# Size Effects on Pumping Rates in High Microbial versus Low Microbial Abundance Marine Sponges

## Abstract

**:**

^{−1}). The scaling analysis of all data sets combined reveals that HMA sponges scale their pumping rates isometrically with size, while LMA sponges scale their pumping rate allometrically. When HMA species are examined separately, however, tropical HMA sponges scaled isometrically, while temperate HMA sponges scaled allometrically. From an ecological perspective, to quantify differences between HMA and LMA sponges for rate functions of interest (e.g., feeding) it is important to remove the effects of size as a covariate, and adjust the Q values of sponges to a standard volume or mass. For multiple species and geographic locations, this analysis shows that LMA sponges always maintain higher Q values. On tropical coral reefs, the differences between HMA and LMA sponges are intrinsic and constrained by strong evolutionary selection resulting in fixed differences in Q, regardless of sponge size.

## 1. Introduction

^{10}cells g

^{−1}sponge tissue), and highly diverse, microbial communities that are specialized to provide increased biochemical functional capacity including the production of defensive secondary metabolites [11]. In contrast, the microbial communities in low microbial abundance (LMA) sponges support lower concentrations of microbes (~10⁶ cells g

^{−1}sponge tissue), that are distinct from HMA sponges, less diverse, and exhibit decreased biochemical functional capacity compared to HMA sponges for most biochemical pathways examined [11,15,16]. These differences in microbial abundance have implications for sponge biology and their trophic ecology [11,12]. But HMA and LMA sponges exhibit other important differences; HMA sponges exhibit increased mesohyl density, low choanocyte densities, and reduced mass specific pumping rates, whereas LMA sponges have decreased mesohyl density, higher choanocyte densities and greater mass-specific pumping rates [17,18]. These differences between symbiotic phenotypes are also associated with a general preference for the uptake of DOM in HMA sponges and POM in LMA sponges [18,19].

^{−1}), where most studies normalize rates of pumping to volume, mass or osculum cross-sectional area [19,22,23] with the assumption of isometry, or geometric similarity. However, studies on the effects of size on Q in sponges have shown that the relationship is often allometric in nature [24]. Allometric relationships can significantly affect the measurement of fluxes in any organism depending on their complexity, and more importantly when, and where, isometry is not the general rule. Deviations from isometry can be described using the power function in the form Y = aM

^{b}, or its log transformed and linearized version log Y = log (a) + b log (M), where M = mass, and a = y-intercept of the fitted line known as the normalization constant used to describe differences in the rate function of interest between two, or more, sets of data, and b = slope of the fitted line, or size exponent, which describes the proportional change in the rate function of interest with size [20,21]. Both the slope and intercept have biological meaning, and both can be used to answer important ecological questions. These relationships have been used extensively in the study of metabolic rates (e.g., respiration measured as oxygen consumption), where a mass scaling exponent of M

^{0.75}[25], the infamous “mouse to elephant” curve, has received the greatest acceptance [20,21].

^{0.75}scaling exponent for metabolism, West et al. [26] developed the Metabolic Theory of Ecology (MTE), to provide a comprehensive description of the metabolic performance of all life history stages of an organism under varying conditions, based principally on the scaling of metabolic rate [27]. The controversy has been which scaling exponent to use; are M

^{0.75}, or other quarter-power exponents, appropriate across all taxa? The MTE scaling coefficient of M

^{0.75}for metabolism is based on the principal that animals maintain a specific fractal network to service organs, tissues, and cells as they increase in size and the subsequent demand for resources, which is a feature of higher, more complex, taxa such as vertebrates (i.e., symmorphosis) [28]. While there is continuing support for the MTE’s predictive capabilities for metabolism using the M

^{0.75}scaling coefficient [29,30,31], there are detractors [32,33,34]. Many of these critics provide support for the use of M

^{0.66}as the universal scaling coefficient for the relationship between size and metabolism [35]. Additionally, the universal use of M

^{0.75}is inconsistent with what we know about scaling exponents for many rate functions measured on invertebrates [35,36,37].

