http://orcid.org/0000-0002-1769-1536
Figures
Abstract
This study addresses the impact of spatial scale on explaining variance in benthic communities. In particular, the analysis estimated the fraction of community variation that occurred at a spatial scale smaller than the sampling interval (i.e., the geographic distance between samples). This estimate is important because it sets a limit on the amount of community variation that can be explained based on the spatial configuration of a study area and sampling design. Six benthic data sets were examined that consisted of faunal abundances, common environmental variables (water depth, grain size, and surficial percent cover), and sonar backscatter treated as a habitat proxy (categorical acoustic provinces). Redundancy analysis was coupled with spatial variograms generated by multiscale ordination to quantify the explained and residual variance at different spatial scales and within and between acoustic provinces. The amount of community variation below the sampling interval of the surveys (< 100 m) was estimated to be 36–59% of the total. Once adjusted for this small-scale variation, > 71% of the remaining variance was explained by the environmental and province variables. Furthermore, these variables effectively explained the spatial structure present in the infaunal community. Overall, no scale problems remained to compromise inferences, and unexplained infaunal community variation had no apparent spatial structure within the observational scale of the surveys (> 100 m), although small-scale gradients (< 100 m) below the observational scale may be present.
Citation: Flanagan AM, Flood RD, Frisk MG, Garza CD, Lopez GR, Maher NP, et al. (2018) The relationship between observational scale and explained variance in benthic communities. PLoS ONE 13(1): e0189313. https://doi.org/10.1371/journal.pone.0189313
Editor: Maura (Gee) Geraldine Chapman, University of Sydney, AUSTRALIA
Received: June 16, 2017; Accepted: November 22, 2017; Published: January 11, 2018
This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.
Data Availability: The Kingston-Saugerties data were provided by email request made to David Strayer (strayerd@caryinstitute.org) at the Cary Institute of Ecosystem Studies, Box AB, Millbrook N.Y. 12545 (www.caryinstitute.org). Similar data requests may be made to the same address. The authors confirm they had no special access to the data.
Funding: This manuscript is a resulting product from project R/CO-7 funded under award 53266 and from project R/CO-6 funded under award 22915 from the National Sea Grant College Program of the U.S. Department of Commerce’s National Oceanic and Atmospheric Administration, to the Research Foundation of the State University of New York on behalf of New York Sea Grant, and from the New York Department of Environmental Conservation “Integrating Fish Trawl, Water Quality, and Benthic Mapping Data in the Peconic Estuary” project. The statements, findings, conclusions, views, and recommendations are those of the authors and do not necessarily reflect the views of any of those organizations.
Competing interests: The authors have declared that no competing interests exist.
Introduction
Understanding the role of scale in freshwater, marine, and terrestrial communities is vital in ecology [1–3]. Scale in processes, data collection, and analysis [4] has relevance to virtually all ecological investigations with its ability to influence the outcome or conclusion of a study [1], [5]. Central to the ecological significance of scale is hierarchy theory [6], which has been used to conceptualize the processes by which multiple, scale-dependent, and potentially interacting phenomena contribute to the biological heterogeneity that is ultimately observed in nature [7], [8].
In benthic environments, geomorphology tends to be complex resulting in conceivably abrupt changes in faunal communities, a pattern expected from hierarchy theory [9]. Careful examination of biological structuring through the lens of hierarchy theory may help to deepen our understanding of the ecological significance of scale. For example, a common practice for ecologists is to simplify nature [2] using habitat classification [8,10–13] as an approach for managing ecosystems. Most habitat classification approaches are based on hierarchy theory in that they are designed to characterize habitat features from large (e.g., basins, boulder fields, etc.) to small (e.g., burrows, sand waves, etc.) spatial scales [8]. Thus, hierarchy theory comprises a natural link between scale, habitat classification, and ultimately spatial analysis.
The observational scale of an ecological study is defined by the grain or size of the sampling unit, the sampling interval (or lag in time series analysis) between samples, and the extent of the study [1,4,14]. Many investigators have focused on grain and extent, and the effects of varying these factors are well known in benthic systems [15,16]. Less understood is the effect of varying the sampling interval (i.e., the geographic distance between samples). The sampling interval is generally limited by the cost and effort of collecting and processing community data [17]. Sampling at small intervals may leave out important controlling environmental factors while sampling at large intervals may make it difficult to identify patterns in the fauna [1]. A relevant question to ask is how much does the sampling interval affect biotic-environmental inferences, since once a sampling regime is chosen, spatial variation occurring at smaller intervals cannot be investigated. Sampling and analysis scale have been historically somewhat arbitrary [18] and potentially biased through anthropocentric perceptions of nature–a problem aptly referred to as “scale arbitrariness” by Wiens (1989) [1]. So, the scales being used in scientific studies may not reflect the scales that are important and/or relevant to the animals and communities that are being investigated.
Field-based sampling methods for examining benthic communities have traditionally involved in situ sampling with grab samplers, corers, and dredges. The distance interval between these samples defines the smallest scale over which the data set can provide information about biotic-environmental relationships. Below that distance, small-scale variations are present [14]. These are presumably due biotic interactions [7], especially at scales approaching the organisms themselves [19], along with small-scale variability in measured environmental variables, other unmeasured environmental factors that become important at small scales, and measurement error.
Recently, uncovering spatial patterns in benthic communities through the application of geospatial tools (e.g., sonar, high-resolution videography, etc.) has emerged as a field in its own right [20–22]. The key advantage to geospatial methods, especially sonar, is that they can provide near to full, high-resolution coverage of the areas surveyed versus the seafloor “snapshots” obtained by traditional in situ sampling [22]. In addition, with the proliferation of techniques for the analysis of sonar data (e.g., acoustic segmentation via visual, supervised, and/or unsupervised classification), acoustically-defined habitats (referred to as “provinces” in the present study) or areas of the seafloor consisting of apparently homogeneous geophysical conditions can be readily derived and used in analysis. Despite its clear potential, not all acoustic features that appear to characterize distinct regions are relevant to benthic community structure [23–26]. For instance, regions defined using acoustic data in areas consisting of unconsolidated sand and gravel sediments did not correspond well to infaunal assemblage boundaries [24]. Further, significant but weak associations between sonar backscatter and community structure have also been observed [25]. Beyond the “seascape” scale, other scales at which sonar data should be analyzed to provide useful information on community structure are unclear. Yet, scale selection for the purposes of analysis can be as critical as the observational scale is for identifying relationships [4].
Multiscale ordination (MSO) extends spatial statistics to examining the structure of biotic-environmental relationships by inserting multivariate regression results from a direct gradient method, such as redundancy analysis (RDA), into an empirical variogram [27–29]. MSO is distance-based, where the spatial structure in a data set is scrutinized using an empirical variogram, a plot of the sum of the mean squared species-specific differences between pairs of samples against their geographic distance [7,27]. MSO takes the fitted and residual output of a nonspatial regression analysis and partitions it at different spatial scales or distance intervals in geographic space. Results are then examined critically for spatial patterns. When fitted and residual variograms are combined and compared to the empirical variogram, they can indicate whether the regression model is misspecified or whether the biotic-environmental relationship changes with spatial scale. The presence of a small-scale trend in the residual variogram may suggest the presence of potentially important species interactions, while a trend at a large spatial scale may be evidence that one or more environmental variables have been missed. Furthermore, spatial correlation structure in the residuals creates non-independence problems that can undermine the data analysis [14,30].
