Stay well, Riccardo!
I worried about Riccardo Papa, a Heliconius researcher at the University of Puerto Rico, so I wrote to him. His reply is below:
Hi Jim, Thank you for you very appreciated email. We are all safe but Puerto Rico is pretty much destroyed. Likewise the university. My lab is gone and I have lost the majority of my samples. No water, no electricity, no gasoline and long lines to go to the grocery. It looks like a post war scenario. Now we are dealing with the post hurricane problems. Well, I guess this is a new experience. Thank you again. Riccardo
On Sep 26, 2017, at 1:30 PM, James Mallet jmallet(at)oeb.harvard.edu wrote: Hi Riccardo, I just wanted to check that you guys are ok! How is the university after Maria? My very best wishes, Jim --
(Photo shared by permission: Keith Willmott)
Nope! Keith Willmott sent me this amazing picture in response to my query about sexually dimorphic mimicry. This is a mating pair of Oleria baizana (Nymphalidae: Ithomiini), in which males and females belong to different “transparent” Müllerian mimicry rings. See also Willmott & Mallet 2004 for some other examples of sexually dimorphic mimicry in the Ithomiini (in the online appendix).
First, the incomparable figure of genetic interactions in the forewing of Heliconius melpomene by John R. G. Turner in 1972 (Zoologica NY vol. 56: 125-155).
Here were my rather feebler efforts for the genetic interactions in the Tarapoto, Peru Heliconius hybrid zones (I remember pasting the lettering onto the drawings! — those were the days!): –
(from Mallet et al. 1990 Genetics 124:921-936)
Here’s some photos of the actual colour patterns in the Peru hybrid zones showing linkage and interactions:
And here’s Chris Jiggins et al. with the molecular loci involved in H. melpomene/cydno mimicry switches:
(From Jiggins et al. 2017 Phil Trans Roy Soc B 372:20150485).
Heliconius numata seems to be able to switch its entire colour pattern (including orange/brown optix patterns) by means of a series of polymorphic inversions in the cortex region:
Illustration of Heliconius numata dominance hierarchy at inversion forms near cortex gene. From Le Poul et al. 2014. Evolution of dominance mechanisms at a butterfly mimicry supergene. Nature Communications 5:5644).
You’ll notice that Chris Jiggins et al. show the red pattern markings shown as being due to action of optix, and the yellow/white pattern markings as being due to action of cortex. But this is highly simplified to make the points he wished to make about developmental gene co-option in that paper.
In Peru Heliconius erato seems to be able to switch its forewing yellow band on or off via action of the optix region (i.e. the DRy colour pattern locus in my own colour pattern diagram, see above). Chris Jiggins and Owen McMillan in the 1990s discovered that the yellow forewing band in himera/erato crosses was switched at the cortex locus, prompting me to look again at my Peru broods from the 1980s, and it is now clear to me that the cortex locus (Cr) also influenced the expression of yellow, explaining some fuzzy intermediate phenotypes in the forewing band in H. erato in those broods.
We also know that in H. melpomene there’s another colour pattern locus “M” that appears to be able to switch on yellow forewing bands recessively (Mallet 1989 Proc Roy Soc). M appears to be linked to the B/D chromosome and therefore to optix (Simon Baxter pers. comm.)! In contrast, the N locus at cortex switches on yellow dominantly (see the Turner 1972 diagram above). And in Turner’s crosses, B and D seem an awfully long way apart on the optix chromosome — they’re linked in repulsion with around 30% recombination rate between them. So are they both really regulators of optix?
I think it’s true to say that we don’t fully understand all of these gene interactions yet, and perhaps we won’t until the regulatory pathways leading to colour pattern expression have been better worked out.
Nick Patterson is currently on sabbatical at the Radcliffe Institute, Harvard. https://www.radcliffe.harvard.edu/news/in-news/man-who-breaks-codes
Thanks to everyone who came to the Heliconius meeting! There were 53 participants in the end (including 3 from Montpellier, who didn’t make it in person because of the strikes, but had a virtual presence through the wonders of teleconferencing). This included representatives from 16 different research organisations spanning 7 countries. It was great to hear about all the work that is going on, across quite a diversity of topics. The programme and abstracts are here if anyone missed the meeting or wants to refresh their memory.
