Scaling aquatic primary productivity: experiments under nutrient- and light-limited conditions
John E. Petersen
INTRODUCTION
Temporal and spatial scales are increasingly recognized as key determinants of the patterns and processes observed in ecological systems (for reviews see O’ Neill 1989, Powell 1989, Wiens 1989, and Hoekstra et al. 1991, Holling 1992). How do we compare behavior between part and whole, between small scale and large scale, and between experiment and nature? Is each situation idiosyncratic, or can we identify fundamental scaling patterns or rules? Can experiments be explicitly designed to reveal scale-dependent behavior? These are questions that are relevant to experimental ecologists operating at all levels of the ecological hierarchy. Yet systematic experimental studies of scaling effects have not been conducted (Frost et al. 1988).
Primary productivity is a critical measure of ecosystem function, and has been used to track aquatic ecosystem response to a wide range of variables, including nutrient concentration (e.g., Oviatt et al. 1993, Taylor et al. 1995) and light intensity (e.g., Copeland 1965, Goldsborough and Kemp 1988). The importance of water depth as a fundamental scale regulating aquatic primary productivity has long been recognized (Riley 1942, Sverdrup 1953). Although primary productivity can be limited by both nutrient and light availability, there are important differences in their respective depth distributions. Light penetrating the surface is absorbed by water and associated dissolved and particulate substances as it passes down through the water column, generating a characteristic vertical profile (Kirk 1994). Nutrient concentrations, on the other hand, are essentially constant with depth in the upper mixed layer of a water column. This distinction suggests the possibility of important depth-dependent scaling differences when productivity is limited by light and by nutrients.
Although the question of depth scaling for aquatic productivity has not been directly addressed previously, there is indirect evidence that under steady-state, nutrient-rich conditions, phytoplankton growth and biomass often adjust such that euphotic depth corresponds with mixed-layer depth (Wofsy 1983). This implies that when phytoplankton are responsible for the majority of light absorption and other factors are held constant, depth-integrated gross primary productivity should be constant in different depth ecosystems. Indeed, similar depth-integrated productivity has been observed in three adjacent eutrophic coastal habitats receiving similar light energy, but dominated by phytoplankton, seagrasses, and benthic microalgae, despite the large (four orders of magnitude) difference in depth among the systems (Sand-Jensen 1989). The generality of these observations and how they might differ under nutrient-limited conditions are unclear, and deserve systematic and controlled examination.
Spatial variability and strong lateral and/or vertical water transport (e.g., Kemp and Boynton 1980) would make rigorous exploration of the dimensional patterns of primary productivity difficult in whole natural ecosystems. Experimental ecosystems (microcosms or mesocosms) provide a means of conducting ecosystem-level experiments under replicated, controlled, and repeatable conditions (Kemp et al. 1980, Odum 1984), and have therefore become widely used and accepted tools in ecology (Ives et al. 1996). As skeptics point out, however, artifacts associated with reduced size and enclosure may limit our ability to relate mesocosm results to natural systems (Schindler 1987, Carpenter 1996). An effective experimental design using mesocosms to study the scaling of primary productivity should therefore consider the impact of these artifacts as well as the impact of more fundamental depth effects.
In addition to depth, two other important spatial factors, system width and volume, should be considered in experimental design. Width determines the perimeter surface area per unit volume, and hence the relative importance of organisms that favor edge habitat (Gamble and Davies 1982, Kuiper et al. 1983). Since algae attached to container walls have been shown to contribute significantly to ecosystem productivity (e.g., Margalef 1967, Lodge et al., in press), we might expect to observe width- as well as depth-dependent scaling patterns in experimental ecosystems. The reduced volume of experimental ecosystems alters species richness (Dickerson and Robinson 1985) and trophic dynamics (e.g., Luckinbill 1974, Martaugh 1983, Peters and Downing 1984), which may in turn influence patterns of primary productivity. Since mesocosms vary widely in their physical dimensions (Gearing 1989, Beyers and Odum 1993), a thorough understanding of the impact of depth, width, and volume on productivity is an important prerequisite for meaningful extrapolation of results. While we are implying that width and volume effects are artifacts of experimental enclosure, these factors most likely represent genuine scaling effects on productivity in small natural ecosystems.
To explore scaling patterns in primary productivity, we constructed a set of cylindrical planktonic-benthic ecosystems scaled in two ways: with a constant depth of 1.0 m as volume was increased from 0.1 to 1.0 to 10 [m.sup.3], and with a constant shape (radius/depth = 0.56) over the same range of volumes. Experiments were conducted in three seasons to consider the scale-dependence of ecosystem productivity under high, low, and intermediate nutrient concentrations.
METHODS
Our experimental system consisted of 15 cylindrical mesocosms with five distinct dimensions and three replicates per dimension [ILLUSTRATION FOR FIGURE 1 OMITTED]. Mesocosms were organized into two series, one with a constant depth (1.0 m), and the other with a constant shape (radius/depth = 0.56). Constant-depth and constant-shape series shared a 1.0-[m.sup.3] intermediate volume dimension. Experimental systems were labeled A, B, C, D, and E in order of increasing container radius. A and B had volumes of 0.1 [m.sup.3], C had a volume of 1.0 [m.sup.3], and D and E had volumes of 10 [m.sup.3]. The constant-depth series was composed of A, C, and E mesocosms; the constant-shape series was composed of B, C, and D mesocosms. The small- and large-volume mesocosms (A and B, D and E) also formed pairs with constant volumes, but different shapes.
