The general continuum model for structured populations, with two case studies in plant ecology

• Main Author: Laurie, Henri De Guise
• Other Authors: Reddy, B Daya
• Format: Doctoral Thesis
• Language: English
• Published: University of Cape Town 2016
• Subjects: Applied Mathematics; Plant Ecology
• Online Access: http://hdl.handle.net/11427/18243

Bibliography: p. 129-143. === The broad aim of this thesis is to investigate the formulation and usefulness of a very general model for plant population dynamics. In chapter 1, the goal of generality is discussed, particularly in the light of the lack of interaction between field and experimental population studies on the one hand and theoretical population dynamics on the other hand. A distinction is ma.de between descriptive and axiomatic theories, and it is suggested that they serve different purposes. The advantages of a. rigorous framework are pointed out and the basic elements of the continuum approach are introduced. In chapter 2, the model is proposed, the existence and uniqueness of solutions to its equations is proved, and an algorithm for numerically -approximating transient solutions is discussed. The question of generality is addressed in two places, and it is argued that the basic framework presented here is in principle adequate to model the processes of plant population dynamics in full detail, though the existence proof cannot to accommodate all possible models. In particular, models with time lags are excluded. Further limitations of the existence proof ill terms of constitutive relations are pointed out. In consequence, the theory here presented does not fully exploit the possibilities for generality inherent in the basic equations. In chapter 3, the question of what data would allow identification of factors determining somatic growth and mortality is investigated computationally. It is shown that using only the average size is insufficient. A class of models which includes all possible combinations of three types of size dependence in somatic growth and mortality is formulated. Qualitative parameter estimation for the various models yields size distributions that can be classified into the following biologically meaningful groups: group (i) has no models that use dependence on relative size; group (ii) has all the models in which somatic growth depends on relative size group (iii) has the models where only mortality depends on relative size. Thus it appears that size distribution may be used to distinguish various forms of size dependence in somatic growth and mortality. In chapter 4, a lottery model criterion for coexistence of plants with disjoint generations is developed, which is shown to require relative density dependence. Computer simulations aiming to initiate the use of exploratory calculations in studies of coexisting serotinous proteoids in fynbos indicate that the aspect of plant population dynamics most sensitive to density dependence is seed production, then somatic growth, while mortality is least sensitive to density dependence.