The Relationship between Mean Length at Maturity and Maximum Length in Coral Reef Fish

: This article proposes a mechanism that triggers first maturation and spawning in coral reef (bony) fish, which allows for predicting their length at first maturity. Thus, mean lengths at first maturity (L m ) and the corresponding maximum lengths (L max ) in 207 populations of 131 species of coral reef fish were assembled and used to test the hypotheses that (a) there is, in coral reef fish, a single value of a size-related parameter acting as a trigger for their maturation and eventual spawning, and (b) that this single value is statistically the same as that published previously for other bony fish. The results, based on the assembled L m and L max data and on estimates of the parameter D, which link the length of fish with the relative surface of their gills, covered 44 families and L max values ranging from 1.8 to 181.6 cm and confirmed that the threshold in (a) exists. Also, we assessed (in b) that this threshold value, i.e., L maxD /L mD = 1.35 ( ± 0.02), is not statistically different from similar estimates for other groups of teleosts, notably semelparous salmonids, cichlids, sturgeons and Chinese and Turkish freshwater and marine fish. One implication is that given ocean warming and deoxygenation, coral reef fish will not only be smaller than they currently are, but also mature and spawn at smaller sizes, and thus produce fewer, smaller eggs.


Introduction
The age and, particularly, the size when fish mature are important parameters of their life history and are important for fisheries management [1,2].Compared to mammals and birds, fish mature at much smaller lengths (L m ) than the maximum lengths reached in the population to which they belong (L max ), a feature even more pronounced when one deals with weight (W), where W m << W max [3,4].
This "early maturation" of fish may have been the reason why ichthyologists and fisheries biologists have believed that the "energy" that was previously used in growth is, once maturity is reached, transferred to gonad development, slowing down their growth all the way until it ceases [5][6][7].However, this belief, which has undoubtedly been reinforced by the perception of a transition in length growth curves, from fast to slow growth following first maturity (Figure 1a), cannot be upheld when growth curves in weight are considered (Figure 1b).
The notion that it is reproduction that slows down the growth of fish, which may be referred to as the "reproductive load hypothesis", is also refuted (i) by every lone goldfish in a bowl, whose growth ceases at some point although they have never reproduced, (ii) by the fact that in 80% of fish species, it is the female who grow to larger sizes, although they have a bigger reproductive effort, and (iii) by the fact that sterile triploid fish do not exhibit higher growth rates than their fertile and diploid conspecifics [8].There are other reasons why the "reproductive load hypothesis" is untenable [3,4], and the time has come to consider an alternative.by the fact that in 80% of fish species, it is the female who grow to larger sizes, although they have a bigger reproductive effort, and (iii) by the fact that sterile triploid fish do not exhibit higher growth rates than their fertile and diploid conspecifics [8].There are other reasons why the "reproductive load hypothesis" is untenable [3,4], and the time has come to consider an alternative.
Figure 1.Two versions of the effect of reproduction on fish growth.(a) Representation of the "Reproductive Drain Hypothesis" (RDH), i.e., the notion that reaching the size at first maturity causes previously "linear" growth (line 1) to decline due to "energy" previously used for somatic growth being transferred to the elaboration of gonads, with the dotted line 2 implying a small, and line 3 a strong, transfer of "energy" (modified from Figure 2 in Lester et al. [9]).(b) When growth in weight is considered, the weight at first maturity (Wm) in most species of fish is reached at a size where growth is accelerating, i.e., well below the weight at which the maximum growth rate is attained (at Wi), as illustrated for yellowbelly threadfin bream (Nemipterus bathybius), based on data in Li et al. [10].This is incompatible with the RDH.
The hypothesis proposed by Pauly [11], based on 34 species and 56 populations of marine bony fish, to replace the reproductive load hypothesis has since been shown to apply to a vast number of other species [12][13][14][15][16].
Here, two hypotheses based on Pauly [11] are tested for 131 species of coral reef fish: (a) that there is, in coral reef fish, a single value of a size-related parameter acting as a trigger for their maturation and eventual spawning, and (b) that this single value is statistically the same as that published previously for bony fish.
The underlying growth model considered here was proposed by Pütter [17], and has the form dW/dt = HW d − kW (1) where dW/dt is the rate of growth, HW d is the rate of protein synthesis, which is dependent on the oxygen supplied by the gills, and kW is the spontaneous denaturation rate of protein, a process requiring no oxygen, but which removes "working" proteins from the bodies of fish, and which, therefore, requires these proteins to be resynthesized [18,19].Important here is that the parameter d in HW d is related to the gill surface area (S, and hence oxygen supply) through a relationship is of the form S ∝ W d (or respiration ∝ W d ), with d < 1.The parameter d < 1 implies that, as weight increases, kW will increase faster than HW d , and that, when the rate of protein synthesis equals the rate of protein denaturation, growth ceases (at Wmax).The overwhelming majority of bony fish (i.e., excluding those breathing air) have d ranging between 0.6 and 0.9 [20,21], but always less than 1 [22,23].
It is commonly accepted that fish start maturing when environmental stimuli "trigger" the hormonal cascade that leads to maturation and spawning [24].However, this does not explain the fact that long-lived fish, despite experiencing-as juveniles-multiple spawning seasons and, thus, being exposed to the same environmental stimuli, do not actually start spawning until later in life, when a critical size is reached [23].

