In ecological systems, as elsewhere, complexity arises because processes interact on multiple scales. It has already been pointed out that different periodicities can interact to produce chaotic patterns. More generally, the interactions among scales--spatial, temporal, and organizational--and the need to study the behavior of systems across scales lend a complexity that is missed in studies that are restricted to a single scale. Any study is necessarily limited spatially and temporally, and in terms of the components that can be described. However, pattern is manifest on multiple scales simultaneously; and the investigator, by choice of perceptual scale, selects only a slice of the pie.

   As suggested in the introduction, even the simplest nonlinear mathematical models describing population dynamics can exhibit very complex behavior (May, 1976). In particular, the discrete logistic,

N(t + 1) = N(t) + rN(t)(1 -N(t)/K), (1)

if initiated from positive population density N(O), will always tend to the carrying capacity K when r is smaller than 2. However, as r is increased, the asymptotic dynamics pass through a sequence of bifurcations to cycles of length 2, 4, 8, 16, ..., finally giving way to chaotic behavior when r is sufficiently large (May, 1974, 1976). The reason for this behavior is that the compensatory responses implicit in the nonlinear feedbacks are too strong, and cause the population density to overshoot the values that would lead to regulation.

   Similar behavior can be observed, for analogous reasons, in continuous time models that include explicit delays, e.g. due to gestation, or even in models where the delay is implicit, as for example where the population is structured into age classes or stage classes. In the latter cases, since individuals must move through a series of explicit stages of development, a potentially stabilizing response that is mediated, for example, in the adult stage cannot be manifest immediately after the stimulus that initiated it; that is, the system exhibits a delay in its compensatory response. This delay is every bit as effective as an explicit one in leading to complex dynamics (Guckenheimer et al., 1977).

   Similar reasoning also can help us to understand the familiar oscillations observed in predator-prey systems, or at least in models of predator--prey systems, although these systems do not show chaotic oscillation. The rise of predator density in response to a rise in prey density is a potential regulator of the system. However, this regulatory response is delayed, because it takes time for the predator population to reach levels adequate to put a brake on prey densities; the same applies to the predator's negative response to reduced prey densities, and to the prey's response to increasing or decreasing predator densities. The delays prevent the system from achieving equilibrium, and result instead in the familiar limit cycle oscillations.

   The problem of forced oscillations has already been mentioned. In systems where these are important, as for example when seasonal dynamics are superimposed on a system that has its own characteristic frequency of oscillation, the system may go through quite complicated fluctuations as the intrinsic and extrinsic periods compete for influence. One of the fundamental problems in examining data sets is to sort out the multiple causes of fluctuation. Methods such as Fourier analysis can be suggestive in identifying the primary modes of oscillation; but such methods lose their effectiveness in highly nonlinear systems in which oscillations are not merely additive.

   The previous comments have been directed to the question of temporal fluctuations. Similar problems are faced in analyzing spatial patterns. In general, the key first step is to determine the degree to which the system is driven by external influences, and the degree to which its dynamics are autonomously controlled. This again is a property of scale; as dimension is increased, the system becomes more heterogeneous, less open to the external environment, and often statistically more regular. The questions of variability and predictability are intimately tied up with the question of scale, and cannot be addressed in the abstract.

   The first observation is that the ecosystem or ecological community is operationally defined, according to the convenience of the investigator. The cell biologist has the luxury of knowing exactly what his or her fundamental unit is; the ecosystem scientist, on the other hand, must recognize that the measured properties of an ecosystem will vary as the scale and extent of description are changed. Different investigators, studying similar systems, are likely to view those systems through different prisms, because of the some-what arbitrary definitions that must be made concerning the scale of description. For this reason alone it would be important to develop methods for studying how the dynamics of systems change across scales.

   There are, however, other and equally compelling reasons. For the evolutionary ecologist it is clear that organisms perceive the environment through their own filters, and that the scales of variability experienced by diverse species, with distinct patterns of dispersal, dormancy, and other life history traits, will be equally diverse. In ecotoxicology the scaling problem is at the core of the science, whose validity rests in large part on the assumption that it is possible to scale up from laboratory bioassays and microcosms, and from field mesocosms to large-scale natural systems. In biotechnology, similar assumptions underlie the use of small-scale field testing of products that are intended for wide-scale applications.

   As our awareness of global climate change and its consequences becomes more acute, so too does the desire in many quarters to couple the predictions of climate change with predictions of impacts on ecological and agricultural systems, and of their mutual effects on one another. But our understanding of these processes is on very different scales; the finest general circulation models, which form the basis for climate change prediction, use a basic grid cell measuring hundreds of miles on a side, whereas ecological models live in a far smaller world. The orders of magnitude difference between the scales of climate and ecological models has turned the attention of many to the need to develop methods to allow us to extrapolate across scales. Similarly, but to a lesser degree, the resolution limits associated with remotely sensed information mean that there are scale differences between the information that comes from those studies, and our understanding of the processes underlying it. The need to relate pattern on one scale to underlying processes on finer scales is a familiar one throughout science, and is the basis for extrapolation beyond the realm of experience.