Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Harmonie Hanley - University of the Virgin Islands
Co-Author(s): Hairol Breton, University of the Virgin Islands, USVI
Coral reefs are essential to both aquatic life and man. They provide habitats to many marine organisms, protect coastlines from damaging effects, and are great for the economy. Sadly, due to many environmental factors, reefs in the Caribbean are experiencing bleaching events making them more susceptible to diseases such as the white plague. Fortunately, a cellular automata can be used to assist in addressing this issue. A cellular automata (CA) consists of a collection of cells arranged in a grid, such that each cell changes its state as time progresses. In past years, they’ve been used to model many real world phenomena such as the spread of forest fires, the growth of crystals, and even the evolution of various biological lifeforms. With the usage of a cellular automata, scientists will now be able to determine whether or not disease among corals will continue to spread. Additionally, they will be able to even predict what coral reefs will look like in the future with the use of accurate data. For our CA, we created two versions that modeled the spread of a random distribution of corals in varying states. In our first version, we created a very simple model which included the following: the Von Neumann Neighborhood consisting of only four neighbors which could be either healthy or diseased, a neighborhood with an area of 1m2, and four simple rules that determined the outcome of the initial cell. From this model we observed that 17% (percentage of diseased corals) is the ‘tipping point’ of whether the reef will remain relatively healthy or become sick all together. In our second cellular automata, our model became more complex. We incorporated 8 neighbors using the Moore Neighborhood which included neighbors that can now be either in a healthy, diseased, or empty/dead state, as well as six rules that governed the state of the corals as the number of steps progressed. In this model, we saw that the new ‘tipping point’ was around 30% to 35% (percentage of diseased corals). The results from both cellular automatas are very informative. They gave us an accurate representation of what coral reefs may look like as time progressed, making these models stable guides in helping scientists improve the results of the reefs in the Caribbean. In the future, our goal is to make a third version in which we will create probabilistic rules to observe geometric patterns in the CA, look for multiple tipping points, and conscientiously look for different time periods where scientists’ intervention, would create the best outcomes for our reefs.
Not SubmittedFunder Acknowledgement(s): I would like to thank Dr. Marilyn Brandt for the information and data provided for the coral reefs. I would also like to thank Dr. Robert Stolz for the support and helping me learn Matlab to construct the cellular automata. Funding was provided by an NSF/ HBCU- UP grant #1137472.
Faculty Advisor: Robert Stolz, rstolz@uvi.edu
Role: While conducting this research, I helped in creating the rules for both models, became familiar with the program MatLab in order to contribute suggestions in creating the code, and also aid in creating various graphs that described the 'tipping points' and the overall outcomes of both cellular automatas.