Lewis Mark A.

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Lewis
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Mark A.
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  • Article
    When can herbivores slow or reverse the spread of an invading plant? A test case from Mount St. Helens
    (University of Chicago, 2005-10-04) Fagan, William F. ; Lewis, Mark A. ; Neubert, Michael G. ; Aumann, Craig ; Apple, Jennifer L. ; Bishop, John G.
    Here we study the spatial dynamics of a coinvading consumer-resource pair. We present a theoretical treatment with extensive empirical data from a long-studied field system in which native herbivorous insects attack a population of lupine plants recolonizing a primary successional landscape created by the 1980 volcanic eruption of Mount St. Helens. Using detailed data on the life history and interaction strengths of the lupine and one of its herbivores, we develop a system of integrodifference equations to study plant-herbivore invasion dynamics. Our analyses yield several new insights into the spatial dynamics of coinvasions. In particular, we demonstrate that aspects of plant population growth and the intensity of herbivory under low-density conditions can determine whether the plant population spreads across a landscape or is prevented from doing so by the herbivore. In addition, we characterize the existence of threshold levels of spatial extent and/or temporal advantage for the plant that together define critical values of "invasion momentum," beyond which herbivores are unable to reverse a plant invasion. We conclude by discussing the implications of our findings for successional dynamics and the use of biological control agents to limit the spread of pest species.
  • Article
    Generational spreading speed and the dynamics of population range expansion
    (University of Chicago Press, 2015-08-06) Bateman, Andrew W. ; Neubert, Michael G. ; Krkosek, Martin ; Lewis, Mark A.
    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.