A General Model for Time-minimising Avian Migration

We develop an optimality model for time-minimising bird migration for any distribution of feeding habitats and qualities along the migratory route. If the fuel deposition rate is constant along the route and feeding is possible everywhere, it is optimal to divide the journey into steps of equal length. The relationship between fuel deposition rate and departure fuel load is not continuous. If the fuel deposition rate is changing monotonically along the route, step lengths are not constant. Step lengths increase if fuel deposition rates increase along the route and decrease if fuel deposition rates decrease along the route. In both cases the relationship between fuel deposition rate and departure fuel load is also not continuous. These qualitative patterns remain unaffected if different flight range equations are used and if the dependence of time spent flying on departure fuel load is included. If ecological barriers are introduced where fuel deposition is impossible it is in most cases optimal to make a stop at an edge of the barrier.