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Collinearity a review of methods to deal with it and a simulation study evaluating their performance
(2013)
Collinearity refers to the non independence of predictor variables, usually in a regression-type analysis. It is a common feature of any descriptive ecological data set and can be a problem for parameter estimation because it inflates the variance of regression parameters and hence potentially leads to the wrong identification of relevant predictors in a statistical model. Collinearity is a severe problem when a model is trained on data from one region or time, and predicted to another with a different or unknown structure of collinearity. To demonstrate the reach of the problem of collinearity in ecology, we show how relationships among predictors differ between biomes, change over spatial scales and through time. Across disciplines, different approaches to addressing collinearity problems have been developed, ranging from clustering of predictors, threshold-based pre-selection, through latent variable methods, to shrinkage and regularisation. Using simulated data with five predictor-response relationships of increasing complexity and eight levels of collinearity we compared ways to address collinearity with standard multiple regression and machine-learning approaches. We assessed the performance of each approach by testing its impact on prediction to new data. In the extreme, we tested whether the methods were able to identify the true underlying relationship in a training dataset with strong collinearity by evaluating its performance on a test dataset without any collinearity. We found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection. Our results highlight the value of GLM in combination with penalised methods (particularly ridge) and threshold-based pre-selection when omitted variables are considered in the final interpretation. However, all approaches tested yielded degraded predictions under change in collinearity structure and the folk lore'-thresholds of correlation coefficients between predictor variables of |r| >0.7 was an appropriate indicator for when collinearity begins to severely distort model estimation and subsequent prediction. The use of ecological understanding of the system in pre-analysis variable selection and the choice of the least sensitive statistical approaches reduce the problems of collinearity, but cannot ultimately solve them.
Within the field of species distribution modelling an apparent dichotomy exists between process-based and correlative approaches, where the processes are explicit in the former and implicit in the latter. However, these intuitive distinctions can become blurred when comparing species distribution modelling approaches in more detail. In this review article, we contrast the extremes of the correlativeprocess spectrum of species distribution models with respect to core assumptions, model building and selection strategies, validation, uncertainties, common errors and the questions they are most suited to answer. The extremes of such approaches differ clearly in many aspects, such as model building approaches, parameter estimation strategies and transferability. However, they also share strengths and weaknesses. We show that claims of one approach being intrinsically superior to the other are misguided and that they ignore the processcorrelation continuum as well as the domains of questions that each approach is addressing. Nonetheless, the application of process-based approaches to species distribution modelling lags far behind more correlative (process-implicit) methods and more research is required to explore their potential benefits. Critical issues for the employment of species distribution modelling approaches are given, together with a guideline for appropriate usage. We close with challenges for future development of process-explicit species distribution models and how they may complement current approaches to study species distributions.
The Brazilian Cerrado is recognized as one of the most threatened biomes in the world, as the region has experienced a striking change from natural Cerrado vegetation to intense cash crop production. This paper reviews the history of land conversion in the Cerrado and the development of soil properties and water resources under past and ongoing land use. We compared soil and water quality parameters from different land uses considering 80 soil and 18 water studies conducted in different regions across the Cerrado to provide quantitative evidence of soil and water alterations from land use change.
Following the conversion of native Cerrado, significant effects on soil pH, bulk density and available P and K for croplands and less-pronounced effects on pastures were evident. Soil total N did not differ between land uses because most of the sites classified as croplands were nitrogen-fixing soybeans, which are not artificially fertilized with N. In contrast, water quality studies showed nitrogen enrichment in agricultural catchments, indicating fertilizer impacts and potential susceptibility to eutrophication. Regardless of the land use, P is widely absent because of the high-fixing capacities of deeply weathered soils and the filtering capacity of riparian vegetation. Pesticides, however, were consistently detected throughout the entire aquatic system. In several case studies, extremely high-peak concentrations exceeded Brazilian and European Union (EU) water quality limits, which were potentially accompanied by serious health implications. Land use intensification is likely to continue, particularly in regions where less annual rainfall and severe droughts are projected in the northeastern and western Cerrado. Thus, the leaching risk and displacement of agrochemicals are expected to increase, particularly because the current legislation has caused a reduction in riparian vegetation. We conclude that land use intensification is likely to seriously limit the Cerrado's future regarding both agricultural productivity and ecosystem stability. Because only limited data are available, we recommend further field studies to understand the interaction between terrestrial and aquatic systems. This study may serve as a valuable database for integrated modelling to investigate the impact of land use and climate change on soil and water resources and to test and develop mitigation measures for the Cerrado. Copyright (C) 2014 John Wiley & Sons, Ltd.