## 2. Materials and Methods

#### 2.1. Sponge Data

^{−1}), and with the assumption that the density of sponge tissue was equivalent for the same species from different geographic areas (Table S1). For the scaling analysis, both HMA and LMA sponges spanned two to three orders of magnitude in sponge volume (mL) or dry mass (g) for the assessment of the relationship between sponge size and Q, where a minimum size range of one order of magnitude is considered essential [42]. Extrinsic factors such as seasonal changes in seawater temperature were not sufficient to elicit significant changes in Q for sponges from the Mediterranean over an annual cycle (mean annual temperature 17.18 ± 0.81 °C (SD), range of 12–23 °C, [24]), and for samples from Florida and Belize the range of temperatures (27.1–29.6 °C) are not significantly different between locations [43]. Samples were collected from 5–10 m depth in the Mediterranean [24], and 15–30 m in Florida and the Caribbean [17,19]. Rates of sponge pumping, or Q, were measured using the dye speed approach with underwater videography [17], dye front speed technique [24] or by acoustic Doppler velocimeter [19]. A detailed description of the dye speed and dye front speed techniques is provided in Morganti et al. [40] and a comparison between these techniques showed no statistical differences in pumping rates [24]. In addition to the fact that the species examined share a common feeding mechanism and higher taxonomic affinities as intrinsic factors, the analytical approaches described below were not applied to address any other factor (e.g., morphology) besides the analysis of size effects, also called contextual allometry [44].

#### 2.2. Analysis of Size Effects on Sponge Pumping

^{b}or Y/Mass = a Mass

^{b}were avoided [42,52,53]. Second, to assess for the effects of size on Q values between HMA and LMA sponges for each dataset described above (Table S1), an analysis of covariance (ANCOVA) was run on untransformed values with symbiotic state as the primary factor and sponge volume or mass as the covariate to assess any potential allometric effects of sponge size on Q. This also allows a direct assessment of the differences in a or the y-intercept between the fitted lines for HMA and LMA sponges given that the respective b, or slope values, are homogeneous as a requirement for ANCOVA [45]. Third, if the slopes from the ANCOVA are not homogeneous a direct assessment of Q values between HMA and LMA sponges is not possible using ANCOVA. In these cases, the slope values from the ordinary least squares regression for Q versus size for symbiont phenotype were used to adjust individual sponge Q values to a sponge of standard volume or mass for each data source and the pooled data [41,45,46,52]. The adjusted Q values were then analyzed using a two-tailed Student’s t-test with symbiotic state as the fixed factor on log transformed values, and back transformed for presentation. All analyses were conducted in JMP (v 16.1.0) on the individual, or combined, data for HMA and LMA sponges.

## 3. Results

#### 3.1. Scaling Analyses

^{0.967}) and 1.172 (±0.038 SEM) when regressed against mass (Log Q = −1.722 + 1.172 × Log Mass, or Q = −1.722 × Mass

^{1.172}) (Figure 2A,B). The analysis of LMA sponges exhibited a slope of 0.727 (±0.021 SEM) when regressed against volume (Log Q = −0.329 + 0.727 × Log Volume, or Q = −0.329 × Vol

^{0.727}) and 0.787 (±0.046 SEM) when regressed against mass (Log Q = 1.297+ 0.727 × Log Mass, or Q = 1.297 × Mass

^{0.787}) (Figure 2C,D). When comparing the slopes of Q regressed against volume between HMA and LMA sponges using a two-tailed Student’s t-test, there is a statistically significant difference (t(323), t-ratio = 6.12, p < 0.0001), where the slopes of HMA sponges are significantly greater than those of LMA sponges (Figure 2A,C), and for Q regressed against mass the slopes of HMA sponges are also significantly greater than those of LMA sponges (t(323), t-ratio = 6.39, p < 0.0001) (Figure 2B,D).

