Variation partitioning of species data matrices: estimation and comparison of fractions

Establishing relationships between species distributions and environmental characteristics is a major goal in the search for forces driving species distributions. Canonical ordinations such as redundancy analysis and canonical correspondence analysis are invaluable tools for modeling communities through environmental predictors. They provide the means for conducting direct explanatory analysis in which the association among species can be studied according to their common and unique relationships with the environmental variables and other sets of predictors of interest, such as spatial variables. Variation partitioning can then be used to test and determine the likelihood of these sets of predictors in explaining patterns in community structure. Although variation partitioning in canonical analysis is routinely used in ecological analysis, no effort has been reported in the literature to consider appropriate estimators so that comparisons between fractions or, eventually, between different canonical models are meaningful. In this paper, we show that variation partitioning as currently applied in canonical analysis is biased. We present appropriate unbiased estimators. In addition, we outline a statistical test to compare fractions in canonical analysis. The question addressed by the test is whether two fractions of variation are significantly different from each other. Such assessment provides an important step toward attaining an understanding of the factors patterning community structure. The test is shown to have correct Type I. error rates and good power for both redundancy analysis and canonical correspondence analysis.     

Spatial connectivity in a large river system: resolving the sources and fate of dissolved organic matter

Large rivers are generally heterogeneous and productive systems that receive important inputs of dissolved organic matter (DOM) from terrestrial and in situ sources. Thus, they are likely to play a significant role in the biogeochemical cycling of the DOM flowing to the oceans. The asymmetric spatial gradient driven by directional flow and environmental heterogeneity contributes to the fate of DOM flowing downstream. Yet, the relative effects of spatial connectivity and environmental heterogeneity on DOM dynamics are poorly understood. For example, since environmental variables show spatial heterogeneity, the variation explained by environmental and spatial variables may be redundant. We used the St. Lawrence River (SLR) as a representative large river to resolve the unique influences of environmental heterogeneity and spatial connectivity on DOM dynamics. We used three-dimensional fluorescence matrices combined with parallel factor analysis (PARAFAC) to characterize the DOM pool in the SLR. Seven fluorophores were modeled, of which two were identified to be of terrestrial origin and three from algal exudates. We measured a set of environmental variables that are known to drive the fate of DOM in aquatic systems. Additionally, we used asymmetric eigenvector map (AEM) modeling to take spatial connectivity into account. The combination of spatial and environmental models explained 85% of the DOM variation. We show that spatial connectivity is an important driver of DOM dynamics, as a large fraction of environmental heterogeneity was attributable to the asymmetric spatial gradient. Along the longitudinal axis, we noted a rapid increase in dissolved organic carbon (DOC), mostly controlled by terrestrial input of DOM originating from the tributaries. Variance partitioning demonstrated that freshly produced protein-like DOM was found to be the preferential substrate for heterotrophic bacteria undergoing rapid proliferation, while humic-like DOM was more correlated to the diffuse attenuation coefficient of UVA radiation.     

A regression strategy for analyzing environmental data generated by spatio-temporal processes

Highly complex spatio-temporal environmental data sets are becoming common in ecology because of the increasing use of large-scale simulation models and automated data collection devices. The spatial and temporal dimensions present real and difficult challenges for the interpretation of these data. A particularly difficult problem is that the relationship among variables can vary in dramatically in response to environmental variation; consequently, a single model may not provide adequate fit. The temporal dimension presents both opportunities for improved prediction because explanatory variables sometimes exert delayed effects on response variables, and problems because variables are often serially correlated. This article presents a regression strategy for accommodating these problems and exploiting serial correlation. The strategy is illustrated by a case study of simulated net primary production (SNPP) that compares ocean-atmosphere indices to terrestrial climate variables as predictors of SNPP across the conterminous United States, and describes spatial variation in the relative importance of terrestrial climate variables towards predicting SNPP. We found that the relationship between ocean-atmosphere indices and SNPP varies substantially over the United States, and that there is evidence of a substantive link only in the western portions of the United States. Evidence of multi-year delays in the effect of terrestrial climate effects on SNPP were also found.     

