An empirical model for estimating aquatic invertebrate respiration


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1. The role of metazoan respiration in aquatic system energetics has been neglected to some extent, particularly because limited resources hamper the simultaneous determination of individual respiration rates across many taxa. As global warming will affect poikilotherm metabolism on an ecosystem scale, we need versatile models to estimate respiration from ‘easy-to-obtain’ parameters.

2. Artificial neural networks were trained to estimate mass specific respiration of aquatic metazoans from 28 parameters: temperature, water depth, 19 taxon categories, body mass and 6 lifestyle parameters. The data base includes 22 920 data sets referring to 915 taxa (836 identified to species, 67 to genus, 12 to higher taxon) from 452 different sources.

3. Overall model fit is good (R2 = 0·847), but there is considerable residual variability of up to two orders of magnitude.

4. Variability of same species measurements between sources is almost as large as same-source variability between species, i.e. a substantial part of the residual variability in the data may represent methodical bias.

5. There are no universally valid scaling factors in the relationships of respiration to body mass and temperature, but a wide range of species-specific factors.

6. The model has been implemented in a Microsoft EXCEL spreadsheet that is available at http://www.thomas-brey/science/virtualhandbook.


Metabolic activity, i.e. the sum of all bodily processes that involve energy and matter transformation, is the foundation of life, as we know it. Therefore, the whole body metabolic rate is central to the understanding of physiological as well as of ecological function. Despite this significance, the role of metazoan respiration in system energetics has been neglected to some extent in aquatic ecology (Del Giorgio & Williams 2005). For instance, the leading aquatic ecosystem modelling tool Ecopath/Ecosim (Christensen, Walters, & Pauly 2005) does not use respiration as an input parameter, but estimates it en passant from other parameters of the energy budget. The significance of metabolic activity for the prediction of global warming effects on aquatic ecosystem functioning (e.g. O’Connor et al. 2009) further emphasizes the need for more intense studies.

Whole body metabolic rate can be approximated directly through the heat loss of an organism, i.e. the inevitable loss of energy tributed to the second law of thermodynamics, by means of calorimetry (see e.g. van Ginneken et al. 1994). The common approach, however, is the measurement of aerobic respiration, i.e. the amount of oxygen consumed per unit of time. Aerobic respiration is a reasonable approximation of metabolism in most animals under standard (=resting) conditions. Starting with Brody & Procter (1932), Kleiber (1932) and others, the standard respiration rate (i.e. of a resting, fasting, non-stressed animal) of literally thousands of species has been measured so far (see e.g. Clarke & Johnston 1999; Glazier 2006; Lovegrove 2000; Makarieva et al. 2008; White, Phillips, & Seymour 2006 for more recent data compilations). Today, the common ground is that mass specific (i.e. per unit of body mass) standard respiration rate MSR scales with body mass M by a power function, MSR ≈ Mb, and exponentially with temperature, MSR ≈ ec/T. However, whether there are universally valid scaling factors b and c is a matter of active debate (see Brown et al. 2004; Glazier 2006; Kozlowski & Konarzewski 2004; White et al. 2006; Seibel 2007 for recent contributions). Apparently, even if such general scaling factors exist, there is substantial natural variability, e.g. owing to specific body designs or during specific phases of ontogenetic development (e.g. Glazier 2006; White et al. 2006).

As fruitful as this ongoing debate is, the applied aquatic ecologist feels a bit left alone when confronted with the task of estimating respiration of metazoan populations, functional groups or even whole communities. More often than not, extensive determination of individual respiration rates deems impossible, owing to limited resources or to logistic constraints. The alternative is the use of empirical models that relate respiration rate to body mass, to environmental parameters (temperature, water depth) and sometimes to other, lifestyle-related parameters. Regrettably, most published models referring to aquatic invertebrates are based on rather small data sets and/or on a limited number, range or resolution of independent parameters (for examples, see e.g. Del Giorgio & Williams 2005; Hernández-León & Ikeda 2005; Begum et al. 2009). Such models may serve well for the specific case, but when applied in a different context, they may be of unreliable or low accuracy.

