The public defense of Tin Nwe Aye doctoral thesis
The public defense of Tin Nwe Aye doctoral thesis in Mathematics and Applied Mathematics will take place at Mälardalen University, room Zeta (Västerås Campus) as well as digitally on zoom at 10:00 on March 26, 2021.
Title:“Population dynamics and Tree Growth Structure in Mathematical Biology”.
The faculty examiner is Professor Christian Engström, Linneuniversitetet, and the examining committee consists of Associate Professor Olof Svensson, Linköping University; Associate Professor Olha Bodnar, Örebro University; Associate Professor Niklas Lundström, Umeå University.
Reserve: Professor Kimmo Eriksson, Mälardalen University
Serial number: 331
Registration: Send an e-mail before March 25th to firstname.lastname@example.org
Mathematical biology/ecology is a fast-growing, well-recognized and useful exciting modern application of mathematics. Ecology is the study of interactions between organisms, populations and their environment. A population is a group of interbreeding organisms of a particular species in the same geographic area over a period of time.
Physiologically structured population models (PSPMs) investigate the population dynamics, that is, the study of change in populations and environment over time. PSPMs are a class of models which explicitly link population dynamics and individual life history, in particular feeding, development, reproduction, and mortality. These processes are dependent on the state of the individual organism itself and the environment in which it lives. Modeling ecological systems with PSPMs have contributed significantly to our understanding of how size-dependent individual life history processes affects the population dynamics.
Individual growth reproduction is food-dependent and varies with population density and environmental changes. The Escalator Boxcar Train (EBT) is a numerical method, used to find solutions to size-dependent PSPMs. The classical algorithm for EBT involves a systems of differential equations where the number of equations grow with time and eventually becomes unmanageable to solve, even on modern computers. We have modified the EBT-method in such a way that the system does not grow, yet accurately finds the solution, which results in the possibility to solve more advanced PSPMs. Another approach to PSPMs is to divide the population sizes into juvenile and adult individuals, this type of model is called a size-structured population model. We study size-structured, biomass-based, consumer-resource models with different kind of resource growth dynamics, both deterministic and stochastic, to investigate emergent properties of the population dynamics.
In forest industry and forest ecology, the classical pipe model has been used to estimate the cross-sectional area of the stem in trees. However, in the original paper, written over half a century ago, the authors explicitly state that this simple pipe model cannot be used for this purpose below the crown of the tree. The stem cross-sectional area increase significantly with tree size and age and is composed mainly by heartwood and sapwood. The heartwood/sapwood composition is important, both in industrial products from trees as well as theoretical uses in theoretical forest ecology. We derive a stem model that predicts the heartwood and the sapwood cross-sectional areas of the stem of the tree. Our model outperforms the simple pipe model.
Tin Nwe Aye