@Article{LionVanBaalen2009,
  Author         = {Lion, Sébastien and van Baalen, Minus},
  Title          = {The evolution of juvenile-adult interactions in
                   populations structured in age and space.},
  Journal        = {Theoretical Population Biology},
  doi            = {10.1016/j.tpb.2009.05.005},
  Volume         = {76},
  Number         = {2},
  Pages          = {132-145},
  URL = {https://evolepid.cefe.cnrs.fr/pub/LionVanBaalen2009.pdf},
  abstract       = {We study the evolution of a spatially structured
                   population with two age classes using spatial moment
                   equations. In the model, adults can either help
                   juveniles by increasing their survival, or adopt a
                   cannibalistic behaviour and consume juveniles. While
                   cannibalism is the sole evolutionary outcome when the
                   population is well-mixed, both cannibalism and parental
                   care can be evolutionarily stable if the population is
                   viscous. Our analysis allows us to make two main
                   technical points. First, we present a method to define
                   invasion fitness in class-structured viscous
                   populations, which allows us to apply adaptive dynamics
                   methodology. Second, we show that ordinary pair
                   approximation introduces an important quantitative bias
                   in the evolutionary model, even on random networks. We
                   propose a correction to the ordinary pair approximation
                   that yields quantitative accuracy, and discuss how the
                   bias associated with this approach is precisely what
                   allows us to identify subtle aspects associated with
                   the evolutionary dynamics of spatially structured
                   populations.},
  keywords       = {space, evolution of social traits},
  year           = {2009}
}