Bayesian areal wombling via adjacency modeling

Recently, public health professionals and other geostatistical researchers have shown increasing interest in boundary analysis, the detection or testing of zones or boundaries that reveal sharp changes in the values of spatially oriented variables. For areal data (i.e., data which consist only of sums or averages over geopolitical regions), Lu and Carlin (Geogr Anal 37: 265–285, 2005) suggested a fully model-based framework for areal wombling using Bayesian hierarchical models with posterior summaries computed using Markov chain Monte Carlo (MCMC) methods, and showed the approach to have advantages over existing non-stochastic alternatives. In this paper, we develop Bayesian areal boundary analysis methods that estimate the spatial neighborhood structure using the value of the process in each region and other variables that indicate how similar two regions are. Boundaries may then be determined by the posterior distribution of either this estimated neighborhood structure or the regional mean response differences themselves. Our methods do require several assumptions (including an appropriate prior distribution, a normal spatial random effect distribution, and a Bernoulli distribution for a set of spatial weights), but also deliver more in terms of full posterior inference for the boundary segments (e.g., direct probability statements regarding the probability that a particular border segment is part of the boundary). We illustrate three different remedies for the computing difficulties encountered in implementing our method. We use simulation to compare among existing purely algorithmic approaches, the Lu and Carlin (2005) method, and our new adjacency modeling methods. We also illustrate more practical modeling issues (e.g., covariate selection) in the context of a breast cancer late detection data set collected at the county level in the state of Minnesota.     

A hierarchical Bayesian non-linear spatio-temporal model for the spread of invasive species with application to the Eurasian Collared-Dove

The spread of invasive species is a long studied subject that garners much interest in the ecological research community. Historically the phenomenon has been approached using a purely deterministic mathematical framework (usually involving differential equations of some form). These methods, while scientifically meaningful, are generally highly simplified and fail to account for uncertainty in the data and process, of which our knowledge could not possibly exist without error. We propose a hierarchical Bayesian model for population spread that accommodates data sources with errors, dependence structures between population dynamics parameters, and takes into account prior scientific understanding via non-linear relationships between model parameters and space-time response variables. We model the process (i.e., the bird population in this case) as a Poisson response with spatially varying diffusion coefficients as well as a logistic population growth term using a common reaction-diffusion equation that realistically mimics the ecological process. We focus the application on the ongoing invasion of the Eurasian Collared-Dove.     

Is spread of invasive species regulated? Using ecological theory to interpret statistical analysis

We investigate a recent proposal that invasive species display patterns of spatial "spread regulation" analogous to density-dependent regulation of population abundances. While invasive species do offer valuable tests of ecological theories about spatial spread, we argue that the statistical approach used in the study is not useful, and that the proposed definition of "spread regulation" is likely to be confusing. While concepts of negative feedbacks in spatial spread may be reasonable, the proposed definition of "spread regulation" encompasses accelerating, constant, or decelerating spread. There is no compelling biological or practical reason to adopt such a definition. Moreover, we show that the statistical patterns (from time series of ratios of newly to recently invaded sites) proposed as evidence of spread regulation are predictable from basic diffusion models or other common models of constant spread with some stochasticity in dynamics and/or observations. Because such a wide range of processes would generate the observed patterns, no clear biological conclusions emerge from the proposed approach to spread analysis. When regarded in the context of the impacts and management of invasive species, the proposed regulation concept has the potential to create costly misunderstandings.     

Protected‐Area Boundaries as Filters of Plant Invasions

Abstract: Human land uses surrounding protected areas provide propagules for colonization of these areas by non‐native species, and corridors between protected‐area networks and drainage systems of rivers provide pathways for long‐distance dispersal of non‐native species. Nevertheless, the influence of protected‐area boundaries on colonization of protected areas by invasive non‐native species is unknown. We drew on a spatially explicit data set of more than 27,000 non‐native plant presence records for South Africa's Kruger National Park to examine the role of boundaries in preventing colonization of protected areas by non‐native species. The number of records of non‐native invasive plants declined rapidly beyond 1500 m inside the park; thus, we believe that the park boundary limited the spread of non‐native plants. The number of non‐native invasive plants inside the park was a function of the amount of water runoff, density of major roads, and the presence of natural vegetation outside the park. Of the types of human‐induced disturbance, only the density of major roads outside the protected area significantly increased the number of non‐native plant records. Our findings suggest that the probability of incursion of invasive plants into protected areas can be quantified reliably.     

