Ecology of ontogenetic body-mass scaling of gill surface area in a freshwater crustacean

However, the 3/4-power law and the resource-transport network (RTN) theory used to support it have received severe criticism. First, the 3/4-power law is not universal: metabolic scaling relationships vary widely, with exponents ranging from 0 to >1, but usually between 2/3 and 1 (reviewed in Glazier, 2005, 2010, 2014b; Agutter and Tuszynski, 2011; Hulbert, 2014; White and Kearney, 2014). Second, variation in metabolic scaling exponents has been linked to various environmental, physiological and developmental factors, thus showing that metabolic scaling cannot be a simple (sole) function of RTNs (Glazier, 2005, 2010, 2014b,c; White and Kearney, 2014). Third, RTN models apply only to a small fraction of existing animal species (mainly vertebrates) that have a closed circulatory system with a single central pump (heart) (Price et al., 2012; Glazier, 2014b). Fourth, no direct (e.g. experimental) evidence supporting predicted effects of RTNs on metabolic scaling yet exists (Glazier, 2014b), though future research may address this deficiency (see Tekin et al., 2016). Fifth, multiple lines of evidence contradict the predictions of RTN models. According to RTN models, the scaling exponent should not vary with activity level, but it does so, and in a systematic way that can be explained by changes in resource demand rather than resource supply (Glazier, 2005, 2010, 2014b,c). According to RTN models, oxygen and nutrients should be more limiting to cells of large versus small organisms, but currently available empirical evidence contradicts this prediction (Kozłowski and Konarzewski, 2004; Helm and Davidowitz, 2013; Harrison et al., 2014; Glazier, 2015a). In addition, current RTN models predict that the scaling exponents for metabolic rate should be lower in organisms that grow predominantly only in one or two dimensions than in organisms that grow isomorphically (West et al., 1999; Banavar et al., 2010; Dodds, 2010), but the opposite has been found in many kinds of shape-shifting pelagic animals (Hirst et al., 2014; Glazier et al., 2015).

To fully understand the extensive variation that exists in the body-mass scaling of the rates of metabolism and other associated biological processes, it is necessary to consider the effects of both resource supply and demand (Glazier, 2014b, 2015b). Resource supply to metabolizing cells is affected not only by RTNs but also by the areas and uptake capacities of various respiratory and digestive surfaces. In fact, the scaling of metabolic rate parallels the scaling of body surface area in skin-breathing pelagic invertebrate animals (Hirst et al., 2014; Glazier et al., 2015), and of pulmonary oxygen diffusion rates in various vertebrate animals (Gillooly et al., 2016). Rates of metabolic waste excretion also appear to be related to body surface area in pelagic invertebrates (Hirst et al., 2017). In addition, body volume-related changes in whole-organism resource demand (associated with growth, food processing and locomotor activity) and other size-specific changes in functional energy expenditure and the relative proportions of tissues with different metabolic activity may significantly affect the scaling of metabolic rate (reviewed in Glazier, 2014b).

A key question regarding the causes of metabolic scaling is: how are size-specific resource supply and demand interrelated and what are the mechanisms involved? Although several studies have examined how the area of respiratory surfaces and their scaling with body size may be related to the intensity and body-mass scaling of metabolic rate in various aquatic animals (e.g. Brown and Shick, 1979; Shick et al., 1979; Johnson and Rees, 1988; Post and Lee, 1996; Rombough and Moroz, 1997; Wegner et al., 2010; White and Seymour, 2011; Hirst et al., 2014; Glazier et al., 2015; Killen et al., 2016), hardly anything is known about how these relationships may be affected by various environmental factors. Furthermore, to our knowledge, no study has examined how various ecological factors may affect the scaling of respiratory surface area among populations of a single species.

