Systems Paleoecology – Regime Shifts II

Tags

alternative states, Atlantic cod, regime shift

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…

Previous posts in this series

1. Welcome Back Video
2. Introduction
3. Malthusian Populations
4. Logistic Populations
5. Logistic Populations II
6. Deviations from Equilibrium
7. r, R, and Bifurcations
8. Quasiperiodicity and Chaos

9. Chaotic Stability
10. Environmental Variation: Expectations and Averages
11. Nonlinearity and Inequality
12. States, Transitions and Extinction
13. Regime Shifts I

The Grand Banks of Newfoundland.

The Atlantic cod, Gadus morhua, has been the foundation of one of the world’s major fisheries for several centuries, with the Grand Banks off Newfoundland (Fig. 1) being amongst the most productive fisheries in the world. Figure 2 (below) shows the estimated population size of the Atlantic cod on the southern Grand Banks from the years 1959 to 2005 (Power et al., 2010), where G. morhua has historically been the most prominent component of that productive fishery. Cod populations, however, declined across the North Atlantic during the second half of the 20^th century, most notably in the northwestern Atlantic. Several factors might have played roles, including warming ocean temperatures and a resurgence of the predatory grey seal across its historic range after implementation of protection from hunting (Neuenhoff et al., 2019). There is little doubt, however, that over-exploitation by commercial fisheries has been one of, if not the most effective driver of the decline. The Grand Banks population initially increased steadily during the monitored period, reaching a maximum in 1966. Thereafter it declined significantly until 1976, after which it appeared to stabilize, before beginning a steady decline in 1985. Fishing mortality of older individuals (> 6 years old) meanwhile fluctuated, peaking in 1975 and again in 1991. Change point analysis, which is used to detect changes in the statistical distribution of data within a time series, suggests that the population underwent significant shifts in 1971, 1985 and 1993. Each time, the mean population sizes of the intervals defined by those shifts descended through transient phases to significantly lower sizes. The first transition, around 1971, was preceded by an interval of highly variable population size, yet those sizes all exceeded population size from 1971 onward. The period from 1975-1985 was characterized by reduced population size and low variability, but another change occurred in 1985, and by 1993 the population size had stabilized at abysmally low numbers, marking the end of the commercially viable fishery.

Estimated population size (connected line) and fishery catch size (red) for the period 1959-2005. Arrows show times of presumed regime shifts, as identified by change point analysis.

It seems reasonable to hypothesize that each interval between the change point transitions represents a stable state or regime of the population, with fishing mortality thus driving or contributing to transitions between multiple alternative states (Fig. 2). The relationship between fishing and population size is relatively straightforward. Initially, an increase of total catch in the late 1960’s followed an increase of population size, but then declined as population size itself began a steep decline in 1967. However, although population size continued to decline, catch size again increased in 1971, coincident with the time marked by the change point analysis as the first transition to a state of smaller population size. Catch size subsequently followed the decline of population size, reaching a minimum during 1978, after which it began to increase again, presumably in response to the relatively “stable” population. Population size increased after 1980, reaching a new maximum in 1985, but then after a sharp increase of catch size, began its decline to the low numbers at the turn of the century.

A phase map (Fig. 3) captures this journey of potential alternative stable states and transitions, and reveals two general types of regime shifts. First, the initial transition to the second state that persisted from the late 1970s to 1985 was likely both precipitated and maintained by fishing pressure. The continued decline of catch size between 1971 and 1978 might have in fact facilitated some recovery of population size. This is the first type of regime shift and the separation of states—an external driver is capable of moving the system between states, and of maintaining the system in at least one of those states. The basic dynamics of this type of regime shift can be understood in terms of external parameters. The second type of shift, however, is less transparent, because it involves intrinsic properties and dynamics of the system. Look closely at the population trajectory from 1995 on, the last transition of the series. Catch size is negligible over a period of ten years, yet there is no sign of population rebound. If, as claimed earlier, population size is driven by catch size, why didn’t the population recover, and what kept it in the final, most recent attractor or state?

Phase map of cod population size, plotting consecutive years against each other. Blue trajectories show intervals of presumed population stability, i.e., stable states. Red trajectories show the pathways of transition between those states.

References
Neuenhoff, R. D., Swain, D. P., Cox, S. P., McAllister, M. K., Trites, A. W., Walters, C. J., and Ham-mill, M. O. (2019). Continued decline of a collapsed population of Atlantic cod (Gadus morhua) due to predation-driven Allee effects. Canadian Journal of Fisheries and Aquatic Sciences, 76(1):168–184.

Power, D., Morgan, J., Murphy, E., Brattey, J., and Healey, B. (2010). An assessment of the cod stock in NAFO divisions 3NO. Northwest Atlantic Fisheries Organization SCR Doc, 10:42.

Systems Paleoecology – Regime Shifts I

Tags

alternative states, attractor, critical transition, regime shift, Tipping point, transience

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…

Previous posts in this series

1. Welcome Back Video
2. Introduction
3. Malthusian Populations
4. Logistic Populations
5. Logistic Populations II
6. Deviations from Equilibrium

7. r, R, and Bifurcations
8. Quasiperiodicity and Chaos
9. Chaotic Stability
10. Environmental Variation: Expectations and Averages
11. Nonlinearity and Inequality
12. States, Transitions and Extinction

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.

