*Article* **Actual and Model-Predicted Growth of Sponges—With a Bioenergetic Comparison to Other Filter-Feeders**

**Hans Ulrik Riisgård 1,\* and Poul S. Larsen 2**

**Abstract:** Sponges are one of the earliest-evolved and simplest groups of animals, but they share basic characteristics with more advanced and later-evolved filter-feeding invertebrates, such as mussels. Sponges are abundant in many coastal regions where they filter large amounts of water for food particles and thus play an important ecological role. Therefore, a better understanding of the bioenergetics and growth of sponges compared to other filter-feeders is important. While the filtration (pumping) rates of many sponge species have been measured as a function of their size, little is known about their rate of growth. Here, we use a bioenergetic growth model for demosponges, based on the energy budget and observations of filtration (*F*) and respiration rates (*R*). Because *F* versus dry weight (*W*) can be expressed as *F* = *a*1*Wb*1 and the maintenance respiratory rate can be expressed as *R*m = *a*2*Wb*2, we show that if *b*1~ *b*2 the growth rate can be expressed as: *G* = *aWb*1, and, consequently, the weight-specific growth rate is *μ* = *G/W* = *aWb*1−1 = *aWb* where the constant *a* depends on ambient sponge-available food particles (free-living bacteria and phytoplankton with diameter < ostia diameter). Because the exponent *b*1 is close to 1, then *b* ~ 0, which implies *μ* = *a* and thus exponential growth as confirmed in field growth studies. Exponential growth in sponges and in at least some bryozoans is probably unique among filter-feeding invertebrates. Finally, we show that the *F/R*-ratio and the derived oxygen extraction efficiency in these sponges are similar to other filter-feeding invertebrates, thus reflecting a comparable adaptation to feeding on a thin suspension of bacteria and phytoplankton.

**Keywords:** bioenergetic growth model; energy budget; filtration rate; respiration; *F/R*-ratio; filter-feeding

#### **1. Introduction**

Sponges are simple multicellular filter-feeders that actively pump volumes of water equivalent to five times or more their body volume per minute through their canal system by using flagellated choanocytes, which constitute the pumping and filtering elements of the smallest particles [1–4]. Sponges feed on suspended microscopic particles, including free-living bacteria and phytoplankton [5,6]. Water enters the sponge body through numerous small inhalant openings (ostia) and passes through incurrent canals, where phytoplankton cells with diameters smaller than the ostia diameter but larger than 5 μm are trapped, leading to the choanocyte chambers, where bacteria and other smaller particles are captured by the collar-filter of the choanocytes. Then, the filtered water flows through excurrent canals to be expelled as a jet through an exhalant opening (osculum) [7–9]. The water pumping also ensures ventilation and a supply of oxygen for respiration via diffusive oxygen uptake [10]. Although sponges lack nerves and muscle tissues, coordinated contraction-expansion responses, including partial or complete closure of the osculum to mechanical and chemical stimuli, are common among sponges due to the presence of contractile cells (myocytes) [10–13], which results in temporary reduced or arrested water flow.

**Citation:** Riisgård, H.U.; Larsen, P.S. Actual and Model-Predicted Growth of Sponges—With a Bioenergetic Comparison to Other Filter-Feeders. *J. Mar. Sci. Eng.* **2022**, *10*, 607. https:// doi.org/10.3390/jmse10050607

Academic Editor: Caterina Longo

Received: 22 March 2022 Accepted: 26 April 2022 Published: 29 April 2022

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**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/).

Sponges are one of the earliest evolved and simplest groups of animals [14], but they share basic characteristics with more advanced and later-evolved filter-feeding invertebrates such as mussels, in which filter-feeding is a secondary adaptation [15]. Sponges are also abundant today, especially in polar-shelf and tropical-reef communities as well as in many coastal regions, where they filter large amounts of water for food particles and thus play an important ecological role [5,16–21]. Therefore, a better understanding of the bioenergetics and growth of sponges in comparison with other filter-feeders is important.

Here, we first use an earlier approach for setting up a bioenergetic growth model, based on the energy budget and observations of filtration and respiration rates, which suggest that the growth of sponges is exponential; next, we use data in the literature to verify this hypothesis. Finally, we compare sponges to other filter-feeding invertebrates in order to compare the evolutionary adaptation of these animals to feed on the same thin soup of bacteria and phytoplankton.

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

Based on sponge data in the literature, we first set up a growth model based on the energy budget for growth (*G*) by making use of near identical exponents in the power functions for filtration rate (*F*) and respiration rate (*R*) versus body dry weight *W*. This development follows the earlier approach for the growth of the blue mussel *Mytilus edulis* [22], for which *F* or *R* = *aW*0.66 leads to a decrease in the weight-specific growth rate of mussels with increasing size, given by: *μ* = *G*/*W* = *aW*0.66 − 1 = *aW*−0.34, which showed good agreement with field data. For many sponges, it is suggested that exponents *b*1 and *b*2 of power functions for *F* and *R* are close to *b*1 ~ *b*2 ~ 1, and, therefore, the model predicts that the weight-specific growth rate must be constant with increasing sponge size, which implies that the growth must be exponential. This hypothesis is subsequently verified by sponge-growth data from the literature obtained in field experiments conducted in periods with positive growth, typically in the spring. The development of sponge size in time intervals was used to estimate the specific growth rates in each interval and was subsequently used for the evaluation of growth patterns. Exponential growth is characterized by a constant specific growth rate, which is reflected as a trendless scatter of the interval-specific growth rates, in contrast to a power function growth pattern, where the interval-specific growth rate will decrease with increasing size; for such data, an exponential curve fit will systematically underestimate the actual data in the first half period and then overestimate the data in the remaining period. Data were replotted from other publications using an in-house graphical program, 'Gtpoints', which generates a table of data point coordinates according to the scales of axes in a \*.bmp image of a given graph.

Exponential regression curves (LM) were fitted in [23] for growth rate estimates based on wet weight, ash-free dry weight, or length of sponge over time.

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

#### *3.1. Sponge Growth Model and Test of Exponents*

The growth of a sponge can be expressed by the energy (or carbon) budget as:

$$G = I - R - E = A - R \tag{1}$$

where *G* = growth (production), *I* = ingestion, *R* = respiration (total) = *R*m (maintenance respiration) + *R*g (growth respiration, i.e., metabolic cost of synthesizing new biomass), *E* = excretion, and *A* = assimilated food. The budget can also be written as *G* = (*F* × *C* × *AE*) – (*Rm + Rg*), where *F* = filtration rate, *C* = food concentration, and *AE* = *A/I* = assimilation efficiency. Thus, equating the rate of the net intake of nutritional energy to the sum of various rates of consumption, the energy balance for a growing sponge may now be written as:

$$G = \left[ \left( F \times \mathbb{C} \times AE \right) - R\_m \right] / a\_0 \tag{2}$$

where the constant a0 is the metabolic cost of growth, which constitutes a certain amount of energy equivalent to a constant percentage of the growth (biomass production). Because the filtration rate (*F*) of a sponge can be estimated from the sponge dry weight (*W*) according to *F* = *a*1*W b*1, and the maintenance respiratory rate (*R*m) can be estimated according to *Rm* = *a*2*W b*2, then if *b*1 ≈ *b*2, the growth rate may now be expressed as:

$$G = \left(\mathbb{C} \times AE \times a\_1 - a\_2\right) \mathcal{W}^{b1} / a\_0 = a \mathcal{W}^{b1} \tag{3}$$

which seems to be an equation that would apply to sponges in general (and other marine filter-feeding invertebrates, see later). Thus, [24] found that *b*1 = 0.914 and *b*2 = 0.927 for Halichondria panicea, while [17] found that *b*1 ≈ *b*2 ≈ 1 for three tropical marine sponges (up to a size of 2.5 l sponge). Because the percentage of oxygen removed from the water pumped through the sponge is rather constant [17], this implies that *b*2 tends to be similar to *b*1, as in a recent review of the volume-specific pumping rate of demosponges versus sponge volume (*V*) approximated by the power-law *F*/*V* = *a*3*Vb*3 [25], where *b*3 = *b*1 − 1, assuming that dry weight was proportional to volume. *B*y comparing the exponents reported by various authors, it appears that *b*1 ≈ 1 or *b*1 ≥ 0.9 [17,24,26–32], but in other cases, *b*1 < 0.9 has been reported [21].

Therefore, if *b*1 ≈ 1 in Equation (3), the resulting model for weight-specific growth rate (*μ* = *G*/*W* = *aWb*1/*W*) becomes:

$$
\mu = a \tag{4}
$$

which is a constant and thus the growth is exponential.

On the other hand, if *b*1 ≈ *b*2 ≈ 0.9, then *b* = 0.9 − 1 = −0.1, and the resulting model may be expressed as:

$$
\mu = a\mathcal{W}^{-0.1} \tag{5}
$$

Here, using published growth data, we first test the prediction of Equation (4), which, with Equation (3), may be expressed as:

$$
\mu = G/W = \left(\mathbb{C} \times AE \times F - R\right) / a\_0 \tag{6}
$$

In the case of *Halichondria panicea*, the following numbers apply: *F* = volume specific filtration rate = 6.1 mL water (ml sponge)−1 min−1 [4], *R* = weight specific respiration rate = 7.93 μM O2 h−1 (g W)−1 ([33] = (7.93 × 32/1000 × 0.7 ) = 0.178 mL O2 h−1 (g W)−1, and *a*0 = 2.39 since the cost of growth (SDA) is equivalent to 139% of the biomass production [24], where W henceforth denotes sponge dry weight. Furthermore, 1 mL sponge = 90.019 mg W [6], 1 mL O2 = 0.46 mg C [34], and 1 mg W = 0.142 g C [24]. Assuming *AE* = 0.8 and inserting numbers in Equation (6), we find: *μ*(d−1) = *G/W* = [[*C* × (μg C L−1) × 0.8 × 6.1 × 60 × 24/1000 (per mL sponge = 12.78 mg C) − 0.178 × 0.46 × 24 (per g *W* = 0.142 g C)]/2.39]/1000, or:

$$
\mu = a = \left[ (C \times 0.55 - 13.8) / 2.39 \right] / 1000 \tag{7}
$$

From this, for *μ* = 0, the maintenance food concentration is estimated at *C*m = (13.8/0.55 =) 25.1 μgCL−1. If the total sponge-available carbon biomass (TCB, i.e., free-living bacteria and phytoplankton with diameters smaller than the ostia diameter) is 5 times as large (i.e., *C* = 125.5 μgCL−1), the predicted specific growth rate is estimated as *μ* = [(125.5 × 0.55 − 13.8)/2.39 = 23.11 μgCd−1/1000 μg C =] 0.023 d−1 = 2.3% d−1, which may be compared with actually measured growth rates in the field as appears from the following examples. It should be mentioned that the influence of temperature, salinity, and spawning have not been addressed in Equation (7) and that *AE* = 0.8 will decrease if the ingestion exceeds the amount of food needed for maximum (biologically possible) growth.

