Historical and emerging practices in ecological topology

“Ecological topology” has recently been highlighted as a “frontier of ecology,” yet the term “ecological topology” only occasionally appears in the literature. On the other hand, the term “topology” appears in a variety of publications in this and other ecologically oriented journals, but its use is varied and applied to a wide cross-section of ecological problems. These variable usages suggest that topology does not have a common meaning to all ecologists. Part of this confusion results from the fact that topological ways of seeing nature are both formally derived from mathematical origins, and informally derived from non-mathematical conceptualizations. Interestingly, parallels occur between both mathematically originated and conceptually originated topology with respect to object-oriented, network topologies (formally derived from Eulerian mathematics), and field-oriented, manifold topologies (formally derived from Poincaréian mathematics). Topological ways of understanding nature and addressing both theoretical and applied problems have served ecology well in the past, but this approach will be improved with a better, more unified understanding among ecologists as to the variety of meanings found and practiced in the science.