Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions

Two statistical modelling techniques, generalized additive models (GAM) and multivariate adaptive regression splines (MARS), were used to analyse relationships between the distributions of 15 freshwater fish species and their environment. GAM and MARS models were fitted individually for each species, and a MARS multiresponse model was fitted in which the distributions of all species were analysed simultaneously. Model performance was evaluated using changes in deviance in the fitted models and the area under the receiver operating characteristic curve (ROC), calculated using a bootstrap assessment procedure that simulates predictive performance for independent data. Results indicate little difference between the performance of GAM and MARS models, even when MARS models included interaction terms between predictor variables. Results from MARS models are much more easily incorporated into other analyses than those from GAM models. The strong performance of a MARS multiresponse model, particularly for species of low prevalence, suggests that it may have distinct advantages for the analysis of large datasets. Its identification of a parsimonious set of environmental correlates of community composition, coupled with its ability to robustly model species distributions in relation to those variables, can be seen as converging strongly with the purposes of traditional ordination techniques.     

From data and theory to environmental models and indices formation

A prerequisite for environmental indices is that they represent environmental pressure, and the state of, and impact on environmental conditions. In other words, they should capture as much as possible of the cause-effect chains they represent and relate pressure and effect to criteria of environmental quality. The approach proposed in the article attempts to link the pressure–state–impact–response framework of indicators to the integrated environmental model, based on the method of response function (MRF). The MRF allows to construct purposeful, credible models from data and prior knowledge or information. The data are usually time series observations of system inputs and outputs, and sometimes of internal states. The output of such models is presented with highly aggregated environmental indices, reflecting the main pressure–state–impact–response cause-effect chains. The proposed approach is illustrated with the example of soil erosion indices.     

On conditional skewness with applications to environmental data

The statistical literature contains many univariate and multivariate skewness measures that allow two datasets to be compared, some of which are defined in terms of quantile values. In most situations, the comparison between two random vectors focuses on univariate comparisons of conditional random variables truncated in quantiles; this kind of comparison is of particular interest in the environmental sciences. In this work, we describe a new approach to comparing skewness in terms of the univariate convex transform ordering proposed by van Zwet (Convex transformations of random variables. Mathematical Centre Tracts, Amsterdam, 1964), associated with skewness as well as concentration. The key to these comparisons is the underlying dependence structure of the random vectors. Below we describe graphical tools and use several examples to illustrate these comparisons.     

Analyzing spatial count data,with an application to weed counts

Count data on a lattice may arise in observational studies of ecological phenomena. In this paper a hierarchical spatial model is used to analyze weed counts. Anisotropy is introduced, and a bivariate extension of the model is presented.     

Composite likelihood approach to the regression analysis of spatial multivariate ordinal data and spatial compositional data with exact zero values

In many environmental and ecological studies, it is of interest to model compositional data. One approach is to consider positive random vectors that are subject to a unit-sum constraint. In landscape ecological studies, it is common that compositional data are also sampled in space with some elements of the composition absent at certain sampling sites. In this paper, we first propose a practical spatial multivariate ordered probit model for multivariate ordinal data, where the response variables can be viewed as the discretized non-negative compositions without the unit-sum constraint. We then propose a novel two-stage spatial mixture Dirichlet regression model. The first stage models the spatial dependence and the presence of exact zero values, and the second stage models all the non-zero compositional data. A maximum composite likelihood approach is developed for parameter estimation and inference in both the spatial multivariate ordered probit model and the two-stage spatial mixture Dirichlet regression model. The standard errors of the parameter estimates are computed by an estimate of the Godambe information matrix. A simulation study is conducted to evaluate the performance of the proposed models and methods. A land cover data example in landscape ecology further illustrates that accounting for spatial dependence can improve the accuracy in the prediction of presence/absence of different land covers as well as the magnitude of land cover compositions.     

Linear regression with Type I interval- and left-censored response data

Laboratory analyses in a variety of contexts may result in left- and interval-censored measurements. We develop and evaluate a maximum likelihood approach to linear regression analysis in this setting and compare this approach to commonly used simple substitution methods. We explore via simulation the impact on bias and power of censoring fraction and sample size in a range of settings. The maximum likelihood approach represents only a moderate increase in power, but we show that the bias in substitution estimates may be substantial.     