#### *3.2. Verification of Hypothesis: Growth Rates of Sponges in the Field*

**Example 1.** *The growth of Halichondria panicea was measured in the inlet to Kerteminde Fjord, Denmark, in a 104-d experiment conducted by* [6]*; see* Figure 1*. The exponential curve fit indicates a weight-specific growth rate of μ = 0.6% d*−*1 (*Figure 1*), which may be compared to the algebraic mean μ = 0.62% d*−*1 (*Table A1*), but the big scatter in calculated μ-values during the time of growth indicates no meaningful correlation between μ and sponge dry weight. The growth experiment was conducted in the period April-August, when the temperature was 20* ◦*C at both the beginning and end of the experiment, with a peak of about 25* ◦*C between June and July. The growth rate of 0.6% d*−*1 indicates, according to Equation (7), that the mean food availability (TCB) had been about 50 μg C L*−*1, which may be compared to the mean TCB of about 90 μgCL*−*1 measured in the ambient water during the sponge-growth period March–August* [6]*.*

**Figure 1.** *Halichondria panicea*. Development of mean ± SD wet weight as a function day of year. Exponential regression curve (LM, t0.015, 13 = 9.3 × 10−5, *p* = 6.8 × 10−13) shows a weight-specific growth rate of 0.6% d−1. Data from [6].

**Example 2.** *Growth of Halichondria panicea in the field at Kiel Bight was measured by* [35,36]*. Replotting the data of* [35] *for the period March-June of intense growth shows an approximately exponential growth AFDW = 83.6 e0.007d (*Figure 2*), which suggests an average specific growth rate of μavg ~ 0.7% d*−*1. Calculated values of specific growth rate μ show a large scatter but the same value of an algebraic average growth rate. Temperature seemed to be the controlling factor for growth during this period, where it was recorded to increase from 1.8 to 13.8* ◦*C (*Table A2*), but the concurrent increase in phytoplankton and bacteria biomass was not monitored. Therefore, both biological and physical effects might have contributed to the accelerated growth during the latter part of the period. Later,* [36] *presents data on biomass changes in a field study on populations of H. panicea at 3 different water depths of 6, 8, and 10 m. Replotting the data for the growth period up to the peak values in August shows growth in terms of sponge biomass (ashfree dry mass) AFDM g m*−*2, with exponential growth constants being μavg = 1.0, 2.2 and 0.6% d*−*1, respectively (*Figure 3*). The temperature at 10 m depth was observed to increase from 1.4 to 16.1* ◦*C during the period of growth from February to August of 1984.*

**Example 3.** *The growth in terms of body length of two Indo-Pacific sponges, Neopetrosia sp. and Stylissa massa, were measured by* [37] *from late November to March of 2003 for various farming conditions. While S. massa showed low or no growth, it was significant for Neopetrosia sp. for most treatments, reaching an exponential growth constant in terms of length L of specimens that we have derived from a replot of* [37] *to be μL,avg = 0.7% d*−*1 (*Figure 4*). To estimate an equivalent exponent for this growth in terms of volume we use the data from* [37] *for initial (i) and end (e) values of length and volume of Neopetrosia sp. and assume the relation V ~ Ln. This leads to the value n = ln(Ve/Vi)/ln(Le/Li) = ln(48.3/10.8)/ln(10.8/5.9) = 2.48, and μV,avg = 2.48* × *0.71 = 1.76% d*−*1.*

**Figure 2.** *Halichondria panicea.* Exponential regression curve (LM, t0.045, 3 = 5.8 × 10−4, *p* = 0.014) showing an approximately average growth rate of 0.7% d−1. Based on data from [35] shown in Table A2.

**Figure 3.** *Halichondria panicea.* Exponential regression curves at 3 water depths (6 m: LM, t0.006, 1 = 1.5 × 10−3, *p* = 0.205; 8 m: LM, t0.030, 2 = 4.6 × 10−4, *p* = 0.002; 10 m: LM, t0.064, 4 = 4.5 × 10−4, *p* = 0.004) showing approximate average growth rates of *μ*avg = 1.0, 2.2 and 0.6% d−1. Based on data from [36] shown in Table A3.

**Example 4.** *The growth rate of the demosponge Haliclona oculata was studied in its natural environment, Oosterschelde, in the Netherlands, by* [38] *who assumed "exponential growth" and found that the maximum average (*±*SD) volume-specific growth rate for 11 monitored specimens was 1.18* ± *0.35% d*−*1 in the beginning of May 2006.*

From the above examples, it appears that sponge growth in the field is approximately exponential and that the weight-specific growth rate is constant, typically a few % d−1 or less. In laboratory and field experiments conducted by [24] with *Halichondria panicea* the maximum measured growth rate was about 4% d−1, and [38,39] give data on wet weight-based exponential growth of the freshwater sponge *Spongilla lacustris*, indicating an exponent of *μ*WW ~ 4.5% d−1 for dark aposymbiotic conditions. Thus, the maximum possible growth rate of sponges seems to be about 4% d−1 and in case of *H. panicea* maximum growth may take place at about 8 times the TCB maintenance concentration of *C*m = 25.1 μgCL−1. At higher TCB concentrations, the *AE* = 0.8 in Equation (7) will decrease, and no further increase in growth can be expected. The specific growth rate linearly increases from *C*m to *C*max (see also Figure A1).

**Figure 4.** *Neopetrosia* sp. Exponential regression curve (LM, t0.006, 5 = 7.9 × 10−5, *p* = 2.0 × 10−7) confirming an essentially constant average growth rate of 0.7% d−1 in terms of specimen length L. Based on data from [37] shown in Table A4.

#### *3.3. Evolutionary Adaptation*

In the following 3 sections, we compare sponges to other filter-feeding invertebrates in order to compare the evolutionary adaptation of these animals to feeding on the same thin soup of bacteria and phytoplankton. In order to understand how sponges comply with the performance requirements for being a true filter-feeder, we first compare the *F/R*-ratio (amount of water filtered per ml of oxygen consumed). Next, based on data from the literature on the *F/R*-ratio in various sponge species, we estimate the oxygen-extraction efficiency to evaluate to what extend the respiration rate may be dependent on the filtration rate. Finally, we discuss how sponges, like other filter-feeders in temperate waters, cope with low phytoplankton concentrations during winter.

#### 3.3.1. *F*/*R*-Ratio

The *F/R*-ratio (liters of water filtered per ml of oxygen respired) can be determined using the above given volume specific rates for *Halichondria panicea*, *F* = [6.1 × 60/1000 = 0.366 L h−1 (mL sponge)−1, or = 0.366/90.019 = 4.07 × 10−3 L h−1] (mg dry weight sponge)−1 and *R* = 0.178 × 10−3 mL O2 h−1 (mg dry weight sponge)−1 as: *F*/*R* = (4.07/0.178 = 22.9 L) water filtered per mL O2 consumed. This *F*/*R*-ratio is well above the minimum reference value of 10 L water (mL O2) −1 for a true marine filter-feeding invertebrate [40], and to balance the sponge's energy requirements, the particulate organic carbon (spongeavailable phytoplankton and free-living bacteria) should be >*C*m = 25.1 μgCL−1. [30] shows the measured *F*/*R*-ratio in the demosponge *Callyspongia vaginalis* to be approximately 0.42 ± 0.03 L water (μmol O2) −1, which converts to *F*/*R* = (420 L/22.4 mL O2) = 18.8 L water (mL O2) −1, thus comparing well with the above example of *H. panicea*. As mentioned earlier, [17] found that *b*1 ≈ *b*2 ≈ 1 for three tropical marine sponges, but an actual growth rate was not reported. However, the F/R-ratios were reported to be: *Mycale* sp. = 22.8 L water (mL O2) −1; Tethya crypta = 19.6 L water (mL O2) −1; and *Verongia giganta* = 4.1 L water (mL O2) −1. The first two species comply with the performance requirement for being a true filter-feeder, whereas *V. giganta* does not, because it "consists of a tripartite community: sponge-bacteria-polychaete" [17]. We think that the *F*/*R*-ratio is a reliable

check in support of *b* ≈ 0 in *Mycale* sp. and *T. crypta*. [30] shows for 5 demosponges that the weight-specific oxygen consumption (*R*) versus weight-specific filtration rate (*F*) could be described as *R* = *a*4*Fb*4 where *b*4 ≈ 1 (or 0.9416), which supports the idea that *b*1 ≈ *b*2 ≈ 1 in these sponges.

#### 3.3.2. Oxygen Uptake and Extraction Efficiency

When the *F*/*R*-ratio is known, the oxygen extraction efficiency may be estimated as the reciprocal of the total amount of oxygen passing through the sponge per ml of oxygen taken up by the sponge. The following conversion factors may be used: 1 mg O2 = 0.7 mL O2; in fully oxygenated seawater there is 9 mg O2 L−1 = 6.3 mL O2 L−1 available, so for 22.9 L there would be 22.9 × 6.3 = 144.3 mL O2 available. But the uptake was only 1 mL O2 for 22.9 L water pumped according to the estimated *F/R*-ratio for *Halichondria panicea*. Therefore, the extraction efficiency in this case was *EE* = 1/144.3 = 0.007, or 0.7%. This is in agreement with [15], who found that the oxygen extraction efficiency is 1% or less in coastal filter feeders. Like in other filter-feeding animals such as mussels, the ventilatory currents are laminar in sponges, and oxygen in the water is only taken up by diffusion, which implies that only a small fraction of the oxygen in the water pumped through the sponge is available for respiration. In *Verongia giganta,* where *F*/*R* = 4.1 L water (mL O2) −1 (see previous section), the extraction efficiency is calculated at *EE* = (1 mL O2/(4.1 × 6.3) mL O2 = 3.9%), which is 5 times higher than for *Mycale* sp., *Tethya crypta*, and the above example with *H. panicea.*

Reduced flow due to increased pressure losses in canal systems [25] or to closure of the osculum will result in low and high values of *F*/*R* and *EE*, respectively, as observed for example for *Verongia giganta*. As shown for the filter-feeding blue mussel *Mytilus edulis* [15], the respiration rate in a sponge is probably independent of filtration rate above about 20% or less of the filtration rate capacity of a sponge because the extraction efficiency increases with a decreasing filtration rate. Like other filter-feeders, sponges also experience low phytoplankton concentrations in temperate waters in the northern hemisphere during winter [6]. The lower threshold of total available carbon concentrations (phytoplankton plus bacterial carbon) covering the maintenance cost of *H. panicea* is found here (Example 1) to be around 50 μgCL−1. *M. edulis* copes with low phytoplankton content during winter by reducing its valve gape during starvation periods [41]. A study by [42] demonstrated that alternating closing-opening of valves causes a simultaneous strong decrease in oxygen concentration in the mantle cavity and thus a reduction of the respiration rate, and in this way *M. edulis* saves energy during starvation periods, a statement supported by a starvation experiment where the metabolic weight loss was reduced 12.3 times during 159 days of starvation [41]. It is well-known that the modular colonial *H. panicea*, with an osculum on each module, is able to close its oscula and thus reduce or stop the water-through flow [4,43,44], which may result in reduced respiration and eventually in internal anoxia [45], and, therefore, closingopening of the oscula during starvation periods might theoretically be an energy-saving mechanism comparable to that found in *M. edulis*. However, our preliminary observations on *H. panicea* do not support the existence of such a mechanism.

