UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Coexistence of species in a fluctuating environment Fitzpatrick, Gordon James


A dynamic model in which multiple consumers of a single nutrient may coexist in a fluctuating environment is given. Only one consumer can persist in a fixed environment, but coexistence may be produced by effects of a fluctuating environmental variable on nutrient utilization differing between consumers. An approximate solution is given for the non-autonomous Lotka-Volterra-Verhulst ordinary differential equations of the model together with heuristic sufficient conditions for construction of a persistent multispecies consumer community. Computational examples demonstrate persistence of an idealized example community for periodic and random environmental fluctuation. Two further examples demonstrate that environmental fluctuation can produce coexistence when environmental variables, standing crops, assimilation efficiencies, primary productivity, utilization rates, and respiration rates are comparable to a tropical grassland, and an oligotrophic temperate lake. The sensitivity of model solutions to functional variations of the component species may be rapidly and accurately calculated. This allows the identification and estimation of unknown species functional responses from time series data of biomasses and a measured environmental variable. Unknown functions of an environmental variable are approximated by a Tchebycheff polynomial expansion in that variable. Unknown coefficients of these expansions are the parameters of the model. These parameters are determined by the unconstrained minimization of the squared deviations of the logarithm of biomass observations and model differential equation solution using a Quasi-Newton algorithm. This least squares estimator was applied to a one year biomass time series of four zooplankton grazers, phytoplankton, and average lake temperature of a small oligotrophic lake. Application of the model to this grazer zooplankton community gives evidence of partial stabilization due to environmental fluctuation in a natural community. It is concluded that environmental variation, which is often assumed on theoretical grounds to be destabilizing, should rather be considered as one of the bases of community persistence.

Item Media

Item Citations and Data


For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.