(Super)paramagnetic nanoparticles as platform materials for environmental applications: From synthesis to demonstration

• The fabrication of monodisperse, (super)paramagnetic nanoparticles is summarized. • Monolayer and bilayer surface coating structures are described. • Mono/bilayer coated nanoparticles showed high sorption capacities for U, As, and Cr. Over the past few decades, engineered, (super)paramagnetic nanoparticles have drawn extensive research attention for a broad range of applications based on their tunable size and shape, surface chemistries, and magnetic properties. This review summaries our recent work on the synthesis, surface modification, and environmental application of (super)paramagnetic nanoparticles. By utilizing high-temperature thermo-decomposition methods, first, we have broadly demonstrated the synthesis of highly monodispersed, (super)paramagnetic nanoparticles, via the pyrolysis of metal carboxylate salts in an organic phase. Highly uniform magnetic nanoparticles with various size, composition, and shape can be precisely tuned by controlled reaction parameters, such as the initial precursors, heating rate, final reaction temperature, reaction time, and the additives. These materials can be further rendered water stable via functionalization with surface mono/bi-layer coating structure using a series of tunable ionic/non-ionic surfactants. Finally, we have demonstrated platform potential of these materials for heavy metal ions sensing, sorption, and separation from the aqueous phase.     

Zero-inflated models with application to spatial count data

Count data arises in many contexts. Here our concern is with spatial count data which exhibit an excessive number of zeros. Using the class of zero-inflated count models provides a flexible way to address this problem. Available covariate information suggests formulation of such modeling within a regression framework. We employ zero-inflated Poisson regression models. Spatial association is introduced through suitable random effects yielding a hierarchical model. We propose fitting this model within a Bayesian framework considering issues of posterior propriety, informative prior specification and well-behaved simulation based model fitting. Finally, we illustrate the model fitting with a data set involving counts of isopod nest burrows for 1649 pixels over a portion of the Negev desert in Israel.     

Maximum likelihood method for parameter estimation in non-linear models with below detection data

The maximum likelihood (ML) method for regression analyzes of censored data (below detection limit) for nonlinear models is presented. The proposed ML method has been translated into an equivalent least squares method (ML-LS). A two stage iterative algorithm is proposed to estimate statistical parameters from the derived least squares translation. The developed algorithm is applied to a nonlinear model for prediction of ambient air CO concentration in terms of concentrations of respirable particulate matter (RSPM) and NO₂. It has been shown that if censored data are ignored or estimated through simplifications such as (i) censored data are equal to detection limit, (ii) censored data are half of the difference between detection limit and lower limit (e.g., zero or background level) or (iii) censored data are equal to lower limit, this can cause significant bias in estimated parameters. The developed ML-LS method provided better estimates of parameters than any of the simplifications in censored data.     

The derivation of species response curves with Gaussian logistic regression is sensitive to sampling intensity and curve characteristics

We investigated quantitatively the sensitivity of plant species response curves to sampling characteristics (number of plots, occurrence and frequency of species), along a simulated pH gradient. We defined 54 theoretical unimodal response curves, issued from combinations of six values for optimum (opt = 3, 4, …, 8), three values for tolerance (tol = 0.5, 1.0, and 1.5, sensu ter Braak and Looman [ter Braak, C.J.F., Looman, C.W.N., 1986. Weighted averaging, logistic regression and the Gaussian response model. Vegetatio 65, 3–11]), and three values for maximum probability of presence (p_max = 0.05, 0.20, and 0.50). For each of these 54 theoretical response curves, we built artificial binary data sets (presence/absence) to test the influence of species occurrence, frequency, or number of available plots. With real data extracted from EcoPlant, a phytoecological database for French forests [Gégout, J.-C., Coudun, Ch., Bailly, G., Jabiol, B., 2005. EcoPlant: a forest sites database linking floristic data with soil characteristics and climatic conditions. J. Veg. Sci. 16, 257–260], we compared the ecological response of 50 plant species to soil pH, based first on a small data set (100 randomly sampled plots), and then based on the whole data set available (3810 plots).     

