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Monographs in Population Biology #35
Complex Population Dynamics: A Theoretical/Empirical Synthesis
Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations.
Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science.
Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.
Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science.
Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.
472 pages, Paperback
First published January 1, 2003
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July 2, 2018
I've been reading a lot of cliodynamics and other human demographic studies recently, and sort of making the tacit assumption that population ecology was a basic concept I more or less learned everything there was to know about in college. After a while, though, a series of questions started to occur to me, questions that seemed like such obvious extensions of the 101 theory that I was shocked how poorly I could answer any of them. Things like, "what are the common patterns of population change?" and "how are those patterns distributed across different phyla, reproductive strategies, niches, etc.?" Or even something as simple as "how commonly are perfect Lotka-Volterra cycles actually observed in nature? How often would we expect them to be observed?"
Complex Population Dynamics answers many of those questions and more. My first Revelation was in the introductory review. I had no idea that Lotka-Volterra cycles were actually observed in nature before (though around the same time and independently of) their mathematical theorization. That sent me on a little diversion into the primary literature, looking at the original snowshoe hare-lynx data and their interpretation by Elton. They are from the Hudson Bay Company records and show exceedingly regular and synchronized patterns in hare and lynx trappings, with a predictable peak every ten years for a century. What I found even more interesting was that these cycles are synchronized across all of North America. You can predict the abundance of hare in Alaska by knowing the abundance of lynx in Newfoundland three years ago.
Seeing Elton try to come up with some exogenous factor capable of causing such cycles that would apply simultaneously to the whole continent (his first thought was sunspot cycles), it's hard not to think of human historians searching for explanations like environmental degradation and climate change to understand events without first checking if endogenous drivers are sufficient on their own. Elton has the excuse that he was (astonishingly – this was less than a hundred years ago, after the discovery of relativity and quantum physics) writing before endogenous dynamics were apparently discovered. Thanks to Turchin, contemporary historians no longer have that.
My next surprise came in the opposite direction. I knew that Turchin moved from population dynamics to human history because he felt that the former was a "mature science," with the implication that its problems were solved. And given the amount of time between Elton that this book, I assumed that meant many of the problems the field were well resolved long before. But when I went to check the contemporary understanding of the hare-lynx system, I found a whole collection of relatively recent papers that seemed completely uncertain about what I would've thought were basic questions. "What part of the system sets the peak population abundance of hares?" "How would you manipulate the system to make the amplitude higher, or the period longer?" As it turned out, ambitious field experiments had returned ambiguous results for the obvious hypothesis, suggesting that something more unexpected was going on. Maybe high density caused stress that limited hare reproductive rate regardless of food supply? Such an idea strikes me as absurd, though that doesn't mean it couldn't turn out to be true. Either way, surely this wasn't what was meant by a "mature science"?
Before he moves into the meat of the book, Turchin takes a moment to ground his "mature science" in a conversation about physics envy and scientific laws. He makes a point I've never heard before, which seems in retrospect fairly obvious: even the basic laws of Newtonian physics cannot be proven as such, only shown to operate as predicted within available experimental conditions. That inertia will cause an object to move infinitely in the absence of opposing forces can no more be proven than the supposition that populations will exhibit exponential growth infinitely in the absence of environmental constraints. Yet both can be considered laws that apply to all relevant objects in their respective fields. I think the broader point here is that physics describes systems that are easier to isolate from confounding variables. We can take the "assume a spherical cow" provisos of physical predictions for granted without doubting that the forces acting on our cow obey well-understood laws. Ecology in contrast seems unduly embarrassed by its cow's legs.
The first half of the book is dedicated to mathematical theory. I didn't take the time to actually parse the equations here and follow the symbology, but still managed to get the gist of most of it. The interesting insight for me was that the basic outline of the Lotka-Volterra model isn't limited to what we would conventionally think of as predators and prey. In fact, every single trophic relationship imaginable can be framed as some variation on this model. Some of the first half of the book is dedicated to exploring the statistical properties of dynamic models – how to extract meaningful parameters from data that would look qualitatively very similar regardless of which mechanisms actually drove their patterns. The rest just explains how you would expect dynamics to differ given different ecological properties for "resource" and "consumer" species. Grasses exhibit a faster recovery cycle than rabbits because grazers only have access to the top half of each individual. Specialist predators have different effects than generalist predators.