Detailed knowledge on the spatial distribution of soils is crucial for environmental monitoring, management, and modeling. However soil maps with a finite number of discrete soil map units are often the only available information about soils. Depending on the map scale or the detailing of the map legend this information could be too imprecise. We present a method for the spatial disaggregation of map units, namely the refinement of complex soil map units in which two or more soil types are aggregated. Our aim is to draw new boundaries inside the map polygons to represent a single soil type and no longer a mixture of several soil types. The basic idea for our method is the functional relationship between soil types and topographic position as formulated in the concept of the catena. We use a comprehensive soil profile database and topographic attributes derived from a 10 m digital elevation model as input data for the classification of soil types with random forest models. We grouped all complex map units which have the same combination of soil types. Each group of map units is modeled separately. For prediction of the soil types we stratified the soil map into these groups and apply a specific random forest model only to the associated map units. In order to get reliable results we define a threshold for the predicted probabilities at 0.7 to assign a specific soil type. In areas where the probability is below 0.7 for every possible soil type we assign a new class "indifferent" because the model only makes unspecific classification there. Our results show a significant spatial refinement of the original soil polygons. Validation of our predictions was estimated on 1812 independent soil profiles which were collected subsequent to prediction in the field. Field validation gave an overall accuracy of 70%. Map units, in which shallow soils were grouped together with deep soils could be separated best. Also histosols could be predicted successful. Highest error rate were found in map units, in which Gleysoils were grouped together with deep soils or Anthrosols. To check for validity of our results we open the black box random forest model by calculating the variable importance for each predictor variable and plotting response surfaces. We found good confirmations of our hypotheses, that topography has a significant influence on the spatial arrangement of soil types and that these relationships can be used for disaggregation.
Questions Can forest site characteristics be used to predict Ellenberg indicator values for soil moisture? Which is the best averaged mean value for modelling? Does the distribution of soil moisture depend on spatial information? Location Bavarian Alps, Germany. Methods We used topographic, climatic and edaphic variables to model the mean soil moisture value as found on 1505 forest plots from the database WINALPecobase. All predictor variables were taken from area-wide geodata layers so that the model can be applied to some 250 000 ha of forest in the target region. We adopted methods developed in species distribution modelling to regionalize Ellenberg indicator values. Therefore, we use the additive georegression framework for spatial prediction of Ellenberg values with the R-library mboost, which is a feasible way to consider environmental effects, spatial autocorrelation, predictor interactions and non-stationarity simultaneously in our data. The framework is much more flexible than established statistical and machine-learning models in species distribution modelling. We estimated five different mboost models reflecting different model structures on 50 bootstrap samples in each case. Results Median R2 values calculated on independent test samples ranged from 0.28 to 0.45. Our results show a significant influence of interactions and non-stationarity in addition to environmental covariates. Unweighted mean indicator values can be modelled better than abundance-weighted values, and the consideration of bryophytes did not improve model performance. Partial response curves indicate meaningful dependencies between moisture indicator values and environmental covariates. However, mean indicator values <4.5 and >6.0 could not be modelled correctly, since they were poorly represented in our calibration sample. The final map represents high-resolution information of site hydrological conditions. Conclusions Indicator values offer an effect-oriented alternative to physically-based hydrological models to predict water-related site conditions, even at landscape scale. The presented approach is applicable to all kinds of Ellenberg indicator values. Therefore, it is a significant step towards a new generation of models of forest site types and potential natural vegetation.
