Monte Carlo analysis of parameter uncertainty in matrix models for the weed Cirsium vulgare

Abstract

Summary 1.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. 2. 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 . 3. 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. 4. 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. 5. 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.

No interaction between competition and herbivory in limiting introduced Cirsium vulgare rosette growth and reproduction

“…This outcome is consistent with mounting evidence documenting significant effects of insect herbivory on parameters of fitness of both native and introduced thistle species (Louda et al 1990;Louda and Potvin 1995;Jackson 1998;Maron et al 2002;Rose et al 2005;Eckberg 2008;Suwa 2008).…”

“…These data require that we reject the hypothesis that there was a synergistic interaction between competition and herbivory in suppressing growth and seed production of C. vulgare in its new, western tallgrass prairie environment. Instead, the results provide strong support for the hypothesis that herbivory by native insects directly contributed significant biotic resistance to invasiveness by C. vulgare in this region, as suggested (Louda and Rand 2002;Tenhumberg et al 2008).…”

“…Louda and Rand (2002) quantified high levels of floral herbivory and hypothesized that such herbivory by native insects limited C. vulgare invasiveness in this region. A recent matrix model supports the strong demographic effect of this floral herbivory on C. vulgare (Tenhumberg et al 2008). However, no study has measured the effect of competition, or the interaction between competition and insect herbivory, on the growth and flowering of C. vulgare rosettes in this region.…”

Cumulative herbivory outpaces compensation for early floral damage on a monocarpic perennial thistle

“…Such herbivory can dramatically and quantitatively reduce plant-reproductive success (Louda and Potvin 1995;McCall and Irwin 2006;LucasBarbosa 2016) and directly affect plant population growth rate (Rose et al 2005;Tenhumberg et al 2008;von Euler et al 2014) and population density (Louda 1983;Jongejans et al 2008;Lehndal et al 2016). Floral herbivore impacts should, therefore, favor plant growth and allocation strategies that can reduce losses, or even improve fitness, under herbivory pressure (Fornoni 2011;Agrawal et al 2012;Carmona and Fornoni 2013).…”

Bounds on the dynamics of sink populations with noisy immigration

“…When immigration is stage structured and time-varying, but crucially bounded, one approach to describe the resulting population envelope is to simulate repeatedly over a range of parameter values and derive statistical moments (means, variances) of growth rates and future densities (Engen et al, 1998;Tenhumberg et al, 2008). Such an approach is computationally intensive -in a five stage model the range of unstructured immigration is the five dimensional hypercube [δ m , δ M ] 5 .…”