Figure 1.
Two versions of the effect of reproduction on fish growth.(a) Representation of the "Reproductive Drain Hypothesis" (RDH), i.e., the notion that reaching the size at first maturity causes previously "linear" growth (line 1) to decline due to "energy" previously used for somatic growth being transferred to the elaboration of gonads, with the dotted line 2 implying a small, and line 3 a strong, transfer of "energy" (modified from Figure 2 in Lester et al. [9]).(b) When growth in weight is considered, the weight at first maturity (W m ) in most species of fish is reached at a size where growth is accelerating, i.e., well below the weight at which the maximum growth rate is attained (at W i ), as illustrated for yellowbelly threadfin bream (Nemipterus bathybius), based on data in Li et al. [10].This is incompatible with the RDH.
The hypothesis proposed by Pauly [11], based on 34 species and 56 populations of marine bony fish, to replace the 'reproductive load hypothesis' has since been shown to apply to a vast number of other species [12][13][14][15][16].
Here, two hypotheses based on Pauly [11] are tested for 131 species of coral reef fish: (a) that there is, in coral reef fish, a single value of a size-related parameter acting as a trigger for their maturation and eventual spawning, and (b) that this single value is statistically the same as that published previously for bony fish.
The underlying growth model considered here was proposed by Pütter [17], and has the form dW/dt = HW d − kW (1) where dW/dt is the rate of growth, HW d is the rate of protein synthesis, which is dependent on the oxygen supplied by the gills, and kW is the spontaneous denaturation rate of protein, a process requiring no oxygen, but which removes "working" proteins from the bodies of fish, and which, therefore, requires these proteins to be resynthesized [18,19].Important here is that the parameter d in HW d is related to the gill surface area (S, and hence oxygen supply) through a relationship is of the form S ∝ W d (or respiration ∝ W d ), with d < 1.The parameter d < 1 implies that, as weight increases, kW will increase faster than HW d , and that, when the rate of protein synthesis equals the rate of protein denaturation, growth ceases (at W max ).The overwhelming majority of bony fish (i.e., excluding those breathing air) have d ranging between 0.6 and 0.9 [20,21], but always less than 1 [22,23].
It is commonly accepted that fish start maturing when environmental stimuli "trigger" the hormonal cascade that leads to maturation and spawning [24].However, this does not explain the fact that long-lived fish, despite experiencing-as juveniles-multiple spawning seasons and, thus, being exposed to the same environmental stimuli, do not actually start spawning until later in life, when a critical size is reached [23].
Therefore, a size-related internal readiness event ought to occur before any external stimuli and their triggering effect are perceived.The hypothesis proposed by Pauly [11] is that this internal readiness is established, in an individual fish, when its metabolic rate (Q m ) relative to its (maintenance) metabolic rate (Q maint ) decreases below a critical level (Q m /Q maint ).It is this readiness that causes the fish to start responding to the external triggers [23].Pauly [11] demonstrated that L max D vs. L m D , with D = 3(1 − d), is algebraically equivalent to Q m vs. Q maint and, based on a variety of marine fish species, that the critical level (Q m /Q maint ) is 1.36 (95% C.I. 1.22-1.53).This estimate was confirmed by studies that produced estimates not significantly different from 1.36, pertaining to 3 species and 51 populations of semelparous freshwater salmonids [12]; 7 species and 41 populations of cichlids [13]; 96 species and 24 populations of marine and freshwater fish from Chinese waters [14]; 22 species of sturgeons [15]; and 57 species and 120 populations of marine and freshwater fish from Turkish waters [16].
The ubiquity of this ratio suggests that this is a trait that has been conserved through millions of years of evolution.Here, we test this ratio on 207 populations in 131 coral reef fish species.

