A mathematical expectation model for bird navigation based on the clock-and-compass strategy.

We present here a mathematical formula for the directional distribution of migratory birds if they use a vector navigation/clock-and-compass strategy to find their winter quarters. It is based on mathematical expectation theory and shows that a simple parabola can describe the expected geographical spread of clock-and-compass birds as a function of migratory distance. Predictions based on this model are then tested against all same autumn ringing recoveries of first-season Pied Flycatchers, Ficedula hypoleuca, ringed in Scandinavia and European Robins, Erithacus rubecula, ringed in Sweden and Finland and recovered north of the Sahara Desert. We find that the predictions of our analytical model fit the ringing recovery distribution of freely migrating conspecifics extremely well.