Background/Question/Methods
Concerns over global change and recent findings about niche dynamics in evolutionary and community contexts highlight the need for robust methods to quantify niche differences between or within taxa. We propose a statistical framework to describe and compare niches in a gridded environmental space. This framework can be used to compare any taxonomical, geographical or temporal groups of occurrences (e.g. sister taxa, subspecies, native/invasive populations, species distributions before/after climate change). We evaluate within this framework several ordination methods for quantifying niche overlap using simulated species with predefined distributions and amounts of niche overlap. The framework involves three steps: calculation of the density of occurrences along the environmental axes of a multivariate analysis, measurement of niche overlap along these axes, and statistical test of niche equivalency and similarity. We illustrate the approaches on the invasive spotted knapweed.

Results/Conclusions
Our results suggest that ordination techniques strongly differ in their ability to quantify niche differences. We show that failure to account for differences in climate availability leads to systematic biases. Among the techniques we considered, PCA-env (i.e. PCA calibrated on the entire range of climatic variability found in the study area) provided the best results. PCA-env is less prone to artificially maximizing differences between species distributions that are not ecologically relevant. We confirm earlier finding that spotted knapweed experienced measurable changes in its environmental niche as it invaded North America, leading to the rejection of the niche equivalency hypothesis. We provide a framework to measure species’ niche overlap that minimizes biases due to sampling, grid resolution and differences in availability of environmental conditions. It also allows performing statistical tests of niche conservatism.  Testing for niche similarity is useful to assess how closely related taxa retain similar niches within phylogenetic trees and explore evolutionary hypotheses. Testing for niche equivalency is useful to assess how successfully niche models can be transferred from one region to another, for instance to predict biological invasions, or from one period to another, for instance to predict species range shift in response to climate change.