Spatial sampling on streams: principles for inference on aquatic networks

For ecological and environmental data, prior inquiries into spatial sampling designs have considered two-dimensional domains and have shown that design optimality depends on the characteristics of the target spatial domain and intended inference. The structure and water-driven continuity of streams prompted the development of spatial autocovariance models for stream networks. The unique properties of stream networks, and their spatial processes, warrant evaluation of sampling design characteristics in comparison with their two-dimensional counterparts. Common inference scenarios in stream networks include spatial prediction, estimation of fixed effects parameters, and estimation of autocovariance parameters, with prediction and fixed effects estimation most commonly coupled with autocovariance parameter estimation. We consider these inference scenarios under a suite of network characteristics and stream-network spatial processes. Our results demonstrate, for parameter estimation and prediction, the importance of collecting samples from specific network locations. Additionally, our results mirror aspects from the prior two-dimensional sampling design inquiries, namely, the importance of collecting some samples within clusters when autocovariance parameter estimation is required. These results can be applied to help refine sample site selection for future studies and further showcase that understanding the characteristics of the targeted spatial domain is essential for sampling design planning. Published 2014. This article has been contributed to by US Government employees and their work is in the public domain in the USA.

[1]  Kathryn M. Irvine,et al.  Spatial designs and properties of spatial correlation: Effects on covariance estimation , 2007 .

[2]  F. Schönhofer.  Monitoring and Assessment , 1991 .

[3]  Dale L. Zimmerman,et al.  Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction , 2006 .

[4]  Noel A Cressie,et al.  Statistics for Spatio-Temporal Data , 2011 .

[5]  Eric Archer,et al.  Quantifying the Extent of and Factors Associated with the Temporal Variability of Physical Stream Habitat in Headwater Streams in the Interior Columbia River Basin , 2011 .

[6]  R. N. Kackar,et al.  Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models , 1984 .

[7]  R. O. Strobl,et al.  A Water Quality Monitoring Network Design Methodology for the Selection of Critical Sampling Points: Part I , 2006, Environmental monitoring and assessment.

[8]  Lisa M. Ganio,et al.  A geostatistical approach for describing spatial pattern in stream networks , 2005 .

[9]  Erin E. Peterson,et al.  A Moving Average Approach for Spatial Statistical Models of Stream Networks , 2010 .

[10]  Carol A. Gotway,et al.  Statistical Methods for Spatial Data Analysis , 2004 .

[11]  W. Fagan.  CONNECTIVITY, FRAGMENTATION, AND EXTINCTION RISK IN DENDRITIC METAPOPULATIONS , 2002 .

[12]  Don L. Stevens,et al.  Sample design, execution, and analysis for wetland assessment , 2009, Wetlands.

[13]  Lee Benda.  Confluence Environments at the Scale of River Networks , 2008 .

[14]  Nancy B. Grimm,et al.  SPATIAL HETEROGENEITY OF STREAM WATER NUTRIENT CONCENTRATIONS OVER SUCCESSIONAL TIME , 1999 .

[15]  Jacques Labonne,et al.  Linking dendritic network structures to population demogenetics: The downside of connectivity , 2008 .

[16]  Y. Rubin,et al.  Bayesian geostatistical design: Task‐driven optimal site investigation when the geostatistical model is uncertain , 2010 .

[17]  Alan E. Gelfand,et al.  Approximately optimal spatial design approaches for environmental health data , 2006 .

[18]  M. Stein,et al.  Spatial sampling design for prediction with estimated parameters , 2006 .

[19]  Jay M. Ver Hoef,et al.  SSN: An R package for spatial statistical modeling on stream networks , 2014 .

[20]  Reza Kerachian,et al.  Revising river water quality monitoring networks using discrete entropy theory: the Jajrood River experience , 2011, Environmental monitoring and assessment.

[21]  James V. Zidek,et al.  Statistical Analysis of Environmental Space-Time Processes , 2006 .

[22]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[23]  J. Hoef,et al.  Spatial statistical models that use flow and stream distance , 2006, Environmental and Ecological Statistics.

[24]  Don L. Stevens,et al.  Spatial properties of design-based versus model-based approaches to environmental sampling , 2006 .

[25]  Werner G. Müller,et al.  A comparison of spatial design methods for correlated observations , 2005 .

[26]  Steven G. Paulsen,et al.  Designing a Spatially Balanced, Randomized Site Selection Process for Regional Stream Surveys: The EMAP Mid-Atlantic Pilot Study , 2000 .

[27]  Milan Stehlík,et al.  Compound optimal spatial designs , 2009 .

[28]  Zhengyuan Zhu,et al.  Spatial sampling design under the infill asymptotic framework , 2006 .

[29]  Walter G. Whitford,et al.  Monitoring and Assessment , 2020, Ecology of Desert Systems.

[30]  N. Cressie,et al.  Mean squared prediction error in the spatial linear model with estimated covariance parameters , 1992 .

[31]  Gascuel-Odouxa,et al.  Variability of variograms and spatial estimates due to soil sampling : a case study , 2002 .

[32]  A. Olsen,et al.  Spatially Balanced Sampling of Natural Resources , 2004 .

[33]  Jay M. Ver Hoef,et al.  Spatial modelling and prediction on river networks: up model, down model or hybrid? , 2009 .

[34]  Cédric Gaucherel,et al.  Momocs: Outline Analysis Using R , 2014 .

[35]  J. Kiefer.  ON THE NONRANDOMIZED OPTIMALITY AND RANDOMIZED NONOPTIMALITY OF SYMMETRICAL DESIGNS , 1958 .

[36]  N. Cressie,et al.  Spatial prediction on a river network , 2006 .

[37]  Zhengyuan Zhu,et al.  Spatial sampling design for parameter estimation of the covariance function , 2005 .

[38]  R. L. Shreve.  Infinite Topologically Random Channel Networks , 1967, The Journal of Geology.

[39]  Steven G. Gilmour,et al.  Optimum design of experiments for statistical inference , 2012 .

[40]  Daniel R. Miller,et al.  The Network Dynamics Hypothesis: How Channel Networks Structure Riverine Habitats , 2004 .

[41]  J. Stanford,et al.  An Ecosystem Perspective of Alluvial Rivers: Connectivity and the Hyporheic Corridor , 1993, Journal of the North American Benthological Society.

[42]  Kalliopi Mylona,et al.  Optimum design of experiments for statistical inference : discussion , 2012 .

[43]  Marie-Josée Fortin,et al.  Modelling dendritic ecological networks in space: an integrated network perspective. , 2013, Ecology letters.

[44]  Jay M. Ver Hoef,et al.  Sampling and geostatistics for spatial data , 2002 .

[45]  Daniel R. Jeske,et al.  Mean Squared Error of Estimation or Prediction under a General Linear Model , 1992 .