An allometric scaling rule as applied to the infaunal size spectrum was previously hypothesized for aerobic respiration vs. DO concentration (Rakocinski, 2009). Analogous to light limitation in plants (Causton, 1983), the proposed scaling rule assumes a hyperbolic relationship between oxygen supply and mass-specific respiration (V_O2). In fact, a hyperbolic aerobic respiration relationship relative to oxygen availability has been applied to various marine metazoans (Bayne, 1971; Bridges and Brand, 1980; Chen et al., 2001). The traditional hyperbolic model for oxygen consumption rate (OCR), OCR = DO/(K1 + K2 × DO) (Bayne, 1971), specifies how the mass-specific OCR should increase with ambient DO concentration (Chen et al., 2001). Moreover, this model can be rearranged to obtain the hypothesized hyperbolic DO limitation relation: OCR = (K2 + K1/DO)⁻¹, from which the horizontal OCR asymptote can be estimated as OCR_max = 1/K2 (Rakocinski, 2009). The OCR parameter, K2, presumably reflects various paths of diffusion and biochemical resistance affecting the conductance of O₂ within the organism (Herreid, 1980). Under an oxyconforming strategy, K2 should reflect metabolic limitations and design constraints in accordance with non-mutually exclusive principles of the Metabolic Theory of Ecology (MTE, 3/4 power law; fractal branching networks) (Brown et al., 2004; Finlay and Esteban, 2007) and Dynamic Energy Budget Theory (DEB, 2/3 power law; surface area: volume scaling) (Kooijman et al., 2008). Specifically, small organisms should show less capacity to regulate oxygen uptake than large organisms as DO availability declines, due to the need to maintain higher mass-specific OCR (Bridges and Brand, 1980). This trade-off is also conveyed by the ratio of the hyperbolic curve parameters, first noted as the oxygen-dependence index by Bayne (1971). The index, K1/K2, is obtained from the linear relationship between ambient P_O2/V_O2 vs. P_O2 (Livingstone and Bayne, 1977; Bridges and Brand, 1980), and reflects the metabolic capacity for regulating aerobic respiration (Chen et al., 2001). Thus, a lower OCR capacity (OCR/OCR_max; where OCR_max = 1/K2) reflects relative oxyconforming as ambient DO declines; and a greater capacity to sustain OCR (i.e., oxyregulation) is signified by a lower K1/K2 ratio. Moreover, a value of 1 for K1/K2 indicates a transitional capacity for regulating OCR (Chen et al., 2001). Indeed, the ratio K1/K2 clearly decreases with body size for marine metazoans (Chen et al., 2001), which implies that larger organisms possess relatively greater oxygen regulation capacity (Bayne, 1971; Taylor and Brand, 1975; Bridges and Brand, 1980).

An allometric metabolic scaling rule proposed by Rakocinski (2009), hypothesized that the slope of the log-log body mass vs. K1/K2 relationship for oxyconforming was −0.285 (i.e., intermediate between 3/4 and 2/3 scaling rules). Furthermore, the proposed relationship was symmetrically centered on 1 (i.e., the transitional capacity for regulating OCR; Chen et al., 2001) across eight common geometric scaled (octaves base 2) size-classes spanning the estuarine infaunal size spectrum for the northern Gulf of Mexico (Qu et al., 2015). However, this metabolic scaling rule has not been tested using any robust data sets. Moreover, the joint effect of temperature and oxygen concentration on the bearing of the proposed hypothesis has not been fully considered.

Higher temperatures intensify metabolic demands (Robinson et al., 1983; Clarke and Fraser, 2004), and hyperbolic mass-specific OCR curves accordingly reach elevated asymptotic levels (i.e., 1/K2). Observed increases in K1/K2 with temperature (Bridges and Brand, 1980) further imply a reduction of oxyregulating capacity at warmer temperatures under declining DO concentrations (Chen et al., 2001). As seen for body size, a concomitant rise in K1/K2 with temperature also reflects higher maintenance costs in the form of an elevated physiological work load (Clarke and Fraser, 2004). Conversely, organisms show a greater capacity to oxyregulate at cooler temperatures (Herreid, 1980). As noted by Chen et al. (2001), aerobic respiration rates appear relatively independent of environmental DO concentration at cooler temperatures. Consequently, large organisms should be especially capable of oxyregulating at cool temperatures; whereas small organisms should be more disposed to oxyconforming at warm temperatures. Here we consider whether the aerobic respiration pattern of a model tolerant polychaete, Capitella teleta (formerly Capitella sp. I), conforms to these expectations in ways that accord with the allometric scaling hypothesis.

