Functional autoregressive forecasting of long-term seabed evolution

There is a need for decadal predictions of the seabed evolution, for example to inform resurvey strategies when maintaining navigation channels. The understanding of the physical processes involved in morphological evolution, and the viability of process models to accurately model evolution over these time scales, are currently limited. As a result, statistical approaches are used to supply long-term forecasts. In this paper, we introduce a novel statistical approach for this problem: the autoregressive Hilbertian model (ARH). This model naturally assesses the time evolution of spatially-distributed measurements. We apply the technique to a coastal area in the East Anglian coast over the period 1846 to 2002, and compare with two other statistical methods used recently for seabed prediction: the autoregressive model and the EOF model. We evaluate the performance of the three methods by comparing observations and predictions for 2002. The ARH model enables a reduction of 10% of the root mean squared errors. Finally, we compute the variability in the predictions related to time sampling using the jackknife, a method that uses subsamples to quantify uncertainties.     

Sensitivity of population viability to spatial and nonspatial parameters using GRIP.

Metapopulation dynamics are influenced by spatial parameters including the amount and arrangement of suitable habitat, yet these parameters may be uncertain when deciding how to manage species or their habitats. Sensitivity analyses of population viability analysis (PVA) models can help measure relative parameter influences on predictions, identify research priorities for reducing uncertainty, and evaluate management strategies. Few spatial PVAs, however, include sensitivity analyses of both spatial and nonspatial parameters, perhaps because computationally efficient tools for such analyses are lacking or inaccessible. We developed GRIP, a program to facilitate sensitivity analysis of spatial and nonspatial input parameters for PVAs created in RAMAS Metapop, a widely applied software program. GRIP creates random sets of input files by varying parameters specified in the PVA model including vital rates and their correlations among populations, the number and configuration of populations, dispersal rates, dispersal survival, initial population abundances, carrying capacities, and the probability, intensity, and spatial extent of catastrophes, while drawing on specified parameter distributions. We evaluated GRIP's performance as a tool for sensitivity analysis of spatial PVAs and explored the consequences of varying spatial input parameters for predictions of a published PVA model of the sand lizard (Lacerta agilis). We used GRIP output to generate standardized regression coefficients (SRCs) and nonparametric correlation coefficients as indices of the relative sensitivity of predicted conservation status to input parameters. GRIP performed well; with a single analysis we were able to rank the relative influence of input parameters identified as influential by the PVA's original author, S. A. Berglind, who used three separate forms of sensitivity analysis. Our analysis, however, also underscored the value of exploring the relative influence of spatial parameters on PVA predictions; both SRCs and correlation coefficients indicated that the most influential parameters in the sand lizard model were spatial in nature. We provide annotated code so that GRIP may be modified to reflect particular species biology, customized for more complex spatial PVA models, upgraded to incorporate features added in newer versions of RAMAS Metapop, used as a template to develop similar programs, or used as it is for computationally efficient sensitivity analyses in support of conservation planning.     

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.     

The Sensitivity of Population Viability Analysis to Uncertainty about Habitat Requirements: Implications for the Management of the Endangered Southern Brown Bandicoot

Abstract:  Whenever population viability analysis (PVA) models are built to help guide decisions about the management of rare and threatened species, an important component of model building is the specification of a habitat model describing how a species is related to landscape or bioclimatic variables. Model-selection uncertainty may arise because there is often a great deal of ambiguity about which habitat model structure best approximates the true underlying biological processes. The standard approach to incorporate habitat models into PVA is to assume the best habitat model is correct, ignoring habitat-model uncertainty and alternative model structures that may lead to quantitatively different conclusions and management recommendations. Here we provide the first detailed examination of the influence of habitat-model uncertainty on the ranking of management scenarios from a PVA model. We evaluated and ranked 6 management scenarios for the endangered southern brown bandicoot ( Isoodon obesulus ) with PVA models, each derived from plausible competing habitat models developed with logistic regression. The ranking of management scenarios was sensitive to the choice of the habitat model used in PVA predictions. Our results demonstrate the need to incorporate methods into PVA that better account for model uncertainty and highlight the sensitivity of PVA to decisions made during model building. We recommend that researchers search for and consider a range of habitat models when undertaking model-based decision making and suggest that routine sensitivity analyses should be expanded to include an analysis of the impact of habitat-model uncertainty and assumptions.     