Therefore, the purpose of this study was to examine whether the ontogenetic scaling of gill surface area (SA) in eight populations of the amphipod Gammarus minus is related to differences in various abiotic and biotic environmental factors among the freshwater springs that they inhabit. Gill SA varies among and within amphipod species from different habitats (Moore and Taylor, 1984; Spicer and Taylor, 1986; Swain and Richardson, 1993; Tsubokura et al., 1998; Roast and Jones, 2003), but environmental effects on the ontogenetic body-mass scaling of gill SA among conspecific populations, and their possible relationship to ontogenetic metabolic scaling, have not yet been studied.

Spring-dwelling amphipods are useful for this kind of investigation because: (1) they are abundant, easy to capture and readily studied in the laboratory; (2) their leaf-like gills are thin and flat (Steele and Steele, 1991), thus facilitating the measurement of their SA; (3) they appear to have limited dispersal ability, as indicated by their significant inter-population genetic differentiation (Gooch, 1990; Gooch and Glazier, 1991; Culver et al., 1995), thus likely accentuating their adaptation to local environmental conditions via natural selection, as indicated by their significant inter-population differentiation in various physiological, morphological and life-history traits (Glazier et al., 1992; Culver et al., 1995; Glazier, 1998, 1999; Glazier and Sparks, 1997; Glazier and Deptola, 2011; Glazier et al., 2011); (4) data on metabolic scaling from five populations are available for comparison (Glazier et al., 2011); and (5) the numerous study springs exhibit remarkably constant intra-site environmental conditions (especially of substrate composition and water temperature, chemistry and flow rates), but several readily measured environmental factors vary considerably among sites, often independently of one another, thus facilitating incisive comparative analyses (Glazier and Gooch, 1987; Glazier et al., 1992, 2011; Glazier, 1999). In general, springs are useful natural laboratories for ecological and evolutionary studies (Glazier, 1998, 2014d). Amphipods also deserve study because they are keystone species in springs and other aquatic habitats, where they play important roles in ecosystem trophic dynamics and nutrient cycling (Glazier, 2014a).

We tested four, not mutually exclusive hypotheses. First, as the gills are the primary sites for oxygen uptake in Gammarus (Sutcliffe, 1984; Maltby, 1995; Roast and Jones, 2003), the body-mass scaling of gill SA should parallel the scaling of metabolic rate, as estimated by rate of oxygen uptake. This hypothesis assumes that the intensity of oxygen uptake per unit gill area is invariant or nearly so (but see Johnson and Rees, 1988). Specifically, the scaling exponent for gill SA should be less in populations inhabiting springs with versus without fish predators, thus matching the difference in metabolic scaling exponents reported by Glazier et al. (2011). Furthermore, as amphipods are less active in the presence of fish (Andersson et al., 1986; Holomuzki and Hoyle, 1990; Wooster, 1998; Åbjörnsson et al., 2000), they should require less gill SA for oxygen uptake than more active amphipods living in the absence of fish.

Second, gill SA should be greater in populations inhabiting warm versus cold springs, to support enhanced metabolic demand, while also compensating for reduced dissolved oxygen in warmer water (again assuming that oxygen uptake per unit gill area is invariant). Metabolic rate (and thus demand for oxygen) increases with increasing temperature, whereas oxygen availability decreases, both of which would favor larger gills with a higher capacity for oxygen uptake. In addition, according to the metabolic-level boundaries hypothesis (Glazier, 2010, 2014c; Killen et al., 2010), the scaling exponent for gill SA should be inversely related to water temperature (assuming that gill SA and metabolic rate are related).

Third, as crustacean gills are multi-functional, not only serving as respiratory gas-exchange organs but also engaging in active ion transport required for ionic and osmotic regulation (Pequeux, 1995; Lingot et al., 2000; Brooks and Mills, 2003; Freire et al., 2008; Henry et al., 2012), gill SA should be smaller in aquatic habitats with high versus low ion concentrations (conductivity), because a less steep ionic gradient between the inside and outside of the body entails a reduced rate of ion loss and thus a lesser demand for compensating ion uptake (assuming that ion uptake per unit gill area is invariant). The lower metabolic demand of ionic regulation in water with high ion concentrations (Sutcliffe, 1984; Glazier and Sparks, 1997) should also require less oxygen uptake, again favoring smaller gills.

