The self-thinning rule and plant population modelling with resource constraints

Abstract

The Japan Agency for Marine-Earth Science and Technology contributed this challenge to the 2016 Mathematics-in-Industry New Zealand Study Group Workshop. It concerned implications of the self-thinning rule for modelling plant population characteristics via a partial differential equation governing the temporal evolution of the density distribution of plants of a particular size. The self-thinning rule is empirically observed for crowded populations under constrained resources. We investigate the theoretical consequences of a resource constraint on the partial differential equation of interest, and through numerical experiments reveal a surprisingly strong link between imposition of the resource constraint, and populations that evolve according to the self-thinning rule. The result is a simple condition between growth and mortality functions that implies self-thinning behaviour, and motivates further mathematical investigation.