Production ecology of agroforestry systems: A minimal mechanistic model and analytical derivation of the land equivalent ratio

Abstract

In this paper, the yield and the land equivalent ratio (LER) of a silvo-arable agroforestry (SAF) system, containing one tree and one crop species, is analyzed analytically using a minimal mechanistic model describing the system dynamics. Light competition between tree and crop is considered using light extinction functions. The tree leaf area is driven by annual increase in the number of leaf-bearing shoots with a seasonal cycle of bud burst, leaf expansion and senescence. The crop leaf area dynamics is driven by the solar radiation, heat sum and the dry matter allocation to the leaves. As a consequence of this, the model consists of six state equations expressing the temporal dynamics of: (1) tree biomass; (2) tree leaf area; (3) number of shoots per tree; (4) crop biomass; (5) crop leaf area index, and (6) heat sum. The main outputs of the model are the growth dynamics and final yields of trees and crops. Daily inputs are temperature and radiation. Planting densities, initial biomass of tree and crop species and growth parameters must be specified. The main parameters are those describing light interception, conversion to dry matter and leaf area. Given the crop cover and the tree parameters, it is shown that under potential growing conditions the land equivalent ratio can be explicitly expressed in terms of these parameters.