A periodic Markov model to formalize animal migration on a network

Regular, long-distance migrations of thousands of animal species have consequences for the ecosystems that they visit, modifying trophic interactions and transporting many non-pathogenic and pathogenic organisms. The spatial structure and dynamic properties of animal migrations and population flyways largely determine those trophic and transport effects, but are yet poorly studied. As a basis, we propose a periodic Markov model on the spatial migration network of breeding, stopover and wintering sites to formally describe the process of animal migration on the population level. From seasonally changing transition rates we derived stable, seasonal densities of animals at the network nodes. We parametrized the model with high-quality GPS and satellite telemetry tracks of white storks (Ciconia ciconia) and greater white-fronted geese (Anser a. albifrons). Topological and network flow properties of the two derived networks conform to migration properties like seasonally changing connectivity and shared, directed movement. Thus, the model realistically describes the migration movement of complete populations and can become an important tool to study the effects of climate and habitat change and pathogen spread on migratory animals. Furthermore, the property of periodically changing transition rates makes it a new type of complex model and we need to understand its dynamic properties.