The gill-oxygen limitation theory (GOLT) and its critics - Science Advances

Posted: 06 Jan 2021 11:12 AM PST

Fish growth versus reproduction

One of the main issues in ichthyology, though it is not often perceived as such, is the relationship between growth and reproduction. The majority of authors writing on this topic repeat the usual belief that the relationship between growth and reproduction is explained by stating that "the growth of fish slows down upon reaching maturity because their energy is redirected from growth to reproduction," or a variant of this phrase (70–77). This notion implies a "biphasic growth" with a rapid growth phase before the length at first maturity is reached, and a slower phase thereafter, as illustrated by Fig. 3A.

Fig. 3 Two views of the relationships between size at first maturity and maximum size.
(A) Traditional view, where "linear" growth slows down when length at first maturity (*L_m*; black star) is reached, with growth then continuing at a reduced pace, depending on circumstances [i.e., a, b, or c; redrawn from (77)]. (B) More appropriate, but uncommon, view, with growth expressed as change in body weight (in line with Eq. 1). This shows not only that weight at first maturity in females and males (*W_m*; black star) is reached when growth is still accelerating (i.e., *W_m < W_i*, the inflexion of the curve) but also that females grow faster and reach larger weights than the males despite investing more in reproduction (see also text and Table 6). Graph based on length growth parameters, a length-weight relationship, and length at first maturity for Alaska pollock (*Gadus chalcogrammus*) in FishBase (www.fishbase.org), which contains hundreds of similar datasets.

What is not realized, however, is that this phrase, like all statements about complex phenomena, is a hypothesis. Moreover, this hypothesis is contradicted by four sets of observations: (i) Fish kept in aquaria and that never mature and spawn reach maximum sizes that are similar to those of reproducing conspecifics in the wild. (ii) In most fish species, the females are larger than the males, although they devote more energy to reproduction. (iii) In most fish species, growth in weight is more rapid after maturity is reached than before. (iv) Mean length at first maturity, in fish, correlates tightly with the maximum length that can be reached in a given environment.

Regarding item (i), popular aquarium fish such as clown loach (Chromobotia macracanthus) do not breed in captivity but still approach a common maximum length of about 16 cm (78). Similarly, most saltwater aquarium fish such as damsels or butterfly fish do not breed in tanks but again reach a common maximum length similar to the one in the wild (79); many of the saltwater or freshwater fish kept by home aquarists never mature and spawn. However, although they are fed ad libitum, they stop growing at some point. In addition, triploid (and thus sterile) fish exhibit growth patterns largely similar to those of their diploid brethren (80). This should suffice to kill the notion that it is reproduction that causes growth to cease. However, it has become a zombie idea: It does not die.

Similarly, regarding item (ii), in over 80% of fish families where females and males look alike, it is the females that eventually reach larger sizes (Fig. 3B), even if this growth dimorphism can become attenuated in certain circumstances (81). This strong female dimorphism should lead to a rethink of the notion that the cost of reproduction causes growth to decline. However, some authors, when confronted with this evidence, have doubled down and suggested that males have the higher reproductive cost.

One such case is (82) (see also Table 6, number 6.2); it was suggested (83), in an effort to refute the claim above (84), that males had the higher reproductive effort. This was backed with a graph from an unpublished thesis that did not even compare male and female reproductive output (see Table 6, no. 6.2). In reality, females are, by definition, the sex with the higher reproductive output, which also can be shown empirically in almost all groups of animals reproducing sexually [reviewed in (85)]. There are a few exceptions (e.g., parental care by male seahorse), but they are not pertinent here.

Table 6 Arguments raised against the GOLT: Spawning versus growth and vice versa.

View this table:

Regarding item (iii), Figs. 1C and 3B show that, in fish, the ratio of weight at first maturity (W_m) to asymptotic weight (W_∞) can be much lower than the corresponding ratio for length (L_m/L_∞), which is frequently not realized because the overwhelming majority of growth curves drawn reflect growth in length (Fig. 3A).

From length growth curves, one can get the impression that spawning strongly affects growth, hence the name "reproductive load" for the L_m/L_∞ ratio (86). However, growth is a process primarily involving mass (see Eq. 1), as reflected in weight growth curves. Weight growth curves have marked inflection points, where growth rate (dw/dt) is highest (at W_i), and thus, the question may be asked whether W_m > W_i or, on the contrary, W_i > W_m. Taking the second derivative of generalized VBGF for weight growth (Eq. 5) and setting it equal to zero allow us to identify W_i, where the growth rate changes from increasing to decreasingWi=W∞·(1−(D/b))b/D(7)

As may be seen from Figs. 1C and 3B, the weight at the inflection point of these curves is higher than the mean weight at first maturity of the population in question (i.e., W_i > W_m). This result, which can easily be reproduced for multiple species of (large) fish (Table 7), implies that as fish reach maturity, their growth in weight is still accelerating, which refutes the reproductive load hypothesis.

