The Cook Book

Recipe for the week of January 15 - 21

CAM8 hits the road: EcoMachines at SFI

Our CAM8 mixmaster has been basking in the bright sun and 60 degree temperatures of New Mexico while attending a workshop on ecological modeling at the Santa Fe Institute. This week's soup shows SFI's new home on Hyde Park Road. I will testify to the blue skies, but cannot speak to the significance of the strangely attractive cosmic TV antennae. For the record, we reproduce the schedule of the workshop and abstracts of the invited talks below.


January 13-16, 1996
Santa Fe Institute
Santa Fe, New Mexico

Sponsored by SFI, with additional funding from the National Science Foundation



1:00 - 2:00
Levin: Evolution in structured environments

2:15 - 3:15
Kinzig: Selection of Microorganisms in Spatially Heterogeneous Environments
& Implications for Plant Access to Nitrogen


3:45 - 4:45
Durrett: When is Space Important in Modelling?



9:15 - 10:15
Ray: Natural Evolution in the Digital Medium - not a model

10:45 - 11:45
Reynolds: Behavior Models in Animation and Games


Options, subject to interest and self-transport, with approximate cost, are:

Bandelier National Monument: 16th century cliff dwellings ($5)
Bradbury Science Museum: history of the Los Alamos Lab ($2)
Santa Fe Detours: guided walking tour of town ($10)
Santa Fe School of Cooking: a class on tapas ($42.50)
A Santa Fe Art Museum exhibit: to be announced ($5)
NFC Title Game: margaritas might assuage the Pack's demise (??)
Read your email at SFI!: how pathetic... (free)

La Tertulia
416 Agua Fria, (505) 988-2769
( Cash bar )



9:15 - 10:15
Gerhardt & Schuster: Cellular Automata -
mathematical amusements or efficient tools of science?

10:45 - 11:45
Boerlijst: Selfstructuring - a substrate for evolution


1:00 - 2:00
Caswell, Etter & Hill: Cellular Automaton Models for
Ecological Interactions in Patchy Environments

2:15 - 3:15
Kapral: Fluctuations, Oscillations and Patterns in Biochemical Systems


3:45 - 4:45
Fisch, Griffeath, Evans & Klopfer: The CAM8 as an EcoMachine -
some preliminary experiments

SHOW & TELL with Pizza



9:00 - 10:00
Langton: The Swarm Simulation System

10:15 - 11:15
Kauffmann: Coevolution to the "Edge of Chaos"? -
tentative evidence for a general attractor



Selfstructuring - a substrate for evolution
Maarten Boerlijst

In the study of evolution selfstructuring and evolutionary processes are themes that are usually studied separately. In this talk we demonstrate that spatial selfstructuring can profoundly change the outcome of evolutionary processes; for instance, positive selection for "altruistic" features becomes possible. We study various systems, ranging from abstract models for the evolution of cooperation, to hypercycle models for pre-biotic evolution, ecological models for predator-prey interactions, and models for aggregation in the slime mould Dictyostelium discoideum.
We show that spatial selfstructuring does not only change the population dynamics, but it can also change the direction of selection. Furthermore, we often observe selection towards a phase transition in the spatial pattern. We argue that evolution can use such selfstructuring patterns as a valuable source of information for creating new possibilities for life. Once a selfstructuring pattern is present it can "trap" the evolutionary dynamics in that they become subordinate to the dynamics of the newly emerged pattern. To consider selfstructuring patterns as "constraints" is, however, in our opinion a gross underestimation of the creative and guiding power of selfstructuring phenomena in the evolution of life.

Cellular Automaton Models for Ecological Interactions in Patchy Environments
Hal Caswell, Ron Etter, and Mark Hill

Cellular automaton (CA) models for ecological processes come in two varieties: those in which the units at each point of the underlying lattice are individuals, and those in which they are patches of habitat. Individual-based CA models can follow individuals in a Lagrangian fashion, whereas the patch-based models take an Eulerian approach. This talk will report on some of our work on patch-based models. The construction of these models depends on a partitioning of the phase space into discrete regions (e.g., presence-absence), and reducing the dynamics to a set of transition rules. In our models, these transition rules are nonlinear, discrete-time Markov chains. Because the models describe patches, in which multiple species may maintain populations, ecological interactions appear in the transition rules within patches, rather than in the interaction of adjacent patches. We will present some results for competition, predator-prey interactions, and the effects of habitat fragmentation on population persistence.

When is Space Important in Modelling?
Rick Durrett

We will answer the question in the title by considering three systems that model the interaction of (1) two strains of the barley yellow dwarf virus, (2) two strains of E. coli, one which produces colicin and one that is sensitive to it, (3) two genotypes in a hybrid zone.

Cellular Automata - mathematical amusements or efficient tools of science?
Martin Gerhardt and Heike Schuster

They were born in the 50's by John von Neumann, awakened to LIFE by Conway, and experienced their childhood with the help of computers in the 80's, serving mostly as nice "pattern makers" and amusing toys for scientists. Nowadays, cellular automata have more and more grown up to serious simulation tools for modelling natural systems, unifying the advantages of efficient computation and an intuitively accessible approach for the complex mechanisms of self-organization in decentralized systems.
One of the best examples of this development can be found in excitable media - ranging from the chemical Belousov-Zhabotinsky reaction to life-threatening arrythmia of the human heart. By providing not only qualitatively, but also quantitatively reliable results, cellular automata open up new perspectives for future simulation of natural systems.

The CAM8 as an EcoMachine - some preliminary experiments
Robert Fisch, David Griffeath, Kellie Evans, and Eric Klopfer

We will demonstrate the CAM8 cellular automaton machine, designed and developed by Norm Margolus at MIT, as a simulation tool for biomathematical prototypes. Simple experiments will be presented to illustrate phase separation, nonlinear growth, complex self-organization along the phase boundaries of a several-dimesnional parameter space, and some density-dependent multi-species predator-prey models.