Congratulations to the student talk prize winners:
1st Bruna Cama (University of York) – Genetic analysis of wing pattern and pheromone composition in two sister species of Heliconius butterflies
2nd Paul Jay (CNRS, Montpellier) – Supergene evolution favoured by the introgression of an inversion in Heliconius
The meeting had a distinctly European feel with especially strong links between the groups in the UK and France and it was suggested that future meetings should alternate between the Americas and Europe, with Montpellier proposed as the venue for 2 years time. However, it is sad to think that it might have been the last meeting to be held in a united Europe.
Why not teach ecology using the simpler Verhulst form of the logistic equation rather than the Gause-Witt form?
The Verhulst form for per capita population growth is:
Of course, it’s the same equation really, because K = r/α.
However, the simpler form above:
1) Is more historically correct. Verhulst, Lotka, and Volterra all introduced the first form; it was Pearl and then Gause who first popularized the r-K form. K was equated with “carrying capacity” only later, only after WWII, as far as I can tell. Today, the r-K form has come to seem intuitively correct, in spite of its many issues given below (in my paper I trace the history).
2) Makes it easier to understand the relation with Lotka-Volterra predation equations.
3) Makes clear why Andrewartha and Birch were insistent that “density – independent” factors control population density. In a sense they’re right; all the density independence is contained in r = (b-d), birth rate – death rate, since if you alter, say the density-independent death rate d, you alter the equilibrium r/α proportionately.
4) Explains “Levins’ Paradox:” that with the r-K formulation, N shoots up to +infinity in finite time given a negative r and N > K initially.
5) Simplifies understanding of the Gause-Witt isoclines in two-species competition, and explains why r is indeed involved in the stability of competitive interactions. The analysis is exactly the same, but about 1000x clearer, once you get used to it.
The simpler, historically correct Lotka-Volterra competition equations look like this:
Here is Fig. 2 from the paper cited below, showing the isoclines and equilibria:
The isoclines hit the N1 axis at r1/α11 (where α11 is the intraspecific competition coefficient, i.e. α in the single species equation above) and r2/α21, and the N2 axis at r2/α22 and r1/α12. Note, r1 and r2 are very much involved in competition stability, as they should be! (But aren’t using the Gause-Witt equations).
6) Clarifies the relationship of natural selection to competition. Natural selection is indeed competition within species. And constant-selection models commonly used in population genetics are simply equivalent to alterations of b or d between genotypes in r with constant α values.
7) Helps to re-unify evolution and population ecology; this work was started by Lotka and Volterra, but became very confused after WWII with ideas such as “r– and K-selection.”
8) Can demonstrate that the actual renewable resources produced in the environment will not in fact be completely used up at equilibrium. In other words, the actual “carrying capacity” is not equal to the equilibrium (r/α) density.
9) Can readily be derived from a consideration of a variety of considerations of consumption of limited renewable resources.
Many mathematical biologists have understood this issue all along (e.g. RA Fisher, FB Christiansen, N Barton), and others are increasingly drawn to this understanding now. However, this simplification has yet to enter any introductory textbook on ecology or evolution.
When I started out on this journey, I thought I was doing original research. Eventually, on sabbatical in 2008-9, I discovered Smouse’s little-cited paper (1976) in Am Nat and realized that everything I knew about the topic had been discovered again and again, and that my new understanding was doomed to be merely a kind of historical overview. Nonetheless I hope it is useful.
Instead of citing me, please do cite the people I cite! (And probably others I don’t know about?) We have here a case of poorly connected-up salami science; we (collectively, at least) understand this issue, but nobody has put it all together yet in our textbooks.
You could be the first to do so…
To read my detailed defense of these opinions, you can find my paper online:
Mallet, J. 2012. The struggle for existence: how the notion of carrying capacity, K, obscures the links between demography, Darwinian evolution and speciation. Evolutionary Ecology Research 14: 627-665. http://www.ucl.ac.uk/taxome/jim/pap/mallet_the_struggle_2012.pdf
Here is a rant that I have had on and off over the last few years, and a recent discussion in my own group has prompted me to post this on the blog, just to try the argument out on a slightly wider audience….