Hence, there is demand for a robust tool that can approximate aquatic invertebrate respiration with acceptable or at least predictable accuracy across a wide range of taxa, environmental conditions and lifestyles. To create such a tool, we need an extensive data base and a suitable modelling approach. Data are abundant in the literature, they just have to be extracted and standardized. All predictive respiration models constructed so far are multiple linear models (MLM), which potentially suffer from two basic problems: (i) they include a priori assumptions about type and consistency of the relationships between dependent and independent parameters that may not be met completely in reality, albeit they might be theoretically well rationalized (e.g. Brown et al. 2004); and (ii) they are very sensitive to intercorrelation between independent parameters (see Draper & Smith 1981). One alternative are artificial neural networks (ANN): they can model complex, nonlinear and non-continuous relationships as encountered in ecological data (Lek & Guégan 2000), although initially they do not offer the same ‘insight’ into the principles of scaling (linear, exponential, etc.) as MLM do. Thus, an ANN provides the opportunity to test whether an MLM is able to catch the essential relationships between parameters, too. ANN are computer programs that are characterized by massively parallel but highly interconnected architecture. They are able to learn and to generalize relationships between input and output data from examples presented to the network (e.g. Dayhoff 1990; Fausett 1994). ANN are increasingly applied to a variety of tasks in aquatic ecology ranging from taxonomic identification to diversity pattern prediction (e.g., Brey, Jarre-Teichmann, & Borlich 1996; Lek & Guégan 2000; Belgrano, Malmgren, & Lindahl 2001, Olden 2003, Pei et al. 2004, Dedecker et al. 2005; Willems et al. 2008).

Thus, the objectives of this are:

  • • to construct an ANN model for the estimation of mass specific standard respiration rate (MSR) in aquatic invertebrates;
  • • to identify and compare major sources of remaining variability in the data set;
  • • to test theory based predictions of the scaling of MSR with body mass and temperature.

Materials and methods

Data acquisition and conditioning

The data base of this study consists of data sets. One data set represents one single measurement of respiration rate, accompanied by information on the animal (body mass, taxonomy, lifestyle), the environment (habitat, water depth) and the respiration measurement setup (temperature, system, sensor).

Relevant literature was tracked through the Aquatic Sciences and Fisheries Abstracts data base (ASFA) of FAO (, through web search engines, and through the catalogue and inventory of the AWI library. Several colleagues provided unpublished data (see Acknowledgements). Each data source was carefully checked for comprehensible procedures, completeness of information and methodical flaws. The temperature at respiration measurement Texp was of particular concern. To qualify for ‘ecophysiologically meaningful’ data, measurements had to meet the following conditions:

  • • Texp must be within the annual temperature range of the habitat;
  • • Texp must be within the range Tcapture ± 50% (temperature at capture);
  • • If Texp <> Tcapture, then acclimatization time must be at least 1 day/1°.

