cuthill et al. (2019) argue that the narrow red forewing band of W. Ecuador H. erato cyrbia (see figure) is an example of advergence towards narrow-banded H. melpomene cythera (rather than the other way round), apparently because the adjacent Colombian H. melpomene vulcanus also displays a somewhat narrower forewing band than H. erato venus in this western part of South America.

However, for (3) most colour pattern features of H. melpomene cythera indicate fuzziness and variability, as expected if melpomene is approximating the tidy and extraordinarily striking pattern of H. e. cyrbia, rather than being mimicked. The already noted dullness of the blue iridescence of melpomene vulcanus compared with erato venus is cranked up to even greater pitch with melpomene cythera versus erato cyrbia. This suggests that H. melpomene evolutionarily attempts to, but finds it so far impossible follow the extreme flashiness of H. erato cyrbia, and here I mean this literally, if you’ve ever seen cyrbia flying in the sunlight.

I’m not convinced by (2) either, since although Hoyal Cuthill et al. picked “colour pattern genes”, these genes were not at the precise location of colour pattern loci, which are known to be largely in gene desert non-coding regions nearby; they mostly appear to be cis-regulatory elements that control the effector genes. Phylogenetic topologies based on these genes are also similar to topologies based on unlinked loci. I remain also unconvinced by (1), in part because it is circumstantial evidence (same age does not equal coevolution), and in part because we don’t really know how to age subspecies via molecular genetic data given the abundant gene flow between subspecies at their hybrid zones (Nadeau et al. 2012).

The discussion ends with a hypothetical model of how some colour pattern traits might recombine across mutualists so that novel traits can evolve in both species as a result of mutual coevolution and convergence. I agree that this would be true if coevolution was the case, but first I’d need to be convinced that coevolution did occur. For instance, a novel trait for Heliconius erato/melpomene mimicry in H. e. cyrbia is the white hindwing fringe checked with black rays, which does not occur in any other race of this species. Heliconius melpomene also has a version of this novel trait in subspecies cythera, but just knowing that does not make it clear which species first invented it or whether it represents a combination due to mutual convergence.

Overall, this is a fascinating and complicated paper. It achieves for the first time a machine learning classification of the mimicry patterns in Heliconius erato and H. melpomene. But I believe it does not yet prove the case for coevolution between these two iconic co-mimics. 

References

Brower, L.P., & Brower, J.V.Z. 1972. Parallelism, convergence, divergence, and the new concept of advergence in the evolution of mimicry. Transactions of the Connecticut Academy of Arts and Sciences 44:57-67

Gilbert, L.E. 1983. Coevolution and mimicry, Pages 263-281 in D.J. Futuyma, ed. Sunderland, Mass., Sinauer Associates

Hoyal Cuthill, J., & Charleston, M. 2012. Phylogenetic codivergence supports coevolution of mimetic Heliconius butterflies. PLoS One 7:e36464

Hoyal Cuthill, J.F., & Charleston, M. 2015. Wing patterning genes and coevolution of Müllerian mimicry in Heliconius butterflies: support from phylogeography, cophylogeny, and divergence times. Evolution 69:3082-3096

Hoyal Cuthill, J.F., Guttenberg, N., Ledger, S., Crowther, R., & Huertas, B. 2019. Deep learning on butterfly phenotypes tests evolution’s oldest mathematical model. Science Advances 5:eaaw4967. https://advances.sciencemag.org/content/advances/5/8/eaaw4967.full.pdf

Mallet, J. 2001. Causes and consequences of a lack of coevolution in Müllerian mimicry. Evolutionary Ecology 13:777-806

Müller, F. 1879. Ituna and Thyridia; a remarkable case of mimicry in butterflies. Proceedings of the Entomological Society of London 1879:xx-xxix

Nadeau, N.J., Whibley, A.C., Jones, R.T., Davey, J.W., Dasmahapatra, K.K., Baxter, S.W., Quail, M.A., ffrench-Constant, R.H., Blaxter, M., Mallet, J., & Jiggins, C. 2012. Genomic islands of divergence in hybridizing Heliconius butterflies identified by large-scale targeted sequencing. Philosophical Transactions of the Royal Society B: Biological Sciences 367:343-353