How to perform modeling with independent and preferential data jointly?

Abstract: Continuous space species distribution models (SDMs) have a long-standing history as a valuable tool in ecological statistical analysis. Geostatistical and preferential models are both common models in ecology. Geostatistical models are employed when the process under study is independent of the sampling locations, while preferential models are employed when sampling locations are dependent on the process under study. But, what if we have both types of data collectd over the same process? Can we combine them? If so, how should we combine them? This study investigated the suitability of both geostatistical and preferential models, as well as a mixture model that accounts for the different sampling schemes. Results suggest that in general the preferential and mixture models have satisfactory and close results in most cases, while the geostatistical models presents systematically worse estimates at higher spatial complexity, smaller number of samples and lower proportion of completely random samples.