*Article* **High-Frequency Responses of the Blue Mussel (***Mytilus edulis***) Feeding and Ingestion Rates to Natural Diets**

**Laura Steeves 1,\*, Antonio Agüera 2, Ramón Filgueira 2,3,\*, Øivind Strand <sup>2</sup> and Tore Strohmeier <sup>2</sup>**


**Abstract:** The feeding activity of bivalves is understood to change in response to a suite of environmental conditions, including food quantity and quality. It has been hypothesized that, by varying feeding rates in response to the available diet, bivalves may be able to maintain relatively stable ingestion rates, allowing them to have constant energy uptake despite changes in food availability. The purpose of this study was to determine if the blue mussel *Mytilus edulis* responds to fluctuations in natural diets by changing feeding rates to maintain constant ingestion rates. Three four-day experiments were conducted to measure pumping and ingestion rates in response to natural fluctuations in food concentration (chlorophyll *a*). Experiments were conducted in a flow-through system over the spring season in south-western Norway. Pumping and ingestion rates were measured with high temporal resolution (every 20 min), which permitted the observation of the intra- and interindividual variability of feeding rates. Results show pumping rates varying within individuals over 4 days, and some individuals pumping on average at high rates (~5 Lh<sup>−</sup>1), and some at low (~1 Lh−1), despite being held in similar conditions. The pumping rate was generally not related to changes in food availability, and population-level ingestion rates increased with increasing food availability. These results suggest that, for this population of *M. edulis*, feeding rates may not vary with the available diet to produce constant ingestion over time.

**Keywords:** *Mytilus edulis*; pumping rate; ingestion rate; natural seston; filter-feeding; blue mussel

#### **1. Introduction**

Suspension-feeding marine bivalves play important ecological roles by filtering plankton and detritus that are suspended in the water column and subsequently producing feces and pseudofeces that sink to the ocean floor. This top-down control on planktonic communities, as well as bottom-up control from bivalve excretion, can affect planktonic community structure and functioning [1–3]. Concomitantly, the quantity and quality of food (seston) available to suspension-feeding bivalves affects their performance in terms of growth and survival [4,5]. Many coastal marine environments are characterized by large fluctuations in seston composition and concentration, over both long (seasonal) and short (diel) timeframes [6]. Understanding the relationships between food availability and bivalve feeding behavior is crucial to predicting both bivalve growth and bivalve–ecosystem interactions.

Suspension-feeding bivalves have several mechanisms by which the quantity and composition of ingested food can be regulated. Pumping rate, the volume of water moved over the gills per unit time (PR), is a metric of feeding activity and may change by several liters per hour in an individual exposed to diets of differing concentration and composition [7–9]. Generally, the initiation of pumping is triggered when food concentration surpasses a minimum threshold level, which may vary both between species and populations [7,10–12]. As food levels continue to increase beyond the minimum threshold, *PR* may remain at a constant maximum or increase with food concentration [7,13–15]. When food levels become

**Citation:** Steeves, L.; Agüera, A.; Filgueira, R.; Strand, Ø.; Strohmeier, T. High-Frequency Responses of the Blue Mussel (*Mytilus edulis*) Feeding and Ingestion Rates to Natural Diets. *J. Mar. Sci. Eng.* **2022**, *10*, 1290. https://doi. org/10.3390/jmse10091290

Academic Editor: Hans Ulrik Riisgård

Received: 15 August 2022 Accepted: 5 September 2022 Published: 13 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

very high, *PR* may decline or become intermittent to avoid overloading the gills [16,17] or the digestive system [18,19], suggesting that the maximum ingestion rate (IR) has been reached. Bivalves may also regulate ingestion rates through the rejection of pseudofeces, a process which is usually not observed in low-seston environments (< ~ 2.5–5 mgL−1), including the site used for this study [20]. Although bivalve *PR* in response to diets of varying composition has been extensively studied, a mechanistic understanding of this process is still relatively unknown [21,22].

For sessile species exposed to high levels of variation in the available diet, the ability to regulate the amount and quality of ingested food is an important mechanism in energy acquisition in bivalves. Although bivalves are exposed to frequently changing diets, these pre-ingestive mechanisms may help to maintain a relatively stable *IR* over time [23]. In the absence of pseudofeces production, *IR* may be estimated as a function of *PR* and food concentration [24]. For situations when food concentration is increasing and *PR* is decreasing, a relatively stable *IR* may be observed [25,26]. It has been theorized that this relationship between *PR* and food availability that can produce stable IRs may also contribute to constant energy uptake by bivalves in a fluctuating food environment [23]. In bivalves, the relationship between *IR* and food concentration is often modeled using Holling functional responses, which describe the relationship between prey density and predator consumption rates [27–29]. Holling functional responses may describe a linear increase (Type I) or asymptotic increases (Type II and III) in consumption rate with increasing prey density. The ability to accurately predict bivalve IRs in variable environmental conditions is a foundational step in predicting how bivalves acquire energy for growth.

The goal of this study was to examine relationships between *PR* and *IR* in response to fluctuation in natural diets and to explore the levels of intra- and interindividual variability in *PR* and IR. Often, the relationships between feeding, ingestion, and the food environment are studied using artificial diets (or natural seawater supplemented with artificial diets) in laboratory experiments [10,12,30]. However, experiments with natural diets are needed to understand the physiological responses of bivalves to the complexities of naturally occurring planktonic communities. Further, the current knowledge on the physiological responses in feeding activity to variability in diet comes primarily from environments with high seston concentration (>4 μgL<sup>−</sup>1), either in laboratory studies or in sites where bivalves are cultivated [1,30]. However, many bivalves reside in environments that usually have lower seston concentrations (below the threshold for pseudofeces production), including the site used in this study [31,32]. It is important to study the physiology of bivalves in these low-seston environments to understand both the dynamics of natural populations and for potential future expansion of aquaculture farms due to space limitations in high-seston environments. Metrics of feeding and ingestion rates are often reported as an average of a group (e.g., one measurement on each individual) or by taking repeated measurements on the same individuals over the course of several hours [17,33]. These studies may overlook the short-term fluctuations in *PR* that can be captured with methodologies that allow high-frequency physiological measurements [34]. This study uses a novel methodology to estimate the feeding and ingestion rates of *M. edulis* with a high temporal resolution (every 18 min, for 4 days), using natural seawater under flow-through conditions. As seston concentration may change over the course of hours and days, this study aims to capture the functional feeding response of *M. edulis* over short timescales. *M. edulis* was selected as a model species as it is widely distributed and commercially important, and its feeding behavior has been extensively studied. It was hypothesized that, as the concentration and composition of the seston varied, *M. edulis* would vary *PR* to maintain constant IRs, above a minimum threshold of food concentration, following [23].

#### **2. Material and Methods**

#### *2.1. Experimental Design*

Three independent 4-day experiments were conducted to measure *Mytilus edulis* pumping rates (PR), ingestion rates (IR), and environmental conditions (Table 1). Dockside experiments were conducted in the spring of 2019 and 2020 at Austevoll Research Station (Institute of Marine Research), Norway (60◦05 12.9" N 5◦15 51.5" E). Experiments 1 and 2 (Exp. 1, 2) were conducted in May and June of 2019, respectively. Experiment 3 (Exp. 3) was conducted in April of 2020. Blue mussels (*M. edulis*) (30–60 mm) were collected from a local population and held at 3 m depth from a dock at the research station in hanging lantern nets for acclimation prior to all experiments. *M. edulis* were collected in February of 2019 (Exp. 1 and 2), and February 2020 (Exp. 3). All experiments used the same experimental set-up, in the same location. At least 24 h prior to each experiment, 10 experimental mussels were removed from the lantern, cleared of epibionts, and measured for shell length. Mussels were then placed in individual flow-through chambers (see [12] for chamber design). The individual chambers were designed to ensure the direct flow of water over the mussels and to avoid recirculation, preventing refiltration [35]. The size of the rectangular chambers (internal measurements) are as follows: width of 3.8 cm, length of 19.5 cm, and height of 8.1 cm. All chambers containing mussels were cleaned of feces every 12 h with a Pasteur pipette to avoid the resuspension of feces. Two chambers had water flowing through them with no mussels, to serve as controls.

**Table 1.** Summary of environmental and *M. edulis* physiology data from all experiments. Values represent the mean for environmental data and the median for physiological data. ±indicates standard deviation, and the coefficient of variation (%) is shown in parentheses.


Ambient, unfiltered seawater was pumped using an air pump (PlusAir: PA.15FVT) directly from the dock where mussels were being held to a water reservoir (600 L). From the water reservoir, seawater was gravity-fed to a header tank located directly above the individual flow-through chambers. From the header tank, water was flowed through 12 individual chambers. Following [36] flow-rates were regulated to aim for the 20–30% particle depletion of particles that are completely captured by mussels. The flow-rate through each chamber was measured a minimum of 4 times per day, and the flow-rates were corrected as needed through a regulating tap at the outflow.