Fourth, as amphipods are cannibalistic (larger individuals often prey on smaller individuals: MacNeil et al., 1997; McGrath et al., 2007; D.S.G., personal observations), secretive behavior and associated reduced activity in small juvenile amphipods may require less oxygen uptake and gill SA in populations with high versus low densities. If so, higher population density should be associated with decreases in juvenile gill sizes, but no effect on adult gill sizes, thus causing steeper scaling of gill SA.

Gammarus minus Say 1818 is an omnivorous detritivore commonly found in springs and streams from the mid-Appalachians to the Ozarks in North America (Holsinger, 1976). Using dip nets, individuals ranging in body length from ∼3 to 12 mm were collected within 10 m of each source of eight rheocrenes (lotic springs): Blue (BL), Ell (EL), Kanesatake (KS), Petersburg (PT) and Warm (WH) springs in Huntingdon County, Williamsburg (WB) spring in Blair County, Big Rock (BR) Spring in Mifflin County and Warm Spring (WP) in Perry County. These spring sites were selected to allow a factorial analysis of the effects of water temperature, conductivity and predation regime on gill SA (see Table 1). Qualitative estimates of G. minus population density were made because variation in substrate composition prevented the use of a single kind of quantitative sampler in all springs.

At the times of amphipod sampling (summer, autumn and winter seasons during 1 July 2013 to 3 March 2015), environmental measurements were made within 10 m of the source of each spring. Water temperature, conductivity and pH were measured with digital conductivity (YSI, Yellow Springs, OH, USA) and pH (Markson LabSales, Henderson, NC, USA) field meters (Table 1). These variables show little monthly variation in our study springs (Table 1; Glazier et al., 1992). Four of the study springs contain fish predators, three with Cottus cognatus (WB, BL, EL) and one with Rhinichthys atratulus (WH) (Table 1). WH also contains several other kinds of relatively large predators including Caudata, Decapoda, Megaloptera and Odonata. Additional environmental characteristics of the study springs are described elsewhere (Glazier and Gooch, 1987; Gooch and Glazier, 1991; Glazier et al., 1992, 2011; Glazier, 1998, 1999).

Juveniles and adult males (identified by enlarged gnathopods) were used for gill-area estimates. Adult females were not used because their body-mass estimates were affected by the mass of developing eggs and embryos. Individuals were maintained in native spring water with detrital leaf food in 1 liter containers at 10°C until body measurements were made (not more than 1 week after capture).

Before measurements were made, each specimen was anesthetized in carbonated spring water. After measuring the body length (±0.1 mm; base of first antenna to base of telson), the fifth coxal gill was removed and photographed using a microscope-mounted camera (Sony CCD-Iris, Tokyo, Japan). This gill was selected because it is morphologically distinct from the neighboring gills, and located between the two longest legs of the organism, thus making it easy to identify and remove [Gammarus species and other gammaridean amphipods typically have six pairs of thoracic gills (Moore and Taylor, 1984; Sutcliffe, 1984; Steele and Steele, 1991; Roast and Jones, 2003)]. We considered the SA of the 5th coxal gill to be a useful relative index of total gill SA because the proportional relationships between the size of this gill and that of other gills is not significantly different from 1 (based on width measurements of the relatively large 4th, 5th and 6th coxal gills in 18 individuals with body lengths ranging from 2.5 to 9.5 mm from the PT and WH populations). Using a photographed ruler as a metric, gill SA was calculated as the area (±0.01 mm²) within a gill's outlined perimeter by using ImageJ photo analysis software (Fig. 1). Dry body mass, including the removed gill, was determined by desiccating each specimen in a 68°C oven (Hotpack, Philadelphia, PA, USA) for 60 h, and then weighing it (±0.001 mg) using a Cahn C-31 microbalance (Cerritos, CA, USA).