^{1.277}) and temperate HMA sponges have a slope of 0.765 (±0.067 SEM) when regressed against volume (Log Q = −1.689 + 0.765 × Log Volume, or Q = −1.689 × Vol

^{0.765}). The slope for tropical sponges is significantly greater than that of temperate sponges (t(197), t-ratio = 3.33, p = 0.001). Tropical HMA sponges have a slope of 1.334 (±0.193 SEM) when regressed against mass (Log Q = −2.743 + 0.1334 × Log Mass, or Q = −2.743 × Mass

^{1.344}) and temperate HMA sponges have a slope of 0.931 (±0.101 SEM) when regressed against mass (Log Q = −1.257 + 0.931 × Log Mass, or Q = −1.257 × Mass

^{0.931}). The slope for tropical HMA sponges is marginally, but significantly, greater than that of temperate HMA sponges (t(197), t-ratio = 2.02, p = 0.045). Lastly, using the slopes from the ANCOVA analysis (i.e., ordinary least squares regression), individual sponge Q values for tropical and temperate sponges were adjusted to a sponge of standard volume or mass and analyzed using a two-tailed Student’s t-test. Volume adjusted Q values for tropical (169.28 ± 223.91 (SEM)) versus temperate (132.81 ± 0.0153 (SEM)) sponges was not significant (t(197), t-ratio = 0.203, p < 0.05), with an effects size of 0.0002 (R

^{2}), while for mass adjusted Q values of tropical sponges (961.95 ± 174.19 (SEM)) versus temperate sponges (40.91 ± 0.157 (SEM)), there was a significant difference (t(197), t-ratio = 6.59, p < 0.0001), with tropical sponges exhibiting significantly greater Q values with an effects size of 0.181 (R

^{2}). However, both the volume and mass adjusted Q values had significantly unequal variances (Volume, Levene’s test, F

_{1,197}= 57.66, p < 0.0001; Mass, Levene’s test, F

_{1,197}= 99.86, p < 0.0001). Conducting a t-test assuming unequal variances (i.e., Welch’s Test) still showed a non-significant difference for volume adjusted Q values (F

_{1,77}= 0.027, p = 0.871), and a significant difference for mass adjusted Q values (F

_{1,77}= 27.96, p < 0.0001), with tropical HMA sponges exhibiting greater Q values than temperate HMA sponges (Figure 3).

#### 3.2. Removing the Effects of Size on Rate Functions

_{1,93}= 0.0008, p > 0.05) and mass (F

_{1,93}= 0.002, p > 0.05), indicating that the slopes were homogeneous, and that the main effects of the model (i.e., Q) were significantly different between HMA and LMA sponges when either volume (F

_{3,92}= 72.68, p < 0.0001), or mass (F

_{3,92}= 53.01, p < 0.0001), are accounted for; LMA sponges exhibited higher Q values. The slopes from the ANCOVA analysis were used to adjust individual sponge Q values of HMA and LMA sponges to a sponge of standard volume or mass, analyzed using a two-tailed Student’s t-test. Volume adjusted Q values for HMA (975.45 ± 145.45 (SEM)) versus LMA (1358.81 ± 6.51 (SEM)) sponges was not significant (t(92), t-ratio = 1.76, p = 0.083), but were also found to have significantly unequal variances (e.g., Levene’s test, F

_{1,92}= 11.08, p = 0.0013). Conducting a t-test assuming unequal variances (i.e., Welch’s Test) showed a significant difference for Q values (F

_{1,64}= 6.93, p = 0.011), with LMA sponges greater than HMA sponges (Figure 4A), and an effects size of 0.032 (R

^{2}). Mass adjusted Q values for HMA (987.22 ± 161.78 (SEM)) versus LMA (1791.99 ± 7.09 (SEM)) sponges were significantly different (t(92), t-ratio = 3.31, p = 0.0013), with LMA sponges greater than HMA sponges (Figure 4A), and an effects size of 0.107 (R

^{2}).

