Fine-scale habitat modeling of a top marine predator: do prey data improve predictive capacity?

Predators and prey assort themselves relative to each other, the availability of resources and refuges, and the temporal and spatial scale of their interaction. Predictive models of predator distributions often rely on these relationships by incorporating data on environmental variability and prey availability to determine predator habitat selection patterns. This approach to predictive modeling holds true in marine systems where observations of predators are logistically difficult, emphasizing the need for accurate models. In this paper, we ask whether including prey distribution data in fine-scale predictive models of bottlenose dolphin (Tursiops truncatus) habitat selection in Florida Bay, Florida, U.S.A., improves predictive capacity. Environmental characteristics are often used as predictor variables in habitat models of top marine predators with the assumption that they act as proxies of prey distribution. We examine the validity of this assumption by comparing the response of dolphin distribution and fish catch rates to the same environmental variables. Next, the predictive capacities of four models, with and without prey distribution data, are tested to determine whether dolphin habitat selection can be predicted without recourse to describing the distribution of their prey. The final analysis determines the accuracy of predictive maps of dolphin distribution produced by modeling areas of high fish catch based on significant environmental characteristics. We use spatial analysis and independent data sets to train and test the models. Our results indicate that, due to high habitat heterogeneity and the spatial variability of prey patches, fine-scale models of dolphin habitat selection in coastal habitats will be more successful if environmental variables are used as predictor variables of predator distributions rather than relying on prey data as explanatory variables. However, predictive modeling of prey distribution as the response variable based on environmental variability did produce high predictive performance of dolphin habitat selection, particularly foraging habitat.     

Testing the Generality of Bird-Habitat Models

Bird-habitat models are frequently used as predictive modeling tools—for example, to predict how a species will respond to habitat modifications. We investigated the generality of the predictions from this type of model. Multivariate models were developed for Golden Eagle (Aquila chrysaetos), Raven (Corvus corax), and Buzzard (Buteo buteo) living in northwest Scotland. Data were obtained for all habitat and nest locations within an area of 2349 km². This assemblage of species is relatively static with respect to both occupancy and spatial positioning. The area was split into five geographic subregions: two on the mainland and three on the adjacent Island of Mull, which has one of United Kingdom's richest raptor fauna assemblages. Because data were collected for all nest locations and habitats, it was possible to build models that did not incorporate sampling error. A range of predictive models was developed using discriminant analysis and logistic regression. The models differed with respect to the geographical origin of the data used for model development. The predictive success of these models was then assessed by applying them to validation data. The models showed a wide range of predictive success, ranging from only 6% of nest sites correctly predicted to 100% correctly predicted. Model validation techniques were used to ensure that the models' predictions were not statistical artefacts. The variability in prediction success seemed to result from methodological and ecological processes, including the data recording scheme and interregional differences in nesting habitat. The results from this study suggest that conservation biologists must be very careful about making predictions from such studies because we may be working with systems that are inherently unpredictable.     

Assumption‐versus data‐based approaches to summarizing species’ ranges

For conservation decision making, species’ geographic distributions are mapped using various approaches. Some such efforts have downscaled versions of coarse‐resolution extent‐of‐occurrence maps to fine resolutions for conservation planning. We examined the quality of the extent‐of‐occurrence maps as range summaries and the utility of refining those maps into fine‐resolution distributional hypotheses. Extent‐of‐occurrence maps tend to be overly simple, omit many known and well‐documented populations, and likely frequently include many areas not holding populations. Refinement steps involve typological assumptions about habitat preferences and elevational ranges of species, which can introduce substantial error in estimates of species’ true areas of distribution. However, no model‐evaluation steps are taken to assess the predictive ability of these models, so model inaccuracies are not noticed. Whereas range summaries derived by these methods may be useful in coarse‐grained, global‐extent studies, their continued use in on‐the‐ground conservation applications at fine spatial resolutions is not advisable in light of reliance on assumptions, lack of real spatial resolution, and lack of testing. In contrast, data‐driven techniques that integrate primary data on biodiversity occurrence with remotely sensed data that summarize environmental dimensions (i.e., ecological niche modeling or species distribution modeling) offer data‐driven solutions based on a minimum of assumptions that can be evaluated and validated quantitatively to offer a well‐founded, widely accepted method for summarizing species’ distributional patterns for conservation applications.     

