Hierarchical analysis of species distributions and abundance across environmental gradients

Abiotic and biotic processes operate at multiple spatial and temporal scales to shape many ecological processes, including species distributions and demography. Current debate about the relative roles of niche-based and stochastic processes in shaping species distributions and community composition reflects, in part, the challenge of understanding how these processes interact across scales. Traditional statistical models that ignore autocorrelation and spatial hierarchies can result in misidentification of important ecological covariates. Here, we demonstrate the utility of a hierarchical modeling framework for testing hypotheses about the importance of abiotic factors at different spatial scales and local spatial autocorrelation for shaping species distributions and abundances. For the two orchid species studied, understory light availability and soil moisture helped to explain patterns of presence and abundance at a microsite scale (<4 m2), while soil organic content was important at a population scale (<400 m2). The inclusion of spatial autocorrelation is shown to alter the magnitude and certainty of estimated relationships between abundance and abiotic variables, and we suggest that such analysis be used more often to explore the relationships between species life histories and distributions. The hierarchical modeling framework is shown to have great potential for elucidating ecological relationships involving abiotic and biotic processes simultaneously at multiple scales.     

Judicious Use of Multiple Hypothesis Tests

Abstract:  When analyzing a table of statistical results, one must first decide whether adjustment of significance levels is appropriate. If the main goal is hypothesis generation or initial screening for potential conservation problems, then it may be appropriate to use the standard comparisonwise significance level to avoid Type II errors (not detecting real differences or trends). If the main goal is rigorous testing of a hypothesis, however, then an adjustment for multiple tests is needed. To control the familywise Type I error rate (the probability of rejecting at least one true null hypothesis), sequential modifications of the standard Bonferroni method, such as Holm's method, will provide more statistical power than the standard Bonferroni method. Additional power may be achieved through procedures that control the false discovery rate (FDR) (the expected proportion of false positives among tests found to be significant). Holm's sequential Bonferroni method and two FDR-controlling procedures were applied to the results of multiple-regression analyses of the relationship between habitat variables and the abundance of 25 species of forest birds in Japan, and the FDR-controlling procedures provided considerably greater statistical power.     

Scale Mismatches,Conservation Planning,and the Value of Social‐Network Analyses

Many of the challenges conservation professionals face can be framed as scale mismatches. The problem of scale mismatch occurs when the planning for and implementation of conservation actions is at a scale that does not reflect the scale of the conservation problem. The challenges in conservation planning related to scale mismatch include ecosystem or ecological process transcendence of governance boundaries; limited availability of fine‐resolution data; lack of operational capacity for implementation; lack of understanding of social‐ecological system components; threats to ecological diversity that operate at diverse spatial and temporal scales; mismatch between funding and the long‐term nature of ecological processes; rate of action implementation that does not reflect the rate of change of the ecological system; lack of appropriate indicators for monitoring activities; and occurrence of ecological change at scales smaller or larger than the scale of implementation or monitoring. Not recognizing and accounting for these challenges when planning for conservation can result in actions that do not address the multiscale nature of conservation problems and that do not achieve conservation objectives. Social networks link organizations and individuals across space and time and determine the scale of conservation actions; thus, an understanding of the social networks associated with conservation planning will help determine the potential for implementing conservation actions at the required scales. Social‐network analyses can be used to explore whether these networks constrain or enable key social processes and how multiple scales of action are linked. Results of network analyses can be used to mitigate scale mismatches in assessing, planning, implementing, and monitoring conservation projects. Discordancia de Escalas, Planificación de la Conservación y el Valor del Análisis de Redes Sociales     

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.     

Detecting and Modeling Spatial and Temporal Dependence in Conservation Biology

Abstract: Due to the structuring forces and large-scale physical processes that shape our biosphere, we often find that environmental and ecological data are either spatially or temporally—or both spatially and temporally—dependent. When these data are analyzed, statistical techniques and models are frequently applied that were developed for independent data. We describe some of the detrimental consequences, such as inefficient parameter estimators, biased hypothesis test results, and inaccurate predictions, of ignoring spatial and temporal data dependencies, and we cite an example of adverse statistical results occurring when spatial dependencies were disregarded. We also discuss and recommend available techniques used to detect and model spatial and temporal dependence, including variograms, covariograms, autocorrelation and partial autocorrelation plots, geostatistical techniques, Gaussian autoregressive models, K functions, and ARIMA models, in environmental and ecological research to avoid the aforementioned difficulties.     

