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Integrodifference Equations in Spatial Ecology pp 161–197Cite as

Applications

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Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 49))

Abstract

The theory studied so far has considered somewhat idealized population dynamics. In this chapter, we present various extensions of this theory to include more realistic conditions and several applications of scalar IDEs to real biological systems. Quite naturally, as soon as we want to model any particular scenario with the simple IDE in (2.1), we find that the model may need to be adjusted in various ways to more accurately describe biological reality. The first example deals with dispersal-induced mortality. Next, we consider the effects of biased dispersal in rivers and along coastlines in the context of the drift paradox. Closely related is the third topic of moving-habitat models, where we incorporate certain aspects of climate change into the equations. We then take a closer look at populations where individuals differ in their dispersal behavior: in one extreme, some individuals could be immobile (sessile); in the other extreme, some individuals may disperse much farther than the majority. We discuss the latter aspects in the context of Reid’s paradox of rapid tree migration. We take a closer look at how to model Allee effects. Finally, we present some applications to two-dimensional domains.

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  1. Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada

    Frithjof Lutscher

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Lutscher, F. (2019). Applications. In: Integrodifference Equations in Spatial Ecology. Interdisciplinary Applied Mathematics, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-030-29294-2_12

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