The goal of this study was to use multiscale ordination to examine the spatial structure and biotic-environmental relationships of infaunal communities using six data sets ranging from freshwater to near marine conditions. It was envisioned that identifying characteristics common to all six data sets would provide valuable and perhaps general insights. Analysis of the data focused on quantifying the fraction of community variation that is below the sampling interval, and therefore below the resolution of the study, estimating the amount of community variation explained by commonly used in situ and seascape-scale explanatory variables, determining whether explanatory variables identified during the model selection process removed spatial structure in the data, or whether unresolved and therefore problematic structure remained, and assessing the effectiveness and limitations of the sampling and analytical scales used. We hypothesized that small scale community variability would be large and impose a limit on the amount of variation that could be explained by in situ and seascape-scale environmental variables. We predicted that spatial structure within the observational scale of the studies would be present but effectively explained by a few common environmental variables. Additionally, it was expected that incorporating spatial scale elements would alter the perceived effectiveness of how well these environmental variables explained community variation, and the altered perception would be large enough to potentially affect research and management directions.
Materials and methods
This study analyzed six benthic biotic-environmental data sets from five study locations in New York, USA including three locations within the Hudson River Estuary and two in eastern Long Island’s Peconic Estuary (Fig 1 & Table 1). The five locations represented a range of benthic environments from freshwater (Kingston-Saugerties) to brackish (Haverstraw Bay and Tappan Zee) to near marine (Robins Island and Shelter Island). Sites are moderate in area, ranging from 3.3 to 16.5 km2.
RPD and LOI refer to the apparent redox potential discontinuity depth and sediment organic matter measured by loss on ignition, respectively.
Acoustic provinces
Seascape or habitat-scale environmental data were generated by segmenting each site into regions of the seafloor with apparently homogeneous geophysical conditions (Table 1). This was based primarily on visual interpretation of backscatter intensity and texture in multibeam and/or sidescan sonar surveys (e.g., Fig 2), assuming that the sonar data represented proxies for a variety of natural features and phenomena (e.g., exposure to subtidal currents, vulnerability to sedimentation, compaction, shell hash) that could govern faunal patterns in the benthos [22,23,31–35]. These regions will be referred to as acoustic provinces in this study. Backscatter data were obtained for the Haverstraw Bay and Robins Island sites with a Kongsberg Simrad EM 3000D multibeam sonar system (300 kHz). Multibeam data were gridded on a 1m resolution with horizontal accuracy of 1m. Sidescan sonar data were acquired for the Kingston-Saugerties, Tappan Zee, and Shelter Island areas using an Edgetech DF-1000 or 272 DT sidescan sonar system (100 kHz), gridded on a 2 m resolution. Chirp sub-bottom seismics, sediment cores, and grain size data from grabs were also used as supplementary information for the identification of acoustic provinces at Kingston-Saugerties and Tappan Zee by Bell et al. (2000) [36], and their province maps for these sites were adopted. Province identification was carried out prior to and independently of any faunal sampling or analysis, and no backscatter or supplementary data used in the identification of provinces were used in the subsequent faunal analyses. Visual interpretation resulted in 10 provinces for Kingston-Saugerties [36,37] 5 provinces for Haverstraw Bay [38], 10 for Tappan Zee [36], and 6 and 7 provinces, respectively, for the Robins Island and Shelter Island sites [39]. Provinces were represented as categorical variables in subsequent data analyses. Although character designators (A-J) were used to identify provinces within a site (e.g., Fig 2), habitat types did not map across sites thereby making general between-site comparisons impossible. For example, there were no freshwater channel deposits at any other site than Kingston-Saugerties. In addition, sampling years and seasons also differed making any potential between-site analysis confounded by time.
Points indicate the location of sampling stations. Basemap from https://nationalmap.gov.
In situ community and environmental data
Faunal and sediment samples were collected in situ using a modified Van Veen grab (20 × 20 cm) at Haverstraw Bay (n = 51), Tappan Zee (n = 100), Robins Island (n = 60), and Shelter Island (n = 70) and a petite PONAR grab (15 × 15 cm) at Kingston-Saugerties (n = 44; 3 pooled samples per station). Sampling locations were random, but stratified by province, to ensure full coverage of the habitats present. The Kingston-Saugerties site was sampled in Fall 2001 and Spring 2002 (designated with a suffix ‘01 and ‘02 in results), and each data set was analyzed separately. Water depth was recorded at the time of sample collection. A sediment subsample for grain size analysis was drawn from each grab sample and the remainder washed through a 0.5 mm sieve for fauna. Macrofauna remaining on the sieve were preserved in 10% buffered formalin. In the lab, grain size analysis to estimate percent gravel, sand, and mud was conducted using the technique described by Folk (1974) [40] for all locations except Kingston-Saugerties, where the hydrometer method for particle size analysis was used instead [37,41]. Faunal samples were sorted under a dissecting microscope, identified to species whenever possible, and species abundance per sample was enumerated.
Surficial percent cover data were obtained from analysis of images extracted from seabed surface videos recorded at Tappan Zee (n = 100), Robins Island (n = 60), and Shelter Island (n = 70) using a 2 megapixel Seatrex HD underwater camera mounted on an aluminum tripod. Videos captured 17.5 × 30 cm areas of the seafloor except at Tappan Zee where the camera had to be lowered closer to the bottom since visibility was limited due to the extremely turbid conditions at this location. Recordings from Tappan Zee covered 13.5 × 23.5 cm areas of the seafloor. Percent cover estimates of the visible surficial components present in each image (e.g., shell, pebble, fauna, etc.) were obtained by supervised maximum likelihood classification analysis in ArcGIS 10.1 (ESRI, Redlands, CA).
Empirical variograms
Spatial variability in the species assemblages was examined by constructing an empirical variogram of the multivariate faunal data for each site [27]:
(1)
where γ(h) is the empirical variance in the faunal data at distance class h, xia and xib are Hellinger transformed abundances for species i (i = 1 to s) in samples a and b, respectively, and the inner summation is over all pairs of samples separated by a geographic distance of approximately h. The Hellinger transformation is the square root of the relative abundance of each species in a sample [42]. As such, it focuses the analysis on compositional differences and downplays the influence of highly abundant species to prevent them from dominating the analysis. In addition, when used in conjunction with Euclidian distance, the ecological distance measure utilized here and in the multivariate regression analyses presented below, it produces good representations of ecological dissimilarity [42]. Summing Eq 1 for all pairs of samples, instead of a distance class subset, yields s2 the total sample variance [43].