All systems were constructed of Sun-Lite (Kalwall, Incorporated, Manchester, New Hampshire), a fiberglass-reinforced glazing material. Experimental ecosystems received light from banks of fluorescent and incandescent bulbs on a 12:12 L:D cycle. Surface light [TABULAR DATA FOR TABLE 1 OMITTED] intensities averaged 147 [[micro]mol.][multiplied by][m.sup.-2][multiplied by][s.sup.-1]. Mean water temperatures were controlled by means of a thermostat-regulated air heating and cooling system.
Mixing was accomplished by means of large, slow-moving PVC impellers driven by motors that were programmed to alternate directions and to cease movement at regular intervals. Impeller dimensions and rotation rates were selected to generate a constant gypsum-dissolution rate among mesocosms, and to simulate the turbulence intensities associated with a semidiurnal tidal cycle in Chesapeake Bay (L.P. Sanford, unpublished manuscript). This mixing regime resulted in essentially no resuspension of bottom sediments. Turbidity due to nonphotosynthetic particles was therefore low throughout all experiments. Mixing was also sufficient to prevent the formation of either horizontal or vertical gradients in dissolved oxygen. A summary of key physical parameters in the mesocosms is provided in Table 1.
Three seasonal experiments were conducted in 1994, with durations of 29, 51, and 46 d, respectively, in the spring (21 April-19 May), summer (6 July-25 August), and fall (18 October-2 December). Initial conditions included sediments (10 cm depth) composed of a mixture of commercial sand and local estuarine muds (1% organic matter after mixing), and a water column composed of unfiltered water from Chesapeake Bay [intake salinity ranged seasonally from 8 to 12 (practical salinity scale)]. Mesocosms were incrementally filled with both sediments and water such that any heterogeneity was well distributed among the different tanks. Although polychaete worms and small crustacea (copepods and amphipods) were included, fish and other major predators were excluded. Prior to each experiment, sediments were moved to a common tank, allowed to go anaerobic to reduce the abundance of benthic infauna, and homogenized by mixing with shovels. During the experiments, 10% of the water in each mesocosm was drained on a daily basis and replaced with filtered estuarine water. Nominal filter sizes were 2.0 in the spring experiment, and 0.5 [[micro]meter] in the summer and fall experiments. Summer and fall experiments were subjected to a nutrient pulse at midexperiment, after nutrient levels in the mesocosms had become depleted. The nutrient pulse was applied starting on Day 34 of the summer experiment and Day 21 of the fall experiment. In both cases, three pulses of nutrients were added at 12-h intervals to bring the concentration of ammonium up to 50 [[micro]mol]/L and phosphate up to 3.0 [[micro]mol]/L. Concentrations of dissolved Si were also adjusted to 50 [[micro]mol]/L to insure nonlimiting levels for diatom growth. Since we were explicitly interested in exploring artifacts associated with experimental ecosystems, a periphyton community was allowed to develop on the walls and impellers of the mesocosms over the course of each experiment.
Rates of ecosystem primary productivity and respiration were measured daily as diel variations in dissolved oxygen (Odum 1956, Welch 1968). Preliminary observations of diel patterns in [O.sub.2] in the experimental ecosystems revealed approximately linear increases and decreases during light and dark periods, respectively. These constant rates of change in [O.sub.2] enabled us to characterize metabolic activity with point measures of [O.sub.2] at dawn (lights on) and dusk (lights off). Routine measures of [O.sub.2] were made using polarographic electrodes (Model 2607, Orbisphere Labs, Emerson, New York) calibrated in air and with periodic Winkler titrations (Carritt and Carpenter 1966).
Characteristic coefficients for [O.sub.2] exchange across the air-water interface for each dimension mesocosm were determined directly. Prior to sediment addition, mesocosm containers were filled with tap water, water columns were sparged with nitrogen gas to reduce the concentration of [O.sub.2] to between 1.0 and 2.0 mg/L, and re-aeration of the water column was traced over time. These diffusion experiments were run under conditions of controlled temperature, salinity, and mixing rates. The diffusion coefficient, or “piston velocity,” was calculated as k = F/S, where k is the diffusion coefficient (meters per hour), F is the rate of [O.sub.2] exchange (grams of [O.sub. 2] per square meter per hour), and S is the saturation deficit (grams of [O.sub.2] per cubic meter). Diffusion coefficients (Table 1) were linearly dependent on mixing (rpm), but only weakly related to temperature and salinity over the range experienced in our experimental facility.
We developed several measures of ecosystem metabolism, including (1) net primary productivity (NPP), defined operationally as the rate of change in [O.sub.2] during the light portion of a day; (2) nighttime respiration (R), defined as the rate of change in [O.sub.2] during the dark (R is taken as a positive number); (3) gross primary productivity (6PP), defined as the sum of NPP and R; and (4) the NPP:R ratio. In our calculations of ecosystem metabolism, corrections for air-water exchange were made by multiplying the average oxygen saturation deficit during each 12-h period by the calculated diffusion coefficients. Saturated [O.sub.2] concentrations were calculated using published empirical relations (Benson and Krause 1984). An additional correction was made to account for [O.sub.2] lost or gained as a result of the 10%/d exchange of water. The derived measures of ecosystem metabolism initially had volumetric units (grams of [O.sub.2] per cubic meter per day). Since the systems were well-mixed, this change in dissolved oxygen represented the average volumetric metabolism rather than the metabolism at any particular depth.