_{1,29}= 3.178, p > 0.05) and mass (F

_{1,29}= 0.052, p > 0.05), indicating that the slopes were homogeneous, and that the main effects of the model (i.e., Q) were significantly different between HMA and LMA sponges when either volume (F

_{3,29}= 4.11, p = 0.016) or mass (F

_{3,29}= 3.28, p = 0.037) are accounted for; LMA sponges exhibited higher Q values. But the regression lines for Q versus mass are crossed, which indicates the regression lines are not isometric. While the slopes from the ANCOVA analysis for both volume and mass were used to adjust individual sponge Q values for HMA and LMA sponges to a sponge of standard volume or mass, the adjustment procedure was a requirement for the mass data, which was then analyzed using a two-tailed Student’s t-test. Volume adjusted Q values for HMA (86.13 ± 46.70 (SEM)) versus LMA (494.31 ± 24.07 (SEM)) sponges were significant (t(28), t-ratio = 8.49, p < 0.0001) with LMA sponges greater than HMA sponges (Figure 4B), and an effects size of 0.387 (R

^{2}). Mass adjusted Q values for HMA (88.99 ± 46.64 (SEM)) versus LMA (281.11 ± 20.97 (SEM)) sponges were also significantly different (t(28), t-ratio = 4.20, p = 0.0002) with LMA sponges greater than HMA sponges (Figure 4B), and an effects size of 0.721 (R

^{2}).

_{1,199}= 58.09, p < 0.0001) and mass (F

_{1,199}= 46.41, p < 0.0001), indicating a lack of homogeneity of slopes, a requirement for the ANCOVA, and that the main effects of the model cannot be interpreted as planned a priori. The slopes from the ANCOVA analysis for both volume and mass were then used to adjust individual sponge Q values for HMA and LMA sponges to a sponge of standard volume or mass, analyzed using a two-tailed Student’s t-test. Volume adjusted Q values for HMA (2.31 ± 0.15 (SEM)) versus LMA (7.14 ± 0.19 (SEM)) sponges were significant (t(197), t-ratio = 19.91, p < 0.0001) with LMA sponges greater than HMA sponges (Figure 4C), and an effects size of 0.668 (R

^{2}). Mass adjusted Q values for HMA (2.23 ± 0.16 (SEM)) versus LMA (4.12 ± 0.25 (SEM)) sponges were also significantly different (t(197), t-ratio = 6.68, p < 0.0001) with LMA sponges greater than HMA sponges (Figure 4C), and an effects size of 0.185 (R

^{2}).

_{1,323}= 0.13, p = 0.719) and mass (F

_{1,323}= 007, p = 0.934), indicating that the slopes were homogeneous, and that the main effects of the model (i.e., Q) were significantly different between HMA and LMA sponges when either volume (F

_{3,323}= 77.96, p < 0.0001), or mass (F

_{3,323}= 6.53, p = 0.0003), are accounted for. But the regression lines for Q versus mass are crossed, which indicates that the regression lines are not isometric. The slopes from the ANCOVA analysis for both volume and mass were used to adjust individual sponge Q values for HMA and LMA sponges to a sponge of standard volume or mass, analyzed using a two-tailed Student’s t-test. Volume adjusted Q values for HMA (293.38 ± 57.52 (SEM)) versus LMA (640.39 ± 84.04 (SEM)) sponges were significant (t(321), t-ratio = 3.52, p = 0.0005) with LMA sponges greater than HMA sponges (Figure 4D), and an effects size of 0.037 (R

^{2}). Mass adjusted Q values for HMA (283.97 ± 62.71 (SEM)) versus LMA (945.16 ± 138.69 (SEM)) sponges were also significantly different (t(321), t-ratio = 4.89, p < 0.0001) with LMA sponges greater than HMA sponges (Figure 4D), and an effects size of 0.069 (R

^{2}).

