Revisit Brown Lemming Population Cycles in Alaska: Examination of Stoichiometry

Resource-consumer models have been applied to explain population cycles of small mammals such as brown lemmings in Alaska. All these models only consider food quantity for small mammals. However, food quality can potentially be a key factor driving the population cycle. To capture both food quantity and quality in the resource-consumer model, we apply the newly emerged method “ecological stoichiometry”, which deals with the balance of fundamental elements in living organisms. A group of stoichiometric models are discussed in this paper for brown lemmings in Alaska, where food quality is measured by phosphorus and food quantity is measured by carbon. Within the framework of our models, we define an index to compare the relative importance of food quality and food quantity. Simulations of this index show that brown lemming cycles in Alaska are mainly controlled by food quantity. Bifurcation diagrams illustrate that the cycle period is an increasing function of the nutrient availability but a decreasing function of the nutrient requirement of lemmings. A striking result arises: high nutrient availability and small nutrient requirement of lemmings drive the low points of the population cycle to be extremely small, leading to high probability of lemmings’ extinction. However, high nutrient availability and small nutrient requirement of lemmings should both benefit lemmings. This paradox needs further examination in theoretical and empirical studies. In addition, we perform sensitivity analysis of periodicity with respect to all parameters.