Inferring the presence and abundance of rare waterbirds species from scarce data

TL;DR

This paper introduces a flexible statistical model for estimating and imputing the presence and abundance of rare waterbird species from scarce, zero-inflated count data, aiding ecological monitoring and conservation efforts.

Contribution

It proposes a novel log-normal Poisson model with a low-rank latent variable for zero inflation, along with a variational EM algorithm for inference, addressing challenges of missing data and overdispersion.

Findings

Effective imputation of missing data demonstrated on degraded datasets

Prediction intervals and trend estimates provided with quantifiable uncertainty

Model successfully applied to real waterbird monitoring data

Abstract

Abundance data are used in ecology for species monitoring and conservation. These count data often display several specific characteristics like numerous missing data, high variance, and a high proportion of zeros, particularly when monitoring rare species. We present a model that aims to impute missing data and estimate the effect of covariates on species presence and abundance. It is based on the log-normal Poisson model, which offers more flexibility in the variance of counts than a Poisson model. A latent variable is added for the overrepresentation of zeros in the data. The imputation of missing data is made possible by assuming that the latent variance matrix has low rank and the inclusion of covariates. \\ We demonstrate the identifiability in the presence of missing data. Since maximum likelihood inference is intractable, we use a variational expectation-maximization algorithm to infer the parameters. We provide an estimate of the asymptotic variance of the estimators and derive prediction intervals for the imputations, an estimate of the temporal trend, and a procedure for detecting a potential change in this trend. \\ We evaluate our imputations and associated prediction intervals using artificially degraded monitoring data set. We conclude with an illustration on a monitoring waterbirds data set.