#### 3.3.3. Growth and Respiration

The specific respiration rate in response to growth (specific dynamic action, SDA) constitutes 139% of the biomass production in *Halichondria panicea* [24]. This percentage, used in the present growth model (see Equation (7)), makes up a very substantial proportion of the total energy released by respiration compared to other filter-feeding invertebrates, where the cost of growth is typically between 12 and 20% of the biomass production [46]. Due to their simple structure, sponges may be regarded as colonies composed of waterpumping choanocytes that are structurally and functionally near identical to free-living choanoflagellates in the sea [47]. In these organisms, with which choanocytes share properties, energy used for maintenance only constitutes a small fraction of the energy required for growth. Thus, a doubling of the specific growth rate of e.g., a flagellate protozoan may

result in a doubling of the specific respiration rate, indicating that the energy cost of growth (mainly macromolecular synthesis) is equivalent to that of the actual growth [46].

As for the maintenance respiration, the total respiration (*R*) as a function of body dry weight (*W*) is usually described by the power function *R* = *a*5*Wb*5 where the *b*5-exponent is frequently close to 0.75. However, the "3/4 power scaling" is not a 'natural constant' because many exponents differ from *b*5 = 0.75 [46]. Thus, *b*5 = 0.66 in the blue mussel *Mytilus edulis* [48], *b*5 = 0.68 in the ascidian *Ciona intestinalis* [49], *b*5 = 0.86 in the jellyfish *Aurelia aurita* [50], *b*5 = 1.2 in the facultative filter-feeding polychate *Nereis diversicolor* [51], *b*5 = 0.93 in the demosponge *Halichondria panicea* [24], and *b*5 = 1 in three tropical sponges [17]. A bioenergetic growth model based on the energy budget and making use of near identical exponents in the power functions for filtration rate (*F*) and respiration rate (*R*) versus *W* (i.e. *F* or *R* = *a*2*Wb*2) has earlier been developed for the blue mussel *Mytilus edulis*, where *b*1 ≈ *b*2 = 0.66 and where it was found that actual growth rates in the field in general were in good agreement with the model and—as predicted—that the weight-specific growth rate decreased with body dry weight as *μ* = *aW* 0.66−1 = *aW*−0.34 [22]. As a consequence, the weight specific growth rate of 7.8% d−1 for a 0.01 g dry weight *M. edulis* exposed to 3 μg chl *a* L−1 gradually decreases to 1.6% d−1 for a 1 g mussel, thus showing that the growth is not exponential. The constant specific growth rate with increasing size and thus exponential growth in sponges (and some bryozoans, see later) is unique and does not exist in other filter-feeding invertebrates where *b*1 ≈ *b*2 < 1.

Referring to the "general" model for metabolic scaling *R* = *aW*0.75, the mass-specific metabolic scaling becomes *R*/*W* = *aW*−0.25, which exponent *b* = −0.25 [20] is found (apparently suggesting that *F*/*V* follows *R*/*W*) to be "consistent with the measured exponent for three of five species" of sponges in which they had measured exponents for volume-specific filtration rate (*F*/*V*) versus sponge volume (*V*): *F*/*V* = *a*3*Vb*3 and found *b3* = −0.19, −0.20, −0.22, −0.49, and −0.70 for the five sponge species, respectively [20]. However, such comparison with a suggested "general" metabolic scaling is unwarranted, and the negative *b3*-exponents may need another explanation (see later).

The volume of a sponge is not always closely related to the living sponge biomass, which is evident from the seasonal variation in the sponge condition index CI = ratio of organic to inorganic matter = AFDW/(DW − AFDW) [35,52]. Thus, a decreasing value of CI reflects a decreasing relative density of water-pumping choanocytes in a sponge, hence a lower pumping rate for a given sponge volume. So, if CI decreases while volume increases, this may explain the negative exponents for volume-specific filtration rate versus sponge volume in these sponges. Thus, it can be put forward as a hypothesis that spicules with decreasing CI form an increasing and major component of the volume in some sponge species, and thus a decreasing volume-specific filtration rate is associated with increasing size; see also [53]. In addition, or alternatively, the observed dependence of filtration rate on size of sponges "might primarily be governed by the hydraulics of pump and pressure losses of the aquiferous system" and not by, e.g., "a reducing density of choanocytes with increasing size", as suggested by [25]; see next section. From the present study, it is obvious that sponges have many features in common with other filter-feeding invertebrates. Thus, the *F/R*-ratios and oxygen extraction efficiencies are comparable because all filter-feeding organisms have to cope with the same challenge of living in a thin soup of suspended microscopic food particles.

Sponges are modular organisms that consist of a set of repetitive modules. Likewise, filter-feeding bryozoans are colonial animals that consist of a set of repetitive zooids, which may also give rise to exponential growth, e.g., in *Celleporella hyalina*, *Electra pilosa* [54,55], *Cryptosula pallasiana*, and other bryozoan species [56]. Because the individual filtration rate and respiration rate of a module, or of a zooid, remain the same when a sponge or bryozoan colony grows, both the total filtration rate (*F*) and respiration rate (*R*) of the organisms increase linearly with the increasing number of modules/zooids (*W*), i.e., *F* and *R* = *a*2*W*, which implies exponential growth according to the bioenergetics growth model. However, in many bryozoan species the rate of asexual zooid replication increases

with colony size [57], and, therefore, the rate of growth in the number of zooids occurs in a different way, following power function. Exponential growth probably does not exist in non-modular and non-colonial filter-feeding invertebrates where the exponents in the equation for *F* and *R* = *a*2*Wb*2 are usually <1 and tend to be equal. In such cases where *b*2 < 1, the growth follows a power function. Thus, for *b*2 = −0.34 in the blue mussel *Mytilus edulis* the weight-specific growth rate as a function of *W* can be described by a power regression line in a log-log plot in which the slope has been found to be close to the predicted *b*2 = −0.34 [21]. In the filter-feeding jellyfish *Aurelia aurita* it has been shown that *b*2 = −0.2, which shows that the weight-specific growth rate is not constant but decreasing with size as reflected in systematic deviation between exponential regression curve fit for *W* versus time that underestimates *W* in the first half of the growth period while it overestimates it in the second period [58]. Thus, although growth versus time may be fitted approximately by an exponential curve a systematic deviation indicates that the specific growth rate is not constant. No such systematic deviations have been observed in the present study, which supports that the growth of sponges is exponential, as does the bioenergetic model and the application of the concept of modules.

An explanation for this may—as a theory—be derived from the high *F/R*-ratio and the low oxygen extraction efficiency in filter-feeding invertebrates. Because the proportion of biomass with low metabolism (e.g., lipid and glycogen store, gonads) may increase with body size, the weight-specific respiration (*R*/*W*) may concurrently decrease due to a negative exponent (*b*2 − 1) in the equation *R*/*W* = *a*2*Wb*2−1. When the biomass of a filterfeeder increases, the total respiration consequently increases, but the oxygen demand should easily be met by an increase in the oxygen extraction efficiency. However, the animal must also increase the filtration rate, and thus the ingestion of food needed to cover the respiratory need to ensure that the *F/R*-ratio remains unchanged because a reduction in the *F/R*-ratio will cause starvation. Thus, the exponents in the equation for *F* and *R* = *a*2*Wb*2 may have (during the evolution) become near equal depending on species and adaptation to living site. Due to the simple structure of sponges, which have no organs or real tissue that may store energy reserves (such as fat, lipids, or glycogen) [6,35] to overcome starvation periods, the exponents for *F* and *R* versus *W* tend to be close to 1, as seen in those sponge species where both *F* and *R* have been measured, supported by growth experiments and model predictions presented in this study.

#### **4. Conclusions**

The power function exponents *b*1~ *b*2~ 1 for F and R versus W may probably apply to most demosponges, and therefore Equation (3) may be a general sponge equation. The resulting model for the weight-specific growth rate is a constant, and the growth is therefore exponential. This prediction is confirmed by actual field growth data for a group of sponges for which the *F/R*-ratios and oxygen extraction efficiencies are comparable to the values of other filter feeders. However, the constant specific growth rate with increasing size in sponges and some bryozoans is unique, and exponential growth probably does not exist in other filter-feeding invertebrates where *b*1≈ *b*2 < 1, giving rise to a decreasing weight-specific growth rate with increasing body size.

**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 help with statistics.

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

#### **Appendix A**

**Table A1.** *Halichondria panicea*. Development of sponge wet weight (*WW*), dry weight (*W*), average dry weight (*W*avg) in time interval and weight-specific growth rate (*μ*) as a function of time (d) in growth experiment with sponge explants in the inlet to Kerteminde Fjord, Denmark. Data used for calculation of μ are from [6].

**Table A2.** *Halichondria panicea.* Development of sponge biomass (AFDW) and temperature obtained by replotting data from [34] based on a field experiment at Boknis Eck, Western Baltic Sea, at 10 m and used here for calculation of the weight-specific growth rate (*μ*).

**Table A3.** *Halichondria panicea.* Development of biomass (AFDW) in natural sponge populations at Boknis Eck, Western Baltic Sea, at 3 different water depths of 6, 8 and 10 m obtained by replotting data from [35]. Day zero = 1 January 1984.

**Table A3.** *Cont*.

**Table A4.** *Neopetrosia* sp. Growth data in terms of specimen length obtained by replotting data from [36].

**Figure A1.** *Halichondria panicea*. Estimated weight-specific growth rate as a function of TCB (total sponge-available carbon biomass) according to Equation (7) and suggested maximum possible growth rate *μ* = 4% d−1 at *C*max = 200 μgCL−1 = 8 × *C*m (maintenance TCB). The increase in specific growth rate is linear between *C*m and *C*max.

#### **References**

## *Review* **A Review on Genus** *Halichondria* **(Demospongiae, Porifera)**

**Josephine Goldstein 1,2 and Peter Funch 2,\***

**Abstract:** Demosponges of the genus *Halichondria* Fleming (1828) are common in coastal marine ecosystems worldwide and have been well-studied over the last decades. As ecologically important filter feeders, *Halichondria* species represent potentially suitable model organisms to link and fill in existing knowledge gaps in sponge biology, providing important novel insights into the physiology and evolution of the sponge holobiont. Here we review studies on the morphology, taxonomy, geographic distribution, associated fauna, life history, hydrodynamic characteristics, and coordinated behavior of *Halichondria* species.

**Keywords:** demosponges; morphology; taxonomy; geographic distribution; holobiont; life history; hydrodynamics; coordinated behavior; model organism

#### **1. Introduction**

The genus *Halichondria* Fleming (1828) [1] (Demospongiae, Porifera; subgenera *Halichondria* and *Eumastia*) contains the most common marine sponge species of the North Atlantic [2], including the common "bread-crumb" sponge *Halichondria (Halichondria) panicea* Pallas (1766) [3] and Bowerbank's horny sponge *H. bowerbanki* Burton (1930) [4]. The most studied species, *H. panicea*, occurs in habitats covering a broad range of salinities, temperatures, turbidities, and flow conditions [5,6] and has been recorded in marine intertidal and sublittoral zones down to depths of more than 500 m [2]. *Halichondria panicea* provides substrate for many other marine organisms, including a large and varied associated fauna [7–9], symbiotic algae [10,11], and numerous bacteria [12,13]. The life histories of *Halichondria* spp. are characterized by different modes of asexual and sexual reproduction [14], with the latter revealing strong species- and habitat-specific adaptations [15–18]. *Halichondria* sponges are filter feeders capable of processing large volumes of seawater (up to six times their own body volume per minute [19]) and efficiently retaining small food particles [20], thus playing a key role in nutrient recycling of coastal marine ecosystems [8]. Modular arrangement of their leuconoid aquiferous systems [21,22] has made it possible to study the hydrodynamic properties of the sponge filter-pump, which may help to shed light on the evolution of complex filter-feeding systems in sponges (cf. [23]). Despite their apparently simple bauplan without a nervous or muscular system, *Halichondria* spp. show coordinated responses to changing environmental conditions, including phototactic responses of larvae [24], sponge body shape changes [25], and contractile behavior [22,26–28]. The detailed mechanisms underlying coordinated behavior in sponges are still unclear [29], but existing data for *Halichondria* points out the importance of cellular communication based on a neuronal-like 'toolkit' and could serve as a milestone towards an improved understanding of tissue organization in the first animals.