The math theory left me with a few solid impressions. One is that, far from being a rare phenomenon with specific ecological causes, population cycling is extremely common and can theoretically be caused by many factors, alone or in concert. Cycles can be reciprocally caused by predators and prey, but they can also emerge from statistical noise (e.g., changing carrying capacity) while a population might otherwise be stabilizing toward a single value. Chaotic properties of complex systems suggest that the amplitude and instability of a population might result not from ecological mechanisms but simply from the unpredictable consequences of initial conditions. Another impression is that the time lag of density dependent mortality is extremely important in evaluating patterns observed in nature. For all the mathematical and ecological mechanisms that can cause population cycles, many ecological hypotheses could not, because they act on an immediate timescale and could not cause the excess mortality responsible for the downward portion of the cycle.
The second half of the book is more accessible and exciting, in so far as it starts to answer the questions raised by the theory. Each chapter addresses a case study for which reliable timeseries data describing population cycling is available but does not, as yet, have a definitive explanation. Turchin applies a simple methodology to each, beginning with a summary of potential hypotheses, applying descriptive statistics to the data, constructing predictive models using observed parameters matching each hypothesis, and then using available experimental evidence and the properties of each model to distinguish which hypothesis best fits the data. Because all of the subject species are herbivores, the hypotheses are all variants on three categories: herbivore over consumes its plant food and crashes until it recovers (variants could be food quality or induced defenses rather than food quantity); herbivore is killed by its predator until both populations crash, allowing them to recover (variants including parasitoids, parasites, and communities of generalist v specialist predators); and some kind of endogenous response to density (increased conflicts between territorial males, changing age at first reproduction, maternal stress, etc.).
I don't mean to come off as even more of a Turchin fan boy than I already do (part because, as in his cliodynamics work, I don't necessarily have the information or inclination to see how well his claims actually hold up), but he brings a clarity and decisiveness to these case studies that previous researchers seem to have failed to apply. You get the impression that many of the people working in these case studies fail to understand basic analytical premises of their study systems, which have prevented them from seeing clear conclusions in the data they collected. His answers tends to favor one of the two trophic responses, and he dismisses out of hand most of the third category, which he often implies are nonsensical or simply incapable of driving the cyclical patterns observed. I got the sense that many of these studies also failed to completely isolate treatments from each other. Regardless, it seems like the mathematical hypothesis- focused methodology Turchin applies would be far more productive than the experimental approach that seems popular otherwise. On the other hand, what do I know, except what he tells me?
Relative to the first half of the book, the case studies drive home a few surprising points. First is that population cycles in nature seem to be overwhelmingly driven by specialist trophic interactions. This is one place I wish he had spent more time discussing population dynamics other than cycles; implicitly, the alternative is just a stable population held at carrying capacity, varying with changes in climate and habitat extent. But that doesn't actually seem to be the only possibility. For instance, the discussion of rodent population dynamics is quite interesting because it provides what might be considered a natural experiment on the removal of generalist predators. In the North, snow cover protects voles from predation by birds and leaves them vulnerable only to weasels. Thus they show the standard cycling with weasel populations. But in southern regions of Europe, where snow cover does not impede predation by birds, generalist predators maintain vole populations at a low, stable abundance. Because the scope of the book only extends to cycles, I felt like the discussion of this contrast was insufficient.
The second surprise was that the effect of chaos seems much less common in nature than the abstract behavior of these models suggests. Only two study systems show chaotic dynamics, and one of them is not included in the book. And both of them show only weak chaotic properties. This suggests that chaos is not necessarily as profound an obstacle to the mechanistic understanding of ecosystems as some might imagine.