#### *2.2. Water Quality Measurements*

Water temperature (◦C) and fluorescence (as a proxy for chlorophyll *a*) (μgL−1) measurements were taken every 30 min in the experimental water reservoir using a CTD (SAIV A/S Model 204). Water from the header tank was also filtered for suspended particulate matter (SPM; mgL−1) and energy density (JL−1). To do this, water filtered from a pressurized tank through pre-combusted and washed 90 mm filters (Whatman GF/D 2.7 μm pore width). The volumes filtered varied between 30–50 L, depending on the filtration rate. The timing of SPM and energy density measurements was similar for Exp. 1 and 2 and changed for Exp. 3 due to the availability of filters. For Exp. 1 and 2, water from the header tank was filtered for SPM and energy density measurements once every 12 h, with six replicates for each measurement. For Exp. 3, SPM and energy density were measured before and after the experiment (2 and 20 April 2020) in replicates of 10 and 5, respectively. All filters were rinsed twice with 50 mL of 0.5 M ammonium formate to remove any salts and kept frozen until analyzed. To measure SPM concentration, filters were dried in a 60 °C oven until weights were stable. Energy-density measurements were estimated from

filters using a bomb calorimeter (BC, IKA model C6000) (Strohmeier et al. in prep). Filters were dried at 60 °C until stable weights were recorded, after which 500 mg of combustion aid (paraffin oil) was added to the filters to aid with complete combustion. Filters were combusted, and the measurement of temperature change (to the nearest 0.0001 K) was used to estimate energy density (JL<sup>−</sup>1). Energy produced by the combustion aid and filter itself were subtracted from overall energy density to report the values of energy from the water column only.

#### *2.3. Mussel Physiology*

The feeding activity of *M. edulis* was measured as both *PR* and *IR* using the flowthrough method [12,35,36]. This method relies on the accurate characterization of particles in the outflow of flow-through chambers (both from those containing a mussel and from the empty control chambers). In this experiment, the outflow of each chamber was connected to a normally closed solenoid valve. When a valve was closed, the outflow from that chamber would be directed to a drain. When opened, the outflow from that chamber was directed to an electronic laser particle counter (PAMAS S4031GO, GmbH, Hamburg, Germany), through silicone tubing. The solenoid valves from each individual chamber were opened sequentially, to ensure that the outflow from only one chamber at a time was delivered to the PAMAS. Solenoid valves were controlled by an Arduino Micro (3.X) connected to a relay board. The outflow of each chamber was sampled by the PAMAS for 60 s (volumetric equivalent of 10 mL), and then the particle counter was flushed for 30 s with the outflow of the following chamber before the next sample was recorded. This flushing period was employed to clean the PAMAS between samples. For Exp. 1 and 2, *PR* and *IR* measurements were taken on each individual and control every 18 min, and, for Exp. 3, measurements were taken on each individual every hour.

The PAMAS estimates particle size as equivalent spherical diameter (ESD, μm) and uses light scattering to count particles by size class at predefined intervals (0.5 μm in this study). From the estimates of particle counts for distinct size classes, both *PR* and *IR* were estimated. The pumping rate was estimated as:

$$PR = \left(\frac{P\_{\mathcal{C}} - P\_{\mathcal{b}}}{P\_{\mathcal{C}}}\right) \times FR \tag{1}$$

where *PR* is pumping rate (Lh<sup>−</sup>1), *Pc* is the count of particles exiting the control chamber, *Pb* is the number of particles exiting the experimental chamber containing a bivalve, and *FR* is flow-rate through the chamber (Lh<sup>−</sup>1) [37]. *Pc* and *Pb* were calculated using only particles understood to be completely captured on the gills (7.25, 7.75, and 8.25 μm ESD) [38]. Three size classes were used to minimize the potential error from a single particle-size count. Although larger particles (>8.25 μm ESD) are also expected to be completely captured, the abundance of these particles in the natural seston was low and were excluded to avoid introducing error into the calculation of *PR*. Chambers were monitored for pseudofeces production during all experiments, and none was observed at any time.

Pumping rates of individual mussels were standardized to gill area following [24]:

$$PR\_{std} = PR \times \left(\frac{GA\_{std}}{GA\_{ind}}\right) \tag{2}$$

where *PRstd* is the standardized *PR*, *GAstd* is the gill area for the averaged size mussel from all experiments (46 mm, 22.38 cm2), and *GAind* is the gill area for the individual mussel being standardized. The gill area was measured for all mussels in Exp. 1 and 2. Mussels were dissected by severing the anterior and posterior adductor muscles with a scalpel and separating both shell halves. In one half shell, gills were exposed by removing inner organs and mantel [39]. The gills were then floated in seawater to avoid contraction, and a photograph was taken from a top-down view. The area of one gill was then measured in ImageJ (v. 1.52 f) and multiplied by 8 (accounting for 4 gills, with 2 sides each), resulting in a total gill area of cm2. For Exp. 3, no gill area pictures were taken, and gill area estimates were made from shell length following the relationship between length and gill area previously established for the same population of mussels: gill area [cm2] = 0.0004 × length [mm]2.85, *r*<sup>2</sup> = 0.79, *n* = 27 [24].

*PRstd* measurements were subsequently corrected for variations in temperature using an Arrhenius function [40]:

$$\begin{aligned} PR(T)\_{std} &= PR\_1 \times \exp\left(\frac{T\_A}{T\_{AL}} - \frac{T\_A}{T}\right) \times \frac{s(T)}{s(T\_1)}\\ s(T) &= \left(1 + \exp\left(\frac{T\_{AL}}{T} - \frac{T\_{AL}}{T\_L}\right) + \exp\left(\frac{T\_{AH}}{T\_H} - \frac{T\_{AH}}{T}\right)\right)^{-1} \end{aligned} \tag{3}$$

where *PR*(*T*)*std* is the *PRstd* corrected to temperature *T*, *T* is the absolute temperature (281.15 K or 8 ◦C), *T*<sup>1</sup> is the reference temperature (K), *PR1* is the uncorrected *PR* at *T*1, *TA* is the Arrhenius temperature (5800 K), and *TAL* (45430 K) and *TAH* (31376 K) are the rates of *PR* decrease at the lower and upper temperature boundaries, respectively. *TL* (275 K) and *TH* (296 K) are the upper and lower temperature tolerance range, respectively. All Arrhenius parameters were obtained from van der Veer et al. (2006).

Ingestion rate was estimated from both *PR* and *F* values from the CTD as:

$$IR = PR(T)\_{std} \times F \tag{4}$$

where *IR* is the ingestion rate (μgh<sup>−</sup>1) calculated using *PR* standardized to both gill area and temperature, and *F* is chlorophyll *a* in μgL<sup>−</sup>1. This calculation of *IR* is valid for conditions in which there is no production of pseudofeces.

#### *2.4. Statistical Analyses*

All statistical analyses were performed in R version 3.6.2 (RStudio version 1.4.1717). For periods during experiments wherein two control measurements were not reliably collected (e.g., if water was not sufficiently sampled from the outflow of the control chamber and air was introduced into the PAMAS, artificially reducing particle counts), all *PR* data were removed. If *PR* values for an individual mussel were unreasonably high (e.g., *Pb* counts ~0), it was assumed that no outflow water was being sampled by the PAMAS, and *PR* data for that individual was removed. For one sampling period (Exp. 1 and 2: 18 min, Exp. 3: 1 h), if fewer than 6 mussels were successfully sampled, all data were removed. Due to limitations in the precision of the particle counter, if *PR*(*T*)*std* was <0.2 Lh<sup>−</sup>1, values were considered indistinguishable from 0, and the data were replaced with 0 but included in the data set. Within each experiment, a one-way repeated-measures ANOVA was run to test for differences in the *PR* between individual mussels. The *PR* data were checked for outliers and tested for normality using visual QQ-plots due to the large sample sizes within each dataset. The assumption of sphericity was checked with the Mauchly's test. If a significant effect of individual was observed on *PR*, post-hoc analyses with a Bonferroni adjustment was applied to observe pair-wise comparisons (*p* < 0.0001).

Within each experiment, median *PR*, *IR*, and chlorophyll *a* was visualized by fitting a locally estimated scatterplot smoothing (LOESS) regression [41]. For this regression, lowdegree polynomials are fit to subsets of the data using weighted least squares. The size of the subsets of the data are determined using a smoothing parameter (α), which is a fraction of the number of datapoints. In this study, α = 0.1, resulting in low-degree polynomials being fit to the data every ~10 h. For the LOESS regression, *PR*, *IR*, and chlorophyll *a* datasets were interpolated with a linear function. To examine general relationships between population-level *PR* and chlorophyll *a* concentration, a non-linear function [12] was visualized on *PR* and chlorophyll *a* observations from all experiments combined:

$$PR = \\$.35 - 0.67(F) + 0.56(ln(F) + 0.001/F) \tag{5}$$

where *F* is chlorophyll *a* concentration in μgL−1. To observe how the data from these experiments may differ from those observed in [12], Equation (5) was fit to the data from these experiments, with new parameters being estimated with nonlinear least squares fitting (RStudio package: nlstools).

#### **3. Results**

#### *3.1. Environmental Conditions*

Environmental conditions varied between all experiments from April to June following a seasonal trend (Table 1). Mean temperature values ranged between 6.9 and 10.5 ◦C, with values being lowest in April (Exp. 3) and highest in June (Exp. 2). Mean chlorophyll *a* concentration varied from 0.7 (Exp. 1) to 3.0 μgL−<sup>1</sup> (Exp. 3; Table 1). Suspended particulate matter (mgL−1) and energy density (JL−1) had similar trends with the lowest values in Exp. 1 (1.7 and 5.8, respectively) and the highest values in Exp. 2 (2.6 and 11.0, respectively; Table 1).

