Population Dynamics Models: A Plea for Plurality

POPULATION DYNAMICS MODELS: A PLEA FOR PLURALITY M.E.J. WOOLHOUSE* Introduction This paper reviews approaches to population dynamics modelling and advocates consideration ofa greater variety of strategies, particularly for the modelling of complex systems, which in ecological parlance means more than two species systems. Existing models of such systems are monogenic, relying on a single modelling approach [1] that, I argue, has a questionable philosophical basis and severe practical limitations. That there is a need for alternatives has been previously recognized (for example , [2]), but the call has gone largely unheeded. I discuss some possible alternative approaches that have received relatively little attention and comment on the type of population problem to which they might usefully be applied. Certain families of models, such as the Lotka-Volterra, NicholsonBailey , and Leslie Matrix models and their derivatives, have been thoroughly reviewed and criticized elsewhere (for example, [3, 4]), and I do not discuss these in any detail here. Although the focus is on complex systems, examples will inevitably be drawn from the one- and twospecies models that predominate in the literature. Special emphasis is placed on arthropod population dynamics; this reflects a personal bias— the arguments should extend beyond the taxonomic confine. Definitions For the purposes of this review a "population" is defined as a collection of individuals of one species coexisting in a delimited space, and "population dynamics" refers to changes in the abundance of a population over time. ?Department of Pure and Applied Biology, Imperial College of Science and Technology , Prince Consort Road, London SW7 2BB, United Kingdom.© 1988 by The University of Chicago. AU rights reserved. 003 1-5982/88/3104-0594$01 .00 510 I M.E.J. Woolhouse ¦ Population Dynamics I define a "model" as a symbolic representation of a real world process . This definition is true to the spirit of many of those suggested elsewhere [5-10], although more restrictive definitions have been proposed : Neyman and Scott [11] confine "symbolic" to "mathematical," and Maynard Smith [12] and Pielou [13] require the "representation" to enhance understanding of a process. The definition declares a model to be nothing more or less than linguistic expression, which does not itself constitute a scientific hypothesis [14, 15; but see also 16]. Rather, models are tools that may be used to express existing hypotheses and may be useful formulations in the logical process leading to the derivation of new hypotheses [11, 17]. Aims ofModeL· The traditional aims of population dynamics models are explanation and prediction [14, 16, 17]. Explanation demands that a model contribute to the understanding of an ecological process, prediction that it can foretell the future behaviour of an ecological system. The explanationprediction distinction has also been referred to as strategic-tactical [15], research-extension [18], and mechanistic-heuristic [13]. Different authors often emphasize one aspect or the other, according to their own interests. Explanatory models are lauded by Maynard Smith [12] (who requires "models" to be explanatory and dismisses purely predictive models as mere "simulations") and others [19, 20]. Disagreement between model prediction and reality can itself, in classical Popperian tradition , contribute to understanding [21]. Meanwhile, a bevy of pragmatists stress the use of models as predictive tools, united by the view that "prediction is the only validation!" [10, 22-24]. The dichotomy is an unfortunate one; explanation and prediction are by no means mutually exclusive [25]. In particular, Holling [1] developed a remarkably influential philosophy of modelling around the goal of achieving both explanation and prediction. This goal is unimpeachable , but the Holling approach espouses a methodology that is not, despite its widespread and uncritical acceptance. MODELLING APPROACHES Holling [1] favours two qualities in a model: realism and precision. Realism denotes an accurate abstract representation of a real world process ; precision requires unambiguous output, usually quantitative. Both realism and precision are, ofcourse, subjective concepts [13, 16]. Holling [1] suggests that real and precise models should be capable of both explaining and predicting ecological processes, and that these qualities can be achieved only by incorporating in a model as much biological Perspectives in Biology and Medicine, 31, 4 ¦ Summer 1988 \ 51 1 detail as possible, a quality termed "wholeness." He also recognizes another desirable quality, "generality," the property...