Estimating biodiversity changes through time is crucial for understanding the history of life. The fossil record provides direct evidence, but suffers from significant biases related to preservation, sampling, and geographic representation. Existing methods, such as rarefaction and maximum likelihood models, often address temporal sampling variations but overlook spatial and taxonomic heterogeneity. This study addresses these limitations by proposing DeepDive, a framework combining stochastic biodiversity simulations with deep learning inference. This novel approach aims to provide more accurate and robust estimates of global biodiversity changes through time, even in the face of substantial sampling biases. The inherent incompleteness of the fossil record and the significant impact of biases are emphasized, making the development of sophisticated statistical and computational methods paramount to gain a better understanding of past biodiversity. The need for spatially explicit studies is highlighted as a shift in research efforts, focusing on integrating the effects of both spatial and temporal biases in biodiversity estimations. Existing methods, while making progress towards this goal, are criticized for failing to address taxonomic bias and spatial heterogeneity.

The paper reviews existing methods for estimating past biodiversity from the fossil record. These include various rarefaction techniques, maximum likelihood and Bayesian models based on Poisson sampling, and lower-bound richness extrapolators. The limitations of these methods are discussed, particularly their insufficient handling of spatial and temporal heterogeneity. The authors highlight that existing methods primarily focus on correcting temporal variation in preservation rates, neglecting the significant impact of spatial and taxonomic biases on global biodiversity estimates. A recent analysis suggesting that spatial sampling heterogeneity accounts for a significant portion (50-60%) of changes in standardized richness estimates for shallow marine fossils is cited to emphasize this point. The review serves as a foundation for the need for a more comprehensive approach that accounts for these previously overlooked biases in generating accurate biodiversity estimations.

DeepDive consists of two main modules: a biodiversity simulator and a deep learning inference framework. The simulator generates synthetic biodiversity records that realistically reflect regional heterogeneities, spatial and temporal sampling biases, and taxonomic variations in preservation. This simulator models species origination and extinction using a stochastic birth-death process, incorporates biogeographic information with a flexible framework for simulating regional carrying capacities and dispersal, and models the incompleteness and biases in the fossil record by introducing heterogeneity in fossil sampling rates across regions, taxa, and time. The parameters of the simulator can be adjusted to reflect specific empirical datasets or assumptions about the evolutionary and biogeographical context. The simulated fossil records, along with the true simulated diversity, are then used to train a recurrent neural network (RNN). The RNN uses features extracted from the simulated fossil record (e.g., number of sightings, localities per region over time) to predict the global diversity trajectory. The RNN architecture explores bidirectional LSTM units to capture patterns at different timescales. Several model architectures were evaluated to identify the most effective one based on validation and test datasets. The training process involves minimizing the mean squared error (MSE) between simulated and predicted diversity. Model performance was assessed using metrics such as rMSE (relative mean squared error) and R². Monte Carlo dropout was incorporated to quantify prediction uncertainty. The methodology highlights the careful selection of features, the customizability of simulation parameters, the choice of RNN architecture for handling temporal dependencies in the data, and the rigorous evaluation of model performance. The training process aims to capture a wide range of diversification scenarios and sampling biases. In the empirical analysis, the simulator parameters are adjusted to reflect the characteristics of the specific datasets being analyzed, such as the number of time bins and biogeographic constraints.

DeepDive outperforms the widely used Shareholder Quorum Subsampling (SQS) method across various simulation scenarios. DeepDive shows lower median MSE (by more than one order of magnitude) and higher median R² (0.958 vs 0.432) compared to SQS. DeepDive's robustness to data gaps and ability to capture both smooth and sudden changes in biodiversity are highlighted. The method's accuracy is shown to be affected by completeness and preservation rates, but DeepDive maintains significantly better performance across various sampling scenarios, including those involving strong temporal, taxonomic, and spatial biases. The addition of mass extinction events and diversity-dependent processes in the training simulations significantly improved model performance in scenarios not well represented in the initial training data. Applying DeepDive to two empirical datasets yielded significant insights. For the Permian-Triassic marine dataset, the analysis indicates a decline of up to 58% of genera during the Permo-Triassic mass extinction (PTME) and a significant loss (up to 66%) around the Triassic-Jurassic boundary. For the proboscidean dataset, DeepDive revealed a gradual increase in diversity followed by a sharp decline in the Pleistocene (up to 70% loss) resulting in the extant diversity found today. These findings suggest a significantly higher diversity of proboscideans in the Miocene compared to previous estimates. The accuracy of DeepDive is verified by comparing generated model features from the simulation and the empirical data, showing a close overlap which suggests the training sets encompassed the full range of observed patterns. Figures demonstrating the workflow and comparative performance with SQS are included, along with figures illustrating the diversity estimates for both the marine and proboscidean datasets.

DeepDive addresses the limitations of existing methods by explicitly incorporating spatial, temporal, and taxonomic biases in the fossil record. The combination of mechanistic simulations and deep learning offers a flexible and powerful approach to estimating biodiversity changes, particularly at global scales. The superior performance of DeepDive compared to SQS is discussed, highlighting its ability to handle incomplete and heterogeneous fossil data and recover complex diversity dynamics. The results of the empirical analyses are discussed in the context of previous studies, emphasizing the insights provided by DeepDive about the magnitude and patterns of biodiversity change during major extinction events and the diversification of proboscideans. The discussion emphasizes that DeepDive’s strengths lie in the generative model's flexibility and the power of the deep learning inference in handling complex biases without making strong prior assumptions. Although there's a risk of erroneous predictions if the training set doesn't capture the range of scenarios found in the empirical data, the authors argue that the implemented generative models were successful in encompassing a wide range of plausible scenarios and that the resulting overlap between features of the simulated and empirical datasets reinforces this.

DeepDive provides a robust and accurate method for estimating global biodiversity patterns through time, accounting for various biases in the fossil record. The method significantly outperforms existing approaches, particularly in scenarios with strong spatial biases. The applications to the Permian-Triassic marine fauna and proboscideans provide compelling new insights into major extinction events and the diversification of this clade. Future work could explore incorporating additional types of biases (e.g., phylogenetic biases) or integrating other data sources (e.g., molecular data).

The accuracy of DeepDive relies on the representativeness of the training simulations. While the model encompasses a broad range of scenarios, the possibility of unforeseen biases or patterns in empirical data not captured in the training set exists. Furthermore, the simplification of biogeography into discrete regions and the lack of explicit modeling of biotic interactions are limitations of the current model. However, the modular design facilitates the incorporation of these complexities in future development.