Sampling bias correction in species distribution models by quasi-linear Poisson point process

Species distribution modeling has an essential role in ecology to investigate habitat suitability based on the relationship between species occurrences and environmental conditions. The presence-only data for organisms is usually assumed to be obtained randomly from the region of interest; however, it is often the case that it is biased toward the areas easily accessed and adversely affects prediction accuracy. To address this sampling bias problem relevant to the prediction accuracy and model fitting of habitat distributions, we propose a new Poisson point process (PPP) model named as a quasi PPP, where environmental effect and sampling bias are explicitly modeled in separate clusters in a framework of quasi-linear modeling. The quasi-linear modeling is designed for capturing homogeneity within clusters and heterogeneity between clusters to improve the estimation accuracy of species distribution. The proposed model includes conventional models such as thinned and superposed PPPs as special cases. We have found that the quasi PPP outperforms the other existing methods in terms of goodness of model fitting. A statistical index based on the quasi-linear modeling is proposed to measure how the presence-only data used for the estimation of the species habitat distribution is affected by the sampling bias. The utility of the quasi PPP has been illustrated using simulation studies as well as the comprehensive vascular plant data in Japan. Our proposed model flexibly incorporates the effect of sampling biases to improve the estimation accuracy of species distributions. The results of data analysis are easily reproducible and applications to other data sets are also easily implementable by a package of qPPP of a statistical software R.