Bimodality and alternative equilibria do not help explain long-term patterns in shallow lake chlorophyll-a

Abstract

Since its inception, the theory of alternative equilibria in shallow lakes has evolved and been applied to an ever wider range of ecological and socioecological systems. The theory posits the existence of two alternative stable states or equilibria, which in shallow lakes are characterised by either clear water with abundant plants or turbid water where phytoplankton dominate. Here, we used data simulations and real-world data sets from Denmark and north-eastern USA (902 lakes in total) to examine the relationship between shallow lake phytoplankton biomass (chlorophyll-a) and nutrient concentrations across a range of timescales. The data simulations demonstrated that three diagnostic tests could reliably identify the presence or absence of alternative equilibria. The real-world data accorded with data simulations where alternative equilibria were absent. Crucially, it was only as the temporal scale of observation increased (>3 years) that a predictable linear relationship between nutrient concentration and chlorophyll-a was evident. Thus, when a longer term perspective is taken, the notion of alternative equilibria is not required to explain the response of chlorophyll-a to nutrient enrichment which questions the utility of the theory for explaining shallow lake response to, and recovery from, eutrophication.

Resilience metrics are robust across data qualities but sensitive to community size.

“…These ‘Early Warning Signals’ (EWSs) can be considered a sub-class of resilience indicator (Dakos et al, 2015) as they quantify resilience when a system has two alternative stable states and the capability to transition/regime shift between them. With current debates over the commonality of alternative stable states in ecology (Dakos et al, 2015; Davidson et al, 2023) and inconsistent ability in real world data (Burthe et al, 2016; Zhang, 2020), the benefit of resilience metrics over EWSs is their ability to quantify stability regardless of the presence of multiple stable states (Lyapunov, 1992; Medeiros et al, 2022; Sugihara et al, 2012). With the complex intrinsic and extrinsic interactions driving ecosystem dynamics possibly masking true multiple stability (Hillebrand et al, 2023) or ecosystems themselves experiencing long transients rather than regime shifts (Hastings et al, 2018), the resilience metrics discussed here are conceptually capable of accurate Jacobian estimation under both heuristics.…”

Basins of attraction of microbiome structure and soil ecosystem functions

“…Further improvements of codes are necessary for inferring stability landscapes at genus-, species-, or strain-level analyses. Third, it should be acknowledged that detailed discussion on ecological processes require time-series datasets (Davidson et al, 2023; Scheffer et al, 2012, 2009). Because our present data lacked the information of temporal changes in community structure, we are unable to discuss the frequency and pace of community structural transitions between basins of attraction.…”

EWSmethods: an R package to forecast tipping points at the community level using early warning signals, resilience measures, and machine learning models

“…Thus far, each of the described techniques assume that the system is at equilibrium when the stress begins to act. In ecological systems, this assumption is not likely to hold (Davidson et al 2023) and so an alternative school of thought suggests quantifying resilience change itself rather than CSD may be more appropriate in such cases (Dakos et al 2015). We consider resilience to be the ‘capacity of system to persist and maintain its state and functions in the face of exogenous disturbance' (Hodgson et al 2015), and consequently consists of two major components: the ability to resist and recover from disturbance (Pimm 1984).…”