One approach to studying evolution is to focus on a single organism or group of organisms, and try to understand different facets of their biology, in order to understand processes that must be more widespread. Such a focus is absolutely necessary – we do not have the resources or time available to study all processes in all species, and a deep understanding of ecology, behaviour and genetics is needed to study processes such as speciation. So we need to study some taxa in great detail (and of course I think that the Heliconius butterflies are a great group in which to study adaptation and speciation). However I hate the term ‘model species’ for these taxa, and I don’t think that the term is helpful in evolutionary biology. The term ‘Model’ comes from the medical literature, where, for example, a ‘mouse model’ of diabetes would be an experimental procedure or strain of mice that has been developed to mimic the human disease. The ‘model’ is just that – a tractable, toy version of the real thing (this question of how useful such models actually are for developing disease treatments is a separate issue which I will not tackle here). We use the term in a similar way to describe mathematical models that are simplified versions of the real world, that can be used to infer general processes.
My problem is where the term has taken on a new meaning, to refer to a particular species in which biological processes are studied. The intended implication seems to be that whatever is discovered can be inferred to be more generally true across the tree of life. This approach has of course been rather extraordinarily successful in cellular biology, where basic cellular processes uncovered in the fruit fly have proven crucial in understanding cancer in humans, for example. But as evolutionary biologists surely we are interested in diversity, so the assumption that processes can be inferred from one group of organisms to many others seems deeply problematic to me.
Some of the processes that we uncover in one group of organisms will turn out to be rather unusual, whilst others will be more widely shared across many organisms. There are many examples that illustrate this, but one of my favourites is the circadian clock. This is a molecular mechanism that regulates the daily rhythm of animals. Studies in mice and fruit flies seemed to suggest that there were major differences in the way that the clock functioned between insects and vertebrates. However, when the circadian clock was studied in a butterfly, it was realised that in fact the fruit fly is unusual. The fruit fly has lost components of the clock, that are otherwise shared between mice and butterflies (Zhu et al., 2008). This suggests that most insects are probably much more like vertebrates in this particular aspect of their biology than was thought from studying the fruit fly.
So even for basic cellular processes that are shared across the animals, such as the circadian clock, we can be seriously misled by studying one or two ‘model’ species. This must be inherently more true of evolutionary processes such as speciation – where some of what we learn from one group of organisms will turn out to be generally true, while other processes will turn out to be unique. Whilst as biologists we certainly hope that we can draw general conclusions from our work, the reality is that some aspects will turn out to be rather arcane and specific. Only once we have studied many different kinds of organisms will the general patterns become clear. Of course it is this diversity of life that is the primary fascination of the evolutionary biologist, so it is best not to get too downhearted about this. Let’s celebrate the diversity of organisms being studied, rather than try to compete to be the best ‘model’ system.
Some people have argued that the term is so embedded, that perhaps we shouldn’t worry and live with it. But I think it is misleading, because it gives a false sense of security. We really need to go out and test whether our conclusions derived from one group of organisms are general to the wider diversity of life. We shouldn’t hide behind the term ‘model’ organism to give us a false sense of complacency about the generality of our findings.
Finally, many people have said that they like the term simply because it is useful as a handle to describe the systems that we study intensively, but actually it isn’t hard to avoid it and say more straightforwardly what you actually mean. So instead of ‘Heliconius is a model for the study of speciation‘, why not just say ‘speciation has been widely studied in Heliconius‘ – see it uses less words and states the case more succinctly…
Okay, rant over for the moment, just don’t get me started on ’emerging model systems’…
Zhu H, Sauman I, Yuan Q, Casselman A, Emery-Le M, Emery P, Reppert SM. 2008. Cryptochromes Define a Novel Circadian Clock Mechanism in Monarch Butterflies That May Underlie Sun Compass Navigation. PLoS Biol 6: e4.