Forest Modelling project 

This project corresponds to the PhD thesis of Zhengyang Zhang


Zhengyang Zhang
        Switzerland 2016

In Genève, Switzerland, July 2016.


Abstract
:
        SORTIE is a forest simulator developed by Pacala, Ribbens, Kobe et al. in 1993-1996. It is based on the forest data observed in and around Great Mountain Forest (GMF), a privately owned 2500ha forest located in northwestern Connecticut (41
°57'N, 73°15'W), USA in the year 1990-1992. SORTIE is an individual based model (IBM). It consists of four submodels (resource, growth, mortality, and recruitment) to determine the behavior of each individual, from which the behavior of the whole forest community can be determined. The main ingredient taken into account in SORTIE is the competition for light between trees.


    In [1] we build a mathematical model (a state-dependent delay differential equation derived from a size-structured model) for the adult population of trees A(t) in two cases (single species case and two-species case) and we compare it with SORTIE. The models are

 state-dependent delay differential
                equation                state-dependent delay
                differential equation two species

Left: single species case; right: two-species case. See [1] for a detailed explanation.


MATLAB code for the single species case: American Beech


MATLAB code for the single species case: Eastern Hemlock


Moreover, we extend our model by incorporating the spatial position of trees.
The model is


                                                                                                  spatial model


MATLAB code for the forest model with two species

This code provides the following figure which is taken from [1].

two species

In this figure we plot the comparison between SORTIE data and the numerical simulation of the two species model. 

MATLAB code for the forest model with two species and with space

This code provides the following figure which is taken from [1].

model with space

In this figure we plot the numerical simulation of the spatial model, describing the spread of the adult population of the two species.




In [2] we use the above model (in the single species case) coupled as a predator-prey system. This is to describe a parasite destroying a pine forest.  The parastite considered is the so called "pinewood nematode" which destroyed a large part of Portuguese pine tree forest. The model we end up with is the following
                                                                                                            forest-parasite model


MATLAB code for the model describing parasites in a single species forest

This code provides the following figure which is taken from [2].

Parasite Forest

In this figure we plot the forest-parasite model with Holling type I functional response in the scenario where the adult population of trees displays the damped oscillation without parasites.

Publications

    [1] P. Magal and Z. Zhang (2017),  Competition for light in forest population dynamics: from computer simulator to mathematical model, Journal of Theoretical Biology 419 , 290-304.

    [2] P. Magal and Z. Zhang (2017), Numerical simulations of a population dynamic model describing parasite destruction in a wild type pine forest, Ecological Complexity (in press).     [3] P. Magal and Z. Zhang, A system of state-dependent delay differential equation modelling forest growth I: semiflow properties, Submitted https://arxiv.org/abs/1705.08823.     [4] P. Magal and Z. Zhang, A system of state-dependent delay differential equation modelling forest growth II: boundedness of solutions, Nonlinear Analysis Series B: Real World Applications (to appear)

    [5]  Z. Zhang, Etude d'une classe d'équations a retard dépendant de l'état et application a la croissance de forêts (PhD thesis).