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Modelling the effect of directional spatial ecological processes at different scales

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Abstract

During the last 20 years, ecologists discovered the importance of including spatial relationships in models of species distributions. Among the latest developments in modelling how species are spatially structured are eigenfunction-based spatial filtering methods such as Moran’s eigenvector maps (MEM) and principal coordinates of neighbour matrices (PCNM). Although these methods are very powerful and flexible, they are only suited to study distributions resulting from non-directional spatial processes. The asymmetric eigenvector map (AEM) framework, a new eigenfunction-based spatial filtering method, fills this theoretical gap. AEM was specifically designed to model spatial structures hypothesized to be produced by directional spatial processes. Water currents, prevailing wind on mountainsides, river networks, and glaciations at historical time scales are some of the situations where AEM can be used. This paper presents three applications of the method illustrating different combinations of: sampling schemes (regular and irregular), data types (univariate and multivariate), and spatial scales (metres, kilometres, and hundreds of kilometres). The applications include the distribution of a crustacean (Atya) in a river, bacterial production in a lake, and the distribution of the copepodite stages of a crustacean on the Atlantic oceanic shelf. In each application, a comparison is made between AEM, MEM, and PCNM. No environmental components were included in the comparisons. AEM was a strong predictor in all cases, explaining 59.8% for Atya distribution, 51.4% of the bacterial production variation, and 38.4% for the copepodite distributions. AEM outperformed MEM and PCNM in these applications, offering a powerful and more appropriate tool for spatial modelling of species distributions under directional forcing and leading to a better understanding of the processes at work in these systems.

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References

  • Blanchet FG, Legendre P, Borcard D (2008a) Forward selection of explanatory variables. Ecology 89:2623–2632

    Article  PubMed  Google Scholar 

  • Blanchet FG, Legendre P, Borcard D (2008b) Modelling directional spatial processes in ecological data. Ecol Model 215:325–336

    Article  Google Scholar 

  • Blanchet C, Maltais-Landry G, Maranger R (in press) Variability in nitrogen content of submerged aquatic vegetation: utility as an indicator of N dynamics within and among lakes. Wat Sci Tech

  • Borcard D, Legendre P (2002) All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecol Model 153:51–68

    Article  Google Scholar 

  • Borcard D, Legendre P, Drapeau P (1992) Partialling out the spatial component of ecological variation. Ecology 73:1045–1055

    Article  Google Scholar 

  • Borcard D, Legendre P, Avois-Jacquet C, Tuosimoto H (2004) Dissecting the spatial structure of ecological data at multiple scales. Ecology 85:1826–1832

    Article  Google Scholar 

  • Caraco NF, Lampman G, Cole JJ, Limburg KE, Pace ML, Fischer D (1998) Microbial assimilation of DIN in a nitrogen rich estuary: implications for food quality and isotope studies. Mar Ecol Progr Ser 167:59–71

    Article  CAS  Google Scholar 

  • Cole JJ, Caraco NF (2001) Carbon in catchments: connecting terrestrial carbon losses with aquatic metabolism. Mar Freshw Res 52:101–110

    Article  CAS  Google Scholar 

  • Cole JJ, Prairie YT, Caraco NF, McDowell WH, Tranvik LJ, Striegl RG, Duarte CM, Kortelainen P, Downing JA, Middelburg JJ, Melack J (2007) Plumbing the global carbon cycle: integrating inland waters into the terrestrial carbon budget. Ecosystems 10:172–185

    Article  Google Scholar 

  • Cressie N, Frey J, Harch B, Smith M (2006) Spatial prediction on a river network. J Agric Biol Environ Stat 11:127–150

    Article  Google Scholar 

  • del Giorgio PA, Pace ML (2008) Relative independence of dissolved organic carbon transport and processing in a large temperate river: the Hudson River as both pipe and reactor. Limnol Oceanogr 53:182–197

    Article  Google Scholar 

  • Dray S, Legendre P, Peres-Neto PR (2006) Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM). Ecol Modell 196:483–493

    Article  Google Scholar 

  • Ezekiel M (1930) Method of correlation analysis. Wiley, New York

    Google Scholar 

  • Fortin MJ, Dale MRT (2005) Spatial analysis: a guide for ecologists. Cambridge University Press, Cambridge

    Google Scholar 

  • Frenette JJ, Arts MT, Morin J, Gratton D, Martin C (2006) Hydrodynamic control of the underwater light climate in fluvial Lac Saint-Pierre. Limnol Oceanogr 51:2632–2645