Movement of organisms is one of the key mechanisms shaping biodiversity, e.g. the distribution of genes, individuals and species in space and time. Recent technological and conceptual advances have improved our ability to assess the causes and consequences of individual movement, and led to the emergence of the new field of ‘movement ecology’. Here, we outline how movement ecology can contribute to the broad field of biodiversity research, i.e. the study of processes and patterns of life among and across different scales, from genes to ecosystems, and we propose a conceptual framework linking these hitherto largely separated fields of research. Our framework builds on the concept of movement ecology for individuals, and demonstrates its importance for linking individual organismal movement with biodiversity. First, organismal movements can provide ‘mobile links’ between habitats or ecosystems, thereby connecting resources, genes, and processes among otherwise separate locations. Understanding these mobile links and their impact on biodiversity will be facilitated by movement ecology, because mobile links can be created by different modes of movement (i.e., foraging, dispersal, migration) that relate to different spatiotemporal scales and have differential effects on biodiversity. Second, organismal movements can also mediate coexistence in communities, through ‘equalizing’ and ‘stabilizing’ mechanisms. This novel integrated framework provides a conceptual starting point for a better understanding of biodiversity dynamics in light of individual movement and space-use behavior across spatiotemporal scales. By illustrating this framework with examples, we argue that the integration of movement ecology and biodiversity research will also enhance our ability to conserve diversity at the genetic, species, and ecosystem levels.
AimAdvancement in ecological methods predicting species distributions is a crucial precondition for deriving sound management actions. Maximum entropy (MaxEnt) models are a popular tool to predict species distributions, as they are considered able to cope well with sparse, irregularly sampled data and minor location errors. Although a fundamental assumption of MaxEnt is that the entire area of interest has been systematically sampled, in practice, MaxEnt models are usually built from occurrence records that are spatially biased towards better-surveyed areas. Two common, yet not compared, strategies to cope with uneven sampling effort are spatial filtering of occurrence data and background manipulation using environmental data with the same spatial bias as occurrence data. We tested these strategies using simulated data and a recently collated dataset on Malay civet Viverra tangalunga in Borneo.
LocationBorneo, Southeast Asia.
MethodsWe collated 504 occurrence records of Malay civets from Borneo of which 291 records were from 2001 to 2011 and used them in the MaxEnt analysis (baseline scenario) together with 25 environmental input variables. We simulated datasets for two virtual species (similar to a range-restricted highland and a lowland species) using the same number of records for model building. As occurrence records were biased towards north-eastern Borneo, we investigated the efficacy of spatial filtering versus background manipulation to reduce overprediction or underprediction in specific areas.
ResultsSpatial filtering minimized omission errors (false negatives) and commission errors (false positives). We recommend that when sample size is insufficient to allow spatial filtering, manipulation of the background dataset is preferable to not correcting for sampling bias, although predictions were comparatively weak and commission errors increased.
Main ConclusionsWe conclude that a substantial improvement in the quality of model predictions can be achieved if uneven sampling effort is taken into account, thereby improving the efficacy of species conservation planning.
The Hazel Grouse Bonasa bonasia is strongly affected by forest dynamics, and populations in many areas within Europe are declining. As a result of the 'wilding' concept implemented in the National Park Bavarian Forest, this area is one of the refuges for the species in Germany. Even though the effects of prevailing processes make the situation there particularly interesting, no recent investigation about habitat selection in the rapidly changing environment of the national park has been undertaken. We modelled the species-habitat relationship to derive the important habitat features in the national park as well as factors and critical threshold for monitoring, and to evaluate the predictive power of models based on field surveys compared to an analysis of infrared aerial photographs. We conducted our surveys on 49 plots of 25 ha each where Hazel Grouse was recorded and on an equally sized set of plots with no grouse occurrence, and used this dataset to build a predictive habitat-suitability model using logistic regression with backward stepwise variable selection. Habitat heterogeneity, stand structure, presence of mountain ash and willow, root plates, forest aisles, and young broadleaf stands proved to be predictive habitat variables. After internal validation via bootstrapping, our model shows an AUC value of 0.91 and a correct classification rate of 87%. Considering the methodological difficulties attached to backward selection, we applied Bayesian model averaging as an alternative. This multi-model approach also yielded similar results. To derive simple thresholds for important predictors as a basis for management decisions, we alternatively ran tree-based modelling, which also leads to a very similar selection of predictors. Performance of our different survey approaches was assessed by comparing two independent models with a model including both data resources: one constructed only from field survey data, the other based on data derived from aerial photographs. Models based on field data seem to perform slightly better than those based on aerial photography, but models using both predictor datasets provided the highest predictive accuracy.
