On the Calibration of an Autonomous Model of the Biological Population of the Tundra Lemming

An autonomous model of a phenomenological type was designed for a biological population of lemmings in complex studies of tundra communities. The population dynamics is described in the model by a difference equation, which relates the population sizes observed in 2 consecutive years and depends on three parameters of biological and ecological nature. A combination of parameter values included in the equation determines a class of one-dimensional unimodal mappings of a dynamical system. Bifurcation properties, asymptotics, and stability of trajectories were studied both analytically and numerically in the class. The problem of model identification is the main focus. The method of identification sets was proposed for calibrating the model. The method is based on the approximation and visualization of small-dimensional projections of a multidimensional graph of the error function specified in a space of three environmental and two population parameters. An example model identification was performed using data on a tundra lemming population of the Taimyr Peninsula. Two biological and ecological parameters were shown to allow a stable location distribution in this case.