    Article  Google Scholar 

  • Fryer G (1977) Studies on the functional morphology and ecology of the atyid prawns of Dominica. Philos Trans R Soc Lond B 277:57–129

    Article  CAS  Google Scholar 

  • Gittleman J, Kot M (1990) Adaptation: statistics and a null model for estimating phylogenetic effects. Syst Zool 39:227–241

    Article  Google Scholar 

  • Griffith DA, Peres-Neto PR (2006) Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses. Ecology 87:2603–2613

    Article  PubMed  Google Scholar 

  • Han G, Lu Z, Wang Z, Helbig J, Chen N, de Young B (2008) Seasonal variability of the Labrador Current and shelf circulation off Newfoundland. J Geophys Res 113:C10013. doi:10.1029/2007JC004376

    Article  Google Scholar 

  • Hopkinson CS, Giblin AE, Garrit RH, Tucker J, Hullar MAJ (1998) Influence of benthos on growth of planktonic estuarine bacteria. Aquat Microb Ecol 16:109–118

    Article  Google Scholar 

  • Hutchinson G (1957) Concluding remarks. Cold Spring Harbor Symp Quant Biol 22:415–427

    Google Scholar 

  • Legendre P (1993) Spatial autocorrelation: trouble or new paradigm. Ecology 74:1659–1673

    Article  Google Scholar 

  • Legendre P, Fortin MJ (1989) Spatial pattern and ecological analysis. Vegetatio 80:107–138

    Article  Google Scholar 

  • Legendre P, Gallagher ED (2001) Ecologically meaningful transformations for ordination of species data. Oecologia 129:271–280

    Article  Google Scholar 

  • Legendre P, Legendre L (1998) Numerical ecology, 2nd English edn. Elsevier, Amsterdam, The Netherland

    Google Scholar 

  • Loder JW, Petrie P, Gawarkiewicz G (1998) The coastal ocean off northeastern North America: a large scale view. In: Robinson AR, Brink KH (eds) The sea, Vol 11. Wiley, New York, pp 105–133

  • Maranger RJ, Pace ML, del Giorgio PA, Caraco NF, Cole JJ (2005) Longitudinal spatial patterns of bacterial production and respiration in a large River-Estuary: implications for ecosystems carbon consumption. Ecosystems 8:318–330

    Article  CAS  Google Scholar 

  • Masin M, Jezbera J, Nedoma J, Straskrabova V, Hejzlar J, Simek K (2003) Changes in bacterial community composition and microbial activities along the longitudinal axis of two canyon-shaped reservoirs with different inflow loading. Hydrobiologia 504:99–113

    Article  Google Scholar 

  • Mitchell MR, Harrison G, Pauley K, Gagné A, Maillet G, Strain P (2002) Atlantic zonal monitoring program sampling protocol. Can Tech Rep Hydrogr Ocean Sci 223: iv + 23

  • Newbold JD, O’Neill RV, Elwood JW, Van Winkle W (1982) Nutrient spiralling in streams: implications for nutrient limitation and invertebrate activity. Am Nat 120:628–652

    Article  Google Scholar 

  • Ohtani K (2000) Bootstrapping R2 and adjusted R2 in regression analysis. Econ Model 17:473–483

    Google Scholar 

  • Pepin P, Head EJH (2009) Seasonal variation in the depth-dependent state of stage 5 copepodites of Calanus finmarchicus in the waters of the Newfoundland Shelf and the Labrador Sea. Deep-Sea Res (Part I) 56:989–1002

    Article  CAS  Google Scholar 

  • Pepin P, Helbig JA (1997) The distribution and drift of cod eggs and larvae on the Northeast Newfoundland Shelf. Can J Fish Aquat Sci 54:670–685

    Article  Google Scholar 

  • Pepin P, Maillet GL, Fraser S, Shears T, Redmond G (2008) Biological and chemical oceanographic conditions on the Newfoundland Shelf during 2007. CSAS Res Doc 2008/034, 61p

  • Peres-Neto PR, Legendre P, Dray S, Borcard D (2006) Variation partitioning of species data matrices: Estimation and comparison of fractions. Ecology 87:2614–2625

    Article  PubMed  Google Scholar 

  • Peterson DL, Parker VT (1998) Ecological scale: theory and application. Columbia University Press, New York

    Google Scholar 

  • Peterson EE, ver Hoef JM (2010) A mixed-model moving-average approach to geostatistical modeling in stream networks. Ecology 91:644–651