#### *3.2. Pumping Rate*

*M. edulis* in Exp. 1 had a median population-level *PR* (2.0 Lh<sup>−</sup>1), with values varying over time between 0.1 and 3.6 Lh−<sup>1</sup> (Table 1, Figure 1A). Notably, the population median *PR* was lowest between 9 and 10 May 2019 (Figure 1A). To further examine the variability in the population *PR*, examples of mussels with mussels high and low in interquartile range (IQR) in *PR* were analyzed (Figure 1B). At the same point in time, the *PR* between two mussels varied as much as ~3 Lh<sup>−</sup>1, which was particularly noticeable at the end of the experiment (11 May 2019) (Figure 1B). Although both mussels periodically stopped pumping (*PR* = 0), the timing and frequency of closures varied between individuals (Figure 1B). Additionally, some individuals had relatively stable *PR*s compared to others (Figure 1C), with the coefficient of variation in *PR* ranging from 28 to 162%. Significant differences were observed between the *PR* of individual mussels in Exp. 1, with average *PR*s ranging from 0.8 to 2.8 Lh−<sup>1</sup> (*F* (6, 168) = 143.7, *p* < 0.0001, generalized eta squared = 0.256). Post-hoc analyses with a Bonferroni adjustment revealed that all of the pairwise differences, between time points, were statistically significantly different (*p* < 0.0001, Figure 1C). Post-hoc analyses with a Bonferroni adjustment indicated a total of 6 statistically significant comparisons between mussel *PR* (*p* < 0.0001, Figure 1C).

*M. edulis* in Exp. 2 had a population-level median *PR* of 3.2 Lh<sup>−</sup>1, and the populationlevel *PR* was also the most stable of all experiments, ranging between 1.2 and 4.0 Lh−<sup>1</sup> (Table 1, Figure 2A). In Exp. 2, one individual was excluded from the population median *PR* calculation, as *PR* was often not distinguishable from zero (Figure 2C, indicated with an asterisk over the boxplot). In general, there was no extended period of time (e.g., days) over which the median population *PR* was generally higher or lower (Figure 2A). In examining the *PR* of the individuals with high and low IQR in *PR* (Figure 2B), it was observed that the individual with the low IQR had a highly stable *PR* over 4 days. This mussel pumped consistently at an intermediate rate of ~ 3 Lh<sup>−</sup>1, with few interruptions, until the end of the experiment. Contrastingly, the individual with the high IQR showed generally high *PR*s for the first 3 days of the experiment (~5 Lh<sup>−</sup>1) and low around the 4th day (~2 Lh−1). This mussel abruptly stopped pumping several times during the first two days of the experiment for short periods of time, before returning to a relatively high *PR* (~4 Lh−1) (Figure 2B). Towards the end of the experiment, this mussel had more gradual changes in *PR*, occurring over the course of several hours. Similar to Exp. 1, at a single point in time, there was, at times, a ~3 Lh−<sup>1</sup> difference in *PR* between two individuals (Figure 2B). Variability in *PR* within individuals was generally lower than in Exp. 1, with a coefficient of variation in *PR* ranging from 11 to 91% (Figure 2C). Significant differences were observed in *PR* between individual mussels over time, with average *PR*s for each individual ranging from 2.0 to 3.7 Lh−<sup>1</sup> (F(3.3, 1202) = 136.6, *p* < 0.0001, generalized eta squared = 0.227, Figure 2C). Post-hoc analyses with a Bonferroni adjustment indicated a total of 5 statistically significant comparisons between mussel *PR* (*p* < 0.0001, Figure 2C).

**Figure 1.** Summary of pumping rate (PR) (Lh−1) data from Exp. 1: (**A**) Median *PR* of all individuals ± SD over 4 days. (**B**) Individual *PR* of two mussels with lowest (blue) and highest (red) interquartile range in PR. (**C**) Boxplots of summarized *PR* of all individuals over the entire experiment; letters a–f above boxplots indicate statistically significant differences at *p* < 0.0001.

**Figure 2.** Summary of pumping rate (PR) (Lh−1) data from Exp. 2: (**A**) median *PR* of all individuals ± SD over 4 days. (**B**) Individual *PR* of two mussels with low (blue) and high (red) interquartile range in PR. (**C**) Boxplots of the summarized *PR* of all individuals over the entire experiment; letters a–e above boxplots indicate statistically significant differences at *p* < 0.0001. \* Indicates individual mussel not included in median measurements.

*M. edulis* in Exp. 3 had a median population-level *PR* of (3.1 Lh−1); however, the variability in *PR* was markedly higher than in the first two experiments, both between and within individuals (Table 1, Figure 3A). The median population *PR* ranged from 1.0 to 7.5 Lh−<sup>1</sup> (Figure 3A). Similar to in Exp. 2, there were no extended periods of high or low median population *PR*s, but *PR*s were generally variable over the 4 days. When examining the individuals with high and low IQR in *PR*, there was a marked difference between their *PR*s during the experiment. Although there were three mussels with lower IQR in *PR* (Figure 3C), the fourth-lowest individual was selected to highlight in Figure 3B, as this individual had a more complete *PR* dataset during the experiment. The mussel with the low IQR in *PR* pumped at low rates over the course of the experiment (1.3 ± 0.9 Lh−1), compared to the mussel with the highest IQR in *PR* (6.1 ± 2.4 Lh−1) (Figure 3B, C). The high level of variability in the mussel pumping at 6.1 Lh−<sup>1</sup> was driven by a decrease in *PR* over the last several days of the experiment (Figure 3B). Further, at a single point in time, there was a difference of ~7 Lh−<sup>1</sup> in *PR* between two individuals (Figure 3B). The variability in *PR* within individuals was generally lower than Exp. 1, with a coefficient of variation in *PR* ranging from 31 to 135% (Figure 3C). Significant differences were observed in *PR* between individual mussels over time, with average *PR*s ranging from 0.5 to 6.1 Lh−<sup>1</sup> (F (3.7, 172) = 91.2, *p* < 0.0001, generalized eta squared = 0.64, Figure 3C). Post-hoc analyses with a Bonferroni adjustment indicated a total of 3 statistically significant comparisons between mussel *PR* (*p* < 0.0001, Figure 3C).

**Figure 3.** Summary of pumping rate (PR) (Lh−1) data from Exp. 3: (**A**) median *PR* of all individuals ± SD over 4 days. (**B**) Individual *PR* of two mussels with low (blue) and high (red) interquartile range in PR. (**C**) Boxplots of the summarized *PR* of all individuals over the entire experiment; letters a–c above boxplots indicate statistically significant differences at *p* < 0.0001. \* Indicates individual mussel not included in median measurements.

#### *3.3. Ingestion Rate*

In Exp. 1, the population-level median *IR* of *M. edulis* was 0.8 μgh−<sup>1</sup> (Table 1, Figure 4A). The ingestion rate closely followed the pattern of median *PR* over time, with low rates between May 9 and 10 and rising on 11 May, matching the increase in *PR* (Figure 4A). The variability in population *IR* in Exp. 1 was 85%; however, the range was the lowest of all experiments (4.3 μgh<sup>−</sup>1) (Table 1, Figure 4A). Exp. 2 has a population-level median *IR* of 4.4 μgh<sup>−</sup>1, with a coefficient of variation of 36% and the second-largest range of all experiments (8.8 μgh<sup>−</sup>1) (Table 1, Figure 4A). In Exp. 2, *IR* more closely followed the trend of chlorophyll *a* compared to *PR* over time, with a marked decrease in *IR* at the end of June 6 and an increase early on June 7, matching the pattern of chlorophyll *a* (Figure 4B). In Exp. 3, the population-level median *IR* was 8.9 μgh−<sup>1</sup> with a coefficient of variation of 45% and the highest range of all experiments (17.4 μgh−1) (Table 1, Figure 4C). Additionally, *IR* did not follow the pattern of either *PR* or chlorophyll *a* for the entire duration of the experiment (Figure 4C). Between April 8–9, *IR* followed the fluctuating pattern of *PR*; however, during the beginning and end of the experiment, *IR* followed the patterns in chlorophyll *a* (Figure 4C).

**Figure 4.** Pumping rate (PR) (Lh<sup>−</sup>1) (black), chlorophyll *a* (F) (μgL<sup>−</sup>1) (green), and ingestion rate (IR) (μgh−1) (gray) averaged for all individual mussels in (**A**) Exp. 1, (**B**) Exp. 2. (**C**) Exp. 3. The gray shaded area is the standard deviation for IR.