Concentrations of dissolved inorganic nitrogen (DIN = [[NH.sub.4].sup.+] + [[NO.sub.3].sup.-] + [[NO.sub.2].sup.-]), dissolved inorganic phosphorous (DIP), and dissolved silica (DSi) were measured twice weekly in each of the experimental ecosystems. Water was removed from the center of the mesocosm by means of a siphoning tube, samples were filtered, and standard automated wet chemical methods were used to measure nutrient concentrations (Parsons et al. 1984; Autoanalyzer 2, Technicon Incorporated, Tarrytown, New York).
Statistical analyses were performed using conventional software (SYSTAT 1992). A t test was used to assess whether the slope of the NPP vs. R regression was significantly different from 1.0. Differences in the mean values of NPP, R, GPP, and nutrient concentrations among mesocosms of different dimensions were assessed for each season with ANOVA. Statistical significance was tested by comparing the variance among mesocosms of different dimensions with variance among replicate mesocosms of a given dimension. In the spring experiment, ANOVA was performed on metabolic rates after averaging over the duration of the experiment for each experimental ecosystem (the first day of the experiment was excluded). Similar statistics were applied to data from summer and fall experiments, except that separate ANOVAs were performed for data from before and after the nutrient pulses (data during [TABULAR DATA FOR TABLE 2 OMITTED] the 2 d following the first injection of nutrients were excluded from the analysis). Three physical factors were used to standardize measurement of productivity and respiration: water volume (in cubic meters), airwater surface area (in square meters), and photosynthetically active radiation (PAR, measured as micromoles of quanta per square meter per second). ANOVAs were performed on metabolism data expressed according to each of these factors. In spite of small differences in light energy received among mesocosms, patterns of GPP, NPP, and R expressed per unit area were generally statistically indistinguishable from patterns expressed per unit PAR. Emphasis is therefore placed on productivity expressed per area and volume. Differences in mean productivity among spring, summer, and fall experiments were also assessed with ANOVA.
RESULTS
Nutrients, light, and temperature
Average DIN and DIP concentrations in the experimental ecosystems were relatively high in the spring, low in the summer prior to the nutrient pulse, and intermediate in the fall prior to the nutrient pulse (Table 2). Nutrient concentrations were successfully raised to target levels during summer and fall nutrient-pulse treatments, and subsequently declined in both experiments. Incident light levels (PAR) at mesocosm water surfaces were held constant in the three experiments. Vertical light attenuation coefficients ([k.sub.d]) tended to increase with decreasing mesocosm radius (Table 1) due to absorbance at the walls, and average PAR levels at the sediment surface generally exceeded 30 [[[micro]mol][multiplied by][m.sup.-2][multiplied by][s.sup.-1]. Although an attempt was made to control room temperature, average temperatures were coolest in the spring, warmer in the fall, and warmest in the summer (Table 2).
Ecosystem productivity and respiration
We observed a clear relationship between NPP and R in all three experiments [ILLUSTRATION FOR FIGURE 2 OMITTED]. The slopes of the regression lines for this relationship are a measure of the NPP:R ratio for each experiment as a whole. These NPP:R ratios were not significantly different from 1.0 in any of the experiments, indicating a near metabolic balance between organic carbon production and consumption. Since values for NPP and R were closely coupled, net diel productivity (NPP – R) does not distinguish clearly between ecosystems that were very metabolically active (NPP and R both high) and ecosystems that were relatively inactive (NPP and R both low). Gross primary productivity (GPP = NPP + R) is a more sensitive integrated measure of the metabolic activity. From a theoretical perspective, GPP is also more directly related to light and nutrient limitation than NPP. Our analysis therefore focuses on GPP as a measure of experimental ecosystem productivity.
A seasonal pattern of increasing GPP (averaged over all mesocosms) with increasing water temperature was observed; mean values of GPP and temperature were highest in the summer experiment (5.1 g [O.sub.2][multiplied by][m.sup.-3][multiplied by][d.sup.-1], 22.9 [degrees] C), intermediate in the fall experiment (3.7 g [O.sub.2][multiplied by][m.sup.-3][multiplied by][d.sup.-1], 22.6 [degrees] C), and lowest in the spring experiment (3.5 g [O.sup.2][multiplied by][m.sup.-3][multiplied by][d.sup.-1], 21.4 [degrees] C). These differences were not, however, statistically significant.
Gross primary productivity in the constant-shape series
In the nutrient-rich spring experiment, there was no significant difference in productivity among mesocosms of different depth in terms of GPP per unit area (GPP/area; [ILLUSTRATION FOR FIGURE 3 OMITTED]). GPP per unit volume (GPP/volume), however, increased with decreasing depth [ILLUSTRATION FOR FIGURE 3B OMITTED]: the shallow B mesocosms were significantly more productive than the intermediate C mesocosms (B [greater than] C, P = 0.00), which were significantly more productive than the deep D mesocosms (C [greater than] D, P = 0.00).
