Density dependence in demography and dispersal generates fluctuating invasion speeds
Edited by Alan Hastings, University of California, Davis, CA, and approved March 30, 2017 (received for review November 23, 2016)
Significance
Mitigating the spread of invasive species remains difficult—substantial variability in invasion speed is increasingly well-documented, but the sources of this variability are poorly understood. We report a mechanism for invasion speed variability. The combined action of density dependence in demography and dispersal can cause invasions to fluctuate, even in constant environments. Speed fluctuations occur through creation of a pushed invasion wave that moves forward not from small populations at the leading edge but instead, from larger, more established populations that “jump” forward past the previous invasion front. Variability in strength of the push generates fluctuating invasion speeds. Conditions giving rise to fluctuations are widely documented in nature, suggesting that an important source of invasion variability may be overlooked.
Abstract
Density dependence plays an important role in population regulation and is known to generate temporal fluctuations in population density. However, the ways in which density dependence affects spatial population processes, such as species invasions, are less understood. Although classical ecological theory suggests that invasions should advance at a constant speed, empirical work is illuminating the highly variable nature of biological invasions, which often exhibit nonconstant spreading speeds, even in simple, controlled settings. Here, we explore endogenous density dependence as a mechanism for inducing variability in biological invasions with a set of population models that incorporate density dependence in demographic and dispersal parameters. We show that density dependence in demography at low population densities—i.e., an Allee effect—combined with spatiotemporal variability in population density behind the invasion front can produce fluctuations in spreading speed. The density fluctuations behind the front can arise from either overcompensatory population growth or density-dependent dispersal, both of which are common in nature. Our results show that simple rules can generate complex spread dynamics and highlight a source of variability in biological invasions that may aid in ecological forecasting.
Data Availability
Data deposition: The code and data to create the figures and run the models have been deposited in the Dryad Digital Repository (https://doi.org/10.5061/dryad.69sq3).
Acknowledgments
We thank J. Pruszenski, E. Strombom, R. Williams, and two anonymous reviewers for comments and support. The initial idea was developed during the 2014 ACKME Nantucket Mathematical Ecology retreat with input from participants and funding from the Woods Hole Oceanographic Institute Sea Grant. The University of Minnesota (UMN) Minnesota Supercomputing Institute provided resources that contributed to the research results reported within this paper (www.msi.umn.edu). The paper was funded in part by the Commonwealth Center for Humanities and Society, University of Louisville. L.L.S. and A.K.S. were supported by startup funds from the UMN (to A.K.S.), B.L. was supported by National Science Foundation (NSF) Grant DMS-1515875, T.E.X.M. was supported by NSF Grant DEB-1501814, and M.G.N. was supported by NSF Grants DEB-1257545 and DEB-1145017.
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Cover image: Pictured is a layer of cloud photographed from the Pic du Midi Observatory in France. Using global aerosol–climate models, Edward Gryspeerdt et al. report that observational data can be used to estimate the effect of aerosol–cloud interactions on cloud reflectivity to within 20% of its actual value. The results could help improve estimates of the anthropogenic contribution to climate change. See the article by Gryspeerdt et al. on pages 4899–4904. Image courtesy of Christophe Bellisario (Imperial College London, London).
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Data Availability
Data deposition: The code and data to create the figures and run the models have been deposited in the Dryad Digital Repository (https://doi.org/10.5061/dryad.69sq3).
Submission history
Published online: April 25, 2017
Published in issue: May 9, 2017
Keywords
Acknowledgments
We thank J. Pruszenski, E. Strombom, R. Williams, and two anonymous reviewers for comments and support. The initial idea was developed during the 2014 ACKME Nantucket Mathematical Ecology retreat with input from participants and funding from the Woods Hole Oceanographic Institute Sea Grant. The University of Minnesota (UMN) Minnesota Supercomputing Institute provided resources that contributed to the research results reported within this paper (www.msi.umn.edu). The paper was funded in part by the Commonwealth Center for Humanities and Society, University of Louisville. L.L.S. and A.K.S. were supported by startup funds from the UMN (to A.K.S.), B.L. was supported by National Science Foundation (NSF) Grant DMS-1515875, T.E.X.M. was supported by NSF Grant DEB-1501814, and M.G.N. was supported by NSF Grants DEB-1257545 and DEB-1145017.
Notes
This article is a PNAS Direct Submission.
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Competing Interests
The authors declare no conflict of interest.
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