Table 7 Theoretical versus empirical predictions of weight at fish maturity.

The "theoretical" predictions of W_m based on the GOLT (Eq. 9) match the empirical estimates based on Eq. 10 (90); the relationship of W_m to the inflexion (W_i; Eq. 7) of weight growth curves is also as predicted (see text).

View this table:

The question thus arises: If the reproductive load concept does not hold, i.e., if reproduction does not cause growth to decline, what then is the relationship between reproduction and growth in fish and, by extension, in other WBE?

Equation 1 with d < 1 implies that the heavier fish get, the less O₂ per unit weight they will get, which should imply—other things being equal—more frequent occurrences of respiratory stress and hypercapnia. All we need to assume, therefore, is the existence of a threshold weight (W_m) at which the high frequency of respiratory stress or hypercapnia events triggers the hormonal cascade that leads to maturation (87). Thus, one can defineA=(W∞1/b/W1/b)D(8)from whichWm=W∞·(1/A)b/D(9)with A being the ratio of gill surface area (or O₂ supply) at W_∞ over the gill surface area (or O₂ supply) at W_m (16, 87).

A first estimate of A = 1.365 was published in 1984 (see Fig. 4C) (87), whose 95% confidence interval is 1.218 to 1.534, as estimated using the Fieller method (88) (see www.graphpad.com/quickcalcs/ErrorProp1.cfm) applied to the data of table S1. These data covered 56 pairs of L_m and L_∞ in 34 different fish species ranging from guppies to tuna and raised to the power of 3/(1 − d), which here substitutes for weights.

Fig. 4 Growing fish mature when their relative gill surface area reaches a threshold.
(A) In the ontogeny of fish, when their relative gill surface area declines, their oxygen supply declines as well; when the latter reaches 1.3 to 1.4 times the oxygen supply required for maintenance and routine activities, i.e., as fish increasingly get "out of breath" (and suffer from hypercapnia), the hormonal cascade is initiated that leads to gonad maturation and spawning. (B) If the same fish are in a stressful, e.g., warmer environment, causing oxygen demand to be elevated, the same 1.3 to 1.4 threshold will cause them to mature and spawn at smaller sizes. (C) Plot, whose 56 points represent the 34 fish species, ranging from guppies to tuna (87) (see the Supplementary Materials) used to estimate the average threshold value of 1.36 (with 95% confidence interval of 1.218 to 1.534). (D) Same plot but for different populations of redband trout (*Oncorhynchus mykiss*). (E) Ditto for Yellowstone cutthroat trout (*Oncorhynchus clarkii*). (F) Ditto for mountain whitefish (*Prosopium williamsoni*).

Because A⁻¹ = 0.733, combining with Eq. 7 and rearranging (see the Supplementary Materials) lead to the conclusion that d > 0.733 implies W_i > W_m, d ≈ 0.733 implies W_i ≈ W_m, and d < 0.733 implies W_i < W_m. Thus, in small fishes, which usually had small values of d (e.g., 0.6 in the diminutive goby M. luzonensis) (16, 62), W_m > W_i, while the opposite, W_m < W_i, applies to larger fishes (e.g., bluefin tuna; see Figs. 1C and 3B).

This also aligns with the empirical relationships between L_m and L_∞ (with and without additional variables) in 265 fish species in FishBase (www.fishbase.org), covering 88 families and 27 orders, with an average scaling factor of ≈0.9 emerging (89). The simplest of these relationships waslog(Lm)=0.898·log(L∞)−0.0782(10)when L_m and L_∞ are in cm.

Equation 10 implies that fish with an asymptotic length of 10 cm reach maturity at a length of 6.6 cm, while fish with asymptotic lengths of 100 and 1000 cm reach maturity at 52 and 412 cm, respectively. These values, when converted to weights, are well within the confidence interval of the value of W_m predicted by Eq. 7 (Table 7).

Unfortunately, Eq. 9 does not work below 1.3 cm, i.e., it predicts L_m > L_∞. It can be hypothesized that all such small fish are semelparous, i.e., will spawn only once before they die, as documented in minute gobies (90). Equation 10 does not work either with large semelparous species such as Pacific salmon (Oncorhynchus spp.), whose reproductive strategy, however, is a derived trait connected with their diadromous life history (91).