The tolerant opportunistic polychaete, Capitella teleta, is often associated with organically enriched sediments, and is widely distributed from temperate to subtropical waters in the northeastern United States, Japan, and the Mediterranean (Grassle and Grassle, 1974, 1976; Blake et al., 2009). This subsurface deposit feeder is well adapted to disturbance and environmental stress (Linke-Gamenick et al., 2000). Consequently, it regularly dominates during hypoxic conditions in the northeastern US (Mangum, 1973; Forbes et al., 1994; Sagasti et al., 2001; Wu, 2002; Levin et al., 2009). Various adaptations to hypoxia and other stressors distinguish C. teleta, including a small body size (i.e., high surface area/mass), short-life span (i.e., r-selected), respiratory pigments, ventilation behavior, and the capacity for anaerobic respiration. As C. teleta is also currently experiencing warming within its geographic range, (Laffoley and Baxter, 2016) http://www.nefsc.noaa.gov/press release/2013/SciSpot/SS1304/, this species is ideal for considering interactive effects of hypoxia and temperature. Stock cultures of C. telata were obtained from the laboratory of Dr. J. Grassle, and maintained at 15°C and 27 psu in order to provide subjects for measuring aerobic respiration (Burns Gillam, 2016). In this paper, we examine mass-specific respiration by C. telata with regard to the metabolic scaling hypothesis.

Aerobic respiration (V_O2; mg O₂/mg/h) was measured in 3 mL of salt water and complete darkness for subjects of various sizes (0.14–14.1 mg WW) exposed to 12 treatment combinations of DO (20, 50, 70 and 100% saturation) and temperature (15, 20, and 25°C) (salinity = 27 psu) (Burns Gillam, 2016). Sizes of subjects spanned across five of the eight geometrically-scaled size classes within the designated infaunal size spectrum (Rakocinski, 2009). Prior to measuring respiration, C. telata were acclimated to treatment conditions for 24 h in the presence of 6 g (ca 5 mm depth) of enriched sediment within a sealed air chamber (BioSpherix) into which nitrogen gas was pumped (Proox Model 360) to reach the target DO saturation level by diffusion. Worms had also been preacclimated to the treatment temperature for an additional 24 h at ambient P_O2 before being introduced into the air chamber. Oxygen consumption was measured for individuals under treatment conditions using either an Oxygen Cuvette (Qubit Systems, Canada) respirometer, accompanied with a polarographic Clark-type O2 electrode connected to a C410 LoggerPro Interface (Vernier Software and Technology, USA) (i.e., 20 and 25°C), or with an optical FireStingO2 oxygen meter (PyroScience, Germany) within 10 mL syringes sealed with stopcocks (i.e., 15°C) (Burns Gillam, 2016). Readings using both instruments (i.e., at 20°C and 100% DO) showed similar spreads in sample residuals relative to the overall allometric relationship, indicating consistent results between instruments. Each of the 12 treatment combinations was represented by respiration measurements from 14 to 21 individuals of various sizes (total n = 208).

Because our primary interest was in relating body-size responses to DO and temperature, a common proportionality constant (a = 0.0096; where V_O2 = aW^b) was estimated as the mean of the twelve coefficients from individually fit V_O2 curves [R package - nonlinear least squares routine (nls)]. The same constant was then used to fit a family of new V_O2 curves for which only the size-related exponent (b) varied. Next, the size-related exponents from the family of V_O2 curves were collectively fit by a non-linear response surface, for which significant terms for a constant, DO saturation, temperature and the DO × temperature interaction were included. The non-significant term for temperature was subsequently excluded from the final response-surface model in order to derive the best predictive tool from the data (Allison, 1999). The fitted model surface describing the response by the size-related exponent: b = −0.7100 + 0.0038 × DO − 0.0002 DO × Temp (R₂ = 0.725; F = 11.863; P = 0.003; Regression df = 3; Residual df = 8; n = 12; Table 1).

