# Cellular Automaton Model of Pine Savanna Dynamics in Response to Fire and Hurricanes

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Savanna state as a function of hurricanes, fire, and an interaction between fire and vegetation on burn probability. Annual probability of a hurricane varies across the set {0, 0.05, 0.1, 0.2, 1}, which corresponds to a return period of {∞, 20, 10, 5, 1} years. Lightning strike intensity on the landscape is distributed as a Poisson random variable with lambda parameter equal to lightning strike intensity multiplied by the number of cells in the landscape. Lightning strike intensity varies across the set {0, 0.0004, 0.004, 0.04, 0.4}, which corresponds to an expectation of {0, 1, 10, 100, 1000} lightning strikes in a cell landscape. The grass-pine interaction term varies across the set {1, 100, 10000, 100000, 1000000}, which corresponds to a maximum odds ratio of the cell burning of {1, 100, 10 000, 100 000, 1 000 000} when the neighborhood of adjacent cells includes four cells of grass and pine.

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Contributed by: Brian Beckage and Jason Cawley (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Introduction: This Demonstration investigates the range of savanna vegetation patterns that can be achieved using a simple set of ecological rules embedded in a cellular automaton model. Pine savanna communities contain pine trees within a grassland matrix. The savanna is gradually invaded by hardwood trees in the absence of disturbance, eventually becoming a closed hardwood forest. Frequent disturbance can bound the system in an open grassland or pine savanna state. Savanna dynamics are modeled using a two-dimensional cellular automaton that incorporates intrinsic processes of dispersal, growth, and succession as well as extrinsic fire and hurricane disturbances. Ecosystem dynamics are explored in response to hurricanes, fire, and interactions between fire and vegetation.

Results: A set of simple ecological rules can reproduce the patterns observed in pine savannas of the southeastern U.S. The model illustrates the potential importance of fire and hurricane disturbance in bounding these communities away from a closed forest in either a savanna or grassland state. An interaction between fire and grass-pine vegetation can facilitate the maintenance of savannas, while also leading to the spatial overdispersion characteristic of pine trees in southeastern savannas.

Conclusions: A simple set of ecological rules can recreate the complex patterns and dynamics observed in savanna vegetation of the southeastern U.S.

*Cells and landscape*: Each cell can be in a grass, pine, or hardwood tree state. Pine and hardwoods could be either in a juvenile ('young') or mature ('adult') state: survivorship in hurricanes and fires varies across these age classes. A landscape of cells is simulated for 100 years from three initial landscape states: grassland savanna, pine woodland, and hardwood forest. Final landscape state is simulated in response to lightning intensity, hurricane frequency, and grass-pine interactions on fire probability. Parameters that describe cell transitions are described in the following.

*Model parameters*:
Annual probability of cell transition (without disturbance) from grass to pine is 0.03, from grass to hardwoods is 0.01, and from pine to hardwoods is 0.02.

Dispersal distance for grass is 1 cell, for pine is 4 cells, and for hardwoods is 1 cell. Burn probability for grass is 0.4, for young pine is 0.1, for adult pine is 0.1, for young hardwoods is 0.05, and for adult hardwoods is 0.05. Survival probability in fire for grass is 1, for young pine is 0.2, for adult pine is 0.8, for young hardwoods is 0.05, and for adult hardwoods is 0.1. Survival probability in hurricane for grass is 1, for young pine is 1, for adult pine is 0.2, for young hardwoods is 1, and for adult hardwoods is 0.2.

Lightning strike intensity: The number of lightning strikes on the landscape is distributed as a Poisson random variable with lambda parameter equal to lightning strike intensity multiplied by the number of cells in the landscape. Lightning strike intensity varies across the set {0, 0.0004, 0.004, 0.04, 0.4}, which corresponds to an expectation of {0, 1, 10, 100, 1000} lightning strikes in a cell landscape. Annual probability of a hurricane is {0, 0.05, 0.1, 0.2, 1}, which corresponds to a return period of {∞, 20, 10, 5, 1} years. Grass-pine interaction on burn probability: The interaction term varies over {1, 100, 10000, 100000, 1000000}, which corresponds to a maximum odds ratio of the cell burning of {1, 100, 10 000, 100 000, 1 000 000} when the neighborhood of adjacent cells includes four cells of grass and pine. For example, if a cell has a baseline probability of burning of 0.1, the g-p interaction term is 1,000, and the neighborhood consists of four cells of grass and four cells of pine, then the adjusted probability of the cell burning is approximately 0.99. If the neighborhood only includes 1 cell of grass (with 4 cells of pine), then the adjusted probability of the cell burning is 0.38. The probability of the cell burning is also adjusted for the number of neighboring cells that are burning: if four or more adjacent cells have burned, then the odds ratio of the focal cell burning is 1.5. Thus, if the baseline probability of a cell burning is 0.1, and between 4 and 8 neighboring cells are burning, then the adjusted burn probability is 0.14.

The initial condition for the simulation is approximately equal: grass (0.34), pine (0.32), and hardwoods (0.34) cells randomly assigned to the landscape.

Snapshot 1: lightning intensity increased to 0.0004; final state is hardwood forest

Snapshot 2: hurricane probability increased to 0.05; final state is mixed woodland forest

Snapshot 3: grass-pine interaction on fire probability increased to 100; final state is pine savanna forest