A plot of γ(h) vs. distance classes h is called a variogram plot and shows how variance between samples changes with spatial scale. Changes in γ(h) with distance indicate the presence of spatial patterns in community structure. Often when spatial structure is present, γ(h) increases from some minimal value at small distances, indicating that community differences increase as samples are collected further apart. This is not the only pattern possible, and variograms with no trend, negative trends, periodic trends, and more complex patterns have been observed [14,44–46],. Important features of the multivariate variogram relevant to the present study include the sill, which is the value of the variance where the variogram plot levels out (if it exists) and the nugget or nugget effect, the value of γ(h) at h = 0 [14,27]. If a sill is present, the range indicates the distance at which community variance is no longer increasing. For reference, definitions of the variogram terms and their ecological interpretations are provided in Table 2. The quantity γ(h) is termed the semivariance in most references on spatial statistics, although Bachmaier and Backes (2008) [43] suggest that the prefix “semi” is applied incorrectly. Because of its common usage, it will be called semivariance in the present study. Variograms were created using the rda(), mso(), and msoplot() functions in the vegan package of R (R Foundation for Statistical Computing, Vienna, Australia). The code for mso() and msoplot() was created and first published by Wagner (2004) [28].
Estimating small-scale variation
Empirical variograms created for each site were fit to a number of common models utilized in spatial statistics [48]. Since no a priori guidance or mechanistic reason was found to choose one model over the others, multiple models with a variety of characteristics, including with/without an inflection at small spatial scales and with/without an asymptotic sill, were fit. The models included the exponential, Gaussian, spherical, piecewise linear, and logistic as follows:
(2)
(3)
(4)
(5)
(6)
In the above equations, c0 is the nugget effect, c0 + c1 is the sill, and a defines the rate and, in the case of the spherical and piecewise linear models, the range at which the sill is reached. For asymptotic models (exponential, Gaussian, and logistic), the range is estimated as the value of h where γ(h) equals 95% of its sill [48].
Models were fit by weighted least squares, as suggested by Cressie (1993) [47], with weighting factors defined by the number of sample pairs in each distance class. Only distance classes less than half the maximum extent of the site (i.e., hmax/2) were utilized, since beyond that distance, sampling locations in the center of the site can no longer contribute to variance estimates, leading to potential bias [27,47]. In the present application, distance classes were set to intervals of 0.25, 0.50, or 0.75 km. The interval was selected for each data set to have plots with about 10 γ(h) values. This usually allowed the distance classes to contain >30 sample pairs, a recommendation suggested by Journal and Huijbregts (1978) [49]. Weighted least squares was carried out using function nls() in the stats package of R (R Foundation for Statistical Computing, Vienna, Australia). It was assumed that the residuals were approximately normally distributed, and model selection was achieved using the small sample, bias-adjusted version of Akaike’s Information Criterion (AICc) [50,51].
Distributional properties of parameter estimates in variogram fits are “not well understood” [47]. Since individual sample points are reused multiple times in creating the variogram (Eq 1), independence assumptions are violated, and application of procedures such as bootstrap, jackknife, or cross-validation to determine errors in parameter estimates are not valid [47]. As a result, no error analysis of parameter estimates was possible.
Multiscale ordination
Multiscale ordination (MSO) extends spatial statistics to examining the spatial structure of biotic-environmental relationships by inserting regression results into the variogram [27–29]. It does this by partitioning the xia and xib pairs in Eq 1 into fitted and residual parts and
, respectively. Substituting these into Eq 1 leads to:
or
(7)
The first two terms on the right-hand side are variograms of the fitted and residual values. The third term is twice the covariance between the fitted and residual differences for distance class h [27]. Multivariate regression estimates of biotic-environmental relationships can be obtained by redundancy analysis (RDA) for small to moderate environmental gradients or canonical correspondence analysis (CCA) for large gradients [28]. Detailed steps to implement this procedure are available in Borcard et al. (2011) [52] and Legendre and Legendre (2012) [14].
In the present study, estimates of predicted and residual Hellinger transformed abundance values were obtained by RDA. RDA is a multivariate method that combines multiple linear regression with ordination. A parsimonious set of explanatory environmental variables was identified by sequentially adding variables in a forward selection process [53]. Candidate variables for each site included water depth, grab penetration depth, apparent redox potential discontinuity (RPD) depth, grain size (% gravel, sand, and mud), sediment organic content measured by loss on ignition (LOI), surficial percent cover (shell, seaweed, and other materials observed in bottom images), and categorical variables as binary 1/0 values representing each acoustic province. At each step in the process, the environmental variable explaining the largest amount of faunal variability was selected, and its effect removed before the next best fitting variable was considered. Variables identified by forward selection were trimmed back to a smaller set by the AICc stopping criterion [54].
Categorical province variables were also combined into smaller sets (e.g., A&E combined, B&D combined, etc.) and regressions evaluated by the AICc criterion to ensure that the smallest number of distinct provinces was selected. Results from multivariate regression tree (MRT) analysis [55] were used to guide the formation of sets of provinces to avoid trying all 2n - 1 unique combinations. Forward selection in RDA was carried out in Canoco 4.5 (Microcomputer Power, Ithaca, NY, USA), and variograms of regression results with the final set of explanatory variables were created using the rda(), mso(), and msoplot() functions in the vegan package of R (R Foundation for Statistical Computing, Vienna, Australia). MRT was run using the mvpart package in R (R Foundation for Statistical Computing, Vienna, Australia).
Following MSO, the spatial structure of the variogram components generated by RDA fitting was analyzed for scale dependence in the biotic-environmental relationship, stationarity of the residuals, and spatial autocorrelation in the residuals using methods in Wagner (2003) [27]. Scale dependence in the biotic-environmental relationship was tested by constructing a Bonferroni-corrected point confidence interval around γ(h) and determining if the sum of the variograms γfit(h)+γres(h) lies wholly within it. If any points in the sum lie outside then γcross(h) is significantly different from 0 at specific distance classes, and the biotic-environmental relationship is scale-dependent. Stationarity of the residuals was examined by determining whether γres(h) reached a sill after short distances and remained there over most of the range. Presence of a spatial trend in γres(h) over large distance classes indicates that important environmental variables were missing in the RDA model. Spatial autocorrelation in the residuals was tested by a series of Bonferroni-adjusted Mantel tests [56] between the distance matrix formed by the residuals and a geographic distance matrix at each distance class interval. The Bonferroni correction set the significance level of the tests at α/n where α = 0.05 and n = the number of distance classes. A significant outcome for a distance class indicates that spatial correlation is present in the residuals [7,28]. The scale dependence and spatial autocorrelation analyses are built into the msoplot() function in the vegan package of R (R Foundation for Statistical Computing, Vienna, Australia).
RDA performance at local vs. habitat-level scales
Variogram measures were recomputed to quantify the extent the RDA models explained local vs. habitat-level community variation. This analysis also assessed the ability of acoustic provinces to serve as proxies for habitats within the study areas. The variogram function mso() was modified slightly to replace the geographic distance matrix between pairs of samples with a matrix of two “distance” classes: within (1) and between (2) acoustic provinces. The output provided the variogram estimates for γ, γfit, and γres for each “distance” class. Assuming that small-scale variation in the data cannot be explained by the RDA models’ biotic-environmental relationships, estimates of the nugget effect were subtracted from γres to assess model performance of only that part of the variation within the observational scale of the surveys.