Competition among eucalyptus trees depends on genetic variation and resource supply

Genetic variation and environmental heterogeneity fundamentally shape the interactions between plants of the same species. According to the resource partitioning hypothesis, competition between neighbors intensifies as their similarity increases. Such competition may change in response to increasing supplies of limiting resources. We tested the resource partitioning hypothesis in stands of genetically identical (clone-origin) and genetically diverse (seed-origin) Eucalyptus trees with different water and nutrient supplies, using individual-based tree growth models. We found that genetic variation greatly reduced competitive interactions between neighboring trees, supporting the resource partitioning hypothesis. The importance of genetic variation for Eucalyptus growth patterns depended strongly on local stand structure and focal tree size. This suggests that spatial and temporal variation in the strength of species interactions leads to reversals in the growth rank of seed-origin and clone-origin trees. This study is one of the first to experimentally test the resource partitioning hypothesis for intergenotypic vs. intragenotypic interactions in trees. We provide evidence that variation at the level of genes, and not just species, is functionally important for driving individual and community-level processes in forested ecosystems.     

A multiscale hierarchical Markov transition matrix model for generating and analyzing thematic raster maps

A model is described for generating hierarchically scaled spatial pattern as represented in a thematic raster map. The model involves a series of Markov transition matrices, one for each level in the scaling hierarchy. In full generality, the model allows the transition matrices to be different at each level, potentially making available a large number of parameters for landscape characterization. The model is self-similar when the transition matrices are all equal. A method is presented for fitting the model to data that take the form of a single-resolution thematic raster map. Explicit analytic solutions are obtained for the fitted parameters. The fitting method is based on a relationship between the hierarchical transitions in the model and spatial transitions at varying distance scales in the data map, a categorical analogy of the geostatistical variogram.     

Responses of phytoplankton and periphytic diatoms to environmental factors in a tropical riverine reservoir北大核心CSCD

Riverine reservoirs have a short water retention time, which is ecologically more similar to that of rivers. Generally, phytoplankton-based approaches are used for lakes and periphytic diatom-based approach for rivers. To understand the differences in the responses of phytoplankton and periphytic diatoms to environmental variables for riverine reservoirs, we collected periphytic diatom samples on artificial substrata as well as phytoplankton samples from a tropical reservoir with a resident time less than 10 days. Our results showed that 131 phytoplankton species and 138 periphytic diatoms were detected; the variation of phytoplankton community was mainly reflected by the dominant species with a strong response to the environmental variables at a time scale, whereas the variation of periphytic diatom community was noted in both the species composition and the dominant species, with a strong response at spatial-temporal scales. The multivariate regression analysis and redundancy analysis showed that environmental factors have higher explanations for the variance of the periphytic diatom community (R2 = 0.27). Temperature was the key explanatory variable for phytoplankton, planktonic diatoms and periphytic diatoms (P < 0.01). However, dissolved oxygen and nitrate were also detected as significant explanatory factors associated with periphytic diatom community (P < 0.01). Thus, the periphytic diatoms were concluded to be more sensitive to environmental change and were associated with more environmental variables than phytoplankton. Periphytic diatoms appear to provide more ecological information than phytoplankton for riverine reservoirs. © 2018 Science Press. All rights reserved.     

Mapping species distributions in one dimension by non-homogeneous hidden Markov models: the case of freshwater pearl mussels in the River Dee

The investigation of species distributions in rivers involves data which are inherently sequential and unlikely to be fully independent. To take these characteristics into account, we develop a Bayesian hierarchical model for mapping the distribution of freshwater pearl mussels in the River Dee (Scotland). At the top of the hierarchy the likelihood is used to describe the sequence of sites in which mussels were observed or not. Given that false observations can occur, and that “not observed” means both that the species was not present and that it was not observed, a Markov prior is introduced at the second level of the hierarchy to represent the sequence of sites in which mussels are estimated to occur. The Markov prior allows modelling the spatial dependency between neighbouring sites. A third level in the hierarchy is given by the representation of the transition probabilities of the Markov chain in terms of site-specific explanatory variables, through a logistic regression. The selection of the explanatory variables which influence the Markov process is performed by means of a simulation-based procedure, in the complex case of association between covariates. Four features were found to be associated with reduced chance of finding a local mussel population: tributaries, bridges, dredging, and waste water treatment works. These results complement the results of a previous study, providing new evidence for the causes of the deterioration of a highly threatened species.     

The role of environmental and spatial processes in structuring lake communities from bacteria to fish

We assessed the relative roles of local environmental conditions and dispersal on community structure in a landscape of lakes for the major trophic groups. We use taxonomic presence-absence and abundance data for bacteria, phytoplankton, zooplankton, and fish from 18 lakes in southern Quebec, Canada. The question of interest was whether communities composed of organisms with more limited dispersal abilities, because of size and life history (zooplankton and fish) would show a different effect of lake distribution than communities composed of good dispersers (bacteria and phytoplankton). We examine the variation in structure attributable to local environmental (i.e., lake chemical and physical variables) vs. dispersal predictors (i.e., overland and watercourse distances between lakes) using variation partitioning techniques. Overall, we show that less motile species (crustacean zooplankton and fish) are better predicted by spatial factors than by local environmental ones. Furthermore, we show that for zooplankton abundances, both overland and watercourse dispersal pathways are equally strong, though they may select for different components of the community, while for fish, only watercourses are relevant dispersal pathways. These results suggest that crustacean zooplankton and fish are more constrained by dispersal and therefore more likely to operate as a metacommunity than are bacteria and phytoplankton within this studied landscape.     

