Summary
In 2022, I published a ‘perspective’ piece in Evolutionary Ecology, on a hypothetical function of colouration in butterflies, and in particular in Heliconius and co-mimics.
This piece contended that:
- Heliconius butterflies are most unlikely to be aposematic,
- The similarities between species could be explained otherwise, specifically as the mimicry of intraspecific signals whose function is to attract conspecifics into night roost aggregations.
In a recent rejoinder, Dr Mallet is ‘astonished’ that an independent researcher working from literature ‘seems to have persuaded the editors and reviewers of an academic journal that his hypothesis might overturn consensus, a century and a half old, on warning colour and Müllerian mimicry’.
This characterisation is incorrect: no actual hypothesis of Müllerian mimicry in Heliconius exists, so there is no theory to overturn; the description of the complex similarities in colours is not a theory but a habit inherited from a defunct theory that rested on group selection (Müller 1879). Elsewhere, Dr Mallet describes Müllerian mimicry in Heliconius as “a venerable one hundred and sixty-year old tradition of study of a topic” (Mallet 2024); indeed, Mallet refers again and again to the age of the idea, which shows, and to its intellectual pedigree, mentioning repeatedly Poulton and Wallace: the tradition is venerable indeed. Where Dr Mallet errs is in considering that pedigree as relevant.
Dr Mallet and I both consider that extraordinary claims require extraordinary evidence. We differ in how we apply this principle: Dr Mallet considers that it would require extraordinaty evidence to overturn this idea (actually a minor upset, but Dr Mallet is a Heliconius specialist, it feels ‘Copernican’ to him) when I assessed that in Heliconius, aposematism and Müllerian mimicry would be extraordinary, that this idea is supported neither by a hypothetical mechanism, nor by any evidence, and should be rejected for now.
Given that rejection, I considered open-mindedly what could explain the puzzling rings of similarities in Heliconius, and proposed a new hypothesis, which makes easily testable predictions.
Dr Mallet’s expertise as a field biologist and Heliconius specialist is not in question. However, the theoretical conditions that allow the maintenance of traits are not his area of expertise, and he appears unaware that the conditions that would enable the maintenance of aposematism (and Müllerian mimicry) are not met in Heliconius and its co-mimics. Dr Mallet’s intuition cannot resolve such theoretical impossibilities, and his theoretical objections are mistaken and incompatible with contemporary evolutionary theory.
The hypothesis proposed in Mouy (2022) makes clear and testable predictions. As a London-based theoretician, I will not undertake field testing in Central or South America. Dr Mallet considers the hypothesis false and reminded us that good science starts by disproving false hypotheses. He is a field biologist with the capacity, and I hope he will exert his ingenuity at disproving it with contradictory observations, and would be the first to recommend abandoning the hypothesis if he does.
Does a theory of aposematism exist in Heliconius?
Mouy (2022) states that none of the mechanisms hypothesised to stabilise aposematism are applicable in Heliconius; not that none has been demonstrated to apply, but that all demonstrably do not apply. This is a simple claim, which is justified in Mouy (2022), and which would be easy to refute – it just takes one plausible mechanism – and which Dr Mallet does not rebut. There is simply no theory of aposematism in Heliconius.
This is not the central claim of Mouy but is important to set the context of why we need to explore alternatives.
Dr Mallet is a field biologist and is unaware of recent developments in theory, incorrectly crediting Mouy’s work with novelty regarding the difficulty of maintaining aposematism. Fisher (1930) demonstrated a clear awareness of the problem, although the definitive analysis was not provided until Leimar et al. (1986), as cited by Mouy. This problem is frequently mentioned in introductions and abstracts of recent research[1]. Dr Mallet also shows little awareness of signalling theory and describes the proposed definition of signal[2] (not aposematism) as obscure, although, as indicated in Mouy (2022), it is a standard definition, marginally modified for the context, derived from a graduate-level textbook (Maynard Smith and Harper 2003).
