Regulatory pathways of phytoplankton regime shifts in shallow lakes: A new insight from non-equilibrium statistical mechanics

Abstract

Phytoplankton regime shifts in shallow lakes have severe effects on ecosystem stability and water quality. However, precise regulation is a formidable task because regime shifts exhibit uncertainties and stochasticity arising from permanent environmental fluctuations. The key challenge lies in capturing their complex non-equilibrium dynamics. Therefore, we developed a potential and flux landscape framework to quantify phytoplankton dynamics. Phytoplankton dynamics showed four distinct temporal patterns in long-term chlorophyll-a records from 80 shallow lakes worldwide: abrupt changes (18.75%), monotonic decline (28.75%), increasing then decreasing trend (17.50%), monotonic increase (35.0%). Phytoplankton bistability was confirmed across all patterns through potential landscape analysis, despite their diverse temporal patterns. Total nitrogen (TN) to total phosphorus (TP) ratios emerged as the dominant driver that induced regime shifts by modulating the potential barrier height. Temperature was identified as the key perturbation because even a slight variation (1%) markedly altered critical transition probability, while larger fluctuation intensities triggered regime shifts within the bistable region. Furthermore, a regulation threshold at TN:TP ≈ 23 was identified by quantifying the driving forces of phytoplankton dynamics through mean flux and entropy production. This threshold reflects thermodynamic reorganization and is detected well before the tipping point where the current state disappears, enabling timely intervention and thereby avoiding delayed responses caused by hysteresis effects. These findings elucidate the regulatory pathways of phytoplankton regime shifts and provide mechanistic insights for managing eutrophication in shallow lakes.

Graphical abstract

Keywords

Phytoplankton bistability / Total nitrogen to total phosphorus ratios / Temperature / Potential landscape / Regulation threshold

Highlight

	● Phytoplankton dynamics quantified by the potential and flux landscape framework.
	● Phytoplankton bistability was proved by potential landscape of 80 shallow lakes.
	● TN:TP driven regime shifts by altering the potential barrier height.
	● Even a 1% temperature change markedly altered the critical transition probability.
	● The regulation threshold was defined as TN:TP ≈ 23 to enable early intervention.

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