The Rise of the Concept of Scale in Ecology

Recognition of the concept of scale occurred rapidly in the 1980s, but the concept itself is far older. The last quarter of the 20th century witnessed major changes in the science of ecology, including increases in skill and rigor in the design of field experiments, the growth of mathematically based theory, computer-mediated advances in analytical capacity, and the accelerating capacity to acquire and retrieve data. These changes were accompanied by growing recognition of the problem of scale (Wiens 1989, Steele 1991, Levin 1992). The problem has three components. First, pressing problems in ecology often exist at the scale of decades and large ecosystems. Second, most variables can only be measured directly in small areas, over short periods of time. Relatively few variables, such as ocean color, can be measured at fine resolution over large areas via remote sensing. Most variables, and in particular most rates, can be measured only on site. Third, patterns measured at small scales do not necessarily hold at larger scales; nor do processes prevailing at small scales necessarily prevail at large scales. Consequently, pressing problems in ecology cannot be automatically addressed by scaling locally measured variables directly to larger areas and longer times. The classic example of the problem of scale is loss of biodiversity. The causes of species extinction occur at the scale of ecosystems, whereas measurements are of necessity confined to smaller areas. Yet no biologist would try to address the problem by direct extrapolation from local samples, because it is well known that species number does not scale directly with area. It has become increasingly clear that the same principle applies to any ecological problem. An example is research on recruitment variability in a major fishery such as that of cod, Gadus morhua(Figure 1). This fishery extended through the entire northeastern continental shelf of North America (Figure 1a) for centuries, until its collapse in the early 1990s. After the collapse, eggs and first-year juveniles were confined to coastal areas, where survival depends on suitable habitat. Habitat surveys can be made at the scale of coves or sections of coast (Figure 1b), but direct measurements of absolute density in relation to habitat can be made only by seine hauls in areas of a few hundred square meters (Figure 1c). Even within these small areas, habitat is highly heterogeneous (Figure 1d). Consequently, the ratio of area of interest (Figure 1a, b) to area surveyed (Figure 1c, d) cannot be used to estimate numbers and survival prospects at larger scales from direct measurements at smaller scales. The three components of the problem of scale are illustrated in diagrammatic form (Figure 2) for the problem of monitoring pollution-induced variation in benthic invertebrate numbers against a background of natural variation in Manukau Harbour, New Zealand (Thrush et al. 1997). Pollutants are dumped at point sources (lower-left part of Figure 2a), but continued dumping and tidal mixing extend the problem to larger scales (upper-right corner, Figure 2a). Experiments and surveys to identify natural sources of variation in benthic populations are confined by costs to areas smaller than the scale of the problem (Figure 2b). At these smaller scales, movement rates exceed mortality rates (Figure 2c); hence an increase in mortality is difficult to detect because of organism movement across the boundaries of monitoring sites. The concept of scale is now widely recognized as a central concern in ecology. How rapidly did this occur? What are the prospects that scaling concepts will lead to theoretical unification in ecology? This article reports on these questions at a convenient point in time, the end of the 20th century. The word scale has multiple meanings, contributing to its ambiguous usage in the ecological literature. The Oxford English Dictionary(Simpson and Weiner 1989) distinguishes 15 different meanings arising from two different roots. The Old Norse root in skal (bowl) gives rise to fish scales, the scales of justice, and hence, by extension, measurement by means of pairwise comparison of objects. Using an old-fashioned scale, one can assign a mass of 1 g to a beetle that balances a 1-g standard mass. The Latin root in scala (ladder) gives rise to musical scales, scaling a wall, and, by extension, measuring a length by counting steps or subdivisions. Using a ladder known to be 2 m in height, one can assign a height of half a ladder (1 m) to a bush. In ecology, the word scale has acquired several common technical meanings. This diversity in acquired technical definition, added to the diversity in origin of the word, works against attempts at standard definition. A more productive approach is simply to ask that the word be used with an appropriate qualifier. The research literature suggests that recognition of the concept of scale occurred suddenly in the 1980s: [1988] Kuhn's concept of a paradigm shift is a useful way to interpret the annual meeting of the ESA [Ecological Society of America]…. Every symposium