Journal of Mathematical Biology

, Volume 73, Issue 2, pp 397–422 | Cite as

Using genetic data to estimate diffusion rates in heterogeneous landscapes

  • L. RoquesEmail author
  • E. Walker
  • P. Franck
  • S. Soubeyrand
  • E. K. Klein


Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to increase the survival of endangered species. In this paper, we propose a mechanistic-statistical method to estimate space-dependent diffusion parameters of spatially-explicit models based on stochastic differential equations, using genetic data. Dividing the total population into subpopulations corresponding to different habitat patches with known allele frequencies, the expected proportions of individuals from each subpopulation at each position is computed by solving a system of reaction–diffusion equations. Modelling the capture and genotyping of the individuals with a statistical approach, we derive a numerically tractable formula for the likelihood function associated with the diffusion parameters. In a simulated environment made of three types of regions, each associated with a different diffusion coefficient, we successfully estimate the diffusion parameters with a maximum-likelihood approach. Although higher genetic differentiation among subpopulations leads to more accurate estimations, once a certain level of differentiation has been reached, the finite size of the genotyped population becomes the limiting factor for accurate estimation.


Reaction–diffusion Stochastic differential equation  Inference Mechanistic-statistical model Allele frequencies Genotype measurements 

Mathematics Subject Classification

35K45 35K57 35Q92 65C30 92D10 92D40 


Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

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Supplementary material 2 (avi 323 KB)

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Supplementary material 5 (avi 351 KB)

Supplementary material 6 (avi 351 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • L. Roques
    • 1
    Email author
  • E. Walker
    • 1
  • P. Franck
    • 2
  • S. Soubeyrand
    • 1
  • E. K. Klein
    • 1
  1. 1.INRA, UR 546 Biostatistique et Processus SpatiauxAvignonFrance
  2. 2.INRA, UR 1115 Plantes et Systèmes de Culture HorticolesAvignonFrance

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