Spatial dynamics of a population with stage-dependent diffusion

•We model the dynamics of a population with diffusion dependent on life stage.•Population comprises juveniles and adults, which can be highly mobile or not.•There is a trade-off between dispersal capacity and fecundity rate.•We show that the front of invasion is led by the most mobile class.•Maximum...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2015-05, Vol.22 (1-3), p.605-610
Main Authors: Azevedo, F., Coutinho, R.M., Kraenkel, R.A.
Format: Article
Language:English
Subjects:
Adults
Diffusion
Dynamical systems
Insects
Invasion speed
Mathematical models
Nonlinear dynamics
Nonlinearity
Population density
Reaction–diffusion equations
Stage structure
Tradeoffs
Wing dimorphism
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Summary:•We model the dynamics of a population with diffusion dependent on life stage.•Population comprises juveniles and adults, which can be highly mobile or not.•There is a trade-off between dispersal capacity and fecundity rate.•We show that the front of invasion is led by the most mobile class.•Maximum invasion speed is attained at intermediate values of diffusion coefficient. We explore the spatial dynamics of a population whose individuals go through life stages with very different dispersal capacities. We model it through a system of partial differential equations of the reaction–diffusion kind, with nonlinear diffusion terms that may depend on population density and on the stage. This model includes a few key biological ingredients: growth and saturation, life stage structure, small population effects, and diffusion dependent on the stage. In particular, we consider that adults exhibit two distinct classes: one highly mobile and the other less mobile but with higher fecundity rate, and the development of juveniles into one or the other depends on population density. We parametrize the model with estimated parameters of an insect species, the brown planthopper. We focus on a situation akin to an invasion of the species in a new habitat and find that the front of invasion is led by the most mobile adult class. We also show that the trade-off between dispersal and fecundity leads to invasion speed attaining its maximum at an intermediate value of the diffusion coefficient of the most mobile class.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2014.07.010