The major theoretical problem of aposematism is its evolutionary stability[3]: aposematism seeks to explain the function of colours, that is, how colours are maintained in populations as warning signals to predators; this concept of biological function, what a trait ‘is for’, is central to evolutionary biology and widely relied upon (Garson 2019).
Not being able to explain how colours maintain themselves in populations as warning signals means we cannot call them aposematic, and this is a major, unresolved problem in Heliconius butterflies: as set out by Mouy (2022), all proposed hypotheses of mechanisms potentially stabilising aposematism can be rejected: there is simply no hypothesis of aposematism in Heliconius butterflies, and calling them aposematic is merely a statement of faith that these difficulties may be resolved one day.
Dr Mallet is oblivious to that problem and points to ample evidence that birds avoid these butterflies; unfortunately, this is not the question – birds will learn to recognise inedible prey regardless of how they look – and while the quicker learning of avoidance of bright colours was shown in laboratory experiments, it can only evidence the function of colours under group selection. Oblivious to that problem, Mallet assumes that Mouy really meant evolution and points out that Mouy did not put forward a rejection of the possibility of evolution (when it does reject all possibilities of maintenance). Obviously, it does not, as how traits evolved is irrelevant.
Weirdly, Mallet states that no evidence is offered after citing Mouy’s ‘None [of the potential mechanisms] are observed in Heliconius.’, although what follows offers precisely that.
Contrary to Mallet’s claim, aposematism is genuinely a problem, and finding ideas that could stabilise aposematism is genuinely a concern. This problem is common to all butterflies, as no mechanism proposed to apply appears workable, and is not apparent only to theoreticians, but also to field biologists such as Dr Kassarov, who dissented from the notion that ‘aposematism [is] a valid concept in predator-prey relationships between birds and butterflies” (Kassarov 1999, 2003). Hypotheses to explain aposematism are still regularly put forward and quietly abandoned – the latest is ‘taste-and-reject’[4] – and we do not even have a hypothesis on how butterflies can be aposematic.
The notion that Heliconius are aposematic is not a proper scientific hypothesis (a causal mechanism), merely a general direction or research. That direction is supported by the bright colours and toxicity of Heliconius: toxicity would explain brightness. This would make no sense if toxic butterflies were not more likely to be brightly coloured than non-toxic ones[5] – but this is not even the case, or at least, as reviewed in Mouy, one study contradicts the correlation, and none supports it – it works better in other insects.
In summary, Mallet offers no substantial rebuttal to the claim in Mouy (2022) that aposematism is an implausible explanation of the colouration of Heliconius, because such colourations could not be maintained for that function. I disagree with Dr Mallet’s statement that such a rejection would be a major upset; this cannot be an upset since there is not even a theory to reject and no scientific publication in the past forty years has stated that a hypothesis of aposematism in Heliconius demonstrably exists. The fact is just upsetting to some, who choose to ignore it.
Does a theory of Müllerian mimicry exist in Heliconius?
Mouy (2022) states that no hypothesis exists on the mechanisms that could stabilise the multiple overlapping mimicry rings of Heliconius butterflies and co-mimics. Again, Mouy does not claim that no hypothesis has been demonstrated, but that all have been conclusively refuted.
Again, this is a simple claim that would be easy to refute. Dr Mallet does not refute it, but contends that evidence overwhelmingly supports Müllerian mimicry – although he cannot point to an actual theory that would be supported.
Heliconius butterflies would not be famous if they did not form complex and overlapping rings of similarities – habitually described as mimicry rings, and precisely as Müllerian mimicry rings. Mouy (2022) concurs that these are mimicry rings, but does not accept that these mimicry rings have daytime predators as selective agents, or that the mechanisms through which they evolved or are somewhat similar to Müllerian mimicry.
