Double machine learning data integration for estimating population trends from opportunistic and structured survey data

Accurately quantifying changes in wildlife populations is essential for assessing ecosystem health and stability. Models for integrated estimation of population change (trends) can expand the inferential scope of spatially-explicit trends estimation while increasing precision and accuracy. Integration needs to account for different observation processes among surveys, sampling coverages (geographic, habitat-related, and temporal), and volumes of data. These differences lead to non-stationary contributions of surveys to spatially explicit trend estimates. To obtain integrated trend estimates with identifiable contributions from each survey, we adapt the multi-study double machine learning (DML) model of Shyr et al. 2025. In our integrated DML trend model we address the potential issue of varying availability of data from each survey using a mixture distribution, sub-model that estimates survey coverage probability based on habitat. The mixture distribution directly weights influence of each survey on integrated estimates. We show through simulation studies that a spatially explicit mixture distribution can improve estimation and statistical power of our integrated DML trend model over independent survey-specific trend models. Using data from the North American Breeding Bird Survey and the eBird project, we show that differences in sampling coverage and data volume reflect regionallyvarying strengths of the surveys, and our integrated DML trend model capitalizes on these strengths allowing each survey to be used to its maximum utility.