#### *3.4. Functional Responses to Food Availability*

To examine the relationships between *PR*, *IR*, and food availability (chlorophyll *a*), the population-level results from all experiments were combined (Figure 5). When considering the population-level response in *PR* to chlorophyll *a* in all the experiments, no consistent trends were observed (Figure 5A). Additionally, the previously described relationship between *PR* and chlorophyll *a* in [12] did not well describe the relationship observed in this study (Figure 5A). *PR* generally did not increase with increasing chlorophyll *a*; however, interindividual variability in *PR* increased at higher chlorophyll *a* concentrations (>2 μgL<sup>−</sup>1) (Figure 5A). For all experiments, population-level *IR* generally increased with increasing chlorophyll *a* (Figure 5B). At low concentrations of chlorophyll *a* (<2 μgL−1), *IR* increases were highly linear with chlorophyll *a*; however, as the chlorophyll *a* concentration increased beyond 2 μgL<sup>−</sup>1, the increase in *IR* became less linear (Figure 5B). Further, interindividual variability in *IR* increased in each subsequent experiment with increasing concentrations of chlorophyll *a* (particularly when chlorophyll *a* was >2 μgL<sup>−</sup>1) (Figure 5B). The relationship between *IR* and increasing chlorophyll *a* was visualized with Holling functional responses (Type I, II, and III) to illustrate the potential response in *IR* being either linear or asymptotic.

**Figure 5.** Relationships between (**A**) pumping rate (PR) (Lh−1) and (**B**) ingestion rate (IR) (μgh−1) and chlorophyll *a* (μgL−1) for all experiments. The dotted line on (**A**) is drawn from Equation (5), and the dashed line is fitted from Equation (5) with parameters fit to this dataset: *PR* = 2.69 − 0.02(*F*) + 0.53(*ln*(*F*) + 0.001/*F*). The drawn lines on (**B**) represent Holling functional responses (Type I, II, and III, solid, dashed, and dotted, respectively) to indicate the potential relationships between fluorescence and IR.

#### **4. Discussion**

This study used a novel flow-through methodology to measure feeding (pumping and ingestion rates) in *M. edulis* in response to natural fluctuations in diet. Although it has previously been hypothesized that bivalves alter pumping rates to maintain relatively constant ingestion rates [23], these compensatory processes were not observed in this study. Pumping rates displayed no consistent response to changes in food availability, as measured by chlorophyll *a* concentration. Further, *IR* generally increased with increasing food availability. The high frequency of pumping and ingestion rate measurement taken in this study permitted the exploration of both intra- and interindividual variability on a much finer temporal scale (minutes) compared to previous studies (hours/days/weeks). High levels of variability in pumping and ingestion rates were observed both between and within individuals during these 4-day experiments.

#### *4.1. Feeding Activity in Response to Natural Fluctuations in Diet*

The range of *PR*s recorded in this experiment (mean ± standard deviation: 3.0 ± 1.8 Lh<sup>−</sup>1) are similar to those reported for *M. edulis* in similar environmental conditions [12,24,42]. Food concentration (or diet quantity) was characterized as chlorophyll *a* concentration and increased with each subsequent experiment from ~1 to ~3 μgL<sup>−</sup>1, which is within the range of values commonly reported during spring in this region [31,32]. In all experiments, *PR* generally was not related to changes in food concentration. Food concentration is understood to be a primary determinant of feeding rates in bivalves, wherein feeding is initiated at a minimum food concentration and quickly increases or switches to a maximum rate as food concentration increases [10,22]; finally, at food levels above a saturation threshold, feeding rates often decline, to avoid overloading the gills or because maximum *IR* may have been reached [16,43]. Although a cessation in the *PR* of mussels has been observed at low food concentrations (<0.5 μgL-1, [44], a previous study on the same population of *M. edulis* used in this study observed *PR*s between 2.5–4.7 Lh−<sup>1</sup> at very low chlorophyll *a* concentrations (0.1–06 μgL−1) [12]. Further, a decline in *PR* was not expected, as food concentrations (<3 μgL−1) did not reach the saturation threshold expected to trigger a reduction in feeding rates [22,43]. Therefore, the lack of a relationship between populationlevel *PR* and chlorophyll *a* in any of the 4-day experiments is not unexpected for the low levels of chlorophyll *a* observed in this study.

In this population of *M. edulis*, relatively stable *PR*s have also been observed, despite changes in a diet of similar quantities (chlorophyll *a* concentration) [12]. It is possible that the lack of relationship between *PR* and chlorophyll *a* observed in this experiment indicates that, for individuals adapted to maximize ingestion rates in low-seston environments, *PR* is initiated at a very low food concentration and remains high as food concentration increases. Bivalves inhabiting low-seston environments have often been observed to have very high feeding rates in field studies [12,45–47]. At chlorophyll *a* levels much higher than those observed in this study (>3 μgL−1), the *PR* of *M. edulis* may decline; however, these conditions are not frequent in this region [31,32]. It has previously been recognized by [48] that the strategy of bivalves to regulate the amount of ingested material may vary by species, wherein *M. edulis* has often been observed to regulate ingestion through pseudofeces production, while continuing to pump at high rates [7,11,45]. As the range in diet observed in this study remained under the threshold for the production of pseudofeces, it is likely that the mussels were continuing to pump at high rates. The lack of a relationship between *PR* and chlorophyll *a* levels observed may also indicate that, for short-term fluctuations in diet quantity, a physiological response in *PR* may not be elicited. This "time-averaged" behavior may be an explanation for why *PR*s do not change in response to diet changes that only last on the scale of minutes to hours [48].

Aspects of diet composition (or diet quality) that may affect feeding rates include seston load and the fraction of non-digestible inorganic material [9,17,19,29,49–51]. By characterizing the diet using chlorophyll *a*, some qualitative aspects of the diet known to influence *PR* may not be captured [9,17]. Although chlorophyll *a* increased from Exp. 1 to Exp. 3, the highest concentrations of suspended particulate matter and energy were observed in Exp. 2, indicating that diet quality was also changing between experiments. Although fluorescence concentration does not comprehensively describe the available diet, it is easily measured with high temporal frequency, compared to the more timeintensive methods required for the filtration of water for SPM and energy concentration [34]. Resultingly, high-temporal-resolution measurements of chlorophyll *a* concentration may provide one of the best available methods to take measurements of diet and feeding physiology on similar temporal scales.

The functional response of *IR* to food concentration in bivalves has been previously described using different Holling functional responses. Most commonly used are the Type II and III functional responses, which are characterized by stable IRs at high food concentrations [28,29]. The population-level *IR* in this experiment generally increased with increasing chlorophyll *a* concentration; however, this relationship had the highest slope when the food concentration was low (<2 μgL<sup>−</sup>1). The population-level response in *IR* to increasing food concentrations in this study suggests that any of the Holling functional responses may statistically represent the observed relationship. However, the data collected in this study is heavily concentrated with observations at low food concentrations (<2 μgL<sup>−</sup>1), compared to higher concentrations (~2–5 μgL−1), which limits the ability to estimate an asymptotic relationship. Although a stable *IR* at high food levels has been previously hypothesized (Holling Type II and III) [23,25,26,52], it is likely that food levels in this experiment did not reach high enough concentrations to observe maximum and constant ingestion rates. As previously described, it is possible that the strategy of individuals adapted to low-seston environments may be to continuously pump at a high rate, resulting in increasing ingestion rates with increasing food concentration [12].

Despite the lack of the clear stabilization of ingestion rates at high food concentrations, the observations revealed increasing levels of inter-individual variability in both ingestion and pumping rates at high chlorophyll *a* concentrations. This variability in feeding physiology at increasing food concentrations may indicate the periodic stopping or slowing of feeding driven by digestive processes (e.g., gut capacity being reached, maximum *IR* being reached) [18,27,53,54]. Accordingly, it is possible that an asymptote in ingestion rates reflective of a Holling Type II or III response may emerge at higher food concentrations (e.g., >3 μgL−1) if the periodic slowing or stopping of *PR* becomes more frequent at the population level.

#### *4.2. Intra- and Interindividual Variability in Feeding Activity*

The high temporal resolution of the methodology used in this experiment was selected to be able to examine both intra- and interindividual variability in pumping and ingestion rates in response to real-time fluctuations in diet. By observing the range of physiological rates within an individual over the scale of hours and days, it is possible to more accurately observe short-term fluctuations in feeding physiology in response to environmental variability in terms of food quantity and quality [55,56]. In previous studies, when physiological rates have been measured only one time per individual or repeatedly on an individual with coarse temporal resolution, it is possible to overlook the full range of intra- and interindividual variability over short timescales [34].

Inter-individual variability was observed during each 4-day experiment between the *PR*s of individual mussels. Despite being exposed to the same conditions, the average *PR* of the mussels ranged ~3 Lh−<sup>1</sup> between individuals. Inter-individual variability in physiological rates, including feeding rates, has been explored as a potential explanation for different growth rates between fast- and slow-growing individuals [57], and similar interindividual variability in feeding rates of bivalves exposed to the same conditions has been observed in other studies [58,59]. In this experiment, differences between experimental individuals were minimized by selecting *M. edulis* of the same size and age-class from the same location. The goal in selecting similar individuals was to minimize differences in inter-individual variability driven by factors not examined in this study. However, it is possible that there were differences between the *M. edulis* used in this study that were not accounted for, including sex (potentially influencing energetic requirements), genetic differences, and maternal effects [60–63]. Future experiments may consider further minimizing differences between individuals by rearing first-generation offspring together in common conditions (e.g., [64]) or by increasing the duration of the experiments to

observe if average physiological rates between individuals are similar across longer periods of time (e.g., seasonally or annually).