or session I attended featured, included, or was structured by the concepts of scale and spatial patterns. I left feeling I had observed one of those rare creatures of the intellectual bestiary, a paradigm shift (Golley 1989, p. 65). [1997] We can no longer…cling to the belief that the scale on which we view systems does not affect what we see…. This is quite a different way of viewing the world than that which was in vogue a decade ago, and it is by no means yet widely embraced by everyone (Wiens 1999, p. 371). Recognition of the importance of scale has been rapid, based on how frequently the word scale appears in the ecological research literature. In a digital version of the associated journals Ecology and Ecological Monographs, the term spatial scale made its first appearance in the early 1970s (Marten 1972, Wiens 1973). The term appears with increasing frequency in the late 1970s (Figure 3a). In the 1980s, frequency of appearance grew exponentially, at a pace 10 times the rate of growth in number of articles per yearly volume (Figure 3a). During that decade, the term appears to have been most commonly used in these two journals to qualify a result as being found at a particular spatial scale. The digital archive ends at 1996, so analysis was extended by reading abstracts. Frequency of use in abstracts (Figure 3b) paralleled that in the text, with some indication of decrease after 1996. The concept of scale currently is explicitly used in about 15% of articles each year in the two publications. The sudden and exponential increase in explicit treatment of the concept of scale also occurred within a relatively old and specialized research area, the pelagic ecology of seabirds. In a comprehensive reference list on the topic (Schneider 1991), the two oldest articles were Collins (1884) and Murphy (1914). Publications that include reference to more than one space or time scale first appeared in 1980 (Schneider 1994b). The growth rate was exponential, at 18.9% yr−1 from 1980 to 1990. In terrestrial ecology, hierarchical levels are used to express the concept of scale (Allen and Starr 1982). The concept of organizational level in biology (cell, tissue, organ, organism) was initially extended to populations and communities in the second edition of Odum's ecology text (1959). The concept of hierarchy in ecology (Allen and Starr 1982) refers to a focal level constrained by large-scale dynamics. O'Neill et al. (1986) developed the idea that levels beyond that of the organism arise during the course of energy dissipation in ecosystems. Because the idea that “scale matters” is central to hierarchy theory in ecology, the increasing frequency of publication on the topic measures the rise in recognition of the concept of scale. A comprehensive list of 231 articles shows that the publication rate grew exponentially from 1969 to 1990 (Figure 3c). If the 63 nonecological publications in the list are removed, publication rate grew exponentially from 1973 through 1991, at 18.2% yr−1. The use of “hierarchy theory” and “spatial scale” indicates rapid recognition in the late 1970s and early 1980s, but the concept of scale in ecology is far older. For example, Johnstone ([1908] 1977) questioned whether catches from a limited area could be used to calculate the density of organisms for the entire Irish Sea. Greig-Smith (1952) quantified spatial patterns in plants and their environment at multiple scales. In a list of books and articles that use multiscale concepts (Schneider 1994a), publication occurs throughout the 20th century, with exponential growth in the 40-year period after World War II (Figure 3d). The drop after 1991 reflects the completion of the reference list in early 1992, with a few articles added during manuscript revisions in 1992 and 1993. The increase in recognition of the concept of scale depends on how the search is defined. Sudden appearance followed by exponential growth was found when the term spatial scale or the concept of hierarchy theory was considered. Sustained growth over nearly a century (interrupted only by World War II) was found in a reference list from a review that aimed at comprehensive coverage of the concept of scale in ecology, regardless of whether the word scale was used (Figure 3d). Figures with both space and time scales as axes first appeared in the ecological literature in 1978, when John Steele modified a diagram used in physical oceanography (Stommel 1963). Stommel's three-dimensional diagram showed variability in sea level against both space and time scales. Steele used Stommel's space and time axes to draw two different diagrams. Steele's first diagram showed the space and time scales of patchiness of phytoplankton, zooplankton, and fish (Figure 4a). This space–time (ST) diagram was conceptual, showing the scales of named phenomena. A conceptual ST diagram first appeared in terrestrial ecology 5 years later (Delcourt et al. 1983). Steele's second diagram compared the time and space scales of coverage by a single oceanographic research cruise with coverage by an oceanographic program using several ships (Figure 4b). This diagram was instrumental