Metabolic patterns in the nutrient-poor summer experiment (prior to the nutrient pulse) were exactly reversed from those in the spring experiment: GPP/area increased significantly with mesocosm depth (D [greater than] C, P = 0.00, C [greater than] B, P = 0.00, [ILLUSTRATION FOR FIGURE 4A OMITTED]), but GPP/volume was not significantly different among different depth mesocosms [ILLUSTRATION FOR FIGURE 4B OMITTED]. Immediately following the nutrient pulse, however, GPP/volume diverged while GPP/area converged: the difference in GPP/area between B, C, and D mesocosms became smaller or insignificant (e.g., D [greater than] C, P = 0.84), while the difference between GPP per unit volume became larger (e.g., C [greater than] D, P = 0.00). GPP also increased in all mesocosms following the pulse, providing further evidence for nutrient limitation.
A neuston layer covering a portion of the water surface of some of the mesocosms appeared following the nutrient pulse, presenting a potentially complicating factor in interpreting post-pulse data. This surface layer was composed primarily of pennate diatoms, and it appeared to result largely from the sloughing off of periphyton from the sides of the mesocosms rather than from material produced at the water surface. Since metabolic gases produced and consumed by organisms in the surface layer could exchange directly with the atmosphere, the contribution of neuston to ecosystem metabolism would not be reflected in measurements of [O.sub.2]. We feel that this contribution was probably small, but have no way of verifying this.
As with nutrient concentrations, the pattern of productivity in the fall experiment was intermediate between spring and summer experiments. Prior to the nutrient pulse, GPP per unit area increased significantly with increasing depth in a manner similar to the summer experiment (D [greater than] C, P = 0.01, C [greater than] B, P = 0.01, [ILLUSTRATION FOR FIGURE 5A OMITTED]). As in the spring experiment, however, GPP/volume increased as depth decreased across the series (B [greater than] C, P = 0.04, C [greater than] D, P = 0.01, [TABULAR DATA FOR TABLE 5B OMITTED]). In the fall experiment, these same patterns held true even after the nutrient pulse: GPP/area increased with increasing depth (B [greater than] C, P = 0.00, C [greater than] D, P = 0.00) while GPP/volume increased with decreasing depth (B [greater than] C, P = 0.00, C [greater than] D, P = 0.00). As in the summer experiment, a surface layer of neuston developed in some of the mesocosms following the nutrient addition.
Gross primary productivity in the constant-depth series
Differences in productivity among mesocosms in the constant-depth series were small relative to differences in the constant-shape series. Since the constant-depth series of mesocosms (A, C, E) are all 1.0 m deep, GPP expressed per unit area is numerically equivalent to GPP per unit volume (GPP/[m.sup.2] = 1 m x GPP/[m.sup.3]). In the spring experiment [ILLUSTRATION FOR FIGURE 6A OMITTED], GPP increased with increasing mesocosm diameter: the wide E mesocosms had higher GPP than the narrow A mesocosms (E [greater than] A, P = 0.05), and the C mesocosms were intermediate in GPP (although C was not statistically different from either A or E). In contrast, in the summer [ILLUSTRATION FOR FIGURE 6B OMITTED] prior to the nutrient pulse, GPP in the A mesocosms was significantly higher than in the E mesocosms (A [greater than] E, P = 0.03). After the pulse, this pattern of increasing productivity with decreasing radius was further amplified (A [greater than] C, P = 0.00, C [greater than] E, P – 0.01). In the fall experiment [ILLUSTRATION FOR FIGURE 6C OMITTED] prior to the nutrient pulse, there were no significant differences in GPP among mesocosms in the constant-depth series. As in the summer experiment, a pattern of increasing productivity with decreasing radius was evident following the nutrient pulse (A [greater than] E, P = 0.01, C [greater than] E, P = 0.02).
Gross primary productivity in constant-volume pairs
Data from the pairs of mesocosms with the same volumes but different shapes were generally consistent with the dimensional patterns evident in the constant-shape series. In the spring experiment, GPP/area in the 10 [m.sup.3] D-E pair was significantly greater in the shallow E than in the deeper D mesocosm (E [greater than] D, P = 0.02). There was, however, no significant difference in productivity per unit area between the 0.1 [m.sup.-3] A-B pain As in the constant-shape series, when the spring data were expressed per unit volume, productivity increased significantly with decreasing depth (B [greater than] A, P = 0.00, E [greater than] D, P = 0.00). In the summer experiment prior to the nutrient pulse, there was no statistical difference in GPP between either the A and B mesocosms or the D and E mesocosms when productivity was expressed per unit volume. When GPP was expressed per unit area, however, productivity was significantly greater in the deeper mesocosms in both pairs (A [greater than] B, P = 0.00, D [greater than] E, P = 0.00). In the fall experiment prior to the nutrient pulse, productivity increased with decreasing depth when expressed per unit volume (B [greater than] A, P = 0.01, E [greater than] D, P = 0.04), but increased with increasing depth when expressed per unit area (A [greater than] B, P = 0.00, D [greater than] E, P = 0.00).