Original units of body mass were converted to Joule using factors provided by the conversion factor collection of Brey (2001). Original units of respiration were converted to J/day using general factors taken from Elliott & Davison (1975), Gnaiger (1983), and Ivlev (1934). Accordingly, the unit of mass specific respiration rate MSR is J/J/day. Taxonomic position was described by a simplified seven-level taxonomic hierarchy, consisting of species, genus, family, superfamily/order, order/subclass, class, (sub-)phylum The corresponding information was retrieved from the Integrated Taxonomic Information System (ITIS) online data base, (, from the World Register of Marine Species ( and from various other online sources. Lifestyle was characterized by feeding type (herbivorous, omnivorous, carnivorous), by mobility type (sessile, crawler, facultative swimmer, permanent swimmer/floater) and by vision type (defined as possession of image-forming eyes sensuSeibel & Drazen 2007, i.e. an optical sense better than just light/dark separation). I presumed vision capability to be present in scallops, cephalopods, euphausiaceans and decapods in general, if not stated otherwise for a particular taxon, and in a few representatives of other taxa with known vision capability such as Cyclopidae (Copepoda). Two parameters described the physiological state of the animal, starved (explicitly starved over longer time, or just unfed), and active (active vs. resting). The experimental setup was described by temperature, measurement system (closed, intermittent flow, continuous flow) and O2 measurement device (the most commonly applied methods are the Winkler method and polarographic electrodes, but Cartesian divers, couloximetry and micro-optodes are frequently used, too). In many cases, respiration data had to be retrieved from figures. These were digitized and analysed by the public domain software ImageJ ( A total of 22 920 data sets referring to 915 taxa (836 identified to species, 67 to genus, 12 to higher taxon, see Appendix S1) from 452 different sources (see Appendix S2) formed the base of this study. After excluding phyla with less than 50 data sets (Bryozoa, Sipuncula, Gnathostomulida, Gastrotricha, Echiura) as well as all data referring to animals in the ‘active’ state, the data base reduced to 22 621 data sets and 904 taxa (Table 1).

Table 1.   Taxonomic distribution of data and species numbers in the initial collection of respiration data
(Sub-) PhylumNDataNSpeciesClassNDataNSpecies
  1. Further data (299 data, 12 species) refering to major taxa Bryozoa (20), Sipuncula (12), Gnathostomulida (17) Gastrotricha (3) and Echiura (7) and data measured in ‘active’ animals (240) were excluded a priori.

Total22621904 22621904

Data transformation and pre-analysis

I transformed the variables MSR and the continuous independent variables body mass M, temperature T and water depth D by approximating linear relationships according to theoretical considerations, published empirical evidence, and the a priori exploration of the present data set. The transformation aimed (i) at a more even distribution of data and of variance in the (M, T, D) space, and (ii) at reducing nonlinearity which both facilitate ANN model fitting capabilities. The relationship between metabolic rate and body mass M follows a power function (MSR ≈ Mb; e.g. Schmidt-Nielsen 1984; Brown et al. 2004), i.e. log(MSR) vs. log(M). Temperature effects are modelled best by a Van’t Hoff–Arrhenius type relationship (MSR ≈ eE/(k*T); e.g. Clarke & Johnston 1999; White et al. 2006), i.e. log(MSR) vs. 1/T. The relationship to water depth is nonlinear, when present (Childress et al. 1990; Herring 2002; Drazen & Seibel 2007; Seibel & Drazen 2007), i.e. log(MSR) vs. log(D) appears to be the appropriate linearization.

Pre-analysis by means of anova indicated that the lifestyle characteristics could be reduced to five significant nominal parameters, sessile, crawler, swimmer, carnivorous and vision. Starting from the (sub-) phylum level, taxonomic resolution was modified through a try-and-error approach to achieve an optimum trade-off between the number of taxonomic categories and model accuracy (Fig. 1). As measurements of ‘active’ animals were excluded, the parameter starved remained as the sole descriptor of the physiological state of the animal. The measurement system exerted no particular effect on MSR, whereas the use of O2 measurement devices was strongly correlated to taxon and body mass, thus such technical parameters were not used in the model.

Figure 1.

 Scheme of the artificial neural network used to predict mass specific respiration rate (MSR) from three continuous parameters (temperature, depth, body mass) and 25 categorial parameters (19 taxa, 5 lifestyle, 1 experimental condition). Mollusca 1: Heterodonta and Paleoheterodonta, Mollusca 2: other Bivalvia, Mollusca 3: Gastropoda, Mollusca 4: other Mollusca. Crustacea 1: Euphausiacea, Crustacea 2: Mysidacea, Crustacea 3: other Malacostraca, Crustacea 4: other Crustacea.

