A metric to quantify analogous conditions and rank environmental layers

Analogous conditions in environmental variables are expected because environments are spatially autocorrelated and often present similar combinations over geographic space. That similar environmental combinations may be found at different localities provides a crucial basis for correlative species distribution modeling. An absolutely analogous variable is constant, while a non-analogous variable has no-repeating values, yet no current method allows researchers to quantify intermediate degrees of analogous conditions and rank environmental layers. I approached this issue from the perspective of dual-space correspondence, in which (a) variable range and modal frequency have a theoretical inverse relationship (y ∝ x-1), and (b) modal values of frequency are limited by the number of pixels in a given raster layer. For two geographic extents and two resolutions (2.5’ and 10’), I obtained range and modal frequency of 19 bioclimatic variables and 5 reference variables. Then, I measured Euclidean distances from candidate variables to the non-analogous variable as a metric for degree of analogous conditions, which were used to rank variables. Bioclimatic layers were plotted in log-log scatterplots of range vs. modal frequency; variables were located inside the upper-right triangle (except for one set), and no layer fit the inverse model. Temperature variables presented higher degrees of analogous conditions than precipitation for South America and the Araucaria Moist Forests ecoregion. Geographic extent and pixel resolution changed the degree of analogous conditions of derived variables (quarterly and monthly); however, a pattern of change was not observed, which suggested ad hoc hypotheses on geographic and temporal idiosyncrasies. Variables with high contribution in previous SDM/ENM studies (e.g., temperature seasonality and annual precipitation) showed low degree of analogous conditions. It is expected that heterogeneous layers would generate better correlational geographic distributional predictions than analogous variables, even though this hypothesis remains untested. Ranking layers can provide grounds for selecting variables in distribution and niche modeling, particularly as regards interpreting spatial projection and transferability. Alternatively, ranking can be used to compare degrees of analogous conditions of the same layer in different time spans