Highlights

We use mathematical modelling to reveal complex interdependences between power supply and survival probabilities across microbial habitats.

We show that the evolution of any dynamical system is related to a predictive asymmetry that quantifies causal connections from limited observations.

We show that marine-based sectors of the Eurasian ice sheet complex collapsed at the Bølling transition and contributed significantly to Meltwater Pulse 1a.

We compute transfer entropy by estimating the invariant measure from the invariant distribution of the transfer operator approximated from time series. We use two methods for approximating the transfer operator, and find that our methods are robust to noise and show promising performance relative to other transfer entropy estimators.

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 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.