Final Paper

Introduction, rational and goals:

The phrase, "this is the space age", now applies to a much broader range of disciplines than Astronomy. Spatial analysis of ecological data is rapidly expanding through the adoption of a landscape perspective and readily available spatial analysis packages in GIS programs. Point pattern analyses, interpolation, trend surface analysis, and spatial regression are common techniques in terrestrially based spatial analysis, but a review of the literature finds few of these approaches used in the spatial analysis of river ecosystems. Instead, spatial analysis of river assemblages has focused on multivariate analyses that may not directly include the spatial arrangement of sites in analysis.

This paper evolved from an exploration of why traditional spatial analyses have not been used in river ecology when rivers are as much a "landscape" as any terrestrial ecosystem (Weins 2002). The goal of this paper is to explore the use of spatial analysis to assess the variability of riverine assemblages. Since explicit spatial analysis is rare in river systems, this is more of a synthesis/idea paper than a formal literature review. This paper is structured in three main sections…

2. A detailed description of the process of using spatial analyses, specifically Moran’s I and semivariograms, to address spatial autocorrelation in river assemblages, and
3. A brief discussion of the use of Mantel’s test to decompose the variance of riverine assemblages including a review of findings from several studies which used this technique in their analysis of fish assemblages.

A river is a network ecosystem. A network can be defined as "a set of links connected at nodes which form a framework through which resources can flow" (Djokie & Maidment 1993). In a river system the "links" are river segments and the "nodes" are confluences (Figure 1). Rivers also have directionality to their flow, and generally predictable physical, biological, and chemical structure based on position in the network. In river networks this directionality is characterized by many sources, the beginnings of headwater tributaries, but only one sink, the mouth of the river (Figure 1). Because of their linear structure, rivers do not exist everywhere in the two-dimensional landscape. Unlike terrestrial systems they are linearly confined and samples are representations of a continuos system. Despite their confined structure, it is well established that many influences on stream assemblages (e.g. catchment land cover/use, geology, topography etc) do operate in the full two-dimensional landscape.

The degree of connectivity within a river is different than in terrestrial ecosystems because so much of what occurs in a river is linked to water flow. On land, there is little consistency to the directionality of connectivity, except in wind-borne organisms or materials. In contrast, river ecology has a long history of not only acknowledging the longitudinal connectivity of river systems, but also including it as a framework for theoretical models of their functioning and structure. Historical approaches to river ecology include the River Continuum Concept that emphasizes the longitudinal linkage of ecosystem process through the downstream flow of water and materials (Vannote et al. 1980) and the serial discontinuity concept that recognizes the zonal structure along a river (Ward and Stanford 1983). Despite the differences in these approaches, both recognize water’s ability to enhance the longitudinal connectivity of river ecosystems through its downstream flow. As in terrestrial systems, though, human activities often decrease the connectivity of river ecosystems through dams, culverts, and channel alteration.

The longitudinal structure and directionality of rivers provide challenges in implementing traditional spatial analysis. Rivers, by nature, are non-stationary and anisotropic thus violating the assumptions of many traditional spatial analysis techniques. Stationarity assumes that the mean and variance of random variables are constant over the region of study. This is rarely the case in river networks. For example, fish species richness is inversely related to water temperature, with diversity being lowest in extremely cold streams and highest in warm water. However, most rivers begin as small, cold water tributaries and as they increases in size (i.e. move downstream in the network) they gradually become warmer. Thus, the expected number of fish species depends on the spatial location within the river system. Similarly, river ecosystems are gradients with clear headwater to mouth directionality, thus the assumption of isotropy, that the pattern is similar in all directions, is clearly violated.

Spatial Autocorrelation: Application in a riverine ecosystem

Ecologists are increasingly calling for the quantification of spatial dependence in all types of ecological study (Koenig 1999, Legendre 1993). Positive spatial autocorrelation, loosely defined as "the property of random variables taking values at a certain distance apart that are more similar than expected for randomly associated pairs of observations" (Legendre 1993) is likely common in river systems but poorly studied and understood. Fundamental questions of assemblage variability, such as ones listed here have not been sufficiently studied in river ecosystems.