## 4. Discussion

^{0.967}) or mass (Mass

^{1.172}), while LMA sponges scale Q allometrically based on volume (Vol

^{0.727}) or mass (Mass

^{0.787}). Despite these scaling differences, Q adjusted for a standard size sponge consistently showed that LMA sponges pump at greater rates than HMA sponges, as in the ratio analysis. Morganti et al. [24] suggested, based on volume-specific pumping rates, that these differences between sponge phenotypes are likely to be caused by the inherent interspecies size differences between HMA and LMA sponges. Here, however, with volume or mass removed as a confounding factor, LMA sponges still maintain higher Q values than HMA sponges. Interestingly, when comparing HMA samples from tropical versus temperate habitats, HMA sponges from the tropics exhibit significantly greater scaling exponents for Q compared to temperate HMA sponges, and when scaling exponents are used to normalize Q values to a standard sized sponge, tropical HMA sponges also pump at greater rates than temperate HMA sponges. However, in their analysis, Morganti et al. [40] found that flow rate scaled isometrically with the individual osculum surface area in all temperate and tropical HMA sponges. An analysis of Spheciospongia vesparium, a tropical HMA sponge, based on the fact that it was the only tropical species with sufficient data points, also scaled isometrically (scaling coefficient =0.98; [40] their Figure S3) but, when removed from the scaling analysis of tropical HMA sponges, a scaling coefficient of 0.78 was observed, suggesting that S. vesparium is either an outlier, or that its large sample size influenced the analysis of scaling for tropical HMA sponges [40]. Here, when the S. vesparium data are analyzed separately using RMA regression on log transformed data, the scaling coefficient for Q as a function of volume is 1.101 ± 0.111 (SEM) and 1.155 ± 0.115 (SEM) for mass. Neither is significantly different from 1.0, indicating that S. vesparium scales isometrically for size, as found for osculum surface area by Morganti et al. [40]. If the slopes are then compared between all tropical sponges (b = 1.277 ± 0.161) and tropical samples minus S. vesparium (1.008 ± 0.261) based on volume, there is no significant difference (t(129), t-ratio = 0.925, p = 0.357). Similarly, there is no significant difference (t(129), t-ratio = 0.886, p = 0.377) based on mass (1.334 ± 0.193) for all tropical sponges compared to tropical sponges without the S. vesparium data included (1.025 ± 0.313). When tropical HMA sponges without the S. vesparium data (1.008 ± 0.261) are compared to temperate HMA sponges (0.765 ± 0.067), there is no significant difference based on volume (t(172), t-ratio = 1.21, p = 0.229), or mass (t(172), t-ratio = 0.365, p = 0.716). While isometry persists in tropical HMA sponges without the S. vesparium data, compared to allometry in the temperate HMA sponges, the loss of power by reducing the degrees of freedom resulted in no statistically significant differences. Given the lack of any biological reason to omit the S. vesparium data, this approach is not advocated for here. For the original analysis, one explanation for the observed differences might be that the HMA species from tropical environments experience less high-pressure resistance (see below) because, as temperature increases, the viscosity of the water decreases compared to temperate HMA species [58]. But Morganti et al. [24] reported minimal to no effect of temperature on pumping rates or kinematic viscosity for both HMA and LMA sponges.

^{b}, and not Y/M = aM

^{b}, was used for the scaling analyses because Y/M is independent (i.e., no autocorrelation) of M only when Y scales isometrically [42,52]. To assess differences in Q, and therefore the feeding ecology of sponges [41], the slopes from the ANCOVA regressions (i.e., ordinary least squares) were used to adjust Q to a sponge of standard volume or size [45,46]. The ordinary least squares regression model is appropriate here given that the purpose of the regression is to predict Y from M, where M is believed to be affecting Y, and not the reverse [52]. Only the symbiotic phenotype of the sponges was considered as a variable, and HMA sponges consistently had greater scaling exponents and lower pumping rates compared to LMA sponges when size was removed as a confounding factor, a result surprisingly similar to the ratio analysis. It should be a matter of practice for quantifying rate functions in sponges, and most other taxa, not to assume that these processes scale isometrically with size, and that size should be removed from these measurements to obtain ecologically meaningful insights. Additionally, while understanding the scaling of Q in sponges is of inherent evolutionary interest, the ability to compare Q values in an ecological context, without the confounding effects of size, was the objective here. Removing the effects of size reveals that LMA sponges consistently have greater Q values than HMA sponges, and this has significant implications for assessing and understanding the trophic ecology of sponges.