The vast majority of studies on *Halichondria* (a total of 11,100 research articles according to Google scholar) are based on *H. panicea* (36.4% of total research articles) with a focus on the biological and ecological aspects, whereas much fewer studies within these research

**Citation:** Goldstein, J.; Funch, P. A Review on Genus *Halichondria* (Demospongiae, Porifera). *J. Mar. Sci. Eng.* **2022**, *10*, 1312. https://doi.org/ 10.3390/jmse10091312

Academic Editor: Caterina Longo

Received: 14 August 2022 Accepted: 13 September 2022 Published: 16 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/).

fields have addressed other species, such as *H. bowerbanki* (4.0%), *H. melanadocia* Laubenfels (1936) [30] (1.5%), *H. moorei* Bergquist (1961) [31] (1.0%), or *H. semitubulosa* Lamarck (1814) [32] (0.2%, Table 1).

**Table 1.** Number of research articles on *Halichondria* Fleming (1828) based on genus- and species-level (cf. [33]) according to Google Scholar (Web of Science) along with the main Web of Science research categories (accessed on 6 July 2022).

Other studies have explored the metabolite chemistry of *Halichondria*, mainly for the species *H. okadai* Kadota (1922) [34] (26.8%, Table 1), for undefined species (*Halichondria* sp./spp., 12.5%), or on a genus-level (6.5%), reflecting partially unresolved and still ongoing taxonomic revisions of *Halichondria* species [35]. Molecular biology, including studies on the sponge microbiome, has mainly been investigated on *H. okadai*, *H. japonica* Kadota (1922) [34] (2.3%), *H. cylindrata* Tanita & Hoshino (1989) [36] (1.6%), and *H. oshoro* Tanita (1961) [37] (0.7%). Few morphological studies exist for *H. melanadocia* and *H. glabrata* Keller (1891) [38] (0.1%), while research on the hydrodynamics of sponges has remained restricted to *H. panicea* and *H. coerulea* Berquist (1967) [39] (0.1%). Despite the relevance of comparative studies on sponge cell biology, most *Halichondria* species have remained understudied (2.1%, Table 1). The aim here is to provide a compilation of studies concerning sponges in the genus *Halichondria* and point out existing knowledge gaps that may aid in future studies of these ecologically important demosponges.

#### **2. Morphology, Taxonomy, and Distribution**

The genus *Halichondria* is placed in the animal phylum Porifera, class Demospongiae, subclass Heteroscleromorpha, order Suberitida, and family Halichondriidae. Growth forms of *Halichondria* species include encrusting, massive, occasionally irregularly branching, or digitate sponges with smooth or papillate surfaces. An important morphological character to separate the two subgenera, *Halichondria* and *Eumastia*, is the absence or presence of short conical papillae on the sponge surface, respectively [2]. Members of the genus *Halichondria* typically form chimneys of variable size (up to 5 cm high) with conspicuous, relatively large oscula (2–4 mm in diameter). They are characterized by their firm but compressible texture and variable color, from olive-green (due to symbiotic algae) over orange-yellow to creamy-yellow [2] (cf. Appendix A, Figure A1). The siliceous spicule skeleton of *Halichondria* consists exclusively of oxeas or oxea derivates in a wide size range, which are arranged in an ectosomal crust (200–300 μm thick) and appear scattered or in tight bundles in the choanosome along with spongin fibers [2,40]. While the functional cell morphology and number of cell types in *Halichondria* has remained largely unknown, 18 distinct cell types which comprise four major cell families, including contractile, digestive, and amoeboid-neuroid cells, have recently been described in the freshwater demosponge *Spongilla lacustris* [41].

Species identification is traditionally based on morphological characteristics, such as the shape and structure of the skeleton and the size and form of spicules [42], but several of these characters show strong intra-specific variation and are, therefore, of rather poor quality to distinguish species. For instance, a variety of growth forms are represented by *H. panicea*, ranging from thin encrusting (Figure A1a) to erect ramose (Figure A1b), which seems to depend on the intensity of ambient water currents [43] (cf. [44]). Moreover, an extensive overlap of spicule sizes in different species has been documented [2]. Molecular data used in phylogenetic studies includes complete mitochondrial genomes of several *Halichondria* species [45–47] and mitochondrial and ribosomal markers [48,49]. The classification of genus *Halichondria*, as defined in [2], is still in need of a major revision at an ordinal level [35,50], as classification based on morphology disagrees with phylogenetic analyses using molecular data. Overall, morphological, biochemical, and molecular characters applied in recent phylogenetic analyses seem to point out that *Halichondria* is nonmonophyletic [51–54].

To date, about 100 *Halichondria* species are accepted [33,55,56]. They occur in different types of marine habitats around the world, being widespread in European [4,11,57,58], American [2], and Brazilian coastal waters of the Atlantic [59], but also in parts of the Baltic Sea [60], the White Sea [61], and the Mediterranean Sea [62]. *Halichondria* species also occur in the North Pacific, including Alaska [63,64], Japan [65], Korea [42,66], and the South China Sea [67]. The closely related species *H. panicea*, *H. bowerbanki*, and other species in this complex may serve as a suitable model to illuminate possible speciation events due to their overlapping distribution in the North Atlantic, where *H. panicea* is mainly found in shallow, protected coastal regions of the eastern parts, and shows adaptation to frequent air exposure, while *H. bowerbanki* is most common in exposed habitats of the western parts, where it tolerates high levels of siltation [11]. A molecular study based on a part of the mitochondrial marker COI suggests that North East Pacific *H.* cf. *panicea* is genetically distant from and forms a sister group to a species complex consisting of European *H. panicea* and *H. bowerbanki* [53]. *Halichondria panicea* has also been reported from the Tropical Southwestern Atlantic, along with other species such as *H. magniconulosa* Hechtel (1965) [68], *H. cebimarensis*, *H. tenebrica*, *H. migottea*, *H. sulfurea* Carvalho & Hajdu (2001) [59] and *H. marianae* Santos et al. (2018) [69]. Common species in the Pacific Ocean

are *H. japonica* [65], *H. okadai*, *H. oshoro* [70], *H. gageoenesis* and *H. muanensis* Kang & Sim (2008) [42], while *H. panicea* and *H. bowerbanki* have been reported from Alaska [63,64] and Korea [66], respectively. Revisions of the classification system should include more molecular data and more species and be used to reevaluate the morphological characters used in the traditional classification [50] (cf. [53,54]).

#### **3. The Holobiont** *Halichondria*

*Halichondria* spp. occur on a variety of inorganic and organic hard substrates, including mussel banks, small stones and rocks, and macroalgae [8,9,43,71]. The sponges themselves provide habitat for a diverse associated fauna and various symbiotic microorganisms. The associated epi- and endofauna of *H. panicea* include various Arthropoda such as skeleton shrimps (*Caprella* spp.) and copepods, but also molluscs, e.g., the scallop *Chlamys varia*, annelids, platyhelminths, and demersal fish that prey almost exclusively upon sponge epifauna [7–10]. Symbiosis with the dinoflagellate *Prorocentrum lima* has been documented in *H. okadai* [72,73], and *H. panicea* seems to harbor (intracellular) green algae [10,11]. However, many *Halichondria* species have not been investigated, indicating numerous other yet undiscovered symbiotic interactions, e.g., with dinoflagellates, cryptophytes, microalgae, and diatoms [73]. While the growth of pathogenic bacteria on *H. panicea* can cause sponge mortality under stagnant flow conditions [74], sponges harbor diverse microbial assemblages that contribute positively to host metabolism and defense [12,75,76]. *Halichondria* spp. are characterized as low microbial abundance (LMA) sponges with high variability in their bacterial diversity across species and environments [12,13,76]. While only 7 operational taxonomic units (OTUs) of microorganisms have been identified in *H. okadai* from Korea [77], about 500 OTUs were detected in *H. panicea* and *H. (Eumastia) sitiens* Schmidt (1870) [78] from the White Sea [76], respectively, and 1779 OTUs seem to be unique to *H. bowerbanki* from the mid-Atlantic region of the eastern United States [13]. The microbiome of *H. panicea* is dominated by a core taxon of Alphaproteobacteria within the class *Amylibacter* which has recently been named 'Candidatus Halichondribacter symbioticus' [12,76,79–82]. Transmission of bacterial symbionts occurs in a mixed vertical (i.e., direct through reproduction) and horizontal mode (i.e., indirect through the environment) in *H. bowerbanki*; it is likely to vary across *Halichondria* species [13]. Metagenomics have revealed that distinct viromes with low similarity to known viral sequences are associated with *H. panicea* and *H. sitiens*, suggesting the existence of bacterial antiphage systems in sponges [76].

*Halichondria* sponges and their microbial symbionts produce a broad spectrum of mainly symbiont-derived bioactive metabolites [83] with cytotoxic or cell growth-inhibiting properties. Substances isolated from *Halichondria* sponges include halichondrin B and okadaic acid in *H. okadai* [72,84,85] or gymnostatins and dankastatins from an *H. japonica*-derived fungal strain [86] which may additionally serve *Halichondria* sponges as a defense mechanism against pathogens, predators, and biofouling [73,87]. Okadaic acid is a biotoxin known for its cyto-, neuro-, immune-, embryo-, and genotoxicity in marine animals [87–89] and has been suggested to protect the demosponge *Suberites domuncula* from bacterial and parasitic infections [87]. Epibiotic *H. panicea* can negatively affect the heart performance of blue mussels (*Mytilus edulis*), which may be due to the sponges' release of excretory/secretory products. Such substances with cytotoxic properties and antimicrobial activity seem to benefit *H. panicea* in the competition for space and food across benthic fouling communities [90]. Neuroactive bacteria-derived compounds in *H. panicea* [73] suggest the relevance of symbiotic interactions for essential physiological processes such as coordinated behavior. The natural variability of sponge-microbe associations in *Halichondria* seems to provide a meaningful framework for modeling symbiotic interactions in metazoans (cf. [91]). In *H. bowerbanki*, for instance, changes in microbial communities after exposure to thermal stress have been documented [92], pointing out the relevance of future studies on sponges for assessing possible shifts in symbiont community composition and structure in response to global warming.

