Theoretical approaches to bird migration

Birds are often considered to be one of the best studied groups of organisms. However, only a few investigations have been devoted to a theoretical analysis of avian migration patterns in time and space. This paper is meant to be a first step into this direction. We start by presenting different types of observational data sets that are available and discuss their advantages and disadvantages for use in quantitative analysis of bird movement and migration. Based on ring recovery and satellite telemetry data we perform a statistical analysis of the migratory patterns of the white stork Ciconia ciconia. We find that standard methods from random walk theory can be applied, but have to be carefully interpreted and possibly modified to analyse migration movement data which are dominated by seasonal drift. Our analysis reveals two different modes of movement - fast, directed migration and slow, undirected resting. Furthermore, we present a conceptional network model of avian migration. In our model a number of discrete breeding, resting and wintering habitats are linked by migration in the form of seasonally driven transition probabilities that are described by a unimodal circular function of time. Our study emphasises the need for more rigorous quantitative data analysis and mathematical modelling to gain a better understanding of the dynamic processes of avian migration.