Invasive species distribution modeling (iSDM): Are absence data and dispersal constraints needed to predict actual distributions?

Species distribution models (SDMs) based on statistical relationships between occurrence data and underlying environmental conditions are increasingly used to predict spatial patterns of biological invasions and prioritize locations for early detection and control of invasion outbreaks. However, invasive species distribution models (iSDMs) face special challenges because (i) they typically violate SDM's assumption that the organism is in equilibrium with its environment, and (ii) species absence data are often unavailable or believed to be too difficult to interpret. This often leads researchers to generate pseudo-absences for model training or utilize presence-only methods, and to confuse the distinction between predictions of potential vs. actual distribution. We examined the hypothesis that true-absence data, when accompanied by dispersal constraints, improve prediction accuracy and ecological understanding of iSDMs that aim to predict the actual distribution of biological invasions. We evaluated the impact of presence-only, true-absence and pseudo-absence data on model accuracy using an extensive dataset on the distribution of the invasive forest pathogen Phytophthora ramorum in California. Two traditional presence/absence models (generalized linear model and classification trees) and two alternative presence-only models (ecological niche factor analysis and maximum entropy) were developed based on 890 field plots of pathogen occurrence and several climatic, topographic, host vegetation and dispersal variables. The effects of all three possible types of occurrence data on model performance were evaluated with receiver operating characteristic (ROC) and omission/commission error rates. Results show that prediction of actual distribution was less accurate when we ignored true-absences and dispersal constraints. Presence-only models and models without dispersal information tended to over-predict the actual range of invasions. Models based on pseudo-absence data exhibited similar accuracies as presence-only models but produced spatially less feasible predictions. We suggest that true-absence data are a critical ingredient not only for accurate calibration but also for ecologically meaningful assessment of iSDMs that focus on predictions of actual distributions.     

Crustacean habitat potential mapping in a tidal flat using remote sensing and GIS

To make a macrofaunal (crustacean) habitat potential map, the spatial distribution of ecological variables in the Hwangdo tidal flat, Korea, was explored. Spatial variables were mapped using remote sensing and a geographic information system (GIS) combined with field observations. A frequency ratio (FR) and logistic regression (LR) model were employed to map the macrofauna potential area for the Ilyoplax dentimerosa, a crustacean species. Spatial variables affecting the tidal macrofauna distribution were selected based on abundance and biomass and used within a spatial database derived from remotely sensed data of various types of sensors. The spatial variables included the intertidal digital elevation model (DEM), slope, distance from a tidal channel, tidal channel density, surface sediment facies, spectral reflectance of the near infrared (NIR) bands and the tidal exposure duration. The relation between the I. dentimerosa and each spatial variable was calculated using the FR and LR. The species was randomly divided into a training set (70%) to analyse habitat potential using FR and LR and a test set (30%) to validate the predicted habitat potential map. The relations were overlaid to produce a habitat potential map with the species potential index (SPI) value for each pixel. The potential habitat maps were compared with the surveyed habitat locations such as validation data set. The comparison results showed that the LR model (accuracy is 85.28%) is better in prediction than the FR (accuracy is 78.96%) model. The performance of models gave satisfactory accuracies. The LR provides the quantitative influence of variables on a potential habitat of species; otherwise, the FR shows the quantitative influence of a class in each variable. The combination of a GIS-based frequency ratio and logistic regression models and remote sensing with field observations is an effective method to determine locations favorable for macrofaunal species occurrences in a tidal flat.     

