This paper provides a theoretical understanding of sampling bias in presence-only data in the context of species distribution modelling. This understanding forms the basis for two integrated frameworks, one for detecting sampling bias of different kinds in presence-only data (the bias assessment framework) and one for assessing potential effects of sampling bias on species distribution models (the bias effects framework). We exemplify the use of these frameworks to museum data for nine insect species in Norway, for which the distribution along the two main bioclimatic gradients (related to oceanicity and temperatures) are modelled using the MaxEnt method. Models of different complexity (achieved by use of two different model selection procedures that represent spatial prediction or ecological response modelling purposes, respectively) were generated with different types of background data (uninformed and background-target-group [BTG]). The bias assessment framework made use of comparisons between observed and theoretical frequency-of-presence (FoP) curves, obtained separately for each combination of species and bioclimatic predictor, to identify potential sampling bias. The bias effects framework made use of comparisons between modelled response curves (predicted relative FoP curves) and the corresponding observed FoP curves for each combination of species and predictor. The extent to which the observed FoP curves deviated from the expected, smooth and unimodal theoretical FoP curve, varied considerably among the nine insect species. Among-curve differences were, in most cases, interpreted as indications of sampling bias. Using BTG-type background data in many cases introduced strong sampling bias. The predicted relative FoP curves from MaxEnt were, in general, similar to the corresponding observed FoP curves. This indicates that the main structure of the data-sets were adequately summarised by the MaxEnt models (with the options and settings used), in turn suggesting that shortcomings of input data such as sampling bias or omission of important predictors may overshadow the effect of modelling method on the predictive performance of distribution models. The examples indicate that the two proposed frameworks are useful for identification of sampling bias in presence-only data and for choosing settings for distribution modelling options such as the method for extraction of background data points and determining the appropriate level of model complexity.
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