Where Do They Go? A Geometric Seed Dispersal model

Abstract

Climate change forces plant species to migrate to other areas via seed dispersal, the process of seeds moving away from the parent plant. The objective of this study is to find a good geometric model of representation that allows us to answer the question: where do the seeds go?

The landscape is represented using a simple polygon with n vertices, and the initial source plants are modelled as a set of m sites. To model the influence of wind, we use a convex distance function based on a polygon with r vertices.

To answer queries such as `What region is covered in plants at a given time?', we use a Voronoi diagram. We prove fundamental properties and design novel algorithms to compute geodesic Voronoi diagrams under a convex distance function. We prove a time complexity of O(((n+m)*r)log((n+m)*r)log n). Our adaptation called the ``lazy approach'' improves that bound to O((n+m*r)log(n+m*r)log n).