Neural dynamic N-mixture model: a deep learning framework to infer demographic rates from count data

François Leroy , Marta A. Jarzyna

Changes in population abundance arise from underlying demographic processes, namely survival and recruitment, and knowledge of these two vital rates is crucial for better understanding biodiversity changes. Although demographic data based on individual encounter histories are often sparse in space and time, the dynamic N-mixture model provides an alternative by inferring survival and recruitment from repeated count data while accounting for imperfect detection. Here, we build on recent advances in neural hierarchical modelling and develop a neural dynamic N-mixture model. Specifically, we implement and optimize the likelihood of this model, including the memory-heavy transition matrix, as a negative log-likelihood loss function within a neural network framework, enabling inference of demographic parameters from count data using gradient-based optimization. We also implement a forward–backward algorithm to estimate latent abundance, survivors, and recruits. Using simulated data, we benchmark our neural implementation against a Bayesian implementation and show improved recovery of parameters and latent states, while substantially reducing computation time. Using computer-vision simulations, we show that the framework can be extended to image-based and other high-dimensional covariates through convolutional neural networks or other network architectures. We further apply the model to a case-study using the Swiss Green Woodpecker monitoring data. Our implementation provides a fast, flexible, and extensible framework for fitting dynamic N-mixture models with neural networks, opening opportunities to combine hierarchical ecological inference with data sources such as remote sensing, acoustic data, and other forms of ecological monitoring at large spatiotemporal scales.