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We leverage the intrinsic dynamical information in empirical records to show that the external forcing of ice volume encompasses insolation signals with a wide range of orbital frequency content, and cannot be fully accounted for by a unique time series.

We review some of the ways in which causal connections can be extracted from palaeontological time series and provide an overview of three recently developed analytical frameworks that have been applied to palaeontological questions.

We show that using formation counts as a sampling proxy to correct the fossil record via residual modelling is ill founded.

We use common and widespread species of planktonic foraminifera in deep-sea sediments and show that the observed global occupancy of planktonic foraminifera has been dynamically coupled to past oceanographic changes captured in deep-ocean temperature reconstructions.

We show that outcrop area contains a signal useful for predicting changes in fossil richness as well as collection and formation counts, whilst the latter two are information redundant with fossil richness. Our results suggest that the widespread use of collection and formation counts to correct the raw richness data may be unwarranted.

We show that coccolithophores were globally more common and widespread, larger, and more heavily calcified in the pre‐34 Ma greenhouse world, and declined along with pCO$₂ during the Oligocene (34–23 Ma). Our results suggest that atmospheric pCO₂ has exerted an important long‐term control on coccolithophores.

We show a significant statistical relationship between variation in geochemical composition and prokaryotic community structure within deep-sea sediments near the hydrothermal vent field Loki’s Castle at the Arctic Mid-Ocean Ridge, in the Norwegian-Greenland Sea.

I show how quantifying directional information transfer between variables can correctly distinguish a common-cause variable from a spurious relationship, even in cases where correlations are misleading.

We show that Phanerozoic records of seawater chemistry and continental flooding contain information on the diversity of marine animals that is independent of sedimentary rock quantity and sampling. Linkages between biodiversity and environmental records likely reflect complex biotic responses to changing ocean redox conditions and long-term sea-level fluctuations driven by plate tectonics.

A non-parametric estimate of information transfer (IT) is used to quantify (1) the relative strength of statistical dependence among three variables, including nonlinear relationships, and (2) the directionality of coupling between two variables, compared to surrogate time series.