Scaling Up in Ecology: Mechanistic Approaches

Ecologists have long grappled with the problem of scaling up from tractable, small-scale observations and experiments to the prediction of large-scale patterns. Although there are multiple approaches to this formidable task, there is a common underpinning in the formulation, testing, and use of mechanistic response functions to describe how phenomena interact across scales. Here, we review the principles of response functions to illustrate how they provide a means to guide research, extrapolate beyond measured data, and simplify our conceptual grasp of reality. We illustrate these principles with examples of mechanistic approaches ranging from explorations of the ecological niche, random walks, and macrophysiology to theories dealing with scale transition, self-organization, and the prediction of extremes. 1 A nn u. R ev . E co l. E vo l. Sy st . 2 01 2. 43 :1 -2 2. D ow nl oa de d fr om w w w . a nn ua lr ev ie w s. or g by S ta nf or d U ni ve rs ity M ai n C am pu s L an e M ed ic al L ib ra ry o n 07 /1 5/ 13 . F or p er so na l u se o nl y. ES43CH01-Denny ARI 1 October 2012 11:53 INTRODUCTION: RELATING PHENOMENA ACROSS SCALES In a classic perspective on the role of modeling in ecology, Levin (1992) noted that “the problem of relating phenomena across scales is the central problem in biology and in all of science. ” Currently, there are three predominant ecological perspectives on this fundamental issue. Proponents of macroecology (e.g., Brown 1995) begin with a search for scaling “laws” through an examination of empirical data measured over wide ranges of scale. If substantial correlations exist—between body mass and metabolic rate, for instance—macroecologists then proceed to test hypotheses concerning the mechanisms that underlie these correlations (McGill & Nekola 2010). In the converse of this “top-down” approach, community ecologists traditionally take a “bottom-up” perspective, using small-scale field observations and experimental manipulation to infer pattern at larger scales (Underwood & Paine 2007). Both top-down and bottom-up perspectives begin with empirical data. In contrast, ecological theorists begin with a conceptual map of how scales might be related. Only after these initial heuristic models have been validated qualitatively are subsequent quantitative models tested empirically. As distinct as they are, these perspectives are not independent. Both macroecologists and experimental ecologists are guided by theoretical concepts, and theorists rely on these researchers to provide observations from which concepts are born and data against which models can be tested. Indeed, it is through the interaction of these perspectives that ecology can best relate phenomena across scales. Interaction is easiest on common ground. Although ecologists of all stripes seem to find pleasure in promoting the differences among their approaches, there is a philosophical unity underlying these disparate perspectives. Each assumes that the connections of biology at one scale of time or space to that at other scales can be described by response functions, mathematical expressions of how systems respond to the conditions in which they find themselves. Although widely used, the concept of a response function appears under a confusing variety of names. For example, in ecology, functional response describes how the rate of prey capture varies with changes in prey density. In physiology, thermal reaction norms quantify the fitness of an organism as a function of its body temperature. In physics, Boyle’s law specifies how the volume of a gas varies as a function of pressure, and Newton’s second law of motion predicts how the acceleration of a mass depends on the force applied to it. Despite the differences in nomenclature, each of these mathematical descriptors is a response function. Biological response functions take three general forms. Conceptual response functions—the grist of theoretical ecology—describe, usually in a simple, abstract, and mathematically tractable form, how a system might respond in an idealized world. They are often used as the first step toward defining connections across scales. By organizing key concepts and processes and providing qualitative answers, they can be used to identify which parameters at one scale are likely to have greatest impact at others. The second category of functions is that of measured response functions, i.e., the measured response to a physical variable, as defined by Huey & Stevenson (1979). Measured response functions provide a practical means by which to connect a process at one level of organization (e.g., escape speed) to that at a higher level (e.g., survivorship). However, without a mechanistic explanation, the connection of measured response functions to processes at lower levels of organization (e.g., muscle physiology) is uncertain. To obtain full understanding of a system across multiple scales, it is therefore necessary to define and test the potential mechanisms that account for measured responses. These are response functions in the sense of the third category defined by Holling (1965): a mechanistic, quantitative explanation of the response of an environmental factor, physiological process, whole organism, population, or community as a function of some physical variable. At their most fundamental, mechanistic response functions 2 Denny · Benedetti-Cecchi A nn u. R ev . E co l. E vo l. Sy st . 2 01 2. 43 :1 -2 2. D ow nl oa de d fr om w w w . a nn ua lr ev ie w s. or g by S ta nf or d U ni ve rs ity M ai n C am pu s L an e M ed ic al L ib ra ry o n 07 /1 5/ 13 . F or p er so na l u se o nl y. ES43CH01-Denny ARI 1 October 2012 11:53 are explicit applications of the principles of physics, engineering, and chemistry; at higher levels, they may apply well-established principles of physiology, behavior, and statistical mechanics. Although their connections can be complex—and unexpected properties may emerge from their interactions—mechanistic response functions form the basis for our understanding of biology. RESPONSE FUNCTIONS: PRINCIPLES AND CHARACTERISTICS Two examples illustrate the formulation and utility of mechanistic response functions. The first describes response to a single variable and the second to multiple variables. Predator-Prey Response Functions In an elegant experiment, Holling (1959) blindfolded a student and had her tap her finger on a wall to locate randomly placed sandpaper discs. When a disc was located, the student removed it, set it aside, and searched again. The rate at which discs were “captured” was analyzed as a function of their spatial density. Noting that the student’s time was divided between searching for and handling discs, Holling derived a simple equation that accurately described how the student (a “predator”) responded to “prey” density (spatial density of disks). The resulting Type II response function (Figure 1) has since been found to accurately describe the response of a wide variety of invertebrate predators (Maynard-Smith 1974). The utility of the Type II function extends beyond its ability to accurately reproduce empirical results. For example, handling and searching times can be quantified directly and used to parameterize a Type II model independent of field measurements of predation. If this independently parameterized model fits field-measured data, we can be reasonably assured that we have discovered the pertinent mechanisms governing prey capture, whereas deviations from measured data provide evidence that the simple assumptions of the Type II model are inadequate. If, for example, refuges are available in which low-density prey can hide, the response function may be sigmoidal (Type III, Figure 1) (Holling 1965). As Nisbet et al. (2000) note, “In the search for mechanisms, deviations from model predictions are at least as instructive as data that support” a model. Prey density Ca pt ur e ra te Type II