Refining logistic regression models for wildlife habitat suitability modeling—A case study with muntjak and goral in the Central Himalayas, India

High quality habitat suitability maps are indispensable for the management and planning of wildlife reserves. This is particularly important for megadiverse developing countries where shortages in skilled manpower and funding may preclude the use of mathematically complex modeling techniques and resource-intensive field surveys. In this study, we propose a simulation based k-fold partitioning and re-substitution approach to refine and update logistic regression models that are widely used for habitat suitability assessment and modeling. We test the modeling strategy using data from a rapid field survey conducted for habitat suitability assessment for muntjak (Muntiacus muntjak) and goral (Naemorrhaedus goral) in the central Himalayas, India. Results obtained from simulations match expectations in terms of model behavior and in terms of published habitat associations of the investigated species. Qualitative comparisons with predictions from the GARP, MaxEnt and Bioclimatic Envelopes modeling systems also show broad agreement with predictions obtained from the proposed technique. The proposed technique is suggested as a rapid-assessment precursor to detailed habitat studies such as patch occupancy modeling in situations where funds or trained manpower are not available.     

Comparing discriminant analysis, neural networks and logistic regression for predicting species distributions: a case study with a Himalayan river bird

We assessed the occurrence of a common river bird, the Plumbeous Redstart Rhyacornis fuliginosus, along 180 independent streams in the Indian and Nepali Himalaya. We then compared the performance of multiple discrimant analysis (MDA), logistic regression (LR) and artificial neural networks (ANN) in predicting this species’ presence or absence from 32 variables describing stream altitude, slope, habitat structure, chemistry and invertebrate abundance. Using the entire data (=training set) and a threshold for accepting presence in ANN and LR set to P≥0.5, ANN correctly classified marginally more cases (88%) than either LR (83%) or MDA (84%). Model performance was assessed from two methods of data partitioning. In a ‘leave-one-out’ approach, LR correctly predicted more cases (82%) than MDA (73%) or ANN (69%). However, in a holdout procedure, all the methods performed similarly (73–75%). All methods predicted true absence (i.e. specificity in holdout: 81–85%) better than true presence (i.e. sensitivity: 57–60%). These effects reflect species’ prevalence (=frequency of occurrence), but are seldom considered in distribution modelling. Despite occurring at only 36% of the sites, Plumbeous Redstarts are one of the most common Himalayan river birds, and problems will be greater with less common species. Both LR and ANN require an arbitrary threshold probability (often P=0.5) at which to accept species presence from model prediction. Simulations involving varied prevalence revealed that LR was particularly sensitive to threshold effects. ROC plots (received operating characteristic) were therefore used to compare model performance on test data at a range of thresholds; LR always outperformed ANN. This case study supports the need to test species’ distribution models with independent data, and to use a range of criteria in assessing model performance. ANN do not yet have major advantages over conventional multivariate methods for assessing bird distributions. LR and MDA were both more efficient in the use of computer time than ANN, and also more straightforward in providing testable hypotheses about environmental effects on occurrence. However, LR was apparently subject to chance significant effects from explanatory variables, emphasising the well-known risks of models based purely on correlative data.     

A GIS-based approach to spatio-temporal analysis of environmental pollution in urban areas: A case study of Prague's environment extended by LIDAR data

Environmental pollution of urban areas is one of key factors that state authorities and local agencies have to consider in the decision-making process. To find a compromise among many criteria, spatial analysis extended by geostatistical methods and dynamic models has to be carried out. In this case, spatial analysis includes processing of a wide range of air, water and soil pollution data and possibly noise assessment and waste management data. Other spatial inputs consist of data from remote sensing and GPS field measurements. Integration and spatial data management are carried out within the framework of a geographic information system (GIS). From a modeling point of view, GIS is used mainly for the preprocessing and postprocessing of data to be displayed in digital map layers and visualized in 3D scenes. Moreover, for preprocessing and postprocessing, deterministic and geostatistical methods (IDW, ordinary kriging) are used for spatial interpolation; geoprocessing and raster algebra are used in multi-criteria evaluation and risk assessment methods. GIS is also used as a platform for spatio-temporal analyses or for building relationships between the GIS database and stand-alone modeling tools. A case study is presented illustrating the application of spatial analysis to the urban areas of Prague. This involved incorporating environmental data from monitoring networks and field measurements into digital map layers. Extra data inputs were used to represent the 3D concentration fields of air pollutants (ozone, NO₂) measured by differential absorption LIDAR. ArcGIS was used to provide spatial data management and analysis, extended by modeling tools developed internally in the ArcObjects environment and external modules developed with MapObjects. Ordinary kriging methods were employed to predict ozone concentrations in selected 3D locations together with estimates of variability. Higher ozone concentrations were found above crossroads with their heavy traffic than above the surrounding areas. Ozone concentrations also varied with height above the digital elevation model. Processed data, spatial analysis and models are integrated within the framework of the GIS project, providing an approach that state and local authorities can use to address environmental protection issues.     

