Generational spreading speed and the dynamics of population range expansion

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Bateman, Andrew W.
Neubert, Michael G.
Krkosek, Martin
Lewis, Mark A.
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Generational spreading speed
Stage structure
Invasion speed
Integrodifference models
Net reproductive number
Graph reduction
Next-generation operator
Some of the most fundamental quantities in population ecology describe the growth and spread of populations. Population dynamics are often characterized by the annual rate of increase, λ, or the generational rate of increase, R0. Analyses involving R0 have deepened our understanding of disease dynamics and life-history complexities beyond that afforded by analysis of annual growth alone. While range expansion is quantified by the annual spreading speed, a spatial analog of λ, an R0-like expression for the rate of spread is missing. Using integrodifference models, we derive the appropriate generational spreading speed for populations with complex (stage-structured) life histories. The resulting measure, relevant to locations near the expanding edge of a (re)colonizing population, incorporates both local population growth and explicit spatial dispersal rather than solely growth across a population, as is the case for R0. The calculations for generational spreading speed are often simpler than those for annual spreading speed, and analytic or partial analytic solutions can yield insight into the processes that facilitate or slow a population’s spatial spread. We analyze the spatial dynamics of green crabs, sea otters, and teasel as examples to demonstrate the flexibility of our methods and the intuitive insights that they afford.
Author Posting. © University of Chicago Press, 2015. This article is posted here by permission of University of Chicago Press for personal use, not for redistribution. The definitive version was published in American Naturalist 186 (2015): 362-375, doi:10.1086/682276.
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American Naturalist 186 (2015): 362-375
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