#### **4. Life History**

The life histories of *Halichondria* species typically include a reproductive period of 2–3 months in temperate regions [15,71,93]. *Halichondria* spp. are ovoviviparous and characterized by asynchronous gameto- and embryogenesis, while habitat-specific differences include successive hermaphroditism in White Sea populations of *H. panicea* and *H. sitiens* [18], simultaneous hermaphroditism in *H. panicea* and *H. bowerbanki* from the southwest coast of the Netherlands [16], incomplete gonochorism in *Halichondria* sp. from Mystic Estuary, US [15], or gonochorism in *H. panicea* from Kiel Bight, Germany [17]. In temperate regions, environmental parameters such as temperature and salinity drive the onset of sexual reproduction in *H. panicea* [17]. Differentiation of gametes from somatic cells has been observed in both *H. panicea* and *H. semitubulosa*, indicating the development of spermatocytes from choanocytes or archaeocytes, a process that may be species-dependent [62,94]. The larvae of *Halichondria* species are typically of parenchymella type and sometimes contain choanocyte chambers before settlement [24,95]. The release of *Halichondria* larvae seems to follow a light cue, being triggered by the onset of darkness in the temperate species *H. panicea* [96], while tropical *H. melanadocia* release larvae on exposure to light following a period of dark adaptation [24]. Phototactic responses of larvae range from positive to neutral to negative before settlement upon various hard substrates [24] (Figure A2a,b).

The growth of *Halichondria* sponges is dependent on temperature [70] and the concentration of available food, which mainly consists of bacteria and phytoplankton [97]. Pumping rates of *H. panicea* increase linearly with temperature and require relatively low energy demands for filtering large volumes of seawater [20,98], as expressed by F/R-ratios ≥15.6 L H2O (mL O2) −1, which are comparable to other filter-feeding marine invertebrates [19]. In contrast, the energetic cost of growth is high in sponges [20,99], with exponential growth at a maximum rate of 4% d−1 in *H. panicea* under natural conditions [100]. The weight-specific growth of *H. panicea* is constant over sponge size, which has been pointed out as a unique feature among most other filter-feeding invertebrates, reflecting the modular organization of sponges [100]. A study of *H. panicea* from the Western Baltic Sea suggested that stored glycogen reserves fueled sexual reproduction and that the sponges degenerated in the end of the following year after reproduction [71]. Tissue regression and high mortality during the colder months of the year have also been reported for temperate *Halichondria* sp. from the Mystic and Thames estuaries, US [57,101] and for *Halichondria bowerbanki* from New England, US [102], respectively, while the longevity of *H. okadai* in Japanese waters may exceed 3 years when considering asexual reproduction, i.e., fission and fusion of sponge fragments [14]. *Halichondria panicea* is capable of rapid regeneration of damaged parts, as expressed in ≥3-fold increased growth rates in response to predation [103] or during the reorganization of the aquiferous system in explant cuttings within approximately 6–10 days [22] (Figs. A2c-f), while other species, such as *H. magniconulosa*, seem to regenerate at slower rates [104]. Several *Halichondria* species, including *H. lutea* Alcolado (1984) [105], *H. magniconulosa*, and *H. melanadocia* have been recognized as important members of the Caribbean mangrove and coral reef communities, where they are preyed upon by fish [106,107]. *H. panicea* can also serve as a food source for hermit crabs, shrimp, large isopods (e.g., *Idothea* sp.), or the nudibranch *Archidoris montereyensis*, which may appear in such high density that it can eliminate large and long-lived sponge populations [63,64]. *Halichondria* sponges play an important role in nutrient recycling of coastal marine ecosystems due to their unique ability to retain small particles (≤0.1 μm) [20,108]. Regular tissue sloughing has been observed in *H. panicea* in response to sedimentation of organic material and settlement of small organisms on the sponge surface [109], along with seasonal remineralization of released *H. panicea* biomass following reproduction [8]. As the water pumping activity of *H. panicea* leads to an accumulation of pollutants, such as heavy metals, in direct proportion to ambient concentrations, their potential use as biomonitoring organisms has been proposed [40,110].

#### **5. Hydrodynamics**

As for other demosponges, the aquiferous system of *Halichondria* is leuconoid [21,40,111] and characterized by choanocytes organized in small spherical chambers which create a unidirectional flow of ambient water through a complex canal system [112,113]. The aquiferous elements of *Halichondria* act like a sieve for particles of variable size due to their aperture diameters (Figure A3a). As documented for *H. panicea*, they include numerous inhalant openings (ostia; 7–32 μm) through which seawater is drawn into incurrent canals (50–200 μm), finer incurrent canal branches (prosodi; 5 μm), and the prosopyles (1–4 μm) of choanocyte chambers (18–35 μm; Figure A3b) [113].  Each choanocyte chamber of *H. panicea* contains about 40–120 choanocytes at an estimated choanocyte chamber density of 18,000 mm−3 [113]. Water leaves choanocyte chambers through an apopyle (7–17 μm; Figure A4b) via excurrent canals (140–450 μm), which drain into an atrium (2.1 mm) from where the water exits the sponge in an excurrent jet through the osculum (1.2 mm) [113] (but see also [21]).

Each osculum represents a functional unit of aquiferous elements in a certain sponge volume (cf. Figure A2b–d), thus characterizing *Halichondria* sponges with multiple oscula as an array of several autonomous aquiferous modules [22,114,115]. The pumping rate of each aquiferous module is directly proportional to the density of choanocyte chambers in *H. panicea* [22], implying constant choanocyte densities for different *Halichondria* species. However, module size seems to determine the volume-specific pumping rates of *H. panicea*, which can reach a maximum of 15 mL min−1 (cm3 sponge)−1 in growing modules, as observed in single-osculum explants [26,27] (Figure A2c,d), while the modules in multi-oscula explants seem to pump at a lower maximum rate of 3 mL min−1 (cm3 sponge)−1 [22], probably due to a decrease in choanocyte chamber density with increasing module volume [116]. Based on the volume-specific pumping rate and choanocyte chamber density of *H. panicea*, the pumping rate per choanocyte chamber in a multi-oscula sponge can be estimated to (3/18,000)/60 = 2.78 × 10−6 mm3 s−1 = 2778 μm−3 s−1, and thus the pumping rate per choanocyte at an average of 80 choanocytes per chamber [113], to (2778/80 = 35 μm3 s−1). This value is in range with a previous estimate of (4.46 × 10−6 mm3 s−1/95 = 47 μm3 s−1) for the demosponge *Haliclona permollis* [113,117] (their Table 1, respectively). A recent hydrodynamic model on the pump characteristics of leuconoid sponges assumed the presence of flagellar vanes along with a glycocalyx mesh which distally connects the microvilli collars of choanocytes, as has been shown for the freshwater sponge *Spongilla lacustris* [118,119], in order to deliver observed pump pressures [23]. These ultra-structural features of choanocytes have so far not been documented in *Halichondria* (cf. Figure A4a), pointing out the need for further studies on ultrastructure and hydrodynamic properties, which may provide valuable insight into the evolution of demosponge filter-pump systems (cf. [120]).

#### **6. Coordinated Behavior**

At least three different basic cell types are found in *Halichondria* species, including choanocytes, pinacocytes, and amoeboid (mesohyl) cells [24,121]. The coordinated behavior of sponge cells mediates the hydrodynamic and physical properties of the aquiferous system required for efficient filter feeding under different environmental conditions. Communication between motile cells is the basic principle underlying continuous tissue reorganization, regeneration, and microscale movements in sponges [122–125]—a topic which has, unfortunately, so far only been addressed by a few studies on *Halichondria* spp. Continuous tissue remodeling in *H. panicea*, as expressed by fusion, shape changes, and movement of sponges, has been observed in aquaria and intertidal rocky pools [25]. *Halichondria japonica* explants have been shown to fuse with explants of the same sponge, while they reject cells from other *H. japonica* sponges or from *H. okadai* [126]. Several types of mesohyl cells seem to be involved in this process of "self and nonself" recognition in *H. japonica*, including amoeboid archaeocytes, motile (granule-rich) gray cells, and collencytes [126]. Recent work on *H. panicea* points out the importance of cellular transport for the removal of inedible particles from the aquiferous system [27]. At the same time, sponge sandwich cultures may provide a suitable method (Figure A2e,f) for studying the cell types and mechanisms mediating capture, transport, and digestion/removal of edible and inedible particles (Figure A5).

Coordinated behavior further includes contraction of various parts of the aquiferous system, including the osculum [26], in- and excurrent canals, ostia and apopylar openings of the choanocyte chambers, resulting in reduction and temporal shut down of the water flow through single-osculum explants of *H. panicea* [27,28]. Contractile behavior is common among sponges and seems to follow species-specific cycles of distinct frequency and intensity [127–131] which can be expressed in asynchronous patterns across conspecifics in *H. panicea* [28,132]. Contractions can occur spontaneously in *H. panicea* explants under undisturbed conditions in the laboratory and can be induced by chemical messengers (γ-aminobutyric acid and L-glutamate) or by mechanical stimulation with inedible particles [28]. Coordinated contractions of different aquiferous modules in *H. panicea* explants with multiple oscula have been observed in response to external stimuli [22]. Peristaltic-like waves of contraction travel through the sponge, resulting in osculum closure at speeds of up to 233 nm s−1 in *H. panicea* (15 ◦C) [28]. Comparatively, observed contraction speeds of up to 12 μm s−1 in the marine demosponge *Tethya wilhema* (26 ◦C) [129] and 122 μm s−1 in the freshwater demosponge *Ephydatia muelleri* (21 ◦C) [131] seem considerably higher, emphasizing the need for future studies on the contraction kinetics of *Halichondria* species. During contractions, *H. panicea* shows reduced pumping activity [19,26,27], an associated decrease in respiration rates [132], and local internal oxygen depletion [133]. These physiological changes have been suggested as adaptations to variable environmental conditions, including food limitation [134], resuspension of sediment during storm events [135] (cf. [136]), seasonal changes in water temperature, changes in illumination period, spawning events of other sponge species [128], and facilitation of suitable habitat for specific symbiotic microorganisms [132,133]. Contractions may serve *Halichondria* sponges as an important mechanism to protect the sponge filter-pump in distinct aquiferous modules from clogging and damage and seem to be mediated by exo- and endopinacocytes [22,27,28,134,137], while the underlying cellular pathways have remained unclear. Previous studies have described contractile epithelial cells in sponges that function based on a 'toolkit' of neuronal-like elements, including sensory cilia, conduction pathways, and signaling molecules [41,134,138–140]. The pinacocytes of other demosponges exhibit actomyosin-based contractility [41,130,137,139,141,142], and myosin type II has been isolated from cells of *H. okadai* [143].

It is likely that communication between sponge cells in *Halichondria* is based on the extracellular spreading of chemical messengers [41,123,144], neuronal-like receptors [145], and cell contacts via cellular processes/membrane junctions [146–148]. As the abovementioned examples emphasize, cellular communication pathways require further attention in future studies. More detailed information on the functional cell morphology of *Halichondria*, as can now be accessed using whole-body single-cell RNA sequencing (cf. [41]), is needed to shed light on the principles underlying coordinated behavior in sponges. We encourage future work on the LMA demosponge *H. panicea* as a model organism to revisit functional coordination pathways with an integral perspective on the underlying morphological structures combining molecular, cytological, and physiological techniques.

#### **7. Conclusions**

*Halichondria* sponges are well-studied and the literature represents a strong base for our present understanding of the ecology and physiology of demosponges. Previous work has mainly focused on *H. panicea*, paving the foundations for modeling spongemicrobe interactions, hydrodynamics of the sponge filter pump, and cell communication in demosponges. We encourage future research to fill in present knowledge gaps regarding the functional cell morphology and filter-pump characteristics of *H. panicea*, along with comparative studies including other *Halichondria* species, to improve and verify existing models based on this ubiquitous demosponge genus.

