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An Interface Between Ecological Theory and Statistical Modelling Ecological Modelling 157 (2002) 101Á/118 www.elsevier.com/locate/ecolmodel Spatial prediction of species distribution: an interface between ecological theory and statistical modelling M.P. Austin CSIRO Sustainable Ecosystems, GPO Box 284, Canberra City, ACT 2601, Australia Abstract Neglect of ecological knowledge is a limiting factor in the use of statistical modelling to predict species distribution. Three components are needed for statistical modelling, an ecological model concerning the ecological theory to be used or tested, a data model concerning the collection and measurement of the data, and a statistical model concerning the statistical theory and methods used. This component framework is reviewed with emphasis on ecological theory. The expected shape of a species response curvetoanenvironmental gradient is a central assumption on which agreement has yet to be reached. The nature of the environmental predictors whether indirect variables, e.g. latitude that haveno physiological impact on plants, or direct variables, e.g. temperature also influence the type of response expected. Straight-line relationships between organisms and environment are often used uncritically. Many users of canonical correlation analysis use linear (straight-line) functions to relate ordination axes to variables such as slope and aspect though this is not a necessary part of the method. Some statisticians have used straight lines for species/environment relationships without testing, when evaluating new statistical procedures. Assumptions used in one component often conflict with those in another component. Statistical models can be used to explore ecological theory. Skewed species response curves predominate contrary to the symmetric unimodal curves assumed by some statistical methods. Improvements in statistical modelling can be achieved based on ecological concepts. Examples include incorporating interspecific competition from dominant species; more proximal predictors based on water balance models and spatial autocorrelation procedures to accommodate non-equilibrium vegetation. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Vegetation models; Species models; Continuum; Niche; Generalised linear models; GLM; Generalised additive models; GAM; Canonical correspondence analysis; CCA; Spatial prediction; Regression; Ordination; Species response curves 1. Introduction Zimmermann, 2000; Elith and Burgman 2002; Scott et al., 2002). A wide variety of statistical The spatial prediction of species distributions and machine-learning methods have been intro- from survey data has recently been recognised as a duced, often in conjunction with geographic in- significant component of conservation planning formation systems (GIS) and remote-sensing (Franklin, 1995; Austin, 1998, 2002; Guisan and (Fitzgerald and Lees, 1992; Aspinall and Veitch, 1993; Pereira and Itami, 1991; Franklin et al., 2000). Guisan and Zimmermann (2000) provide an E-mail address: [email protected] (M.P. Austin). extensivereview of these developments, identifying 0304-3800/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 0 0 ( 0 2 ) 0 0 2 0 5 - 3 102 M.P. Austin / Ecological Modelling 157 (2002) 101Á/118 many of the alternative statistical approaches that experiment, by theoretical analysis or by repeating may be used. Various forms of regression analysis the study at a different location. Another use of predominate in the literature. Generalised linear statistical models is calibration, where biotic data models (GLM, McCullagh and Nelder, 1989; are used to estimate past environmental condi- Austin and Cunningham, 1981) and generalised tions, an approach of increasing importance in additive models (GAM, Hastie and Tibshirani, palaeoecology. Birks (1998) states ‘‘The most 1990; Yee and Mitchell, 1991) with logistic regres- significant development in quantitative palaeolim- sion using presenceÁ/absence survey data appear to nology has been the creation of many modern be increasingly popular as the statistical model to calibration data-sets of biotic assemblages and be used (Franklin, 1995; Guisan and Zimmer- associated environmental data. Such calibration mann, 2000; Scott et al., 2002). sets, when analysed by appropriate procedures, In the majority of cases, the purpose of the have the potential to transform fossil biostratigra- statistical modelling is the prediction of species phical data into quantitative estimates of the past distribution. The detection of functional relation- environment.’’ These calibration methods (ter ships between species and environment and the Braak and Verdonschot, 1995) are not considered testing of ecological theory tend to be secondary further except where they relate to ecological considerations (Guisan and Zimmermann, 2000). assumptions. It will be argued in this paper that neglect of There are three major components in any ecological knowledge is a limiting factor in the framework for statistical modelling in plant ecol- application of statistical modelling in ecology and ogy. There needs to be an ecological model, a data conservation planning. At the interface between model, and a statistical model. The ecological ecology and statistics, it is possible for statisticians model consists of the ecological knowledge and to assume inadequate ecological models that may theory to be used or tested in the study. The data confound their evaluation of new statistical meth- model consists of the decisions made regarding ods. On the other hand, ecologists may construct how the data are collected and how the data will simpler statistical models than they believe are be measured or estimated. The statistical model necessary because they are unaware of the power involves the choice of statistical method, error of modern statistical methods, A synthesis of function and significance tests. Each model inter- current ecological theory and modern statistical acts in both obvious and subtle ways with the models is badly needed. This paper reviews some other models to determine the success of any of the current problems and tries to assemble some statistical modelling exercise. of the components necessary for a synthesis to be The ecological model may contain assumptions produced. The review is mainly concerned with to be incorporated into the analysis or hypotheses plant community ecology, though similar argu- to be tested. It may, for example be assumed that ments can be applied to other fields of ecology vegetation and species composition are primarily (Austin, 1999a,b). determined by environment rather than by succes- sional status or by time since last disturbance (Franklin et al., 2000). The functional link between 2. A framework for statistical modelling in plant plants and environment may be assumed to be all community ecology straight-line relationships (Austin, 1999a). A hy- pothesis might test whether species respond to Statistical models are based on correlation and environmental variables or gradients with a unim- often have as their purpose prediction. It is not odal, symmetric, response function. possible to determine causation from correlation, An important example of the data model is that but a description of functional relationships can be used by classical phytosociologists (Braun-Blan- achieved (Sokal and Rohlf, 1981; Box, 1966). The quet, 1964; Westhoff and van der Maarel, 1978). reality of such relationships and the causal me- Samples (plots) are selected subjectively by the chanisms responsible should then be pursued by ecologist without any statistical sampling design M.P. Austin / Ecological Modelling 157 (2002) 101Á/118 103 considerations. Species abundances are estimated for the selection of resources by animals but is very using a mixed cover/abundance scale with unequal similar to estimating plant species response curves class intervals, the statistical implications of which (Boyce et al., 2002). The ecological model and the have not been considered until recently. Guisan data model for plants and animals differ. An and Harrell (2000, Guisan 2002) point out that this important difference is the difficulty of estimating cover/abundance measurement is an ordinal vari- the non-use of a resource by an animal. Even able that requires, therefore, special attention estimating the absence from a habitat or site of a when selecting the statistical model. Franklin et mobile or cryptic animal is a non-trivial problem. al. (2000) consider a number of problems that can Consequently the statistical models may differ. arise with the data model. These include problems However, Boyce et al.’s discussion of evaluation of the appropriate scale of observations and procedures has general applicability. locational accuracy when ecological field data are The focus here is on the many ecological used with GIS and databases. The scale of resolu- assumptions and theories that can impact on tion and types of errors associated with digital spatial modelling of vegetation. Prediction can be terrain models were also discussed. The authors achieved without the regression equation having included satellite imagery derived variables in their any necessary ecological process basis, but the case studies. Such remotely-sensed variables have result is unlikely to be robust. The more that their own data models, which need to be evaluated knowledge of ecological process can be incorpo- for compatibility with ecological models. Franklin rated, the more robust the prediction and the more et al. (2000) provide a useful
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