Browsing by Author "Deutscher, K."
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- ItemModelling the Southwestern Alberta grizzly bear population using ordinary differential equations(2019) Bica, Ion; Solomonovich, Mark; Burak, K.; Deutscher, K.; Garrett, A.; Peacock, H.The Alberta grizzly bear population was listed as “threatened” by the Alberta Wildlife Association in 2010. This particular species is important, as it is an umbrella species for a variety of other animals. Our goal in this project was to create a model using ordinary differential equations, based on the logistic growth model, to determine whether the Southern Alberta grizzly bear population is recoverable. We aimed to calculate the rate at which the population was growing and its carrying capacity.
- ItemUrsus arctos horribilis: dynamic modeling of Canadian population(2019) Bica, Ion; Solomonovich, Mark; Deutscher, K.; Garrett, A.; Burak, K.; Peacock, H.The grizzly bears are K-strategists and their innate tendency is to reach homeostasis. In the First Nations folklore grizzly bears are viewed as “spirits” that bring balance in their untamed habitat where they roam, this being an indication that they do not overpopulate their habitat and their gene flow is “designed” to reach homeostasis without surpassing it. In the present article we study the dynamics of the grizzly bear population in the Southwest Alberta, Canada. Based on the dynamical model with three parameters, we obtain estimates for the carrying capacity and the minimum viable population of the grizzly bear population in their dynamical habitat. The article starts with the discussion of the rationale for choosing the Logistic Growth Model as the most appropriate for describing the dynamics of grizzly population. In addition to the usual for this kind of models parameters of the growth rate and the carrying capacity, in the current model we consider the parameters of Minimum Viable Population (MVP) and Safe Harbour (SH) – a measurement introduced by the Alberta Grizzly Bear Recovery Plan. The first of these parameters (MVP) is determined by the essential number of the individuals that would allow the survival of the species. The latter measurement (SH) is related to the so-called Grizzly Bear Priority Areas, where the risk of mortality is low. Then, based on Verhulst model and Statistical data, the carrying capacity and growth rate for the female grizzly bears in Alberta have been obtained. Mathematical analysis of the model has shown that the equilibria at K (carrying capacity) and MVP·SH are, respectively, stable and unstable. The time of possible extinction for the populations with the initial conditions below the threshold MVP·SH has been numerically estimated. The correlation between the system parameters and its influence on the survival of the population has been analyzed and the recommendations on ensuring the survival have been given.