Least squares regression analysis was used to compare gill SA with dry body mass for each population (Fig. 2); log10 values were used to normalize the data variation and to produce linear, proportional relationships (see Kerkhoff and Enquist, 2009; Glazier, 2013; Mascaro et al., 2014). Significant differences between specific scaling slopes were determined using the 95% confidence intervals (CI). If a mean value was outside the 95% CI of another mean value and vice versa, they were considered significantly different (P<0.05), following Smith (1997). The gill SA scaling relationships, including slopes, and calculated gill SA values at dry body masses of log₁₀ −0.25 (0.631 mg), log₁₀ 0 (intercepts at 1 mg) and log₁₀ 0.25 (1.778 mg), were compared between springs with versus without fish predators using t-tests, and among springs with different G. minus population densities and water temperatures, pH values and conductivities using Pearson's product-moment correlation analyses (Table 2). Gill SA values were calculated at the designated small and large body masses given above because they were substantially different and equally distant from the intercept, without being beyond the recorded body-mass range of any population (see Table 1, Fig. 3A).

Highly significant relationships between gill SA and dry body mass were found within each of the eight study populations of G. minus (Fig. 2). The mean (±s.e.m.) scaling slope for gill SA was significantly lower for the populations in springs with fish (0.667±0.034) versus those without fish (0.763±0.019; Table 2, Fig. 3B). Pooling samples from all populations in each type of spring also revealed that the scaling slope (±95% CI) was significantly lower for the fish-containing spring populations (0.628±0.049) than for the fishless spring populations (0.749±0.038; Fig. 4). In addition, the mean (±s.e.m.) calculated gill SA at the large (1.778 mg) dry body mass was significantly lower in springs with fish (0.323±0.021 mm²) versus those without fish (0.403±0.020 cm²; Table 2, Fig. 3A). However, the intercept (log₁₀, ±s.e.m.) and mean (±s.e.m.) calculated gill SA at the small (0.631 mg) dry body mass were not significantly lower in springs with fish (−0.660±0.029, 0.150±0.011 mm², respectively) versus those without fish (−0.587±0.022, 0.168±0.009 mm², respectively; Table 2).

Among all eight populations, the slopes, intercepts and calculated gill SA at small and large body sizes were not significantly related to water temperature, conductivity or G. minus population density (Table 2). Although the slopes and calculated gill SA at the small body size were not significantly related to pH, significant inverse relationships were found for the intercept and calculated gill SA at the large body size in relation to pH (Table 2).

We found highly significant allometric scaling relationships (slopes <1) between gill SA and body mass in all eight study populations of G. minus, as has been observed in other Gammarus species (Moore and Taylor, 1984; Maltby, 1995). Furthermore, these scaling relationships vary significantly among populations in relation to specific ecological factors. No other animal study has documented ecologically sensitive intraspecific variation of the body-mass scaling of gills or any other respiratory structure.

Our results most strongly support the hypothesis that the scaling of gill SA should parallel that of metabolic rate, as mediated by the effect of size-specific predation by visually hunting fishes. As predicted, the gill SA scaling slopes tended to be lower for the populations in springs with fish versus those without fish (Fig. 3), as was also observed for the scaling slopes of resting metabolic rate (Glazier et al., 2011). In fact, the scaling slopes for gill SA and metabolic rate are not significantly different (within each paired group, the 95% CI of each mean overlaps the mean of the other) for the pooled data of all study populations in the fish-containing springs (0.628±0.049 versus 0.598±0.070) and in the fishless springs analyzed separately (0.749±0.038 versus 0.760±0.080) (n=125, 230, 115 and 190, respectively: data from Fig. 4 and Glazier et al., 2011). A predation effect is also supported by the observation that, among the fish-containing spring populations, the gill SA scaling slope was lowest for the two populations with the highest density of fish predators (WB) or the most diverse assemblage of predators (WH), whereas the population (EL) exposed to a relatively low density of fish predators showed a gill SA scaling relationship most similar to that of the populations in springs without fish (Fig. 3). Similarly, the WB population showed a lower metabolic scaling exponent than the EL population (Glazier et al., 2011).