Die Bedeutung der Zeit

The consideration of time in environmental research allows new insights into the fundamentals of environmental research and new pathways for perceiving and answering questions which might arise in environmental research. In order to take this all into account, one must realize that ecological systems have a history and that both the spatial aspects and the chronological expansion of these systems must be taken into consideration. Considering temporalities, rhythms and time scales as well as their interdependencies in environmental research and environmental protection enables us to obtain a better understanding. The significance of relationships and functions in ecological systems can be perceived better as well. The impact of pollutants as well as the outcome of human actions in ecology, and in economics and politics, is consequently mandatory for not only a spatial, but also for the involved temporal scales.     

A methodological framework for integrating computational fluid dynamics and ecological models applied to juvenile freshwater mussel dispersal in the Upper Mississippi River

Interdisciplinary research in hydraulics and ecology for river management and restoration must integrate processes that occur over a wide range of spatial and temporal scales, which presents a challenge to ecohydraulics modelers. Computational fluid dynamics (CFD) models are being more widely used to determine flow fields for ecohydraulics applications. In the Upper Mississippi River (UMR), the mussel dynamics model was developed as a tool for management and conservation of freshwater mussels (Unionidae), which are benthic organisms, imperiled in North America, that are inextricably linked with the hydraulics of river flow. We updated the juvenile dispersal component of the mussel dynamics model by using stochastic Lagrangian particle tracking in a three dimensional flow field output from CFD models of reaches in the UMR. We developed a methodological framework to integrate hydrodynamic data with the mussel dynamics model, and we demonstrate the use of the juvenile dispersal model employed within the methodological framework in two reaches of the UMR. The method was used to test the hypothesis that impoundment affects the relationship of some hydraulic parameters with juvenile settling distribution. Simulation results were consistent with this hypothesis, and the relationships of bed shear stress and Froude number with juvenile settling were altered by impoundment most likely through effects on local hydraulics. The methodological framework is robust, integrates Eulerian and Lagrangian reference frameworks, and incorporates processes over a wide range of temporal and spatial scales, from watershed scale hydrologic processes (decades), to reach scale (km) processes that occur over hours or days, and turbulent processes on spatial scales of meter to millimeter and times scales of seconds. The methods are presently being used to assess the impacts of pre- and early post-settlement processes on mussel distributions, including the effects of bed shear stress, and the sensitivity of the location of the host fish when juveniles excyst, on juvenile settling distribution.     

Modeling freshwater fish distributions using multiscale landscape data: A case study of six narrow range endemics

Species distribution models (SDMs) have become integral tools in scientific research and conservation planning. Despite progress in the assessment of various statistical models for use in SDMs, little has been done in way of evaluating appropriate ecological models. In this paper, we evaluate the multiscale filter framework as a suitable theoretical model for predicting freshwater fish distributions in the upper Green River system (Ohio River drainage), USA. The spatial distributions of six fishes with contrasting biogeographies were modeled using boosted regression trees and multiscale landscape data. Species biogeography did not appear to affect predictive performance and all models performed well statistically with receiver operating characteristic area under the curve (AUC) ranging from 0.87 to 0.98. Predictive maps show accurate estimations of ranges for five of six species based on historical collections. The relative influence of each type of environmental feature and spatial scale varied markedly with between species. A hierarchical effect was detected for narrowly distributed species. These species were highly influenced by soil composition at larger spatial scales and land use/land cover (LULC) patterns at more proximal scales. Conversely, LULC pattern was the most influential feature for widely distributed at all spatial scales. Using multiscale data capable of capturing hierarchical landscape influences allowed production of accurate predictive models and provided further insight into factors controlling freshwater fish distributions.     

Paleobiology, community ecology, and scales of ecological pattern

The fossil record provides a wealth of data on the role of regional processes and historical events in shaping biological communities over a variety of time scales. The Quaternary record with its evidence of repeated climatic change shows that both terrestrial and marine species shifted independently rather than as cohesive assemblages over scales of thousands of years. Larger scale patterns also show a strong individualistic component to taxon dynamics; assemblage stability, when it occurs, is difficult to separate from shared responses to low rates of environmental change. Nevertheless, the fossil record does suggest that some biotic interactions influence large-scale ecological and evolutionary patterns, albeit in more diffuse and protracted fashions than those generally studied by community ecologists. These include: (1) the resistance by incumbents to the establishment of new or invading taxa, with episodes of explosive diversification often appearing contingent on the removal of incumbents at extinction events; (2) steady states of within-habitat and global diversity at longer time scales (10(7)-l0(8) yr), despite enormous turnover of taxa; and (3) morphological and biogeographic responses to increased intensities of predation and substratum disturbance over similarly long time scales. The behavior of species and communities over the array of temporal and spatial scales in the fossil record takes on additional significance for framing conservation strategies, and for understanding recovery of species, lineages, and communities from environmental changes.     