Multivariate outliers in the sample space [log(MSR), log(M), log(D), 1/T] were identified by Mahalanobis Jackknife distances (Barnett & Price 1995) and excluded from further analysis.

Predictive model construction

Artificial neural networks of the backpropagation type (Hagan, Demuth, & Beale 1996) consisted of 28 input nodes (X), four hidden nodes (H), and one output node (Y), i.e. log(MSR), see Fig. 1. The network was parameterized as follows:

Y = (a0a1 × H1 + a2 × H2 + a3 × H3 + a4 × H4) × a5 +a5,


H1 = ƒ(b0 + b1 × X1 + b2 × X2 + … + b28 × X28),

H2 = ƒ(c0 + c1 × X1 + c2 × X2 + … + c28 × X28),

H3 = ƒ(d0 + d1 × X1 + d2 × X2 + … + d28 × X28),

H4 = ƒ(e0 + e1 × X1 + e2 × X2 + … + e28 × X28),

and the sigmoid transfer function ƒ(x) = 1/(1 + ex). Note that internally the input data are normalized (mean = 0, SD = 1) and that the network parameter values are adjusted accordingly.

To avoid over-fitting of an ANN, the data were split randomly in 75% training data and 25% test data (Lek & Guégan 2000). The ANN ‘learned’ the relationship between dependent and independent variables from the training data. Subsequently, I tested the generalization capability of the ANN by comparing prediction accuracy in training and test data as measured by the correlation between measured and predicted values. Five ANN, each trained on a different set of data, were pooled into a composite prediction model, i.e. the predicted value is the average of the predictions made by five ANN. This approach allows us to compute confidence limits of the prediction, too. The ANN constructed in this study have been implemented in a Microsoft EXCEL spreadsheet which is available for download at http://www.thomas-brey/science/virtualhandbook (Brey 2001). This file includes two routines: ‘Estimate’ predicts MSR from a set of 28 input variables provided by the user, and ‘Explore’ allows to check the data base for potential bias at any taxonomic level by means of the residual plot.

To see to what extent taxonomic diversity and methodical bias account for remaining variability in model estimates of MSR, I analysed differences in residual MSR of the same species but measured by different references as well as differences in residual MSR of different species but measured by the same reference. Further, I used the MLM:

log(MSR) = a + b1 * log(M) + b2/T; [J/J/day, J, K],

to explore the between-species variability of the relationships between MSR and body mass (all species with ≥25 data sets and body mass range ≥1 order of magnitude), and between MSR and temperature (all species with ≥25 data and temperature range ≥4 K).


Mahalanobis Jackknife distance analysis identified 616 outliers (P = 0·975), thus reducing the data to 22 005 data sets (853 taxa). These data cover 10 orders of magnitude in terms of body mass (10−3·5 to 106·7 J), whereas temperature ranges from 271 K to 309 K, and water depth from 0·5 m to 2500 m (whereby intertidal is set to 1 m depth always, but some freshwater sites are shallower than 1 m), albeit with the majority of data referring to shallow waters <100 m (Fig. 2).

Figure 2.

 Distributon of the 22 005 data sets used for model building with respect to temperature, water depth and body mass.

Goodness-of-fit of the 28 parameter ANN as measured by the correlation (R2) between predicted and measured log(MSR) ranges from 0·828 to 0·835 for training data and from 0·824 to 0·830 for test data in the five ANN models, on average R2 of test data is 0·005 lower. R2 of the composite ANN model amounts to 0·847. For comparison, the corresponding MLM [log(MSR) vs. log(M), log(D), 1/T, interaction terms log(MSR) × log(M), log(MSR) × log(D), taxon with 19 levels, mobility with 3 levels, carnivorous, vision, starved, log(D) × vision, mobility × vision, carnivorous × vision) achieves an R2 of 0·768.

