A gradient analytic perspective on distribution modelling
Authors: Halvorsen Rune 
Published: February 2013

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.