    Article  PubMed  Google Scholar 

  • Peterson EE, Theobald DM, ver Hoef JM (2007) Geostatistical modelling on stream networks: developing valid covariance matrices based on hydrologic distance and stream flow. Freshw Biol 52:267–279

    Article  Google Scholar 

  • Planque B, Batten SD (2000) Calanus finmarchicus in the North Atlantic: the year of Calanus in the context of interdecadal change. ICES J Mar Sci 57:1528–1535

    Article  Google Scholar 

  • Pyron M, Covich AP, Black RW (1999) On the relative importance of pool morphology and woody debris to distributions of shrimp in a Puerto Rican headwater stream. Hydrobiologia 405:207–215

    Article  Google Scholar 

  • Rees GN, Beattie G, Bowen PM, Hart BT (2005) Heterotrophic bacterial production in the lower Murray River, south-eastern Australia. Mar Freshw Res 56:835–841

    Article  CAS  Google Scholar 

  • Šidák Z (1967) Rectangular confidence regions for the means of multivariate normal distributions. J Am Stat Assoc 62:626–633

    Article  Google Scholar 

  • Smith DC, Azam F (1992) A simple, economical method for measuring bacterial protein synthesis rates in seawater using 3H-leucine. Mar Microb Food Webs 6:107–114

    Google Scholar 

  • Therriault JC, Petrie B, Pepin P, Gagnon J, Gregory D, Helbig J, Herman A, Lefaivre D, Mitchell M, Pelchat B, Runge J, Sameoto D (1998) Proposal for a northwest Atlantic zonal monitoring program. Can Tech Rep Hydrogr Ocean Sci 194: vii + 57

  • ver Hoef JM, Peterson EE (2010) A moving average approach for spatial statistical models of stream networks. J Am Stat Assoc 105:6–18

    Article  CAS  Google Scholar 

  • ver Hoef JM, Peterson EE, Theobald DM (2006) Spatial statistical models that use flow and stream distance. Environ Ecol Stat 13:449–464

    Article  Google Scholar 

  • Vis C, Hudon C, Carignan R, Gagnon P (2007) Spatial analysis of production by macrophytes, phytoplankton and epiphyton in a large river system under different water-level conditions. Ecosystems 10:293–310

    Article  Google Scholar 

  • Wetzel RG (1992) Gradient-dominated ecosystems: sources and regulatory functions of dissolved organic matter in freshwater ecosystems. Hydrobiologia 229:181–198

    Article  CAS  Google Scholar 

  • Zar JH (1999) Biostatistical analysis, 4th edn. Prentice Hall, Upper Saddle River, NJ

    Google Scholar 

Download references

Acknowledgements

The work reported in this paper was supported by NSERC grant no. 7738-07 to P. Legendre. The work on Capesterre River was funded by grants from the Direction Régionale de l’Environnement de la Guadeloupe and the Parc National de la Guadeloupe to D. Monti. The work on Lake St-Pierre was funded by an NSERC Discovery and an FQRNT Strategic Professor grant to R. Maranger. The work off Newfoundland is the result of activities of the Atlantic Zone Monitoring Programme of Fisheries and Oceans Canada. The research conducted in this study is in compliance with the current laws of the country in which they were performed.

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  1. F. Guillaume Blanchet

    Present address: Department of Renewable Resources, University of Alberta, 751 General Service Building, Edmonton, AL, T6G 2H1, Canada

Authors and Affiliations

  1. Département de Sciences Biologiques, Université de Montréal, Succursale Centre-ville, C.P. 6128, Montréal, QC, H3C 3J7, Canada

    F. Guillaume Blanchet, Pierre Legendre & Roxane Maranger

  2. EA-926 DYNECAR, Laboratoire de Biologie Marine, Université des Antilles et de la Guyane, Campus de Fouillole, BP 592, 97157, Pointe-à-Pitre Cedex, Guadeloupe, French West Indies

    Dominique Monti

  3. Department of Fisheries and Oceans, P.O. Box 5667, St John’s, NL, A1C 5X1, Canada

    Pierre Pepin

Authors
  1. F. Guillaume Blanchet
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  2. Pierre Legendre
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  3. Roxane Maranger
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  4. Dominique Monti
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  5. Pierre Pepin
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Correspondence to F. Guillaume Blanchet.

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Communicated by Craig Osenberg.

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Blanchet, F.G., Legendre, P., Maranger, R. et al. Modelling the effect of directional spatial ecological processes at different scales. Oecologia 166, 357–368 (2011). https://doi.org/10.1007/s00442-010-1867-y

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