Results
Summary of faunal and environmental data
An abundant and diverse fauna occurred at each study site. Mean abundance per m2, mean species density per sample, and species richness at each site are summarized in Table 3. Species richness varied from 25 taxa at Haverstraw Bay to 95 taxa at Shelter Island. The study sites represented a wide range of benthic environments ranging from freshwater at Kingston-Saugerties, to mesohaline at Haverstraw Bay and Tappan Zee (salinity ranges of 8.5–14.5 during sampling), to almost marine conditions at Robins Island and Shelter Island (salinity ranges of 28.5 to 31 during sampling). Average water depth varied from 5.7 to 9.9 m among study locations, and depth measurements varied widely at sampling stations within study areas (Table 4). The greatest variation in depth occurred at Kingston-Saugerties with sampling stations ranging from 1 to 22 m. The smallest variation was at Shelter Island with a range of 3 to 11 m. The sediments across all locations were mostly sandy or muddy and rarely contained substantial gravel, with some notable exceptions at individual sampling stations (Table 4). Nevertheless, the grain size range varied broadly; for example, percent mud ranged from less than 4% to greater than 83% within each study area.
Mean values (and range) of the grab-scale environmental variables acquired via in situ sampling. RPD and LOI refer to the apparent redox potential discontinuity depth and sediment organic matter measured by loss on ignition, respectively.
The surficial percent cover classes from maximum likelihood analysis of seafloor images varied moderately among study locations (Table 5). A total of 5 cover classes were identified at Tappan Zee, with the majority of the sampling stations at this site composed of mud, silty shell, or other silt-covered material. Robins Island and Shelter Island had 9 and 14 cover classes, respectively. Surficial sediments at these two sites were predominantly combinations of rock, pebble, sand, mud, shell, shell hash, and silty material. Occasionally, biotic cover consisting of live slipper snails (Crepidula fornicata) and sponges (Microciona porifera) was present.
Empirical variograms of community data and estimates of small-scale variation
The emprirical variance γ(h) increased with geographic distance class across all study locations, indicating that spatial structure was present in the species assemblages (Fig 3). At small distance classes, γ(h) was dominated by pairs of samples that were within the same acoustic province, and γ(h) reached a sill once it became dominated by between-province sample pairs at large distance classes. The shape of γ(h) was smooth for the Haverstraw Bay, Tappan Zee, Robins Island and Shelter Island sites, but more variable in the Kingston-Saugerties data sets. The pattern for Kingston-Saugeties probably reflects the elongated north-south structure of this study area in the Hudson River where short east-west distances can place sample pairs in different provinces but long north-south distances can still lead to within-province pairs contributing to γ(h).
Distance intervals ranged from 0.25 to 0.75 km among study locations. Arrows on the vertical and horizontal axes indicate nugget and range estimates, respectively.
Based on estimates of the nugget effect in the variogram models, small-scale variability represented a substantial fraction of the overall community variance across all data sets, ranging from 36 to 59% of the total faunal variance (Table 6). A piecewise linear model was selected for 2 of the 6 data sets (Kingston-Saugerties ‘01, Robins Island), a spherical model for 3 data sets (Kingston-Saugerties ‘02, Tappan Zee, and Shelter Island), and an exponential model was selected for Haverstraw Bay. The range over which spatial variation was apparent in the data sets varied between 0.62 and 3.87 km or over 16–26% of the maximum extent in the study areas. There was no relationship between scaled values of the nugget and range (product-moment correlation, r = 0.23, p = 0.66).
c0 is an estimate of the nugget effect and c0/s2 is an estimate of the fraction of the total variance represented by small-scale variability. The sum c0 + c1 is the sill, and a defines the rate and, in the case of the spherical and piecewise linear models, the range at which the sill is reached. For the exponential model, the range was estimated as the distance where the variogram model reached 95% of the sill. The maximum extent is the largest geographic distance between two sampling locations in a study.
Nonspatial RDA results
The forward selection process in RDA resulted in the selection of 5 to 7 explanatory variables and r2 values representing 42 to 52% of the total variance (Fig 4; Table 7). Acoustic provinces dominated the analysis at all sites, but other environmental variables identified in forward selection and subsequently retained by the AICc model selection criterion were water depth (Kingston-Saugerties’01, Haverstraw Bay, Robins Island, and Shelter Island), percent sand (Kingston-Saugerties’01 and ‘02, Haverstraw Bay, and Shelter Island), percent mud (Tappan Zee) and the percent cover classes from image analysis including % shell fragment cover at Tappan Zee, and % mud cover, % shell fragment cover, and % M. porifera cover at Robins Island. LOI and RPD were not selected in the RDA.
Scores for individual samples plotted as points. Sample points close to one another tend to have similar faunal structure than those further apart. Different point shapes and color represent samples collected from different acoustic provinces. Polygons enclose samples from each province. Continuous explanatory variables and individual taxa are plotted as vectors. The vector arrowheads represent high, the origin averages, and the tail (when extended through the origin) low values of the selected environmental variables. Projections of sample points onto an individual taxa vector approximate the Hellinger transformed abundances for that taxon. For clarity, only species with the highest amounts of explained variance (typically those with > 10%) are plotted. Acca = Acteocina canaliculata, Antr = Anadara transversa, Baca = Batea catharinensis, Baim = Balanus imporvisus, Balamp = Balanus amphitrite, Boclig = Boccardia ligerica, Cdeco = Chironomus decorus, Chispp = Chironomidae sp., Crfo = Crepidula fornicata, Crpl = Crepidula plana, Crychi = Cryptochironomus sp., Cscap = Coelotanypus scapularis, Cpoli/Cypo = Cyathura polita, Dstag = Dorylaimus cf. stagnalis, Elle = Elasmopus levis, Endi = Ensis directus, Eusa = Eumida sanguinea, Geudem = Geukensia demissa, Gtigr = Gammarus tigrinus, Hefi = Heteromastus filiformis, Hofl = Heteromysis formosa, Hypgra = Hypaniola grayi, Ifrey = Isochaetides freyi, imTubwo = immature Tubificidae without hair setae, Lepplu/Lepl = Leptocheirus plumulosus, Lesm = Lembos smithi, Lhoff = Limnodrilus hoffmeisteri, Lyhy = Lyonsia hyalina, Mazo = Macroclymene zonalis, Melnit/Meni = Melita nitida, Meme = Mercenaria mercenaria, Mula = Mulinia lateralis, Mytleu/Myle = Mytilopsis leucophaeata, Neasuc/Nesu = Neanthes succinea, Nema = Nematode, Olig = Oligochaeta, Ophi = Ophiuroidea, Pago = Pandora gouldiana, Pahe = Panopeus herbstii, Phalt = Polypedilum halterale, Pygo = Polygordius sp., Racu/Racun = Rangia cuneata, Scfr = Scoloplos fragilis, Stbe = Streblospio benedicti, Teag = Tellina agilis, and Thsp = Tharyx sp.
Minimum AICc values are indicated in bold. Capital letters listed in the “Variable” column are provinces, and the variables are listed in order of selection.
Multiscale ordination
MSO results indicated that the spatial dependence in the faunal data was captured by the explanatory variables selected in the RDA, and that the residuals contained no detectible spatial structure (Fig 5). Variograms formed from RDA predictions γfit(h) had evident spatial structure at all sites and strongly paralleled the shape of the empirical variograms, suggesting that the functional form of the RDA model was not misspecified. Points in the variograms formed by the sum γfit(h)+γres(h) lay within the Bonferroni-corrected point confidence interval around γ(h), indicating that there were no problems with scale dependence in the biotic-environmental relationships. The variogram of γres(h) quickly reached a sill and did not continue to increase with distance class, indicating that the stationarity assumption was met and no unknown environmental factor(s) was present influencing the spatial structure of the residuals. In addition, Bonferroni-adjusted Mantel tests between residuals and a geographic distance matrix at each distance class interval were non-significant, excluding the possibility of autocorrelated residuals.
