# Complex Population Dynamics: A Theoretical/Empirical Synthesis (MPB-35)

PETER TURCHIN
Pages: 456
https://www.jstor.org/stable/j.ctt24hqkz

1. Front Matter
(pp. i-iv)
(pp. v-x)
3. Preface
(pp. xi-xiv)
4. Mathematical Symbols
(pp. xv-xviii)
5. ### Part I THEORY

• CHAPTER 1 Introduction
(pp. 3-16)

Population dynamics is the study of how and why population numbers change in time and space. Thus, population dynamicists document the empirical patterns of population change and attempt to determine the mechanisms explaining the observed patterns. Temporal population dynamics is not the only subject that population ecologists study.Among other things, they are also interested in statics (what sets the level around which populations fluctuate) and population structure (e.g., age distribution). More recently, there has been a lot of progress in spatiotemporal dynamics of populations. Nevertheless, population dynamics in time has been at the core of population ecology ever since the...

• CHAPTER 2 Population Dynamics from First Principles
(pp. 17-46)

Ecologists rarely discuss the philosophical foundations of research into population dynamics. Foundational issues tend to work in the background shaping inquiry, and are rarely hauled out into the daylight to be closely examined (Cooper 2001). Several controversies in population ecology can be traced to a misunderstanding or a disagreement at the very basic level, for example, the density dependence debate (section 5.4).

My goal in this chapter is to explicitly discuss the logical foundations of population dynamics. The starting point is provided by a set of “self-evident truths” or postulates, from which much of the logical structure of the theory...

• CHAPTER 3 Single-Species Populations
(pp. 47-77)

In this chapter I present an overview of mathematical models for single-species populations. The basic format is to show and explain model equations, and then to discuss the dynamical behaviors that the models can exhibit. As I stated in the preface, I will not discuss how the results are obtained, but simply provide the references to the appropriate literature. I will also not attempt to provide a comprehensive account of models of single-population dynamics. My primary focus is on models that can potentially exhibit complex dynamics, although I will review some models that are not capable of complex dynamics, but...

• CHAPTER 4 Trophic Interactions
(pp. 78-136)

Consumer-resource interactions are inherently prone to oscillations and are, therefore, the obvious suspect to investigate as a potential mechanism of a population cycle. However, not all models of trophic interactions exhibit cycles. The purpose of this chapter is to survey the theory of consumer-resource dynamics, and ask two major questions: how is the propensity to cycle affected by (1) structural assumptions of the model, and (2) parameter values? Theoretical literature on resource-consumer interactions is enormous, and even answering this narrow question could take a whole book in itself. To make the task more manageable, I shall primarily focus on models...

• CHAPTER 5 Connecting Mathematical Theory to Empirical Dynamics
(pp. 137-160)

In this chapter, I review different kinds of dynamical behaviors that ecological models can exhibit, and interpret these mathematical predictions in terms of observable variables. The basic premise underlying the material here is that inasmuch as mathematical models reflect ecological reality, the “bestiary” of model-predicted dynamics provides us with patterns that might be matched with behaviors of real populations. Until recently, ecologists interested in nonlinear dynamics tended to focus exclusively on behaviors of deterministic models, that is, population fluctuations resulting only from endogenous factors (Schaffer 1985; Pimm 1991). Real-world populations are always affected by exogenous factors (“noise”), and the taxonomy...

6. ### Part II DATA

• CHAPTER 6 Empirical Approaches: An Overview
(pp. 163-172)

There are three general approaches to studying population fluctuations: statistical analysis of observational (e.g., time-series) data, mathematical modeling of mechanisms, and experiments. Until recently, ecologists (at least, in North America) have tended to emphasize manipulative experiments astheway to address ecological questions. For example, the eminent empirical ecologist C. J. Krebs argues against both time-series analysis and mathematical models. He suggests that we should avoid collecting long-term data simply for the purpose of analyzing it for density dependence, because “this approach has been a bankrupt paradigm” (Krebs 1991:6). Furthermore, “mathematical models are more seductive than useful at this stage of the...

• CHAPTER 7 Phenomenological Time-Series Analysis
(pp. 173-196)

At the start of an investigation into population dynamics of some specific system we typically do not know enough about it to begin formulating intelligent hypotheses about its behavior. Thus, the first phase of the investigation should be exploratory, and we need to answer the following questions (see chapter 5): Are dynamics periodic? What kind of stability does the system possess? What is the process order of fluctuations? What are relative contributions of endogenous and exogenous factors? To answer these questions, we need to fit to data some generic, or phenomenological, models. The goal of this chapter, therefore, is to...

