ABSTRACT
Aim
Determining how ecological processes vary across space is a major focus in
ecology. Current methods that investigate such effects remain constrained by
important limiting assumptions. Here we provide an extension to geographically
weighted regression in which local regression and spatial weighting are used in
combination. This method can be used to investigate non-stationarity and spatialscale
effects using any regression technique that can accommodate uneven weighting
of observations, including machine learning.

Innovation
We extend the use of spatial weights to generalized linear models and
boosted regression trees by using simulated data for which the results are known,
and compare these local approaches with existing alternatives such as geographically
weighted regression (GWR). The spatial weighting procedure (1) explained up
to 80% deviance in simulated species richness, (2) optimized the normal distribution
of model residuals when applied to generalized linear models versus GWR, and
(3) detected nonlinear relationships and interactions between response variables
and their predictors when applied to boosted regression trees. Predictor ranking
changed with spatial scale, highlighting the scales at which different species–
environment relationships need to be considered.

Main conclusions
GWR is useful for investigating spatially varying species–
environment relationships.However, the use of local weights implemented in alternativemodelling
techniques can help detect nonlinear relationships and high-order
interactions that were previously unassessed. Therefore, this method not only
informs us how location and scale influence our perception of patterns and processes,
it also offers a way to deal with different ecological interpretations that can
emerge as different areas of spatial influence are considered during model fitting.