**Author Contributions:** Conceptualization, J.G. and P.F.; writing—original draft preparation, J.G.; writing—review & editing, P.F.; visualization, J.G.; project administration, P.F.; funding acquisition, P.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Independent Research Fund, grant number 8021-00392B.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We are grateful to three anonymous reviewers for providing valuable feedback on the manuscript. We further thank Héloïse Hamel and Janni Magelund Degn Larsen for supplementary photographs. Stereo-, light and scanning electron microscopy (SEM) images were acquired at the Marine Biological Research Centre, Kerteminde, University of Southern Denmark, and at the Interdisciplinary Nanoscience Center (iNANO), Aarhus University, Denmark.

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

#### **Appendix A**

**Figure A1.** Growth forms of *Halichondria panicea* Pallas (1766) in the inlet to Kerteminde Fjord, Denmark (55◦26 59" N, 10◦39 41" E). (**a**) Growing on a piece of rope, collected in November 2020 and (**b**) with finger-shaped chimneys, found on wood in November 2020. Pictures: Héloïse Hamel.

**Figure A2.** Aquiferous module formation in *Halichondria panicea*. (**a**) Sponge cells after larval settlement, (**b**) development of choanocyte chambers (cc), excurrent canals (ex-c) and an osculum (osc) in a juvenile sponge, (**c**) single-osculum explant (side-view), (**d**) explant (top-view) with visible incurrent (in-c) and excurrent canals (ex-c), (**e**) sandwich culture with choanocyte chambers (cc), spicules (sp), and endopinacoderm (enp) lining aquiferous canals, (**f**) sandwich culture after addition of edible particles (tp) for tracing water flow in the incurrent canal (in-c) which is separated from the flow in the excurrent canal (ex-c) by endopinacocytes (enp) and mesohyl (m).

**Figure A3.** Schematic illustration of the aquiferous system in a functional module of *Halichondria panicea*. (**a**) Left: external surface with ostia (open circles), right: canal system with choanocyte chambers (black circles) and flow direction towards osculum indicated by arrows (**b**) water flow (arrows) through choanocyte chambers (cf. [111,117], their Figures 9d and 2b, respectively). Abbreviations: exp = exopinacoderm, os = ostium, in-c = incurrent canal, enp = endopinacoderm, pro = prosopyle, cc = choanocyte chamber, ap = apopyle, m = mesohyl, sp = spicule, ex-c = excurrent canal, at = atrium, osc = osculum.

**Figure A4.** *Halichondria panicea*. SEM of cryo-fractured explants. (**a**) Choanocyte chamber with choanocytes (**c**) and their microvilli collars (mv) surrounding the flagellum (fl), (**b**) the fracture shows components of the aquiferous system with prosopyles (pro) and apopyles (ap) connected to incurrent (in-c) and excurrent canals (ex-c), respectively, embedded in mesohyl (m) with choanocyte chambers (cc) and spicules (sp).

**Figure A5.** Exposure of *Halichondria panicea* to different particle types. Single-osculum explant (topview) after (**a**) feeding on *Rhodomonas salina* (Cryptophyceae); note the red color originating from added algae, (**b**) exposure to inedible ink (Pelikan Scribtol, 2 × 104-fold diluted) for 1 h; note black color, and (**c**) recovery in particle-free seawater for 24 h. Pictures: Janni Magelund Degn Larsen.

#### **References**

## *Review* **Size-Specific Growth of Filter-Feeding Marine Invertebrates**

**Poul S. Larsen 1,\* and Hans Ulrik Riisgård 2**

**Abstract:** Filter-feeding invertebrates are found in almost all of the animal classes that are represented in the sea, where they are the necessary links between suspended food particles (phytoplankton and free-living bacteria) and the higher trophic levels in the food chains. Their common challenge is to grow on the dilute concentrations of food particles. In this review, we consider examples of sponges, jellyfish, bryozoans, polychaetes, copepods, bivalves, and ascideans. We examine their growth with the aid of a simple bioenergetic growth model for size-specific growth, i.e., in terms of dry weight (*W*), μ = (1/*W*) d*W*/d*t* = *aW* b, which is based on the power functions for rates of filtration (*F* ≈ *W* b1) and respiration (*R* ≈ *W* b2). Our theory is that the exponents have (during the evolution) become near equal (*b*1 ≈ *b*2), depending on the species, the stage of ontogeny, and their adaptation to the living site. Much of the compiled data support this theory and show that the size-specific rate of growth (excluding spawning and the terminal phase) may be constant (*b* = 0) or decreasing with size (*b* < 0). This corresponds to the growth rate that is exponential or a power function of time; however, with no general trend to follow a suggested 3/4 law of growth. Many features are common to filter-feeding invertebrates, but modularity applies only to bryozoans and sponges, implying exponential growth, which is probably a rather unique feature among the herein examined filter feeders, although the growth may be near exponential in the early ontogenetic stages of mussels, for example.

**Keywords:** filtration; respiration; bioenergetic growth model; exponential growth; power function growth

#### **1. Introduction and Growth Model**

Filter-feeding (or suspension-feeding) marine invertebrates are important animals in the food chains of the sea [1,2]. They trap food particles, such as phytoplankton and bacteria, from a feeding current that is created by their own pumping device or by the ambient, and the mechanisms that are used in order to capture and transport the particles to be ingested reflect various secondary adaptations to filter feeding among species [3]. The rate of growth of individuals is of interest in estimating the population grazing impact at a particular site, hence its ecological significance. However, the growth rates may also be of commercial interest, e.g., in mussel farming [4].

Here, we focus on the somatic growth of filter-feeding marine invertebrates under favorable conditions and exclude the release of biomass that is associated with spawning and terminal growth. We consider sponges (*Halichondria panicea*), jellyfish (*Aurelia aurita*), bryozoans (*Electra pilosa* and *Celleporella hyalina*), polychaetes (*Nereis diversicolor* and *Sabella spallanzanii*), crustaceans (calanoid copepods), bivalves (*Mytilus edulis*), and ascideans (*Ciona intestinalis*). Among these, only *N. diversicolor* is a facultative filter feeder that may switch to surface deposit feeding or scavenging.

Filter feeding in all marine invertebrates is a secondary adaptation. The blue mussel, *Mytilus edulis,* is a well-known example where the gills have become the water-pumping and particle-capturing organ, while the original function as gills has become superfluous [1,5]. In crustaceans, the secondary adaptation to filter feeding has evolved independently in many groups, and often filter feeding is only one of several feeding methods

**Citation:** Larsen, P.S.; Riisgård, H.U. Size-Specific Growth of Filter-Feeding Marine Invertebrates. *J. Mar. Sci. Eng.* **2022**, *10*, 1226. https://doi.org/10.3390/ jmse10091226

Academic Editor: Azizur Rahman

Received: 22 July 2022 Accepted: 31 August 2022 Published: 2 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/).

that are adopted by one species. A common feature is that the filter-feeding process is true sieving, where the mesh size of the filter determines the size of the captured food particles [6]. However, a secondary adaptation to filter feeding must have involved the development of a filter pump that can cover the need for food energy in order to cover the respiration requirements. When the respiration (*R*) increases with increasing body mass, the filtration (*F*) must necessarily follow and, therefore, our theory is that the exponents in the equation *F* = *a*1*W* b1 and *R* = *a*2*W* b2 have (during their evolution) become near equal (*b*1 ≈ *b*2), depending on the species, the stage of ontogeny, and their adaptation to the living site.

Here, *Mytilus edulis* is a good example as *b*1 ≈ 1 in very small juvenile mussels but decreases to *b*1 = 0.66 in larger mussels [7]. This makes the bioenergetic growth model [8,9] particularly simple, expressing the growth rate as *G* = *aW* b1 and the weight-specific growth rate as follows:

$$
\mu \equiv (1/W) \,\mathrm{d}W/\mathrm{d}t = a\mathcal{W}^b; b = b\_1 - 1,\tag{1}
$$

where the coefficient *a* = (*C* × *AE* × *a*1 − *a*2)/*a*0 depends on the food concentration (*C*), the assimilation efficiency (*AE*), and the cost of growth (*R*g/*G*), i.e., the metabolic cost of synthesizing new biomass, being the equivalent fraction of *a*0 − 1 of the growth itself. Because the proportion of the biomass with a low metabolism (e.g., lipid and glycogen store, gonads) may increase with the body size, the weight-specific respiration may concurrently decrease due to a negative exponent (*b* = *b*1 − 1).

Depending on the species that is investigated, the growth parameter of the dry body weight (*W*) could be the tissue volume (*V*) (sponges), the area (*A*) or number (*N*) of zooids in an encrusting colony (bryozoans), or a characteristic length (ascidians). Furthermore, it is of interest to note that the growth function *W*(*t*) may take two specific forms that are simply related to the specific growth rate, i.e., exponential growth, as follows:

$$\mathcal{W}(t)\text{-}\text{exp}(at),\,\upmu = a,\,\tag{2}$$

and power function growth as follows:

$$\mathcal{W}(t) \sim t^{\text{cl}}, \,\mu \sim \mathcal{W}^{-1/\text{cl}}.\tag{3}$$

If *b*1 ≈ *b*2 ≈ 1, hence *b* = 0 in a filter-feeding animal, then μ = *a*, and the growth is exponential, but otherwise the weight-specific growth rate will decrease with increasing body size.

The present theory of near-equal *b*-exponents forms the underlying basis of this review, where we consider examples of filter-feeding invertebrates and examine if their growth functions are exponential or power functions of time. The *b*-exponents of rates of filtration and respiration that have been found for the examined filter feeders are compiled in Table 1, from which it appears that, in many cases, *b*1 ≈ *b*2 in support of the theory, and the typical growth rates are listed in Table 2.

**Table 1.** *b*-exponents of rates of filtration *b*1 (in *F* = *a*1*W* b1) and respiration *b*2 (in *R* = *a*2*W* b2) of some filter-feeding invertebrates. *Halichondria panicea,* "small" = single osculum sponge explant; "large" = multi-oscula sponge.

**Table 2.** Specific growth rates of some filter-feeding marine invertebrates. Growth is measured as the change in size of the following: (W) = dry weight, (A) = colony area, (N) = number of zooids, (L) = body length. Cost of growth = *R*g/*G*.

#### **2. Sponges**

Sponges are one of the earliest evolved and simplest groups of animals [29]. They are multicellular filter feeders that actively pump volumes of water, which are equivalent to about six times their body volume per minute, through their canal system by means of flagellated choanocytes that are arranged in choanocyte chambers. They feed on free-living bacteria that are trapped on the array of microvilli of the collars of their choanocytes, and on larger phytoplankton cells that are drawn into the inhalant canal system, where they are captured and phagocytosed [30–35]. The water enters the sponge body through numerous small inhalant openings (ostia) and passes through incurrent canals, the choanocyte chambers, and through excurrent canals to be expelled as a jet through an exhalant opening (osculum). The water flow also ensures a supply of oxygen for respiration via diffusive oxygen uptake [36].

The experimental results that were summarized in [19] for the demosponge *Halichondria panicea* show the exponential growth at rates of μ = 0.6% to 1.18% d−1, and the maintenance food concentration (at no growth) was estimated for a given specimen to be *C*m = 25.1 μgCL−1. The highest reported growth rate of *H*. *panicea* of 4% d−1 [11] corresponds to an available total carbon biomass (TCB) of *C* = 8 *C*m, i.e., eight times that of the maintenance food concentration. The growth rate may thus be expected to increase linearly with *C* to a maximal value that is not exceeded, irrespective of how high *C* becomes.