Crosshairs are the sum of fitted and residual variograms, solid lines are Bonferroni-corrected point confidence envelope of the empirical variogram, open diamonds represent the fitted variogram, and open squares are the residual variogram. Numbers above the distance axis are the number of sample pairs in each distance class. See the explanation of Eq 7 definitions of these quantities. Solid squares, although absent in all cases, would indicate the presence significant spatial autocorrelation in the residuals (detected via Mantel tests). Distances are in kilometers.
RDA performance at local vs. habitat-level scales
Subtracting the nugget estimates of small-scale variability from RDA regression residuals altered the perception of RDA model performance both overall and at local vs. habitat levels (Fig 6). With small-scale variability removed from the residuals, the nonspatial RDA explained >71% of the remaining variance in community structure. When comparisons were restricted to sample pairs within the same acoustic province, the RDA model explained 21–100% of the remaining variance in community structure. The within-province comparisons were notably weak for Haverstraw (33%), Tappan Zee (24%), Robins Island (42%), and Shelter Island (23%). When comparisons were restricted to sample pairs in different acoustic provinces, the RDA model explained >73% of the remaining variance in community structure. Negative residual values in the two Kingston-Saugerties data sets are addressed in the discussion.
For each data set, comparisons are made for the entire nonspatial RDA and for results broken down into components representing variation within and between acoustic provinces.
Discussion
In this study, the nugget estimates of small-scale variability represented a substantial proportion of the total community variation across all data sets analyzed (36–59%). The estimates were only about 10% less than the variation present at the smallest distance class in the empirical variograms; thus, even if these observed values were substituted for the nugget effect estimates, the results would not change substantially. Since the nugget estimates were based on the analysis of empirical variograms, they are independent of the multivariate RDA regressions. Potential causal factors for the small-scale variation include biotic interactions [7] and patchiness in settlement [57], especially at a scale approaching the organisms themselves [19], small-scale variability in measured environmental variables, other unmeasured environmental factors that become important at small scales [58,59] and measurement error.
Small-scale variability of this magnitude has been reported in other benthic faunal studies [60–64]. Chapman et al. (2010) [63] examined intertidal macrofauna and microalgae and found that samples 50 cm apart were highly variable and no larger amount of variation was added at scales between 2 and 400 m. They concluded that large-scale processes were less important than small-scale environmental variation in structuring benthic biota. Fraschetti et al. (2005) [60] sampled the rocky intertidal fauna along the Apulian coast of Italy and Greece and concluded that the largest variation was at meter spatial scales relative to 10s to 100s of kilometers. Johnson et al. (2007) [61] determined that > 90% of the variability in salt marsh annelids occurred at < 50m. In their study of soft sediment macrofauna in the Baltic Sea, Kraufvelin et al. (2011) [64] observed most variability at the smallest sampled level (10 m). Sampling infauna off coastal New Jersey at multiple spatial scales, Ramey et al. (2009) [62] found more variability between troughs and crests of sand ripples < 1 m apart than similar features 2 m to 4 km apart. In the current study, large-scale habitat differences in the faunal assemblages were evident. It is striking, therefore, that small-scale variation is still such a dominant characteristic.
A common feature of these benthic studies is the use of a hierarchical nested sampling design and analysis of resulting data by nested ANOVA. This has been a dominant experimental design and analysis approach in marine studies of spatial patterning (see citations in Fraschetti et al. 2005 [60]), especially in the intertidal. It is a powerful technique, one that has led to significant understanding of the relative importance of biotic and physical processes at different scales (e.g., [1,64–67]. It requires a priori knowledge of the important spatial scales of variability [68–70] a feature not known for the sites in the current study. It has been shown, for example, that regions derived from backscatter data do not necessarily correspond to distinct faunal assemblages [24,25,71].
It should also be noted that other methods have been developed and successfully applied to examine spatial patterning. Two in particular, spectral analysis [70,72] and Moran’s eigenvector maps [14,52,73] are particularly appropriate for detecting spatial patterns, characterizing them, identifying the characteristic scales if they exist, and relating biotic-abiotic variables by linking them through a spatial structure analysis. The current study had a more limited scope of determining whether a set of commonly collected set of environmental variables accounted for the spatial patterns in the fauna assemblages. Multiscale ordination was well suited to addressing this question.
The combination of commonly used in situ and sonar-derived province variables in the RDA regressions consistently accounted for the spatial structure in all of the data sets. The evidence supporting this result is very strong in the variogram analysis where the fitted variogram paralleled the empirical variogram, the residuals at large spatial scales exhibited no trend, and there was no suggestion that the biotic-environmental relationship changed with spatial scale. This outcome held across all six infaunal data sets from markedly different environments ranging from freshwater to near marine conditions. Of the explanatory variables considered, categorical acoustic province variables were dominant in the analyses and accounted for 51–80% of the fitted community variance. This suggests that acoustic provinces were good proxies for habitat in all six of the data sets, a result not wholly expected given the evidence of weak biotic associations with acoustic features found in other studies [23–26]. Strayer et al. (2006) [37] has suggested that large, seascape-scale predictors may function to integrate the dominant controlling processes. The importance of these categorical variables at the six locations examined in this study suggests that benthic infaunal community structure is patchy on a seascape scale, in contrast to a more continuous gradational structure. Additionally, since the scaled range estimated from the data was only 14–26% of the maximum extent of the study areas (Table 6), the surveys were well suited to detect community structure differences driven by large-scale environmental changes.
Assuming that the substantial small-scale variability, as measured by the nugget estimates obtained from the fitted empirical variograms, represents faunal variability below the resolution of the sampling surveys, subtracting it from the residual variance provides a more honest way to assess RDA performance. After doing so, RDA accounted for greater than 71% of the faunal variance remaining (Fig 6). The variance explained was much higher for Robins Island (79%), and probably even greater for the two Kingston-Saugerties data sets. There, estimated small-scale variation exceeded the residual from RDA, resulting in a negative variance. As with any regression analysis, estimates from fitting an empirical variogram and a nonspatial RDA both have uncertainty. Errors in the RDA residual can be assessed by a cross-validation method [74], but unfortunately errors in parameter estimates in fitting empirical variograms have not been evaluated [47]. Perhaps not coincidently, both Kingston-Saugerties data sets had the largest relative nugget estimates, both exceeding 50% of the total faunal variation, and largest absolute standard errors of γ(h) as evidenced by the confidence intervals in Fig 5. These two data sets also had the least regular transition from within to between province sample pair comparisons with distance (Fig 3). Both the precision and shape of an empirical variogram is known to vary with the configuration of sampling locations [68,69,75], and these factors could certainly have played a role in the nugget effect estimates [76]. In any event, estimates of explained variance at all sites are substantially above an amount that would be considered acceptable in a multivariate study of biotic-environmental relationships.
