This is just a brief note to let everyone know I'm spending the summer at IIASA, a scientific policy research institute located just outside of Vienna. IIASA focus on systems analysis of global problems such as climate change, land use, demographic changes, public health, ecology, and energy. They don't seem to use the phrase "complex systems" much, but they're clearly talking about the same thing.
I happen to be one of 53 lucky graduate students to be selected for this year's Young Scholars Summer Program, meaning I get to paid to live in Vienna and do research. Can't really complain about that. Tomorrow I get to hear mini-presentations on everyone's research proposals, which should be very interesting. My own project will be on the long term, gradual evolution of cooperation in spatially structured populations, using a mathematical framework known as adaptive dynamics.
I'm expecting to learn a lot here, and I'll share as much as I can with you readers. Looking forward to it!
Congratulations and good luck! Is there somewhere that we can see what a list of the research proposals? They look like interesting stuff.
ReplyDeleteEnjoy Vienna!
ReplyDeleteI saw a recent paper in Nature, "Adaptation and the evolution of parasite virulence in a connected world", which looks like the sort of thing a knowledgeable evolutionary dynamics researcher should write a technical comment about: their "islands" are connected by a fixed, complete graph, for example, so that each island is one hop from every other and this situation never changes. To me, this seems like it'd drastically curtail the possibilities for spatial dispersal; the authors' conclusions might not hold for, say, islands on a grid network.
@sami-Actually, yes! A pdf containing biosketches and research abstracts of all the participants can be found here; my own abstract appears on page 7.
ReplyDelete@blake-thanks for the paper---it actually connects very well to a project someone else here is working on.
You're right that the connected graph model they use limits the dispersal effects. However, their project was simply to show that spatial structure promotes reduced virulence, which they do. For a less-connected graph I would expect the same results to hold, only more so.
The tone of the paper kind of bugs me. It seems to fall into the kin-selection-versus-group-selection-why-can't-you-realize-you-are-talking-about-the-same-thing trap that was frustrating us a year ago.
I think having a static island structure kind of misses the point about the spatial grid ecology models: in those, "islands" (defined by where hosts live) arise and die out dynamically. The islands are emergent, to use a stylish word. I can't help but suspect that that'll make the math harder; the analogue for their equation for change of fitness in terms of change of virulence might not be very tractable.
ReplyDeleteLast year, we discussed the Lion and van Baalen paper cited in their reference list, "Self-structuring in spatial evolutionary ecology". Lion and van Baalen argue that kin and group selection are two verbalizations of the same mathematics, an equivalence which in that case I'm happy to accept. However, they define the success of an invading mutant genotype by the eigenvalues of a dynamical system linearized around a fixed point. (The details of the matrix relating dp/dt to p are horrendous and depend on the specific version of the model, but that's roughly the gist of it.) The positivity of an eigenvalue can tell you whether an injected gene is successful over a few generations, but not whether that strain suffers a Malthusian catastrophe in two hundred generations. A technique which depends on linearization is blind to effects which happen outside the linear regime, or so it seems to me.
(A physicist's analogy: Lagrangian and Hamiltonian mechanics are provably equivalent. However, if your Lagrangian or your Hamiltonian is nonrelativistic, the predictions of your model will diverge from experiment when speeds approach that of light, no matter which formalism you choose.)
One of my side projects now is to investigate this line of argument and see if "temporally extended phenotypes" leading to localized Malthusian catastrophes really are outside the eigenvector/eigenvalue description. If they are, then I think the case would be stronger that such phenomena are poorly served by either verbalization of the standard mathematics. This requires getting code running — I've implemented a model of islands connected in a topology of the user's choosing. On a grid topology, when the carrying capacity of each island is set to 1, this reduces to the predator/prey models we'd seen before (with a slightly different parameterization, which I don't think really matters). On a complete-graph topology with the carrying capacity set to an integer > 1, it becomes the model from the Nature paper. My code is running, but I still have to make sure it's doing what I expect it to do, and I ought to figure out what the analogues are of the various conditional probabilities defined in the literature where Lion and van Baalen's paper lives.
O frabjous day. . . .
One thing to keep in mind is that the Lion/Van Baalen article was talking about a Prisoner's Dilemma games--which itself maybe thought of as trying to incorporate some of the nonlinear behavior that arises from predator/prey dynamics (i.e. a defector may be thought of as an organism that over-depletes its environment; such a defector would grow in the short term but decline as the environment degrades)
ReplyDeleteThat said, they of course make highly simplifying assumptions for the sake of doing math. Not only do they linearize, but they also use pair approximation, a simplification that effectively erases all aspects of the spatial topology except for the degrees of the nodes. I think these two simplifications are probably connected, in that the interesting nonlinear behavior likely comes from the "higher" topological features of space. But simulation, as you are doing, is probably the only way to capture these effects.
I'd be eager to see what you have on this when I'm back in Boston.
For reference, here are the two models I'll be incorporating in my summer research:
Traulsen & Nowak - "Evolution of cooperation by multilevel selection."
Here the model is similar to that in the Nature paper you linked to: semi-isolated groups with some limited migration in between. But they conceptualize these as social groups rather than island communities.
Ohtsuki et al. "A simple rule for the evolution of cooperation on graphs and social networks."
This one uses a spatial, graph-theoretic model, but again, pair approximation is needed to obtain mathematical results.