*For abstracts, see below.
*

- Biodiversity
- Spatial evolution and host-pathogen systems
- Pattern formation
- Fractal geometry
- Digital physics

Erik M. Rauch, Mark M. Millonas and Dante R. Chialvo. Pattern
Formation and Functionality in Swarm Models. *Physics Letters A*
**207** 185-193 (1995). [html]
[postscript]
[pdf]

Erik M. Rauch and Mark M. Millonas. The Role of
Trans-membrane
Signal Transduction in Turing-type Cellular Pattern Formation. *Journal of
Theoretical
Biology* 226: 401-407 (2004). [pdf]

J. Asikainen, A. Aharony, B.B. Mandelbrot, E.M. Rauch, and J.-P.
Hovi.
Fractal geometry of
critical
Potts clusters. *
European Physical Journal B* 34: 479 (2003). [pdf]

Erik M. Rauch. Discrete,
Amorphous Physical Models. *International
Journal of Theoretical Physics* 42: 329-348 (2003).

M. A.M. de Aguiar, H. Sayama, E. M. Rauch, Y. Bar-Yam, and M.
Baranger. Stability
and Instability of Polymorphic Populations and the Role of Multiple
Breeding
Seasons in Phase III of Wright's Shifting Balance Theory. *Physical **Review E* 65:
031909
(2002). [pdf]

Erik M. Rauch, Hiroki Sayama and Yaneer Bar-Yam. The
relationship
between measures of fitness and time scale in evolution. *Physical Review Letters* 88:
228101
(2002). [pdf]

Erik M. Rauch, Hiroki Sayama and Yaneer Bar-Yam. Dynamics and
genealogy
of strains in spatially extended host-pathogen models. *Journal of
Theoretical
Biology* 221: 655-664 (2003). [pdf]

M.A.M. de Aguiar, E. M. Rauch, and Y. Bar-Yam. Mean-field approximation
to a
spatial host-pathogen model. *Physical
Review E* 67: 047102 (2003). [pdf]

M.A.M. de Aguiar, E. M. Rauch, and Y. Bar-Yam. Invasion and Extinction
in the
Mean Field Approximation for a Spatial Host-Pathogen Model. *Journal of
Statistical
Physics* 114: 1417-1451 (2004). [pdf]

Erik M. Rauch and Yaneer Bar-Yam. Theory
predicts the uneven distribution of genetic diversity within species.
Nature 431, 449-452 (2004).

Global efforts to conserve species have been strongly influenced by the heterogeneous distribution of species diversity across the Earth. This is manifest in conservation efforts focused on diversity hotspots. The conservation of genetic diversity within an individual species is an important factor in its survival in the face of environmental changes and disease. Here we show that diversity within species is also distributed unevenly. Using simple genealogical models, we show that genetic distinctiveness has a scale-free power-law distribution. This property implies that a disproportionate fraction of the diversity is concentrated in small sub-populations. It holds even when the population is well-mixed. Small groups are of such importance to overall population diversity that even without extrinsic perturbations, there are large fluctuations in diversity due to extinctions of these small groups. We also show that diversity can be geographically non-uniform, potentially including sharp boundaries between distantly related organisms, without extrinsic causes, such as barriers to gene flow or past migration events. We obtain these results by studying the fundamental scaling properties of genealogical trees. Our theoretical results agree with field data from global samples of Pseudomonas bacteria. Contrary to previous studies, our results imply that diversity loss due to severe extinction events is high and focusing conservation efforts on highly distinctive groups can save much of the diversity.

Erik M. Rauch, Hiroki Sayama and Yaneer
Bar-Yam. The
relationship
between measures of fitness and time scale in evolution. *Physical Review Letters* 88:
228101
(2002). [pdf]

Erik M. Rauch, Hiroki Sayama and Yaneer Bar-Yam. Dynamics and genealogy of strains in spatially extended host-pathogen models.

We examine the dynamics of evolution in a generic spatial model of a pathogen infecting a population of hosts, or an analogous predator-prey system. Previous studies of this model have found a range of interesting phenomena that differ from the well-mixed version. We extend these studies by examining the spatial and temporal dynamics of strains using genealogical tracing. When transmissibility can evolve by mutation, strains of intermediate transmissibility dominate even though high-transmissibility mutants have a short-term reproductive advantage. Mutant strains continually arise and grow rapidly for many generations but eventually go extinct before dominating the system. We find that, after a number of generations, the mutant pathogen characteristics strongly impact the spatial distribution of their local host environment, even when there are diverse types coexisting. Extinction is due to the depletion of susceptibles in the local environment of these mutant strains. Studies of spatial and genealogical relatedness reveal the self-organized spatial clustering of strains that enables their impact on the local environment. Thus, we find that selection acts against the high-transmissibility strains on long time-scales as a result of the feedback due to environmental change. Our study shows that averages over space or time should not be assumed to adequately describe the evolutionary dynamics of spatially distributed host-pathogen systems.

M.A.M. de Aguiar, E. M. Rauch, and Y. Bar-Yam. Mean-field approximation to a spatial host-pathogen model.

We study the mean-field approximation to a simple spatial host-pathogen model that has been shown to display interesting evolutionary properties. We show that previous derivations of the mean-field equations for this model are actually only low-density approximations to the true mean-field limit. We derive the correct equations and the corresponding equations including pair correlations. The process of invasion by a mutant type of pathogen is also discussed.

M.A.M. de Aguiar, E. M. Rauch, and Y. Bar-Yam. Invasion and Extinction in the Mean Field Approximation for a Spatial Host-Pathogen Model.

We derive the mean field equations of a simple spatial host-pathogen, or predator-prey, model that has been shown to display interesting evolutionary properties. We compare these equations, and the equations including pair-correlations, with the low-density approximations derived by other authors. We study the process of invasion by a mutant pathogen, both in the mean field and in the pair approximation, and discuss our results with respect to the spatial model. Both the mean field and pair correlation approximations do not capture the key spatial behaviors|the moderation of exploitation due to local extinctions, preventing the pathogen from causing its own extinction. However, the results provide important hints about the mechanism by which the local extinctions occur.

M. A.M. de Aguiar, H. Sayama, E. M. Rauch, Y. Bar-Yam, and M.
Baranger. Stability
and Instability of Polymorphic Populations and the Role of Multiple
Breeding
Seasons in Phase III of Wright's Shifting Balance Theory. *Physical **Review E* 65:
031909
(2002). [pdf]

Erik M. Rauch, Mark M. Millonas and Dante R.
Chialvo. Pattern
Formation and Functionality in Swarm Models. *Physics Letters A*
**207** 185-193 (1995). [html]
[postscript]
[pdf]

Erik M. Rauch and Mark M. Millonas. The Role of
Trans-membrane
Signal Transduction in Turing-type Cellular Pattern Formation. *Journal of
Theoretical
Biology* 226: 401-407 (2004). [pdf]

J. Asikainen, A. Aharony, B.B. Mandelbrot, E.M.
Rauch, and J.-P. Hovi.
Fractal geometry of
critical
Potts clusters. *
European Physical Journal B* 34: 479 (2003). [pdf]

Erik M. Rauch. Discrete,
Amorphous Physical Models. *International
Journal of Theoretical Physics* 42: 329-348 (2003).

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