The concept of predator-mediated mimicry[6] is not challenged in Mouy (2022); there are well-proven cases of such mimicry. Most vertebrates and some invertebrates, both predators and herbivores, will learn to recognise food from non-food. To a typical predator, non-food is a broad category, and many potential prey attempt to disguise themselves as non-food. Predator-mediated mimicry is the most common form of mimicry, but not the only, and observing similarities proves neither mimicry – colours can converge under close selective pressures – nor, obviously, predator-mediated mimicry.
Mallet emphasises, as sole evidence for predator-mediated mimicry in Heliconius and co-mimics, that these butterflies are inedible, a long-documented fact. This is beyond debate, but is not evidence of mimicry, and there are severe, well-documented, and unresolved difficulties with the notion that the convergence between these butterflies is caused by mimicry.
For daytime predators to be the selective agents for such overlapping mimicry rings, we predators and butterflies to segregate into separate communities. This is not found: butterflies do not segregate at all by day when birds could attack them, and birds segregate very weakly at best (Merrill et al. 2015; Mouy 2022). Only one alternative to segregated predator-prey communities has been proposed, a combination of a hypothesised predator behaviour (‘optimal sampling strategy’) and some population structure, fails; however, it ‘does not explain the existence of the coexisting mimicry rings we observe in nature’ (Aubier & Sherratt, 2015). The authors conclude that ‘more work should be done to understand how they can be generated and maintained’, without offering any research direction: the field does not even have a standing hypothesis of how Müllerian mimicry is possible.
It seems curious that Mallet writes that ‘very little effort seems to have been expended by Mouy (2022) to rebut the perceived consensus’: indeed, no effort was needed, as this is not new. The idea worked under Müller (1879) because group selection was an acceptable method of reasoning (Mallet 2010); however, it has not been valid since the rejection of group selection.
We need a revision.
Mallet writes: ‘In science, no hypothesis is actually proved. Rather, we tend to disprove alternatives, or at least to show why the alternative hypotheses are unlikely.’. I fully subscribe to this. As shown above, aposematism and mimicry in Heliconius are extremely unlikely – and I generously treat these ideas as hypotheses; they are not even that, mere general research directions, or, as Mallet aptly described ‘traditions of study’.
This tradition of study could be justified if it looks like a proper theory could come out of it, and
it appeared that such a theory would have some explanatory value. However, no theory lurks around the corner, and there is no potential explanatory value of aposematism in butterflies.
Aposematism and Müllerian mimicry were correct explanations when they rested on the premise of group selection. These premises have been rejected conclusively over half a century ago, are research now attempts to retrofit a theory on these old ideas that do not work anymore.
Mallet (2024) alleges that a severe revision or rejection of aposematism and Müllerian mimicry in Heliconius would be a ‘major upset in evolutionary biology’. The major upset came some time ago, with Fisher and Hamilton’s gene-based approach of evolution. It so happens that all the consequences of this major upset have not been drawn yet. If it were invented today, the idea that Heliconius butterflies form Müllerian mimicry rings would be never pass peer review. We shouldn’t be sentimental about these old ideas, although be may be about the geniuses that produced them.
In summary, within the modern paradigm, no theory allows us to understand how Heliconius could be aposematic or the salient characteristic of their mimicry rings, and there is no evidence that either constitutes an adaptation to signal towards daytime predators. It is weird to keep considering Heliconius as a prime example of both.
Novel claims of Mouy (2022)
As described above, there is no novelty in the claims that aposematism and Müllerian mimicry are implausible and unsupported in Heliconius. It so happens that some scientists hope for a solution to these problems and continue to treat these ideas as if they were valid, but the ideas are not supported, and no mechanistic explanation of either exists.
However, there are some new claims:
- The function of colouration in butterflies is poorly understood, and the currently proposed explanations leave significant gaps, including bright species for which no explanation is available.
Such species, Mouy suggested, may comprise some mimicry rings in two widespread, non-toxic Eurasian butterfly families: the blues and sulphurs.