I inferred overall scaling factors and lifestyle effects on MSR present in the ANN model from an anova of ANN estimates log(MSRANN) vs. log(M), 1/T, log(D), mobility, carnivorous, vision and starved. The interspecific scaling factors amount to MSRANN ≈ M−0·200, MSRANN ≈ e−6402·374/T and MSRANND−0·030. This anova and the corresponding partial leverage plots (Fig. 3) confirm that body mass has the strongest and water depth the weakest effect on MSRANN. Moreover, there is no significant deviation from linearity, i.e. the ANN model confirms the general suitability of the presumed scaling principles. MSR of mobility types ranks swimming >sessile > crawling (P < 0·001). MSR is lower in animals without vision than in those with vision, in carnivorous than in non-carnivorous, and in starved compared with non-starved animals (all P < 0·001).

Figure 3.

 Overall effects of temperature, water depth and body mass on MSR as modelled by the artificial neural networks (ANN). Partial leverage plots of the linear model: log(MSRANN) = 8·416 − 0·200 × log(M) − 2780·516/ T − 0·030 × log(D) + X1 + X2 + X3 + X4. X1 = −0·168, 0·011, 0·157 for crawling, sessile, swimming; X2 −0·032, 0·032 for carnivorous, non-carnivorous; X3 0·081, −0·081 for vision, no-vision; X4 = −0·024, 0·024 for starved, non-starved. The plots show the residual of each data point both with (distance from solid line) and without (distance from horizontal stippled line) the corresponding effect in the model. The wider the angel between both lines the stronger is the effect of the corresponding parameter.

Despite the good overall correlation, there is considerable residual variability for single MSR estimates (Fig. 4). On the level of taxonomic classes, however, average residuals are <0·10 in 26 out of 29 cases (Fig. 5). Predictions of MSR are particularly biased in Secernentea (Nemata), and two classes of echinoderms, Ophiuroidea and Asteroidea. anova of differences in residual MSR of the same species but measured by different references and of differences in residual MSR of different species but measured by the same reference indicated a strong effect of both species and reference. Species effects were significant (P < 0·01) in 69% of all cases analysed (N = 76), whereas reference effects were significant in 60% of all cases (N = 62, Fig. 6).

Figure 4.

 Plot of residuals (predicted − measured log(MSR)) vs. estimated log(MSR) of the composite artificial neural networks (ANN) model. Superimposed are the residuals of the cephalopod superorders Decabrachia (N = 99, mean = −0·1367, dots) and Octobrachia (N = 89, mean = 0·1628, squares).

Figure 5.

 Mean residual (predicted − measured log(MSR)) of the composite artificial neural networks (ANN) model for all classes with ≥25 data sets or ≥3 species. Numbers in brackets indicate Nspecies; Ndata.

Figure 6.

 Comparison of reference effects on MSR (left) with species effects on MSR (right). Distribution of significance level (P) of anova of residual log(MSR) of the composite artificial neural networks (ANN) model vs. reference within one species (≥2 references/species, ≥10 data/reference; 76 cases tested) and anova of residual log(MSR) vs. species within one reference (≥2 species/reference, ≥10 data/species; 62 cases tested).

On average, species-specific MSR scales with body mass by a power of −0·278 (SD = 0·115, N = 164), Values vary by one order of magnitude, from −0·664 to −0·064 (Fig. 7), but nevertheless the average is significantly different from −0·25 (P = 0·017) as well as from −0·33 (P < 0·001, Wilcoxon signed rank test). MSR scales with the inverse of temperature on average with an exponent of −7726·136 (SD = 3477·860, N = 81). If we interpret this relationship as driven by biochemical kinetics according to the Van’t Hoff–Arrhenius model, i.e. MSR ≈ eE/(k*T), a hypothetical activation energy E (kJ mol−1) can be computed from the exponent (E = slope · k · NA, where k is the Boltzmann constant, 1·3806504 × 10−23 J/K, and NA is the Avogadro constant, 6·02214179 × 1023). Mean E amounts to 64 kJ mol−1 (range 24–180 kJ mol−1; Fig. 8), and does not differ significantly (P = 0·567, Wilcoxon signed rank test) from the average E of biochemical reactions (±58 kJ mol−1, Gillooly et al. 2001).