1. Does the variability of assemblages with distance differ with differing location on the river network? It has been hypothesized that in headwaters, where environmental gradients are steep, the biological assemblages may vary more with distance than in main stem reaches where physical conditions are more homogeneous. I.e. does the variogram representing the relationship between assemblage similarity and distance vary with general location in the network?
2. The factors causing spatial autocorrelation of river assemblages have received minimal attention. How much of the spatial autocorrelation is due to environmental gradients/changes, and dispersal vs. non-dispersal movement of organisms? What is the relative importance of these causes?
3. Does the degree and scale of spatial autocorrelation in river ecosystems vary with the taxa studied (e.g. fish vs. invertebrates vs. periphyton)?

I begin by clarifying the components that we need for the final stage of analysis, calculation of Moran’s I and construction of semivariograms, and then discuss the specific development of those components for river systems. Both techniques require some univariate measure of the assemblage at each site. Typical univariate measures of assemblages include species diversity measures, Hilsenhoff Biotic index scores for invertebrates (Hilsenhoff 1988) and Index of Biotic Integrity scores for fishes (Karr 1986). An alternative is to limit analysis to one particular species of particular interest. Global and local measures of Moran’s I are common measures of spatial autocorrelation and require an adjacency matrix that defines whether two observations are neighbors or not. Structure functions, such as variograms, allow us to quantify spatial dependency and partition it along various distance classes. Therefore an appropriate measure of distance is necessary for their construction. Once the adjacency and distance matrices are established, calculations of Moran’s I and construction of variograms should mirror those in terrestrial spatial analysis

The first step in any analysis is to ask whether the non-stationarity and anisotropy of river ecosystems should be ignored or included in the analysis. Although important to the interpretation of distance and its relationship to the similarity in assemblages (i.e. similarities due to proximity and not similarity in habitat), I argue in rare circumstances these trends and directionality in the data may not need to be considered. For example, if a researcher’s goal is to simply document where in a river network spatial autocorrelation is highest and lowest, s/he may not be concerned about the cause of the spatial autocorrelation, just that it exists. However in general, I feel analysis would be much better if non-stationarity and anisotropy were considered. Several approaches for incorporating these in assemblage analysis exist. Non-stationarity issues, i.e. the fact that rivers are gradients and thus longitudinal position does matter, may be accounted for by building a multiple linear regression relating assemblages to the structure of the stream (physical, chemical, etc). If the regression is sufficient at explaining the large-scale global trends, traditional analysis of the spatial autocorrelation of the residuals should suffice. Additionally, this is one potential approach to isolating the causes of spatial autocorrelation in river assemblages. If trends are removed and there is no spatial autocorrelation of the residuals, it suggests that spatial autocorrelation in habitat is sufficient to explain the spatial autocorrelation in the biological assemblage. The unique approach necessary for defining neighbors and distance in river networks may help eliminate the problems associated with anisotropy or the directionality of river ecosystems.

The second step is the definitions of adjacency and distance. The definition of neighbors in rivers can be quite simple or very complex. Neighbors can simply be the sites immediately upstream or downstream or a target site, or can be defined by some distance function, i.e. sites within 100 km are neighbors. Neighbors can also be based on directionality, rationalized as an accounting for the downstream flow of water in river systems. An example might be including one upstream site as neighbor status but including two downstream sites as neighbors.

The definition of distance in rivers can be quantified two fundamentally different ways, Euclidean or "swim" distance, the shortest in-water path between two sites (Figure 2). Jager et al. (1990) argued that for alkalinity, which is dependent on local features such as geology that operate in the full two dimensions, simple Euclidean distances appear to suffice (Jager et al. 1990). However, Little et al. (1997) who used kriging to interpolate various water quality measures in an estuary found that using "swim" distance instead of Euclidean distance improved the prediction accuracy of their models by 10-30%. Although models connecting catchment features to in-stream biology are common, the predictive ability of these models are generally low (R² = 0.3 to 0.6 typically). Perhaps some of this unexplained variation is due to limits on dispersal or non-dispersal movements of the biology. For this reason, since the biological assemblage is perhaps less dependent on the catchment features in the full two-dimensions, and more on the degree of connectedness of the system, the use of "swim" distance definition could be very useful when assessing spatial autocorrelation in biological assemblages. Similarly, the use of a "swim" based distance matrix should be more important for organisms confined to the aquatic realm, such as fish, and perhaps less critical to aquatic organisms that disperse terrestrially as adults such as aquatic insects.