DISCUSSION
Nutrient and light conditions
Primary productivity in aquatic ecosystems can be limited by nutrients and by light (e.g., Takahashi et al. 1973). Half-saturation constants for the uptake of key nutrients have frequently been used as a reference by which to assess the potential for kinetic nutrient limitation of primary productivity (e.g., Day et al. 1989). Nitrogen is typically the limiting nutrient in coastal environments, but phosphate and silica concentrations may also limit productivity under certain conditions (Ryther and Dunstan 1971, Valiela 1995).
Nitrogen availability varied seasonally in our experimental systems (Table 2) in much the same way that it does in temperate coastal waters (e.g., D’Elia et al. 1986, Fisher et al. 1992). Half-saturation constants for DIN uptake by coastal phytoplankton ([k.sub.n]) range from -2.5 [[micro]mol]/L for large phytoplankton (Eppley et al. 1969) to 0.5 [[micro]mol]/L for small phytoplankton (Goldman and Glibert 1983). Although there was a decline in DIN levels over the course of our spring experiment, concentrations remained well above reported [k.sub.n] values throughout. In our summer experiment, on the other hand, the average DIN concentrations (0.3-1.4 [[micro]mol]/L) were at or below the range of published half-saturation constants. The average concentrations of DIN in our fall experiment (2.4-4.1 p, [[micro]mol]/L) were close to or slightly above the range of half-saturation constants.
Concentrations of DIP were low in all seasons, and were near our detection limit of 0.01 [[micro]mol]/L during the summer. Reported half-saturation constants for DIP uptake vary widely, with typical values ranging from 0.05 to 0.2 [[micro]mol]/L for mixed-species assemblages of coastal phytoplankton (Furnas et al. 1976). Concentrations of DIP were within this range during the spring experiment, and below it during the summer and fall experiments (Table 2), with DIP concentrations lower in the summer than in the fall. The existence of substantial internal storage pools and differences in the bioavailability of orthophosphate render conventional values reported for [k.sub.p] somewhat ambiguous as indices of nutrient limitation (Fisher and Butt 1994). The pattern we observed here, however, at least suggests potential phosphorous limitation in the summer and possibly fall experiments.
The concentration of dissolved silica remained well above the range of half-saturation constants of 0.1-2.5 [[micro]mol]/L reported for mixed-species assemblages of marine diatoms (e.g., Azam and Chisholm 1976, Paasche 1980) in all three experiments. Similar values for half-saturation coefficients for nitrogen, phosphorous, and silica have been reported for microbial communities occupying benthic and periphytic habitats (e.g., Admiraal 1977, Welch et al. 1992).
In contrast to natural conditions, our experimental ecosystems were exposed to the same artificial light regime in spring, summer, and fall experiments. While there are several factors that can limit productivity, we assume that the rates we have reported tended to be limited by light when nutrient concentration exceeded the reported range of kinetic half-saturation coefficients, and by nutrients when concentrations were below half-saturation.
Gross primary productivity vs. depth under light-limited conditions
An important distinction between nutrients and light is that nutrients are typically quantified on a volumetric basis (e.g., micromoles per Liter), while light energy is quantified on an areal basis (e.g., micromoles of quanta per square meter per second). This distinction is a logical one in well-mixed aquatic ecosystems where primary producers experience nutrient concentration (and kinetic nutrient limitation) on a volumetric basis. Light energy, on the other hand, is received at the water surface on an areal basis and is absorbed as photons pass down through the water column.
In temperate lakes and estuaries, there is often a seasonal pattern in which primary productivity is limited by light in the spring and by nutrients in the summer (e.g., Wetzel 1975, Day et al. 1989). The dimensional differences in the way phototrophic organisms experience nutrients and light can he used to explore these seasonal patterns in primary productivity. Let P(z) equal productivity per unit volume at a particular depth in the water column. We can integrate this over depth z to derive [P.sub.a], the areal productivity,
[P.sub.a] = [integral of] P(z) dz. between limits z and 0 (1)
Average volumetric productivity, [P.sub.v], is obtained by dividing by depth,
[P.sub.v] = 1/z [integral of] P(z) dz = [P.sub.a]/z between limits z and 0. (2)
Light-dependent productivity is commonly modeled with hyperbolically shaped relations such as Ivlev or Michaelis-Menton (e.g., Kirk 1994). The initial slope of the light-saturating curve is linear, and a simple first-order equation can therefore be used to describe situations that are strongly light limited,
P(z) = [Alpha][I.sub.0] [e.sup.-[K.sub.d]z] (3)
where [Alpha] is the initial slope of the photosynthesis-irradiance curve, [I.sub.o][e.sup.-[K.sub.d]z] is the Beer-Lambert law of attenuation in which [I.sub.o] is the surface irradiance, and [K.sub.d] is the diffuse down-welling light attenuation coefficient (e.g., Kirk 1994). This equation can be integrated over depth (Eq. 1) to yield
[P.sub.a] = [Alpha][I.sub.o]/[K.sub.d] (1 – [e.sup.-[K.sub.d]z]. (4)
A special case of Eq. 4 occurs when [K.sub.d]Z, the optical depth, is large. Note that this term can be large as a result of a deep euphotic depth and/or high [K.sub.d]. In shallow eutrophic systems, high phytoplankton biomass can result in a high [K.sub.d] and large optical depth. In “optically deep” water columns, the (1 – [e.sup.-[K.sub.d]z]) term goes to 1 and
[P.sub.a] [approximately equal to] [Alpha][I.sub.o]/[K.sub.d]. (5)
The important consequence is that under these conditions, [P.sub.a] is independent of depth.
