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

Temporal changes of abundance arise from the difference between recruitment rate (i.e. proportion of new individuals entering the population through birth or immigration) and loss rate (i.e. proportion of individuals removed from the population by death or emigration). The interplay between these vital rates and how they change through time at large spatio-temporal scales remains largely unexplored, mainly given the cost of gathering such mark-recapture data. Bridging this knowledge gap would provide deeper insights into the mechanisms of the ongoing biodiversity crisis and help shape effective conservation strategies.

Here, we combine advances in Hidden Markov Models with Neural Hierarchical Models and develop a Neural Dynamic N-mixture model, to infer latent recruitment and survival (and thus loss) from repeated abundance data. Our approach combines decades of development in N-mixture models for ecological datasets with the predictive power and flexibility of neural networks to capture complex and non-linear relationships from high-dimensional datasets.

We optimize a custom loss function (namely negative log-likelihood) that integrates transition matrices and the forward algorithm to enable gradient-based learning. We then validate the model through simulations and demonstrate the ability of our model to infer cross-level, nonlinear relationships. We also compare its performance with traditional Bayesian implementations of dynamic N-mixture models.

Our results show that leveraging the relevance of N-mixture models for ecological datasets within a deep learning framework is a promising avenue for inferring demographic parameters. While the architecture of our Neural Network is, so far, a Multilayer Perceptron, this framework could be easily extensible to multi-modal data and more complex network architectures, such as Convolutional Neural Networks, to infer demographic rates from satellite imagery, camera trap and/or audio loggers.