Updating coarse-scale species distribution models using small fine-scale samples

Large, fine-grained samples are ideal for predictive species distribution models used for management purposes, but such datasets are not available for most species and conducting such surveys is costly. We attempted to overcome this obstacle by updating previously available coarse-grained logistic regression models with small fine-grained samples using a recalibration approach. Recalibration involves re-estimation of the intercept or slope of the linear predictor and may improve calibration (level of agreement between predicted and actual probabilities). If reliable estimates of occurrence likelihood are required (e.g., for species selection in ecological restoration) calibration should be preferred to other model performance measures. This updating approach is not expected to improve discrimination (the ability of the model to rank sites according to species suitability), because the rank order of predictions is not altered. We tested different updating methods and sample sizes with tree distribution data from Spain. Updated models were compared to models fitted using only fine-grained data (refitted models). Updated models performed reasonably well at fine scales and outperformed refitted models with small samples (10-100 occurrences). If a coarse-grained model is available (or could be easily developed) and fine-grained predictions are to be generated from a limited sample size, updating previous models may be a more accurate option than fitting a new model. Our results encourage further studies on model updating in other situations where species distribution models are used under different conditions from their training (e.g., different time periods, different regions).     

Improving effectiveness of systematic conservation planning with density data

Systematic conservation planning aims to design networks of protected areas that meet conservation goals across large landscapes. The optimal design of these conservation networks is most frequently based on the modeled habitat suitability or probability of occurrence of species, despite evidence that model predictions may not be highly correlated with species density. We hypothesized that conservation networks designed using species density distributions more efficiently conserve populations of all species considered than networks designed using probability of occurrence models. To test this hypothesis, we used the Zonation conservation prioritization algorithm to evaluate conservation network designs based on probability of occurrence versus density models for 26 land bird species in the U.S. Pacific Northwest. We assessed the efficacy of each conservation network based on predicted species densities and predicted species diversity. High‐density model Zonation rankings protected more individuals per species when networks protected the highest priority 10‐40% of the landscape. Compared with density‐based models, the occurrence‐based models protected more individuals in the lowest 50% priority areas of the landscape. The 2 approaches conserved species diversity in similar ways: predicted diversity was higher in higher priority locations in both conservation networks. We conclude that both density and probability of occurrence models can be useful for setting conservation priorities but that density‐based models are best suited for identifying the highest priority areas. Developing methods to aggregate species count data from unrelated monitoring efforts and making these data widely available through ecoinformatics portals such as the Avian Knowledge Network will enable species count data to be more widely incorporated into systematic conservation planning efforts.     

Modeling and Predicting Species Occurrence Using Broad-Scale Environmental Variables: an Example with Butterflies of the Great Basin

Abstract: If occurrence of individual species can be modeled as a function of easily quantified environmental variables (e.g., derived from a geographic information system [GIS]) and the predictions of these models are demonstrably successful, then the scientific foundation for management planning will be strengthened. We used Bayesian logistic regression to develop predictive models for resident butterflies in the central Great Basin of western North America. Species inventory data and values for 14 environmental variables from 49 locations (segments of canyons) in the Toquima Range ( Nevada, U.S.A.) were used to build the models. Squares of the environmental variables were also used to accommodate possibly nonmonotonic responses. We obtained statistically significant models for 36 of 56 (64%) resident species of butterflies. The models explained 8–72% of the deviance in occurrence of those species. Each of the independent variables was significant in at least one model, and squared versions of five variables contributed to models. Elevation was included in more than half of the models. Models included one to four variables; only one variable was significant in about half the models. We conducted preliminary tests of two of our models by using an existing set of data on the occurrence of butterflies in the neighboring Toiyabe Range. We compared conventional logistic classification with posterior probability distributions derived from Bayesian modeling. For the latter, we restricted our predictions to locations with a high ( 70%) probability of predicted presence or absence. We will perform further tests after conducting inventories at new locations in the Toquima Range and nearby Shoshone Mountains, for which we have computed environmental variables by using remotely acquired topographic data, digital-terrain and microclimatic models, and GIS computation.     

