The oscillation of animal populations—the periodic abundance and disappearance of lemmings, hares, voles, and forest insects—has been observed for as long as humans have kept records of the natural world, yet it has resisted a settled scientific explanation. In Complex Population Dynamics: A Theoretical/Empirical Synthesis (Princeton University Press, 2003), the ecologist Peter Turchin takes up this puzzle not merely as a catalogue of case studies but as an occasion to ask a much larger question: can ecology, a discipline still comparatively young, mature into a quantitative and predictive science in the manner of classical physics? Turchin's answer is cautiously affirmative, and the argument he builds to defend it is as much about the philosophy of scientific method as it is about lemmings.

The book's point of departure is historical. Turchin traces the study of population cycles to Charles Elton, who in 1923 passed through the Norwegian town of Tromsø and, unable to read Norwegian, nonetheless noticed an apparently periodic pattern of abundance in a book on Norwegian mammals by Robert Collett. Elton had the volume translated and, in 1924, published "Periodic Fluctuations in the Number of Animals: Their Cause and Effects," inaugurating the empirical study of population oscillations. He would go on to mine the fur-trading records of the Hudson's Bay Company, reconstructing the boom-and-bust cycles of Canada lynx and snowshoe hare pelts back to 1736. Almost simultaneously, and quite independently, Alfred Lotka and Vito Volterra were developing the mathematical theory of consumer-resource interaction that now bears their names. Turchin's central historiographical observation is that these two traditions—the empirical and the mathematical—developed in parallel for three-quarters of a century before beginning, only recently, to converge. The book positions itself as an argument for, and an instrument of, that convergence.

What gives the book its intellectual bite, however, is not the history but the methodological stance Turchin stakes out in his opening chapter. He rejects the Popperian model of science, dominant among many ecologists, in which theories are proposed and then discarded the moment data contradict them. Data, he argues, are never simply "hard facts" against which a theory can be cleanly falsified; and because any mathematical formalization of a theory necessarily simplifies the world, every such theory is, in a strict sense, already wrong before it is tested. Rigorous falsification, taken to its logical end, becomes trivial: collect enough data on any point and a theory will eventually fail somewhere. Turchin invokes Dennis Chitty's memoir Do Lemmings Commit Suicide? as a cautionary tale of where naive rejectionism leads—Chitty's relentless falsification of every testable hypothesis about lemming cycles left him, in the end, only with explanations nobody could test at all. In place of falsificationism, Turchin proposes that science should be understood as a contest among competing theories, adjudicated by data, in which the goal is not certainty but comparative improvement: a theory survives not because it is true but because it is, for now, the "least wrong" available account, a standard to be bettered rather than a claim to be either vindicated or discarded.

This philosophy structures the book's tripartite architecture. Part I develops population dynamics "from first principles," building upward from exponential growth and the self-limiting logistic model to Lotka-Volterra consumer-resource oscillations, before introducing the concept of process order—the number of past states that must be tracked to predict a system's future—as a key to why some populations cycle and others merely fluctuate. Later chapters extend this apparatus to age- and stage-structured populations (illustrated by laboratory flour beetle dynamics), to competing explanations of rodent cycles such as the maternal effect and kin favoritism hypotheses, and to the full taxonomy of predator behavior—functional, aggregative, and numerical responses—that governs trophic interactions from grazing systems to host-parasite dynamics. Part II turns to method proper, describing how time-series data can be probed for the statistical signatures of density dependence and how mechanistic models can be fitted to field observations through techniques such as nonlinear forecasting. Part III then submits the theoretical apparatus to sustained empirical trial across six systems that have each generated decades of dispute: the larch budmoth, the southern pine beetle, the red grouse, voles and other rodents, the snowshoe hare, and ungulates—cases in which Turchin weighs rival hypotheses against time-series patterns and, where possible, experimental manipulation.

The cumulative effect is less a triumphant unification than a demonstration of a research program in motion. Turchin does not claim to have solved the puzzle of population cycles so much as to have shown that the puzzle is tractable when mathematical theory, statistical inference, and experiment are made to answer to one another rather than pursued in isolation. His deeper wager—that ecology's oscillating populations might play the role for biology that planetary orbits played for Newtonian mechanics, revealing simple laws beneath apparently complex behavior—is speculative, and Turchin is candid that it remains unproven. But the book's lasting contribution may lie less in any single resolved case than in its model of disciplined pluralism: a demonstration that a science can advance not by settling on final truths but by rigorously comparing its available imperfect ones, and retiring the worse for the better.