Materials and Methods
The maximum length (L max ; fork length; in cm) and mean length at first maturity (L m ; fork length; in cm) of coral reef fish from various geographical locations were collected from the published literature on dioecious fish, i.e., hermaphroditic species-when known as such-were excluded.Care was taken to assemble data that (i) covered most families of coral reef fish (ii) originating from the Atlantic, Indian and Pacific Oceans, and the waters of both economically developed and developing countries, and (iii) which spanned a wide range of sizes.In total, 207 pairs were assembled and used for analysis.In cases where only the asymptotic length (L inf ) was available, L inf was multiplied by 0.95 to obtain an approximate value of L max [25].
The L max values were then converted into W max estimates using the parameters (a, b) of the length-weight relationship (LWR) obtained from FishBase (www.fishbase.org) in the form of W = a•L b .Length-weight relationships from the same locality were used when available.In cases where several LWRs were available (e.g., in Acanthurus chirurgus) or in cases where no LWRs were available for the species in question, the Bayesian estimates of a and b from FishBase were used, which account for seasonal variations and other sources of uncertainly in the LWR [26].Also, note that the precision of the a and b estimates of the LWR had a minimal effect on the consideration that follows.
We used the empirical equation Based on estimates of d from gill surface area and respiratory studies in 27 populations of 24 species of teleost fish ranging from guppies to tuna [18,27], we estimated d values with W max in g; then, D was computed from D = 3(1 − d) to simplify things.
Table 1 presents the compiled life history traits and the resulting L max D and L m D values for the 207 coral reef cases that were assembled for this study.
The mean ratio L max D vs. L m D was estimated as the slope of a regression of L max D vs. L m D , along with its 95% confidence interval (C.I.), by running a Bayesian regression model with the intercept forced at zero using the brm function in the brms R package in R Statistical Software (v4.3.1, [28,29]).
To test for the effect of phylogeny on the estimated value, the effect of phylogenetic biases was accounted for by associating the mean L max D and L m D of each species with the full phylogeny tree obtained from the Fish Tree of Life through the R package fishtree [30].A number of species (n = 131 − 11 = 120) that were not available in the Fish Tree of Life were removed from further analysis.Using the brm function [29], we re-estimated the slope with and without the phylogenetic component.
Comparing the results of the regression models with and without the phylogenetic component should allow for testing whether the inclusion of shared evolutionary history between species is an important factor to consider in the relationship between L max D and L m D .Although the model with the phylogenetic component requires a Bayesian framework, it is comparable to the widely used phylogenetic generalized least squares regression [29].Furthermore, by employing Bayesian methods to estimate these models, we are provided removed from further analysis.Using the brm function [29], we re-estimated the slope with and without the phylogenetic component.
Comparing the results of the regression models with and without the phylogenetic component should allow for testing whether the inclusion of shared evolutionary history between species is an important factor to consider in the relationship between Lmax D and Lm D .Although the model with the phylogenetic component requires a Bayesian framework, it is comparable to the widely used phylogenetic generalized least squares regression [29].Furthermore, by employing Bayesian methods to estimate these models, we are provided with the advantage of generating a distribution of the slopes (i.e., a posterior distribution), which enables better comparison among slope estimates.

Results
In total, 207 Lmax and Lm data pairs accounting for 131 species from 44 different families were collected.Out of the 131 species in the dataset of this study, 11 species did not have resolved phylogenetic positions on the Fish Tree of Life, leaving 120 species to be further analyzed separately with and without phylogeny taken into consideration.
Considering all Lmax D vs. Lm D data pairs, the resulting slope was Lmax D = 1.35•LmD •(±0.02).For species that were on the Fish Tree of Life, but without phylogeny, the result was similar, with Lmax D = 1.34•LmD •(±0.03) (Figure 2a, Table 1).When phylogeny was considered, the resulting slope was Lmax D = 1.20•LmD •(±0.11), i.e., not statistically different, but with the mean exhibiting a bias that is discussed below (Figure 2b, Table 1).Thus, L m in coral reef fish can be estimated from L m = L max /1.35 1/D , with the D value estimated from D = 3(1 − d) and d from Equation (2).As for its C.I., it can be estimated by using the standard error of 1.35, i.e., ±0.02.Note, however, that the uncertainty in L m values obtained by this relationship is likely to be an underestimate, because, while it accounts for the uncertainty in the 1.35 ratio, it does not account for the uncertainly in L max and D.