As discussed above and in Mouy (2022), there is no extant hypothesis of aposematism in butterflies, so all colours currently explained by aposematism should be considered as poorly understood. However, even assuming the issue could be resolved – unlikely – there are many other bright species for which no explanation has been offered. The purpose of Mouy (2022) is to offer an additional explanation, and to assess whether is appears consistent with observations.
Mallet does not dispute that some colours of butterflies are unexplained.
- One of the functions of bright colours in butterflies is to signal towards conspecifics to attract them and reduce predatory pressure from the dilution of predation.
Contrary to Mallet’s statement, it is not suggested that colours “evolved ‘purely as an aggregation signal’”; that quotation described the model, not the hypothesis: isolating a potential function for assessment is a common practice among theoreticians, of which Dr Mallet appears unaware.
Mouy does not claim to displace all ideas on the colouration of a wide range of insects; instead, Mouy offers a supplementary theory, and we need new explanations.
- The complex mimicry rings of Heliconius could be explained by colours constituting an aggregation signal towards conspecifics and the mimicry of this signal.
This is the central new claim: the novel idea above could explain the puzzling mimicry rings observed in Heliconius, and in particular, this hypothesis is highly consistent with the co-mimics’ tendency to roost at similar heights and occasionally together.
A substantive criticisms of Mallet (2024)
Dr Mallet’s knowledge of Heliconius is unquestionably greater than mine, and I acknowledge that expertise with respect. I can only regret, however, that one anonymous reviewer of Mouy (2022) – evidently also a Heliconius specialist – chose to focus on theory rather than observations, where their expertise could have provided constructive criticism.
In the proposedhypothesis, the primary function of colouration is to attract co-roosters.
As Dr Mallet points out, ‘we expect unprofitable prey (including aposematic prey) to be more prone to aggregate than profitable prey’, and palatable species could benefit from dilution thanks to the satiation of predators. Weirdly, Dr Mallet does not realise that it is the point: these animals do have an incentive to aggregate, and a greater incentive in gathering along similar and unpalatable individuals, hence the mimicry.
Mallet then makes a substantive point, also made in Mouy, which Mallet cites here: Heliconius are extremely similar, which seems to require that selective agents for such a level of similarity can discriminate between closely resembling individuals, and birds have a considerably better visual acuity than butterflies.
Butterflies would indeed be unlikely to tell a good from a poor mimic from a distance of more than a foot so that poor mimics would initially attract them. The question is whether, once at a short distance, allowing discrimination, they react to poor mimics. This is a valid and testable question (even if butterflies could not discriminate between close morphs, the hypothesis would be salvageable[7]).
Mallet goes on to discuss his studies of mate choice in Heliconius and suggests, towards the end, that mating cues were co-opted ‘to facilitate aggregation behaviour.’ I suppose the point he obliquely makes is that studies of mate choice are relevant for assessing the proposed hypothesis. Indeed, and if butterflies can discriminate in the context of mating, it sounds plausible that they do in the context of aggregations.
However, as shown above, the problem lies in the existence of polymorphism and a multiple mimicry ring. We know that sexual selection can drive polymorphism along geographic radiation, for instance in frogs (Yang et al. 2019), and that could well be the case in Heliconius, although Dr Mallet does not appear to support this idea (Mallet and Gilbert 1995) – Mallet is confused when indicating that I ignore these observations, since Mouy never discusses divergence, but convergence, and does not discuss sexual signals. While sexual selection cannot drive mimicry between species, let alone complex overlapping mimicry rings, aggregation signals can, and, as I show in the original paper, apparently do. Dr Mallet’s statement that ‘intraspecific preferences do sometimes make use of differences in mimetic colour patterns’ shows the hypothesis to be plausible.
Besides being a plausible explanation of the colouration and convergence of colours in Heliconius, this hypothesis can plausibly explain divergences, which Dr Mallet considers unexplained, and the recurrent evolution of overlapping mimicry rings. A ‘magic trait’ is a trait subject to both diversifying disruptive selection and assortative mating, which could produce polymorphism, radiation, and speciation (Rueffler et al. 2006; Servedio et al. 2011).
