Structured population models (e.g. matrix models, integral projection models) have long been an important tool in invasion biology. By scaling the response of individuals to the population level, such methods can inform management about critical life cycle transitions and population growth rates. However, the stage of invasion and landscape heterogeneity can have important implications for how we interpret the value of population growth rates (λ). For example, in the early stages of invasion, populations can experience habitat filtering such that individuals may be more likely to exist in lower quality microhabitats than might be the case for more established populations. This can result in a transient reduction in λ until more individuals accumulate in the most favorable microhabitats. Here we apply a recently-developed methodology that incorporates spatial heterogeneity into integral projection models to an experimental plant invasion (Persicaria lapathifolia introduced into a novel ecosystem). By accounting for the variances/covariances among the random effect terms associated with space across vital rate models, this approach estimates the distribution of λ values across microhabitats. We use this approach to examine how experimental manipulations to precipitation and interspecific competition influence invasibility.
Results/Conclusions
The precipitation and competition manipulations resulted in a substantial range of invader demographic and population-level responses, with landscape-level λ values ranging from essentially zero to nearly 2. However, as is the case with most population models, the value of λ is based on the implicit assumption that all seeds are dispersed uniformly, or equivalently that there is only a single habitat. By explicitly incorporating spatial heterogeneity we were able to quantify the Invasible Habitat Fraction (IHF; fraction of microhabitats with local λ > 1) as a new population-level metric. We observed many experimental treatment combinations with landscape-level λ < 1, but which exhibited IHF values of up to 30%. This result has important implications for how we interpret invasibility: according to more traditional (non-spatial) determinations of λ we would conclude that the ecosystem is not invasible, whereas a substantial fraction of it actually is. Similar to λ, IHF can also be readily incorporated into existing population modeling analysis frameworks. In our case we were able to apply a Life Table Response Experiment (LTRE) analysis to IHF in order to demonstrate that effects of biotic resistance (competition) on individual plant growth reduced IHF by 25% in one year.