New approaches to modelling fish-habitat relationships

Ecologists often develop models that describe the relationship between faunal communities and their habitat. Coral reef fishes have been the focus of numerous such studies, which have used a wide range of statistical tools to answer an equally wide range of questions. Here, we apply a series of both conventional statistical techniques (linear and generalized additive regression models) and novel machine-learning techniques (the support vector machine and three ensemble techniques used with regression trees) to predict fish species richness, biomass, and diversity from a range of habitat variables. We compare the techniques in terms of their predictive performance, and we compare a subset of the models in terms of the influence each habitat variable has for the predictions. Prediction errors are estimated by cross-validation, and variable importance is assessed using permutations of individual variable values. For predictions of species richness and diversity the tree-based models generally and the random forest model specifically are superior (produce the lowest errors). These model types are all able to model both nonlinear and interaction effects. The linear model, unable to model either effect type, performs the worst (produces the highest errors). For predictions of biomass, the generalized additive model is superior, and the support vector machine performs the worst. Depth range, the difference between maximum and minimum water depth at a given site, is identified as the most important variable in the majority of models predicting the three fish community variables. However, variable importance is highly dependent upon model type, which leads to questions regarding the interpretation of variable importance and its proper use as an indicator of causality. The representation of ecological relationships by tree-based ensemble learners will improve predictive performance, and provide a new avenue for exploring ecological relationships, both statistical and causal.     

Using habitat suitability index and particle dispersion models for early detection of marine invaders.

Eradication and control of invasive species are often possible only if populations are detected when they are small and localized. To be efficient, detection surveys should be targeted at locations where there is the greatest risk of incursions. We examine the utility of habitat suitability index (HSI) and particle dispersion models for targeting sampling for marine pests. Habitat suitability index models are a simple way to identify suitable habitat when species distribution data are lacking. We compared the performance of HSI models with statistical models derived from independent data from New Zealand on the distribution of two nonindigenous bivalves: Theora lubrica and Musculista senhousia. Logistic regression models developed using the HSI scores as predictors of the presence/absence of Theora and Musculista explained 26.7% and 6.2% of the deviance in the data, respectively. Odds ratios for the HSI scores were greater than unity, indicating that they were genuine predictors of the presence/ absence of each species. The fit and predictive accuracy of each logistic model were improved when simulated patterns of dispersion from the nearest port were added as a predictor variable. Nevertheless, the combined model explained, at best, 46.5% of the deviance in the distribution of Theora and correctly predicted 56% of true presences and 50% of all cases. Omission errors were between 6% and 16%. Although statistical distribution models built directly from environmental predictors always outperformed the equivalent HSI models, the gain in model fit and accuracy was modest. High residual deviance in both types of model suggests that the distributions realized by Theora and Musculista in the field data were influenced by factors not explicitly modeled as explanatory variables and by error in the environmental data used to project suitable habitat for the species. Our results highlight the difficulty of accurately predicting the distribution of invasive marine species that exhibit low habitat occupancy and patchy distributions in time and space. Although the HSI and statistical models had utility as predictors of the likely distribution of nonindigenous marine species, the level of spatial accuracy achieved with them may be well below expectations for sensitive surveillance programs.     

Predicting abundance of desert riparian birds: validation and calibration of the Effective Area Model.