• CHAPTER 8 Fitting Mechanistic Models
(pp. 197-210)

While the previous chapter focused on exploring the structure of density dependence, without worrying too much about the mechanistic content, in this chapter we shall consider more mechanistic approaches to analyzing time-series data. Recollect that phenomenological methods employ lagged population densities as state variables. The distinguishing feature of the approaches reviewed here is that we, at the very least, can postulate the ecological nature of state variables that drive the dynamics. The functional forms of dependencies between state variables may be completely known, in which case we need to estimate only the numeric values of parameters. Alternatively, we may have...

7. ### Part III CASE STUDIES

• CHAPTER 9 Larch Budmoth
(pp. 213-238)

If there were a beauty contest for complex population dynamics, then population oscillations of the larch budmoth (LBM),Zeiraphera diniana, in the Swiss Alps would be a credible contender for first place (figure 9.1). Not onlyare these oscillations remarkablyre gular, but the moth population swings through a stunning range of densities during a typical cycle, covering five orders of magnitude! It is, therefore, not surprising that the larch budmoth was featured as one of the best examples of complex population systems in a recent news article inScience(Zimmer 1999). However, the ecological mechanisms that drive this remarkable oscillation have not...

• CHAPTER 10 Southern Pine Beetle
(pp. 239-271)

The southern pine beetle,Dendroctonus frontalis, belongs to the family of scolytid bark beetles. Its generic name,Dendroctonus, can be loosely translated as “tree death.” This is an apt name for this beetle, because it is the most important agent of mortality for several pine species, most notably the loblolly (Pinus taeda), in the southern United States, Mexico, and parts of Central America (Flamm et al.1988). The estimated damage due to the southern pine beetle (SPB) over the last three decades is well over \$1 billion (see Price et al.1992).

Pine trees protect themselves from insects and fungi by exuding resin. As...

• CHAPTER 11 Red Grouse
(pp. 272-295)

Periodic dynamics are not common in bird populations (Kendall et al.1998: table 1). A major exception to this general pattern is birds of the grouse family (Tetraonidae, order Galliformes) (Middleton 1934; Williams 1954). Population cycles have been reported in Scottish rock ptarmigan (Watson et al. 1998); black grouse, capercaillie, and hazel grouse (Lindén 1989); ruffed grouse and prairie grouse (Keith 1963); and red grouse (Potts et al. 1984; Williams 1985). Most nontetraonid examples of oscillations in bird populations appear to be exogenously driven (e.g., owls feeding on cyclic voles or arctic geese periodically suffering from lemming predators; see chapter 12)....

• CHAPTER 12 Voles and Other Rodents
(pp. 296-343)

Ecologists who are not working on small rodents may consider that the subject of population cycles in voles and lemmings remains as muddled as ever, if not increasingly more muddled. Small rodent ecologists appear to be in the business of proposing new hypotheses rather than rejecting old ones: the number of hypotheses has increased with time instead of being reduced to (ultimately) one plausible explanation. For example Batzli (1992) lists more than twenty distinct hypotheses, and more were added since the publication of his article (e. g., Boonstra 1994; Jedrzejewski and Jedrzejewska 1996; Inchausti and Ginzburg 1998).

In a recent...

• CHAPTER 13 Snowshoe Hare
(pp. 344-364)

The snowshoe hare–lynx population cycles, like cycles in rodents, lie at the very beginnings of the systematic study of complex population dynamics (Finerty 1980). Although rodent cycles chronologically were first to be noticed by Charles Elton (see section 1.1.1), at the time there were no quantitative time-series data for rodents to be analyzed. But there were long-term records of fur returns at the Hudson’s Bay Company, so for several decades the main focus of research shifted from the shorter rodent cycles in Fennoscandia to the 10-year hare-lynx cycles in boreal North America.

Early theories attempting to explain the biological...

• CHAPTER 14 Ungulates
(pp. 365-382)

Mechanisms underlying population dynamics of North American cervids (such as white-tailed deer, reindeer, elk, and moose) are a subject of some controversy. The current debate centers on the importance of predation versus interactions with food, and the dynamical role of exogenous factors (as far as is known, social population controls are lacking in deer). For example, Mech et al. (1987) argued that the main determinant of moose dynamics is their interaction with food as modified by weather (specifically, the cumulative effect of snowy winters), and that predation by wolves is secondary to winter weather in influencing moose populations. By contrast,...

• CHAPTER 15 General Conclusions
(pp. 383-396)

Now that we have done so much work trying to understand the specific mechanisms responsible for complex population dynamics in each of the case studies (chapters 9–14), it is time to step back and see if any patterns emerge. Table 15.1 brings together the conclusions for these case studies, together with some other studies that I did not have space to review in this book, but for which sufficient information exists for informed judgment. One pattern is immediately obvious: all cases for which we can reach a reasonably well-supported conclusion belong to one general category of ecological processes: trophic...

8. Glossary
(pp. 397-404)
9. References
(pp. 405-436)
10. Index
(pp. 437-450)
11. Back Matter
(pp. 451-452)