Growth-rate distributions at stationarity
arXiv:2603.29916v1 Announce Type: new Abstract: We propose new analytical tools for describing growth-rate distributions generated by stationary time-series. Our analysis shows how deviations from normality are not pathological behaviour, as suggested by some traditional views, but instead can be accounted for by clean and general statistical considerations. In contrast, strict normality is the effect of specific modelling choices. Systems characterized by stationary Gamma or heavy-tailed abundance distributions produce log-growth-rate distributions well described by a generalized logistic distribution, which can describe tent-shaped or nearly normal datasets and serves as a useful null model for these observables. These results prove that, for large enough time lags, in practice, growth-r
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Abstract:We propose new analytical tools for describing growth-rate distributions generated by stationary time-series. Our analysis shows how deviations from normality are not pathological behaviour, as suggested by some traditional views, but instead can be accounted for by clean and general statistical considerations. In contrast, strict normality is the effect of specific modelling choices. Systems characterized by stationary Gamma or heavy-tailed abundance distributions produce log-growth-rate distributions well described by a generalized logistic distribution, which can describe tent-shaped or nearly normal datasets and serves as a useful null model for these observables. These results prove that, for large enough time lags, in practice, growth-rate distributions cease to be time-dependent and exhibit finite variance. Based on this analysis, we identify some key stylized macroecological patterns and specific stochastic differential equations capable of reproducing them. A pragmatic workflow for heuristic selection between these models is then introduced. This approach is particularly useful for systems with limited data-tracking quality, where applying sophisticated inference methods is challenging.
Comments: 9 pages, 3 figures
Subjects:
Data Analysis, Statistics and Probability (physics.data-an); Populations and Evolution (q-bio.PE); Quantitative Methods (q-bio.QM)
Cite as: arXiv:2603.29916 [physics.data-an]
(or arXiv:2603.29916v1 [physics.data-an] for this version)
https://doi.org/10.48550/arXiv.2603.29916
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Edgardo Brigatti [view email] [v1] Tue, 31 Mar 2026 15:57:12 UTC (358 KB)
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