Figure 7.

 Intraspecific relationship between mass specific respiration rate MSR and body mass M. Distribution of values for slope b1 in the linear model log(MSR) = a + b1* log(M) + b2/T (J/J/day, J, K) for those 163 species with N ≥ 25, body mass range ≥1 order of magnitude and significant slope b1 (P < 0·05).

Figure 8.

 Intraspecific relationship between mass specific respiration rate MSR and temperature T. Distribution of values for activation energy E derived from slope b2 in the linear model log(MSR) = a + b1 × log(M) + b2/T (J/J/day, J, K) for those 81 species with N ≥ 25, temperature range ≥4 K and significant slope b2 (P < 0·05).


Our ANN model confirms that body mass and body temperature (equivalent to water temperature in ectotherms) are by far the most significant determinants of respiration rate, whereas water depth is of lesser overall significance (Fig. 3). A negative effect of depth on MSR has been observed in several taxa across a much wider depth range, e.g. Childress et al. (1990), Seibel & Drazen (2007) and Torres, Belman, & Childress (1979). These may be residual temperature effects (Childress et al. 1990) or behavioural adaptations, whereas pressure is unlikely to affect respiration rate (Teal 1971). Drazen & Seibel (2007) and Seibel & Drazen (2007) demonstrate that distinct depth effects are present in visually oriented pelagic animals (e.g. finfish and squids). They hypothesize that declining light levels discriminate against highly mobile visual predators with corresponding high-metabolic activity. The ANN model confirms this view to a certain extent: for instance, respiration rate of swimming malacostraceans without vision capability is independent of water depth, whereas in swimming malacostraceans with vision capability, the model predicts a decrease in MSR with water depth that starts at about 250 m (Fig. 9). Seibel & Drazen (2007) found no depth effect in a number of other taxa with different lifestyle. However, it remains to be seen whether this holds true for all invertebrates. The present data set, for instance, indicates significant (anova, P < 0·001, slope <−0·1) depth effects in Echinoidea (slope = −0·172, N = 1001), Asteroidea (slope = −0·140, N = 43) and Sagittoidea (slope = −0·276, N = 456).

Figure 9.

 The significance of vision capability for the effect of water depth on mass specific standard respiration rate (MSR). Contour plot of log(MSRANN) (J/J/day) vs. 1000/T (K) and log(D) (m) in swimming Malacostraca without (a) and with (b) vision capability. Contours are created from a 20 × 20 × 20 matrix in the log(MSRANN) × 1/T × log(D) space.

Regarding mobility, it comes as a surprise that MSR is lowest in crawling animals compared with sessile and swimming ones. It might well be that we have a definition problem of ‘standard’ metabolism here. Most sessile animals use the same water transport mechanism for ventilation and food gathering, e.g. sponges, bivalves, cirripeds, tunicates. That is, the costs for water transport are part of the standard MSR. During respiration measurements, swimmers are usually restrained from roaming wide distances, but the costs of staying afloat are part of standard MSR, too. Crawling animals, in contrast, are not able to move around much during measurements usually. Their costs of locomotion are not included in standard metabolism, albeit they can be substantial (e.g. McNeill Alexander 2005). Thus, in the active state, crawlers may well show higher MSR than sessile animals. The higher MSR in non-carnivorous compared with carnivorous animals is difficult to interpret. In this data base, there are nearly as much crawling carnivores (N = 3045) as swimming ones (N = 3749). Most of these do not resemble our picture of a typical highly active prey-chaser such as finfish or cephalopods. Many are rather slow moving scavengers than true predators, e.g. among crustaceans and echinoderms. And, as discussed above, crawlers have a lower standard MSR anyway. On average, MSR is higher in animals with vision, but the MLM indicates complex albeit significant interactions between vision and water depth, carnivorous and mobility type (see above).

