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Fishery Bulletin 120(2) 
term in Equation 6 corresponds to the oxygen supply to a 
growing fish or invertebrate, and the catabolic term corre- 
sponds to its maintenance oxygen requirements or demand, 
because of the fact that denatured proteins and other mol- 
ecules need to be replaced for an animal’s body to maintain 
itself. Therefore, when the anabolism exceeds the catabo- 
lism, growth occurs (given that food is also available). How- 
ever, as the anabolic term grows with a power of weight 
d <1 (here: d=2/3), the catabolic term, which generates an 
oxygen demand proportional to weight, will eventually 
catch up—and growth will become zero, at the asymptotic 
volume V,, or the corresponding asymptotic weight W... 
There are various debates about this interpretation, 
with some arguing that the respiratory surface providing 
the oxygen required for anabolism is capable of growing 
proportionately to weight (i.e., d=1) and hence that oxy- 
gen supply cannot be limiting to the growth of fish spe- 
cies and other WBE. This notion was refuted by Pauly and 
Cheung (2017) on the basis of numerous metanalyses of 
gill surface areas in fish and other WBE (e.g., Hughes and 
Morgan, 1973; de Jager and Dekkers, 1974), which con- 
sistently have estimated d as <1, and by (Pauly, 2021a), 
who grouped the detractors’ arguments in detailed tables 
depending on their nature (e.g., not appreciating the 2-D 
nature of gills, mistaking causes and effects, and making 
unfalsifiable claims) and refuted them point by point with 
references to the aforementioned metanalyses and other 
reliable peer-reviewed sources. 
Surface-to-volume issues also apply to sponges, because 
the cumulative cross section of the pores through which 
water enters their bodies is a surface. This (2-D) surface, 
at least in compact sponges such as the wool sponge, can- 
not keep up with the growth of (3-D) bodies. Therefore, as a 
compact sponge grows, its interior will become increasingly 
hypoxic (Hoffmann et al., 2005; Lavy et al., 2016), and tis- 
sue maintenance will be increasingly compromised. 
Sponges have therefore evolved a complex symbiotic 
relationship with microbes to deal with the geometric 
constraints imposed on sponge physiology. The sponge 
canal system operates as subdivided units among which 
pumping rates (1.e., oxygen acquisition) vary, creating spa- 
tiotemporally variable zones of hypoxia and anoxia that 
serve to support the respiratory activity of anaerobic sym- 
bionts (Lavy et al., 2016). Nevertheless, in some sponge 
species, the development of internal hypoxic zones appar- 
ently leads to tissue necrosis, as suggested by Storr (1964), 
who, however, attributed central tissue “death” in large 
wool sponges to lack of food, rather than to lack of oxygen. 
In comparison, in fish tissues subject to increased hypoxia, 
the reduced availability of oxygen leads to an increase of 
the role of glycolytic enzymes, which, as individual fish 
grow, gradually replace oxidative enzymes (Somero and 
Childress, 1980; Burness et al., 1999; Norton et al., 2000; 
Davies and Moyes, 2007). 
Storr (1964), with regard to 12 in being the maximum 
diameter attained by spherical wool sponges, wrote the fol- 
lowing: “This is confirmed in the observed growth of wool 
sponges by the death of the central portion of the sponge 
when this diameter is reached. The form of the sponge from 
then on becomes more and more doughnut in shape. Con- 
tinued growth beyond a 12-inch diameter suggests that one 
other growth factor operates as the sponge approaches the 
limit of growth indicated by the formula. Since the sponge 
is uniform in structure and the intake of water carrying 
the food is through the sides, the greatest amount of food 
uptake is in the periphery of the sponge. This area, there- 
fore, continues to grow vigorously, but the rate of food 
intake is not sufficient nor the rate of food transfer through 
the sponge efficient enough to support active metabolism in 
the central portion of the sponge when the diameter of the 
sponge is 12 inches or over. The growth formula obtained 
would probably be directly applicable to the rate of sponge 
growth except for this phenomenon of sponge physiology.” 
Therefore, the growth phase documented herein pertains 
to spherical wool sponges; beyond this phase, wool sponges 
change shape, a shift that leads to different ratios between 
respiratory surfaces and the mass of oxygen-consuming tis- 
sues. This transition could be modeled by using a biphasic 
version of the VBGF (Soriano et al., 1992), but we did not 
attempt such modeling, mainly because the second-phase 
growth of this sponge species is not well documented and is 
of little interest to the sponge fishing and farming industries. 
Longevity 
Storr (1964) wrote, “Little is known of the life span of wool 
sponges although the records have indicated that they can 
live at least 25 years. Presumably, the limiting factor to 
continued growth is the capability of the sponge to draw 
in sufficient food for self-maintenance. Any lack of food 
intake is counteracted in part by the dying of the central 
portion of the sponge so that after a certain point in growth 
in diameter, the volume of the sponge remains a constant 
in relation to the surface area.” 
In fish, it is commonly observed that the longest-lived 
individuals of a population reach about 95% of their L,, 
(Taylor, 1958); therefore, longevity is approximately equal 
to the time required to reach 0.95L,.. Therefore, given 
Equation 4, we also have the following equation: 
longevity = 3/K, (7) 
which assumes that the parameter ft) can be neglected. 
A rough estimate of the uncertainty inherent in Equation 7 
is provided by assuming that the longest-lived individual 
reaches at least 90% or at most 99% of their asymptotic 
length (i.e., 2.3/K and 4.6/K). 
Another useful model, from Hoenig (1983), links longev- 
ity with the instantaneous rate of total mortality (Z, year ') 
in fish, mollusks, and other marine animals (134 popula- 
tions in 79 species) and which has the following form: 
In(Z) = 1.44 — 0.982In(t ax); (8) 
where t,,,x = the age (in years) of the oldest individuals in 
a population; and 
Z = the annual mortality experienced by a popu- 
lation (NV) between time ¢, and f, or 
NIN, = eh(t2 = tl) (9) 
