The importance of space, time, and stochasticity to the demography and management of Alliaria petiolata

As population modeling is increasingly called upon to guide policy and management, it is important that we understand not only the central tendencies of our study systems, but the consequences of their variation in space and time as well. The invasive plant Alliaria petiolata (garlic mustard) is actively managed in the United States and is the focus of a developing biological control program. Two weevils (Coleoptera: Curculionidae: Ceutorhynchus) that reduce fecundity (C. alliariae) and rosette survival plus fecundity (C. scrobicollis) are under consideration for release pending host specificity testing. We used a demographic modeling approach to (1) quantify variability in A. petiolata growth and vital rates and (2) assess the potential for single- or multiple-agent biocontrol to suppress growth of 12 A. petiolata populations in Illinois and Michigan studied over three plant generations. We used perturbation analyses and simulation models with stochastic environments to estimate stochastic growth rates (λS) and predict the probability of successful management using either a single biocontrol agent or two agent species together. Not all populations exhibited invasive dynamics. Estimates of kS ranged from 0.78 to 2.21 across sites, while annual, deterministic growth (λ) varied up to sevenfold within individual sites. Given our knowledge of the biocontrol agents, this analysis suggests that C. scrobicollis alone may control A. petiolata at up to 63% of our study sites where λ_S > 1, with the combination of both agents predicted to succeed at 88% of sites. Across sites and years, the elasticity rankings were dependent on k. Reductions of rosette survival, fecundity, or germination of new seeds are predicted to cause the greatest reduction of λ in growing populations. In declining populations, transitions affecting seed bank survival have the greatest effect on λ. This contrasts with past analyses that varied parameters individually in an otherwise constant matrix, which may yield unrealistic predictions by decoupling natural parameter covariances. Overall, comparisons of stochastic and deterministic growth rates illustrate how analyses of individual populations or years could misguide management or fail to characterize complex traits such as invasiveness that emerge as attributes of populations rather than species.