A comparison of two models with Landsat data for estimating above ground grassland biomass in Inner Mongolia,China

Two models, artificial neural network (ANN) and multiple linear regression (MLR), were developed to estimate typical grassland aboveground dry biomass in Xilingol River Basin, Inner Mongolia, China. The normalized difference vegetation index (NDVI) and topographic variables (elevation, aspect, and slope) were combined with atmospherically corrected reflectance from the Landsat ETM+ reflective bands as the candidate input variables for building both models. Seven variables (NDVI, aspect, and bands 1, 3, 4, 5 and 7) were selected by the ANN model (implemented in Statistica 6.0 neural network module), while six (elevation, NDVI, and bands 1, 3, 5 and 7) were picked to fit the MLR function after a stepwise analysis was executed between the candidate input variables and the above ground dry biomass. Both models achieved reasonable results with RMSEs ranging from 39.88% to 50.08%. The ANN model provided a more accurate estimation (RMSE_r = 39.88% for the training set, and RMSE_r = 42.36% for the testing set) than MLR (RMSE_r = 49.51% for the training, and RMSE_r = 53.20% for the testing). The final above ground dry biomass maps of the research area were produced based on the ANN and MLR models, generating the estimated mean values of 121 and 147 g/m², respectively.     

Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.     

Emergy analysis using US economic input-output models with applications to life cycles of gasoline and corn ethanol

A commonly encountered challenge in emergy analysis is the lack of transformity data for many economic products and services. To overcome this challenge, emergy analysts approximate the emergy input from the economy via a single emergy/money ratio for the country and the monetary price of economic inputs. This amounts to assuming homogeneity in the entire economy, and can introduce serious uncertainties in the results. This paper proposes and demonstrates the use of a thermodynamically augmented economic input-output model of the US economy for obtaining sector-specific emergy to money ratios that can be used instead of a single ratio. These ratios at the economy scale are more accurate than a single economy-wide emergy/money ratio, and can be obtained quickly for hundreds of economic products and services. Comparing sector-specific emergy/money ratios with those from conventional emergy studies indicates that the input-output model can provide reasonable estimates of transformities at least as a stop-gap measure until more detailed analysis is completed. A hybrid approach to emergy analysis is introduced and compared with conventional emergy analysis using life cycles of corn ethanol and gasoline as examples. Emergy and transformity data from the hybrid approach are similar to those from conventional emergy analysis, indicating the usefulness of the proposed approach. In addition, this work proposes the metric of return on emergy investment for assessing product alternatives with the same utility such as transportation fuels. The proposed approach and data may be used easily via web-based software.     

Assessing conservation status with extensive but low-resolution data: Application of frequentist and Bayesian models to endangered Athabasca River rainbow trout

Use of extensive but low-resolution abundance data is common in the assessment of species at-risk status based on quantitative decline criteria under International Union for Conservation of Nature (IUCN) and national endangered species legislation. Such data can be problematic for 3 reasons. First, statistical power to reject the null hypothesis of no change is often low because of small sample size and high sampling uncertainty leading to a high frequency of type II errors. Second, range-wide assessments composed of multiple site-specific observations do not effectively weight site-specific trends into global trends. Third, uncertainty in site-specific temporal trends and relative abundance are not propagated at the appropriate spatial scale. A common result is the propensity to underestimate the magnitude of declines and therefore fail to identify the appropriate at-risk status for a species. We used 3 statistical approaches, from simple to more complex, to estimate temporal decline rates for a designatable unit (DU) of rainbow trout in the Athabasca River watershed in western Canada. This DU is considered a native species for purposes of listing because of its genetic composition characterized as >0.95 indigenous origin in the face of continuing introgressive hybridization with introduced populations in the watershed. Analysis of abundance trends from 57 time series with a fixed-effects model identified 33 sites with negative trends, but only 2 were statistically significant. By contrast, a hierarchical linear mixed model weighted by site-specific abundance provided a DU-wide decline estimate of 16.4% per year and a 3-generation decline of 93.2%. A hierarchical Bayesian mixed model yielded a similar 3-generation decline trend of 91.3% and the posterior distribution showed that the estimate had a >99% probability of exceeding thresholds for an endangered listing. We conclude that the Bayesian approach was the most useful because it provided a probabilistic statement of threshold exceedance in support of an at-risk status recommendation.