Intraindividual variability was observed in all experiments, wherein *PR* and *IR* varied within individuals over the 4-day periods. Variability in the feeding physiology of bivalves may be driven by changes in environmental conditions, including those previously discussed (e.g., temperature, diet) [14,15,65]. However, the periodic cessation of feeding in *M. edulis* observed in this study was unsynchronized between individuals, suggesting that feeding rates may have been regulated by internal drivers rather than external environmental conditions under the environmental conditions of these experiments. For example, if gut capacity is reached, feeding rates may slow down; however, gut capacity may not be reached at the same time for all individuals [18,19]. The high temporal resolution of the *PR* data presented here indicates that *PR* activity varies between individuals in terms of how consistent *PR* is over time, maximum and minimum rates, and how quickly *PR* may increase or decrease (e.g., on the scale of minutes to hours). Observing intraindividual variability in the feeding physiology of *M. edulis* and characteristics of the natural diet at high temporal resolution provides insights into the drivers of the feeding physiology of bivalves. Further, although the unsynchronized individual responses observed in these experiments suggest that *PR* is not driven by environmental factors, their influence in feeding physiology cannot be disregarded, and further experiments under broader environmental conditions are warranted.

#### *4.3. Energy Acquisition*

Chlorophyll *a* is used in this study as a proxy for food concentration; however, chlorophyll *a* is limited as a proxy for the amount of food that is captured and ingested from the seston by *M. edulis.* Chlorophyll *a* alone is not able to capture the complexity of the seston in terms of particle sizes and surface properties, which both may affect particle capture efficiency [66]. Capture efficiency describes the proportion of particles captured on the gill, compared to those in the water, and is often described according to particle size, wherein capture efficiency increases with increasing particle size to some maximum, beyond which all particles are captured [67,68]. However, capture efficiency has also been related to other particle characteristics including hydrophobicity [69], lectin–carbohydrate interactions [70], and chlorophyll *a* [71]. Additionally, capture efficiency has been observed to vary in *M. edulis* across seasons in response to natural seston composition [24,72]. As *IR* is described in this experiment using chlorophyll *a*, if changes in capture efficiency occurred, it would not be accounted for in estimates of ingestion. Further, estimation of *IR* using chlorophyll *a* instead of the total volume of ingested material may not be used to estimate gut capacity, which may limit maximum ingestion rates [18,19].

It has been theorized that, as the quality and quantity of their diet changes, bivalves will make use of behavioral and physiological mechanisms to maintain constant energy uptake [10,18,23,26]. Although in this study, constant ingestion rates were not observed as food concentration changed, it is possible that other mechanisms were employed to maximize energy uptake. Specifically, changes in digestive processes may contribute to constant levels of energy absorption despite variability in the quantity and quality of diet in the digestive system [54,73–75]. For example, changing in digestive enzyme activity may increase the absorption efficiency of bivalves acclimated to low-quality diets [76]. In addition, gut passage time may increase in response to diets of low quality to prolong the time available for digestion and absorption of nutrients [76]. The relationships between digestive processes and diet quantity and quality are complex, particularly as natural diets may fluctuate on both short- and long-term timescales; however, they have been empirically modeled [18,77,78]. Changes in digestive processes may contribute to stable energy uptake, despite variations in IR.

#### **5. Conclusions**

This study examined the functional relationships between pumping and the ingestion rate in *M. edulis* in response to changes in the diet concentration in a low-seston environment. Results indicated that there were no clear relationships between the population-level pumping rate and food concentration, measured as fluorescence; however, the ingestion rate increased with increasing food concentration. Using novel methodology that permitted the measurement of feeding activity with high temporal resolution, approximately every 20 min, this study highlights the variability in physiological rates both between and within individuals exposed to the same environmental conditions. Both intra- and interindividual variability in pumping and ingestion ranges were observed in all experiments. Understanding the range of both intra- and interindividual variability in physiological rates is beneficial when scaling physiological rates from the individual to population level and for estimating interactions between suspension-feeders and food source. This study contributes to our knowledge of how bivalves acquire energy in dynamic food environments.

**Author Contributions:** Conceptualization, methodology, validation, all authors.; resources, R.F., T.S., Ø.S.; data curation, L.S., A.A.; writing–original draft preparation, L.S.; writing–reviewing and editing, all authors.; visualization, L.S.; supervision, R.F., Ø.S.; funding acquisition, R.F., Ø.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by a graduate Natural Sciences and Engineering Research Council of Canada (NSERC) award, a Killam Predoctoral Scholarship, and a Mitacs Globalink Research Award to L.S., an NSERC Discovery Grant to R.F., and the project "Sustainable Low-Trophic Aquaculture" at the Institute of Marine Research (Bergen, Norway).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Authors thank Cathinka Krogness, Justin Trueman, and Tom Koppenol for their assistance with data collection.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Filtration Rates and Scaling in Demosponges**

**Hans Ulrik Riisgård 1,\* and Poul S. Larsen <sup>2</sup>**

	- psl@mek.dtu.dk

**Abstract:** Demosponges are modular filter-feeding organisms that are made up of aquiferous units or modules with one osculum per module. Such modules may grow to reach a maximal size. Various demosponge species show a high degree of morphological complexity, which makes it difficult to classify and scale them regarding filtration rate versus sponge size. In this regard, we distinguish between: (i) small single-osculum sponges consisting of one aquiferous module, which includes very small explants and larger explants; (ii) multi-oscula sponges consisting of many modules, each with a separate osculum leading to the ambient; and (iii) large single-osculum sponges composed of many aquiferous modules, each with an exhalant opening (true osculum) leading into a common large spongocoel (atrium), which opens to the ambient via a static pseudo-osculum. We found the theoretical scaling relation between the filtration rate (*F*) versus volume (*V*) for (i) a single-osculum demosponge to be *<sup>F</sup>* <sup>=</sup> *<sup>a</sup>*3*V*2/3, and hence the volume-specific filtration rate to scale as *<sup>F</sup>*/*<sup>V</sup>* <sup>≈</sup> *<sup>V</sup>*<sup>−</sup>1/3. This relation is partly supported by experimental data for explants of *Halichondria panicea*, showing *F/V* = 2.66*V*<sup>−</sup>0.41. However, for multi-oscula sponges, many of their modules may have reached their maximal size and hence their maximal filtration rate, which would imply the scaling *F/V* ≈ constant. A similar scaling would be expected for large pseudo-osculum sponges, provided their volume was taken to be the structural tissue volume that holds the pumping units, and not the total volume that includes the large atrium volume of water. This may explain the hitherto confusing picture that has emerged from the power-law correlation (*F/V* = *aV*b) of many various types of demosponges that show a range of negative *b*-exponents. The observed sharp decline in the volume-specific filtration rate of demosponges from their very small to larger sizes is discussed.

**Keywords:** allometric scaling; sponge module; choanocyte density; specific filtration rate

#### **1. Introduction**

There are nearly 9500 living species of sponges, and the class of demosponges contains 82% of all sponge species [1]. All demosponges are modular filter-feeding organisms that are made up of aquiferous units or modules with one osculum per module [2,3]. The many different species of demosponges show a high degree of morphological complexity [4]. Therefore, they are not easy to classify and scale regarding basic features, such as filtration rate versus sponge size. In the present study, we distinguish between: (i) small singleosculum single-module sponges consisting of one aquiferous module, which includes very small [5] and larger explants [6] (Figure 1); (ii) multi-oscula multi-modular sponges consisting of many aquiferous modules each with a separate osculum leading to the ambient, which could be small explants [7] or larger sponges, such as *Halichondria panicea* [8–10]; and (iii) large single-osculum multi-modular sponges (or large single-pseudo-osculum sponges) composed of many aquiferous modules each with an exhalant opening (true osculum) leading to a common large spongocoel (atrium), which opens to the ambient via a static pseudo-osculum, such as *Xestospongia muta* [11,12]. A contraction of the true oscula in the atrial lining of *Verongia gigantea* was described by [13] and only "very small specimens" with a body volume <200 mL were able to occlude the joint pseudo-osculum.

**Citation:** Riisgård, H.U.; Larsen, P.S. Filtration Rates and Scaling in Demosponges. *J. Mar. Sci. Eng.* **2022**, *10*, 643. https://doi.org/10.3390/ jmse10050643

Academic Editor: Azizur Rahman

Received: 29 March 2022 Accepted: 6 May 2022 Published: 8 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Figure 1.** Sketch of a single-osculum demosponge showing the water flow from outside through ostia into inhalant canals (ICs) to the water pumping choanocyte chambers (CCs), where the water is filtered, then further into exhalant canals (ECs) and subsequently out through the osculum. The thin wall separating the tapered inhalant and exhalant canals is for a great part made up of CCs embedded in the mesenchyme. Adapted from [9].