Population dynamics and control of invasive Spartina alterniflora: inference and forecasting under uncertainty

Managing invaded ecosystems entails making decisions about control strategies in the face of scientific uncertainty and ecological stochasticity. Statistical tools such as model selection and Bayesian decision analysis can guide decision-making by estimating probabilities of outcomes under alternative management scenarios, but these tools have seldom been applied in invasion ecology. We illustrate the use of model selection and Bayesian methods in a case study of smooth cordgrass (Spartina alterniflora) invading Willapa Bay, Washington. To address uncertainty in model structure, we quantified the weight of evidence for two previously proposed hypotheses, that S. alterniflora recruitment varies with climatic conditions (represented by sea surface temperature) and that recruitment is subject to an Allee effect due to pollen limitation. By fitting models to time series data, we found strong support for climate effects, with higher per capita seedling production in warmer years, but no evidence for an Allee effect based on either the total area invaded or the mean distance between neighboring clones. We used the best-supported model to compare alternative control strategies, incorporating uncertainty in parameter estimates and population dynamics. For a fixed annual removal effort, the probability of eradication in 10 years was highest, and final invaded area lowest, if removals targeted the smallest clones rather than the largest or randomly selected clones. The relationship between removal effort and probability of eradication was highly nonlinear, with a sharp threshold separating -0% and -100% probability of success, and this threshold was 95% lower in simulations beginning early rather than late in the invasion. This advantage of a rapid response strategy is due to density-dependent population growth, which produces alternative stable equilibria depending on the initial invasion size when control begins. Our approach could be applied to a wide range of invasive species management problems where appropriate data are available.     

Temporal limits to simulating the future spread pattern of invasive species: Buddleja davidii in Europe and New Zealand

The spread of invasive species is a major ecological and economic problem. Dynamic spread modelling is a potentially valuable tool to assist regional and central government authorities to monitor and control invasive species. To date a lack of suitable data has meant that most broad scale dispersal models have not been validated with independent datasets, and so their predictive ability and reliability has remained unscrutinised. A dynamic, stochastic dispersal model of the widely invasive plant Buddleja davidii was calibrated on European spread data and then used to project the temporal progression of B. davidii's distribution in New Zealand, starting from several different historical distributions. To assess the model's performance, we constructed an occupancy map based on the average number of simulation realisations that have a population present. The application of Receiver Operating Characteristic (ROC) curves to occupancy maps is introduced, but with specificity substituted by the proportion of available area used in a realisation. A derivative measure, the partial area under these curves when assessed through time (pAUC), is introduced and used to assess overall performance of the spread model. The model was able to attain a high level of model sensitivity, encompassing all of the known locations within the occupancy envelope. However, attempting to simulate the spread of this invasive species beyond a decade had very low model specificity. This is due to several factors, including the exponential process of spread (the further a population spreads the more sites exist from which it can spread stochastically), and the Markovian chain property of the stochastic system whereby differences between realisations compound through time. These features are seen in many reports of spread models, without being explicitly acknowledged. Our measure of pAUC through time allows a model's temporal performance and its specificity to be simultaneously assessed. While the rapid deterioration in model performance limits the utility of this type of modelling for forecasting long-term broad-scale strategic management of biological invasions, it does not necessarily limit its attractiveness for informing smaller scale and shorter term invasion management activities such as surveillance, containment and local eradication.     

Predator–prey models: an application for the plankton dynamics of lake Geneva

In this paper we present a hierarchical Bayesian analysis for a predator–prey model applied to ecology considering the use of Markov Chain Monte Carlo methods. We consider the introduction of a random effect in the model and the presence of a covariate vector. An application to ecology is considered using a data set related to the plankton dynamics of lake Geneva for the year 1990. We also discuss some aspects of discrimination of the proposed models.     

