Systems Paleoecology – Introduction

Tags

dynamics, ecology, evolution, modeling, networks, paleoecology, paleontology

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.

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.

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.

 

 

 

 

New paper: Comparing paleo-ecosystems

Tags

dynamics, ecology, evolution, modeling

Modeled ecological dynamics in South Africa 1 million years after the end Permian mass extinction, showing the highly uncertain response of the community to varying losses of primary production.

We have a new paper on paleo-food web dynamics in the Journal of Vertebrate Paleontology! The paper is one in a collection of 13 (and 27 authors), all focused on the “Vertebrate and Climatic Evolution in the Triassic Rift Basins of Tanzania and Zambia”. The collection covers work done in the Luangwa and Ruhuhu Basins of Zambia and Tanzania, surveying the vertebrates who lived there during the Middle Triassic, approximately 245 million years ago (mya). This is a very interesting period in the Earth’s history, being only a few million years after the devastating end Permian mass extinction (251 mya). They are also very interesting places, capturing some of our earliest evidence of the rise of the reptilian groups which would go on to dominate the terrestrial environment for the next 179 million years. The evidence includes Teleocrater, one of the earliest members of the evolutionary group that includes dinosaurs and modern birds.

Our paper, “Comparative Ecological Dynamics Of Permian-Triassic Communities From The Karoo, Luangwa And Ruhuhu Basins Of Southern Africa” is exactly that, a comparison of the ecological communities of southern Africa before, during and after the mass extinction. Most of our knowledge of how the terrestrial world was affected by, and recovered from the mass extinction comes for extensive work on the excellent fossil record in the Karoo Basin of South Africa, but that leaves us wondering how applicable that knowledge is to the rest of the world. We therefore set out to discover how similar or varied the ecosystems were over this large region, comparing both the functional structures (what were the ecological roles and ecosystem functions) and modeling ecological dynamics across the relevant times and spaces of southern Africa. We discovered that during the late Permian, before the extinction, the three regions (South Africa, Tanzania, Zambia) were very similar. In the years leading up to the extinction, however, communities in South Africa were changing, becoming more robust to disturbances, but the change seemed slower to happen further to the north. The record becomes silent during the mass extinction, and for millions of years afterward, but when it does pick up again in the Middle Triassic of Tanzania, the communities in South Africa and Tanzania are quite distinct in their composition. The ecosystem in South Africa was dominated by amphibians and ancient relatives of ours, whereas to the north we see the earliest evidence of the coming Age of Reptiles. Yet, and this is where modeling can become so cool, the two systems seemed to function quite similarly. We believe that this a result of how the regions recovered from the mass extinction. Evolutionarily, they took divergent paths, but the organization of new ecosystems under the conditions which prevailed after the mass extinction lead to two different sets of evolutionary players, in two different geographic regions, playing the same ecological game. As we say in the paper, “This implies that ecological recovery of the communities in both areas proceeded in a similar way, despite the different identities of the taxa involved, corroborating our hypothesis that there are taxon-independent norms of community assembly.”

And finally, this work would not have been possible without the generous support of the United States National Science Foundation’s Earth Life Transitions program.

A very brief introduction

Tags

dynamics

This is a very short video about our work and the questions that we ask. Courtesy of the Academy‘s Visualization Studio.

Community Stability

Tags

dynamics, extinction, food webs, Permian-Triassic extinction, stability, theoretical ecology

A community stability “landscape”. Green depressions represent regions of stability (the basins). There are two stable communities (balls) in the basin. The one on the left is disturbed, and returns smoothly to its original position. The one on the right amplifies the displacement, either returning eventually to its original position, or possibly transitioning to another basin, or alternate state.