Reliable prediction of the effects of landscape change on species abundance is critical to land managers who must make frequent, rapid decisions with long-term consequences. However, due to inherent temporal and spatial variability in ecological systems, previous attempts to predict species abundance in novel locations and/or time frames have been largely unsuccessful. The Effective Area Model (EAM) uses change in habitat composition and geometry coupled with response of animals to habitat edges to predict change in species abundance at a landscape scale. Our research goals were to validate EAM abundance predictions in new locations and to develop a calibration framework that enables absolute abundance predictions in novel regions or time frames. For model validation, we compared the EAM to a null model excluding edge effects in terms of accurate prediction of species abundance. The EAM outperformed the null model for 83.3% of species (N=12) for which it was possible to discern a difference when considering 50 validation sites. Likewise, the EAM outperformed the null model when considering subsets of validation sites categorized on the basis of four variables (isolation, presence of water, region, and focal habitat). Additionally, we explored a framework for producing calibrated models to decrease prediction error given inherent temporal and spatial variability in abundance. We calibrated the EAM to new locations using linear regression between observed and predicted abundance with and without additional habitat covariates. We found that model adjustments for unexplained variability in time and space, as well as variability that can be explained by incorporating additional covariates, improved EAM predictions. Calibrated EAM abundance estimates with additional site-level variables explained a significant amount of variability (P < 0.05) in observed abundance for 17 of 20 species, with R2 values >25% for 12 species, >48% for six species, and >60% for four species when considering all predictive models. The calibration framework described in this paper can be used to predict absolute abundance in sites different from those in which data were collected if the target population of sites to which one would like to statistically infer is sampled in a probabilistic way.     

Landscape evaluation in conservation: molecular sampling and habitat modeling for the Iberian lynx.

Conservation of endangered species requires comprehensive understanding of their distribution and habitat requirements, in order to implement better management strategies. Unfortunately, this understanding is often difficult to gather at the short term required by rapidly declining populations of many rare vertebrates. We present a spatial habitat modeling approach that integrates a molecular technique for species detection with landscape information to assess habitat requirements of a critically endangered mammalian carnivore, the Iberian lynx (Lynx pardinus), in a poorly known population in Spain. We formulated a set of model hypotheses for habitat selection at the spatial scale of home ranges, based on previous information on lynx requirements of space, vegetation, and prey. To obtain the required data for model selection, we designed a sampling protocol based on surveys of feces and their molecular analysis for species identification. After comparing candidate models, we selected a parsimonious one that allowed (1) reliable assessment of lynx habitat requirements at the scale of home ranges, (2) prediction of lynx distribution and potential population size, and (3) identification of landscape management priorities for habitat conservation. This model predicted that the species was more likely to occur in landscapes with a higher percentage of rocky areas and higher cover of bushes typical of mature mediterranean shrubland mosaics. Its accuracy for discriminating lynx presence was approximately 85%, indicating high predictive performance. Mapping model predictions showed that only 16% of the studied areas constitute potential habitat for lynx, even though the region is dominated by large extents of well-preserved native vegetation with low human interference. Habitat was mostly clumped in two nearby patches connected by vegetation adequate for lynx dispersal and had a capacity for 28-62 potential breeding territories. The lynx population in Sierra Morena is probably the largest persisting today, but it is still critically small for optimism about its long-term persistence. Model results suggest habitat conservation and restoration actions needed for preserving the species, including reconciliation of hunting management with preservation of mature shrubland over large areas (particularly in rocky landscapes). The approach presented here can be applied to many other species for which the ecological information needed to develop sound habitat conservation strategies is lacking.     

Selecting pseudo-absence data for presence-only distribution modeling: How far should you stray from what you know?

An important decision in presence-only species distribution modeling is how to select background (or pseudo-absence) localities for model parameterization. The selection of such localities may influence model parameterization and thus, can influence the appropriateness and accuracy of the model prediction when extrapolating the species distribution across time and space. We used 12 species from the Australian Wet Tropics (AWT) to evaluate the relationship between the geographic extent from which pseudo-absences are taken and model performance, and shape and importance of predictor variables using the MAXENT modeling method. Model performance is lower when pseudo-absence points are taken from either a restricted or broad region with respect to species occurrence data than from an intermediate region. Furthermore, variable importance (i.e., contribution to the model) changed such that, models became increasingly simplified, dominated by just two variables, as the area from which pseudo-absence points were drawn increased. Our results suggest that it is important to consider the spatial extent from which pseudo-absence data are taken. We suggest species distribution modeling exercises should begin with exploratory analyses evaluating what extent might provide both the most accurate results and biologically meaningful fit between species occurrence and predictor variables. This is especially important when modeling across space or time—a growing application for species distributional modeling.     

