Non-parametric habitat models with automatic interactions

Abstract Questions: Can a statistical model be designed to represent more directly the nature of organismal response to multiple interacting factors? Can multiplicative kernel smoothers be used for this purpose? What advantages does this approach have over more traditional habitat modelling methods? Methods: Non-parametric multiplicative regression (NPMR) was developed from the premises that: the response variable has a minimum of zero and a physiologically-determined maximum, species respond simultaneously to multiple ecological factors, the response to any one factor is conditioned by the values of other factors, and that if any of the factors is intolerable then the response is zero. Key features of NPMR are interactive effects of predictors, no need to specify an overall model form in advance, and built-in controls on overfitting. The effectiveness of the method is demonstrated with simulated and real data sets. Results: Empirical and theoretical relationships of species response to multiple interacting predictors can be represented effectively by multiplicative kernel smoothers. NPMR allows us to abandon simplistic assumptions about overall model form, while embracing the ecological truism that habitat factors interact.

[1]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[2]  J. Michael Scott,et al.  Predicting Species Occurrences: Issues of Accuracy and Scale , 2002 .

[3]  C. Gotway,et al.  Comparison of kriging and inverse-distance methods for mapping soil parameters , 1996 .

[4]  Jerome H. Friedman.  Multivariate adaptive regression splines (with discussion) , 1991 .

[5]  J. Booth,et al.  Resampling-Based Multiple Testing. , 1994 .

[6]  塚原 玲子,et al.  Trend-Surface Analysis , 1980, Encyclopedia of GIS.

[7]  Suzanne E. Bayley,et al.  Bryophyte response surfaces along climatic, chemical, and physical gradients in peatlands of western Canada , 1991 .

[8]  Cort J. Willmott,et al.  Spatial statistics and models , 1984 .

[9]  N. Gotelli.  Predicting Species Occurrences: Issues of Accuracy and Scale , 2003 .

[10]  John R. Jones,et al.  Statistical Models for Limiting Nutrient Relations in Inland Waters , 1994 .

[11]  O. Loucks,et al.  Ordinating Forest Communities by Means of Environmental Scalars and Phytosociological Indices , 1962 .

[12]  B. Cade,et al.  A gentle introduction to quantile regression for ecologists , 2003 .

[13]  E. L. Little.  Atlas of United States trees. , 1971 .

[14]  S. Berryman,et al.  Epiphytic macrolichens in relation to forest management and topography in a western Oregon watershed , 2002 .

[15]  Antoine Guisan,et al.  Predictive habitat distribution models in ecology , 2000 .

[16]  M. Austin.  Spatial prediction of species distribution: an interface between ecological theory and statistical modelling , 2002 .

[17]  A. Martínez-Taberner,et al.  Prediction of potential submerged vegetation in a silted coastal marsh, Albufera of Majorca, Balearic Islands , 1992 .

[18]  Ralph Mac Nally,et al.  Validation Tests of Predictive Models of Butterfly Occurrence Based on Environmental Variables , 2003 .

[19]  E. Odum.  Fundamentals of ecology , 1972 .

[20]  C. Daly,et al.  A Statistical-Topographic Model for Mapping Climatological Precipitation over Mountainous Terrain , 1994 .

[21]  F. Harrell,et al.  Prognostic/Clinical Prediction Models: Multivariable Prognostic Models: Issues in Developing Models, Evaluating Assumptions and Adequacy, and Measuring and Reducing Errors , 2005 .

[22]  Brian Huntley,et al.  Climatic control of the distribution and abundance of beech (Fagus L.) in Europe and North America. , 1989 .

[23]  H. Olff,et al.  A hierarchical set of models for species response analysis , 1993 .

[24]  Toshio Odanaka,et al.  ADAPTIVE CONTROL PROCESSES , 1990 .

[25]  S. Bayley,et al.  Bryophyte response surfaces along ecological and climatic gradients , 1991, Vegetatio.

[26]  Gavin A. Begg,et al.  Environmental and stock effects on spatial distribution and abundance of mature cod Gadus morhua , 2002 .

[27]  R. Bellman,et al.  V. Adaptive Control Processes , 1964 .

[28]  A. Galston.  Fundamentals of Ecology , 1972, The Yale Journal of Biology and Medicine.

[29]  E. W. Beals,et al.  Bray-curtis ordination: an effective strategy for analysis of multivariate ecological data , 1984 .

[30]  S. Ormerod,et al.  New paradigms for modelling species distributions , 2004 .

[31]  Robert H. Whittaker,et al.  Vegetation of the Great Smoky Mountains , 1956 .

[32]  Eric R. Ziegel,et al.  The Elements of Statistical Learning , 2003, Technometrics.

[33]  David G. Reid,et al.  Identifying the effects of oceanographic features and zooplankton on prespawning herring abundance using generalized additive models , 1997 .

[34]  Kung-Sik Chan,et al.  NONADDITIVE EFFECTS OF THE ENVIRONMENT ON THE SURVIVAL OF A LARGE MARINE FISH POPULATION , 2004 .

[35]  B. McCune,et al.  Gradients in Epiphyte Biomass in Three Pseudotsuga-Tsuga Forests of Different Ages in Western Oregon and Washington , 1993 .

[36]  Atle Mysterud,et al.  Nonlinear effects of large-scale climatic variability on wild and domestic herbivores , 2001, Nature.

[37]  John H. Cissel,et al.  Use of a smoother to forecast occurrence of epiphytic lichens under alternative forest management plans , 2003 .

[38]  J. T. Curtis,et al.  The Vegetation of Wisconsin , 1962 .

[39]  W. Cramer,et al.  Special Paper: Modelling Present and Potential Future Ranges of Some European Higher Plants Using Climate Response Surfaces , 1995 .

[40]  J. Friedman.  Multivariate adaptive regression splines , 1990 .

[41]  B. McCune,et al.  Analysis of Ecological Communities , 2002 .

[42]  B. Manly.  Randomization, Bootstrap and Monte Carlo Methods in Biology , 2018 .