The conclusion of the book and Turchin’s drastic change of field of study are a major power move. He more or less suggests that we have the tools we need to understand any kind of population dynamics, here is how you use them, and it’s up to other people to just collect the data and apply them. The field doesn’t seem to be acting like these problems are solved (there are still red grouse papers coming out acting like the question is inconclusive) but as far as Turchin was concerned, the interesting work was done. Once again, I don't know how well that decision will hold up in retrospect. Overall, though, this book gave me a lot more confidence in the application of something analogous to trophic interaction in describing population cycles in humans.
Complex Population Dynamics answers many of those questions and more. My first Revelation was in the introductory review. I had no idea that Lotka-Volterra cycles were actually observed in nature before (though around the same time and independently of) their mathematical theorization. That sent me on a little diversion into the primary literature, looking at the original snowshoe hare-lynx data and their interpretation by Elton. They are from the Hudson Bay Company records and show exceedingly regular and synchronized patterns in hare and lynx trappings, with a predictable peak every ten years for a century. What I found even more interesting was that these cycles are synchronized across all of North America. You can predict the abundance of hare in Alaska by knowing the abundance of lynx in Newfoundland three years ago.
Seeing Elton try to come up with some exogenous factor capable of causing such cycles that would apply simultaneously to the whole continent (his first thought was sunspot cycles), it's hard not to think of human historians searching for explanations like environmental degradation and climate change to understand events without first checking if endogenous drivers are sufficient on their own. Elton has the excuse that he was (astonishingly – this was less than a hundred years ago, after the discovery of relativity and quantum physics) writing before endogenous dynamics were apparently discovered. Thanks to Turchin, contemporary historians no longer have that.
My next surprise came in the opposite direction. I knew that Turchin moved from population dynamics to human history because he felt that the former was a "mature science," with the implication that its problems were solved. And given the amount of time between Elton that this book, I assumed that meant many of the problems the field were well resolved long before. But when I went to check the contemporary understanding of the hare-lynx system, I found a whole collection of relatively recent papers that seemed completely uncertain about what I would've thought were basic questions. "What part of the system sets the peak population abundance of hares?" "How would you manipulate the system to make the amplitude higher, or the period longer?" As it turned out, ambitious field experiments had returned ambiguous results for the obvious hypothesis, suggesting that something more unexpected was going on. Maybe high density caused stress that limited hare reproductive rate regardless of food supply? Such an idea strikes me as absurd, though that doesn't mean it couldn't turn out to be true. Either way, surely this wasn't what was meant by a "mature science"?
Before he moves into the meat of the book, Turchin takes a moment to ground his "mature science" in a conversation about physics envy and scientific laws. He makes a point I've never heard before, which seems in retrospect fairly obvious: even the basic laws of Newtonian physics cannot be proven as such, only shown to operate as predicted within available experimental conditions. That inertia will cause an object to move infinitely in the absence of opposing forces can no more be proven than the supposition that populations will exhibit exponential growth infinitely in the absence of environmental constraints. Yet both can be considered laws that apply to all relevant objects in their respective fields. I think the broader point here is that physics describes systems that are easier to isolate from confounding variables. We can take the "assume a spherical cow" provisos of physical predictions for granted without doubting that the forces acting on our cow obey well-understood laws. Ecology in contrast seems unduly embarrassed by its cow's legs.
The first half of the book is dedicated to mathematical theory. I didn't take the time to actually parse the equations here and follow the symbology, but still managed to get the gist of most of it. The interesting insight for me was that the basic outline of the Lotka-Volterra model isn't limited to what we would conventionally think of as predators and prey. In fact, every single trophic relationship imaginable can be framed as some variation on this model. Some of the first half of the book is dedicated to exploring the statistical properties of dynamic models – how to extract meaningful parameters from data that would look qualitatively very similar regardless of which mechanisms actually drove their patterns. The rest just explains how you would expect dynamics to differ given different ecological properties for "resource" and "consumer" species. Grasses exhibit a faster recovery cycle than rabbits because grazers only have access to the top half of each individual. Specialist predators have different effects than generalist predators.
