Pareto front analysis of flight time and energy use in long-distance bird migration


  • Jasper A. Vrugt,

  • Jelmer Van Belle,

  • Willem Bouten

J. Vrugt (correspondence), Earth and Environmental Sciences Division, Los Alamos National Laboratory, Mail Stop T003, Los Alamos, NM 87545, USA. E-mail: − J. van Belle and W. Bouten, Institute for Biodiversity and Ecosystems Dynamics, Nieuwe Achtergracht 166, 1018 WV, Amsterdam, The Netherlands.


Optimality models are frequently used in studies of long distance bird migration to help understand and predict migration routes, stopover strategies and fuelling behaviour in a spatially varying environment. These models typically evaluate bird behaviour by focusing on a single optimization currency, such as total migration time or energy-use, without explicitly considering trade-offs between the involved objectives. In this paper, we demonstrate that this classic single-objective approach downplays the importance of variability in bird behaviour. In the light of these considerations, we therefore propose to use a full multi-criteria optimization method to isolate the set of non-dominated, efficient or Pareto optimal solutions. Unlike single-objective optimization where there is only one combination of bird behaviour maximizing fitness, the Pareto solution set represents a range of optimal solutions to conflicting objectives. Our results demonstrate that this multi-objective approach provides important new ways of analyzing how environmental factors and behavioural constraints have driven the evolution of migratory behaviour.