Extending this small-scale nugget adjustment to comparisons of sample pairs laying within and between provinces (Fig 6) provides some useful insights on the effectiveness of RDA results at local and seascape scales. In comparing pairs of samples from different provinces, RDA accounted for >73% of the remaining faunal variation after nugget adjustment. This again verifies the effectiveness of acoustic provinces as relevant seascape scale explanatory variables. The outcome was more mixed for pairs of samples occurring within the same province. After subtracting the nugget effect, the RDA explained high fractions of the remaining faunal variance (74–84%) for the two Kingston-Saugerties data sets, but it explained relatively low faunal variance at the Haverstraw (33%), Tappan Zee (24%), Robins Island (42%), and Shelter Island (23%) sites.
One potential explanation for the weak within-province results at Haverstraw, Tappan Zee, Robins Island, and Shelter Island is that the fauna were responding to a patchy rather than gradational environmental driver that would have been detected in the residual variogram. If that were the case, one possible avenue of analysis would be to take advantage of the more complete coverage that sonar provides to generate potentially useful explanatory variables. Neighborhood statistics for high-resolution bathymetry and backscatter data are readily available in GIS and specialized sonar processing software such as Fledermaus (Quality Positioning Services, Portsmouth, NH, USA). These applications can estimate a variety of derived, integrated variables such as grey-level co-occurrence measures [77], angular range analysis measures [78], rugosity [79], exposure to wave action and subtidal currents (e.g., aspect and bathymetric position index (BPI)), and vulnerability to sedimentation (slope, BPI). Adjusting the radius surrounding sampling locations when calculating neighborhood statistics is one way to alter the scale of the derived measures. Given the study results to date, this exploration clearly should be focused on assessing within-province rather than between-province variation in community structure.
Accepting the evidence that the study locations are patchy at a seascape-scale defined by the acoustic provinces, the empirical variogram for each site (Fig 3) should be regarded as a complex composite formed from multiple within and between habitat spatial relationships. It is possible that community assemblages within each province have unique and perhaps quite different spatial structures leading to differences in variogram shape, nugget, sill, and range characteristics. In the current study, four of the six variograms appear well behaved with a simple, smooth shape trending to a sill, suggesting that the spatial patterns of the fauna across provinces are similar. The variograms from the Kingston-Saugerties data sets are the exceptions, where the spatial relationships forming the composite variogram seem more complex. The two variograms are similar in shape with pronounced maxima. Sampling locations were repeated in the two seasonal studies at this site, allowing the possibility that the pattern includes an interplay between the actual sample and/or habitat configuration. While some methods exist for estimating variances when combining heterogeneous strata with differing spatial characteristics for univariate data [80] and for combining multiple independent spatial processes within a single region for multivariate data [76], no general method exists for predicting the effects on variance of complex combinations of study area shapes, extents, and sampling intervals [4].
Decomposing a large-scale variogram containing multiple habitats could be approached by a sampling study with a large enough sampling effort to generate empirical variograms for each bottom type. The variogram criteria used in present study required a minimum of 10 distance classes with 30 pairs of samples within each class [47]. Ten distance classes were selected to ensure variance estimates at enough spatial scales to fit a variogram model but not too many to make the Bonferroni-adjusted tests examining RDA results too conservative. Meeting these criteria would require a minimum of 35 sampling locations within each acoustic province to examine within habitat spatial structure. This level of sampling would be substantially greater than the 5–10 samples per province in the present study, and it may be difficult to achieve in practical terms. Sampling density at the sites in the current study ranged from 1.7 to 18 samples per km2 and collection and processing effort for each survey required 9 to 18 months. The high cost of sampling is one reason that in situ sampling tends to be sparse in many studies [17,22]. Consistent with ecological interpretations of hierarchy theory [6–8,27,28] biotic interactions would tend to become increasingly dominant at smaller spatial scales, so a study at substantially increased sampling density would have to shift emphasis at least in part to assessing biotic processes in addition to measuring small-scale environmental variation. This might begin, therefore, to provide an insight into why the nugget was such a large fraction of the total variance.
None of the six surveys, consisting of 45–100 benthic samples collected across 4–7 habitats in moderate sized areas (3.3 to 16.5 km2), suffered from the problem of scale arbitrariness [1]. Spatial structure in the infaunal community was effectively explained by commonly collected environmental variables, and therefore, biotic-environmental inferences were not compromised by the presence of spatial structure in the data. On the other hand, a large fraction of community variation (36–59%) was below the resolution of the surveys and within-province variation was only moderately explained in four of the six data sets. Both these results highlight further challenges to understanding heterogeneity in benthic communities.
Acknowledgments
The authors wish to acknowledge David Strayer (Cary Institute of Ecosystem Studies), Frank Nitsche (Lamont-Doherty Earth Observatory of Columbia University), and Robin Bell (Lamont-Doherty Earth Observatory of Columbia University) for contributing to the data sets used in this study, and thank David Strayer for taking the time to review this manuscript and for providing helpful comments and revisions. We would also like to thank Matthew Pawley and three other anonymous reviewers for their constructive comments, which largely improved this manuscript.
References
- 1. Wiens JA. Spatial scaling in ecology. Funct Ecol. 1989; 3: 385–397.
- 2. van de Koppel J, Kumar L, van Langevelde F, Prins HHT. The ecology of scale. Ecol Modell. 2002; 149: 1–4.
- 3. Kinlan BP, Gaines SD. Propagule dispersal in marine and terrestrial environments: a community perspective. Ecology 2003; 84: 2007–2020.
- 4. Dungan JL, Perry JN, Dale MRT, Legendre P, Citron-Pousty S, Fortin MJ et al. A balanced view of scale in spatial statistical analysis. Ecography. 2002; 25: 626–640.
- 5. Clarke RK, Somerfield PJ, Airoldi L, Warwick RM. Exploring interactions by second-stage community analyses. J Exp Mar Bio Ecol. 2006; 338(2006): 179–192.
- 6.
Allen TFH, Starr TB. Hierarchy: Perspectives for Ecological Complexity. Chicago: University of Chicago Press; 1982.
- 7. Legendre P. Spatial autocorrelation: Trouble or new paradigm? Ecology. 1993; 74(6): 1659–1673.
- 8.
Auster PJ, Heinonen KB, Witharana C, McKee M. A habitat classification scheme for the Long Island Sound region. 2009 June [cited 15 June 2017]. In: Long Island Sound Study Technical Report [Internet]. Stamford: EPA Long Island Sound Office. [83 pp]. Available from: http://longislandsoundstudy.net/wp-content/uploads/2010/02/Auster-et-al_EPA-Final-Technical-Report_Habitat-Classification_June-09.pdf
- 9. Wu J, Loucks OL. From balance of nature to hierarchical patch dynamics: A paradigm shift in ecology. Q Rev Biol. 1995; 70: 439–466.
- 10.
Cowardin LM, Carter V, Golet FC, LaRoe ET. Classification of wetlands and deepwater habitats of the United States. 1979 December [cited 15 June 2017]. In: U.S. Fish and Wildlife Service FWS/OBS-79/31 [Internet]. [142 pp.]. Available from: https://www.fws.gov/wetlands/Documents/Classification-of-Wetlands-and-Deepwater-Habitats-of-the-United-States.pdf
- 11. Greene HG, Yoklavich MM, Starr RM, O’Connell VM, Wakefield WW, Sullivan DE et al. A classification scheme for deep seafloor habitats. Oceanologica Acta. 1999; 22: 663–678.