The Use of Bayesian Model Averaging to Better Represent Uncertainty in Ecological Models

Abstract:   In conservation biology, uncertainty about the choice of a statistical model is rarely considered. Model-selection uncertainty occurs whenever one model is chosen over plausible alternative models to represent understanding about a process and to make predictions about future observations. The standard approach to representing prediction uncertainty involves the calculation of prediction (or confidence) intervals that incorporate uncertainty about parameter estimates contingent on the choice of a "best" model chosen to represent truth. However, this approach to prediction based on statistical models tends to ignore model-selection uncertainty, resulting in overconfident predictions. Bayesian model averaging (BMA) has been promoted in a range of disciplines as a simple means of incorporating model-selection uncertainty into statistical inference and prediction. Bayesian model averaging also provides a formal framework for incorporating prior knowledge about the process being modeled. We provide an example of the application of BMA in modeling and predicting the spatial distribution of an arboreal marsupial in the Eden region of southeastern Australia. Other approaches to estimating prediction uncertainty are discussed.     

The Influence of Model Structure on Conclusions about the Viability and Harvesting of Serengeti Wildebeest

We investigate how the viability and harvestability predicted by population models are affected by details of model construction. Based on this analysis we discuss some of the pitfalls associated with the use of classical statistical techniques for resolving the uncertainties associated with modeling population dynamics. The management of the Serengeti wildebeest (Connochaetes taurinus) is used as a case study. We fitted a collection of age-structured and unstructured models to a common set of available data and compared model predictions in terms of wildebeest viability and harvest. Models that depicted demographic processes in strikingly different ways fitted the data equally well. However, upon further analysis it became clear that models that fit the data equally well could nonetheless have very different management implications. In general, model structure had a much larger effect on viability analysis (e.g., time to collapse) than on optimal harvest analysis (e.g., harvest rate that maximizes harvest). Some modeling decisions, such as including age-dependent fertility rates, did not affect management predictions, but others had a strong effect (e.g., choice of model structure). Because several suitable models of comparable complexity fitted the data equally well, traditional model selection methods based on the parsimony principle were not practical for judging the value of alternative models. Our results stress the need to implement analytical frameworks for population management that explicitly consider the uncertainty about the behavior of natural systems.     

Model correlation in stochastic forest simulators—A case of multilevel multivariate model for seedling establishment

Forest development can be predicted by the use of forest simulators based on various statistical models describing the forest and its dynamics. One potential approach to study the reliability of the simulators is to utilise Monte Carlo simulation techniques to generate a predictive distribution of a forest characteristic. One problem in examining the effect of model uncertainty in forestry decision making, however, is correlation between the models. If this is not taken into account, predictions of the model systems may become biased, and the effect of errors on decision making may be underestimated. In reality, the models often are interdependent, but the correlations usually are not known because the models have been estimated in separate studies. The aim of this paper is to study the impacts of between-model dependencies on the predictive distribution of forest characteristics by Monte Carlo simulation techniques. We utilise a case of predicting seedling establishment of planted Norway spruce (Picea abies (L.) Karst.) stands as an example with multivariate multilevel model structures. Regardless of low cross-correlations between the models, ignoring them led to significant underestimation of the amount of competing broadleaves to be removed in pre-commercial thinning. Therefore, we recommend that between-model dependencies are clarified and considered in stochastic simulations. In our case, between-model interdependencies can be reliably estimated with a limited dataset. In addition, estimating the models separately and using the model residuals to estimate interdependencies between models were also sufficient to take the between-model dependencies into account when producing stochastic predictions for silvicultural decision making.     

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.     

Sensitivity Analyses of Spatial Population Viability Analysis Models for Species at Risk and Habitat Conservation Planning

Abstract:  Population viability analysis (PVA) is an effective framework for modeling species- and habitat-recovery efforts, but uncertainty in parameter estimates and model structure can lead to unreliable predictions. Integrating complex and often uncertain information into spatial PVA models requires that comprehensive sensitivity analyses be applied to explore the influence of spatial and nonspatial parameters on model predictions. We reviewed 87 analyses of spatial demographic PVA models of plants and animals to identify common approaches to sensitivity analysis in recent publications. In contrast to best practices recommended in the broader modeling community, sensitivity analyses of spatial PVAs were typically ad hoc, inconsistent, and difficult to compare. Most studies applied local approaches to sensitivity analyses, but few varied multiple parameters simultaneously. A lack of standards for sensitivity analysis and reporting in spatial PVAs has the potential to compromise the ability to learn collectively from PVA results, accurately interpret results in cases where model relationships include nonlinearities and interactions, prioritize monitoring and management actions, and ensure conservation-planning decisions are robust to uncertainties in spatial and nonspatial parameters. Our review underscores the need to develop tools for global sensitivity analysis and apply these to spatial PVA.     