Two issues for river ecologists to consider when constructing the distance matrix are the scale of the distance classes and the weighting of the distance matrix. The home ranges of the two most commonly studied taxa in river ecology, fish and invertebrates, can vary widely both within and between the two groups. Thus, the concept of "adjacency" and required scaling of sampling must be considered to establish appropriate distance classes. Distances downstream and upstream in rivers may have fundamentally different roles in rivers because of the net movement of materials and organisms downstream and the resistance to upstream movements due to streamflow. Therefore, in river based distance matrices it may be appropriate to weight the downstream distance more highly than upstream distance. Although this results in an asymmetric distance matrix, calculations proceed in the same manner as with symmetric matrices.

Actually calculating distance matrices such as these is a whole other issue. Pre-packaged data analyses packages available for Arc8 that are typically used for spatial analysis, such as Geostatisitcal Analyst and Spatial Analyst, are not designed to calculate spatial autocorrelation for data on network systems, such as rivers. Despite its widespread use in the transportation sector, and the similarities to river networks such as directionality of flow, connectivity and impedances, network analysis programs have been sparsely used in water resource applications (Djokie & Maidment 1993). The extension Network Analyst available for Arc8 and the network functions in ArcInfo provide the tools necessary for construction of adjacency and distance matrices required for spatial analysis of river assemblages. The network system is established as diagramed in Figure 1 through a series of links and nodes. Defining the mouth of a river as a "sink" determines the correct flow direction through the network. The distance function allows you to calculate the distance between an "origin" and "destination" using network ("swim"), Euclidean, and Manhattan distances. The inclusion of impedances, resistance to movement, in the network can also represent barriers to dispersion in locations with dams, culverts or channel alterations (ArcInfo Doc & ArcGIS help).

Limitations of spatial analysis in river systems

Several limitations to the use of these approaches exist in river ecology including the multivariate nature of assemblages, a lack of sufficiently large data sets, questions about the appropriate scale of sampling, and lack of comprehensive analysis packages designed to complete spatial analysis on network systems. Moran’s I and variograms are designed to use only univariate data while biological assemblages by nature are multivariate. Reducing the dimensionality of assemblage data into simple univariate measures may be undesirable. Second, spatial autocorrelation techniques including calculations of Moran’s I and semivariograms require large amounts of data. Rossi (1992) suggests that a good "rule of thumb" for constructing semivariograms is a minimum of 30-50 pairs of points in each lag or distance class. Assessment of invertebrate and/or fish assemblages is generally costly and time consuming so few data sets exist that will provide the level of data required. However, several current programs are attempting to rectify that problem although most involve large geographic units (Table 1). Third, the patterns observed in spatial autocorrelation will depend on the grain and extent of sampling. Sampling units that are too large will miss much of the spatial structure present at smaller scales but sampling units that are too small will add little to our understanding of the variability of river assemblages other than sampling costs (Dixon et al. 1999). Cooper et al. (1997) suggest collecting data from river reaches of varying size or sample-unit spacing and the use of semivariograms to calculate spatial metrics for each of a nested series of reaches differing in extent or spacing of sample units. Finally, extensions for GIS software, such as Spatial Analyst and Geostatistical Analyst, need to be integrated with network analysis programs to facilitate easier spatial analysis of network systems. The use of networks for river analysis is rare, but possible (See Yang et al. 1999 and 2002 who simulate river pollution and agricultural runoff movements through a river network).