Spatial variogram estimation from temporally aggregated seabird count data

Seabird abundance is an important indicator for assessing impact of human activities on the marine environment. However, data collection at sea is time consuming and surveys are carried out over several consecutive days for efficiency reasons. This study investigates the validity of aggregating those data over time to estimate a spatial variogram that is representative for spatial correlation in species abundance. For this purpose we simulate four-day surveys of seabird count data that contain spatial and temporal correlation arising from temporal changes in the spatial pattern of environmental conditions. Estimates of the aggregated spatial variogram are compared to a variogram that would arise when data were collected over a single day. The study reveals that, under changing environmental conditions over surveys days, aggregating data over a four-day survey increases both the non-spatial variation in the data and the scale of spatial correlation in seabird data. Next, the effect of using an aggregated variogram on the statistical power to test the significance of an impact is investigated. The impact concerns a case of establishing an offshore wind farm resulting in seabird displacement. The study shows that both overestimation and underestimation of statistical power occurs, with power estimates differing up to a factor of two. We conclude that the spatial variation in seabird abundance can be misrepresented by using temporally aggregated data. In impact studies, such misrepresentation can lead to erroneous assessments of the ability to detect impact.     

Predicting tree distributions in an East African biodiversity hotspot: model selection, data bias and envelope uncertainty

The Eastern Arc Mountains (EAMs) of Tanzania and Kenya support some of the most ancient tropical rainforest on Earth. The forests are a global priority for biodiversity conservation and provide vital resources to the Tanzanian population. Here, we make a first attempt to predict the spatial distribution of 40 EAM tree species, using generalised additive models, plot data and environmental predictor maps at sub 1 km resolution. The results of three modelling experiments are presented, investigating predictions obtained by (1) two different procedures for the stepwise selection of predictors, (2) down-weighting absence data, and (3) incorporating an autocovariate term to describe fine-scale spatial aggregation. In response to recent concerns regarding the extrapolation of model predictions beyond the restricted environmental range of training data, we also demonstrate a novel graphical tool for quantifying envelope uncertainty in restricted range niche-based models (envelope uncertainty maps). We find that even for species with very few documented occurrences useful estimates of distribution can be achieved. Initiating selection with a null model is found to be useful for explanatory purposes, while beginning with a full predictor set can over-fit the data. We show that a simple multimodel average of these two best-model predictions yields a superior compromise between generality and precision (parsimony). Down-weighting absences shifts the balance of errors in favour of higher sensitivity, reducing the number of serious mistakes (i.e., falsely predicted absences); however, response functions are more complex, exacerbating uncertainty in larger models. Spatial autocovariates help describe fine-scale patterns of occurrence and significantly improve explained deviance, though if important environmental constraints are omitted then model stability and explanatory power can be compromised. We conclude that the best modelling practice is contingent both on the intentions of the analyst (explanation or prediction) and on the quality of distribution data; generalised additive models have potential to provide valuable information for conservation in the EAMs, but methods must be carefully considered, particularly if occurrence data are scarce. Full results and details of all species models are supplied in an online Appendix.     

Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses

Recently, analytical approaches based on the eigenfunctions of spatial configuration matrices have been proposed in order to consider explicitly spatial predictors. The present study demonstrates the usefulness of eigenfunctions in spatial modeling applied to ecological problems and shows equivalencies of and differences between the two current implementations of this methodology. The two approaches in this category are the distance-based (DB) eigenvector maps proposed by P. Legendre and his colleagues, and spatial filtering based upon geographic connectivity matrices (i.e., topology-based; CB) developed by D. A. Griffith and his colleagues. In both cases, the goal is to create spatial predictors that can be easily incorporated into conventional regression models. One important advantage of these two approaches over any other spatial approach is that they provide a flexible tool that allows the full range of general and generalized linear modeling theory to be applied to ecological and geographical problems in the presence of nonzero spatial autocorrelation.     

