Pollination networks play a critical role in natural and agricultural systems, and deepening our understanding of plant-pollinator interactions may produce valuable insights for resource management. Typically, the numbers of interspecific interactions are estimated based on morphological traits and species abundance. The data, however, have an intrinsic problem that the counts are only partially observed due to imperfect detection. A common approach to under-counting in ecology is the N-mixture model, a hierarchical statistical model of two layers: 1) one for modeling true, latent interaction counts and 2) one for modeling imperfect detection. Nevertheless, there is a limitation that the N-mixture model relies solely on known covariates to determine interspecific interactions. There could be other unmeasured (i.e., latent) factors shared at a community level beyond individual morphological traits and abundance. In computer science, nonnegative matrix factorization (NMF) is a well-known technique to predict the values of unobserved interactions from inferred latent factors, but it does not handle the effect of imperfect detection. Thus, we propose a unified framework called the Poisson NMF-based N-mixture model that combines the N-mixture model and the NMF model for interaction counts.
Results/Conclusions
We evaluated the performance of our proposed model and its competitors in two ways: 1) parameter estimation of latent factors and detection probability with synthetic data, and 2) prediction accuracy on observed counts with two real datasets: plant-pollinator interactions and host-parasite interactions. The former was collected by ~30 undergraduate researchers at the HJ Andrews Long-Term Ecological Research (LTER) site and the latter is a part of the Sevilleta LTER program. We compared the proposed model to approaches that do not account for the imperfect detection. Overall, we found that fitting a model without an imperfect detection solution degraded its performance in both parameter estimation and species interaction prediction. In addition, we compared models with latent factors against models with known features. The models with latent factors provide more accurate results on predicting observed interaction counts. This finding reveals the potential value of latent factors in understanding species interaction processes. Interpretation of the inferred latent factors is an open research question, but expert knowledge can shed light on the meaning of the factors. In continuing work, we are developing nonlinear versions of this model and designing strategies for selecting the most important features for each component of the model.