Journal of Mathematical Biology

, Volume 68, Issue 1, pp 505–531

On the maintenance of bird song dialects

  • Robert Planqué
  • Nicholas F. Britton
  • Hans Slabbekoorn
Article

DOI: 10.1007/s00285-012-0632-8

Cite this article as:
Planqué, R., Britton, N.F. & Slabbekoorn, H. J. Math. Biol. (2014) 68: 505. doi:10.1007/s00285-012-0632-8

Abstract

Many bird species, especially song birds but also for instance some hummingbirds and parrots, have noted dialects. By this we mean that locally a particular song is sung by the majority of the birds, but that neighbouring patches may feature different song types. Behavioural ecologists have been interested in how such dialects come about and how they are maintained for over 45 years. As a result, a great deal is known about different mechanisms at play, such as dispersal, assortative mating and learning of songs, and there are several competing hypotheses to explain the dialect patterns known in nature. There is, however, surprisingly little theoretical work testing these different hypotheses at present. We analyse the simplest kind of model that takes into account the most important biological mechanisms, and in which one may speak of dialects: a model in which there are but two patches, and two song types. It teaches us that a combination of little dispersal and strong assortative mating ensures dialects are maintained. Assuming a simple, linear frequency-dependent learning rule has little effect on the maintenance of dialects. A nonlinear learning rule, however, has dramatic consequences and greatly facilitates dialect maintenance. Adding fitness benefits for singing particular songs in a given patch also has a great impact. Now rare song types may invade and remain in the population.

Keywords

Mathematical biology Dialects Bird song Modeling  Difference equations Behavioural ecology 

Mathematics Subject Classification

37N25 92A18 

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Robert Planqué
    • 1
  • Nicholas F. Britton
    • 2
  • Hans Slabbekoorn
    • 3
  1. 1.Department of MathematicsVU University AmsterdamAmsterdamThe Netherlands
  2. 2.Department of Mathematical Sciences and Centre for Mathematical BiologyUniversity of BathBathUK
  3. 3.Institute of Biology LeidenLeiden UniversityLeidenThe Netherlands

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