Single-osculum and multi-oscula sponges have contraction–inflation behavior, including the closure and opening of the osculum; furthermore, in these sponges, the speed of the exhalant jet correlates to the size of the osculum [5,6,14]. Here, [6] suggested the following theoretical allometric scaling parameters for the osculum jet speed (*U*), osculum cross-sectional area (*OSA*), and pumping rate (=filtration rate, *F*) could be expressed as:

$$
\Omega I = a\_1 OSA^{\bf b} \\
\text{'} ; b\_1 = 1/2 \\
\tag{1}
$$

$$F = a\_2 OSA^{\text{b2}}; b\_2 = 3/2 \tag{2}$$

These scaling parameters, which rely on the suggested uniform density of pumping units (choanocyte chambers), were found to agree with the measurements on both singleosculum explants [6] and multi-oscula explants of *Halichondria panicea* [7]. However, to examine how the theoretical scaling relationships applies to larger sponges, [15] measured in situ the filtration rate of 20 sponge species and found that their results showed "an opposite trend of an allometric decrease in *U* with *OSA* for two-thirds (12 out of 18) of the species", and they concluded that the allometric scaling parameters did not apply to large sponges with "fully open and static oscula", but only to small explants that "dynamically constrict and expand their oscula" [15] found that their data showed a different scaling than that of Equations (1) and (2), because the decrease in volume-specific pumping rate with increasing sponge size for the larger sponges indicated that the density of choanocyte chambers decreases with increasing sponge volume.

To help in the understanding of the allometric data correlations [16], the compiled available data on the volume-specific filtration rate (*F/V*) versus sponge volume (*V*) approximated as *F/V* ≈ *<sup>V</sup>*<sup>b</sup> in demosponges, but the observed large and confusing variations could not be immediately explained. Therefore, an important aspect of the present study is to clear up this situation. It is our hypothesis that *F/V* versus *V* of (i) single-osculum single-module demosponges decreases with increasing size, while it remains essentially constant for (ii) multi- and (iii) single-oscular multi-modular demosponges, provided that volume is considered to be that of structural sponge tissue, which, again, is proportional to the sponge dry weight.

Here, we first examine the scaling relation between the filtration rate and body volume in (i) single-osculum single-module explants before we compare it with scaling in (ii) multi-oscular multi-modular sponges. Next, we examine if (iii) a large single-osculum multi-modular sponge may be regarded as a population of modules that share the characteristics of single-osculum explants, or if such sponges have different scaling characteristics. Finally, we discuss how to arrive at a better understanding of specific filtration rates in demosponges. We arrive at the classification of demosponges from the concept of "modules", which is then used in the scaling of the filtration rates.

#### **2. Materials and Methods**

We used published data on single-osculum sponge explants consisting of one aquiferous module of various sizes obtained from colonies of the demosponge *Halichondria panicea*. Branches of the collected sponges were either cut into very small pieces without an osculum [5] or in fragments of various sizes with a single osculum [6]. The cut-off pieces were individually fixed with whipping twine on substrate plates in flowing seawater and were allowed to develop into explants over a couple of weeks, which reorganized their elements of the aquiferous system [3] in such a way that each osculum cross-sectional area (*OSA*) became adjusted to the size (volume, *V*) of the individual sponge explant. The experimental data obtained for these explants at 15 ◦C were used to scale the filtration rate with the size of the sponge module. Due to the very low volume-specific filtration rates in the single-osculum explants reported by [7], we suggest that these explants may not have been fully reorganized, and therefore not used in the present study. Power-function regression curves (LM) were fitted the in [17] for growth rate estimates, based on the sponge body volume over time.

#### **3. Results and Discussion**

In the present study, the scaling relation between the filtration rate and volume of single-osculum explants is presented and compared with scaling in multi-oscular sponges. The findings are discussed in order to obtain a better understanding of how to deal with specific filtration rates in demosponges.

#### *3.1. Scaling in Single-Osculum Single-Module Demosponges*

A scaling relation between the water-pumping rate and sponge-body volume may be derived by considering a single inhalant canal of length *L* in a single-osculum demosponge (Figure 1). The thin wall separating the tapered inhalant and exhalant canal system is for a great part (30% to 50%) made up of water-pumping choanocyte chambers with a diameter of approximately 30 μm embedded in mesenchyme. The pumping rate (=filtration rate, *F*) from these chambers is proportional to the product of pumping rate (*F*CC) of each choanocyte chamber and their number, which is proportional to the wall area (~*L*2) of the canal, i.e., *<sup>F</sup>* ≈ *<sup>L</sup>*2, and the sponge volume associated with canals and walls would scale as *<sup>V</sup>* <sup>~</sup> *<sup>L</sup>*<sup>3</sup> for the isometric growth. It follows that *<sup>F</sup>* ≈ (*V*1/3) <sup>2</sup> and thus:

$$F = a\_3 V^{\text{kb3}}; b\_3 = \text{2/3} \tag{3}$$

Hence, the volume-specific filtration rate would scale as *F*/*V* = *V*2/3−<sup>1</sup> = *V*<sup>−</sup>1/3, which indicates a decrease with increasing sponge volume. This scaling may be expected to apply when a small single-osculum sponge grows bigger. Thus, [5] measured the filtration rate in 15 small single-osculum *Halichondria panicea* explants of the same size (*V* = 0.018 mL) and found that the mean filtration rate was *<sup>F</sup>* = 0.28 ± 0.06 mL min−1, which indicates a volume-specific filtration rate of *F/V* = 0.28/0.018 = 15.6 min−1, thus showing that the explant filters an amount of water that is equivalent to 15.6 times its body volume per min. Using Equation (3) *F* = *a*3*V*2/3 the filtration rate (*F*, mL min<sup>−</sup>1) versus sponge body volume (*V*, mL) can be predicted to be *F* = 3.97*V*2/3 because *a3* = *F*/*V*2/3 = 0.28/0.0182/3 = 3.97 and consequently caused the volume-specific filtration rate to be *F/V* = 3.97*V*2/3−<sup>1</sup> = 3.97*V*<sup>−</sup>1/3. The predicted *F/V* versus *V* is depicted in Figure 2. Furthermore, [5] measured *F/V* in a number of single-osculum *H. panicea* explants with various body sizes (*V* = 0.018 to 1.977 mL), which are also shown in Figure 2. It can be observed that the model-predicted curve describes the experimental data fairly well. Another example of a single aquiferous module is the sponge branch cut from a colony of *Haliclona urceolus* [9], for which *F* = 6 mL min−<sup>1</sup> and *V* = 1.726 mL was measured. These results lead to *F*/*V* = 3.48 min−<sup>1</sup> and in are good agreement with the foregoing example, which implies *a3* = *F*/*V*2/3 = 4.17. Furthermore, the regression analysis of the measured filtration rate and size of 8 *H. urceolus* specimens [8] produced *F*/*V* = 3.96*V*<sup>−</sup>0.39. Likewise, the exponent (*b*<sup>3</sup> = 0.59) for the power function regression line for *F* versus *V* for the same data is close to the model-predicted (Equation (1)) *b*<sup>3</sup> = 0.66 (Figure 3). We should add that the same results from [6] were shown in [7], where, we as co-authors, erroneously assume the linear scaling relation *F* = *aV* now replaced by *F* = 2.66 *V*0.59. The same mistake was made in [7].

**Figure 2.** *Halichondria panicea*. Volume-specific filtration rate (*F/V*) as a function of body volume (*V*) of single-osculum explants. The model-predicted curve (dotted) based on [5] (open symbol) is shown along with the power-function regression line for all data (dashed, solid symbols) for data obtained from [6] (LM, t0.2969, 12 = −2.859, *p* = 0.0013).

**Figure 3.** *Halichondria panicea*. Filtration rate (*F*) of single-osculum explants as a function of spongebody volume (*V*). The power-function regression line has been shown along with its equation. The *b*3 exponent is 0.59, which may be compared to the model-predicted *b*<sup>3</sup> = 2/3 [5,6] (LM, t0.2964, 12 = 4.099, *p* = 0.0015).

An aquiferous module is "a certain volume in the sponge that is supplied by a system of choanocyte chambers and aquiferous canals associated with a single osculum. Therefore, a sponge represents a modular organism" [18]. A demosponge, such as *Halichondria panicea* consists of multiple modules, each with an osculum (Figure 4). If a module is only able to grow until it has obtained a certain volume, most of the whole modular sponge organism will consist of full-grown modules with a near similar *F/V* ratio. Therefore, the *F/V* ratio of a growing multi-oscula sponge in which most of the modules are full-grown should be expected to also be constant. Thus, the present scaling, Equation (3) only applies when a small single-osculum sponge—or an aquiferous module—grows larger.

**Figure 4.** *Halichondria panicea.* Underwater photo (29 July 2019) from the inlet to Kerteminde Fjord, Denmark, showing erect branching (ramose) sponges of type (ii) with multi-modules each with an osculum.

#### *3.2. Scaling in Multi-Oscula Multi-Modular Demosponges*

To our knowledge, the first attempt to outline the size and number of aquiferous modules in a multi-oscular sponge was made by [7] in explants of branching *Halichondria panicea*. Here, the boarders of each module were identified through observations of incurrent and excurrent water flow using fluorescein deposited on the sponge surface (exopinacoderm) using a micromanipulator, and subsequently the volume (*V*mod) of each module was measured by cutting along the borders and weighing the module. Because the modules were not growing, a plot of *F/V* versus *V* showed no trend, i.e., *F/V* = constant, and for modules of sizes between 0.5 and 2.7 mL, the mean *F/V* was found to be 1.2 ± 0.8 min−<sup>1</sup> [7]. Similar studies in other multi-oscula multi-modular demosponges are awaiting in order to verify if *F/V* ~ constant.