Does scale matter in predicting species distributions? case study with the Marbled Murrelet.

Hierarchical selection orders (selection of microsite, patch, home range, population block, and geographic range) are ideal for dictating spatial grain and extent of animal habitat models, but the resultant conditional models are poor for creating predictive maps. I proposed a two-step approach for accurately mapping probability of animal use that incorporates a single-grain analysis of each selection order in the first step and creates a multi-grain model that combines key variables from each selection order in the second step. Such two-step multi-grain models are strongly recommended because they allow interpretation of the scale of selection for a variable. Using a large data set for the Marbled Murrelet (Brachyramphus marmoratus) as a case study and five selection orders, information theory criteria provided strong support that such models are superior to simpler one-step single-grain models for the murrelet. However, a single-grain model can produce high classification accuracy if it represents the most limiting scale. Notably, accuracy of the two-step multi-grain model was no better than a traditional one-step multi-grain model that ignores selection orders, indicating the advantage of two-step modeling is in elucidating scaling effects, not necessarily in improving accuracy of species distribution maps.     

Uncertainty propagation in vegetation distribution models based on ensemble classifiers

Ensemble learning techniques are increasingly applied for species and vegetation distribution modelling, often resulting in more accurate predictions. At the same time, uncertainty assessment of distribution models is gaining attention. In this study, Random Forests, an ensemble learning technique, is selected for vegetation distribution modelling based on environmental variables. The impact of two important sources of uncertainty, that is the uncertainty on spatial interpolation of environmental variables and the uncertainty on species clustering into vegetation types, is quantified based on sequential Gaussian simulation and pseudo-randomization tests, respectively. An empirical assessment of the uncertainty propagation to the distribution modelling results indicated a gradual decrease in performance with increasing input uncertainty. The test set error ranged from 30.83% to 52.63% and from 30.83% to 83.62%, when the uncertainty ranges on spatial interpolation and on vegetation clustering, respectively, were fully covered. Shannon’s entropy, which is proposed as a measure for uncertainty of ensemble predictions, revealed a similar increasing trend in prediction uncertainty. The implications of these results in an empirical distribution modelling framework are further discussed with respect to monitoring setup, spatial interpolation and species clustering.     

The evaluation strip: A new and robust method for plotting predicted responses from species distribution models

Increasing use is being made in conservation management of statistical models that couple extensive collections of species and environmental data to make predictions of the geographic distributions of species. While the relationships fitted between a species and its environment are relatively transparent for many of these modeling techniques, others are more ‘black box’ in character, only producing geographic predictions and providing minimal or untraditional summaries of the fitted relationships on which these predictions are based. This in turn prevents robust evaluation of the ecological sensibility of such models, a necessary process if model predictions are to be treated with confidence. Here we propose a new but simple method for visualizing modeled responses that can be implemented with any modeling method, and demonstrate its application using five common methods applied to the prediction of an Australian tree species. This is achieved by insetting an “evaluation strip” into the spatial data layers, which, after predictions have been made, can be clipped out and used for creating plots of the modelled responses. We present findings of the application strip for algorithms GLMs, GAMs, CLIM, DOMAIN and MARS. Evaluation strips can be constructed to investigate either uni-variate responses, or the simultaneous variation in predicted values in relation to two variables. The latter option is particularly useful for evaluating responses in models that allow the fitting of complex interaction terms.     

