WHAT IS ECOLOGICAL STABILITY ? In 2019 I posed this question informally to colleagues, using Twitter, a professional workshop that I lead, and a conference. Respondents on Twitter consisted mostly of ecological scientists, but the workshop included paleontologists, biologists, physicists, applied mathematicians, and an array of social scientists, including sociologists, anthropologists, economists, archaeologists, political scientists, historians and others. And this happened…

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Numerous terms, with roots across multiple disciplines that deal with dynamic complex systems, are used interchangeably in the study of transitions to some extent because they are related by process and implication. But they do not necessarily always refer to the same phenomena, and it is useful to be explicit in one’s usage (maybe at the risk of usage elsewhere). Regime shift, critical transition and tipping point are three of the more commonly applied terms in the ecological literature. They form a useful general framework within which to explore the concept of multiple states and transitions, and into which more detailed concepts can be introduced. Regime shift is defined here as an abrupt or rapid, and statistically significant change in the state of a system, such as a change of population size (Fig. 1A). Transient deviations or excursions from previous values, e.g. those illustrated in Fig. 1B}, are not regime shifts. “Regime” implies that the system has been observed to have remained at a stationary mean or within a range of variation over a period of time, and to then have shifted to another mean and range of variation. Regimes can be maintained by external or intrinsic processes, or sets of interacting external parameters and internal variables, but the ways in which the processes are organized can vary. Sets of processes can be dominant, reinforcing the regime; understanding this simply requires one to associate a regime with our previous discussions of system states and attractors. Regime shifts occur then when sets of processes are re-organized, and dominance or reinforcement shifts to other parameters and variables.

Regime shifts may be distinguishable from variation within a state, or continuous variation across a parameter range, by the time interval during which the transition occurs, if the interval is notably shorter than the durations of the alternative states. This of course potentially limits the confirmation of regime shifts as we can never be certain that observation times were sufficient to classify the system as being in an alternative state. The interpretation though is that the duration of the transition was relatively short because the system entered into a transient phase, i.e. moving from one stable state to another. The transition itself may be precipitated in several different ways, dependent on the type of perturbation and the response of the system. The perturbation could be a short-term excursion of a controlling parameter that pushes the system into another state, with the transition being reversed if the threshold is crossed again. More complicated situations arise, however, if internal variables of the system respond to parameter change without a measurable response of the state variable itself, and if the system can exist in multiple states within the same parameter range. These various characteristics of regime shifts serve to distinguish important processes and types of shifts that are more complex than simple and reversible responses to external drivers, such as “critical transitions” and “tipping points”.

We have already discussed several model systems with multiple states, one of those being a trivial state of population extinction ($X=0$), and the other being an attractor when $X>0$. Zero population size was classified as an unstable state, because the addition of any individuals to the population — $X_1>X_0=0$— leads immediately to an increase of population size, and the system converges to a non-zero attractor. This is true regardless of the nature of the attractor (e.g. static equilibrium, oscillatory, chaotic), and makes intuitive sense — sprinkle a few individuals into the environment and the population begins to grow. This is not always the case, however, and there are situations where zero population size, or extinction, can be a stable attractor, or where $X$ converges to different attractors, dependent either on population size itself, or forcing by extrinsic parameters. The system is then understood to have multiple alternative states. I reserve this definition for circumstances where $X$ does not vary smoothly or continuously in response to parameter change (e.g. Fig. 1), but will instead remain in a state, or at an attractor, within a parameter range, and where the states are separated by a parameter value or range within which the system cannot remain, but will instead transition to one of the alternative states. Thus, the multiple states are separated in parameter or phase space by transient conditions.

We will explore a real-life example in the next post, and here is a teaser.

Vocabulary
Attractor – A compact subset of phase space to which system states will converge.
Regime shift – An abrupt or rapid, and statistically significant change in the state of a system.
System state – A non-transient set of biotic and abiotic conditions within which a system will remain unless acted upon by external forces.
Transient state – The temporary condition or trajectory of a population as it transitions from one system state to another.