#### *3.3. Scaling in Single-Osculum Multi-Modular Demosponges*

Many large tropical single-osculum sponges are composed of many modules, each with a true osculum that opens into a common spongocoel (atrium), which opens to the ambient water via a fully open motionless pseudo-sculum. Here, *Aplysina lacunosa* may serve as an example of a typically large tropical species, which has a tubular shape with a large pseudo-osculum on top [19]. Another example is *Verongia gigantea* in which the (pseudo)osculum becomes unable to occlude when the diameter becomes greater than about 15 mm, whereas the atrial wall with true oscula shows periodic cessation [13].

For clarity, when dealing with multi-oscular sponges, we define "structural volume *V*str" as that of the sponge-tissue structure that excludes any large spongocoel (atrium cavity), while the "total volume *V*tot" of a sponge includes the atrium. Here, *V*str may be expected to be proportional to the dry weight of sponge tissue, *W*. Small single-osculum explants have no large atrium, just exhalant canals that join to one canal leading to the osculum; therefore, here, there is no significant difference between the 2 volumes. Likewise, in a multi-oscular sponge, such as *Halichondria panicea*, each module has its own osculum. However, for large vase, jar, urn- or tube-shaped sponges, the 2 volumes may be quite different, as it appears from the following.

In [11], it was found that the relationship between the spongocoel volume (*V*spongo) and total sponge volume (*V*tot) could be described by the following allometric equation: *V*spongo = α*V*tot1.214 where the exponent β = 1.214 indicates that the relative volume of the spongocoel may increase by as much as 20 to 25% for sponge sizes of 50 to 200 L for the total volume of *Xestospongia muta*. Other β-exponents may apply for other large sponge species with a spongocoel of various shapes, and therefore a scaling of *F/V* in one sponge species may not apply to another species. Furthermore, [15,20] found in some twenty sponge species that the *F/V* ratio decreases with increasing *Vtot* calculated from photos, including the spongocoel. Here, it is noteworthy that [21] excluded the spongocoel ("atrial cavity") when the field sizes of the three demosponges *Mycale* sp., *Verongia gigantea*, and *Tethya crypta*, were determined, in which the tissue-volume specific filtration rate was found to be constant, independent of the sponge body size [22]. This trend of constancy is the same as the above suggestion that the *F/V* ratio of a multi-oscular sponge tends to be constant because all the modules that build up the sponge body are not growing and/or of comparable size with a comparable *F/V* ratio.

Determining the "flux per unit sponge tissue" for 14 species, [23] found volumespecific filtration rates that were also essentially constant, *b* = 0.045. Data by [24] shows that 24 to 27 ◦C leads to *b* = –0.071 for *Cinachyrella* cf. *cavernose*, while including their data at 30 to 33 ◦C leads to *b* = 0.23, which suggest an increase in their size rather than a decrease, which is difficult to explain.

For five Mediterranean sponge species, [20] determined exponents *b*<sup>4</sup> and *b*<sup>5</sup> in the correlations *<sup>W</sup>* <sup>~</sup> *<sup>V</sup>*totb4 and *<sup>F</sup>* <sup>~</sup> *<sup>V</sup>*totb5 from which we calculated the exponent *<sup>b</sup>*<sup>6</sup> <sup>=</sup> *<sup>b</sup>*5/*b*<sup>4</sup> − <sup>1</sup> in *F/W* <sup>~</sup> *<sup>W</sup>* b6 as the values of *<sup>b</sup>*<sup>6</sup> <sup>=</sup> −0.63, −0.10, −0.17, −0.13, and −0.42. The near-zero value of *b*<sup>6</sup> for three of the sponges (*Crambe crambe*, *Petrosia ficiformis*, and *Chondrosia reniformis*) suggest that they have a nearly constant weight-specific filtration rate. This example shows that an increasing fraction of the sponge volume in these types of sponges is made up of canals with water. Therefore, for these types of sponges, specific filtration rates should be based on the dry weight (*W*), in which case, the specific filtration rates appear to be nearly independent of size in this sense.

Although many big vase-, jar-, urn-, or barrel-type sponges have only one common exhalant opening (pseudoosculum), these sponges cannot be directly compared to singleosculum modules because a large (unknown) number of modules enter into, e.g., a giant barrel sponge and because, possibly, the majority of these modules have grown to their maximum size. In the study of allometry and scaling of sponges, it appears to be essential to distinguish between types of sponges as described in Sections 1–3, and specifically employ the structural volume in *F*/*V*. However, *F/W* versus *W* (or biomass, AFDW) for the same species would probably show that *F/W* = constant.

As can be observed from the literature, there is a considerable interest in estimating the grazing impact from observed populations of given species of sponges at a given site. This has led to the much data on the filtration rate versus size in terms of the volume of various species of demosponges summarized by [16], who compiled available data on volume-specific filtration rate (*F/V*) versus sponge volume (*V*) approximated as *F/V* = *aV*<sup>b</sup> in demosponges. However, the observed variations were large and confusing and could not be immediately explained. However, the present assessment should help to clarify the situation. The scaling represented by Equation (3) does not apply for multi-oscula multi-modular sponges and single-osculum multi-modular demosponges, which explains the confusing picture of the species shown in Figure 1 of [16], in which all the various types of demosponge species have been shown together and approximated by the power-law *F/V* = *aV*b1−<sup>1</sup> = *aV*b, whereb~0 when *b*<sup>1</sup> is close to 1, but without a more precise definition of *V* (i.e., sponge-body volume with or without spongocoel).

#### **4. Filtration Rate,** *OSA***, and Size**

From the foregoing, it appears that a multi-oscula demosponge may be regarded as a population of modules each sharing the characteristics of a single-osculum explant, but also that the scaling of *F/V* versus *V* in single-osculum modules does not apply to multi-oscula sponges, which, due to their population of modules, obtained different and scaling characteristics for *F/V* versus the total sponge volume *V*.

The scaling relations between the filtration rate and osculum cross-sectional area is of interest because "the number of oscula and their *OSA* were the best predictors" of the filtration rate of sponges [15]. However, again, we must distinguish between the different types of demosponges. Thus, *F* = *a*2*OSA*b2 and *b*<sup>2</sup> = 3/2 in Equation (2) for singleosculum modules but have the values of *b*<sup>2</sup> = 0.75 to 1.07 for single-osculum multi-modular demosponges [15].

As an example of scaling, Figure 4 shows an underwater photo of *Halichondria panicea*, which consists of multi-oscular multi modules, each with an osculum with a mean diameter of 1.9 ± 0.6 mm (29 July 2019), giving rise to *OSA* = 2.84 mm2, *<sup>V</sup>* = 3.2 mL, *<sup>F</sup>* = 7.4 mL min<sup>−</sup>1, and *F/V* = 2.3 min−<sup>1</sup> when using Equation (2) *F* = *a*2*OSA*3/2 with *a*<sup>2</sup> = 1.55 [6], and *a*<sup>3</sup> = 3.97 in *F* = *a*3*V*2/3 (Equation (3)) shown in Figure 2. Obviously, the in situ measurement of *F* and the calibration of the scaling relations to the actual temperature are desirable in order to verify the predictions, but the example illustrates how scaling relations may be useful in field studies because only the dimensions of the oscula need to be measured to obtain information about both the size and filtration rate of each module of a multi-oscula sponge, which can be considered as a population of modules.

The size of an aquiferous sponge module and its *OSA* are closely interconnected and follow a fixed scaling, but the module size and the *OSA* are not stable as evident from the following, where *Halichondria panicea* again serves as an example. An earlier measurement of the average size of *OSA* in *H. panicea* at the same field location (Figure 4) was measured by [7] to the lower value of 1.0 ± 0.6 mm<sup>2</sup> (17 December 2018). Thus, it is likely that the mean size of otherwise full-grown modules and concurrently the *OSA* and *F* change over the season, along with pronounced changes in the condition index [25,26]. Furthermore, [27] observed that the range of the oscular diameter in *H. panicea* was 1 to 4 mm of sponges from sites with "medium to high current velocities", but smaller, 0.5 to 2 mm, at "low current" sites. From these observations, it can be concluded that the size of modules and their *OSA* vary between localities and over the season, and that the size and shape of the individual modules of *H. panicea* are not stable, but depend on the living site and time of the year. The degree of polymorphism in this sponge is "much higher than observed in most other sponges", and its growth form may be encrusting, lumpy, or ramose (Figure 4), depending on the current velocities and degree of exposure to waves [27].

#### **5. Density and Filtration Rates of Choanocyte Cambers in a Single-Osculum Module**

The prerequisite for the scaling leading to Equation (3) is that the "area specific filtration rate" of the thin wall separating the inhalant and exhalant canals is constant, i.e., the wall-specific density of choanocytes (CCs) and their individual filtration rate is constant. The suggested scaling is verified by the experimental data shown in Figure 2. Because of this scaling, the CC density decreases with increasing *V*, whereas the filtration rate of the single choanocyte may be reduced due to increasing the system resistance when the canals become longer.