Modeling a spatially restricted distribution in the Neotropics: How the size of calibration area affects the performance of five presence-only methods

We here examine species distribution models for a Neotropical anuran restricted to ombrophilous areas in the Brazilian Atlantic Forest hotspot. We extend the known occurrence for the treefrog Hypsiboas bischoffi (Anura: Hylidae) through GPS field surveys and use five modeling methods (BIOCLIM, DOMAIN, OM-GARP, SVM, and MAXENT) and selected bioclimatic and topographic variables to model the species distribution. Models were first trained using two calibration areas: the Brazilian Atlantic Forest (BAF) and the whole of South America (SA). All modeling methods showed good levels of predictive power and accuracy with mean AUC ranging from 0.77 (BIOCLIM/BAF) to 0.99 (MAXENT/SA). MAXENT and SVM were the most accurate presence-only methods among those tested here. All but the SVM models calibrated with SA predicted larger distribution areas when compared to models calibrated in BAF. OM-GARP dramatically overpredicted the species distribution for the model calibrated in SA, with a predicted area around 10⁶ km² larger than predicted by other SDMs. With increased calibration area (and environmental space), OM-GARP predictions followed changes in the environmental space associated with the increased calibration area, while MAXENT models were more consistent across calibration areas. MAXENT was the only method that retrieved consistent predictions across calibration areas, while allowing for some overprediction, a result that may be relevant for modeling the distribution of other spatially restricted organisms.     

Use of Coarse‐Resolution Models of Species’ Distributions to Guide Local Conservation Inferences

Abstract: Distribution models are used increasingly for species conservation assessments over extensive areas, but the spatial resolution of the modeled data and, consequently, of the predictions generated directly from these models are usually too coarse for local conservation applications. Comprehensive distribution data at finer spatial resolution, however, require a level of sampling that is impractical for most species and regions. Models can be downscaled to predict distribution at finer resolutions, but this increases uncertainty because the predictive ability of models is not necessarily consistent beyond their original scale. We analyzed the performance of downscaled, previously published models of environmental favorability (a generalized linear modeling technique) for a restricted endemic insectivore, the Iberian desman (Galemys pyrenaicus), and a more widespread carnivore, the Eurasian otter (Lutra lutra), in the Iberian Peninsula. The models, built from presence–absence data at 10 × 10 km resolution, were extrapolated to a resolution 100 times finer (1 × 1 km). We compared downscaled predictions of environmental quality for the two species with published data on local observations and on important conservation sites proposed by experts. Predictions were significantly related to observed presence or absence of species and to expert selection of sampling sites and important conservation sites. Our results suggest the potential usefulness of downscaled projections of environmental quality as a proxy for expensive and time‐consuming field studies when the field studies are not feasible. This method may be valid for other similar species if coarse‐resolution distribution data are available to define high‐quality areas at a scale that is practical for the application of concrete conservation measures.     

Habitat classification modeling with incomplete data: pushing the habitat envelope.

Habitat classification models (HCMs) are invaluable tools for species conservation, land-use planning, reserve design, and metapopulation assessments, particularly at broad spatial scales. However, species occurrence data are often lacking and typically limited to presence points at broad scales. This lack of absence data precludes the use of many statistical techniques for HCMs. One option is to generate pseudo-absence points so that the many available statistical modeling tools can bb used. Traditional techniques generate pseudo-absence points at random across broadly defined species ranges, often failing to include biological knowledge concerning the species-habitat relationship. We incorporated biological knowledge of the species-habitat relationship into pseudo-absence points by creating habitat envelopes that constrain the region from which points were randomly selected. We define a habitat envelope as an ecological representation of a species, or species feature's (e.g., nest) observed distribution (i.e., realized niche) based on a single attribute, or the spatial intersection of multiple attributes. We created HCMs for Northern Goshawk (Accipiter gentilis atricapillus) nest habitat during the breeding season across Utah forests with extant nest presence points and ecologically based pseudo-absence points using logistic regression. Predictor variables were derived from 30-m USDA Landfire and 250-m Forest Inventory and Analysis (FIA) map products. These habitat-envelope-based models were then compared to null envelope models which use traditional practices for generating pseudo-absences. Models were assessed for fit and predictive capability using metrics such as kappa, threshold-independent receiver operating characteristic (ROC) plots, adjusted deviance (D(adj)2), and cross-validation, and were also assessed for ecological relevance. For all cases, habitat envelope-based models outperformed null envelope models and were more ecologically relevant, suggesting that incorporating biological knowledge into pseudo-absence point generation is a powerful tool for species habitat assessments. Furthermore, given some a priori knowledge of the species-habitat relationship, ecologically based pseudo-absence points can be applied to any species, ecosystem, data resolution, and spatial extent.     