Effects of Climate Change,Invasive Species,and Disease on the Distribution of Native European Crayfishes

Climate change will require species to adapt to new conditions or follow preferred climates to higher latitudes or elevations, but many dispersal‐limited freshwater species may be unable to move due to barriers imposed by watershed boundaries. In addition, invasive nonnative species may expand into new regions under future climate conditions and contribute to the decline of native species. We evaluated future distributions for the threatened European crayfish fauna in response to climate change, watershed boundaries, and the spread of invasive crayfishes, which transmit the crayfish plague, a lethal disease for native European crayfishes. We used climate projections from general circulation models and statistical models based on Mahalanobis distance to predict climate‐suitable regions for native and invasive crayfishes in the middle and at the end of the 21st century. We identified these suitable regions as accessible or inaccessible on the basis of major watershed boundaries and present occurrences and evaluated potential future overlap with 3 invasive North American crayfishes. Climate‐suitable areas decreased for native crayfishes by 19% to 72%, and the majority of future suitable areas for most of these species were inaccessible relative to native and current distributions. Overlap with invasive crayfish plague‐transmitting species was predicted to increase. Some native crayfish species (e.g., noble crayfish [Astacus astacus]) had no future refugia that were unsuitable for the modeled nonnative species. Our results emphasize the importance of preventing additional introductions and spread of invasive crayfishes in Europe to minimize interactions between the multiple stressors of climate change and invasive species, while suggesting candidate regions for the debatable management option of assisted colonization. Efectos del Cambio Climático, Especies Invasoras y Enfermedades sobre la Distribución de Cangrejos de Río Europeos Nativos     

Use of Community‐Composition Data to Predict the Fecundity and Abundance of Species

Abstract: Species distribution models are critical tools for the prediction of invasive species spread and conservation of biodiversity. The majority of species distribution models have been built with environmental data. Community ecology theory suggests that species co‐occurrence data could also be used to predict current and potential distributions of species. Species assemblages are the products of biotic and environmental constraints on the distribution of individual species and as a result may contain valuable information for niche modeling. We compared the predictive ability of distribution models of annual grassland plants derived from either environmental or community‐composition data. Composition‐based models were built with the presence or absence of species at a site as predictors of site quality, whereas environment‐based models were built with soil chemistry, moisture content, above‐ground biomass, and solar radiation as predictors. The reproductive output of experimentally seeded individuals of 4 species and the abundance of 100 species were used to evaluate the resulting models. Community‐composition data were the best predictors of both the site‐specific reproductive output of sown individuals and the site‐specific abundance of existing populations. Successful community‐based models were robust to omission of data on the occurrence of rare species, which suggests that even very basic survey data on the occurrence of common species may be adequate for generating such models. Our results highlight the need for increased public availability of ecological survey data to facilitate community‐based modeling at scales relevant to conservation.     

Knowledge gain and behavioral change in citizen-science programs

Citizen-science programs are often touted as useful for advancing conservation literacy, scientific knowledge, and increasing scientific-reasoning skills among the public. Guidelines for collaboration among scientists and the public are lacking and the extent to which these citizen-science initiatives change behavior is relatively unstudied. Over two years, we studied 82 participants in a three-day program that included education about non-native invasive plants and collection of data on the occurrence of those plants. Volunteers were given background knowledge about invasive plant ecology and trained on a specific protocol for collecting invasive plant data. They then collected data and later gathered as a group to analyze data and discuss responsible environmental behavior with respect to invasive plants. We tested whether participants without experience in plant identification and with little knowledge of invasive plants increased their knowledge of invasive species ecology, participation increased knowledge of scientific methods, and participation affected behavior. Knowledge of invasive plants increased on average 24%, but participation was insufficient to increase understanding of how scientific research is conducted. Participants reported increased ability to recognize invasive plants and increased awareness of effects of invasive plants on the environment, but this translated into little change in behavior regarding invasive plants. Potential conflicts between scientific goals, educational goals, and the motivation of participants must be considered during program design.     