in that it showed the capacity of a particular instrument (research vessel in Figure 4b). An instrumental ST diagram first appeared in terrestrial ecology 13 years later (Firbank 1991). ST diagrams are highly effective in comparing space and time scales of ecological questions to the capacity of research programs. In agricultural research, Firbank (1991) used an instrumental diagram to compare the space and time scales of experiments with those of surveys. In general, surveys extended beyond 10 km, with time scales of days to decades. Experiments were at the scale of a meter, with times scales ranging for 1 to 100 years. ST diagrams comparing phenomena to instrumental capacity have been published in research on disturbances in arctic ecosystems (Walker and Walker 1991) and on benthic experiments (Schneider et al. 1997). The format used by Steele (1978) was modified by Horne and Schneider (1994) to show critical scales that mark change in prevailing dynamics. In these diagrams, a contour line marks the space and time scales at which two rates are of the same order of magnitude. At larger scales one rate prevails, while at smaller scales the other rate prevails. Figure 2c shows critical scales for movement versus mortality in the benthic bivalve Macomona liliana. Comparison with Figure 2b shows that experimental data occur in the “domain of scale” (Wiens 1999) dominated by kinematics (movement) rather than demographics (mortality). A search of the literature turned up more than 60 diagrams with axes showing both space and time scales. The list excluded reprints of earlier diagrams, which were common, but did include modified versions of earlier diagrams. These graphical expressions of the concept of scale increased exponentially from 1980 to 1998 (Figure 3e). Conceptual ST diagrams (such as Figures 2a and 4a) were common during the 1980s, whereas critical-scale diagrams (such as Figure 2c) accounted for many of the plots after 1996. Instrumental ST diagrams (such as Figures 2b and 4b) appeared throughout the period. In an instrumental ST diagram, the distance between two points is called the scope, or ratio of extent to resolution. In Figure 4b, the spatial scope of the multiship Fladen experiment is roughly 100 km / 0.8 km = 125, compared to a fish stock survey, with a spatial scope of roughly 1000 km / 20 km = 50. The idea of scope is widely applicable. The scope of a meter stick with a resolution of 0.001 m is 1 m / 0.001 m = 103. The scope of a survey of 200,000 km2 sampled with plots of 50 m by 100 m is 200,000 km2 / 0.005 km2 = 4 × 107. A computational model representing population dynamics at half-day intervals for 3 years has a scope of 1095 days / 0.5 days = 2190. Halving the time step doubles the scope to 4380. Until recently, power laws in ecology came mostly from the literature on species-area curves or body-size allometry. Rosenzweig (1995) discussed 48 articles that included species-area curves. In this list, the number of articles grew exponentially, at 4.8% yr−1 from 1920 to 1980. In organismal biology, Peters (1983) listed 251 articles containing 1050 power laws that scale organism form or function to body size. Growth in the number of articles (Figure 5a) was linear from 1950 to 1980. Growth in the number of power laws (Figure 5b) was exponential from 1930 to 1980. Power laws for species-area curves and body-size allometry (Figure 5) were not derived from theory. These scaling relations were empirical, estimated by regression rather than calculated from a set of theoretical statements. These empirical power laws do not meet Hempel's criterion (1964) that a theory must state the conditions leading to a result that can be tested against data. Nevertheless, several scaling theories do meet Hempel's criterion (1964). An example is the theory (Sarrus and Rameaux 1839, in Kleiber 1947) that respiration scales with euclidean surface area, which in turn scales as volume2/3 and, hence, mass2/3. Another example is the theory that respiration scales with fractal surface area of the lung and hence scales as volume2.17/3 or mass0.72 (Pennycuick 1992, Schneider 1994a). More recently, West et al. (1999) theorized that supply rate in a branched network such as a vascular system scales with internal surface area A = L2+ϵ, and active tissue volume V = L3+ϵ+ζ; hence delivery scales as V(2+ϵ)/(3+ϵ+ζ). Delivery is maximized at ϵ = 1 and ζ = 0, hence delivery scales as volume3/4 or mass3/4. Another theory that meets Hempel's criterion (1964) is that power laws arise from local interactions in disorganized physical systems when they near some critical state (Widom 1965, Wilson 1971). The appearance of a power law describing structure when dynamics are near a critical state is called universal scaling or complexity theory (Milne 1988). heterogeneous systems that to critical are called et al. 1988). An example of is the appearance of power law of in the at in and at multiple scales because with the result being collapse that to scales larger than those of In population biology, Levin and of large-scale patterns from locally as in the of In structure at the scale of a from