While Eq. 5 entails a few assumptions, the result is consistent with the rather intuitive idea that under light-limited conditions in which phytoplankton are responsible for the majority of light absorption, depth-integrated productivity should scale directly to the light energy delivered to the system. In dimensional terms, if incident light intensity is constant among systems of varying depth, then productivity per unit area as well as productivity per unit light energy should also be constant among these systems. On the other hand, if productivity is expressed per unit volume (Eq. 2), shallower systems will have higher rates than the deeper systems, for the simple reason that they receive more light energy per unit volume. Indeed, if productivity per unit area is constant ([P.sub.a] = [C.sub.pa]), then Eq. 2 dictates that productivity per unit volume ([P.sub.v]) should equal the constant productivity per unit area divided by z,
[P.sub.v] = [C.sub.pa]/z. (6)
Note that Eq. 6 describes a hyperbolic relationship between productivity (per unit volume) and euphotic depth. In our mesocosms, as in well-mixed shallow ecosystems in nature in which light extends to the bottom, water column depth, mixed-layer depth, and the euphotic depth are essentially synonymous terms. In deeper natural ecosystems, the argument presented here would apply only to productivity integrated over the euphotic depth.
Following the reasoning presented above, and assuming that the relatively high nutrient concentrations during the spring experiment resulted in light-limited conditions, we would expect vertically integrated GPP (i.e., GPP/area) to be constant among mesocosms in the constant-shape series, despite the fivefold variation in water column depth. Indeed, there were no statistical differences in GPP/area among these mesocosms ([ILLUSTRATION FOR FIGURE 7A OMITTED]: open circles, solid line). Because the shallow mesocosms received more light per volume than the deep mesocosms, Eq. 6 predicts that GPP/volume should increase with decreasing depth under light-limited conditions. This pattern was clearly evident in the spring data for mesocosms in the constant-shape series and for the constant-volume pairs ([ILLUSTRATION FOR FIGURE 7A OMITTED]: closed squares, dotted line corresponds to Eq. 6). Thus, the relationships between GPP and depth in the spring experiment are consistent with the patterns to be expected under light-limited conditions. It is important to recognize that in aquatic ecosystems with high inorganic turbidity or dissolved organic color, light absorbance by abiotic substances could substantially alter this scaling relationship between productivity per unit area and depth (e.g., Wofsy 1983).
Gross primary productivity vs. depth under nutrient-limited conditions
The dimensional pattern of nutrient limitation stands in contrast to that of light limitation. As with light limitation, the relationship between nutrients and productivity is commonly modeled with a hyperbolically shaped equation such as the Michaelis-Menton formulation. The linear portion of the curve for nutrient-limited productivity can be expressed in a manner similar to Eq. 3,
P(z) = [P.sub.max]/[2K.sub.s] (7)
where [P.sub.max] is the maximum rate of productivity, [K.sub.s] is the half-saturation constant for uptake of the limiting nutrient, and N is the concentration of the limiting nutrient. Since N is constant with depth in a well-mixed water column, the integration of Eq. 7 over depth is trivial,
[P.sub.a] = ([P.sub.max]/[2K.sub.s] N) z. (8)
For a particular nutrient concentration, the quantities in parentheses are constants and the equation can be simplified so that it is clear that integrated productivity increases as a simple first-order function of depth,
[P.sub.a] = [C.sub.pv]z (9)
where [C.sub.pv] = P(z) = [P.sub.v]. Note that Eq. 9 describes a linear relationship between productivity per unit area and water depth.
The low nutrient concentrations (typically below half-saturation values for N and P) evident during the prepulse period of the summer experiment indicate a strong potential for nutrient limitation. The increase in GPP following nutrient addition [ILLUSTRATION FOR FIGURE 4 OMITTED] provides further evidence for nutrient limitation. If these experimental ecosystems were, in fact, nutrient limited during this period, then the argument presented above implies constant GPP per unit volume among all mesocosms. Consistent with this expectation, we detected no statistical difference in GPP per unit volume among the mesocosms when rates were averaged over the prepulse period of the summer experiment ([ILLUSTRATION FOR FIGURE 7B OMITTED]: closed squares, dotted line). Likewise, productivity increased with increasing depth when expressed per unit area in reasonable accordance with Eq. 9 ([ILLUSTRATION FOR FIGURE 7B OMITTED]: open circles, solid line corresponding with Eq. 9). This pattern of constant productivity per unit volume and increasing productivity per area with increasing depth is also significant in the constant-volume mesocosm pairs (A-B and D-E). Thus, prior to the nutrient pulse, productivity rates from the summer experiment were consistent with the pattern expected under nutrient-limited conditions.
The nutrient pulse administered to each mesocosm midway through the summer experiment provided an opportunity to explore dimensional changes in productivity as the ecosystems presumably shifted from nutrient limitation to light limitation. Results are consistent with expectations based on scaling arguments [ILLUSTRATION FOR FIGURES 4A, B OMITTED]: immediately following the pulse, GPP/volume diverged significantly, while GPP/area converged significantly. In response to the nutrient pulse, the pattern of GPP among mesocosms of different depths became more like that of the light-limited spring experiment.