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

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

Remote sensing: Using the spatial domain

Objects in the terrestrial environment interact differentially with electromagnetic radiation according to their essential physical, chemical and biological properties. This differential interaction is manifest as variability in scattered radiation according to wavelength, location, time, geometries of illumination and observation and polarization. If the population of scattered radiation could be measured, then estimation of these essential properties would be straightforward. The only problem would be linking such estimates to environmental variables of interest. This review paper is divided into three parts. Part 1 is an overview of the attempts that have been made to sample the five domains of scattered radiation (spectral, spatial, temporal, geometrical, polarization) and then to use the results of this sampling to estimate environmental variables of interest. Part one highlights three issues: first, that relationships between remotely sensed data and environmental variables of interest are indirect; second, our ability to estimate these environmental variables is dependent upon our ability to capture a sound representation of variability in scattered radiation and third, a considerable portion of the useful information in remotely sensed images resides in the spatial domain (within the relations between the pixels in the image). This final point is developed in Part 2 that explores ways in which the spatial domain is utilized to describe spatial variation in remotely sensed and ground data; to design optimum sampling schemes for image data and ground data and to increase the accuracy with which remotely sensed data can be used to estimate both discontinuous and continuous variables. Part 3 outlines two specific uses of information in the spatial domain; first, to select an optimum spatial resolution and second, to inform an image classification.     

GIS-based niche modeling for mapping species' habitat

Ecological "niche modeling" using presence-only locality data and large-scale environmental variables provides a powerful tool for identifying and mapping suitable habitat for species over large spatial extents. We describe a niche modeling approach that identifies a minimum (rather than an optimum) set of basic habitat requirements for a species, based on the assumption that constant environmental relationships in a species' distribution (i.e., variables that maintain a consistent value where the species occurs) are most likely to be associated with limiting factors. Environmental variables that take on a wide range of values where a species occurs are less informative because they do not limit a species' distribution, at least over the range of variation sampled. This approach is operationalized by partitioning Mahalanobis D2 (standardized difference between values of a set of environmental variables for any point and mean values for those same variables calculated from all points at which a species was detected) into independent components. The smallest of these components represents the linear combination of variables with minimum variance; increasingly larger components represent larger variances and are increasingly less limiting. We illustrate this approach using the California Gnatcatcher (Polioptila californica Brewster) and provide SAS code to implement it.     

Variation in Pesticide Tolerance of Tadpoles among and within Species of Ranidae and Patterns of Amphibian Decline

Abstract: There is significant variation among and within amphibian species with respect to reports of population decline; declining species are often found in environments that are physiograpically similar to environments where the same species is thriving. Because variability exists among organisms in their sensitivity to environmental stressors, it is important to determine the degree of this variation when undertaking conservation efforts. We conducted both lethal (time-to-death) and sublethal (activity change) assays to determine the degree of variation in the sensitivity of tadpoles to a pesticide, carbaryl, at three hierarchical levels: among ranid species, among several populations of a single ranid species (   Rana sphenocephala ), and within populations of R. sphenocephala . We observed significant variation in time to death among the nine ranid species and among the 10 R. sphenocephala populations we tested. Four out of eight R. sphenocephala populations exhibited significantly different times to death among families. The magnitude of the activity change in response to exposure to sublethal carbaryl levels was significantly different among species and within R. sphenocephala populations. Chemical contamination, at lethal or sublethal levels, can alter natural regulatory processes such as juvenile recruitment in amphibian populations and should be considered a contributing cause of declines in amphibian populations.     

Understanding abundance patterns of a declining seabird: implications for monitoring.

The Kittlitz's Murrelet (Brachyramphus brevirostris) is a rare, non-colonial seabird often associated with tidewater glaciers and a recent candidate for listing under the Endangered Species Act. We estimated abundance of Kittlitz's Murrelets across space and time from at-sea surveys along the coast of Alaska (USA) and then used these data to develop spatial models to describe abundance patterns and identify environmental factors affecting abundance. Over a five-week period in the summer of 2005, we recorded 794 Kittlitz's Murrelets, 16 Marbled Murrelets (B. marmoratus), and 70 unidentified murrelets. The overall population estimate (N, mean +/- SE) during the peak period (3-9 July) was 1317 +/- 294 birds, decreasing to 68 +/- 37 by the last survey period (31 July-6 August). Density of Kittlitz's Murrelets was highest in pelagic waters of Taan Fjord (18.6 +/- 7.8 birds/km2, mean +/- SE) during 10-16 July. Spatial models identified consistent "hotspots" of Kittlitz's Murrelets, including several small areas where high densities of murrelets were found throughout the survey period. Of the explanatory variables that we evaluated, tidal current strength influenced murrelet abundance most consistently, with higher abundance associated with strong tidal currents. Simulations based on the empirically derived estimates of variation demonstrated that spatial variation strongly influenced power to detect trend, although power changed little across the threefold difference in the coefficient of variation on detection probability. We include recommendations for monitoring Kittlitz's Murrelets (or other marine species) when there is a high degree of uncertainty about factors affecting abundance, especially spatial variability.     

