A probabilistic framework for windows of opportunity: the role of temporal variability in critical transitions

Abstract

The establishment of young organisms in harsh environments often requires a window of opportunity (WoO). That is, a short time window in which environmental conditions drop long enough below the hostile average level, giving the organism time to develop tolerance and transition into stable existence. It has been suggested that this kind of establishment dynamics is a noise-induced transition between two alternate states. Understanding how temporal variability (i.e. noise) in environmental conditions affects establishment of organisms is therefore key, yet not well understood or included explicitly in the WoO framework. In this paper, we develop a coherent theoretical framework for understanding when the WoO open or close based on simple dichotomous environmental variation. We reveal that understanding of the intrinsic timescales of both the developing organism and the environment is fundamental to predict if organisms can or cannot establish. These insights have allowed us to develop statistical laws for predicting establishment probabilities based on the period and variance of the fluctuations in naturally variable environments. Based on this framework, we now get a clear understanding of how changes in the timing and magnitude of climate variability or management can mediate establishment chances.

Introducing desirable patches to initiate ecosystem transitions and accelerate ecosystem restoration

“…Within the context of ecosystem restoration, it has been noted that environmental fluctuations may provide windows of opportunity for recovery, examples including forest regeneration during prolonged periods of high precipitation or coastal ecosystem recovery during prolonged periods of reduced hydrodynamic stress (Holmgren & Scheffer, 2001; Hu et al, 2015). While previous research has focused on windows of opportunity for the establishment of individuals of the desired community (van Belzen et al, 2022), our work suggests that this concept could also be applied to entire patches of the desired community. More specifically, patches below the critical patch size needed to survive average environmental conditions may utilize a window of opportunity to expand beyond this critical patch size, meaning that expansion can subsequently be sustained even when environmental conditions return to normal.…”

Establishing cordgrass plants cluster their shoots to avoid ecosystem engineering

“…Contrary to our expectations, prevailing environmental conditions did not induce a shift from a sparse organization in exposed environments, to dense clumped organization in sheltered conditions. Therefore, we hypothesize that larger and older plants may instead alter their shoot organization pattern by filling in space between clusters once the plants reach a certain minimum patch size‐dependent tolerance threshold (Van Belzen et al, 2022). In other words, we expect that lateral expansion is initiated with clustered growth, after which shoot density increases by filling open spaces.…”

“…Van Wesenbeeck, Van De Koppel, Herman, & Bouma, 2008) with less clustering (personal observations). We hypothesize that plants shift (through a process called space filling) from stress avoidance to engineering after reaching size‐dependent tolerance thresholds (Van Belzen et al, 2022). Possibly the timing of switches differs depending on the environment and exposure at different salt marshes.…”

Adventures of salt marsh recruits

“…The WoO is framed to include an initial short-term disturbance-absent window (WoO-1) that provokes seedling rooting and subsequent long-term windows (WoO-2 and WoO-3) in which hydrodynamic and associated erosion disturbances remain below the resistance of seedling (Fig. 1.4b;Balke et al, 2011;van Belzen et al, 2022). All windows are stochastic in timing and their effectiveness is highly correlated with the species-specific temporal evolution of seedling resistance against dislodgement (Hu et al, 2021).…”

“…This may cause an overestimation of the longterm buoyancy of the dispersal units because the floating of small units is supported by surface tension. However, the floating period can be much shorter in moving water in which turbulence can break the surface tension (Vogel, 1988;van den Broek et al, 2005). Another flaw in assessing the long-term buoyancy of dispersal units is the use of tap or purified water rather than natural seawater, without assessing the validity of these alternatives (Xiao et al, 2009(Xiao et al, , 2016.…”