The Traill island model for lemming dynamics, how it compares to Fennoscandian vole dynamics models, and a proposed simplification

TL;DR

This paper analyzes the Traill island model of lemming and predator dynamics, compares it to other models, and proposes a simplified version that retains key features, with implications for modeling Arctic rodent populations.

Contribution

It introduces a low-dimensional approximation of the Traill island model that captures essential dynamics and provides MATLAB codes for implementation.

Findings

The simplified model replicates cycle periodicity and amplitude.

Generalist predation impacts population declines differently than in other models.

The approach is applicable to snow-growing lemming populations.

Abstract

The Traill island model of Gilg et al. (2003) is a landmark attempt at mechanistic modelling of the cyclic population dynamics of rodents, focusing on a high Arctic community. It models the dynamics of one prey, the collared lemming, and four predators : the stoat, the Arctic fox, the long-tailed skua and the snowy owl. In the present short note, we first summarize how the model works in light of theory on seasonally forced predator-prey systems, with a focus on the temporal dynamics of predation rates. We show notably how the impact of generalist predation, which is able here to initiate population declines, differs slightly from that of generalist predation in other mechanistic models of rodent-mustelid interactions such as Turchin & Hanski (1997). We then provide a low-dimensional approximation with a single generalist predator compartment that mimics the essential features of the Traill island model: cycle periodicity, amplitude, shape, as well as generalist-induced declines. This simpler model should be broadly applicable to model other lemming populations that predominantly grow under the snow during the winter period. Matlab computer codes for Gilg et al. (2003), its two-dimensional approximation, as well as alternative lemming population dynamics models are provided.