RNA:DNA ratios of the hydrothermal-vent vestimentiferans Ridgeia piscesae and R. phaeophiale indicate variations in growth rates over small spatial scales

The ratio of RNA to DNA (RNA:DNA) was used to assess the relative growth rates of the hydrothermal vent vestimentiferans Ridgeia piscesae Jones and R. phaeophiale Jones. This biochemical indicator of growth is especially valuable when actual growth rates are difficult to measure. Tubeworms were collected from five hydrothermally active sites along the Juan de Fuca Ridge, in the Northeast Pacific Ocean in the summers of 1984 and 1986. We found significant variation in RNA:DNA among Ridgeia spp. from the five sites which was not due to size of the tubeworms or to a species-specific difference. Instead, differences in RNA:DNA were related to site of collection. Mean RNA:DNAs of 2.1 and 3.9 for R. piscesae from two sites were significantly different from each other, but not from that of tubeworms from a third site (mean=2.9). Similarly, mean RNA:DNAs of 2.3 and 4.5 for R. phaeophiale from two sites were significantly different. These patterns in RNA:DNA may reflect differences in growth rates arising from variation in environmental factors over spatial scales as small as 2 m.     

Power evaluation of focused cluster tests

Many statistical tests have been developed to assess the significance of clusters of disease located around known sources of environmental contaminants, also known as focused disease clusters. The majority of focused-cluster tests were designed to detect a particular spatial pattern of clustering, one in which the disease cluster centers around the pollution source and declines in a radial fashion with distance. However, other spatial patterns of environmentally related disease clusters are likely given that the spatial dispersion patterns of environmental contaminants, and thus human exposure, depend on a number of factors (i.e., meteorology and topography). For this study, data were simulated with five different spatial patterns of disease clusters, reflecting potential pollutant dispersion scenarios: (1) a radial effect decreasing with increasing distance, (2) a radial effect with a defined peak and decreasing with distance, (3) a simple angular effect, (4) an angular effect decreasing with increasing distance and (5) an angular effect with a defined peak and decreasing with distance. The power to detect each type of spatially distributed disease cluster was evaluated using Stone’s Maximum Likelihood Ratio Test, Tango’s Focused Test, Bithell’s Linear Risk Score Test, and variations of the Lawson–Waller Score Test. Study findings underscore the importance of considering environmental contaminant dispersion patterns, particularly directional effects, with respect to focused-cluster test selection in cluster investigations. The effect of extra variation in risk also is considered, although its effect is not substantial in terms of the power of tests.     

Spatial heterogeneity influences native and nonnative plant species richness

Spatial heterogeneity may have differential effects on the distribution of native and nonnative plant species richness. We examined the effects of spatial heterogeneity on native and nonnative plant species richness distributions in the central part of Rocky Mountain National Park, Colorado, USA. Spatial heterogeneity around vegetation plots was characterized using landscape metrics, environmental/topographic variables (slope, aspect, elevation, and distance from stream or river), and soil variables (nitrogen, clay, and sand). The landscape metrics represented five components of landscape heterogeneity and were measured at four spatial extents (within varying radii of 120, 240, 480, and 960 m) using the FRAGSTATS landscape pattern analysis program. Akaike's Information Criterion adjusted for small sample size (AICc) was used to select the best models from a set of multiple linear regression models developed for native and nonnative plant species richness at four spatial extents and three levels of ecological hierarchy (i.e., landscape, land cover, and community). Both native and nonnative plant species richness were positively correlated with edge density, Simpson's diversity index and interspersion/juxtaposition index, and were negatively correlated with mean patch size. The amount of variation explained at four spatial extents and three hierarchical levels ranged from 30% to 70%. At the landscape level, the best models explained 43% of the variation in native plant species richness and 70% of the variation in nonnative plant species richness (240-m extent). In general, the amount of variation explained was always higher for nonnative plant species richness, and the inclusion of landscape metrics always significantly improved the models. The best models explained 66% of the variation in nonnative plant species richness for both the conifer land cover type and lodgepole pine community. The relative influence of the components of spatial heterogeneity differed for native and nonnative plant species richness and varied with the spatial extent of analysis and levels of ecological hierarchy. The study offers an approach to quantify spatial heterogeneity to improve models of plant biodiversity. The results demonstrate that ecologists must recognize the importance of spatial heterogeneity in managing native and nonnative plant species.