Andrew Sugden & Jim Mallet with air-freight bound for the Oxford Guajira Research Expedition (OGRE), June 1975. The photographer and third member of the expedition was Peter Knappett.
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 <email@example.com> 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
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