Last, regarding item (iv) above, there is the huge environmental plasticity of fish, which can manifest itself both in individuals used for aquarium experiments (92, 93) and in the wild. Regarding the latter, it was noted that "tropical fishes living near the limit of their tolerance for low temperature grow to larger size at such temperatures" (94). In such cases, i.e., when the maximum length (L_max) or the computed asymptotic length (L_∞) changes, the mean length at first maturity (L_m) also changes in the same direction such that the ratio L_m/L_max or L_m/L_∞ remains approximately constant.

The GOLT provides an explanation for the near constancy of L_m/L_max or L_m/L_∞ by postulating that spawning is induced by the same mechanism that also causes growth to decline (i.e., asymptotic growth). As fish grow in weight, their gills, whose surface area has grown with the scaling factor d < 1, deliver less O₂ per unit of body weight (Fig. 4A).

Thus, growing fish will gradually experience more respiratory stress and hypercapnia, and a level of either is finally reached that initiates the hormonal cascade leading to maturation (95, 96). Gonadal products are elaborated, often by using fat accumulated in the summer and fall as a fuel (97). When, in spring, the gonadal products are released, the gill surface area/body weight ratio increases again, and summer growth can resume, etc.

With time, however, the fish grow heavier despite generating an increasing reproductive output, and the ratio of gill surface area/body weight declining further (Fig. 4, A and B). Thus, growth gradually ceases, but life (and reproduction) does not need to, as exemplified by adult whitefish (Coregonus spp., Salmonidae) that can live a decade or more after they have ceased to grow (98). The same occurs in a number of coral reef fishes, for example, in the families Acanthuridae and Scaridae (99, 100).

The threshold gill surface area, and hence the relative metabolic rate at which spawning is initiated, is similar among different fish families (see Fig. 4C and fig. S2) because such a critical threshold would be conserved through evolutionary time. Thus, when the growth of teleosts causes their metabolic rate to drop to about 1.3 to 1.4 times their maintenance metabolic rate (i.e., something that fish can monitor in real time), then sexual maturation is initiated. Figure 4 (D to F) provides further examples of this generalization [see also (101)].

Temperature and maximum sizes

The major critique (42) of a contribution based on the GOLT that predicted that ocean warming would reduce the maximum size of fish (7) proposed no alternative explanation as to why fish should remain smaller at higher temperatures. Thus, another contribution (102) is examined here, in some detail, as its authors attempt to answer the question whether "oxygen limitation in warming waters is a valid mechanism to explain decreased body size in aquatic ectotherms" (Fig. 5A).

Fig. 5 Fish, at higher temperatures, tend to grow fast toward smaller maximum sizes.
(A) "Observed phenomenon" that needs to be explained [adapted from an insert in figure 1 of (*102*)]. (B) Simplified version of figure 1 in (25). (C) Atlantic cod (*G. morhua*) has wide geographic and temperature ranges; in Eastern Iceland (1° to 10°C), they reach much larger sizes than in French waters (8° to 18°C), based on data in (*138*, *139*).

Answering this question would also solve the riddle posed earlier by an author (92) who was surprised by his observation, based on guppies raised at different temperatures that "[t]he results indicate that the differences in growth rate established in young fish do not persist throughout life. Initially slow-growing fishes may surpass initially fast-growing fishes, and finally reach a greater length-at-age," as reported and illustrated earlier (Figure 5B) (25) and well documented in the literature, for example, for Atlantic cod (Gadus morhua) (Fig. 5C).

Six potential explanations were presented and discussed by these authors (102), as documented in their figure 1, from which all quotes below are extracted. These potential explanations are then summarized, illustrated (Fig. 6, A to F), and commented upon. All but the first of these potential explanations can be viewed as alternatives to the GOLT:

Fig. 6 Simplicity versus scope in explaining why higher temperatures lead to smaller sizes.
The six explanatory models are adapted from (*102*) and were presented in two columns, as "intrinsic mechanisms" (A to D) and "extrinsic mechanisms" (E and F). Here, they are arranged according to the perceived complexity of the mechanism(s) they require (abscissa) and their generality or "scope" (ordinate).

1) The GOLT [or "GOL hypothesis" in (102)]. The GOLT, based on the inherent properties of gills as 2D surface that must remain exposed to an oxygen-laden water flow, assumes that they will provide decreasing amount of oxygen per unit weight to the bodies of growing WBE (Fig. 6A). Hence, increased temperatures, which increase oxygen demand, will force them to remain smaller [Fig. 5C; see also (7)]. However, the fish kept at higher temperature may, at first, experience a more rapid growth than those kept at low temperature, which also explains the above quote [from (92)]. Note also that many inferences on the growth of fish and other WBE are based on juveniles, whose growth is usually accelerated by temperature increases, and not on adults, whose growth is often depressed by increased temperature (Table 1). The preference of researchers for working with juvenile fish is understandable (they require smaller aquaria, require less food, etc.), but it can lead to confusion, as illustrated by one of the few aquatic biologists who raised fish (albeit small ones) under different temperatures from larvae to adults (92) and who penned the quote above.

