Monte Carlo analysis of parameter uncertainty in matrix models for the weed Cirsium vulgare.
Abstract
Parameter uncertainty challenges the use of matrix models because it violates key assumptions underlying elasticity analyses. We have developed a matrix model to compare Monte Carlo methods with elasticity analyses for estimation of the relative importance of factors in the asymptotic population growth rate, λ, of Cirsium vulgare (spear thistle) in Nebraska, USA. We calculated λ for a base model using 11 parameter estimates available for Nebraska populations plus eight extracted from the literature, causing parameter uncertainty. We then calculated λ for 10 000 alternative models using Monte Carlo parameter estimation; parameters were drawn from the full range of each parameter in the literature and partial rank correlation analysis (PRCC) was used to order the parameters by the magnitude of their effect on λ. Monte Carlo analysis found that insect floral herbivory, affecting the regeneration transition, was the most important parameter affecting λ, whereas elasticity analyses suggested that the transition from small to medium size was the most significant. Statistical comparison, using PRCC vs. lower level elasticity (LLE), showed that the Monte Carlo analysis provided a more accurate assessment. As λ>1 in 99% of the model runs even with significant floral herbivory, we added two parameters influenced by weed management (probability of large thistles dying without producing seed and proportion of seeds that failed to germinate). Simulations that included reductions in these parameters, along with floral herbivory, led to λ<1 in 17% of the runs, suggesting these three factors interact to produce the low densities observed for this invasive thistle in our study area. Synthesis and applications. This study demonstrates the utility of the Monte Carlo approach for modelling weed dynamics with parameter uncertainty and multiple, potentially interacting, parameters. Invasive population growth by C. vulgare could be limited by a combination of weed management practices and the biotic resistance imposed by native floral herbivores.