- 12.
Davies CE, Moss D, Hill MO. EUNIS Habitat Classification. 2004 October [cited 30 November 2017]. In: European Environment Agency European Topic Centre on Nature Protection and Biodiversity Report [Internet]. [310 pp.]. Available from: http://www.emodnet-seabedhabitats.eu/PDF/GMHM1%20EUNIS_Habitat_Classification_Revised_2004.pdf
- 13.
[FGDC]. Federal Geographic Data Committee. Coastal and Marine Ecological Classification Standard (CMECS). 2012 [cited 15 June 2017]. Available from: http://www.csc.noaa.gov/digitalcoast/_/pdf/CMECS_Versionpercent20_4_Final_for_FGDC.pdf
- 14.
Legendre P, Legendre L. Numerical Ecology, 3rd ed. Amsterdam: Elsevier; 2012.
- 15. Thrush SF, Hewitt JE, Herman PMJ, Ysebaert. Multi-scale analysis of species-environment relationship. Mar Ecol Prog Ser. 2005; 302: 13–26.
- 16. Garza C. Relating spatial scale to patterns of polychaete species in coastal estuaries of western United States. Landsc Ecol. 2008; 23: 107–121.
- 17. Verfaillie E, Degraer S, Schelfaut K, Willems W, Van Lancker V. A protocol for classifying ecologically relevant marine zones, a statistical approach. Estuar Coast Shelf Sci. 2009; 83: 175–185.
- 18. Wheatley M, Johnson C. Factors limiting out understanding of ecological scale. Ecological Complexity. 2009; 6: 150–159.
- 19. Shumchenia EJ, King JW. Comparison of methods for integrating biological and physical data for marine habitat mapping and classification. Cont Shelf Res. 2010; 30(2010): 1717–1729.
- 20. Diaz RJ, Solan M, Valente RM. A review of approaches for classifying benthic habitats and evaluating habitat quality. J Environ Manage. 2004; 73: 164–181.
- 21. Kostylev VE, Todd BJ, Gordon BJF, Courtney RC, Gordon DMC, Pickrill RA. Benthic habitat mapping on the Scotian Shelf based on multibeam bathymetry, surficial geology, and sea floor photographs. Mar Ecol Prog Ser. 2001; 219: 131–137.
- 22. Brown CJ, Smith SJ, Lawton P, Anderson JT. Benthic habitat mapping: A review of progress towards improved understanding of the spatial ecology of the seafloor using acoustic techniques. Est Coast Shelf Sci. 2011; 92: 502–520.
- 23. Brown CJ, Cooper KM, Meadows WJ, Limpenny DS, Rees HL. Small-scale mapping of sea-bed assemblages in the eastern English Channel using sidescan sonar and remote sampling techniques. Est Coast Shelf Sci. 2002; 54: 263–278.
- 24. Eastwood PD, Souissi S, Rogers SI, Coggan RA, Brown CJ. Mapping seabed assemblages using comparative top-down and bottom-up classification approaches. Can J Fish Aquat Sci. 2006; 63: 1536–1548.
- 25. Brown CJ and Collier JS. Mapping benthic habitat in regions of gradational substrata: An automated approach utilizing geophysical, geological, and biological relationships. Est Coast Shelf Sci. 2008; 78: 203–214.
- 26.
Flanagan AM. Quantitative Benthic Community Models: The Relationship Between Explained Variance and Scale. Ph.D. Thesis, Stony Brook University. 2016.
- 27. Wagner HH. Spatial covariance in plant communities: Integrating ordination, geostatistics, and variance testing. Ecology. 2003; 84(4): 1045–1057.
- 28. Wagner HH. Direct multi-scale ordination with canonical correspondence analysis. Ecology. 2004; 85(2): 342–351.
- 29. Wagner HH, Fortin MJ. Spatial analysis of landscapes: Concepts and statistics. Ecology. 2005; 86: 1975–1987.
- 30. Griffith DA. Effective geographic sample size in the presence of spatial autocorrelation. Ann Am Assoc Geogr. 2005; 95: 740–760.
- 31. Jackson DR, Briggs KB. High-frequency bottom backscattering: roughness vs. sediment volume scattering. J Acoust Soc Am. 1992; 92: 962–977.
- 32. Borgeld JC, Hughes Clark JE, Goff JA, Mayer JA, Curtis LA. Acoustic backscatter of the 1995 flood deposit on the Eel shelf. Mar Geol. 1999; 154: 197–210.
- 33. Urgeles R, Locat J, Schmitt T, Hughes Clarke JE. The July 1996 flood deposit in the Sanguenay Fjord, Quebec, Canada: implications for sources of spatial and temporal backscatter variation. Mar Geol. 2002; 1884: 41–60.
- 34. Nitsche FO, Bell RE, Carbotte SM, Ryan WBF, Flood RD. Process related classification of acoustic data from the Hudson River Estuary. Mar Geol. 2004; 209: 131–145.
- 35.
Nitsche FO, Carbotte SM, Ryan WBF, Bell RE. A seabed classification approach based on multiple acoustic sensors in the Hudson River Estuary. In: Fitzgerald DM and Knight J (Eds), High-Resolution Morphodynamics and Sedimentary Evolution of Estuaries, Coastal Systems and Continental margins. Springer, Netherlands, pp. 33–35. 2005.
- 36.
Bell RE, Flood RD, Carbotte SM, Ryan WBF, McHugh C, Cormier M, Versteeg R, Chayes D, Bokuniewicz H, Ferrini. Hudson River Estuary Program Benthic Mapping Project Revised Final Report. Submitted to the New York State Department of Environmental Conservation. Lamont-Doherty Earth Observatory. 2000.
- 37. Strayer DL, Malcom HM, Bell RE, Carbotte SM, Nitsche FO. Using geophysical information to define benthic habitats in a large river. Freshw Biol. 2006; 51: 25–38.
- 38.
Cerrato RM, Flanagan AM, Flood RD. Haverstraw Bay Benthic Habitat Characterization. 2015 [cited 15 June 2017]. In: Marine Sciences Research Center Special Report No. 141 [Internet]. Stony Brook. [53pp]. Available from: http://commons.library.stonybrook.edu/somas_articles/
- 39.
Cerrato RM and Maher NP. Benthic Mapping for Habitat Classification in the Peconic Estuary: Phase I Ground Truth Studies. 2004 [cited 15 June 2017]. In: Marine Sciences Research Center Special Report No. 134 [Internet]. Stony Brook. [276 pp]. Available from: http://commons.library.stonybrook.edu/somas_articles/
- 40.
Folk RL. Petrology of Sedimentary Rock, Austin: Hemphill Publishing Company; 1974.
- 41.
Gee GW, Bauder JW. Particle size analysis. In: Klute A, editor. Methods of Soil Analysis. Part 1. Physical and Mineralogical Methods. Madison: American Society of Agronomy; 1986. pp. 383–411.
- 42. Legendre P and Gallagher ED. Ecologically meaningful transformations for ordination of species data. Oecologia. 2001; 129: 271–280. pmid:28547606
- 43. Bachmaier M and Backes M. Variogram or semivariogram? Understanding the variances in a variogram. Precision Agriculture. 2008; 9: 173–175.
