Finslerian diffusions in forest ecology: Retrospective and open problems

Abstract

Based on ideas of botanist, J.L. Harper and ecologist, F.E. Clements, the mathematical theory known as Analytical Trophodynamics (AT) and its stochastic extension (SAT) are recounted historically and with details. Finslerian geometry and Finslerian noise are fundamental to the applications made in Forest Ecology and several recent problems are discussed. The important role played by curvature of production space for Feynman-Kac solutions to Cauchy initial boundary value problems is stressed. Several open problems are described.