In fair agreement with the observed exponential growth of *Halichondria panicea*, [11] found that exponents of the power functions of the filtration and respiration rates were *b*1 = 0.914 and *b*2 = 0.927, while [37] found that *b*1 ≈ *b*2 ≈ 1 for three larger tropical marine sponges. It is, therefore, of interest to see how the filtration rates of sponges depend on their size, which was summarized in [38] and approximated by the power function *F*/*V* = *a*3*V* b3, because this implies that *b*3 = *b*1−1 = *b* of Equation (1), assuming that the dry weight was proportional to the volume (*V*). Many values of the exponents b3, which have been reported by various authors that were cited in [38], suggest that b ≈ 0, implying exponential growth. However, in other cases, *b* < −0.2, and as low as −0.7, implying power function growth, which, however, is subject to the uncertainty of the assumption *V*~*W* for larger sponges.

Related to these considerations of volume-specific filtration rate is a recent discussion of its possible scaling to the size of demosponges. Here, according to [10], demosponges are modular filter feeders where the early stages of single-osculum aquiferous modules have volume-specific pumping rates that scale as *F*/*V* = *a*3*V* b3, *b*3 ≈ −1/3 (hence *b*2 =1+ *b*3 = 2/3, Table 1), as measured for small explants of *Halichondria panicea* [39,40]. Such modules only grow to a certain size [41,42], such that new modules will be formed for a growing sponge. Larger multi-oscular sponges consist mainly of single-oscular modules that have reached their maximal size, hence *b*3 ≈ 0, as noted for some species that were mentioned in [38]. A similar situation may be expected for large pseudo-oscular sponges (e.g., *Xestospongia muta* [43,44]), provided that the volumes were taken to be that of structural tissue and not the total volume that includes the large atrium volume of water. In summary, these considerations and *b*1 ≈ *b*2 suggest that *b* ≈ −1/3 for growing single-osculum demosponges and *b* ≈ 0 for multi-oscula sponges, according to Equation (1).

#### **3. Jellyfish**

Medusae of the common jellyfish *Aurelia aurita* are voracious predators that filter feed on zooplankton. They occur in many coastal ecosystems where they can be very abundant and so exert a considerable predation impact on the zooplankton; thus, they play an important role as a key organism in the ecosystem [45]. The predation impact can be evaluated when the population density and the individual clearance rate of the jellyfish are known. The weight-specific growth rate μ can be determined from the time interval collection, measuring their umbrella diameters, and converting that to dry weight.

Controlled laboratory experiments have used brine shrimp *Artemia* sp. as prey, for which the retention efficiency (60%) [46] is much higher and well defined than for natural prey, such as copepods, probably due to a lack of escape behavior. A study [20] found a typical growth rate of μ = 10% d−1 and the exponent *b* = −0.2 in Equation (1) for fully fed larger specimens (*W* = 154 mg, *d* = 56.9 mm umbrella diameter) with a diet of five *Artemia* L−1. A value of *b* = −0.2 is in fair agreement with the values *b*1 = 0.78 and *b*2 = 0.86, which were determined earlier [12,13]. For smaller specimens (*W* = 2.2 mg, *d* = 12.7 mm), the growth rate was μ = 24.4% d−1, which was in good agreement with the growth model of Equation (1) for *b* = −0.2. Similar experiments [21] showed *b* = −0.24 and a mean growth rate of μ = 6.28% d−1 over a size range of 115 to 1887 mg. According to the growth model of Equation (1), μ increases from zero (at the maintenance concentration, 1.23 *Artemia* L−1) linearly with the prey concentration, but only to a maximal value (at about five times that of the maintenance concentration), above which there is no further increase, and such maximal values depend on the size, see [45].

The growth rates from the field data, as indicated by the values of *b* = −0.43 to −0.84, which are summarized in [45], decrease much more with increasing size than those from the laboratory, which were close to the suggested theoretical value of *b* < −0.2. This difference can be explained by the lower retention efficiency and the fluctuating prey concentrations.

#### **4. Bryozoans**

Bryozoans are sessile, colonial filter feeders that mainly feed on phytoplankton that are drawn in with the flow into the tentacle crown (lophophore) by the cilia on the tentacles, which act as pumps and help to retain and transfer the prey to the mouth. In encrusting bryozoans, the filtered water flows under the lophophore canopy in order to escape at the edges of the colony or as jets from 'chimneys' inside of the colony, which, as a biomixing process, may help to prevent re-filtration. Encrusting bryozoans may form colonies of

essentially identical zooids, which have the same filtration rates, and hence may be considered to be modules of an 'organism', the colony [19]. The growth occurs by adding zooid modules along the periphery and may be measured by the increase with time of the area (*A*) or the number (*N*) of zooids in the colony. By denoting the area of one zooid as *A*z, the relation for incremental growth may be written as d*A* = *A*z d*N*. If *A*z remains constant during the growth, the specific growth rates - μA and μN would be equal, but if *A*z decreased with growth, we expect μA < μN.

The growth rates of colonies of *Electra pilosa* and *Celleporella hyalina* that were placed on microscope slides in both field and laboratory tests were measured in [22]. For the laboratory tests at an algal concentration of about 5000 *Rhodomonas* cells mL−1, representing well-fed conditions, the growth was found to be exponential, with specific growth rates for *E. pilosa* being μA = 0.09 ± 0.02 d−1 and μN = 0.11± 0.02 d−1, and for *C. hyaline* being μA = 0.10 ± 0.01 d−1 and μN = 0.12± 0.01 d−1. From the ratio of number-to-area, the density was in the range of five to eight zooids per mm2. The higher growth rate, which was based on the number of zooids, implies an increasing density of zooids with increasing colony size. The field data for *C. hyaline* (genotype H) showed similar exponential growth rates but had slightly smaller specific growth rates, which was likely due to the larger zooid size and the lower algal concentration (<1500 cells mL−1). The absence of the influence of the current velocity was ascribed to the fact that the thin layer of encrusting bryozoans is well within the low velocity viscous sublayer.

Among the 23 laboratory and field data sets for different species [22] the average specific growth rates were μA~0.09 to 0.14 d−1, while some lower and higher values could be caused by high algal concentrations (> 5000 cells mL−1). The low values (0.06–0.08 d−1) were observed for the natural colonies that were feeding on macroalgae. This study gives the orders of magnitude of specific growth rates and indicates the growth rate to be exponential.

Ref. [23] analyzed the datasets from [47] for the growth rate of five fouling marine cheilostome colony species and found the growth rate to follow power functions (*N* = *a*p *t* d), with exponent *d* = 2.266 ± 0.214 d−1 as the average of 10 groups. Apparently, the rate of asexual zooid replication increases with the colony size in many bryozoan species, hence the switch from exponential growth to power function growth. Thus, according to Equation (3), the number-specific growth rate (μN = (1/*N*) d*N*/d*t* = *d a*p 1/d *N*−1/d) decreases with increasing colony size as μN~*N*−0.44, according to the data for July to August of [23] from μN = 0.12 d−1 at *N* = 100 zooids to μN = 0.041 d−1 at *N* = 600 zooids. Interestingly, the first value of the specific growth rate is close to that observed in [22] for a growth up to a size of about 100 zooids, however, it became smaller in the larger colonies. This trend is similar to that observed for the blue mussel and may be ascribed to a change in the composition of the biomass. Although it is not supported by explicit data, it is possible that the rates of both filtration and respiration may be proportional to the number of zooids in a smaller growing colony of modules of developed zooids, which would imply *b*1 = *b*2 ≈ 1, hence *b* = 0 in the bioenergetics model of Equation (1), implying exponential growth, as found in [22]. However, for the larger colonies, the growth follows a power function, as found in [23].

#### **5. Polychaetes**

The facultative filter-feeding polychaete *Nereis diversicolor* can feed by pumping water through a mucus net-bag that is attached to the entrance of its U-shaped burrow in the sediment. The retained food particles in the net are then ingested with the rolled-up net. Switching from surface deposit feeding to filter feeding in *N. diversicolor* is an adaptation that is useful for the near-bottom dweller in shallow waters, where the concentration of suspended food particles varies widely. Filter feeding, in place of surface deposit feeding or scavenging/predation, is preferred when there is a sufficient concentration of suspended algal cells; however, the full growth potential of the polychaete is not always achieved near to the bottom due to food depletion in the absence of efficient vertical mixing. Field growth

studies [24] were therefore carried out with the worms placed in glass tubes at 15 cm above the bottom. This showed the weight-specific growth rates increasing to μ = 3.9% d−1 for an increasing concentration of Chl *a* of available algal cells, which is comparable to the results from the laboratory studies showing μ = 3.1% d−1, and the cost of growth was estimated to be only 8% of the total growth. Later laboratory studies [15] showed a growth rate of μ = 3.0% d−1 for a *Rhodomonas* algal diet but μ = 7% d−1 for a shrimp meat diet, and in both cases the weight-specific respiration (*R*/*W*) increased linearly with the specific-growth rate μ. This increase, which is also called 'specific dynamic action', indicated an energy cost of growth that was equivalent to 26% of the total growth, which is similar to some of the other filter feeders that are shown in Table 2. These studies show the effect of the nutritional value of the diet, from algae to shrimp meat, apparently raising both the weight-specific growth rate and cost of growth by the same factor of approximately two.

The obligate filter-feeding polychaete *Sabella spallanzanii* lives in a tube from which it extends its feeding organ that consists of a filament crown with closely spaced pinnules whose rows of compound latero-frontal cilia pump the water through the space between the pinnules and retain the food particles. It lives in patches and [25] recorded a density of 150 ind. m−2 and observed the growth in terms of the mean length of the tubes from L = 10 to 18 cm during the period from April to August of 1992, implying a mean length-specific growth rate of μL = 100 × ln(18/10)/120 = 0.49% d−1. They also reported an increase in the biomass (that we assume is proportional to the dry mass of the animals) from 60 g m−2 to 75 g m−2 for one month, which may be interpreted as a mean weight-specific growth rate over that period of μ = (1/*W*) d*W*/d*t* = 100 × ln (75/60)/30 = 0.74% d−1. The relationship between these specific growth rates agrees with the relationship between the biomass *W*(g) and the total worm length *L*(cm) that is given approximately as *W* = 0.0021 *L*2 − 0.0098 *L*, which is derived from [25].

#### **6. Copepods**

Raptorial feeding is probably primary in copepods, whereas filter feeding is a specialized condition that has been developed within the order of calanoid copepods. For example, the calanoid copepod *Acartia tonsa* uses ambush feeding when it slowly sinks through the water with extended antennae that perceive motile prey, or it uses filter feeding by generating a feeding current with which phytoplankton cells are captured by a filter that is formed by setae on its appendages. Copepods need to consume a large number of phytoplankton per day in order to cover their nutritional needs. They are characterized by a relatively fast growth rate [48] and page 428 of [6].

The growth rates of three calanoid copepods were determined in [49]. The growth rates were low, particularly during the summer. The specific growth rates of the copepodites were moderately high for *Eurytemora affinis* in the spring as follows: 23% and 15% d−1 for the early and late stages, respectively, and were low for *Pseudodiaptomus forbesi* in the summer as follows: 15% and 3% d−1, respectively (not shown in Table 2).