We suggest that the gill SA scaling difference between fish-containing versus fishless spring populations may have resulted from different size-specific net effects of growth and activity on oxygen demand, and thus the amount of oxygen uptake needed by the gills. The importance of growth is revealed by shallower ontogenetic scaling of growth rate in relation to body mass in the fish-containing versus fishless spring populations (Glazier et al., 2011), thus paralleling that observed for metabolic rate and gill SA. Prematurational growth is as high or higher in small young amphipods inhabiting fish-containing versus fishless springs, presumably because of strong selection to reach maturity and reproduce before being eaten. By contrast, postmaturational growth is significantly lower in large older amphipods inhabiting springs with versus without fish, presumably because of the selective advantage of remaining as small and inconspicuous as possible to visually hunting fish predators (Glazier et al., 2011). Fish (e.g. C. cognatus) prefer to feed on large versus small amphipods (Newman and Waters, 1984).

In addition, the presence of fish favors secretive and relatively sedentary behavior in amphipods (Andersson et al., 1986; Holomuzki and Hoyle, 1990; Starry et al., 1998; Wooster, 1998; Åbjörnsson et al., 2000; Glazier et al., 2011; Szokoli et al., 2015), especially those that are large and relatively conspicuous (Andersson et al., 1986). Therefore, the presence of fish should influence relative oxygen demand more in large older versus small younger amphipods. In fish-containing springs, oxygen demand for both growth and activity should be reduced in large older amphipods, but only for activity and probably to a lesser extent in small younger amphipods. In addition, a possibly higher metabolic demand of growth in small, young amphipods in springs with versus without fish may partially or wholly counterbalance a reduced activity demand for oxygen. The net effect should be a shallower scaling of oxygen demand in populations from springs with versus without fish, which should favor a similar scaling difference for oxygen-uptake capacity, as indexed by gill SA (Fig. 5).

An extrapolation of the linear regression line for the populations in the fish-containing springs beyond the range of measured data points suggests that a crossover of the gill SA scaling relationships may occur (Figs 4 and 5), and, if so, this pattern would parallel that observed for metabolic rate (Glazier et al., 2011), thus further supporting our hypothesis that these scaling relationships should respond similarly to size-specific predation. Additional data on the gill SA of very small amphipods in both fish-containing and fishless springs are needed to test this inference, which we found difficult to obtain because of problems in extracting their gills without damage, and thus accurately measuring their SA.

Contrary to the other hypotheses proposed in the Introduction, water temperature, conductivity and G. minus population density showed no significant correlations with the body-mass scaling of gill SA, including slopes, intercepts and calculated gill SA at small and large body sizes (Table 2). Perhaps the differences in water temperature (and associated oxygen demand and availability) were not great enough to necessitate the evolution of changes in gill SA. In the two warm springs of this study, dissolved oxygen concentrations were never observed to be below 5 mg l⁻¹ (Glazier and Gooch, 1987; D.S.G., personal observations), above which only small adjustments in oxygen uptake (metabolic rate) and ventilation rate in Gammarus are observed (Sutcliffe, 1984; Maltby, 1995). However, Gammarus duebeni had significantly larger gills in a hypoxic sewage treatment area compared with its native estuarine habitat (Roast and Jones, 2003). Therefore, larger gills may facilitate oxygen uptake when oxygen availability is very low.

No apparent effect of conductivity on gill SA scaling was observed, possibly because of limited differences in conductivity among the study springs, and because gills are not the only sites for ion regulation in crustaceans (Kikuchi and Matsumasa, 1997). However, among Gammarus species, freshwater species tend to have larger gills than marine species (Moore and Taylor, 1984). This habitat difference is consistent with the hypothesis that amphipods in water with lower ionic concentrations should have larger gills to facilitate ion uptake.