Ecohydrology analyses the interactions of biotic and abiotic aspects of our ecosystems and landscapes. It is a highly diverse discipline in terms of its thematic and methodical research foci. This article gives an overview of current German ecohydrological research approaches within plant-animal-soil-systems, meso-scale catchments and their river networks, lake systems, coastal areas and tidal rivers. It discusses their relevant spatial and temporal process scales and different types of interactions and feedback dynamics between hydrological and biotic processes and patterns. The following topics are considered key challenges: innovative analysis of the interdisciplinary scale continuum, development of dynamically coupled model systems, integrated monitoring of coupled processes at the interface and transition from basic to applied ecohydrological science to develop sustainable water and land resource management strategies under regional and global change.
The Middle Spotted Woodpecker (Dendrocopos medius) is the bird species which Germany has the greatest global responsibility to protect. It is an umbrella species for the entire assemblage of animals associated with mature broadleaved trees, especially oak. Even though well studied in small to medium scale stands, the validity of habitat suitability analysis for this species in larger forests has not previously been proved. Aim of this study was to test suitability of permanent forest inventory plots for modelling its distribution in a 17,000 ha forest landscape and to derive habitat threshold values as a basis for formulating management guidelines. Based on 150 randomly selected 12.5 ha plots we identified mean age and basal area of oaks as the most important habitat factors using a backward selection logistic model. Internal validation showed an AUC of 0.89 and a R-2(N) of 0.58. Determination of thresholds using maximally selected rank statistics found higher probability of occurrence in stands with a mean age >95 years. Above that age the probability increased again in stands with more than 6.4 m(2) basal area oak/ha. Our results show that widely available forest inventory data can serve as a valuable basis for monitoring the Middle Spotted Woodpecker, either within the framework of the Natura 2000 Network, or more generally in integrated forest management with the aim of providing suitable habitats for the entire assemblage of species on old deciduous trees, especially oak.
How much suitable habitat is left for the last known population of the Pale-Headed Brush-Finch?
(2004)
The Pale-headed Brush-Finch (Atlapetes pallidiceps) is threatened with extinction due to loss of habitat. The only remnant population consists of 30-35 pairs and is confined to a single valley in the Andes of southwestern Ecuador. We investigated the habitat types used by this species in order to quantify the amount of available suitable habitat. The species used semiopen habitat types featuring a mosaic of dense scrub 2-4 In tall and grassy patches. Low continuous scrub was also used in larger proportions than on average available; forest and open country were not included in territories. Suitable habitat covered 28% of the area, and 16% was still available for new brush-finch territories. We identified a minimum of seven coherent patches that could support eight further pairs of the species. The valley can thus potentially support 40-50 pairs. The occupied habitat as described here should serve as a guideline in searching for new habitat
Annual plants under cyclic disturbance regime : better understanding through model aggregation
(2008)
In their application for conservation ecology, 'classical' analytical models and individual-based simulation models (IBMs) both entail their specific strengths and weaknesses, either in providing a detailed and realistic representation of processes or in regard to a comprehensive model analysis. This well-known dilemma may be resolved by the combination of both approaches when tackling certain problems of conservation ecology. Following this idea, we present the complementary use of both an IBM and a matrix population model in a case study on grassland conservation management. First, we develop a spatially explicit IBM to simulate the long-term response of the annual plant Thlaspi perfoliatum (Brassicaceae), claspleaf pennycress, to different management schemes (annual mowing vs. infrequent rototilling) based on field experiments. In order to complement the simulation results by further analyses, we aggregate the IBM to a spatially nonexplicit deterministic matrix population model. Within the periodic environment created by management regimes, population dynamics are described by periodic products of annual transition matrices. Such periodic matrix products provide a very conclusive framework to study the responses of species to different management return intervals. Thus, using tools of matrix model analysis (e.g., loop analysis), we can both identify dormancy within the age-structured seed bank as the pivotal strategy for persistence under cyclic disturbance regimes and reveal crucial thresholds in some less certain parameters. Results of matrix model analyses are therefore successfully tested by comparing their results to the respective IBM simulations. Their implications for an enhanced scientific basis for management decisions are discussed as well as some general benefits and limitations of the use of aggregating modeling approaches in conservation.