Another approach to assemblage variability assessment: The Mantel’s test

This paper would be incomplete if I did not also briefly address the Mantel’s test, (1967) another statistical approach for assessing variability in biological assemblage. Mantel’s test is a specific nonparametric technique for decomposing variation in biological assemblages. In its original form, Mantel’s test is designed to answer the question of spatial dependence, i.e. are samples that are close together compositionally similar? Mantel’s test and its variants (see Urban 2001 for a list and Smouse et al. 1986 for development) are explicitly designed to include the spatial distance between sites and may be used to decompose the variance of biological assemblages into variation caused by environmental variables, distance, and random error. The flexibility in the approach stems from its use of varying regression approaches and the use of a dissimilarity matrix for the assemblages/variables, thus permitting use of categorical, rank, interval or ratio data in analysis. These dissimilarity matrices also permit the use of multivariate assemblage data. Analyses can include only the assemblage dissimilarity matrix and a geographic distance matrix or also include an environmental dissimilarity matrix. The significance of the test is evaluated using permutation procedures (Urban 2001).

Although Mantel’s test has enjoyed frequent use in genetics studies, its use in river ecology has been limited. Recently, three studies have used Mantel’s test and other statistical techniques to assess the importance of distance and environmental effects on fish assemblage similarity. I found no studies that used Mantel’s test to assess invertebrate assemblages in rivers although such analyses were suggested by Cooper et al. (1997). Magalhães et al. (2002) found that spatial autocorrelation of fish assemblages was high at short "river" distances. Neighborhood effects (defined by distance between sites) explained about 30% of the variation in fish assemblages while environmental variables and spatial trends accounted for between 37-58% of the variation. Explanations for the low explanatory power of their models included current and historical barriers to fish dispersion. In a study of fish assemblages in the Mississippi, Matthews and Robinson (1998) found that basin connectivity (as defined by number of river nodes separating small basins within the Mississippi) predicted the similarity of fish fauna composition. In contrast, Wilkinson & Edds (2001) found that environmental factors were the primary factors organizing the fish community at the basin scale, however, they also note that biotic processes were important in maintaining community structure at nodes between tributaries and the mainstem. Partial Mantel tests also indicate that although environmental variables explained differences in species presence/absence, contagion could alternately explain variations in species abundances.

Concluding remarks

The explicit inclusion of space in river assemblage analysis is possible if we more away from traditional multivariate techniques and adopt the types of spatial analyses discussed in this paper. Mantel’s test is growing in popularity and I expect its use to continue because of its flexibility. However, it is not currently widely available. The potential usefulness of Moran’s I and variogram based spatial analysis in river ecology is high, but substantial applicatory hurdles must be overcome. First, large data sets with spatial locations must be established and analyses/sampling must occur at difference scales, especially at the catchment and smaller scales. Secondly, software designed to complete spatial analysis on network systems must be developed and made readily available. Despite these formidable hurdles, the benefits from spatial analyses of river assemblages should be sufficient to drive the rapid development of such data and programs. Spatial autocorrelation, variogram analyses, and use of the Mantel’s test can provide measures that are explicit functions of spatial scale and capture long-neglected aspects of spatial heterogeneity in river assemblages.
 
 

Literature Cited

ArcInfo Doc & ArcGIS desktop help. Available through University of Michigan ITD computer network. Accessed 12-10-02.

Cooper S. D., L. Barmuta, O. Sarnelle, K. Kratz & S. Diehl. 1997. Quantifying spatial heterogeneity in streams. Journal of the North American Benthological Society 16:174-188.

Dixon, W., G. K. Smith, & B. Chiswell. 1999. Optimized selection of river sampling sites. Water Resources 33:971-978.

Djokie, D. & D. R. Maidment. 1993. Application of GIS network routines for water flow and transport. Journal of Water Resources Planning and Management 119:229-245.

Hilsenhoff, W. L. 1988. Rapid field assessment of organic pollution with a family level biotic index. The Journal of the North American Benthological Society 7:65-68.

