Systems Paleoecology – r, R, and Bifurcations

Tags

attractor, bifurcation, ecology, mathematical model, paleoecology, population growth, resilience, theoretical ecology

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

In chaos, there is fertility. Anais Nin

The importance of r (and R)

The previous post outlined the circumstances in which an intrinsically stable logistic population can deviate from equilibrium, or its attractor, when perturbed by the external environment. Those deviations are brought about by either direct perturbation of the population, or an alteration of the environment’s carrying capacity (for that species). There is a third parameter, however, that determines dynamics in our models, and that is the rate of increase (r or R). It is a life-history trait determined by the evolutionary history of the species (and population), and interaction of that trait with the environment. Its influence on X(t) is generally to accelerate (or decelerate) the overall rate of population growth, with higher values causing higher overall rates. We can see this by repeating the earlier perturbation example, but with a smaller value of r (Fig. 1). The rate at which a population recovers from a disturbance is therefore determined by its intrinsic rate of increase. This is one measure of resilience. Resilience has (too many) varied meanings in ecology and other sciences, and is typically applied to communities or ecosystems, i.e. multi-population systems. In this instance, however, resilience means specifically the time taken for the system to return to equilibrium, and can therefore be applied to our population. Holling (Holling, 1973) has termed this type of resilience engineering resilience, as the concept has broad application in physics and engineering. Under this definition, populations that recover more quickly are considered to be more resilient. Thus, the rate at which a population recovers from a negative perturbation is directly proportional to its intrinsic rate of increase.

Two populations with different intrinsic rates (blue, R=0.25; orange, R=0.5; K=100) recovering from simultaneous and numerically equal direct perturbations. The population with the higher r recovers faster to equilibrium, and thus has greater engineering resilience.

Importantly, however, a population isolated from conspecific populations can never grow faster than its intrinsic rate of increase.

Bifurcations

The intrinsic rate of increase can also be a source of dynamics more complex than those presented so far. This is particularly acute in the discrete time, or difference, models because of the recursive feedback loop present in those models (i.e. X(t + 1) is a direct function of X(t)). May (1976) highlighted this using a discrete logistic model.

EQ. 1: (future population size) = [(intrinsic growth rate) x (current population size)] x (growth limited by carrying capacity)

where x is population size standardized to a carrying capacity of 1 and is restricted to the interval 0 < x < 1, and r is the intrinsic growth rate.

May showed that very complex dynamics, such as chaos, can emerge from this very simple model of population growth with non-overlapping generations, as r is increased. The same holds true for the discrete Ricker logistic model presented earlier (Eq. 1). In that model, values of R < 2.0 yield the expected equilibrium logistic growth, but even at values as low as 1.8 < R ≤ 1.9, interesting behaviours begin to emerge — approaching the carrying capacity, population size will overshoot K very slightly before converging to it (Fig. 2A). This is a transient, pre-equilibrium excursion. At R = 2.0 the system undergoes a dramatic shift from the single-valued equilibrium point to an oscillation between two values around the carrying capacity (Fig. 2B). You will notice that the transient overshoot is preserved, and in fact the amplitude of the oscillation is initially large, but the system eventually converges to two fixed values. Those values represent a new attractor, because the system will always converge to an oscillation between them. The value R = 2.0 is a critical point at which the system is said to undergo a bifurcation, with the equilibrium now consisting of two population sizes.

Transitions of a discrete logistic function with increasing R. Values of R, from upper plot to lower: 1.9, 2.0. K=100, and X(0)=1.0. The upper plot illustrates a quasiperiodic series, while the lower plot is chaotic. Each series was iterated for 30 generations. Plots on the left show population size, while on the right they plot the attractor for the entire series.

The amplitude of the oscillations grows as R increases, and the system eventually undergoes further bifurcations, e.g. where the population oscillates between four fixed points. Is the population still stable? The determination of stability now depends on two factors, the first of which is the timescale at which the population is observed. Population sizes and the attractor are repeating cycles, with X(t) cycling (or “orbiting”) between an ordered set of points. Therefore, if the length of time over which X is observed exceeds the period of the attractor, one will observe the system repeating itself, but if it is shorter, the question of stability remains open unless the underlying dynamical law is known. Second, the observation of multiple cycles allows a complete description of the system’s dynamics, and one could then conclude that the system is confined to a compact subset of the phase space. Most importantly, one would conclude that the system is deterministic and predictable. Recall that deterministic means that the entire future trajectory of the system is knowable, given the law by which the system evolves or unfolds over time, i.e. the dynamic equation and the initial condition of the system (X(0)). This is a very Newtonian system which will continue in this manner unless or until acted upon by an external force. The system is as stable as it was when it possessed a simple equilibrium, the only difference being that the attractor now traces a fixed trajectory in phase space comprising multiple values rather than occupying a single point. We can therefore refine our definition of stability.

