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Presence/absence data and presence-only data are the two customary sourcesfor learning about species distributions over a region. We illuminate thefundamental modeling differences between the two types of data. Most simply,locations are considered as fixed under presence/absence data; locations arerandom under presence-only data. The definition of "probability of presence" isincompatible between the two. So, we take issue with modeling strategies in theliterature which ignore this incompatibility, which assume thatpresence/absence modeling can be induced from presence-only specifications andtherefore, that fusion of presence-only and presence/absence data sources isroutine. We argue that presence/absence data should be modeled at point level.That is, we need to specify a surface which provides the probability ofpresence at any location in the region. A realization from this surface is abinary map yielding the results of Bernoulli trials across all locations.Presence-only data should be modeled as a point pattern driven by specificationof an intensity function. We further argue that, with just presence/absencedata, preferential sampling, using a shared process perspective, can improveour estimated presence/absence surface and prediction of presence. We alsoargue that preferential sampling can enable a probabilistically coherent fusionof the two data types. We illustrate with two real datasets, onepresence/absence, one presence-only for invasive species presence in NewEngland in the United States. We demonstrate that potential bias in samplinglocations can affect inference with regard to presence/absence and show thatinference can be improved with preferential sampling ideas. We also provide aprobabilistically coherent fusion of the two datasets to again improveinference with regard to presence/absence.

Preferential sampling for presence/absence data and for fusion of presence/absence data with presence-only data