Nutrient conditions in the fall experiment were intermediate between spring and summer conditions. Prior to the nutrient pulse, GPP/area in the fall experiment increased significantly with increasing depth, suggesting nutrient limitation as in the summer experiment ([ILLUSTRATION FOR FIGURE 7C OMITTED]: open circles, solid line). When the data were expressed per unit volume, however, productivity increased with decreasing depth, suggesting light limitation as in the spring experiment ([ILLUSTRATION FOR FIGURE 7C OMITTED]: closed squares, dotted line). Unlike spring and summer experiments, neither Eq. 6 (light-limited conditions) nor Eq. 9 (nutrient-limited conditions) fit the data closely. Thus, dimensional patterns point toward simultaneous light and nutrient limitation during the fall experiment prior to the nutrient pulse. Interestingly, these same patterns of increasing GPP/area with increasing depth and increasing GPP/volume with decreasing depth held true even after the nutrient pulse in the fall.
Gross primary productivity vs. mesocosm width
The arguments presented thus far consider only the effect of water column depth, and suggest that productivity in mesocosms of constant depth should be constant regardless of diameter and regardless of nutrient status. Indeed, the differences in productivity among mesocosms in the constant-depth series during spring, summer, and fall experiments were small relative to differences among mesocosms in the constantshape series [ILLUSTRATION FOR FIGURES 7A, B, C OMITTED]. Depth appears to be a first-order length-scale that regulated patterns of primary productivity in our experimental ecosystems. There were, however, patterns and statistical differences in GPP among mesocosms in the constant-depth series that warrant consideration.
As stated previously, productivity per area and productivity per volume are numerically equivalent in the 1.0 m deep constant-depth series. Mesocosms in the constant-depth series differed from each other in both volume and radius. An important consequence of decreasing radius is an increasing ratio of wall area per unit volume. As a result of this changing ratio, the relative contributions of wall periphytic communities to total ecosystem metabolism increased with decreasing radius (Chen et al., in press). In addition, decreasing container radius resulted in increased vertical attenuation of light (Table 1). These two factors, combined with nutrient concentrations, provide clues to help explain seasonal differences in GPP among mesocosms in the constant-depth series.
The negative relationship between the light attenuation coefficient and mesocosm diameter was evident even when mesocosm walls were cleaned and the systems were filled with filtered water (Table 1). Since neither suspended particulate material nor periphyton on the walls were present when measurements were made, this variation in attenuation is largely attributable to light absorbed or scattered by the walls themselves. If most of this light was absorbed by the walls, then a smaller percentage of the incident light entering the narrow mesocosms would have been available for photosynthetic productivity than in the wider mesocosms. This implies that under the light-limited conditions, we should expect higher productivity in the wide mesocosms than in the narrow mesocosms. This explanation is consistent with the significant increase in productivity from the narrow A to the wide E mesocosms evident in the spring experiment [ILLUSTRATION FOR FIGURES 6A, 7A OMITTED]. This wall effect may be analogous to the presence of dissolved and suspended materials that compete with phytoplankton for light in turbid natural environments. Indeed, clever application of dimensional analysis might allow for simulation of deep and/or high-turbidity light conditions by manipulating the radius and light-absorbing properties of mesocosm tank walls.
Under low-nutrient conditions, differences in the relative contribution of wall periphyton and water column phytoplankton to total ecosystem productivity may play a more important role in explaining differences among mesocosms than light effects. An important difference between phytoplankton and periphyton in these experimental ecosystems was that 10% of the phytoplankton was washed out in daily water exchange, while wall periphyton remained relatively fixed in place. This means that narrow mesocosms with a higher wall area to volume ratio retained a larger percentage of their primary producers and associated nutrients (tied up in biomass) than did wide systems. It is also likely that nutrient cycling within the periphyton community was tighter and more efficient than nutrient cycling in the water column (see Bebout et al. 1994). This advantage of narrow mesocosms over wider systems may help explain the pattern of significant increase in GPP with decreasing radius evident in the summer experiment prior to the nutrient pulse [ILLUSTRATION FOR FIGURES 6B, 7B OMITTED]. The amplification of this pattern, which occurred following nutrient addition, can be explained by the simple fact that there was more plant biomass present (walls plus water column) to take advantage of the added nutrients in the narrow mesocosms. In the fall experiment, there was no statistically significant difference between mesocosms in the constant-depth series prior to the pulse, consistent with the intermediate nutrient status of the experimental ecosystems during this season.
Relative importance of depth, radius, and volume
It is important to consider a potential for confounding effects in the constant-shape series. Scaling for a constant shape as depth is increased necessarily entails both that mesocosm volume increase with increasing depth and that wall area per unit volume decrease with increasing depth. Thus, the effects of volume and wall area per unit volume are superimposed on depth effects. The fact that differences in GPP between mesocosms in the constant-depth series were small relative to differences in the constant-shape series suggests that volume and wall area per unit volume effects were second order with respect to depth effects. The fact that the constant-volume pairs (A and B, D and E) exhibited depth-dependent patterns of productivity that were similar to those in the constant-shape series provides further evidence that depth, rather than volume or surface area, was the scaling factor most responsible for observed differences in GPP in the constant-shape series.
