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PhDs in progress

PhDs in progress
The UMR currently has 7 PhD students.

[ Date de démarrage : novembre 2022 ]

Clarisha Nijman

A Population Harvesting Model with an Optimal Height Dependent Control Function in a Multi-Species Structured Tropical Forest

  • Directeur : Abdennebi Omrane (UG - UMR EcoFoG)
  • Encadrants : Loïc Louison (UG - UMR EcoFoG) et S. Venetiaan 
  • Financeur : 
  • ED 587 (UG)

Abstract

Faced to a high population growth in French Guiana, the timber industry is having a significant increase in wood production of approximately 80,000 m3 of logs per year, carried out in the permanent forest domain of over 2.5 million hectares. One of the strategic directions of the regional forest and wood program (PRFB) in French Guiana is to increase the volumes of wood produced while preserving sustainable management. Scientists have therefor been thinking about mathematical models to help forest managers to find a balance between the demand of wood production and keeping the ecosystem as pure as possible.

In 2022 Ainseba et all designed a mathematical model consisting of partial differential equation in combination with an initial and a boundary condition to model the population dynamics in a homogeneous forest. Their model captured concepts of the nature such as the growth rate of trees, the natural mortality, the birth of new trees, the competition for light, and the fact that trees are being harvested regularly. The aim of that model was to decide whether a harvest function can be indicated as an optimal harvest function.

In this study the Ainseba et all model (2022) will be used for a heterogeneous tropical forest; a forest with different species each containing their own typical characteristics such as the growth rate and the natural growth of trees. Moreover the harvest or control function will be expanded with a next dimension: the height. The aim of this actual study is to find a two dimensional optimal control function to advise managers how much trees of a specific species could be cut on a specific time.

This mathematical control optimization problem consists of a profit function for harvesting the forest and a system of nonlinear initial value bounded problems. First the focus will be on validating this model as a well posed mathematical problem. Then this model will be approximated with the backward Euler scheme (finite element method). As it regards a large system heuristics as the conjugate gradient method will be used to find a good approximation for the optimal solution. Finally the results will be compared with the reality in order to evaluate how practical the harvest function is