Jager, H. I., M. J. Sale & R. L. Schmoyer. 1990. Cokriging to assess regional stream quality in the southern Blue Ridge Province. Water Resources Research 26: 1401-1412.

Karr, J.R., K. D. Fausch, P. L. Angermeier, P. R. Yant, & I. J. Schlosser. 1986. Assessing biological integrity in running waters -- a method and its rationale. Illinois Natural History Survey Special Publication Number 5, 28 p.

Koenig, W. D. 1999. Spatial autocorrelation of ecological phenomena. Trends in Ecology and Evolution 14:22-26.

Legendre, P. 1993. Spatial autocorrelation: Trouble or new paradigm. Ecology 74:1659-1673.

Little, L.S., D. Edwards, D. E. Porter. 1997. Kriging in estuaries: as the crow flies, or as the fish swims? Journal of Experimental Marine Biology and Ecology 213: 1-11.

Mangalhães, M. F., D. C. Batalha & M. J. Collares-Pereira. 2002. Gradients in stream fish assemblages across a Mediterranean landscape: contributions of environmental factors and spatial structure. Freshwater Biology 47:1015-1031.

Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Research 27:209-220.

Matthews, W. J & H. W. Robinson. 1998. Influence of drainage connectivity, drainage area and regional species richness on fishes of the interior highlands in Arkansas. The American Midland Naturalist 139:1-19.

Rossi, R. E., D. J. Mulla, A. G. Journel, & E. H. Franz. 1992. Geostatistical tools for modeling and interpreting ecological spatial dependence. Ecological Monographs 62:277-314.

Smouse, P.E., J. C. Long, & R. R. Sokal. 1986. Multiple regression and correlation extensions of the Mantel test of matrix correspondence. Systematic Zoology 35:627-632.

Urban, D. 2001. Spatial analysis in ecology: Mantel’s test. Available online at http://www.env.duke.edu/landscape/classes/env352/mantel.pdf.

Vannote, R. L., G. W. Minshall, K. W. Cummins, J. R. Sedell & C. E. Cushings. 1980. The river continuum concept. Canadian Journal of Fisheries and Aquatic Sciences 37: 130-137.

Ward, J. V. & J. A. Stanford. 1983. The serial discontinuity concept of lotic ecosystems. In: Dynamics of Lotic Ecosystems (Editors: Fontaine and S. M. Bartell), pp. 347-356. Ann Arbor Science Publishers, Ann Arbor, MI.

Weins, J. A. 2002. Riverine landscapes: taking ecology into the water. Freshwater Biology 47:501-515.

Wilkinson, C. D. & D. R. Edds. 2001. Spatial pattern and environmental correlates of a midwestern stream fish community: Including spatial autocorrelation as a factor in community analyses. The American Midland Naturalist 146:271-289.

Yang, X., S. Amri & A. McLean. 1999. Simulating river pollution movement using GIS network analysis. Available on line at http://clio.mit.csu.edu.au/gis/ginf99_70.pdf.

 Yang, X., Q. Zhou & M. Melville. 2000. An integrated drainage network analysis system for agricultural drainage management. Part 1: the system. Agricultural Water Management 45:73-86.
 
 
 
 
 
 

Table 1: A partial list of studies with sufficient data available to complete spatial analysis.
 

Project	Lead Research Scientists/Contacts	Data Available
Muskegon River Assessment (MI)	Michael Wiley & Catherine Riseng	80+ Fish and Invertebrate sampling sites throughout the catchment including main stem sites
Michigan Rivers Inventory	Paul Seelbach & Michael Wiley	~675 of river sites representative of rivers draining the Lower Peninsula of Michigan (Michigan Department of Natural Resources Fisheries Technical Report No. 97-3, 1997)
Ohio EPA Bioassessment program	Maam Osman & Jeff DeShon (contacts)	~300-400 sampling sites throughout the state in  10-15 different study areas
AUSRIVAS (Australia)	Richard Norris	~300 to 400 sites sampled for invertebrates

 

Figure 1: Network structure of a hypothetical river.
 

Figure 2: Illustration of Euclidean vs. "Swim" distance.