Modelling species distributions with penalised logistic regressions: A comparison with maximum entropy models

An important aspect of species distribution modelling is the choice of the modelling method because a suboptimal method may have poor predictive performance. Previous comparisons have found that novel methods, such as Maxent models, outperform well-established modelling methods, such as the standard logistic regression. These comparisons used training samples with small numbers of occurrences per estimated model parameter, and this limited sample size may have caused poorer predictive performance due to overfitting. Our hypothesis is that Maxent models would outperform a standard logistic regression because Maxent models avoid overfitting by using regularisation techniques and a standard logistic regression does not. Regularisation can be applied to logistic regression models using penalised maximum likelihood estimation. This estimation procedure shrinks the regression coefficients towards zero, causing biased predictions if applied to the training sample but improving the accuracy of new predictions. We used Maxent and logistic regression (standard and penalised) to analyse presence/pseudo-absence data for 13 tree species and evaluated the predictive performance (discrimination) using presence-absence data. The penalised logistic regression outperformed standard logistic regression and equalled the performance of Maxent. The penalised logistic regression may be considered one of the best methods to develop species distribution models trained with presence/pseudo-absence data, as it is comparable to Maxent. Our results encourage further use of the penalised logistic regression for species distribution modelling, especially in those cases in which a complex model must be fitted to a sample with a limited size.     

Validation of ecological state space models using the Laplace approximation

Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.     

Generality of Models that Predict the Distribution of Species: Conservation Activity and Reduction of Model Transferability for a Threatened Bustard

Abstract:  Predictive models can help clarify the distribution of poorly known species but should display strong transferability when applied to independent data. Nevertheless, model transferability for threatened tropical species is poorly studied. We built models predicting the incidence of the critically endangered Bengal Florican ( Houbaropsis bengalensis ) within the Tonle Sap (TLS) floodplain, Cambodia. Separate models were constructed with soil, land-use, and landscape data and species incidence sampled over the entire floodplain (12,000 km²) and from the Kompong Thom (KT) province (4000 km²). In each case, the probability of Bengal Florican presence within randomly selected 1 × 1 km squares was modeled by binary logistic regression with multimodel inference. We assessed the transferability of the KT model by comparing predictions with observed incidence elsewhere in the floodplain. In terms of standard model-validation statistics, the KT model showed good spatial transferability. Nevertheless, it overpredicted florican presence outside the KT calibration region, classifying 491 km² as suitable habitat compared with 237 km² predicted as suitable by the TLS model. This resulted from higher species incidence within the calibration region, probably owing to a program of conservation education and enforcement that has reduced persecution there. Because both research and conservation activity frequently focus on areas with higher density, such effects could be widespread, reducing transferability of predictive distribution models.     

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.     

Predictive vegetation modeling for conservation: impact of error propagation from digital elevation data.

The effect of digital elevation model (DEM) error on environmental variables, and subsequently on predictive habitat models, has not been explored. Based on an error analysis of a DEM, multiple error realizations of the DEM were created and used to develop both direct and indirect environmental variables for input to predictive habitat models. The study explores the effects of DEM error and the resultant uncertainty of results on typical steps in the modeling procedure for prediction of vegetation species presence/absence. Results indicate that all of these steps and results, including the statistical significance of environmental variables, shapes of species response curves in generalized additive models (GAMs), stepwise model selection, coefficients and standard errors for generalized linear models (GLMs), prediction accuracy (Cohen's kappa and AUC), and spatial extent of predictions, were greatly affected by this type of error. Error in the DEM can affect the reliability of interpretations of model results and level of accuracy in predictions, as well as the spatial extent of the predictions. We suggest that the sensitivity of DEM-derived environmental variables to error in the DEM should be considered before including them in the modeling processes.     

Predicting aquaculture-derived benthic organic enrichment: Model validation

A sediment trap validation study was conducted near the commercial sea bass and sea bream fish farm in order to assess the predictive capability of a particle tracking deposition model. The validation procedure consisted of two distinct phases. First, the deposition of particulate waste (i.e. fecal pellets and excess feed) was measured near a single net pen containing 19 tons of sea bass. Afterwards, the model quality was determined by statistical comparison of predicted and observed values.Goodness of fit analysis indicates that the model successfully accounts for more than 75% of variance in the observed deposition. At 5% significance level, predictions do not underestimate or overestimate observations and there is no bias. Mean absolute relative error of ±48.9% compares favorably to other published deposition models. Obtained results affirm the reliability of particle tracking techniques in modeling the aquaculture-derived benthic organic enrichment.