Modelling Casuarina junghuhniana dispersal in Tengger sea of sands of Bromo Tengger Semeru National Park using cellular automata

Abstract

The growing of population of a pioneer species may show a unique behavior. Casuarina junghuhniana is reported as a pioneer species, this is because of its tolerance to adverse environment and transform it to become inhabitable for other organism. A comprehensive method involving field observation, the use of mathematical model and computation to understand plants behavior still needs to be developed. This paper is attempting to show a method to build a model for showing unique dispersal behavior of Casuarina junghuhniana. A relatively straightforward use of Fisher’s reaction diffusion equation, cellular automata based modeling and programming can show behavior easier to understand on a grid space. Some assumption must be used to represent the C. junghuhniana dispersal. As it is known that C. junghuhniana can reproduce both vegetatively and generatively, and both were assumed to have different dispersal behavior. Vegetative reproduction using shoots emerging from roots has pattern to spread close to each other. While generative reproduction by seeds which is lightweight has possibility spread further with the help of wind. The total model area of 1km 2 was divided into 300 × 300 cells which represents 1 km 2 area. Cellular automata apply the same rule to each cell and the result was observed from the pattern of cells interaction. A simple program was developed using Python with Jupyter Notebook an interactive computing environment. The number of iteration was limited before observed simulation reached one of area boundaries. The simulation running time was greatly reduced using Graphical Processing Unit (GPU) parallel processing. NUMBA was used as an interface between python and Compute Unified Device Architecture (CUDA), the GPU programming API. The simulation showed behavior of the trees spread downward along the slope. The wind direction simulation with additional data from wind rose available from internet was also demonstrated in the simulation. Modeling dispersal with influence from wind showed more sporadic pattern at further distance from originating parents cluster. The trees in the simulation showed clusters in dispersal pattern when rely more on generative reproduction. When the trees rely on vegetative reproduction by roots shoots, the population showed more like continuous cover. When concerning real 3 dimensional aspect, this simulation still can not distinguish vertical (z axis) aspect. It means two points would be seen as close to each other although they actually have far vertical distance. At this stage, the simulation has not yet been optimized to easily convert input from the wind rose. The wind information still needs to be written as code into the program.