Biodiversity and Ecosystem Function

In at least some circumstances, biodiversity affects various ecosystem functions and the ways in which ecosystems respond to disturbance. Because these interactions occur at many spatial and temporal scales and throughout all levels of biological organization, it is difficult to decide where to focus attention on interactions between biodiversity and ecosystem function. The loci for initial attention is important for setting research priorities to understand these interactions further, for organizing known information to instruct the development of natural resource policies, and for identifying biodiversity conservation priorities. Holling (1992) argues that ecosystem behavior can be understood from a few dominating ecological processes that structure the ecosystem. In the temporal dimension, these key structuring processes dictate a few dominant temporal frequencies that drive other processes. Thus, the most effective strategy for studying interactions between biodiversity and ecosystem function is to focus on the key structuring processes at intermediate scales of space and time. Thereafter, other ecological conditions signify situations in which the interactions between biodiversity and ecosystem function are particularly strong: early to midsuccessional status, low soil fertility, intermediate levels of disturbance, biotic interactions only where there is collaborative indication of importance, invading species that differ significantly from native species in resource acquisition or utilization, and ecotones.     

Effects of spatial autocorrelation and sampling design on estimates of protected area effectiveness

Estimating the effectiveness of protected areas (PAs) in reducing deforestation is useful to support decisions on whether to invest in better management of areas already protected or to create new ones. Statistical matching is commonly used to assess this effectiveness, but spatial autocorrelation and regional differences in protection effectiveness are frequently overlooked. Using Colombia as a case study, we employed statistical matching to account for confounding factors in park location and accounted for for spatial autocorrelation to determine statistical significance. We compared the performance of different matching procedures—ways of generating matching pairs at different scales—in estimating PA effectiveness. Differences in matching procedures affected covariate similarity between matched pairs (balance) and estimates of PA effectiveness in reducing deforestation. Independent matching yielded the greatest balance. On average 95% of variables in each region were balanced with independent matching, whereas 33% of variables were balanced when using the method that performed worst. The best estimates suggested that average deforestation inside protected areas in Colombia was 40% lower than in matched sites. Protection significantly reduced deforestation, but PA effectiveness differed among regions. Protected areas in Caribe were the most effective, whereas those in Orinoco and Pacific were least effective. Our results demonstrate that accounting for spatial autocorrelation and using independent matching for each subset of data is needed to infer the effectiveness of protection in reducing deforestation. Not accounting for spatial autocorrelation can distort the assessment of protection effectiveness, increasing type I and II errors and inflating effect size. Our method allowed improved estimates of protection effectiveness across scales and under different conditions and can be applied to other regions to effectively assess PA performance.     

Linking chronic wasting disease to mule deer movement scales: a hierarchical Bayesian approach.

Observed spatial patterns in natural systems may result from processes acting across multiple spatial and temporal scales. Although spatially explicit data on processes that generate ecological patterns, such as the distribution of disease over a landscape, are frequently unavailable, information about the scales over which processes operate can be used to understand the link between pattern and process. Our goal was to identify scales of mule deer (Odocoileus hemionus) movement and mixing that exerted the greatest influence on the spatial pattern of chronic wasting disease (CWD) in northcentral Colorado, USA. We hypothesized that three scales of mixing (individual, winter subpopulation, or summer subpopulation) might control spatial variation in disease prevalence. We developed a fully Bayesian hierarchical model to compare the strength of evidence for each mixing scale. We found strong evidence that the finest mixing scale corresponded best to the spatial distribution of CWD infection. There was also evidence that land ownership and habitat use play a role in exacerbating the disease, along with the known effects of sex and age. Our analysis demonstrates how information on the scales of spatial processes that generate observed patterns can be used to gain insight when process data are sparse or unavailable.     