Here, it should be mentioned that Figure 1 is very schematic. Thus, although "the exhalant system, in a crude sense, mirrors the inhalant system" [4], the two systems serve different functions. Food particles >5 μm are filtered out of the inflowing water in the inhalant canal system and phagocytosed here, whereas smaller particles are retained in the CCs [28]. The exhalant canal system acts as a sewage system, which carries filtered water, excretion products, and indigestible matter out of the sponge, and it is noteworthy that the diameter of the exhalant apertures are more than two times larger than the inhalant apertures [4,29]. The significance of this difference in the aperture diameter remains unknown, but the resistance to flow may be relatively lower in the larger exhalant canals.

#### *5.1. Filtration Rates*

It is our hypothesis that the volume specific filtration rate (*F/V*) versus sponge volume (*V*) of single-osculum single-module demosponges decreases with the increasing size, while it remains essentially constant for multi-oscular multi-modular and single-osculum multi-modular demosponges, provided the sponge volume is that of the structural sponge tissue, which, again, is proportional to the sponge dry weight. Furthermore, we seek to understand the cause of the observed strong decrease in *F/V* with increasing *V*. The specific filtration rate equals the product of density (*n*CC) and filtration rate (*F*CC) of the choanocyte chambers, *F/V* = *n*CC × *F*CC, where each factor may decrease in the process of growth, *n*CC due to an increasing volume fraction of the tissue, *F*CC due to the changing choanocyte pump performance related to seal imperfections in pumps and/or increasing pressure losses in the aquiferous system with increasing size.

For 5 sponges, [20] shows very large volume-specific pumping rates (10 to 40 min−1) for small individuals that then decrease with increasing size to more typical values (2 to 6 min−1); however, these results may be subject to corrections for the use of total volume rather than structural tissue volume. Furthermore, based on the decreasing *F/V* with increasing *V* observed "in most of the sponges" studied by [15], the authors suggested that the CC density was concurrently reduced. This possibility is now discussed by considering some examples of the demosponge *Halichondria panicea*.

A very small explant of volume *V* = 0.018 mL was found to have the high-volume specific filtration rate of *F*/*V* = 15.6 min−<sup>1</sup> [5], while the larger, near full grown explant of volume *V* = 1 mL had the smaller value *F*/*V* = 2.66 min−<sup>1</sup> [6]. For an estimate of the order of magnitude of *n*CC and *F*CC, we considered a *Halichondria panicea* specimen having *F*/*V* = 6.1 min−<sup>1</sup> [30] and *n*CC = 18,000 mm−<sup>3</sup> [4], which produced *F*CC = (6.1/18,000)/60 = 5.65 × <sup>10</sup>−<sup>6</sup> mm3 <sup>s</sup>−<sup>1</sup> = 5650 <sup>μ</sup>m3 <sup>s</sup><sup>−</sup>1.

As a first scenario, we assumed *F*CC = 5650 μm3 s−<sup>1</sup> to prevail for the small and the larger explants. This would imply that the choanocyte chamber density should decrease from *<sup>n</sup>*CC = (15.6 × 109/5650)/60 = 46,018 mm−<sup>3</sup> to *<sup>n</sup>*CC = 7847 mm−3, i.e., by a 5.9 factor, as determined by the ratio of *F*/*V* values. Furthermore, assuming a typical chamber diameter of 30 μm, the volume fraction of the chambers would be <sup>π</sup>/6 × <sup>30</sup><sup>3</sup> × 46,018 × <sup>10</sup>−<sup>9</sup> × 100 = 65% and 11%, respectively, leaving little space for aquiferous canals and other structure in the first case, which can be justified by the very short canals in a very small explant.

The density (*n*CC = 18,000 mm−3) reported by [4] represents "mature regions with relatively stable dimensions" in *Halichondria panicea*, and the attainment of samples from "growth points" was deliberately avoided. Because the very small explant represents

a "growth point", this may suggest a higher chamber density here, but verification awaits further information on the structure and dimensions of the canal system at these "growth points".

With 80 choanocytes in a CC [4], the filtration rate of a single choanocyte in *Halichondria panicea* was estimated at *F*ch = (5650/80 =) 70.6 μm<sup>3</sup> s−1. With 95 choanocytes per CC in *Haliclona permollis* [4] and *F/V* = 6.0 min−<sup>1</sup> measured in the closely related *H. urceolus* [8], it was estimated that *<sup>F</sup>*ch = (6.0 × 60)/(12,000 × <sup>95</sup> × 103) = 0.32 × <sup>10</sup>−<sup>6</sup> mL h−<sup>1</sup> or <sup>89</sup> <sup>μ</sup>m3 <sup>s</sup><sup>−</sup>1. For the comparison with other demosponges, [22] found that the tropical demosponge *Tethya crypta* had a volume-specific filtration rate of *F/V* = 10.8 min−1, and from this, it was estimated (using CC density and number of choanocytes per CC reported by [31] that *<sup>F</sup>*ch = 648/(14,403 × <sup>99</sup> × 103) = 0.46 × <sup>10</sup>−<sup>6</sup> mL h−<sup>1</sup> or 128 <sup>μ</sup>m3 <sup>s</sup>−1. Other, but strongly varying, values were calculated by [32]) using the data reported by [31]. Thus, *F*ch was calculated from the measured *F/V* ratio divided by the CC density. However, the CC density was determined for sponge tissue, whereas *V* was "calculated by measuring the dimensions of the sponge from images taken of whole animals in situ" [31], and this may explain some of the strong variations in *F*ch between species, but also the differences between CC density in "growth points" and "full grown" modules may have contributed to the variation.

In the second scenario, we assume that the CC density was constant, which would lead to a change in the CC filtration rate produced by the factor 5.9 of the *F*/*V* ratio of the very small explant to the larger one. Using the aforementioned value of *F*CC = 5650 μm3 s<sup>−</sup>1, or *F*ch = 70.6 μm3 s−<sup>1</sup> for 80 choanocytes per CC, for the larger explant, it would suggest a high value of *<sup>F</sup>*ch = 70.6 × 5.9 = 416 <sup>μ</sup>m3 <sup>s</sup>−<sup>1</sup> for the very small explant. Although an increase in *F*ch would be expected for the much shorter canals in the very small explant, it would be less than suggested here unless the choanocyte pumps at this stage were more efficient. A value of 453 μm<sup>3</sup> s−<sup>1</sup> for an opposing system pressure of 1 mm H2O was computed by [32], provided good seals represented by the second reticulum (acting as a "gasket") and the glycocalyx mesh on the upper part of the collar.

By comparing the two scenarios, it appears that the main contribution to the decrease in the *F*/*V* ration during growth of the single-osculum explant module was due to the decrease in the chamber density because of the increase in the volume of structural elements and increased aquiferous system. No similar decrease should be expected for multi-oscular or single-module multi-oscular sponges, where most of the modules are full grown with a relatively low and constant chamber density. For these cases, any reported decrease in the chamber density (and filtration rate), as suggested by [15], would arise if based on the total sponge volume, including an increasing spongocoel volume.

#### *5.2. Closing Remarks: Towards a Better Understanding*

From our present examination of *F/V* versus *V*, we realized that certain assumptions presented in our recent article on the pumping rate and size of demosponges [16] were not completely correct. Thus, the modeling of a tubular-type demosponge, equivalent to a single-osculum module, was made on the assumption of the constant choanocyte density, which we now find to be unlikely. Furthermore, we realized that the present scaling for (i) single-osculum module (*F/V* ~ *V*−1/3) cannot be applied to (ii) multi-oscular multimodular and (iii) single-osculum multi-modular demosponges. We think that the observed and modeled dependence of the filtration rate on the sponge volume for growing singleosculum modules may primarily be governed by a decreasing density of choanocytes with increasing *V* in all sponge species. However, the hydraulics of the pump and pressure losses of the aquiferous system possibly resulting in a reduction in the choanocyte filtration rate may also play a role, which awaits further assessment. However, the present assessment of *F/V* versus *V* among various types of demosponge species should help to clarify the large and confusing variations that we observed, but could not immediately explain.

#### **6. Conclusions**

The concept of "modules" was used to classify the demosponges and develop the scaling laws of growth at different stages and the types of sponges. The scaling analysis for single osculum explants leads to a volume-specific filtration rate that scales as *F*/*V* = *V*<sup>−</sup>1/3, which also applies when an aquiferous module grows larger. A multi-oscula sponge is a population of modules each sharing the characteristics of a single-osculum explant. However, many of their modules may have reached their maximal size, and hence their maximal filtration rate, which would imply the scaling *F/V* ≈ constant. A similar scaling would be expected for large pseudo-osculum sponges, provided their volume was taken to be the structural tissue volume that holds the pumping units, and not the total volume that includes the large atrium volume of water. The observed decrease in the *F/V* ratio by a factor of 5.9 when a very small *Halichondria panicea* explant grows to a near full-grown explant is primarily ascribed to a decrease in the density of the choanocyte chambers.

**Author Contributions:** H.U.R. and P.S.L. equally contributed with input and text writing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Thanks are due to Josephine Goldstein for aid with the technical drawing and statistics, and to 4 anonymous reviewers for constructive comments on the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

