Initial conditions and their effect on invasion velocity across heterogeneous landscapes

Partial differential equation models for invasive species spread in the presence of spatial heterogeneity

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread which appear qualitatively similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasions and must be considered when designing models of invasive species spread.

The spread of a wild plant pathogen is driven by the road network

Spatial analyses of pathogen occurrence in their natural surroundings entail unique opportunities for assessing in vivo drivers of disease epidemiology. Such studies are however confronted by the complexity of the landscape driving epidemic spread and disease persistence. Since relevant information on how the landscape influences epidemiological dynamics is rarely available, simple spatial models of spread are often used. In the current study we demonstrate both how more complex transmission pathways could be incorpoted to epidemiological analyses and how this can offer novel insights into understanding disease spread across the landscape. Our study is focused on Podosphaera plantaginis, a powdery mildew pathogen that transmits from one host plant to another by wind-dispersed spores. Its host populations often reside next to roads and thus we hypothesize that the road network influences the epidemiology of P. plantaginis. To analyse the impact of roads on the transmission dynamics, we consider a spatial dataset on the presence-absence records on the pathogen collected from a fragmented landscape of host populations. Using both mechanistic transmission modeling and statistical modeling with road-network summary statistics as predictors, we conclude the evident role of the road network in the progression of the epidemics: a phenomena which is manifested both in the enhanced transmission along the roads and in infections typically occurring at the central hub locations of the road network. We also demonstrate how the road network affects the spread of the pathogen using simulations. Jointly our results highlight how human alteration of natural landscapes may increase disease spread.

Its all about connections: hubs and invasion in habitat networks

During the early stages of invasion, the interaction between the features of the invaded landscape, notably its spatial structure, and the internal dynamics of an introduced population has a crucial impact on establishment and spread. By approximating introduction areas as networks of patches linked by dispersal, we characterised their spatial structure with specific metrics and tested their impact on two essential steps of the invasion process: establishment and spread. By combining simulations with experimental introductions of Trichogramma chilonis (Hymenoptera: Trichogrammatidae) in artificial laboratory microcosms, we demonstrated that spread was hindered by clusters and accelerated by hubs but was also affected by small-population mechanisms prevalent for invasions, such as Allee effects. Establishment was also affected by demographic mechanisms, in interaction with network metrics. These results highlight the importance of considering the demography of invaders as well as the structure of the invaded area to predict the outcome of invasions.

Multiscale connectivity and graph theory highlight critical areas for conservation under climate change

Conservation planning and biodiversity management require information on landscape connectivity across a range of spatial scales from individual home ranges to large regions. Reduction in landscape connectivity due changes in land use or development is expected to act synergistically with alterations to habitat mosaic configuration arising from climate change. We illustrate a multiscale connectivity framework to aid habitat conservation prioritization in the context of changing land use and climate. Our approach, which builds upon the strengths of multiple landscape connectivity methods, including graph theory, circuit theory, and least-cost path analysis, is here applied to the conservation planning requirements of the Mohave ground squirrel. The distribution of this threatened Californian species, as for numerous other desert species, overlaps with the proposed placement of several utility-scale renewable energy developments in the American southwest. Our approach uses information derived at three spatial scales to forecast potential changes in habitat connectivity under various scenarios of energy development and climate change. By disentangling the potential effects of habitat loss and fragmentation across multiple scales, we identify priority conservation areas for both core habitat and critical corridor or stepping stone habitats. This approach is a first step toward applying graph theory to analyze habitat connectivity for species with continuously distributed habitat and should be applicable across a broad range of taxa.

Quantifying the reliability of dispersal paths in connectivity networks

Many biological systems, from fragmented landscapes to host populations, can be represented as networks of connected habitat patches. Links between patches in these connectivity networks can represent equally diverse processes, from individuals moving through the landscape to pathogen transmissions or successive colonization events in metapopulations. Any of these processes can be characterized as stochastic, with functional links among patches that exist with various levels of certainty. This stochasticity then needs to be reflected in the algorithms that aim to predict the dispersal routes in these networks. Here we adapt the concept of reliability to characterize the likelihood that a specific path will be used for dispersal in a probabilistic connectivity network. The most reliable of the paths that connect two patches will then identify the most likely sequence of intermediate steps between these patches. Path reliability will be sensitive to targeted disruptions of individual links that form the path, and this can then be used to plan the interventions aimed at either preserving or disrupting the dispersal along that path. The proposed approach is general, and can be used to identify the most likely dispersal routes in various contexts, such as predicting patterns of migrations, colonizations, invasions and epidemics.

Understanding effects of barriers on the spread and control of rabies

This chapter reviews the evidence for the impact of natural and anthropogenic barriers on the spread of rabies using evidence mainly drawn from the epidemics of fox and raccoon variant rabies virus over the past 60 years in North America. Those barriers have both directed and inhibited the spread of rabies and, at a regional scale, have been integrated with rabies control efforts in North America. Few studies have been done, however, to examine how the texture (grain) and configuration of the habitat at finer scales affect rabies control, particularly the massive oral vaccination campaigns in operation along the Atlantic coast and southeastern Canada (Ontario, Québec, New Brunswick). To explore these questions, the authors used stochastic simulation. The model of choice was the Ontario Rabies Model (ORM) adapted for use on the high performance computing resources network in Québec (RQCHP-Réseau québécois de calcul de haute performance; http://rqchp.qc.ca). The combination of the ORM and RQCHP allowed us to run many thousands of experiments to explore interactions between nine landscape grain/configuration combinations and vaccination barriers with varying widths and immunity levels. Our results show that breaches of vaccine barriers increase as the grain size of the landscape increases and as the landscape becomes more structured. We caution that mid levels of vaccination can be counterproductive resulting in rabies persistence rather than control. We also note that our model/computing system has the flexibility and capacity to explore a wide range of questions pertinent to improving the efficacy of rabies control.

Landscape connectivity and seed dispersal characteristics inform the best management strategy for exotic plants

Exotic plant invasions have triggered environmental and economic problems throughout the world. Our ability to manage these invasions is hindered by the difficulty of predicting spread in fragmented landscapes. Because the spatial pattern of invasions depends on the dispersal characteristics of the invasive species and the configuration of suitable habitat within the landscape, a universal management strategy is unlikely to succeed for any particular species. We suggest that the most effective management strategy may be an adaptive one that shifts from local control to landscape management depending on the specific invader and landscape. In particular, we addressed the question of where management activities should be focused to minimize spread of the invading species. By simulating an invasion across a real landscape (Antietam National Battlefield in Maryland, USA), we examined the importance of patch size and connectivity to management success. We found that the best management strategy depended on the dispersal characteristics of the exotic species. Species with a high probability of random long-distance dispersal were best managed by focusing on the largest patches, while species with a lower probability of random long-distance dispersal were best managed by considering landscape configuration and connectivity of the patches. Connectivity metrics from network analysis were useful for identifying the most effective places to focus management efforts. These results provide insight into invasion patterns of various species and suggest a general rule for managers in National Parks and other places where invasive species are a concern.