To compare projected (i.e., observed) oxygen consumption rates (OCR) to expected OCR based on the metabolic scaling hypothesis, four dynamic (i.e., fluctuating) 32 d exposure scenarios characterizing relatively severe vs. moderate hypoxia at warmer vs. cooler temperatures were created (Rakocinski, 2009). For each dynamic scenario, 768 h OCR values were generated for each of the eight geometric body-size classes within the size spectrum. The fitted response surface for b was used to generate maximum respiration (OCR_max) values (from OCR b' = V_O2^(1+b)), by holding DO saturation at 100% and salinity at 27 psu (i.e., the experimental salinity) for each hourly temperature value within the series. Accordingly, OCR_max was estimated at 1/K2 (i.e., asymptote) from the predicted OCR curve for 100 percent DO saturation at the specified temperature.

The OCR_max values were used for obtaining expected OCR proportions (OCR_prop = OCR_exp/OCR_max), and projected OCR proportions (i.e., OCR_proj = OCR_obs/OCR_max). Observed (OCR_obs) oxygen consumption values were obtained for each hourly observation in the simulated exposure series using the fitted nonlinear response surface for b (DO as saturation using O2.saturation function for R; Miller, 2014). Expected proportions were also calculated for each hourly observation as OCR_prop = OCR_exp/OCR_max; where OCR_exp = (K2 + K1/DO)⁻¹ (Rakocinski, 2009), and K1 = the hypothetical scaling factor (i.e., hypothetical K1/K2) multiplied by K2 [i.e., K1 = (K1/K2 × K2)]. Scaling factors were obtained for each size-class by applying the point-slope rule, assuming a slope of −0.285 and a value of 0 (i.e., K1/K2 value of 1) corresponding with the mid-size spectrum point for the log-log form of the relationship between K1/K2 with body size. The parameter K2 was obtained from OCR_max = 1/K2, as 1/ OCR_max, and DO concentration was in mg L⁻¹, following Chen et al. (2001). For the cooler temperature series, warmer series values were decremented by 10°C (i.e., Q10).

To compare expected and observed oxygen consumption for the four dynamic exposure scenarios in light of the proposed metabolic scaling hypothesis, mean expected vs. mean observed OCR proportions were plotted for the eight size classes. The extent to which expected vs. observed OCR proportions followed a 1:1 linear relationship within the plot indicated agreement with the scaling hypothesis, and the extent to which values followed a horizontal line at 1.0 on the y-axis indicated agreement with an oxyregulating strategy. To consider how abruptly or gradually aerobic respiration strategies transitioned with respect to temperature and DO saturation, OCR proportions for the eight size classes were also examined for 12 static combinations of DO saturation (20, 50, and 75%) and temperature (15, 20, 25, and 30°C).

The family of allometric V_O2 curves for which the size exponent (b) varied (i.e., while a was constrained) accurately fit the data; curves were significant relative to body size for every combination of temperature and DO saturation (t = 43.86–102.30; P < 0.0001; Figure 1). Fitted size exponents (b) varied from −0.80 to −0.58. Conversely, inferred exponents (b') for allometric oxygen consumption (OCR) curves (i.e., b' = 1 + b) varied from 0.20 to 0.42 (i.e., considerably lower than metabolic scaling exponents of 0.67 or 0.75). Clearly, V_O2 curves were higher and steeper at warm temperatures (i.e., 25°C) than at cooler temperatures, reflecting higher mass-specific respiration, in particular by small organisms (Figure 1). Individuals exhibited the highest V_O2 values under high levels of temperature and DO.

The response surface describing how the V_O2 size exponent (b) changes relative to joint variation in DO saturation and temperature was expressed in a complex nonlinear form (Figure 2; Table 1). The fitted response surface reflected the influence of a significant constant, as well strong effects of DO, and a synergistic interaction between DO and temperature (Table 1).