The proposed selection for attracting co-roosting mates would constitute a disruptive selection as it requires one signal per roosting habitat, and roosting habitats will change with localities: Heliconius would indeed ‘exploits a continuously varying resource’ of roosting sites, as required to cause diversification (Rueffler et al. 2006). As noted by Mallet, the colour and patterns of Heliconius’s wings are subject to assortative mating – such colours are not required to keep the species apart, which he points out they do not.
A short reply to methodological criticisms of Mouy (2022)
Besides the remarks to which I replied above, Dr Mallet makes a few notes on the methods in Mouy.
- Reliance on crowd-sourced photographs
Mouy (2022) tests the plausibility of the idea that butterflies’ colours serve to attract one another by assessing if they do attract one another. This is based on the analysis of a large amount of enthusiast photographs, almost entirely in the United Kingdom[8], Mallet (2024) apparently resents the intrusion of amateurs (and independent scientists) and describes these as ‘some blurry photos on a British butterfly amateur website’; I let readers judge that the photographs published on UK Butterflies are all of excellent quality and correctly classified.
Mallet points to resource patchiness as explaining aggregations, but this entirely fails to address the finding: bright butterflies are 8 times more likely to be found in groups than dull ones. Incidentally, in many cases, aggregations (e.g., collective puddling) are manifestly not the result of resource scarcity; many butterflies may congregate densely on a small fraction of a river bank when plenty of other access are available.
- Modelling itself
Mallet (2024) correctly identifies the only claim of the model: In some circumstances, brighter colours can be beneficial if they attract both predators and prey. This model assumes some dilution effect, which is expected to be present in all species, albeit stronger in toxic species, as mentioned in Mouy (2022) and Mallet (2024). Unfortunately, noting that some of the assumptions are similar to those of the models of aposematism, Mallet (2024) then criticises the model for not being a model of aposematism[9] and searches in vain for a “recognisable model of populations or their evolution over time”, which is indeed not present.
Dr Mallet is clearly unaware of game-theoretic modelling: it is banal not to model populations explicitly, and it is habitual to single out one particular type of interaction in models, ignoring others, which says nothing about the existence of those other interactions.
Dr Mallet also apparently overlooked the caption of Figure 2 and is befuddled by negative changes in predation risk (having probably overlooked the term ‘change’). Unsurprisingly, the extensive explanations in the appendix, which attracted no criticism for clarity, are unclear to Dr Mallet, who did not consider it appropriate to reach out to me for clarifications.
Conclusion
Mallet expresses his astonishment that my research was published in an academic publication. In the ensuing confusion, Dr Mallet read statements that were not part of the research and failed to understand those that were.
Indeed, it is not common for a non-academic to publish in a reputable scientific journal a piece challenging a ‘venerable one hundred and sixty-year old tradition of study’ – and since an additional five – which should alert Mallet to the potential intrinsic merit of the pieces and brittleness of his belief system.
The ideas defended by Mallet (2024), regarding aposematism and Müllerian mimicry in Heliconius butterflies, are not scientific hypotheses; they ceased to be hypotheses when the theoretical framework underlying them – group selection – was superseded by a gene-based view of evolution and evolutionary game theory. This last subject is almost mathematics, and I cannot fault Dr Mallet for being unaware of the fine points of this speciality. However, the repeated mentions of the antiquity of these ideas, and of their excellent pedigree, show an unwelcome sentimentality that apparently prevents Dr Mallet from letting these ideas go.
Whether the alternative hypothesis I am offering has any merit is moot: if we had only one theory and abandoned it, we would only be following the excellent example of Darwin, who, on several occasions, gave up hypotheses without having a replacement, despite the anxiety this caused him (Loehle 1987).