Stochastic gravity models for modeling lake invasions

Freshwater aquatic systems in North America are being invaded by many different species, ranging from fish, mollusks, cladocerans to various bacteria and viruses. These invasions have serious ecological and economic impacts. Human activities such as recreational boating are an important pathway for dispersal. Gravity models are used to quantify the dispersal effect of human activity. Gravity models currently used in ecology are deterministic. This paper proposes the use of stochastic gravity models in ecology, which provides new capabilities both in model building and in potential model applications. These models allow us to use standard statistical inference tools such as maximum likelihood estimation and model selection based on information criteria. To facilitate prediction, we use only those covariates that are easily available from common data sources and can be forecasted in future. This is important for forecasting the spread of invasive species in geographical and temporal domain. The proposed model is portable, that is it can be used for estimating relative boater traffic and hence relative propagule pressure for the lakes not covered by current boater surveys. This makes our results broadly applicable to various invasion prediction and management models.     

A state-dependent model for the optimal management of an invasive metapopulation.

Management of invasive species involves choosing between different management strategy options, but often the best strategy for a particular scenario is not obvious. We illustrate the use of optimization methods to determine the most efficient management strategy using one of the most devastating invasive forest pests in North America, the gypsy moth (Lymantria dispar), as a case study. The optimization approach involves the application of stochastic dynamic programming (SDP) to a metapopulation framework with different infestation patch sizes, with the goal of minimizing infestation spread. We use a novel "moving window" approach as a way to address a spatially explicit problem without being explicitly spatial. We examine results for two cases in order to develop general rules of thumb for management. We explore a model with limited parameter information and then assess how strategies change with specific parameterization for the gypsy moth. The model results in a complex but stable, state-dependent management strategy for a multiyear management program that is robust even under situations of uncertainty. The general rule of thumb for the basic model consists of three strategies: eradicating medium-density infestations, reducing large-density infestations, and reducing the colonization rate from the main infestation, depending on the state of the system. With specific gypsy moth parameterization, reducing colonization decreases in importance relative to the other two strategies. The application of this model to gypsy moth management emphasizes the importance of managing based on the state of the system, and if applied to a specific geographic area, has the potential to substantially improve the efficiency and cost-effectiveness of current gypsy moth eradication programs, helping to slow the spread of this pest. Additionally, the approach used for this particular invasive species can be extended to the optimization of management programs for the spread of other invasive and problem species exhibiting metapopulation dynamics.     

The Robert H. MacArthur Award Lecture. Timescales, dynamics, and ecological understanding

Explicit consideration of timescales and dynamics is required for an understanding of fundamental issues in ecology. Endogenous dynamics can lead to transient states where asymptotic behavior is very different from dynamics on short timescales. The causes of these kinds of transients can be placed in one of three classes: linear systems with different timescales embedded or exhibiting reactive behavior, the potentially long times to reach synchrony across space for oscillating systems, and the complex dynamics of systems with strong density-dependent (nonlinear) interactions. It is also important to include the potentially disparate timescales inherent in ecological systems when determining the endogenous dynamics. I argue that the dynamics of ecological systems can best be understood as the response, which may include transient dynamics, to exogenous influences leading to the observed dynamics on ecologically relevant timescales. This view of ecosystem behavior as responses of ecological systems governed by endogenous dynamics to exogenous influences provides a synthetic way to unify different approaches to population dynamics, to understand mechanisms that determine the distribution and abundance of species, and to manage ecosystems on appropriate timescales. There are implications for theoretical approaches, empirical approaches, and the statistical approaches that bridge theory and observation.     

Comparing geographic boundaries in songbird demography data with vegetation boundaries: a new approach to evaluating habitat quality

To plan for the habitat needs of forest songbirds of conservation concern, managers need to understand how spatial heterogeneity in forest conditions influences habitat quality. I used difference boundary detection (wombling) and spatially constrained clustering to delineate boundaries in various combinations of four forest vegetation variables (understory height, understory density, percent deciduous vs. conifer understory, and percent canopy closure) in two Michigan northern hardwood forests. My goal was to identify vegetation boundaries that corresponded with boundaries in an understory-dependent songbird’s distribution, and with boundaries in demographic measures for this songbird that indicate habitat quality (e.g., occupancy by older vs. yearling males, reproductive success). Both forests were actively-managed, mature stands: The first site (78 ha) was heavily deer-browsed (HB), with many browse-resistant conifers in the understory, and the second (62 ha) was less-browsed (LB), with deciduous-dominated understory. I compared the vegetation difference and cluster boundaries to difference boundaries based on 6 years of distribution and demographic data for black-throated blue warblers (Dendroica caerulescens). At the HB site, warbler boundaries overlapped strongly with vegetation boundaries that included all four variables, and clustering effectively divided the habitat into areas with different warbler occupancy and demographic characteristics. At the LB site, warbler distribution showed high overlap with difference and cluster boundaries based on just the height and density of understory vegetation, and cluster boundaries again effectively partitioned the study area into sites that varied in habitat quality. Thus, geographic boundary analysis is likely to be a useful tool for identifying key vegetation variables for management, and for delineating clusters (habitat patches) within sites that capture differences in habitat quality.