Intrinsic stability: An intrinsically stable population expresses a finite set of infinitely repeating values.

This definition encompasses both our earlier simple equilibrium, and our newer oscillatory equilibria. It also encompasses further bifurcations that the system undergoes as R is increased, e.g. to a four point attractor.

Vocabulary
Bifurcation — The point at which a (nonlinear) dynamic system develops twice the number of solutions that it had prior to that point.
Engineering resilience — The time taken for a system displaced from equilibrium to return to equilibrium.

References
Holling, C. S. (1973). Resilience and stability of ecological systems. Annual review of Ecology and Systematics, 4(1):1–23.
May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261(5560):459–467.

Systems Paleoecology – Logistic Populations II

Tags

ecology, logistic growth, mathematical model, paleoecology, population growth

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

The logistic equation, covered in the previous post, is a differential equation, where time is divided up into infinitesimal bits to model the growth and size of X (“infinitesimal” knots your stomach? I cannot recommend Steven Strogatz’s “Infinite Powers” enough!). We can also simulate the logistic model in discrete time to get a better feeling for it, where X(t + 1) is population size in the next “time step” or generation. This approach is instructive because anyone can play with the calculations using a calculator or spreadsheet! Here is an example of a discrete version of logistic growth, the Ricker difference equation (Ricker, 1954).

EQ. 1: (FUTURE POPULATION SIZE) = (CURRENT POPULATION SIZE) x (EXPONENTIAL REPRODUCTION LIMITED BY CARRYING CAPACITY AS IN THE LOGISTIC MODEL)

r has been replaced by R, the main difference between the logistic equation and Eq. 1 being that, because we no longer measure time as continuous but instead step discretely from one generation to the next, we measure the intrinsic rate of increase as the “net population replacement rate”. The population again, after an initial interval of near-exponential growth, settles down to a fixed value at K (Fig. 1). Both the continuous and discrete logistic patterns of population growth are, by all definitions, stable populations in equilibrium. They are stable because, at least within the scope of the models, once a population attains its carrying capacity there is no more variation of population size. This brings us to our first definition of stability.

Stability: An absence of change.

Discrete time logistic growth, showing population sizes per discrete generation. X(0) = 1 and K = 100. R = 1.0.

In the following sections we will cover a real-world example of logistic growth, and then go through the derivation of the logistic function itself.

An Example of Logistic Growth

The state of Washington in the United States employed a program of harbor seal (Phoca vitulina) culling during the first half of the twentieth century. The seals were considered to be direct competitors to commercial and sport fishermen. The state sponsored monetary bounties for the killing of seals until 1960, by which time seal populations must have been reduced significantly below historical levels. Additional relief arrived for the seals in 1972 with passage of the United States Marine Mammal Protection Act. Monitoring of seal populations along the coast, estuaries and inlets of Washington, primarily by the Washington Department of Fish and Wildlife, and the National Marine Mammal Laboratory provided a time series of seal population size, spanning the beginning of recovery in the 1970’s to the end of the century (Jeffries et al., 2003). Population sizes from one region of the coastal stock, the “Coastal Estuaries”, show a logistic pattern of growth (Fig. 2). The function fitted to the data (using a nonlinear least squares regression) is y = 7511.541/[1 + exp[−0.265(x − 1980.63)]] (r-squared = 0.98; p < 0.0001; note that “r-squared” is the coefficient of correlation, not our intrinsic rate of increase). Given an initial population size of X(0) = 1,694 in year 1975, the function yields estimates of r = 0.265 and K = 7,511. This excellent example of logistic growth in the wild, or recovery in this case, was unfortunately brought to us courtesy of the ill-informed belief that the success of human commercial pursuits necessitate, or even benefit from, the destruction of wild species.

Logistic recovery of a harbor seal (Phoca vitulina) population in Washington state, U.S.A., after the cessation of culling and passing of the Marine Mammal Protection Act. Orange circles are observed population sizes, the blue line is the fitted logistic curve, and the red horizontal line is the estimate carrying capacity.

