A gradient analytic perspective on distribution modelling

Abstract

After massive proliferation over the last decade, distribution modelling (DM) – research with the purpose of modelling the distribution of observable objects of a specific type – has grown into an independent branch of ecological science. There is consensus that this new discipline needs a stronger theoretical foundation. I describe DM as an inductive scientific process with 12 steps, organised into three composite steps: ecological model, data model, and statistical model. Step 8, modelling of the overall ecological response, places DM unambiguously among gradient analysis techniques and motivates for a gradient analytic (GA) perspective on DM. DM terminology is reviewed and revised accordingly. Three fundamental insights of the GA perspective are described: (1) that external ‘factors’ do not influence the species one by one, but act on the species in concert; (2) that a few major complex-gradients normally account for most of the variation in species composition that can be explained environmentally; and (3) that species occur within a restricted interval along each major complex-gradient. These insights are developed into a theoretical platform for DM. General patterns of species performance variation along environmental complex-gradients and the structuring processes responsible for these patterns are reviewed. Three categories of ecoclines, i.e., gradients of variation in species composition and the environment, are recognised: regional ecoclines, local ecoclines, and condition or impact ecoclines. Causes and implications of the unimodal shape of species’ responses to environmental complex-gradients are reviewed. Structuring processes are divided into three categories: limited physiological tolerance, interspecific interactions, and demographic processes. Relationships between categories of ecoclines, the processes responsible for variation in species performance along them, and the spatial and temporal scale intervals in which variation is large, are reviewed. The GA perspective forms the basis for discussions of important steps in the DM process. Initially, the controversial concepts of the habitat and the niche are reviewed and their role in the ecological model (Step 1) discussed. I conclude that neither of these concepts are necessary, nor useful, for DM. As an alternative to conceptual models based upon the niche concept, I propose a new conceptual modelling framework for DM, the HED framework, which is rooted in the gradient analytic perspective. I show how this new framework can be used, in initial phases of a DM study to formulate a meta-model for factors that influence distributions, and in the analytic phase to guide important choices of methods and options and to assist interpretation of modelling results. Important data model issues are: collection of data for the modelled target and preparation of raw response variables (Steps 2 and 6); collection of explanatory data (Step 3); conceptualisation of the study area (Step 4); collection of data for calibration and evaluation (Step 9); and transformation of explanatory variables to derived variables subjected to DM (Step 5,ii). Important statistical model issues are: statistical model formulation, i.e. choice of method (Step 7,i) and model specification (Step 7,ii); model selection and internal assessment of model performance (Steps 8,i and 8,ii); and model evaluation (Step 10). Two points are emphasised: (1) that modelling purpose should inform choice of methods and options; and (2) the importance of an independently collected presence/absence data set, which can be used to calibrate, evaluate and iteratively improve models. Finally I list seven challenges of particular importance for progress in DM: (1) that more knowledge of patterns of natural variation is needed; (2) that a better mechanistic understanding of causes of patterns of natural variation is needed; (3) that the availability of relevant rasterised explanatory variables needs to be improved; (4) that more studies of patterns at local and micro spatial scales, in addition to multiple-scale studies using DM methods, are needed; (5) that evaluation by independent data should be established as a standard in DM; (6) that further insights into statistical modelling methods and their options, with particular reference to appropriateness for different types of data and DM purposes, are needed; and (7) that DM methods should be incorporated in studies with a broader scope. I conclude that there are considerable potentials for improvement of DM methods and practice. Increased return from DM in terms of contributions that improve our understanding of patterns of natural variation and their causes, should be expected.

Modelling bird richness and bird species presence in a boreal forest reserve using airborne laser-scanning and aerial images

“…probably better done with simulated data where the population is known, or by use of independently collected data for model evaluation (Guisan & Zimmermann 2000, Austin 2007, Halvorsen 2012). However, our conclusions are strengthened by the fact that logistic regression and RF models yielded similar results in our evaluation by cross-validation.…”

“…Cross-validation was preferred rather than splitting the data into one set for training and one set for evaluation of models because of relatively sparse data and because such splitting of the data does not solve the problem that effects of potential sampling bias will be left undetected (Halvorsen 2012). For each of the models, we carried out a 10-fold cross-validation by splitting the data into ten roughly equal-sized parts (folds), and then performed a leaveone-fold-out cross-validation, i.e.…”

Gradients in Traits Composition and Their Relation to Environmental Complex-Gradients and Structuring Processes: a Study of Marine Sediment Species Communities

“…There is no lack of studies reporting how marine benthic communities are structured by environmental variation [e.g., [4][5][6][7][8]. However, while the mechanisms by which each of these structuring processes influence the species are generally quite well known, marine benthic ecology lacks tradition for a unified approach by which gradients in species composition (i.e., coenoclines, which are axes of unconstrained ordination methods) [9] are related to intercorrelated environmental gradients (i.e., environmental complex-gradients) [9,10]. Such identifyication and interpretation of the co-variation of coenoclines and environmental complex-gradients are important for generating new hypotheses that can be addressed both hypothetico-deductively and inductively in future studies.…”

Identification of Fine-Scale Marine Benthic Ecoclines by Multiple Parallel Ordination

“…It is important to note that both the ecoclines and the major complex-gradients [15] are abstract concepts or hypotheses resulting from inductive methods [16] which subsequently can be tested using hypothetico-deductive methods. While plant ecologists have embraced indirect gradient analysis as a most valuable tool for exploring speciesenvironment relationships, marine ecologists, especially marine benthic ecologists, have generally had a much more applied focus in their research.…”

“…The extracted ordination axes represent the major gradients in species composition, that is, coenoclines [14]. A species-by-site matrix typically contains between one and four coenoclines [15]. (2) To relate recorded environmental variables to the extracted coenoclines.…”