The challenge of managing threatened invasive species at a continental scale

The European Union's (EU) environmental legislation establishes common measures to prevent the entry and spread of invasive non-native species and to minimize their impacts. However, species that are native to at least one member state but non-native and potentially invasive in others (NPIS) are in limbo because they are neither legally regulated at the EU level nor in most member states. We used the Communication and Information Resource Centre for Administrations, Businesses and Citizens (CIRCABC) raw data on NPIS (317 taxa) to analyze their distribution across the EU and identify which biogeographical regions are the main sources of invasions. We additionally evaluated the conservation challenge posed by NPIS that are threatened within their native ranges. We performed a pairwise analysis summarizing the number of species that are native to a given member state but non-native to another and vice versa. Although distribution patterns of NPIS varied across taxa groups, overall, southern and central EU countries were both donors and recipients of NPIS. Eastern countries were mainly a source, and western and northern countries mostly received NPIS. Around 27% of NPIS were threatened in some of their EU native ranges, which is a challenge for conservation and management because some of them have serious negative effects on European biodiversity, but hitherto remain outside the scope of the EU regulation of invasive non-native species. This highlights an unresolved paradox because efforts to manage species as invasive conflict with efforts to protect them as threatened within the same territory.     

Roads and Landscape Pattern in Northern Wisconsin Based on a Comparison of Four Road Data Sources

Abstract:  Roads are important components of landscapes; they fragment habitat, facilitate invasive species spread, alter hydrology, and influence patterns of land use. Previous research on the ecological impacts of roads may have underestimated their effect because currently available sources of road data do not include the full road network. We compared differences in road density and landscape pattern among U.S. Census Bureau TIGER line files, U.S. Geological Survey 1:100,000-scale digital line graphs, and U.S. Geological Survey 1:24,000-scale digital raster graphics in northern Wisconsin to road data derived from 1:40,000-scale digital orthophotos. Road density measured from digital orthophotos (2.82 km/km²) was significantly greater than that of digital raster graphics (1.62 km/km²) and more than double that of digital line graphs (1.21 km/km²) and TIGER (1.27 km/km²) data. The increased road densities in raster graphics and orthophoto data were mainly due to the addition of minor roads. When all roads were used to define patch boundaries, landscape metrics produced with orthophoto data showed significantly greater levels of fragmentation than those based on line or raster graphics. For example, maximum patch size was 1074 ha and total edge was 109 km for line graphs, compared with 686 ha and 211 km for orthophoto data. Roads are missing in commonly used data, primarily because mapping standards systematically exclude minor roads. These standards are not ecologically based and may result in false assumptions about the ecological effects of roads. We recommend that future studies take special consideration of the completeness of road data and consider whether all ecologically relevant roads are included.     

A trait-based test for habitat filtering: convex hull volume

Community assembly theory suggests that two processes affect the distribution of trait values within communities: competition and habitat filtering. Within a local community, competition leads to ecological differentiation of coexisting species, while habitat filtering reduces the spread of trait values, reflecting shared ecological tolerances. Many statistical tests for the effects of competition exist in the literature, but measures of habitat filtering are less well-developed. Here, we present convex hull volume, a construct from computational geometry, which provides an n-dimensional measure of the volume of trait space occupied by species in a community. Combined with ecological null models, this measure offers a useful test for habitat filtering. We use convex hull volume and a null model to analyze California woody-plant trait and community data. Our results show that observed plant communities occupy less trait space than expected from random assembly, a result consistent with habitat filtering.