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The most dangerous aspect of being trapped in the digital library’s virtual basement stacks is that you don’t want to come out.

Simon A. Levin (1992), “The Problem of Pattern and Scale in Ecology” Ecology 73, 6: pp. 1943–67. [JSTOR] [PDF].

It is argued that the problem of pattern and scale is the central problem in ecology, unifying population biology and ecosystems science, and marrying basic and applied ecology. Applied challenges, such as the prediction of the ecological causes and consequences of global climate change, require the interfacing of phenomena that occur on very different scales of space, time, and ecological organization. Furthermore, there is no single natural scale at which ecological phenomena should be studied; systems generally show characteristic variability on a range of spatial, temporal, and organizational scales. The observer imposes a perceptual bias, a filter through which the system is viewed. This has fundamental evolutionary significance, since every organism is an “observer” of the environment, and life history adaptations such as dispersal and dormancy alter the perceptual scales of the species, and the observed variability. It likewise has fundamental significance for our own study of ecological systems, since the patterns that are unique to any range of scales will have unique causes and biological consequences. The key to prediction and understanding lies in the elucidation of mechanisms underlying observed patterns. Typically, these mechanisms operate at different scales than those on which the patterns are observed; in some cases, the patterns must be understood as emerging form the collective behaviors of large ensembles of smaller scale units. In other cases, the pattern is imposed by larger scale constraints. Examination of such phenomena requires the study of how pattern and variability change with the scale of description, and the development of laws for simplification, aggregation, and scaling. Examples are given from the marine and terrestrial literatures.

Gyorgy Szabo, Gabor Fath (2007), “Evolutionary games on graphs” Physics Reports 446, 4-6: 97–216. [DOI] [arXiv].

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

Sébastien Lion, Minus van Baalen (2007), “From Infanticide to Parental Care: Why Spatial Structure Can Help Adults Be Good Parents” American Naturalist 170: E26–E46. [HTML] [PDF].

We investigate the evolution of parental care and cannibalism in a spatially structured population where adults can either help or kill juveniles in their neighborhood. We show that spatial structure can reverse the selective pressures on adult behavior, leading to the evolution of parental care, whereas the nonspatial model predicts that cannibalism is the sole evolutionary outcome. Our analysis emphasizes that evolution of such spatially structured populations is best understood at the level of the cluster of invading mutants, and we define invasion fitness as the growth rate of that cluster. We derive an analytical expression for the selective pressures on the trait and show that relatedness and Hamilton’s rule are recovered as emergent properties of the spatial ecological dynamics. When adults can also help other adults, the benefits to each class of recipients are weighted by the class reproductive value, a result consistent with that of other models of kin selection. Finally, we advocate a different approach to moment equations and argue that even though the development of moment closure approximations is a necessary line of research, much-needed ecological and evolutionary insight can be gained by studying the unclosed moment equations.

Sébastien Lion, Minus van Baalen (2008), “Self-structuring in spatial evolutionary ecology” Ecology Letters 11, 3: 277–295. [HTML] [PDF].

Spatial self-structuring has been a focus of recent interest among evolutionary ecologists. We review recent developments in the study of the interplay between spatial self-structuring and evolution. We first discuss the relative merits of the various theoretical approaches to spatial modelling in ecology. Second, we synthesize the main theoretical studies of the evolution of cooperation in spatially structured populations. We show that population viscosity is generally beneficial to cooperation, because cooperators can reap additional benefits from being clustered. A similar mechanism can explain the evolution of honest communication and of reduced virulence in host–parasite interactions. We also discuss some recent innovative empirical results that test these theories. Third, we show the relevance of these results to the general field of evolutionary ecology. An important conclusion is that kin selection is the main process that drives evolution of cooperation in viscous populations. Many results of kin selection theory can be recovered as emergent properties of spatial ecological dynamics. We discuss the implications of these results for the study of multilevel selection and evolutionary transitions. We conclude by sketching some perspectives for future research, with a particular emphasis on the topics of evolutionary branching, criticality, spatial fluctuations and experimental tests of theoretical predictions.

This concludes your information overload for the day.


  1. An important conclusion is that kin selection is the main process that drives evolution of cooperation in viscous populations.

    Told ya! ;)

  2. The content of the paper is more interesting than the abstract:

    Evolution of cooperation in viscous populations can be interpreted using three main arguments: kin selection, group selection (clusters of altruists do better) or network reciprocity. We argue that these three arguments are in a large measure equivalent. This can be shown either with a top–down approach, by showing that the results of evolutionary graph theory can be retrieved as special cases of a general kin selection model (Rousset 2004; Grafen 2007; Lehmann et al. 2007b; Taylor et al. 2007a); or with a bottom–up approach, by showing that relatedness and Hamilton’s rule can be recovered as emergent properties of the ecological spatial dynamics (van Baalen & Rand 1998; Lion & van Baalen 2007).

    In the latter case, which the authors consider “more intuitive,” what van Baalen and company do is treat a population as a dynamical system and linearize around the fixed point of a genetically homogeneous population (say, one comprised entirely of selfish individuals). Hamilton’s rule emerges as a positivity criterion for the eigenvalue which governs the dynamics near that fixed point, and the eigenvector corresponding to that eigenvalue characterizes the cluster of invading individuals (e.g., altruistic mutants entering a selfish population). Such a cluster becomes what I believe would be called a “vehicle of selection,” although the authors call it a “unit of selection”; either way, fitness as measured by invasion rate is an inclusive property of the cluster, not the individual.

    The limitation of this approach, I think, is that it’s restricted to phase-space regions near fixed points, which inherently limits the timescales it can address. If you have a “tragedy of the commons” situation where excessively voracious predators or overly virulent pathogens are depleting the resources they need to survive, this damage to their local environment might not become noticeable until several generations have passed. Van Baalen and Rand’s method will show that, yes, a voracious mutant can grow into a cluster and start invading the placid population, but I’m betting that it will miss that cluster consuming all its resources and dying out — that phenomenon is just outside the scope of its analysis.

    (The details of their math seem almost intentionally obfuscated, but I think this would enter as a nonlinearity in the time-evolution equation when the local mutant densities no longer equilibrate.)

  3. The content of the paper is more interesting than the abstract

    Hey! I did read the paper, too! ;)

    I can’t really evaluate the math here, but it’s nice to see that this paper also makes it clear that Hamilton’s original models already break the “mean field assumption”.

  4. Yeah. I haven’t dug all the way back, but I have seen remarks in “spatial ecology” books that mention 1930s work by Fisher which, at least in retrospect, was looking at deviations from mean-field predictions. See Levin and Pacala (1997).

    Pacala. . . Pacala. . . sounds like a witch’s name!

    God, I need to get out more.

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