Discussion
As was the case with previous tests, this study generated results compatible with the two-part hypotheses of Pauly [11] that in coral fish (i) the same relative individual size induces a readiness to perceive environmental stimuli that trigger maturation and spawning and (ii) that this relative size is not significantly different from L m = L max /1.35 1/D .More precisely, the slope of the plot of L max D vs. L m D in Figure 2a (=1.35; 95% C.I. = 1.33-1.37)overlaps with confidence intervals reported in previous contributions dealing with other bony fish [11][12][13][14][15][16], implying that the slope estimates are not statistically different.
When phylogeny is considered (Figure 2b), the change in slope is similar to what was observed by Warren [31] for cartilaginous species, i.e., that the correlation was weak, with a wide confidence interval, which is apparently a common result when including phylogenetic signals into analyses such as ours [32,33].While some authors have suggested that statistical analyses without phylogenetic elements are "flawed" or "biased" [32], it has also been demonstrated that "poor statistical performances" will be the result when phylogenetic methods based on incorrect assumptions are applied to regression models [34].Our coral reef fish dataset is phylogenetically extremely diverse, which suggests that the consideration of phylogeny in our analysis may not only be superfluous, but also result in misleading results [32].Therefore, we are focusing our remaining discussion solely on the results derived from the data without considering phylogeny, as these are more likely to provide a reliable basis for our conclusion.
The estimated critical threshold of the L max D vs. L m D ratio (1.35) varies slightly between populations and species because it is a heuristic [35] used by individual fish to determine when to start perceiving the external stimuli that make them start their maturation process [23].As such, this heuristic can generate predictions (i.e., values of L m ) that are too low (thus leading to an egg production that is lower than would have been possible by allowing more growth before first maturity) or too high (thus exposing the individual to an elevated risk of being predated upon before having spawned at least once).This explains some of the differences between the lines and the dots in Figure 2a,b, the rest of these differences being mostly caused by imprecisions in the estimation of L m and L max .
What this study establishes, however, is that coral reef (bony) fish, for all the specificities associated with the singular ecosystems within which they evolved, initiate their maturation and reproduction under the same respiratory constraints as other teleosts.Notably, our results add to the evidence against the "Reproductive Drain Hypothesis", and in favor of the alternative hypothesis as presented in Pauly and Liang [4]; see also refs.[11][12][13][14][15][16].Our results, thus, also suggest that generalizations concerning other aspects of the biology of coral reef fish, e.g., their respiratory physiology, would also benefit from being compared with the respiratory physiology of well-studied temperate fish, including freshwater species, rather than being a priori assumed to be different from other fish.
Some studies have shown that reef-associated fish have evolved a relatively high hypoxia tolerance, probably due to the fact that coral reefs go through daily cycles of oxygen levels [36][37][38].However, the above considerations lead one to predict that the increased stress of ocean deoxygenation and increased temperatures [39] will not only lead to smaller maximum sizes in coral reef fish, but also to smaller sizes at first maturity, generally associated with fewer and smaller eggs [40] and, thus, with reduced fitness.

Conclusions
The Gill Oxygen Limitation Theory (GOLT) as proposed by Pauly [11] suggests that the triggering of maturation in fish occurs when the growth-induced reduction in gill surface area relative to body weight (and hence oxygen supply) reaches a critical level.This study confirms that this triggering effect also occurs in coral reef fish and that its level is the same as in other fish populations.Understanding the size and age of maturity of fish is an important aspect of effective fisheries management.The results of this study suggest that with increasing temperature and deoxygenation, coral reef fish will mature at smaller sizes and, as a result, will produce smaller eggs.These changes will influence the factors that must be considered in the management of coral reef fisheries.

Institutional Review Board Statement:
The research that we have done in our manuscript does not involve direct research on humans or animals.The data we used was assembled by compiling the results from various published literature sources.Therefore, the requirement for ethical committee approval does not apply to our manuscript.

Appendix A
Table 1.Assembled data on reef-associated species for the analysis of the relationship between length at first maturity (L m ) and maximum length (L max ), arranged alphabetically by family and by species names.Lengths are in fork lengths.L max values in brackets were estimated from L inf using L max = 0.95×L inf .W max estimated from L max using length-weight relationship coefficients from FishBase.(F = female; M = male; U = unsexed).

Figure 2 .
Figure 2. Plot of Lmax D vs. Lm D for (a) all 207 cases; (b) 120 species on the Fish Tree of Life with phylogenetic affinities considered.Shaded area indicates the 95% confidence interval of slope.Thus, Lm in coral reef fish can be estimated from Lm = Lmax/1.35 1/D , with the D value estimated from D = 3(1 − d) and d from Equation (2).As for its C.I., it can be estimated by using the standard error of 1.35, i.e., ±0.02.Note, however, that the uncertainty in Lm values obtained by this relationship is likely to be an underestimate, because, while it accounts for the uncertainty in the 1.35 ratio, it does not account for the uncertainly in Lmax and D.

Figure 2 .
Figure 2. Plot of L max D vs. L m D for (a) all 207 cases; (b) 120 species on the Fish Tree of Life with phylogenetic affinities considered.Shaded area indicates the 95% confidence interval of slope.

Table 1 .
Comparison of estimated coefficients and their 95% confidence interval for different subsets in the relationship between length at first maturity and maximum length.(1.33-1.37)Species on FishTree with phylogeny considered 120 1.20 (1.09-1.31)Species on FishTree without phylogeny considered 120 1.34 (1.31-1.37)

Table 1 .
Comparison of estimated coefficients and their 95% confidence interval for different subsets in the relationship between length at first maturity and maximum length.