Living in a stressed environment : mathematical models and applications

• Main Author: Saifuddin, Rashed
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: UNSW, Sydney 2020
• Subjects: Mathematical Application; Stressed environment; Mathematical models; Svalbard
• Online Access: http://hdl.handle.net/1959.4/66381; https://unsworks.unsw.edu.au/bitstreams/f11357ef-c8d5-400d-9c1b-9daa5c599c2f/download; https://doi.org/10.26190/unsworks/21803

Ecosystems can be stressed when an environment is under pressure, such as when resources deplete due to biological invasion. Randomness in nature is an inherent source of environmental stress affecting resident species. Central to ecologists is the concept of a carrying capacity -- maximum population sustained by an environment. Many models consider the carrying capacity, a proxy for the environment, as unchanging. It is recognised that this is not the case. We propose an approach that accounts for a variable carrying capacity. This permits us to model changes in a population due to environment stress. A couple of different approaches to modelling the dynamics of a reindeer population is discussed. One is based on survival modelling -- the effects of a stressed environment on a reindeer population is investigated employing well known survival functions. Survival probability is calculated by applying a hazard function directly and indirectly to the reindeer. The second is based on a system of differential equations that couples the population to the environment via the carrying capacity. We employ seven different response functions in an effort understand their population dynamics. We find that a Type II response function is suited to reindeer populations that show a gradual decline in the population size, such as on St. George Island and George Reserve. Whereas a Type VI (ratio-dependent) response function for populations that exhibit a sharp decline, as on St. Paul and Svalbard Islands. We also consider the role of lichen regrowth and the effects of an environmental delay in response to grazing by reindeer. We show that regrowth is an important ingredient in the model even though its growth rate is very slow compared to its consumption rate by reindeer. Further, the inclusion of a delay greatly improves the model for the reindeer on St. George Island.