## Supplementary Materials

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Ratio analysis of sponge pumping (i.e., Q values). (

**A**) Data from Weisz et al. [17], (

**B**) data from McMurray et al. [19] and Gantt et al. [22], (

**C**) data from Morganti et al. [24], (

**D**) data pooled from all sources. HMA = High Microbial Abundance, LMA = Low Microbial Abundance. Asterisks in legend indicate significant (p < 0.05) differences for Q values for volume or mass based on two-tailed t-test.

**Figure 2.**Scaling analysis based on combined log-transformed values of Q and size regressed (red line) using a Reduced Major Axis regression model. (

**A**) HMA data regressed against volume, (

**B**) HMA data regressed against mass, (

**C**) LMA data regressed against volume, (

**D**) LMA data regressed against mass. HMA = High Microbial Abundance, LMA = Low Microbial Abundance.

**Figure 3.**Comparison of adjusted Q values between HMA sponges from tropical and temperate locations. HMA = High Microbial Abundance. Asterisks in legend indicate significant (p < 0.05) differences for Q values for volume or mass based on two-tailed t-test and presented as mean ± SEM.

**Figure 4.**Q values adjusted to a common size, volume or mass, using the slopes from an Ordinary Least Squares regression model. (

**A**) Data from Weisz et al. [17], (

**B**) data from McMurray et al. [19] and Gantt et al. [22], (

**C**) data from Morganti et al. [24], (

**D**) data combined from all sources. HMA = High Microbial Abundance, LMA = Low Microbial Abundance. Asterisks in legend indicate significant (p < 0.05) differences for Q values for volume or mass based on two-tailed t-test and presented as mean ± SEM.

**Table 1.**Taxonomic groups of the sponge species analyzed from the Mediterranean Sea, Florida Keys and Belize.

Region | Class | Order | Family | Species | Symbiotic Phenotype * |
---|---|---|---|---|---|

Mediterranean Sea | Demospongiae | Dictyoceratida | Dysideidae | Dysidea avara | LMA |

Demospongiae | Poecilosclerida | Crambeidae | Crambe crambe | LMA | |

Demospongiae | Haplosclerida | Petrosiidae | Petrosia ficiformis | HMA | |

Demospongiae | Chondrosiida | Chondrosiidae | Chondrosia reniformis | HMA | |

Demospongiae | Agelasida | Agelasidae | Agelas oroides | HMA | |

Florida Keys and Belize | Demospongiae | Agelasida | Agelasidae | Agelas conifera/tubulata | HMA |

Demospongiae | Haplosclerida | Callyspongiidae | Callyspongia vaginalis | LMA | |

Demospongiae | Verongiida | Aplysinidae | Aplysina archeri | HMA | |

Demospongiae | Haplosclerida | Callyspongiidae | Callyspongia plicifera | LMA | |

Demospongiae | Dictyoceratida | Irciniidae | Ircinia strobilina | HMA | |

Demospongiae | Haplosclerida | Niphitidae | Niphates digitalis | LMA | |

Demospongiae | Haplosclerida | Petrosiidae | Xestospongia muta | HMA | |

Demospongiae | Clionaida | Clionaidae | Spheciospongia vesparium | HMA | |

Demospongiae | Verongiida | Aplysinidae | Verongula gigantea | HMA | |

Demospongiae | Verongiida | Aplysinidae | Verongula reiswigi | HMA | |

Demospongiae | Poecilosclerida | Mycalidae | Mycale laxissima | LMA |

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**MDPI and ACS Style**

Lesser, M.P.
Size Effects on Pumping Rates in High Microbial versus Low Microbial Abundance Marine Sponges. *Oceans* **2023**, *4*, 394-408.
https://doi.org/10.3390/oceans4040027

**AMA Style**

Lesser MP.
Size Effects on Pumping Rates in High Microbial versus Low Microbial Abundance Marine Sponges. *Oceans*. 2023; 4(4):394-408.
https://doi.org/10.3390/oceans4040027

**Chicago/Turabian Style**

Lesser, Michael P.
2023. "Size Effects on Pumping Rates in High Microbial versus Low Microbial Abundance Marine Sponges" *Oceans* 4, no. 4: 394-408.
https://doi.org/10.3390/oceans4040027