One of the central questions of our paper was, “How stable are ecological communities during a mass extinction?” This might seem a bit of a silly question at first glance, with the obvious answer “Not stable at all!” But that is not necessarily the case. Consider yourself standing on the deck of a leaky shop which is filling gradually with water. You know that the ship is going down, but  your situation is stable as long as the deck remains level, or at least until the water begins to lap around your knees. We often tend to think of mass extinctions as chaotic dramas, perhaps being influenced by the end Cretaceous event, 66 million years ago (mya), when a 10 kilometer asteroid collided with the Earth and much hell really did break loose. There is also a lot of talk these days about collapsing ecosystems, because we continue to warm up the planet, eat all the fish we can eat, and so on. But what would a Sixth Mass Extinction really look like? Would ecosystems collapse, or wind down slowly to shadows of their former selves? Did the citizens of a Roman city in Gaul turn out the lights one night in the 5th century CE, bid the ancient world farewell and lay out their clothes for the next morning’s Middle Ages? Or did they rather one day, in corner market conversation, question how the heck all those Germans wound up in government anyway? A little bit of both I suspect.

So getting back to our question of mass extinctions at the end of the Permian, some 252 mya, were ecosystems stable before the extinction, collapsing as species extinctions spiralled out of control, or were they whittled down to a hardy core? Did they become more sensitive to smaller insults, such as storms or droughts, or were they hardy cores? Answering these questions depends surprisingly on what you mean by “stability”. The term is used in various ways in ecology, and I’ve even been accused of using it in a rather narrow sense, in contrast to others who believe that there are many kinds of stability. I am not convinced that the latter is really the case, and even if it is, I would argue that there is only one important type of stability, and that is the likelihood that the community will persist, that is, continue to exist in pretty much the same form, under non-extreme environmental conditions. The conditions that have prevailed during the history of a stable community, including seven year droughts, megastorms, the occasional disease epidemic, etc., did not cause the community to collapse or its species to become extinct. This definition encompasses many aspects of stability. Consider again our boat, this time with no leaks. Whether it is at anchor in a calm bay, sailing steadily on smooth seas, heaving rhythmically on rolling waves, or pitching about chaotically in a storm, the most important question is, are you and the boat still afloat the next day? I therefore do not believe that there are many different kinds of community stability, but instead different aspects to the likelihood of persistence, and different ways to measure it.

In our paper we looked at one particular aspect of stability, commonly termed “local”. Let me explain why. Imagine our community is represented by a small ball, and its state is represented by its position on a landscape (Fig. 1; scientists love to imagine states as positions on an imaginary landscape). The landscape is rugged and hilly, and is shaped by the environment. If our ball is on a slope, it won’t stay there for very long, and its state will change. It is unstable. If it is located at the bottom of a basin though, then it will remain there, as long as nothing disturbs it. It is stable. If it is displaced by a small amount, remaining in the basin’s depression, then it will roll downhill and return to the bottom of the basin as soon as the displacing force is removed. Interestingly, with a little care one could also balance the ball on one of the peaks, and it will remain there, but that position is precarious and fragile. Any relatively minor force would serve to start a downhill roll. The basin is an “attractor“.

Now, there are a number of limitations to using local stability to describe the behaviours (dynamics) of which your community is capable. A perhaps obvious one is what happens as you increase the distance by which the ball is displaced. One possibility is that the community does not return to the basin of origin, but specifically what does happen to it depends on the topography of the landscape. A slightly more subtle set of questions, and the ones which we pursued, is what happens to the community between the time at which it is displaced (a little), and its return to the bottom of the basin? Is it a simple, Sisyphusean roll back down to the bottom of the basin? Does it happen quickly? What if the ball is kicked again before it’s finished rolling? These are important questions to ask when the planet is undergoing a slow, persistent environmental meltdown as it did 252 mya.

There are probably many interesting and important transient dynamics between departure and return. These can be very difficult to predict. To appreciate this, let us agree that our community really isn’t a ball at all, but is better described as a large collection of balls (species populations), many of which are connected to each other with ropes, pulleys and springs. The contraption now could even amplify a displacement, weaving about the slope, perhaps shifting to a new basin, or losing species along the way. These transient dynamics might be fairly common in real communities, and communities might in fact never really spend any time at the bottoms of basins, instead rolling about, tracing out complicated pathways in response to displacing forces, according to their system of species, ropes and springs.

So, what did our South African ecosystem do 252 mya as the planet became less and less hospitable?