- 44. Dray S. A new perspective about Moran’s coefficient: Spatial autocorrelation as a linear regression problem. Geogr Anal. 2011; 43: 127–141.
- 45. Saul SE, Walter JF III, Die DJ, Naar DF, Donahue BT. Modelling the spatial distribution of commercially important reef fishes on the West Florida Shelf. Fish Res. 2013; 143: 12–20.
- 46. Boldina I, Beninger PG, Le Coz M. Effect of long-term mechanical perturbation on intertidal soft-bottom meiofaunal community spatial structure. J Sea Res. 2014; 85: 85–91.
- 47.
Cressie NAC. Statistics for Spatial Data. New York: John Wiley and Sons; 1993.
- 48.
Zimmerman DL and Stein M. Classical Geostatistical Methods. Chapter 3. Handbook of Spatial Statistics. (Gelfand AE, Diggle PJ, Fuentes M., and Guttorp P., eds), pp. 29–44. CRC Press, Taylor and Francis Group, Boca Raton, Fl; 2010.
- 49.
Journal AG, Huijbregts CJ. Mining Geostatistics. New York: Academic Press; 1978.
- 50.
Akaike H. 1973. Information theory and an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory (B. N. Petrov and F. Cztiki, eds), Budapest: Akademiai Kiado; 1973. pp. 267–281.
- 51. Banks HT, Joyner ML. AIC under the framework of least squares estimation. Appl Math Lett. 2017; 74:33–45.
- 52.
Borcard D, Gillet F, Legendre P. Numerical Ecology with R. New York: Springer; 2011.
- 53.
Jongman RHG, ter Braak CJF, Van Tongeren OFR. Data analysis in community and Landsc Ecol. New York: Cambridge University Press; 1995.
- 54.
Burnham KP and Anderson DR. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. New York: Springer; 2002.
- 55. De’ath G. Multivariate regression trees: a new technique for modelling species-environment relationships. Ecology. 2002; 83(4):1105–1117.
- 56. Mantel N. The detection of disease clustering and a generalized regression approach. Cancer Res. 1967; 27: 209–220. pmid:6018555
- 57. Pineda J, Porri F, Starczak V, Blythe J. Causes of decoupling between larval supply and settlement and consequences for understanding recruitment and population connectivity. J Exp Mar Bio Ecol. 2010; 392: 9–21.
- 58. Fleeger JW, Yund PO, Sun B. Active and passive processes associated with initial settlement and post-settlement dispersal of suspended meiobenthic copepods. J Mar Res. 1995; 53: 609–645.
- 59. Rossi F, Underwood AJ. Small-scale disturbance and increased nutrients as influences on intertidal macrobenthic assemblages: experimental burial of wrack in different intertidal environments. Mar Ecol Prog Ser. 2002; 241:29–39.
- 60. Fraschetti S, Terlizzi A, Benedetti-Cecchi L. Patterns of distribution of marine assemblages from rocky shores: Evidence of relevant scales of variation. Mar Ecol Prog Ser. 2005; 296:13–29.
- 61. Johnson DS, Fleeger JW, Galvan KA, Moser EB. Worm holes and their space-time continuum: Spatial and temporal variability of macroinfaunal annelids in a Northern New England salt marsh. Estuaries Coast. 2007; 30: 226–237.
- 62. Ramey PA, Grassle JP, Grassle JF, Petrecca RF. Small-scale, patchy distributions of infauna in hydrodynamically mobile continental shelf sands: Do ripple crests and troughs support different communities? Cont Shelf Res. 2009; 29: 2222–2233.
- 63. Chapman MG, Tolhurst TJ, Murphy RJ, Underwood AJ. Complex and inconsistent patterns of variation in benthos, micro-algae and sediment over multiple spatial scales. Mar Ecol Prog Ser. 2010; 398: 33–47.
- 64. Kraufvelin P, Perus J, Bonsdorff E. Scale-dependent distribution of soft-bottom infauna and possible structuring forces in low diversity systems. Mar Ecol Prog Ser. 2011; 426: 13–28.
- 65. Underwood A. J., and Chapman M. G. Scales of spatial patterns of distribution of intertidal snails. Oecologia. 1996; 107: 212–224. pmid:28307307
- 66. Benedetti-Cecchi L, Bulleri F, Cinelli F. The interplay of physical and biological factors in maintaining midshore and low-shore assemblages on rocky coasts in the north-west Mediterranean. Oecologia. 2000; 123: 406–417 pmid:28308596
- 67. O’Leary JK, Potts DC. Using hierarchical sampling to understand scales of spatial variation in early coral recruitment. Coral Reefs. 2011. 30: 1013–1023.
- 68. Cole RG. Staggered nested designs to identify hierarchical scales of variability. N. Z. J. Mar. Freshwater Res. 2001a; 35: 891–896.
- 69. Cole RG, Healy TR, Wood ML, Foster DM. Statistical analysis of spatial pattern: a comparison of grid and hierarchical sampling approaches. Environ Monit Assess. 2001b; 69: 85–99. pmid:11393546
- 70. Denny MW, Helmuth B, Leonard GH, Harley CDG, Hunt LJH, Nelson EK. Quantifying scale in ecology: Lessons from a wave-swept shore. Ecol Monogr. 2004; 74: 513–532.
- 71. McGonigle C, Brown C, Quinn R, Grabowski J. Evaluation of image-based multibeam sonar backscatter classification for benthic habitat discrimination and mapping at Stanton Banks, UK. Estuar Coast Shelf Sci. 2009; 81: 423–437.
- 72. Tamburello L, Bulleri F, Bertocci I, Maggi E, Benedetti-Cecchi L. Reddened seascapes: experimentally induced shifts in 1/f spectra of spatial variability in rocky intertidal assemblages. Ecology. 2013; 94: 1102–1111. pmid:23858650
- 73. Dray S, Legendre P, Peres-Neto PR. Spatial modelling: a comprehensive framework for principle coordinate analysis of neighbor matrices (PCNM). Ecol Modell 2006; 106: 483–493.
- 74. Flanagan AM, Cerrato RM. An approach for quantifying the efficacy of ecological classification schemes as management tools. Cont Shelf Res. 2015; 109(2015): 55–66.
- 75. Schlup BM, Wagner HH. Effects of study design and analysis on the spatial community structure detected by multiscale ordination. J Veg Sci. 2008; 19(5): 621–632.
- 76.
Wackernagel H. Multivariate Geostatistics. Berlin: Springer-Verlag; 1995.
- 77. Haralick RM, Shanmugam K, Dinstein I. Textural Features for Image Classification. IEEE Trans Syst Man Cybern Syst. 1973; 3(6): 610–621.
- 78. Fonseca L, Mayer L. Remote estimation of surficial seafloor properties through the application Angular Range Analysis to multibeam sonar data. Mar Geo Res. 2007; 28: 119–126.
- 79. Jenness JS. Calculating landscape surface area from digital elevation models. Wildl Soc Bull. 2004; 32: 829–839.
- 80. Domburg P, de Gruijter JJ, Brus DJ. A structured approach to designing soil survey schemes with prediction of sampling error from variograms. Geoderma. 1994; 62: 151–164.