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Paleobiologists often employ network-based methods to analyze the inherently complex data retrieved from geohistorical records. However, they lack a common framework for designing, performing, evaluating, and communicating network-based studies, hampering reproducibility and interdisciplinary research. The high-dimensional and spatiotemporally resolved data also raise questions about the limitations of standard network models to represent the local-, regional-, and global-scale systems considered in paleobiology. By assuming independent pairwise links, standard network models wash out higher-order node interactions and can obscure paleontological patterns. These challenges provide an opportunity to move paleobiology research beyond standard network representations toward higher-order models better suited for the complex relational structure of the geohistorical data. Higher-order representations can represent the spatiotemporal constraints on the information paths underlying geohistorical data, capturing the high-dimensional patterns more accurately. Here we describe how to use the Map Equation framework for designing higher-order models of geohistorical data, address some practical decisions involved in modeling complex dependencies, and discuss critical methodological and conceptual issues that make it difficult to compare results across studies in the growing body of network paleobiology research. We illustrate multilayer networks, hypergraphs, and varying Markov time models for higher-order networks in case studies based on the fossil record and delineate future research directions for current challenges in …