Deriving the logistic equation
Equation 1 in the previous post is the logistic growth rate of the population, but it is not the logistic function itself. That function is obtained by integrating the growth rate dX/dt, and the process is instructive because, as illustrated in later sections, our ability to do so with more complicated dynamic equations is quite limited.

The logistic growth rate is first re-written to eliminate the X/K ratio (makes it easier to proceed)


and then re-arranged to separate variables,

The logistic function is derived by integrating both sides, but doing so with the left hand side (LHS) requires simplification using partial fractions (some of you might remember those from high school math; or not).




The solutions to the final equation are A=1 and B-A=0, yielding B=1. Therefore

Now if we wish to integrate our logistic differential equation,
,
we can substitute our partial fractions solution and proceed as follows.


And if you recall our integration of the Malthusian Equation, the solution is


Let , a constant. Then



which is the equation for logistic population growth! Whew.

References
Jeffries, S., Huber, H., Calambokidis, J., and Laake, J. (2003). Trends and status of harbor seals in Washington State: 1978-1999. The Journal of Wildlife Management, 67:207–218.
Ricker, W. E. (1954). Stock and recruitment. Journal of the Fisheries Board of Canada, 11:559–623.

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.

 

 

 

 

The more things change…

Tags

ecology, evolution, simulations

The Paleozoic Marine Evolutionary Faunas. Shown above are Sheehan’s revision of Boucot’s Ecologic Evolutionary Units. (Drawn by Ashley Dineen).

Every paleontologist, and hopefully everyone who has taken a paleontology course in the past 25 years, recognizes this figure. The main part of it shows one version of the famous Sepkoski curves. By analyzing occurrences of marine invertebrates through the Phanerozoic (past 540 million years or so), Sepkoski noted that the history of marine invertebrates can be divided into three temporally successive, but overlapping “faunas”, named in order the Cambrian, Paleozoic and Modern faunas. Each one is characterized by two features: First, they tend to be dominated by particular types of animals. For example, trilobites are a dominant Cambrian group, brachiopods a dominant Paleozoic group, and bivalved molluscs a dominant Modern group. “Dominant” itself is applied because species of a fauna tend to be present in most of the communities of the fauna, and are often numerically dominant, meaning that they are among the most abundant type of fossil organism in the community. The second feature is the longevity of a fauna; these things persisted for at least tens of millions of years, in the case of the Cambrian Fauna, to hundreds of millions of years in the case of the Paleozoic and Modern! Identification of the faunas, in my opinion, is one of the pillars of the revolution that took place in paleontology between the late 1970’s to early 1980’s, setting paleontology onto its current course, the mainstream of which seeks nothing less than the geobiological processes that explain the history of life on Earth.

In that sense, Sepkoski’s discovery cemented a feature of that history that has been recognized since we started to organize the fossil record back in the days of Cuvier and Lyell, and it is this: Whereas the mechanisms that generate Life’s history, namely variation of the geosphere (climate, tectonics, etc.) and Darwinian evolution, are mechanisms of inexorable change, Life’s history itself is one of fits and starts. By this I mean that at many evolutionary and ecological levels, change simply does not happen for very long spans of time. Steve Gould‘s hypothesis of Punctuated Equilibrium will immediately come to the minds of many readers, and indeed morphological stasis is a real and frequent phenomenon among fossil species. But it goes much further than that. If we examine Sepkoski’s faunas closely, we begin to realize that we can subdivide each one repeatedly into units that are smaller in size (diversity), and shorter in duration, but which also persist relatively unchanged for what are ecologically and evolutionarily long periods of geological time. Look at the figure again, and you will see a scale at the top entitled “EEUs”, or Ecologic Evolutionary Units. These were first described by the paleontologist Art Boucot (later revised by Peter Sheehan), to describe communities that at the genus level remained unchanged for tens of millions of years. EEU’s are not the end, however, and can be subdivided yet again into smaller, shorter units, such as Bambach and Bennington’s “community types” (see below). The bottom line, regardless of scale, is this: In spite of underlying mechanisms of change, ecological communities are organized into a nested hierarchy characterized by non-change.

