Table E-l. Model and description (continued) 
Diffusion. Suarez et al. (2001) use a stratified diffusion model to reconstruct invasion dynamics of the Argentine 
ant ( Linepithema humile) because it uses more than one dispersal process. The authors use museum records, 
personal surveys, literature, and unpublished communications at three different scales (worldwide, regional, and 
I local) to determine patterns of dispersal. The authors find that human-induced “jump-dispersal” plays an important 
role in invasion patterns after establishment. The authors recommend that control measures focus on new foci or 
preventing new toci. They state that identifying the range of long-distance jump-dispersal will help future modeling 
efforts, and reconstructing spatial scales of invasion dynamics may make strategies for management and eradication 
more effective. 
Reaction-diffusion model. Grosholz (1996) uses a reaction-diffusion model to highlight differences in invasions 
between marine and terrestrial species describes population behavior at the population level. Use of the model 
requires the assumption of “random movement, continuous positive population growth, a homogenous environment, 
and no taxis or interspecific interactions.” It provides insights on invasions at a broader scale (not individual scale). 
The results show that using data on one invasion may not be a good predictor of other conspecific invasions. The 
author concludes that invasions may not accurately predict invasions for conspecifics and that diffusion models are 
useful for predicting general invasion patterns but not for predicting spread rates for specific invasions. 
Reaction-diffusion model. Lonsdale (1993) tests whether Skellam’s model for areal spread describes Mimosa 
pigra invasion and finds that it does not. Skellam’s model is continuous, deterministic, and requires users to assume 
(1) population increasing exponentially; (2) diffusing outward randomly; and (3) normally distributed distribution. 
The author finds that climatic conditions such as rainfall and flooding increase rate of spread. The author concludes 
that Skellam’s model does not sufficiently describe the growth of M. pigra and that population dynamics of invasive 
species are relatively simple. 
Discrete event simulation. Hill et al. (1998) use a discrete event simulation model to determine the development 
and colonization of the green alga Caulerpa taxifolia. The model accounts for sensitive physical and biological 
factors and assesses and predicts C. taxifolia propagation a various scales. In addition to simulating and predicting 
expansion, the model produces GIS maps. The authors find that the simulation model is sound and reliable enough 
to be partially valid, especially the element of the model that predicted unidentified C. taxifolia settlements. The 
authors conclude that problems do exist with the model, but that with additional simulations at other sites, the model 
will become more reliable. 
— 
Integrodifference Equation models and Integrodifference Matrix Population models. Neubert and Parker 
(2004) review Integrodifference Equation (IDE) models to show how they can predict spread rates of invasive 
species populations and Integrodifference Matrix Population (IMP) models to show how demographic and spatial 
I models can be combined. The authors find that IMPs are especially useful for classifying individuals by stage rather 
than age, and IMPs are easy to use and analyze. The authors’ primary conclusion is that IMPs are useful for 
managers because the models can help them understand the likely results of various management alternatives for 
invasive species. 
Stochastic mathematical models. Mollison (1986) describes how stochastic models (models with discrete 
individuals) can be used to predict dispersal, establishment, spread, and persistence. He concludes that for species 
I arrival, the shape of dispersal and distribution are important; for establishment, high reproductive rates are 
important; for spread population growth rate and mean dispersal distance are important; and for persistence, carrying 
capacity is important. Mollison recommends using stochastic models over deterministic and diffusion models for 
modeling control zones to prevent spread of invasive species. 
Discriminant analysis.* Cumutt (2000) uses multiple, discriminant analyses to determine correlation between 
species distribution and climatic variables to predict plant species invasions. The model identifies areas in Australia, 
Africa, and the Americas as areas that may harbor South Florida invasive species. The model functions to match 
climate variables of a species native habitat to that of host habitat to predict invasions. The author concludes that 
climatic-matching can be an important part of a multi-level management strategy and recommends that future 
research focus on determining whether species live in similar habitats as the host region to which they are invasive. 
E-3 