The two dynamic scenarios comprising 32 d fluctuating DO series in combination with alternate temperature series illustrate how hourly DO-temperature exposure regimes might vary latitudinally (Figure 3). The warmer series portrays temperatures near the thermal limit and outside the normal regime to which the test species is adapted. When paired with the severe hypoxia series, hourly temperature series (n = 768) averaged 30.2°C ± 0.7 and 20.2°C ± 0.7 (mean ± SD) for warm and cool series, respectively. Likewise, DO saturation averaged 22.1% ± 8.7 (mean ± SD) (mean DO = 1.4 mgL⁻¹ warm and 1.7 mgL⁻¹ cool) for the severe hypoxia series, for which all 768 DO values were <4 mgL⁻¹, 762 were less than 3 mgL⁻¹, and 658 were less than 2 mgL⁻¹. When paired with moderate hypoxia series, hourly temperatures (n = 768) averaged 30.5° C ± 1.1 and 20.5° C ± 1.1 for warm and cool series, respectively. Likewise, DO saturation averaged 69.8% ± 18.9 (mean DO = 4.4 and 5.4) for the moderate hypoxia scenarios, for which 305 DO values were <4 mgL⁻¹, 67 were <3 mgL⁻¹, and 8 were <2 mgL⁻¹.

Depending on the corresponding temperature series, scenario projections based on the C. telata model exemplified divergent aerobic respiration strategies, as delineated by reference lines within proportional OCR space (Figure 4). Moreover, the oxyconforming patterns for the scenarios closely agreed with the proposed scaling hypothesis (Figure 4A). Specifically, under the higher temperature scenarios, observed OCR_proj values for the size classes closely tracked expected OCR_prop values based on the hypothetical scaling rule (Figure 4A). As expected, smaller organisms oxyconformed to a greater extent than larger organisms, which also infers relatively greater metabolic depression for smaller organisms. Notably, size-classes were displaced to positions indicating less stringent oxyconforming along the metabolic scaling line under the moderate hypoxia-high temperature scenario compared to the severe hypoxia-high temperature scenario.Coordinates for size-classes were less spread out under moderate hypoxia than severe hypoxia for both warm and cool scenarios.

For scenarios at cooler temperatures, size series tended to follow the oxyregulation reference line (Figure 4A). However, OCR_proj values were positioned noticeably above the oxyregulation line for the severe hypoxia scenario at cool temperatures, indicating hyper-regulation relative to normoxia at the same temperature for all size classes. Relatively greater hyper-regulation reflected higher metabolic costs for small organisms. Size series converged closer to the oxyregulation reference line and shifted toward the intersection of the oxyregulation and metabolic scaling reference lines under the moderate hypoxia regime. Hyper-regulation was accordingly relaxed for small organisms, and all sizes regulated better under moderate than severe hypoxia at cooler temperatures. Consequently, size series were less separated within proportional OCR space between the two temperature regimes under moderate than severe hypoxia. In general, all size classes oxyconformed at higher temperatures, and oxyregulated at lower temperatures. Moreover, all size classes oxyregulated better under moderate hypoxia than under severe hypoxia.

To consider how abruptly organisms transitioned between respiration strategies, observed OCR_proj vs. expected OCR_prop values were compared for the eight size classes under static combinations of three DO saturation levels (20, 50, and 75%) crossed with four temperature levels (15, 20, 25, and 30°C). Coordinates for the size classes within proportional OCR space at 20 and 30°C agreed closely with the dynamic scenarios, which were at similar temperatures. However, observed OCR_proj vs. expected OCR_prop values at 15°C under hypoxia indicated even greater hyper-regulation by all sizes compared to the cool dynamic scenarios. Again, smaller organisms showed greater hyper-regulation than larger organisms at 15°C. Indeed, the smallest size class exhibited a 2-fold higher respiration rate at 15°C and 20 % DO than at 15°C and 100 % DO.

Size spectra tracked close to the metabolic scaling reference line at 25°C; however, they were visibly displaced from the reference line within the oxyconforming portion of proportional OCR space (Figure 4B). Size spectra shifted progressively and converged toward the metabolic scaling reference line with increasing DO saturation at 25°C. Again, small sizes exhibited lower observed OCR_proj values than large organisms. Thus, 25°C approaches the pivotal temperature for showing how size spectra transition from oxyregulating to oxyconforming respiration strategies, as projected by the C. telata model.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.