Extremes in the resource consumption process: A mathematical model of the irruption of the moose population on Isle Royale. Part 1—Ecological background and model development

The development of a mathematical model of the moose-browse interaction on Isle Royale, Michigan, from the time of the establishment of the moose population in the early 1900s until the time of the arrival of wolves on the island about the mid-twentieth century is described. A brief history of the observations that were made during that period of the dynamics of the moose population and its resulting impact upon the vegetation is given. The simplifying assumptions that were made, the processes that were judged important enough to be represented in the model, the state variables that were selected and the input variables that were considered are delineated. A rationale is developed for the mathematical form of each of the terms used in the state equations. The literature that was utilized and the methodologies that were employed to obtain estimates of the parameters of the equations and the values of the initial conditions of the state variables are described.