The math theory left me with a few solid impressions. One is that, far from being a rare phenomenon with specific ecological causes, population cycling is extremely common and can theoretically be caused by many factors, alone or in concert. Cycles can be reciprocally caused by predators and prey, but they can also emerge from statistical noise (e.g., changing carrying capacity) while a population might otherwise be stabilizing toward a single value. Chaotic properties of complex systems suggest that the amplitude and instability of a population might result not from ecological mechanisms but simply from the unpredictable consequences of initial conditions. Another impression is that the time lag of density dependent mortality is extremely important in evaluating patterns observed in nature. For all the mathematical and ecological mechanisms that can cause population cycles, many ecological hypotheses could not, because they act on an immediate timescale and could not cause the excess mortality responsible for the downward portion of the cycle.
The second half of the book is more accessible and exciting, in so far as it starts to answer the questions raised by the theory. Each chapter addresses a case study for which reliable timeseries data describing population cycling is available but does not, as yet, have a definitive explanation. Turchin applies a simple methodology to each, beginning with a summary of potential hypotheses, applying descriptive statistics to the data, constructing predictive models using observed parameters matching each hypothesis, and then using available experimental evidence and the properties of each model to distinguish which hypothesis best fits the data. Because all of the subject species are herbivores, the hypotheses are all variants on three categories: herbivore over consumes its plant food and crashes until it recovers (variants could be food quality or induced defenses rather than food quantity); herbivore is killed by its predator until both populations crash, allowing them to recover (variants including parasitoids, parasites, and communities of generalist v specialist predators); and some kind of endogenous response to density (increased conflicts between territorial males, changing age at first reproduction, maternal stress, etc.).
I don't mean to come off as even more of a Turchin fan boy than I already do (part because, as in his cliodynamics work, I don't necessarily have the information or inclination to see how well his claims actually hold up), but he brings a clarity and decisiveness to these case studies that previous researchers seem to have failed to apply. You get the impression that many of the people working in these case studies fail to understand basic analytical premises of their study systems, which have prevented them from seeing clear conclusions in the data they collected. His answers tends to favor one of the two trophic responses, and he dismisses out of hand most of the third category, which he often implies are nonsensical or simply incapable of driving the cyclical patterns observed. I got the sense that many of these studies also failed to completely isolate treatments from each other. Regardless, it seems like the mathematical hypothesis- focused methodology Turchin applies would be far more productive than the experimental approach that seems popular otherwise. On the other hand, what do I know, except what he tells me?
Relative to the first half of the book, the case studies drive home a few surprising points. First is that population cycles in nature seem to be overwhelmingly driven by specialist trophic interactions. This is one place I wish he had spent more time discussing population dynamics other than cycles; implicitly, the alternative is just a stable population held at carrying capacity, varying with changes in climate and habitat extent. But that doesn't actually seem to be the only possibility. For instance, the discussion of rodent population dynamics is quite interesting because it provides what might be considered a natural experiment on the removal of generalist predators. In the North, snow cover protects voles from predation by birds and leaves them vulnerable only to weasels. Thus they show the standard cycling with weasel populations. But in southern regions of Europe, where snow cover does not impede predation by birds, generalist predators maintain vole populations at a low, stable abundance. Because the scope of the book only extends to cycles, I felt like the discussion of this contrast was insufficient.
The second surprise was that the effect of chaos seems much less common in nature than the abstract behavior of these models suggests. Only two study systems show chaotic dynamics, and one of them is not included in the book. And both of them show only weak chaotic properties. This suggests that chaos is not necessarily as profound an obstacle to the mechanistic understanding of ecosystems as some might imagine.
The conclusion of the book and Turchin’s drastic change of field of study are a major power move. He more or less suggests that we have the tools we need to understand any kind of population dynamics, here is how you use them, and it’s up to other people to just collect the data and apply them. The field doesn’t seem to be acting like these problems are solved (there are still red grouse papers coming out acting like the question is inconclusive) but as far as Turchin was concerned, the interesting work was done. Once again, I don't know how well that decision will hold up in retrospect. Overall, though, this book gave me a lot more confidence in the application of something analogous to trophic interaction in describing population cycles in humans.
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