Figure 1.
Atlas records of where the tree species Eucalyptus apiculata has been reported to be present, west of Sydney, Australia. These values are superimposed on a map of distance from nearest main road (in km). Note that species presences tend to be more likely to have been recorded in areas that are closer to a main road, which can be understood as a product of observer bias.
Figure 2.
A simple demonstration of how pseudo-absence bias correction confounds the true occurrence rate of a target species with species richness.
(a) Example occurrences in 20 grid cells for each of two habitat types; (b) Corresponding occurrence rates and compositional rates of occurrence in each habitat; (c) Predicted probabilities from simulation, as estimated using a model-based approach and using a pseudo-absence approach. Note that the occurrence patterns for species A–C are identical for both habitats (b), hence model-based predicted probabilities are the same for these species (c). However, the addition of species D–F at Habitat II doubled its species richness, meaning that the compositional rate halved in (b), thus pseudo-absence predicted probabilities halved in (c) e.g. Species A reduced from being half of all occurrences in Habitat I to being only a quarter at Habitat II, even though the absolute occurrence rate was unchanged.
Figure 3.
Maps of estimated intensity (in presence points per square kilometre) of Eucalyptus apiculata from three different models.
(a) As a function of environmental variables only; (b) As a function of environmental and observer bias variables; (c) As a function of environmental variables, having modelled and conditioned on a common level of observer bias. Note that (c) predicts a higher intensity of E. apiculata in more remote, inland areas.
Figure 4.
Comparison of predictive performance of different methods of correcting for observer bias.
Measured as area under the ROC curve (AUC), for 62 different Myrtaceae species in the Sydney Basin. Model-based bias correction (“”) is compared to: (a) No bias correction (“
”); and (b) The pseudo-absence approach using point-event data (“
”). Note that most points lie above the line, suggesting that the model-based bias correction typically outperforms both alternative methods. The solid point on each plot represents results for the Eucalyptus apiculata models of Figure 3.
Figure 5.
Diagnostic plots for a point process analysis of the Eucalyptus apiculata data.
(a) Inhomogeneous -function with simulation envelope; (b) Spatially smoothed Pearson residuals. Note from (a) that the
function of the observed data (solid line) runs through the centre of the simulation envelope, suggesting no evidence of inter-point dependence. Note from (b) that the spatially smoothed residual is always close to zero (always between −0.03 and 0.03), suggesting little spatial trend hence a plausible model for intensity of E. apiculata.