To evaluate the joint explanatory power of the 25 categorical parameters (taxon, lifestyle), I constructed five ANN with input parameters body mass, temperature and depth only (three input nodes, three hidden nodes, one output node). Goodness-of-fit of the average of these ANN was R2 = 0·698, i.e. the categorical variables contribute about 17% to overall explanatory power of the model (R2 = 0·847).

Despite our sophisticated ANN modelling approach and the resulting good model fit (R2 = 0·847), there is considerable residual variance of up to two orders of magnitude in terms of single MSR predictions (Fig. 4). That is, our model shows good overall accuracy, but relatively low precision. There are four likely sources of this variance: (i) incomplete representation of the existing variability by the current set of parameters, (ii) faulty data generation, (iii) neglected biological and ecological factors, and (iv) suboptimal network architecture.

The most recent attempts to establish a ‘general model for the origin of scaling laws’ (West, Brown, & Enquist 1997; see also Gillooly et al. 2001; Brown et al. 2004 and others) spurred a lot of criticism for conceptual shortcomings (e.g. Kozlowski & Konarzewski 2004) as well as for lack of empirical evidence (e.g. Lovegrove 2000; Glazier 2006; White et al. 2006; Duncan, Forsyth, & Hone 2007; Seibel 2007). However, the fundamental criticism of such models that derive ‘one fits all species’ scaling factors from structural constraints argues that such constraints are not dogmatic, but allow for a certain range of evolutionary driven ‘interpretation’ through morphological, physiological and ecological modifications (e.g. Kozlowski, Konarzewski, & Gawelczyk 2002; Duncan et al. 2007). That is, natural selection will cause the relationships between MSR and body mass and between MSR and temperature to differ among species. The wide range in intraspecific scaling factors found here confirms this view. The universal scaling factors proposed so far, −0·33 (e.g. Kleiber 1932) or −0·25 (e.g. Gillooly et al. 2001) for body mass, and E ≈ 58 kJ mol−1 in MSR = a · eE/(k*T) (Gillooly et al. 2001) are not generally valid, and for body mass they even do not resemble the true mean of our data (Figs 7 and 8). Such differences will show up as variability in across-species empirical models, if we do not introduce either species itself as an independent parameter or are able to fully quantify and parameterize those morphological, physiological and ecological interspecific differences.

Obviously, both attempts are illusive: there are just not enough data for each species to build a reliable model, and higher precision comes at the expense of generality, i.e. the validity of the model for species not covered would be questionable. Nevertheless, one might consider a slight increase of taxonomic resolution, currently rather modest with 19 taxonomic units representing 853 species. Those taxa causing particular trouble (Figs 4 and 5) would be prime candidates for being represented by their own input node, however, they are represented by just too few data (Table 1, Fig. 4). The lifestyle parameters applied here represent a rather sketchy image of morphological, physiological and ecological interspecific differences, but better data are hard to come by. A higher resolution of mobility, e.g. incorporating relative speed of movement, might have helped (Schmidt-Nielsen 1972, Schmidt-Nielsen 1984, Bejan & Marden 2006), but data are rare except in finfish (e.g. Dabrowski 2007). The parameter vision is problematic in sofar as sound information is available from just a few species and thus I had to use a rather broad definition. One could consider additional parameters such as body shape or feeding mode, too, but these must be parameterized first and than measured.

