Characterising the interplay of dynamics and artefacts: a multifractal analysis of historical humpback whale recordings

While humpback whale songs are known for their complexity, a quantitative understanding of their temporal structure remains elusive. We apply Multifractal Detrended Fluctuation Analysis (MFDFA) to a large historical dataset of songs spanning four decades (1950s-1990s). Our analysis confirms the songs are robustly multifractal but reveals significant heterogeneity, with distinct signatures strongly correlated with the recording year. Notably, 1992 recordings exhibit a markedly different dynamic higher complexity (ω) and strong persistence (α0>1.0) in stark contrast to the anti-persistent nature (α0<0.5) of 1950s recordings. These differences are partially confounded by variations in recording quality (SNR), as our characterisation of the ambient background shows it to be a highly persistent, yet strictly monofractal, process. This work thus provides quantitative evidence for long-term shifts in song dynamics, while highlighting the critical challenge of disentangling an anti-persistent, multifractal biological signal from persistent, monofractal environmental noise.