Relating results from mesocosms to natural ecosystems
It has been suggested that mesocosms are best viewed as ecosystems in their own right that share certain characteristics with larger natural ecosystems, but that also possess properties uniquely attributable to size and enclosure (Odum et al. 1963, Oviatt et al. 1977, Leffler 1980). If this is the case, then the ability to meaningfully relate results from experimental ecosystems to nature is dependent on a clear understanding of these scaling effects.
Two classes of scaling effects can be distinguished. The first class might be termed “fundamental scaling relations.” These include differences in the behavior of ecosystems that can be directly attributed to fundamental aspects common to all ecosystems of a type. Understanding these fundamental scaling effects is a first step towards developing a set of “scaling rules” (sensu Frost et al. 1988) that can be used to quantitatively compare the behavior of different natural ecosystems as well as to relate results from small-scale experimental ecosystems to nature.
We view the dimensional patterns of seasonal productivity (vs. depth) in the constant-shape series mesocosms as an example of a fundamental scaling relation inferred from experimental ecosystem studies. These data provide strong evidence that primary productivity scales proportionally to surface area under light-limited conditions and to volume under nutrient-limited conditions. While the theoretical and empirical work of others (e.g., Wofsy 1983, Sand-Jensen 1989) implies depth effects on productivity in eutrophic aquatic ecosystems, a systematic investigation had not been conducted. No previous work had examined the dimensional control of productivity under nutrient-limited conditions.
The second class of scaling effects associated with experimental ecosystems might best be termed “artifacts of enclosure.” These are characteristics of experimental ecosystem structure and function that differ from natural ecosystems, purely as a result of enclosure. Artifacts of enclosure in aquatic systems include differences that can be attributed to periphyton growth on mesocosm walls, alteration in material exchange rates, and distortions in the mixing and light regimes that often occur in experimental ecosystems. We believe that the differences in productivity between mesocosms in the constant-depth series of our study are largely attributable to artifacts of enclosure. While perhaps of less inherent interest than fundamental scaling relations, artifacts of enclosure are also highly scale dependent, and a thorough understanding of these characteristics is essential for rational extrapolation of results from mesocosms to natural ecosystems.
As with simulation models, experimental models such as those used in this study are simplifications and abstractions of nature. A number of variables, including upper trophic levels and suspended sediments were intentionally excluded from our model ecosystems in order to isolate the “bottom-up” effects of nutrients and light on primary productivity in planktonic-benthic ecosystems. The great advantage of conducting mesocosm experiments is that these simplified and controlled conditions allow for the unambiguous identification of cause and effect. Given the characteristic variability of light and nutrient conditions and related factors in natural coastal ecosystems (e.g., Costanza et al. 1993), it is difficult to imagine how scaling relations for ecosystem productivity could have been easily derived from field experiments. Indeed, previous efforts to compare ecosystem productivity rates between adjacent estuarine regions along a depth gradient have been confounded by spario-temporal variability in [O.sub.2] associated with physical transport (e.g., Kemp and Boynton 1980).
The complexity and variability that characterize natural aquatic ecosystems also make straightforward extrapolation difficult. In Chesapeake Bay, our proximate natural analog, there are times when upper trophic levels and resuspended sediments probably alter the pattern of productivity from what we observed in our experiments. There are also, however, conditions under which the components that we included in our system probably dominate ecosystem productivity. Yet even when the governing processes are the same, differences in temperature and precise nutrient concentration complicate comparison. While our mesocosms provide evidence for fundamental patterns in the physical scaling of primary productivity, confident quantitative extrapolation to nature remains a significant challenge.
Our results suggest that research in experimental ecosystems can be used to clarify and provide initial tests of scaling hypotheses. Further evaluation of these hypotheses in the less controlled and more variable natural environment is a logical next step. We believe that the current debate regarding the utility of mesocosm research vs. direct manipulation of natural ecosystems (e.g., Schindler 1987, Carpenter 1996) is misdirected: both are valuable and complementary approaches from which to observe and explore ecosystem behavior. The direct extrapolation of results from experimental ecosystems to nature will likely remain a challenge for some time to come. We are, however, optimistic that experiments such as ours can be used to elucidate both fundamental scaling relations and artifacts of enclosure, and that the information gleaned from such studies will render experimental ecosystems considerably more valuable tools in the future.
ACKNOWLEDGMENTS
The research described in this paper was funded by the Environmental Protection Agency (EPA) as part of the Multiscale Experimental Ecosystem Research Center (MEERC) at the Center for Estuarine and Environmental Studies of the University of Maryland (grant number R819640). The work of John Petersen was performed under appointment to the Graduate Fellowships for Global Change Program administered by Oak Ridge Associated Universities for the U.S. Department of Energy (DOE), Office of Health and Environmental Research, Atmospheric and Climate Research Division. We gratefully acknowledge the technical assistance of numerous individuals, including Jennifer Goermer, Tim Goertemiller, Elgin Perry, and Tom Wazniak. We are indebted to several colleagues, including Marlon Lewis, Jeff Cornwell, Todd Kana, and Tom Malone for discussions regarding analysis and interpretation of these experiments. Finally, we wish to thank Victor Kennedy, Tom Frost, and James Grover for thoughtful reviews of the manuscript and constructive suggestions for improvement.
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