Predicting biomass partitioning and maximum tree height based on optimality principles

Carbon (C) allocation is the process by which photosynthate is partitioned to different functional pools, including leaves, woody tissues and fine roots. A long-standing, qualitative theory explains patterns of C allocation as maximizing growth subject to the availability of different resources. Here we outline a quantitative model based on this theory. We define net carbon profit (NCP) as the total C taken up by photosynthesis, minus the costs of constructing and maintaining leaves and the below-ground C investments required to supply them with water and nutrients. We hypothesize that leaf area index (LAI) tends to the value that maximizes gross primary production; this leads to an explicit prediction of maximum (energy-limited) LAI. We assume that the demands of leaf and root production are satisfied with highest priority, and that excess C is allocated to stems in such a way as to maximize height growth and therefore competitive success. High NCP is predicted not only in tropical and subtropical forests, but also in the Pacific Northwest of the USA and in SE Australia, where the tallest trees are found. Moreover, wood density can be related to woody biomass turnover time, τ (estimated from biomass data and net primary production) – trees with denser wood have longer lifespans. In highly productive ecosystems τ tends to be small, e.g. tropical forests; τ can be larger in temperate and boreal forests. We combine predicted τ with biomass-density relationships and mechanical constraints to predict maximum tree heights, testing our predictions using the global Forest Carbon database (ForC) and observations of maximum vegetation height.