Coevolution to the "Edge of Chaos"? - tentative evidence for a general attractor
Stuart Kauffman

The metaphor of evolution on a "fitness landscape" reaches back at least to Sewall Wright in 1932. In a coevolutionary process, most commonly modeled in terms of evolutionary game theory as introduced by Maynard Smith in 1973, the set of strategies of an organism consists in its set of genotypes. The payoff to each organism is a function of its current strategy and the strategy of its coevoltionary partners. If each agent can only make "local moves" in its strategy space, for example, changing by single mutation variants, then each agent can be thought of as evolving on a fitness landscape that may be persistently deformed by the adaptive moves of other agents. Two regimes generically exist in such systems: 1) An ordered regime exists where each agent reaches a local peak in its fitness landscape consistent with the peaks attained by its coevolving partners. This is a "local Nash" equilibrium and an analogue to Maynard Smith's "evolutionary stable strategies". 2) A chaotic or disordered regime exists where agents keep "hill climbing" on ever deforming landscapes. This is the analogue of the "Red Queen" regime.
A coevolutionary process, therefore, depends upon the ruggedness of the fitness landscapes each agent explores, and how richly coupled landscapes are with a few or many other ecosystem "neighbors". These couplings govern how dramatically each agent's landscape deforms due to the adaptive moves of other agents.
I will discuss recent results based on a spin-glass family (the NK family) of coupled rugged fitness landscapes, where the agents are able: 1) to evolve ON their deforming landscapes; 2) to evolve the very ruggedness of their own landscapes; 3) to invade one another's niches and thereby drive the invaded player "extinct" while "speciating" a copy of the invader if it is fitter than the invaded player. By mechanism 3) players with "good" landscape ruggedness are replicators, carrying "good landscape" structures with them.
Our results show that in such model ecosystems, as if by an invisible hand, each agent (species) evolves the ruggedness of its own fitness landscape for its own advantage such that the mean fitness is sharply increased (maximized?), the probability of extinction is sharply decreased (minimized?), yet a power law distribution of avalanches of small and large extinction and speciation events propagate through the ecosystem. These model results fit the current best, but still questionable, estimates of the distribution of sizes of extinction events in the Record, and the life time distributions of Genera. The same results fit extinction avalanche distributions in "Tierra". And the same model seems to fit qualitatively to economic concepts concerning Schumpeterian "gales of creative destruction" and firm life-time distributions. Thus, the model suggests a general attractor for coevolving complex systems in the biosphere and econosphere.
Reference: At Home in the Universe. Oxford University Press, 1995.

Fluctuations, Oscillations and Patterns in Biochemical Systems
Raymond Kapral

The role of internal fluctuations on reaction-diffusion dynamics will be described. The emphasis will be on the character of the spatial and temporal dynamics in systems with small populations of reactive species, such as reactions occurring in single cells or even population dynamics where the numbers of individual species is not large. Questions concerning the applicability of macroscopic reaction-diffusion models and the effects of fluctuations on reaction rates and pattern formation processes will be addressed.
Lattice-gas cellular automaton models will be used to investigate these questions. A lattice-gas model whose mean field limit is the FitzHugh-Nagumo equation will be described and used to illustrate fluctuation effects on pattern formation resulting from front propagation and instability. Lattice gas models for systems whose mean field limit yields chaotic dynamics will also be discussed.

Selection of Microorganisms in Spatially Heterogeneous Environments
& Implications for Plant Access to Nitrogen

Ann Kinzig

Microorganisms can create spatial heterogeneities in the soil system and engineer favorable nitrogen and carbon environments for themselves. Simulations show that these self-created heterogeneities can lead to selection of microbial types differing from those found in a homogeneous environment. Moreover, plant access to nitrogen is frequently increased due to selection of mutualistic microorganisms in this heterogeneous environment, and plants can evolve strategies to exploit the heterogeneities and increase population densities of favorable microbial types.

The Swarm Simulation System
Chris Langton

Swarm is a general purpose simulation package for the investigation of concurrent, distributed systems: systems in which hundreds or thousands of autonomous agents interact with one another and with a dynamically changing environment. Swarm provides general purpose utilities for designing, implementing, running, and analyzing such multi-agent systems.
I'll talk about the architecture of Swarm and give examples of applications in ecology, economics, and other domains.

Evolution in structured environments
Simon Levin

It will be shown by example that the evolution of a wide variety of phenotypic traits of ecological importance can occur only in a spatially structured environment. Examples will be given of altruistic behavior, such as prudent predation, reduced parasitic virulence and reduced exploitation rates, as well as of spiteful behavior such as allelopathy. Interacting particle systems will serve as the mathematical tool of choice, and methods will be introduced for analysis and scaling.

Natural Evolution in the Digital Medium - not a model
Tom Ray

Life on Earth is the product of evolution by natural selection operating in the medium of carbon chemistry. However, in theory, the process of evolution is neither limited to occuring on the Earth, nor in carbon chemistry. Just as it may occur on other planets, it may also operate in other media, such as the medium of digital computation. And just as evolution on other planets is not a model of life on Earth, nor is natural evolution in the digital medium.

Behavior Models in Animation and Games
Craig Reynolds

This talk will review some simple models of volition and behavior, particularly related to the path a simulated creature steers through its world. Examples will include systems constructed by hand, such as the Boids model (of flocking, herding, and schooling) and a behavioral model of hockey players. Also included will be behavioral models constructed by evolutionary computation, such as for corridor following and for the game of tag.

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Last modified: January 11, 1996 by Kimberly Bodelson

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