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Using spatial gradient analysis to clarify species distributions with application to South African protea


  • Maria Terres


  • Alan Gelfand


Typical ecological gradient analyses consider variation in the response of plants along a gradient of covariate values, but generally constrain themselves to predetermined response curves and ignore spatial autocorrelation. In this paper, we develop a formal spatial gradient analysis. We adopt the mathematical definition of gradients as directional rates of change with regard to a spatial surface. We view both the response and the covariate as spatial surfaces over a region of interest with respective gradient behavior. The gradient analysis we propose enables local comparison of these gradients. At any spatial location, we compare the behavior of the response surface with the behavior of the covariate surface to provide a novel form of sensitivity analysis. More precisely, we first fit a joint hierarchical Bayesian spatial model for a response variable and an environmental covariate. Then, after model fitting, at a given location, for each variable, we can obtain the posterior distribution of the derivative in any direction. We use these distributions to compute spatial sensitivities and angular discrepancies enabling a more detailed picture of the spatial nature of the response–covariate relationship. This methodology is illustrated using species presence probability as a response to elevation for two species of South African protea. We also offer a comparison with sensitivity analysis using geographically weighted regression. We show that the spatial gradient analysis allows for more extensive inference and provides a much richer description of the spatially varying relationships. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Maria Terres & Alan Gelfand, 2015. "Using spatial gradient analysis to clarify species distributions with application to South African protea," Journal of Geographical Systems, Springer, vol. 17(3), pages 227-247, July.
  • Handle: RePEc:kap:jgeosy:v:17:y:2015:i:3:p:227-247
    DOI: 10.1007/s10109-015-0215-5

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    References listed on IDEAS

    1. David Wheeler & Catherine Calder, 2007. "An assessment of coefficient accuracy in linear regression models with spatially varying coefficients," Journal of Geographical Systems, Springer, vol. 9(2), pages 145-166, June.
    2. David Wheeler & Lance Waller, 2009. "Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests," Journal of Geographical Systems, Springer, vol. 11(1), pages 1-22, March.
    3. P. Congdon, 2003. "Modelling spatially varying impacts of socioeconomic predictors on mortality outcomes," Journal of Geographical Systems, Springer, vol. 5(2), pages 161-184, August.
    4. Abby Israels, 1984. "Redundancy analysis for qualitative variables," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 331-346, September.
    5. Finley, Andrew O. & Banerjee, Sudipto & Carlin, Bradley P., 2007. "spBayes: An R Package for Univariate and Multivariate Hierarchical Point-referenced Spatial Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i04).
    6. Christopher Bitter & Gordon Mulligan & Sandy Dall’erba, 2007. "Incorporating spatial variation in housing attribute prices: a comparison of geographically weighted regression and the spatial expansion method," Journal of Geographical Systems, Springer, vol. 9(1), pages 7-27, April.
    7. Majumdar, Anandamayee & Munneke, Henry J. & Gelfand, Alan E. & Banerjee, Sudipto & Sirmans, C.F., 2006. "Gradients in Spatial Response Surfaces With Application to Urban Land Values," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 77-90, January.
    8. Jennifer Miller & Janet Franklin, 2006. "Explicitly incorporating spatial dependence in predictive vegetation models in the form of explanatory variables: a Mojave Desert case study," Journal of Geographical Systems, Springer, vol. 8(4), pages 411-435, October.
    9. repec:eee:ecomod:v:228:y:2012:i:c:p:49-58 is not listed on IDEAS
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    1. repec:spr:testjl:v:27:y:2018:i:4:d:10.1007_s11749-018-0619-x is not listed on IDEAS

    More about this item


    Directional derivative; Gaussian process; Generalized linear model; Geographic weighted regression; Bayesian analysis; Species response curves; C3; Q2;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation


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