So, when we combine dominance and the absence of change, one could accuse the fossil record, at those evolutionary and ecological levels, of being rather boring! But of course it isn’t (personal biases aside), and one huge reason for this, whether you’ve recognized it previously or not, is that the non-change of the ecological units serve to emphasize, highlight, “punctuate” the times when things do change! Dramatic changes? The history of life has those in spades: evolution of multicellularity, evolution of photosynthesis, evolution of skeletonized bodies, invasion of the land; all certainly mark the beginning of new ecologic-evolutionary epics. And, of course, things also have endings, and the endings of our units are marked by extinctions. The bigger the extinction, the bigger the unit lost. Or perhaps, the bigger the unit lost the bigger the extinction? The decline and fall of Sepkoski’s first two faunas are marked by mass extinctions, the standout being the Permian-Triassic mass extinction 251 million years ago. To paraphrase Dave Jablonski, mass extinctions remove dominance. Is there a mechanistic relationship between our EEUs and extinction? How are EEUs made, and how do they persist unchanged? Can only extinction bring them to an end? And if so, how are new EEUs made and why are they different?

To me, these are among the most interesting and important questions in paleontology today, and not only because they touch on big pieces of the fossil record. Our modern world is composed of the latest EEUs, which range in age from the end of the last ice age, to a couple million years (when the current ice ages began). Our modern world might also be teetering on the brink of a new, sixth global mass extinction. I therefore believe that answering the preceding questions are very important to the preservation of our modern biosphere, and a sustainable relationship between it and our own complex society. Toward that end, my colleagues and I have been working for several years on the relationship between large fossil ecosystems and mass extinctions, and we recently published a paper in which we present a new hypothesis to explain not only how EEUs arise, but also how they are transformed by mass extinctions. I had a lot of fun writing this paper, but it is probably a bit dry and technical (if I am being honest). So, over the next few weeks I intend to take interested readers through the paper, bit by bit, in a series of posts on this blog. I’ll wrap it up here for now, but will leave you with both a link to a free, unpublished version of the paper, and a figure as a preview (with very little explanation! For now). It’s a “mathematical space” illustrating the relative global stabilities of two alternative type of communities.

Roopnarine, Peter, Kenneth Angielczyk, AllenWeik, and Ashley Dineen. 2018. “Ecological Persistence, Incumbency and Reorganization in the Karoo Basin During the Permian-triassic Transition.” PaleorXiv. November 1. doi:10.1016/j.earscirev.2018.10.014.

An ecological “space” comparing the late Permian Upper Daptocephalus Assemblage Zone of the Karoo Basin, South Africa, to alternative eco-evolutionary histories.

Bambach, Richard K., and J. Bret Bennington. “Do communities evolve? A major question in evolutionary paleoecology.” Evolutionary Paleobiology: University of Chicago Press, Chicago (1996): 123-160.

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.

Pyron’s Puzzling Post Piece

Tags

Alexander Pyron, Conservation, ecology, environment, evolution, extinction, science

(Peter Roopnarine)

Alexander Pyron, a professor of biology at George Washington University, recently wrote an inflammatory op-ed for the Washington Post, entitled “We don’t need to save endangered species. Extinction is part of evolution.” The post outraged many, among them an awful lot of scientists. Needless to say, the piece is a seriously misguided bit of poor reasoning and inaccurate science, particularly with regards to extinction. Myself and colleague Luiz Rocha, also at the California Academy of Sciences, wrote our own response, published several days ago in bioGraphic. Regardless of your opinion on species conservation, Pyron’s article cannot be used as the basis for sound argument, because it is a collection of fundamentally flawed arguments. You can read our own reasoning here: Betting on Conservation.

The image, by the way, shows the fossilized burrows of tiny marine snails in sediments dating to about 250 million years ago. The fossils are from a geological exposure in the mountains of Hubei, China, and is some of the earliest evidence there of the biosphere struggling back from the devastating end Permian mass extinction of 251 million years ago. There are no guarantees in the History of Life.

I’ve edited this post to add a little addendum: While I disagree strongly with Pyron’s opinions, I cannot agree with or support the personal attacks which have been leveled against him by others. The core power of rationalism and modern science is open and free discourse. I think that his science in this case is wrong, and I disagree with his moral stance, but I would not place this in the same category of, for example, charlatan climate change deniers who have alternative and exploitative agendas. So let’s keep the discussion civil.

New paper: Red queen for a day: models of symmetry and selection in paleoecology

Tags

biodiversity, ecology, evolution, paleoecology, Robustness, top-down cascade

Red queen for a day: models of symmetry and selection in paleoecology . Evolutionary Ecology DOI: 10.1007/s10682-011-9494-6