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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA


Kerensa Alley

Class of 2008


Kerensa Alley is a PhD student in the Department of Plant Biology at the University of Vermont. Her research interests primarily relate to understanding the distribution and abundance of plant species and the composition and dynamics of plant communities. Her approach is to develop models of ecological patterns and processes that are testable using data from natural communities.

Project: Aggregate Growth with Resource Limitations and Abundance Thresholds

This project is an investigation of how the geometry and extent of growth of a living "aggregate" depend on resource density and on living-neighbor and resource-availability thresholds. Aggregate growth models have traditionally been used to model tumor growth, but by incorporating resource dependency should be extendable to the growth of sessile populations and communities (e.g. lichens or forest within savanna).

Growth in these models begins with a single "living" cell, and new cells are born sequentially in randomly chosen locations that have the necessary conditions for birth. In the most general sense, the requirements for the birth of a cell are 1) the cell is not already alive, 2) there is at least one living cell in the cell's neighborhood, and 3) there are sufficient "resources" in the cell's neighborhood. Resources (black cells) are randomly distributed on the grid and remain fixed throughout a simulation. The parameters to be varied in this study include the allowed number of neighboring living cells, the amount of resources locally available, the average density of resources, and the presence or absence of resource density gradients.

Favorite Radius 3/2 Rule

Rule 10089

I chose Rule 10089 because it displays two types of complex spatial patterns that are of great interest to ecologists.

1) The presence of an abrupt transition between two phases in the CA. Abrupt transitions in vegetation types often occur along smooth environmental gradients, or even without environmental factors playing a direct role (self organization). Understanding the mechanisms behind these types of transitions will help ecologists understand what limits the distribution of species.

2) The presence of irregular and "randomly" distributed patches of regular "motif" patterns. This rule demonstrates a particularly large diversity of patch types. An important goal of ecology is to understand the mechanisms driving the patchy distribution of plant species.