Species distribution models are useful for identifying driving environmental factors that determine earthworm distributions as well as for predicting earthworm distribution patterns and abundances at different scales. However, due to large efforts in data acquisition, studies on larger scales are rare and often focus on single species or earthworms in general. In this study, we use boosted regression tree models (BRTs) for predicting the distribution of the three functional earthworm types, i.e. anecics, endogeics and epigeics, in an agricultural area in Baden-Wurttemberg (Southwest Germany).
First, we predicted presence and absence and later earthworm abundances, considering predictors depicting land management, topography, and soil conditions as well as biotic interaction by using the abundance of the other functional earthworm types. The final presence-absence models performed reasonably well, with explained deviances between 24 and 51% after crossvalidation. Models for abundances of anecics and endogeics were less successful, since the high small-scale variability and patchiness in earthworm abundance influenced the representativeness of the field measurements. This resulted in a significant model uncertainty, which is practically very difficult to overcome with earthworm sampling campaigns at the catchment scale.
Results showed that management practices (i.e. disturbances), topography, soil conditions, and biotic interactions with other earthworm groups are the most relevant predictors for spatial distribution (incidence) patterns of all three functional groups. The response curves and contributions of predictors differ for the three functional earthworm types. Epigeics are also controlled by topographic features, endogeics by soil parameters.
Predicting the species composition of Nardus stricta communities by logistic regression modelling
(2004)
Predictive habitat models are an important tool for ecological research and conservation. A major cause of unreliable models is excessive model complexity, and regularization methods aim to improve the predictive performance by adequately constraining model complexity. We compare three regularization methods for logistic regression: variable selection, lasso, and ridge. They differ in the way model complexity is measured: variable selection uses the number of estimated parameters, the lasso uses the sum of the absolute values of the parameter estimates, and the ridge uses the sum of the squared values of the parameter estimates. We performed a simulation study with environmental data of a real landscape and artificial species occupancy data. We investigated the effect of three factors on relative model performance: (1) the number of parameters (16, 10, 6, 2) in the 'true' model that determined the distribution of the artificial species, (2) the prevalence, i.e. the proportion of sites occupied by the species, and (3) the sample size (measured in events per variable, EPV). Regularization improved model discrimination and calibration. However, no regularization method performed best under all circumstances: the ridge generally performed best in the 16-parameter scenario. The lasso generally performed best in the 10-parameter scenario. Variable selection with AIC was best at large sample sizes (EPV >= 10) when less than half of the variables influenced the species distribution. However, at low sample sizes (EPV < 10), ridge and lasso always performed best, regardless of the parameter scenario or prevalence. Overall, calibration was best in ridge models. Other methods showed overconfidence, particularly at low sample sizes. The percentage of correctly identified models was low for both lasso and variable selection. Variable selection should be used with caution. Although it can produce the best performing models under certain conditions, these situations are difficult to infer from the data. Ridge and lasso are risk-averse model strategies that can be expected to perform well under a wide range of underlying species-habitat relationships, particularly at small sample sizes.