Small copepods grow fast at high temperatures accompanied with an ample food supply, as shown in [26], which is a study from the East China Sea. Thus, the weightspecific growth rates ranged from 4% to 135% d−1 in the 50 to 80 μm size fraction, and from 1% to 79% d−1 in the 100 to 150 μm size fraction, showing that the growth rates were positively related to the temperature and were negatively related to the body size. The strong size dependence could imply a power function growth with a small negative *b*-value, as indicated by the exponent *b* of Equation (1), increasing from *b* = −0.88 to *b* = −0.32 for the two size fractions [26]. However, according to Table 1 of [16] for calanoid copepods, the exponents of the power functions of weight-specific rates of clearance and respiration take the following values: *b*1 = −0.16 + 1.0 = 0.84, *b*2 = −0.22 + 1.0 = 0.78, or *b*1 ≈ *b*2 ≈ 0.8, hence *b* = −0.2 for the weight-specific growth rate of Equation (1). The value of *b* = −0.2 may be compared with the somewhat higher value *b* = −0.06 in Table 1 of [16], both of which seem to suggest power-function growth.

#### **7. Bivalves**

Most filter-feeding bivalve species have flat gills and employ essentially the same feeding mechanism. There is a wide diversity of gill types, and two different principles are used for food capture, depending on the presence or absence of latero-frontal cirri (see reviews [3,50]). We can direct attention to the blue mussel, *Mytilus edulis,* because it is the most abundant and most studied, which is partly because of its role in commercial aqua farming. The pump that draws in the water through an inhalant mantel opening into the mantel cavity, through W-shaped gills, and discharges it through an exhalant siphon as a jet, is the lateral cilia on the sides of the gill filaments. The separation of the food particles from the pumped current and their retention is handled by the latero-frontal cirri, ensuring a near 100% retention of particles above about 4 μm in size, which includes most phytoplankton. Filter feeding is a secondary adaptation where the gills have become greatly enlarged—far more than what is needed for respiration—which may be suggested to be 'evolutionary adapted' to the prevailing (often low) level of phytoplankton in the surrounding water [5].

The growth rates may change with the increasing size of the specimens. For *Mytilus edulis*, there is a shift at a dry weight of around *W* = 10 mg, corresponding to the shell length *L* = 10 mm, moving from the smaller post-metamorphic mussels of near-exponential growth to the larger juvenile specimens of power function growth. This is reflected by the following values of exponents for the rates of filtration and respiration, which are summarized in [51]: *W* < 10 mg: *b*1 = 1.03 and *b*2 = 0.887, or *b*1 ≈ *b*2 ≈ 0.9 and *W* > 10 mg: *b*1 ≈ *b*2 ≈ 0.66 (see Table 1).

In order to appreciate the influence of the food concentration on the weight-specific growth rate, Equation (1), with appropriate numerical coefficients (see [9]), takes the following form:

$$
\mu \equiv (0.871 \times \mathcal{C} - 0.986) \,\,\text{W} - ^{0.34}; \,\text{W} > 0.01 \text{ g} \tag{4}
$$

where units are μ (% d−1), *C* (μg Chl *a* L−1), and *W*(g). The measured growth rates in the field at *C* = 2.8 μg to 3.6 μg Chl *a* L−1 [4] are in good agreement with Equation (4), which also shows that starvation should occur at *C* ≤ 0.986/0.871 = 1.13 μg Chl *a* L−1, while saturation has been found to occur at *C* ≈ 8 μg Chl *a* L−1 [52]. For a typical value of *C* ≈ 3 μg Chl *a* L−1, the growth rate decreases as μ = 7.8% to 1.6% d−1 for a dry weight increase of *W* = 0.01 to 1.0 g.

The growth rates, in terms of the shell length, may be obtained from Equation (4) by the use of the allometric relation *W*(μg) = 2.15 *L*(mm)3.40, which shows that *W* = 0.01 g to 1.0 g corresponds to *L* = 12 mm to 46 mm. Furthermore, Equation (1) may be integrated in time in order to show the time that it takes to grow a mussel of a certain size. Finally, the bioenergetic model of Equation (1) has been extended to include the effects of low temperature and low food concentration [53].

#### **8. Ascidians**

The benthic ascidian *Ciona intestinalis* may often exert a significant grazing impact because of its dense populations in shallow waters. It retains food particles, including free-living bacteria of < 2 μm, on its mucous net with 80% to 100% efficiency [54]. It is characterized by rapid growth, early maturation, and a high reproductive output.

The rate of oxygen consumption was found in [18] to be dependent on the dry weight to the power *b*2 = 0.831, which would suggest power function growth according the bioenergetic model for *b*1 ≈ *b*2 as μ~*W* −0.17. It is important to note, however, the lower value of *b*1 = 0.68 in Table 1. However, growth can be exponential until it reaches a body length of 10 mm [55], which could suggest a switch from μ~constant for smaller specimens to a decreasing μ for large specimens.

The growth, in terms of length, has been reported to be 10 mm to 20 mm per month [56], 0.26 mm to 0.76 mm in diameter in seven days [57], or 0.7% d−1, increasing to a maximum of 1.4% to 3% d−1 [27]. The weight-specific growth rate increases with increasing temperature and algal concentration to about 7.7% d−1 [17,56], and it appears that a condition index, which is defined as the ratio of the dry weight of the soft parts to the total dry weight, is a

good indicator of growth as it increases linearly with the weight-specific growth rate up to 8% d−1 [27,28].

#### **9. Adaptation to Filter Feeding**

The present theory of near-equal *b*-exponents of filtration and respiration laws, which forms the underlying basis of the present review, is supported by the examples of filterfeeding invertebrates that are compiled in Table 1, from which it appears that *b*1 ≈ *b*2. Furthermore, Figures 1A and 2A of [16] confirm this theory by showing that, for a large number of marine pelagic animals, *b*1 ≈ *b*2 ≈ 1 on the average, but with considerable scatter, and perhaps not *b*1 ≈ *b*2 ≈ 3/4, as was suggested by the authors. For a specific animal, however, the values of the exponents often take values that are different from 1 and 3/4, as seen from Table 1 of [16] and Table 1 herein, which suggests that there may not be a universal 3/4-law.

All obligate filter-feeding invertebrates (apart from predatory jellyfish) face the same challenge of growing on a thin soup of bacteria and phytoplankton. This fact suggests the existence of some common traits among these animals, which have been identified in [19], as at least the following two features: the magnitude of the filtration–respiration ratio (*F*/*R*) and the oxygen extraction efficiency (EE).

One interpretation of the *F*/*R* ratio is its relation to food uptake. Here, the estimated *F*/*R* = 22.9 L of water per mL of O2 consumed by a specimen of the demosponge *Halichondria panicea* [19] is well above the minimum value of *F*/*R*m = 10 L of water (mL O2) −1 [58] for a true filter feeder. Here, *F*/*R*m = 10, being the maintenance value = 20/(0.8 × 2.5), 20 J, i.e., the metabolic equivalent of 1 mL of O2 and filtering water with a phytoplankton concentration of 1.5 μg Chl *a* L−1 (= 2.5 J L−1) with 100% retention and an 80% assimilation efficiency. The minimum value of *F*/*R*m = 10 L water (mL O2) −1 was based on a phytoplankton concentration of 1.5 μg Chl *a* L−1 (= 1.5 × 40) = 60 μgCL−1. However, sponges also feed on free-living heterotrophic bacteria, cyanobacteria, and other small (0.2−2 μm) picoplankton, as shown in [59], which measured *F*/*R* = 22.9 L of water per mL of O2 for *H. panicea*, which appears to agree with the reported carbon concentrations of 40 μg to 200 μgCL−1. Other values for demosponges, which were cited in [19], include 22.8 for *Mycale* sp. and 19.6 for *Tethya crypte,* which are of a similar magnitude. However, the much smaller value of 4.1 for *Verongia gigante* signifies a species that is not a true filter feeder, because it "consists of a tripartite community: sponge-bacteria-polychaete" [37]. [58] shows the *F*/*R* > 10 L of water per mL of O2 values for most of the species that are mentioned of the following taxonomic groups: sponges, bryozoans, copepods, polychaetes, bivalves, ascidians, and lancelets. Thus, the *F*/*R* ratio is an indicator of the ability of a filter-feeding invertebrate to survive on a pure diet of phytoplankton of 1.5 Chl *a* L−1. Any excess of the minimum for maintenance, 10 L water (mL O2) −1, is available for growth and reproduction, but if there is less than the minimum, there must be sources of food other than phytoplankton or it implies starvation.

Another interpretation of the *F*/*R*-ratio is related to the oxygen uptake. For example, the reciprocal of *F*/*R* = 22.9 L of water per mL of O2, i.e., *R*/*F* = 0.044 mL O2 (L water)−1 may be compared to the actual O2 content of water, which, at saturation, amounts to 6.3 mL O2 (L water)−1. The ratio, *EE* = 0.044/6.3 = 0.007 = 0.7% is denoted by the oxygen extraction efficiency. It is low for true filter feeders because the diffusive uptake readily provides the necessary oxygen, but it will increase if the flow is restricted by something, e.g., the reduced valve gape of mussels that occurs during periods of food depletion. The high value *EE* = 1/(4.1 × 6.3) = 0.039 = 3.9% of *Verongia gigante* signifies an atypically high O2 uptake, which is demanded by the symbiotic bacterial community within the sponge.

Finally, the metabolic cost of growth (*R*g/*G*) that enters the bioenergetic growth model in the coefficient *a*0 and represents the cost of synthesizing new biomass, which is mainly macromolecular synthesis, is generally low (8% to 23%, Table 2) but is very high (139%) for the sponge *Halichondria panicea* [11]. The latter high value is probably due to the early evolutionary simple structure that is mainly composed of the choanocyte pumps so that

energy that is used for maintenance only constitutes a small fraction of the energy that is required for growth.

#### **10. Conclusions**

For the filter-feeding invertebrates that are examined herein, the results in Table 1 show that the theory of *b*1 ≈ *b*2 appears to be approximately satisfied. The values of these *b*-exponents range from 0.66 to 1.0, implying size-specific growth rates of μ ≈ *W* −0.34 to *W* 0 = constant, i.e., from a power function growth that is decreasing with increasing size to exponential growth. Exponential growth is a feature of modularity, which among filter feeders only applies to some bryozoans and sponges. Here, the filtration rate of a bryozoan colony, for example, increases in proportion to its size, hence its number of individual zooids each have the same filtration rate. Similarly, the filtration rate and the growth increase in proportion to the size of a larger sponge if it is composed mostly of fully grown aquiferous units (modules) of an equal filtration rate. In addition to modularity, the growth may be near exponential in the early ontogenetic stages of filter-feeding invertebrates, such as mussels.

There seems to be no indication that *b*-exponents should take a suggested universal value of 3/4 [16], which is a trend that seems to appear when pooling data from a large number of organisms covering a large span of sizes [59,60]. The magnitude of size-specific growth rates range from less than 1% d−1 to more than 100% d−1 (Table 2), tending to be high for small organisms or those in the early stages of growth and decreasing with size.

**Author Contributions:** Conceptualization, writing—review and editing, P.S.L. and H.U.R. 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.

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

#### **References**

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