Predicting the Range of Chinese Mitten Crabs in Europe

Abstract:  Ecological niche modeling provides a means for predicting the potential future distribution of a nonindigenous species based on environmental characteristics of the species' native range. We applied this method to the Chinese mitten crab (Eriocheir sinensis) , a catadromous crustacean with a long history of invasion in Europe. We used genetic algorithm for rule-set prediction to predict the potential European distribution of mitten crab based on its distribution in 42 locations in its native Asia. The climatic variables, air temperature, number of days, amount of precipitation, and wetness index, contributed significantly to predictions of native distribution limits. Although the genetic algorithm for rule-set prediction model was developed for the native range, the species' extensive distribution in Europe ( n = 434) allowed independent validation of the predictions. Application of the model to Europe was successful, with 84% of occurrences in regions predicted to be suitable by >80% of the models and <4% of occurrences in areas predicted suitable by <50% of the models (mainly along the northern range). At the watershed scale, areas with established mitten crab populations had significantly higher habitat matching than sites that were not invaded. The independent validation of the Asian-based model by the European distribution revealed that predictions were highly accurate. The model also identified large areas of Europe, particularly along the Mediterranean coast, as vulnerable to future invasion. These predictions can be used to develop strategies to control the spread of mitten crab by preventing introductions into vulnerable areas.     

Appreciating Ecological Complexity: Habitat Contours as a Conceptual Landscape Model

Abstract:  Organisms respond to their surroundings at multiple spatial scales, and different organisms respond differently to the same environment. Existing landscape models, such as the "fragmentation model" (or patch-matrix-corridor model) and the "variegation model," can be limited in their ability to explain complex patterns for different species and across multiple scales. An alternative approach is to conceptualize landscapes as overlaid species-specific habitat contour maps. Key characteristics of this approach are that different species may respond differently to the same environmental conditions and at different spatial scales. Although similar approaches are being used in ecological modeling, there is much room for habitat contours as a useful conceptual tool. By providing an alternative view of landscapes, a contour model may stimulate more field investigations stratified on the basis of ecological variables other than human-defined patches and patch boundaries. A conceptual model of habitat contours may also help to communicate ecological complexity to land managers. Finally, by incorporating additional ecological complexity, a conceptual model based on habitat contours may help to bridge the perceived gap between pattern and process in landscape ecology. Habitat contours do not preclude the use of existing landscape models and should be seen as a complementary approach most suited to heterogeneous human-modified landscapes.     

General methods for sensitivity analysis of equilibrium dynamics in patch occupancy models

Sensitivity analysis is a useful tool for the study of ecological models that has many potential applications for patch occupancy modeling. Drawing from the rich foundation of existing methods for Markov chain models, I demonstrate new methods for sensitivity analysis of the equilibrium state dynamics of occupancy models. Estimates from three previous studies are used to illustrate the utility of the sensitivity calculations: a joint occupancy model for a prey species, its predators, and habitat used by both; occurrence dynamics from a well-known metapopulation study of three butterfly species; and Golden Eagle occupancy and reproductive dynamics. I show how to deal efficiently with multistate models and how to calculate sensitivities involving derived state variables and lower-level parameters. In addition, I extend methods to incorporate environmental variation by allowing for spatial and temporal variability in transition probabilities. The approach used here is concise and general and can fully account for environmental variability in transition parameters. The methods can be used to improve inferences in occupancy studies by quantifying the effects of underlying parameters, aiding prediction of future system states, and identifying priorities for sampling effort.