In order to control invasive species, we need to understand how their populations grow and spread. This process is not constant – there is a great deal of variability in the rate that species invade, and the reasons for these fluctuations are not well understood. Experimental data show that a population’s growth varies even when conditions such as weather and terrain features are stable.

MSI PI Allison Shaw, an assistant professor in the Department of Ecology, Evolution, and Behavior (College of Biological Sciences), and Dr. Lauren Sullivan, a post-doc in the Shaw lab, have developed mathematical models that show the speed variability of invasive species. The models incorporate the Allee effect, where low density causes populations to grow more slowly, plus overcompensatory population growth (when populations grow suddenly past their equilibrium point) and density-dependent dispersal (which links a population’s spread with its density). The models using these combined factors may be useful for researchers interested in combating the spread of invasive species. The authors used MSI resources for their computational work. Co-authors on the paper include colleagues from the University of Louisville, Rice University, and the Woods Hole Oceanographic Institute.

The paper can be found on the website of the *Proceedings of the National Academy of Sciences of the USA*: Lauren L. Sullivan, Bingtuan Li, Tom E.X. Miller, Michael G. Neubert, Allison K. Shaw. 2017. Density dependence in demography and dispersal generates fluctuating invasion speeds. *PNAS* 114(19): 5053-5058. DOI: 10.1073/pnas.1618744114. The University of Minnesota News website also featured this research: Species spread in spurts – and here’s why.

**Image description:** Invasion dynamics under different types of density dependence and dispersal. (*A*) With compensatory growth at high densities, the wave shape and invasion speed are both constant, which is true with and without low-density Allee effects (AEs) (overcompensatory model: σ2=0.25, a=0, and r=0.9). (*B*) With overcompensatory population growth and no AE, population density exhibits fluctuations behind the front, but the leading edge progresses at a constant speed (overcompensatory model: σ2=0.25, a=0, and r=2.7). (*C*) However, when overcompensation combines with low-density AEs, the invasion speed fluctuates (overcompensatory model: σ2=0.25, a=0.4, and r=2.7). Variability in invasion speed can also occur when AEs combine with density dependence in (*D*) the proportion of dispersing offspring (propensity model: a=0.2, λ=0, n^=0.9, p0=0.05, pmax=1, and α=50) or (*E* and *F*) dispersal distance. In the latter model, dispersal distance (*E*) decreases with population density (distance model: a=0.2, λ=0, n^=0.9, β=−50, σ02=0.05, and σmax2=1) or (*F*) increases with density (distance model: parameters as in *E* except β=50). Initial population densities are either (*A–C*) 2 or (*D–F*) 0.8 times the standard normal probability density truncated at |x|=5. Image and description: L.L. Sullivan et al. *PNAS* 2017;114:5053-5058. © National Academy of Sciences.

*posted on June 26, 2017*