I do not think, however, that this alternative should be buried already: Dr Mallet’s long reply addresses none of the substantive points made in Mouy (2022). Dr Mallet’s hostility to my hypothesis is most welcome, as he will certainly now put his ingenuity as a field scientist to work and attempt to disprove it.
Acknowledgement: I am grateful to Dr Mallet for publishing his commentary on my original work, as I had invited him to do, and for offering me the opportunity to respond on Heliconius.org without editorial control.
Note: This post was hastily written in February 2024 as a quick reply to Dr Mallet’s post and later edited for clarity and concision, with the last edit in November 2025.
References
Fisher R (1930) The Genetical Theory of Natural Selection. The Clarendon Press
Garson J (2019) What Biological Functions Are and Why They Matter, 1st edn. Cambridge University Press
Hämäläinen L, Thorogood R (2020) The signal detection problem of aposematic prey revisited: integrating prior social and personal experience. Phil Trans R Soc B 375:20190473. https://doi.org/10.1098/rstb.2019.0473
Kassarov L (1999) Are Birds Able To Taste And Reject Butterflies Based On “Beak Mark Tasting”? A Different Point Of View. Behav 136:965–981. https://doi.org/10.1163/156853999501676
Kassarov L (2003) Are Birds the Primary Selective Force Leading to Evolution of Mimicry and Aposematism in Butterflies? An Opposing Point of View. Behav 140:433–451. https://doi.org/10.1163/156853903322127922
Kitamura T, Imafuku M (2015) Behavioural mimicry in flight path of Batesian intraspecific polymorphic butterfly Papilio polytes. Proc R Soc B 282:20150483. https://doi.org/10.1098/rspb.2015.0483
Leimar O, Enquist M, Sillén-Tullberg B (1986) Evolutionary Stability of Aposematic Coloration and Prey Unprofitability: A Theoretical Analysis. The American Naturalist 128:469–490
Loehle C (1987) Hypothesis Testing in Ecology: Psychological Aspects and the Importance of Theory Maturation. The Quarterly Review of Biology 62:397–409. https://doi.org/10.1086/415619
Mallet J (2024) Colour patterns in Lepidoptera evolved mainly as signals to predators. Heliconius are indeed Müllerian mimics. Reply to Mouy (2022). In: Heliconius.org
Mallet J (2010) Group selection and the development of the biological species concept. Phil Trans R Soc B 365:1853–1863. https://doi.org/10.1098/rstb.2010.0040
Mallet J, Gilbert LE (1995) Why are there so many mimicry rings? Correlations between habitat, behaviour and mimicry in Heliconius butterflies. Biological Journal of the Linnean Society 55:159–180. https://doi.org/10.1111/j.1095-8312.1995.tb01057.x
Mallet J, Joron M (1999) Evolution of Diversity in Warning Color and Mimicry: Polymorphisms, Shifting Balance, and Speciation. Annu Rev Ecol Syst 30:201–233. https://doi.org/10.1146/annurev.ecolsys.30.1.201
Maynard Smith J, Harper DM (2003) Animal signals, Nouvelle éd. Oxford university press, Oxford
Merrill RM, Dasmahapatra KK, Davey JW, et al (2015) The diversification of Heliconius butterflies: what have we learned in 150 years? J of Evolutionary Biology 28:1417–1438. https://doi.org/10.1111/jeb.12672
Mouy H (2022) Colours as aggregation signals in Lepidoptera: Are Heliconius Müllerian mimics? Evolutionary Ecology 36:341–353. https://doi.org/10.1007/s10682-022-10183-8
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[1] As an example, the first line of the abstract of Hämäläinen and Thorogood (2020) states ‘Ever since Alfred R. Wallace suggested brightly coloured, toxic insects warn predators about their unprofitability, evolutionary biologists have searched for an explanation of how these aposematic prey evolve and are maintained in natural populations.’ .
[2] Mouy (2022): In the context of aposematism, a signal is defined as (derived from Smith & Harper, 2003): “A visible structure which alters predators behaviours, which evolved or failed to disappear because of that effect and which is effective because predators either evolved or learned a response to that signal.”
