Environmental Engineering Reference
In-Depth Information
Chapter 16
Stage-Structured Integro-Differential Models:
Application to Invasion Ecology
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lie Garnier and Jane Lecomte
Abstract Modelling dispersal processes requires a quantitative measure of the
amount of individuals dispersed at each distance, which is conveniently summar-
ized in a dispersal kernel. The framework of stage-structured integro-differential
models provides spatially explicit population dynamics models that couple a
stage-structured life-cycle with a dispersal kernel. This framework is flexible
and can notably incorporate density-dependence and stochasticity in demography
and dispersal. We first present the general formalism of stage-structured integro-
differential models and then provide two examples of application, both from
invasion ecology. The first model was developed for the spread of feral oilseed
rape along road verges. It is a one-dimensional deterministic invasion model, with
a complex dispersal kernel that includes the combined action of various dispersal
vectors. The second model was developed for the invasion of grasslands by pines
and is a two-dimensional stochastic model with a life-cycle that accounts for
the maturity age (10 years) and the dependence of cone production to tree height
and tree density.
16.1
Introduction
Dispersal is a major evolutionary force (Clobert et al. 2001) that determines the
ability to colonize new habitats, the intensity of competition between kins and
the structure of gene flow between populations. Within a population dynamics
point of view (i.e. when focusing on individuals rather than genes), measuring and
modelling dispersal are crucial aspects in biogeography, metapopulation ecology
and invasion ecology (Bullock et al. 2002). Dispersal kernels are known to be a
particularly effective tool in modelling dispersal processes because these probability
density functions quantify the proportion of individuals dispersing at each distance
