Density dependence in demography and dispersal generates fluctuating invasion speeds

Lauren L. Sullivan, Bingtuan Li, Tom E.X. Miller, Michael G. Neubert, Allison K. Shaw

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)5053-5058
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number19
StatePublished - May 9 2017

Bibliographical note

Funding Information:
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 ( 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.


  • Allee effects
  • Biological invasion
  • Density-dependent dispersal
  • Integrodifference equations
  • Invasive species


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