Detecting stabilizing dynamics in biased biodiversity time series using Haar fluctuation analysis

Characterizing how biodiversity has changed through Earth's history and uncovering the processes that have driven those changes remain a significant challenge. Haar fluctuation analysis, a recently developed time-series method, has been suggested as a powerful new tool to infer macroevolutionary drivers and assess system stability. Yet the ability of this method to identify unique drivers or the timing and dynamics of biodiversity, particularly in biased time series, has not been demonstrated. Here, we assess Haar fluctuation analysis and cross-Haar correlations using process-based ecological simulations that incorporate realistic sampling and depositional biases. We find that simpler (neutral) mechanisms can produce patterns observed in the Phanerozoic record, and that uneven sampling and sedimentary hiatuses can distort scaling relationships, cautioning against mechanistic interpretations. Nonetheless, Haar fluctuation analysis can reliably distinguish stabilizing from non-stabilizing dynamics, even under severe sampling bias, supporting the identification of a long-term equilibrium in Phanerozoic marine biodiversity. Our results suggest that Haar fluctuation analysis will be robust for detecting stability whenever the time series is of sufficient resolution relative to duration, and duration relative to the system's return time. More broadly, these findings underscore the value of time-scale-based approaches for studying biodiversity dynamics.