Developing hierarchical density-structured models to study the national-scale dynamics of an arable weed

Population dynamics can be highly variable in the face of environmental heterogeneity, and understanding this variation is central in the study of ecology. Robust management decisions require that we understand how populations respond to management at a range of scales, and under a broad suite of conditions. Population models are potentially valuable tools in addressing this challenge. However, without adequate data, models can fail to produce useful results. Populations of arable weeds are particularly problematic in this respect, as they are widespread and their dynamics are extremely variable. Owing to the inherent cost of collecting data, most studies of weed population dynamics are derived from localized experiments under a small range of environmental conditions, limiting the extent to which variance in population dynamics can be measured. Density-structured models provide a route to rapid, large-scale analysis of population dynamics, and can expand the scale of ecological models that are directly tied to data. Here we extend previous density-structured models to include environmental heterogeneity, variation in management, and to account for inter-population variation. We develop, parameterize and test hierarchical density-structured models for a common agricultural weed, black-grass (Alopecurus myosuroides). We model the dynamics of this species in response to crop management, using survey data gathered over 4 years from 364 fields across a network of 45 UK farms. We show that hierarchical density-structured models provide a substantial improvement over their non-hierarchical counterparts. Using these models, we demonstrate that several alternative crop-rotations are effective in reducing weed densities. Rotations with high wheat prevalence exhibit the most severe infestations, and diverse rotations generally have lower weed densities. However, a key outcome is that in many cases the effect of crop rotation is small compared to the high variability arising from spatio-temporal heterogeneity. This result highlights the need to monitor and model population dynamics across large spatial and temporal scales in order to account for variation in the drivers of plant dynamics. Our framework for data collection and modelling provides a means to achieve this.

Methods
Density-structured surveys of black-grass populations collected across a network of UK arable fields. 

Data collection is detailed in Freckleton et al (2011) 10.1086/657621 and  Queensborough et al (2011) 0.1111/j.2041-210X.2010.00075.x.