Statistical inference using the g or K point pattern spatial statistics

Spatial point pattern analysis provides a statistical method to compare an observed spatial pattern against a hypothesized spatial process model. The G statistic, which considers the distribution of nearest neighbor distances, and the K statistic, which evaluates the distribution of all neighbor distances, are commonly used in such analyses. One method of employing these statistics involves building a simulation envelope from the result of many simulated patterns of the hypothesized model. Specifically, a simulation envelope is created by calculating, at every distance, the minimum and maximum results computed across the simulated patterns. A statistical test is performed by evaluating where the results from an observed pattern fall with respect to the simulation envelope. However, this method, which differs from P. Diggle's suggested approach, is invalid for inference because it violates the assumptions of Monte Carlo methods and results in incorrect type I error rate performance. Similarly, using the simulation envelope to estimate the range of distances over which an observed pattern deviates from the hypothesized model is also suspect. The technical details of why the simulation envelope provides incorrect type I error rate performance are described. A valid test is then proposed, and details about how the number of simulated patterns impacts the statistical significance are explained. Finally, an example of using the proposed test within an exploratory data analysis framework is provided.     

Scale-dependent interaction of fire and grazing on community heterogeneity in tallgrass prairie

Natural disturbances affect spatial and temporal heterogeneity in plant communities, but effects vary depending on type of disturbance and scale of analysis. In this study, we examined the effects of fire frequency (1-, 4-, and 20-yr intervals) and grazing by bison on spatial and temporal heterogeneity in species composition in tallgrass prairie plant communities. Compositional heterogeneity was estimated at 10-, 50-, and 200-m2 scales. For each measurement scale, we used the average Euclidean Distance (ED) between samples within a year (2000) to measure spatial heterogeneity and between all time steps (1993-2000) for each sample to measure temporal heterogeneity. The main effects of fire and grazing were scale independent. Spatial and temporal heterogeneity were lowest on annually burned sites and highest on infrequently burned (20-yr) sites at all scales. Grazing reduced spatial heterogeneity and increased temporal heterogeneity at all scales. The rate of community change over time decreased as fire frequency increased at all scales, whereas grazing had no effect on rate of community change over time at any spatial scale. The interactive effects of fire and grazing on spatial and temporal heterogeneity differed with scale. At the 10-m2 scale, grazing increased spatial heterogeneity in annually burned grassland but decreased heterogeneity in less frequently burned areas. At the 50-m2 scale, grazing decreased spatial heterogeneity on 4-yr burns but had no effect at other fire frequencies. At the 10-m scale, grazing increased temporal heterogeneity only on 1- and 20-yr burn sites. Our results show that the individual effects of fire and grazing on spatial and temporal heterogeneity in mesic prairie are scale independent, but the interactive effects of these disturbances on community heterogeneity change with scale of measurement. These patterns reflect the homogenizing impact of fire at all spatial scales, and the different frequency, intensity, and scale of patch grazing by bison in frequently burned vs. infrequently burned areas.     

Quantifying the importance of local niche-based and stochastic processes to tropical tree community assembly

Although niche-based and stochastic processes, including dispersal limitation and demographic stochasticity, can each contribute to community assembly, it is difficult to quantify the relative importance of each process in natural vegetation. Here, we extend Shipley's maxent model (Community Assembly by Trait Selection, CATS) for the prediction of relative abundances to incorporate both trait-based filtering and dispersal limitation from the larger landscape and develop a statistical decomposition of the proportions of the total information content of relative abundances in local communities that are attributable to trait-based filtering, dispersal limitation, and demographic stochasticity. We apply the method to tree communities in a mature, species-rich, tropical forest in French Guiana at 1-, 0.25- and 0.04-ha scales. Trait data consisted of species' means of 17 functional traits measured over both the entire meta-community and separately in each of nine 1-ha plots. Trait means calculated separately for each site always gave better predictions. There was clear evidence of trait-based filtering at all spatial scales. Trait-based filtering was the most important process at the 1-ha scale (34%), whereas demographic stochasticity was the most important at smaller scales (37-53%). Dispersal limitation from the meta-community was less important and approximately constant across scales (-9%), and there was also an unresolved association between site-specific traits and meta-community relative abundances. Our method allows one to quantify the relative importance of local niche-based and meta-community processes and demographic stochasticity during community assembly across spatial and temporal scales.     

