The shape of ecological communities: from pollinators to Purple Martins

Ecological systems are increasingly at risk. At the same time, we have more data describing these systems than ever before. Mathematicians can respond by making insights from these datasets accessible to researchers, citizen scientists, and others. We show how mathematical analysis of the shape of an ecological community generates both actionable information and new questions. This work focuses on the analysis of interactions in plant-pollinator communities and explores the detection of aggregations of swallows using weather surveillance radar.

Animal pollinators are crucial for biodiversity and agriculture. There are many
available datasets which record plant-pollinator interactions. In these interactions, the plant provides a resource to the pollinator, and the pollinator provides a resource to the plant. Resource use can be naturally represented using a topological object called a simplicial complex. We build on foundations of previous work on foraging graphs and simplicial complexes with an emphasis on topological persistence and new data. We analyze a small dataset collected at the University of Delaware and more comprehensive data from around the H.J. Andrews Experimental Forest in Oregon. We frequently encounter nontrivial topological features, and discuss the significance of these findings.

We introduce RoostRingSearch, a Python tool developed in collaboration with the University of Delaware Aeroecology Lab. RoostRingSearch uses weather surveillance radar data to search for roost ring features created by large groups of swallows leaving their communal roosting sites. Our algorithm is interpretable with few parameter choices. We discuss preliminary results using data from radar stations in Delaware and Michigan and recommend next steps for improved detection.