Respiration measurements are notoriously tricky, and the strong ‘reference effect’ on measurements within one species (Fig. 6) indicates that methods may account for a good share of residual variability. Basically, respiration measurements should not depend on the particular method of O2 determination applied (Lawton & Richards 1970). Errors may be introduced by inaccuracies and bias in oxygen determination, such as inappropriate calibration or neglected sensor drift (e.g. Gnaiger & Forstner 1983; Gatti et al. 2002), or by stress induced by inappropriate maintenance and handling of organisms prior to and during measurements (e.g. Davis & Schreck 1997; Morris & Oliver 1999). Body mass determinations are error prone, too: Measurement errors, inappropriate mass-to-energy conversion factors, or the use of energy units as a proxy for body mass can introduce bias. The latter is of particular concern, as body fat has a high-energy content but low-metabolic activity. Therefore, fat-free mass is used in mammal research some times (e.g. Weinsier, Schutz, & Bracco 1990). In aquatic organisms, a protein-proxy such as nitrogen content might be an alternative to energy content as in photoautotrophs (see Makarieva et al. 2008), albeit higher precision may come at the cost of loosing significant lifestyle information (see Ikeda et al. 2006; Childress, Seibel, & Thuesen 2008).

Finally, we can expect biologically and/or ecologically caused differences in the physiological state of the organisms under investigation. There are ‘known unknowns’, i.e. factors that are known but have not been quantified, such as effects of age and season (e.g. Sukhotin, Abele, & Pörtner 2002), of alimentation state (e.g. Brockington & Peck 2001), or of parasites and diseases (e.g. Wołowicz, Smolarz, & Sokołowsk 2005). And there may be ‘unknown unknowns’, i.e. environmental or endogenous factors that we just do not know about.

Modifying the network architecture by increasing the number of hidden nodes (Fig. 1) is an another option to enhance model fit, albeit again at the cost of generality. Trial runs indicated indeed that more than four hidden nodes lead to over-fitting, i.e. the prediction of training data becomes significantly better than the prediction of test data.

To sum up, this study confirms the view that generality and accuracy are contradistinctive objectives in predictive models that are based on empirical data. The model introduced here represents the optimum trade-off between these objectives, and thus it is not suitable to estimate the respiration of one particular animal under particular conditions. However, precision will rapidly increase if single estimates are pooled into respiration of a group of animals, as individual errors tend to cancel out each other (cf. Figs 4 and 5). This effect will be the stronger, the larger and the more diverse this group of animals will be in terms of body mass, taxonomy and lifestyle. Therefore, integral ecological studies that become particularly relevant for the modelling of global warming effects on aquatic ecosystems (O’Connor et al. 2009) are the principal application of the model. Specific examples are ecosystem food web analyses (see Belgrano et al. 2005 for examples), and the evaluation of large ecosystem compartments such as mesozooplankton (e.g. Hernández-León & Ikeda 2005), benthos (e.g. Schwinghamer et al. 1986) or even the global open ocean (Del Giorgio & Duarte 2002).


This study is based on the careful and laborious work of hundreds of colleagues. I am especially indebted to D. Abele, I.Y. Ahn, W.E. Arntz, H. Auel, M. Balarin, I.B. Baums, S. Brockington, O. Carrillo, A. Clarke, L. Coston-Clements, E. Díaz-Iglesias, H.M. Dierssen, A. El-Haj, I. Fraga, C. Friedrich, P.W. Froneman, G.S. Galich, O. Heilmayer, L.J. Holmes, R. Kiko, P.J. Kuun, S. Kruse, R.R. Langford, D.C. Lasenby, A. Mackensen, A. Miller, M.W. Miller, S. Morley, D.J. Morris, EA. Pakhomov, L. Peck, E. Perera, H.-O. Poertner, R. Robertson, B.A. Seibel, M. Sejr, J.H. Shim, H. Shimauchi, D. Storch, A.A. Sukhotin, A.M. Szmant, E. Taylor, C. Tesch, P.A. Tester, S. Uye, R.J. Waggett, P. Wencke, and I. Werner. The careful and constructive reviews of Andrew Clarke and a further, anonymous colleagues were extraordinary helpful.