An unexpected result was that the intercept and calculated gill SA at large body size were both negatively related to pH (Table 2). However, we believe that these associations are probably coincidental rather than causal. First, the pH range among the study springs was small (only 6.69 to 7.07; Table 1) and thus probably not biologically meaningful. The intra-site variation in pH often encompassed the inter-site range in pH (Table 1). Second, no significant effect of pH on the calculated gill SA at small body size was observed (Table 2). If pH truly influenced gill SA, then one would expect it to have had this effect on amphipods of all sizes, and especially those with small sizes and thus large surface area to volume ratios. Third, the pH correlation is likely due to a coincident association of relatively high pH with the presence of fish predators (t=3.11, P=0.021: mean±s.e.m. pH=7.025±0.027 in fish-containing springs versus 6.801±0.064 in fishless springs; data from Table 1). The primary effect of fish predators would explain why the pH correlation was only observed for large amphipods and not small amphipods. However, a possible direct effect of pH on amphipod gill SA requires more study.

The hypotheses proposed in this study all assume that oxygen or ion uptake is proportional to gill SA. Although this is probably true at least approximately, oxygen or ion uptake may also be increased by enhancing the permeability, transport ability or ventilation of the gills, thus increasing the rate of oxygen or ion uptake per unit area of gill surface. Johnson and Rees (1988) showed that oxygen uptake per unit gill SA varies among crab species. In the blue crab, ion uptake and water permeability per unit gill SA may also vary with salinity (Li et al., 2006). Therefore, future research should examine the effects of various ecological factors on both gill SA and the intensity of oxygen or ion uptake per unit gill SA, and whether they are due to phenotypic acclimation versus adaptive genotypic evolution (cf. Harrison, 2015).

Our study raises further questions requiring investigation. In particular, what are the benefits and costs of enlarging gill SA? Our results suggest that adult amphipods with high levels of metabolic demand (growth and behavioral activity) in fishless springs benefit from enlarged gills because they enable increased oxygen uptake. To further test this hypothesis, measurements of active (including maximal) metabolic rates and their scaling with body mass are required for populations in both fish-containing and fishless springs. Presumably, gill SA relates to not only resting metabolic rate (including oxygen demand for growth), as indicated by their similar body-mass scaling, but also active metabolic rate (including oxygen demand for behavioral activity; Fig. 5). However, why do adult amphipods in springs with fish have smaller gills? Presumably there is a resource cost to producing and maintaining large gills, and thus if metabolic demand is routinely low, selection should favor smaller gills. Large gills may also entail higher osmoregulatory costs than small gills, as observed in fish (e.g. Brill, 1996). Further studies are needed to measure these costs in amphipod gills of different sizes.

A growing number of studies show that the body-mass scaling of metabolic rate is ecologically sensitive and evolutionarily malleable (e.g. Killen et al., 2010; Glazier et al., 2011; and others, reviewed by Glazier, 2005, 2014b,c). Our study extends this conclusion to the scaling of respiratory structures. The scaling slope for gill SA is significantly different in G. minus populations in springs with versus without fish predators. Our study also provides a mechanistic explanation for this difference. We hypothesize that size-selective fish predation has driven the evolution of size-specific changes in metabolically expensive growth and activity, which has in turn altered the body-size scaling of oxygen use (metabolic rate) and uptake (a function of gill SA). However, empirical support for this mechanism is entirely correlational, and experimental selection studies are needed to further test it (following Garland and Rose, 2009).

Some popular explanations of metabolic scaling have invoked internal resource supply constraints as the primary cause (e.g. RTN models of West et al., 1997; Banavar et al., 2010), but our study provides support for an alternative view that metabolic scaling is the result of a co-adjustment between resource supply and demand (Glazier, 2014b, 2015b). The parallel effects of fish predators on the body-mass scaling of growth, metabolism and gill SA can be more readily explained as being the result of changes in resource demand and the secondary adjustment of resource supply, rather than vice versa. Although constraints on resource supply may sometimes have important effects on metabolic scaling (Glazier, 2010, 2014b,c; Hirst et al., 2014; Glazier et al., 2015), adaptive, size-specific resource demand may often be a primary driver of metabolic rate and its scaling with body mass, with resource supply playing a secondary supporting role (Glazier, 2014b, 2015b).

The authors thank Ethan Habbershon and two anonymous reviewers for comments on an earlier version of the manuscript.