An adjoint data assimilation approach for estimating parameters in a three-dimensional ecosystem model

In this paper an ecosystem model, including phytoplankton, zooplankton, nitrate, ammonium, phosphate and detritus, is described. The model is driven by physical fields derived from a three-dimensional physical transport model. Simulation includes nitrate input from a river. Simulated results are then sampled and the sampled data are used in sequential numerical experiments to assess the ability of using an adjoint data assimilation approach for estimating the poorly known parameters of the ecosystem model, such as growth and death rate, half-saturation constant of nutrients, etc. Data with different spatial and temporal resolution over 1 week are assimilated into the ecosystem model. Assimilation of data at 30 grid stations with a sampling interval of 6 h is proved to be adequate for recovering all the parameters of the ecosystem model. Both the spatial and temporal resolution of the data are mutually complementary in the assimilative model. Thus, improvement of either of them can result in improvement of model parameter recoveries. The assimilation of phytoplankton data is essential to recover the model parameters. Phytoplankton is the core of the food web and without the information on phytoplankton, the structure of the ecosystem cannot be constructed correctly. The adjoint method can work well with the noisy data. In the twin experiments with noisy data, the parameters can be recovered but the error is increased. The results of the model and parameter recovery are sensitive to the initial conditions of state variables, so the determination of the initial condition is as important as that of the model parameter. The spatial and temporal resolution and the data type of the observations in Analysis and Modelling Research of the Ecosystem in the Bohai Sea (AMREB) are suitable for the recovery of the model parameters used in this study.     

Wildfire, landscape diversity and the Drossel-Schwabl model

How simple can a model be that still captures essential aspects of wildfire ecosystems at large spatial and temporal scales? The Drossel-Schwabl model (DSM) is a metaphorical forest-fire model developed to reproduce only one pattern of real systems: a frequency distribution of fire sizes resembling a power law. Consequently, and because it appears oversimplified, it remains unclear what bearings the DSM has in reality. Here, we test whether the DSM is capable of reproducing a pattern that was not considered in its design, the hump-shaped relation between the diversity of succession stages and average annual area burnt. We found that the model, once reformulated to represent succession, produces realistic landscape diversity patterns. We investigated four succession scenarios of forest-fire ecosystems in the USA and Canada. In all scenarios, landscape diversity is highest at an intermediate average annual area burnt as predicted by the intermediate disturbance hypothesis. These results show that a model based solely on the dynamics of the fuel mosaic has surprisingly high predictive power with regard to observed statistical properties of wildfire systems at large spatial scales. Parsimonious models, such as the DSM can be used as starting points for systematic development of more structurally realistic but tractable wildfire models. Due to their simplicity they allow analytical approaches that further our understanding under increasing complexity.     

Windows of change: temporal scale of analysis is decisive to detect ecosystem responses to climate change

Long-term ecological research has become a cornerstone of the scientific endeavour to better understand ecosystem responses to environmental change. This paper provides a perspective on how such research could be advanced. It emphasizes that a profound understanding of the mechanisms underlying these responses requires that records of ecologic processes be not only sufficiently long, but also collected at an appropriate temporal resolution. We base our argument on an overview of studies of climate impacts in limnic and marine ecosystems, suggesting that lakes and oceans respond to (short-term) weather conditions during critical time windows in the year. The observed response patterns are often time-lagged or driven by the crossing of thresholds in weather-related variables (such as water temperature and thermal stratification intensity). It becomes clear from the previous studies that average annual, seasonal or monthly climate data often fall short of characterizing the thermal dynamics that most organisms respond to. To illustrate such literature-based evidence using a concrete example, we compare 2?years of water temperature data from Müggelsee (Berlin, Germany) at multiple temporal scales (from hours to years). This comparison underlines the pitfalls of analysing data at resolutions not high enough to detect critical differences in environmental forcing. Current science initiatives that aim at improving the temporal resolution of long-term observatory data in aquatic systems will help to identify adequate timescales of analysis necessary for the understanding of ecosystem responses to climate change.     

Spatial factors affecting statistical power in testing marine fauna displacement

Impacts of offshore wind farms on marine fauna are largely unknown. Therefore, one commonly adheres to the precautionary principle, which states that one shall take action to avoid potentially damaging impacts on marine ecosystems, even when full scientific certainty is lacking. We implement this principle by means of a statistical power analysis including spatial factors. Implementation is based on geostatistical simulations, accommodating for zero-inflation in species data. We investigate scenarios in which an impact assessment still has to be carried out. Our results show that the environmental conditions at the time of the survey is the most influential factor on power. This is followed by survey effort and species abundance in the reference situation. Spatial dependence in species numbers at local scales affects power, but its effect is smaller for the scenarios investigated. Our findings can be used to improve effectiveness of the economical investment for monitoring surveys. In addition, unnecessary extra survey effort, and related costs, can be avoided when spatial dependence in species abundance is present and no improvement on power is achieved.