2) "Different temperature dependence of DNA replication (development) results in smaller cells and faster division at warmer temperatures." Fish that remain smaller at higher temperatures have, to the author's knowledge, never been shown to have smaller cells, and if they did, this would be the reason for their smaller size in warm water only if they had the same number of cells, as do, e.g., tardigrades and small nematodes. This, as well, has never been demonstrated. Hypothesis (2) (Fig. 6B) is probably another case of cause and effect being inverted (Table 4), as often happens when things correlate (103). Some of the largest fish, e.g., tuna, have very small cells, while the much smaller lungfish have large cells (104–106). It seems that in fish at least, cell size is linked with DNA content and activity level but not with size (107). On the other hand, the higher cellular turnover implied by "faster cell division at warmer temperatures" would be associated with a higher rate of protein denaturation, which is a central tenet of the GOLT (see above).

3) "Decreasing growth efficiency at higher temperatures means that less energy is converted to growth." This is not an explanation because it shifts that which must be explained from "reduced growth when temperature is high" to "decreased growth efficiency" (Fig. 6C), which is a restatement of the issue at hand. The GOLT explains decreased growth efficiency [i.e., K₁, growth increment/food ingested (108, 109)] by pointing out that when WBE are exposed to higher temperatures, more of their oxygen supply is diverted to basal metabolism, leaving less available to assimilate food. Hence, the amino acid pool of fish spills over and "is excreted by the gills and kidney as incompletely oxidized nitrogenous compound"—the latter point from (110), which cites (111–115) [see also (116)].

4) "Higher size-specific allocation to reproduction at higher temperatures […] leaves less energy for growth." This argument (Fig. 6D), for which no supporting evidence was presented, is not pertinent in any case because the effects of temperature on fish growth manifest themselves well before size at first maturity is reached (see Fig. 5C).

5) "Faster increases in energy demand (metabolism, activity cost, etc.) compared with food availability leaves [less] energy for growth and reproduction in […] warmer environments." This is a complex hypothesis, implying that tropical ecosystems make less food available to consumers than colder ecosystem (Fig. 6E), which would be hard to test. Fortunately, there is no need to because experiments can be and have been conducted in vitro where food is provided ad libitum and where fish kept at cooler temperatures grow to be larger than those at higher temperatures (92, 117, 118). The only reason this point is perhaps not obvious is that laboratory growth experiments are difficult to run with large/old fish and thus are mostly conducted with juvenile fish, with the initial growth acceleration due to higher temperatures leaving the strongest impression. Only when small, short-lived fishes are monitored over their entire life spans does the phenomenon appear, which was found so puzzling (92).

6) "Increased predation mortality at higher temperatures drives an evolutionary response of higher net energy allocation to reproduction versus growth." This is hypothesis (4) in another guise (Fig. 6F). Evoking a complex "evolutionary response" is not an explanation of anything because, as was said so elegantly, "nothing in biology makes sense except in the light of evolution" (119). The point, rather, is to identify the mechanism in question. However, it will be quite difficult, given that, as stated for (4), fish grown under experimental conditions and without opportunity to spawn remain smaller at higher temperatures (92, 117, 118). The critique of items (2) to (6) is serious: Proposed hypotheses should be able to withstand a confrontation with common sense observations. Moreover, several of the hypotheses in Fig. 6 were only complex restatements of the issue at hand.

In contrast, the GOLT proposes a mechanism for the reduced body size of fish and invertebrates under global warming that is simpler than what needs to be explained and that is based on consensual knowledge, including that gills cannot be perceived as trans-dimensional Escher-like objects (42). In addition, the GOLT makes numerous predictions pertaining to domains that, at first glance, appear to be unrelated to temperature affecting the size of fish.

This is because the constraints on the surface area of gills are real: Their surface area was optimized in the course of evolution to allow their owners to reach first maturity relatively fast, after which growth can gradually slow down.

The notion that gill surface area cannot be limiting because lamellae can be added as required (42) is false because gills function similarly to a sieve, i.e., must be perpendicular to the water that flows through them. This means that they can grow in height and in breadth, but not in depth: They cannot grow in the third dimension, and thus, 3D bodies must experience a declining oxygen supply as they grow. Moreover, gills are a favorite site for parasite infestation, and fish and aquatic invertebrates have good reasons to keep them as small as possible (102, 120). Thus, gill surface area is not limiting to young/small fish, but they are to big adults.

The GOLT offers a coherent framework for exploring these phenomena and a vast number of related observations. This is not the case for just-so hypotheses.

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