Compare with Maynard Smith and Harper (2003), page 3: “any act or structure which alters the behaviour of other organisms, which evolved because of that effect, and which is effective because the receiver’s response has also evolved”.
There are material differences. In particular, Mouy (2022) excludes acts, else, e.g., gazelle stotting would be an aposematic act, and the definition of aposematism would be even more haphazard than it already is. It also makes allowance for the signal receptor to have not evolved but learned to respond to the signal.
[3] A strategy is an ESS if it cannot be displaced by another strategy that would be initially rare.
In the case of a Heliconius erato with red patches on the wings, for instance, the red patch could be marginally smaller or marginally duller. Unless a marginally less bright individual would sustain come costs for that reduced signal, signalling will eventually collapse through the invasion of progressively weaker signals.
As outlined in Mouy (2022), all hypotheses put forward on how that collapse can be prevented can be rejected.
[4] Taste-and-reject proposes that the warning signals of aposematic butterflies is stable as birds, after catching a toxic butterfly, would reject it.
This hypothesis comes from a creative effort to find stabilising mechanisms (they are really a problem) and the observation (later shown to be unsound) that in museum collections, butterflies of species assumed to be inedible had more beak marks than those of other species. Until then, beak marks were used as a proxy for predatory pressure, so this, obviously didn’t reconcile well, as those ‘aposematic’ species should be under a much weaker pressure. Hence a motivated U-turn: beak mark became evidence of a reduced predatory pressure.
Kassarovs’ objections that colours are largely irrelevant received recent confirmatory evidence (Páez et al. 2021), and another showed mimicry in flight patterns not colours, also consistent with Kassarovs’ objections (Kitamura and Imafuku 2015). This last study engages with Kassarov’s arguments but the rebuttal is peculiarly ineffective: authors suggest that ‘aposematic coloration [may evolve] for protection against predation in the early morning’. That a study which is neither about colouration nor about aposematism dedicates a significant fraction of its discussion to defending aposematism and Müllerian mimicry against its own findings is very currious.
[5] Although aposematism does not require toxicity, only unprofitability, if toxicity was one cause of unprofitability among many, a correlation would still be found. Similarly, if we knew only who is smoking brand X of cigarettes, although brand X cigarettes are only one among many of lung cancer, we could find a very strong correlation between smoking brand X cigarettes and subsequently developing lung cancer. The existence of other brands of cigarettes would not affect correlation, unless everyone smoked one brand or another. But if all butterflies were defended, what woud be the point of signalling at all?
[6] I use ‘predator-mediated’ rather than ‘Batesian’ as many authors consider that ‘Batesian’ mimicry must be for aposematic signals, when predator-mediated mimicry can be of any colour or pattern, including cryptic.
[7] The most interesting characteristic of the Heliconius mimicry rings is their membership, and the weird overlaps in membership between groups of species depending on locality. For instance, in one locality, species {A, B, C} may form an obvious group, and {D, E, F} another group, while in another {A, B, D} and {C, E, F} look similar, and still in another place, it is {A, E, F} and {B, C, D}. This cannot be explained by predator-mediated mimicry. If mimicry membership could be explained, this would be a huge progress. As noted repeatedly, Heliconius butterflies and many of their co-mimics are unpalatable, and avian predators clearly have some awareness of their unpalatability and rarely attack these. If would, then, not seem absurd that, given mimicry rings which would have evolved as aggregation signals, further convergence would be selected for by avian predators and similarities improved.
[8] Hence, unlilely to show any heterospecific aggregation of American species, a defect pointed by Mallet (2024), but this was never the point.
[9] Mallet: “dilution effect is involved in all hypotheses of aposematism and Müllerian mimicry, as well as of aggregation under conditions of predation, this requires modelling frequency-dependent or “number-dependent” selection (Mallet and Joron 1999), both of which are conspicuously absent from the authors’ mathematical model”