Fig. 1A – Hypothetical regime shift

Fig. 1B – Two populations of red-wing blackbirds. See here for an explanation.

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 (), and the other being an attractor when . Zero population size was classified as an unstable state, because the addition of any individuals to the population — — 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 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 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.

Cod in the North Atlantic.

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.

Systems Paleoecology – States, Transitions, and Extinctions

Tags

alternative states, Complexkty, critical transition, Tipping point

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…

Previous posts in this series

1. Welcome Back Video
2. Introduction
3. Malthusian Populations
4. Logistic Populations
5. Logistic Populations II
6. Deviations from Equilibrium

7. r, R, and Bifurcations
8. Quasiperiodicity and Chaos
9. Chaotic Stability
10. Environmental Variation: Expectations and Averages
11. Nonlinearity and Inequality

The product of zero multiplied by zero is zero — Brahmagupta

The state of a population, as discussed to this point, is the result of intrinsic control exerted by internal variables (e.g. a life-history influenced trait such as R), the impacts of external parameters (e.g. water temperature), and often the response of internal variables to those parameters. These three factors, coupled with preservational conditions, underlie all the stratigraphic dynamics of an idealistically isolated fossil species. Even the dynamics of an isolated population will vary over time, though, because of evolutionary change and environmental variation and change. Thus the state of the population is expected to vary temporally. The states that we have so far considered have been either steady, or vary predictably with parameter changes (e.g. Fig. 1). It is now broadly recognized, however, that dynamic systems often behave or respond in non-smooth ways, where a system may transition discontinuously, and often unexpectedly, from one state to another. The surprises are twofold in nature: first, single systems may possess multiple states —multiple attractors. Second, the transitions between states are often abrupt. Such transitions bear various names that have entered into conventional ecological literature and everyday conversation, including tipping point, critical transition, and regime shift.

Two populations with different intrinsic rates responding to and recovering from a sudden loss of individuals. See here for an explanation.

Discussions of multiple states generally reference communities and ecosystems, e.g. clear vs. turbid lakes, forests vs. grasslands, and coral-dominated vs. algal-dominated tropical reefs. Transitions and multiple states in such multispecies systems are facilitated by nonlinear relationships among species, enhancing and balancing (positive and negative) feedback mechanisms among demographic variables and environmental parameters, and asynchronicity (or synchronicity) of driving and response processes. Can transitions and multiple states occur in the single species population systems on which we have focused so far? Hypothetically, it is possible, but we will have to re-examine and re-think some of the simpler models of environmental shifts and responses outlined in earlier posts. When the community to which a population belongs undergoes a transition between states, it is probable that the population will also change states, but not necessarily so. A species could persist within the multiple states of a community and yet maintain a stable population size or remain within a single attractor. Shifts and responses, however, may also yield a population with distinct stable states separated by a parameter threshold, or parameter range that is much shorter than the ranges within which the population would remain stable — an abrupt transition. “Abrupt” need not refer to time only, but instead more properly refers to the relatively narrow parameter range separating different system states. The state of the population within the transitional parameter range is transient, and we can therefore describe the dynamics of the population as comprising multiple stable states, separated by transient transitional conditions. And, whereas most work in this are has focused on communities and ecosystems, there are situations where transitions can be understood within the framework of single populations. Furthermore, such transitions often have implications for the persistence or extinction of the population. Those transitions and what they imply about population growth and extinction will be the focus of the remainder of this series.

However, before digging into the dirt that I love best, I will offer a rather random assortment of readings and other resources. State transitions, particularly those occurring within complex systems, are all the rage these days. This is the area, in my opinion, where systems science truly serves as a unifying concept across multiple parts of the real world, ranging from universal to microscopic scales, and across boundaries of the physical, biological, and human worlds. I wish that I could reach behind me right now and pull my favourite books off the shelves and list them for you, but, alas, I cannot. Why? Because here in the San Francisco Bay Area my institution remains closed (with most of my library) because of the awful intersection of complex little bundles of viral proteins and nucleic acids and complex human systems, including the biological, sociological, and economic. So, if you the reader is a fellow resident of the United States, I will leave you with a polite and humble request: Please wear your damned mask. Okay, now a few resources.

• Scheffer, Marten. Critical transitions in nature and society. Vol. 16. Princeton University Press, 2009. An absolutely outstanding and accessible presentation. Luckily, because I own multiple copies (not sure why), I actually have a copy at home.
• Complexity, a web resource at the University of Southampton.
• BioTip. This is a flagship program funded by the German government, and maaaybe the world would have a brighter future if this program was emulated elsewhere.
• Regime Shifts DataBase. An ambitious and super program from the Stockholm Resilience Centre.
• David Krakauer & Geoffrey West. The Damage We’re Not Attending To. A recent and very nice article of the great relevance of systems thinking.
• And finally, how about something hot of the presses? Lewis, K. M., G. L. van Dijken, and K. R. Arrigo. “Changes in phytoplankton concentration now drive increased Arctic Ocean primary production.” Science 369.6500 (2020): 198-202.