Multi-scale methods predict invasion speeds in variable landscapes

Spread rates of invasive plant species depend heavily on variable seed/seedling survivorships over various habitat types as well as on variability in seed dispersal induced by rapid transport of propagules in open areas and slow transport in vegetated areas. The ability to capture spatial variability in seed survivorship and dispersal is crucial to accurately predict the rate of spread of plants in real world landscapes. However, current analytic methods for predicting spread rates are not suited for arbitrary, spatially heterogeneous systems. Here, we analyze invasion rates of the invasive plant Phragmites australis (common reed) over variable wetland landscapes. Phragmites is one of the most pervasive perennial grasses, outcompeting native vegetation, providing poor wildlife habitat, and proving difficult to eradicate across its invasive range in North America. Phragmites spreads sexually via seeds and asexually via underground (rhizomes) and aboveground (stolons) stems. We construct a structured integrodifference equation model of the Phragmites life cycle capturing variable seed survivorship in a seed bank, sexual and asexual recruitment into a juvenile age class, and differential competition among all classes with adults. The demographic model is coupled with a homogenized ecological diffusion/settling seed dispersal model that allows for seed deposition that varies with habitat type. The dispersal kernel we develop does not require local normalization and can be implemented efficiently using standard computational techniques. The model generates a traveling wave of isolated patches, establishing only in suitable habitats. We use the method of multiple scales to predict invasion speed as a solvability condition at large scales and test the predictions numerically. Accurate predictions are generated for a wide range of landscape parameters, indicating that invasion speeds can be understood in landscapes of arbitrary structure using this approach.