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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…

We have a capacity for imagining situations that are not implied by the data. . . Lee Smolin

The concept of “stability” in science is an evolving one, partly because of the advent of systems approaches to multiple disciplines. To the extent that the 20th century was the century of the small (the atom, the gene, the bit), we can claim the 21st century to be the century of systems: ecological, genomic, socio-eco-economic, information, and so on. In the end I don’t think that we yet have a complete understanding of stability, or perhaps we do not yet fully know what it is that we need to understand.

The workshop took place at the Leibniz Center in Berlin, during May, 2019.

The workshop took place at the Leibniz Center in Berlin, during May, 2019.

In this blog series I will outline my own current views on what stability means in paleocology — the study of the ecological aspects of the history of life. Although stability is a multi-disciplinary concept, my discussion will be biased heavily toward ecological and paleoecological systems as those are my areas of expertise. However, the concepts and discussion are hopefully general enough to be of multi- and trans-disciplinary interest. In instances where they are not, or fall short of being applicable in another discipline, I urge others working in those areas to formulate terms and definitions as needed so that in the end we have a comprehensible and comprehensive terminology, and can truly understand what stability means in all the dynamic systems that we are dealing with today.

Paleoecological concepts

Ecology, including paleoecology, is a fundamentally observational discipline for which a large and broad array of explanatory principles and theories has been developed, e.g. the principle of competitive exclusion (Gause’s law, Grinnell’s principle), the Theory of Island Biogeography, and Hubbell’s Unified Neutral Theory of Biodiversity. These laws, principles and theories differ from foundational theories in other scientific disciplines, such as General Relativity, quantum mechanics, evolution by natural selection, and population genetics, in being limited in the numerical capabilities or precision of their predictions. E.g., many species that compete for resources will coexist in the wild without exclusion, and assemblages of species competing for resources often do not behave neutrally. Despite this, there is an underlying strength to predictive ecological theories and models when they are based on sound inductive reasoning, for the limits of their applicabilities to the real world or inconsistencies with empirical data expose the sheer complexity and high dimensionality of ecological systems — competitors may coexist because of differing life history traits (e.g. dynamics of birth-death rates), incomplete or intermittent resource overlap, spatial and temporal refuges from superior competitors, pressure from predators, and so forth. This complexity of ecological systems is in turn driven by four main factors: the geosphere, evolution on short timescales, history on long timescales, and emergent properties.

The geosphere, atmosphere and hydrosphere, including tectonic, oceanographic and atmospheric processes, affect ecological systems on multiple spatio-temporal scales. Geospheric dynamics determine the appearance and disappearance of islands, the erection and removal of barriers to dispersal and isolation, patterns and rates of ocean circulation and mixing, climate, and weather. The mechanisms of genetic variation and natural selection determine whether, how and how quickly populations of organisms can acclimatize or adapt to their ever-changing, dynamic environments. Those accommodations in turn feedback to their abiotic and biotic environments. No ecological system, however, is solely or even largely a product of processes occurring on generational, ecological, or contemporaneous timescales, for the collection of species that occupy a particular place and time — a community — arrived at that point via path-dependent histories. What you see now depends very much on what came before. Those histories are themselves a cumulative set of past responses of populations, species and communities to their abiotic and biotic environments. And those populations of multiple species, when interacting, are complex systems with emergent properties such as stability. Emergent properties can act as additional drivers of population and community dynamics in feedback loops that both expand and contract the scope within which ecological dynamics deviate from the pure predictions of principle-based theories and models.


The following work will make extensive use of mathematical models, because I believe that they are useful and somewhat underutilized in paleoecology, and because I like them. One guide to understanding the utility of model-based approaches in ecology and paleoecology is to question the soundness of their underlying assumptions, and to explore why those assumptions might appear to be inaccurate when a particular approach is applied to the real world. And both ecological and paleoecological theories are laden with assumptions, sometimes explicit, but often implicit. Ask yourself the following questions: Do real populations ever attain carrying capacity? Are the sometimes complex dynamics predicted by intrinsic rates of population growth ever realized in nature? Are populations ever in equilibrium? What are the relative contributions of intrinsic and extrinsic processes to a population’s dynamics? Are communities stable? If they are, is stability a function of species properties, or of community structure, and if the latter, where did that structure come from? Is community stability always a result of a well-defined set of general properties, or is the set wide-ranging, variable, and idiosyncratic? And, are the answers to these questions based on laws that have remained immutable throughout the history of life on our planet, or have the laws themselves evolved or varied in response to a dynamic and evolving biogeosphere? In the posts that follow, I will introduce basic concepts that are essential to understanding ecological stability, and to equip us to further explore more extensive and sophisticated models that are beyond the scope of the blog. I will attempt to build the concept of stability along steps of hierarchical levels of ecological organization, and to relate each of those steps to paleoecological settings, concepts and studies. This will not be a series on analytical methods. It is about concepts and conceptual models. There are already rich resources and texts for paleoecological methodologies.

The Series

The posts will be divided into parts, each successive part building on the previous one by expanding the complexity of the systems and the levels of organization under consideration. Part I deals with isolated populations, an unrealistic situation perhaps, but an idealization fundamental to understanding systems of multiple species. And, it is populations that become extinct. This part contains a lot of introductory material, but it is essential for laying groundwork for later sections that both deal with more advanced and original material. Advanced readers might wish to skip over these posts, but there is original matter in there, and I welcome feedback! Part II addresses community stability, with an emphasis on paleoecological models and applications. Part III explores the evolutionary and historical roots of ecological stability, including the origination of hierarchical structure and community complexity, stability as an agent of natural selection, and the selection and evolution of communities and ecosystems.

Caveat lector!

The discussion will be technical in some areas, because “systems” is a technical concept. Mathematical models are used extensively because I have found them to be a more accessible way to understand the necessary ecological concepts, sometimes in contrast to actual ecological narratives. Ecological systems are complicated and complex, and models offer a way for us to focus on specific
questions, distilling features of interest. Useful models are in my opinion simple, and they can serve as essential guides to constructing narratives and theories of larger and more complete systems. I will therefore taken great care to outline and explain basic concepts and models (Do not fear the equations! But feel free to ignore them..). Examples of real-world data and analyses will be included in many sections. Additionally, code for many of the models will also included. I use the Julia programming language exclusively (but I have also used C++, Octave and Mathematica extensively in the past, and recommend them highly). I regard R‘s power with awe, but I am not a fan of its syntax.

My hope is that the series will successfully build on concepts and details progressively, and that at no point will readers find themselves unable to continue. I don’t think that a technical mastery is at all necessary, but it can deepen one’s qualitative grasp significantly. And one should never underestimate the power to impress at a party if you can explain mathematical attractors and chaos!

And finally, what follows is unlikely to comprise my final opinions on this topic.