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Two Interacting Populations

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Integrodifference Equations in Spatial Ecology

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

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Abstract

Most biological populations do not exist in isolation but interact with other species in many ways that may increase or decrease their reproductive ability, affect their survival, or alter their dispersal behavior. Species interactions can lead to phenomena such as sustained population oscillations or competitive exclusion. In this chapter, we present some of the spatial aspects of population interaction in the context of IDEs. We begin with a brief background on nonspatial models before we move to study critical patch-sizes for predator and prey systems. Some of the most surprising and beautiful results in this section relate to dispersal-induced pattern formation in these systems. Spatial invasion dynamics of predator and prey show rich and complex behavior. We then present the phenomenon of anomalous spreading speeds in mutualism systems. Finally, we consider several aspects of persistence and invasion of competing species.

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Notes

  1. 1.

    Strictly speaking, there are four possibilities: a species can activate itself and the other, it can inhibit itself and the other, it can activate itself and inhibit the other, or it can inhibit itself and activate the other. Classically, we speak of an activator (inhibitor) if the species activates (inhibits) itself and the other. An activator–inhibitor system is one that consists of an activator and an inhibitor in the classical sense.

  2. 2.

    Diffusion-driven instability can also arise when one species activates itself and inhibits the other, and the other species inhibits itself and activates the other. This combination is sometimes referred to as positive feedback.

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

    Frithjof Lutscher

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Lutscher, F. (2019). Two Interacting Populations. In: Integrodifference Equations in Spatial Ecology. Interdisciplinary Applied Mathematics, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-030-29294-2_14

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