by and Power law in data when dynamics and 1997). Figure shows the of in a population model as the between and loss In this example, in time scales of rates to the variability over multiple scales, from any one scale. Figure shows the appearance of dynamics in a time model as the rate the between and A relation of in number to scale a line on a as the time in the of in Figure A few of the theory of dynamics do not theory in ecology. a large number of problems in ecology are to analysis by this theory. A and widely known example is the number of species in systems The dynamics meet the conditions for the of from extinction on species that via or and Wilson an theory of loss versus in ecosystems. dynamics a more theory, leading to or on whether on with a analysis on the critical point at which the of local only the analysis a way of the of in of habitat. ecology on ecological processes against of spatial structure such as of habitat are more listed for and The structure of suggests that rates are at versus versus In ecology, one can to rates a power law (such as a habitat At time scales, a change in species number can be as the of extinction rates on the of as these rates with to each is in the of species number through time. The problem of and scale is the central problem in ecology, population biology and and and ecology 1992, p. the concept that “scale matters” is a central concern of ecology, we have only of a theory of scaling (Wiens 1999, p. has become a central concept in ecology. it become a The could not have been years The of the of Ecology were in a in Ecology and of the major in ecology at the time, only three on multiscale the word scale explicitly or that “scale than 20 years and the concept of scale at the of their a of the theory of dynamics exceed It is not that the concept of scale, and in particular the theory of dynamics will some theoretical to ecology. In systems where loss and where is no and where does not theory is to In systems where rates where is and where does dynamics are of and “hierarchy suggests that recognition of the problem of scale in ecology occurred as a sudden shift in the late 1970s and early The concept itself is far older. treatment of the the use of the word scale, early in the 20th century. treatment both space and time scales in treatment based on power laws 1920 for the scaling of species number to area and for the scaling of organism form and function to body size. In power laws that from interactions near critical In biology, power laws arise from dynamics when and exponential or The theory of dynamics applies to a of phenomena. It has the to some theoretical to ecology. to for in and for research on scaling theory came from the and The manuscript was during a at the of of with from the of the I and for and on early The manuscript was in to by three The of measurement scale distinguishes variables quantified on a scale an scale an scale such as and a ratio scale steps and known such as scale is the ratio of the distance on a to the distance on the A of the world has a scale of about refers to the extent to the of a by time or space (Wiens 1989, Schneider 1994a). so have a area or time period or within some of measurement or For example, a annual changes over periods of of years. In multiscale the in a measured or the relation of two measured is with a of different scales. This is by the between measurements or the for measurements (Milne 1997). Ecological scaling Peters refers to the use of power laws that scale a to body to a scales as hence, a in body increases by = rather than by a of scale as the distance some of interest The problem of scale in ecology. of cod, Gadus in rates at the scale of in the habitat variation at the scale of surveys. Habitat variation at the scale of direct measurement of density in seine Habitat variation at the scale of experimental of survival The problem of scale in ecology. the of coastal on benthic of are throughout Manukau in New data to the natural and variation in benthic population are confined to limited areas from Schneider et al. 1997). At the scale of surveys and experiments, rates of movement exceed mortality rates in the bivalve Macomona use of the concept of scale in ecology. periods in which growth rate was with the term spatial scale in the with the word scale in the and books on hierarchy theory. and books that more than one space or time scale, whether or not the word scale is of the concept of scale, as measured by publication of diagrams with axes as use of space–time diagrams in ecology from Steele Conceptual diagram showing versus in and fish shows mixing scales, measured as relation of of in with time in Instrumental space–time diagram showing space and time scales by of in of the concept of scale by power laws that organism form or function to body size. of articles with power laws listed by Peters of power laws listed by Peters (1983) Figure of from exponential In a time population model with loss on time increase as the rate increases from = / time to = / time In the the time and scales as per time step as in the The increases from two steps to 50 steps as from to