A reconceptualization of the interactions between spawning and growth in bony fish

INTRODUCTION

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Fish spawning is a process that fisheries scientists and ichthyologists are familiar with, so much so that for several decades they have failed to re-examine whether their view of this process is compatible with all the specifics we also know about spawning.

Figure 1 illustrates the conventional conceptualization of fish spawning, in which it is perceived as a costly process wherein “energy” is transferred from somatic to gonad growth, thus abruptly impacting on somatic growth (which is strangely and erroneously viewed as a linear process). Thus, depending on the extent of the “energy” transfer, somatic growth is slowed down or even stopped. However, it is generally not appreciated that this conceptualization, of which multiple variants exist (see, e.g., Hubbs 1926Hubbs C.L. 1926. The structural consequence and modifications of the development rate in fishes, considered in reference to certain problems of evolution. Am. Nat. 60: 57-81. https://doi.org/10.1086/280071 , Charnov 2008Charnov E. 2008. Fish growth: Bertalanffy k is proportional to reproductive effort. Environ. Biol. Fishes. 83: 185-187. https://doi.org/10.1007/s10641-007-9315-5 , Quince et al. 2008Quince C., Abrams P.A., Shuter B.J., Lester N.P. 2008. Biphasic growth in fish I: Theoretical foundations. J. Theor. Biol. 254: 197-206. https://doi.org/10.1016/j.jtbi.2008.05.029 ), is only a hypothesis which, like all scientific statements about the world, is subject to being rejected if it is incompatible with well-established facts.

Fig. 1. - Representation of the “reproductive drain hypothesis”, i.e. the notion that reaching the size at first maturity relationship causes previously “linear” growth (line A) to decline due to “energy” previously used for somatic growth being transferred to the elaboration of gonads, with line B implying a small and line C a large transfer of “energy” (modified from in ).

The first and perhaps most important reason for the survival of this conceptualization-here called the “reproductive drain hypothesis” (RDH)-is that its outward plausibility rests on the representation of growth as proceeding in length, which it does not, as “energy” certainly does not have the dimension of length. Once somatic growth is-correctly-viewed in terms of mass or weight (Fig. 2), the RDH is refuted. As soon as (iteroparous) fish can reach a maximum weight exceeding a few grams, they tend to reach first maturity at sizes below that at which they experience their highest growth rate.

Fig. 2. - Illustrating the fact that, when growth in weight is considered, in fish reaching more than about 10 cm maximum length, the weight at first maturity (W_m) is reached at a size at which growth is accelerating, i.e. well below the weight at which maximum growth rate is attained (at Wi); A, largehead hairtail (Trichiurus japonicus), based on data in ); B, yellowbelly threadfin bream (Nemipterus bathybius), based on data in ; C, rock carp Procypris rabaudi), based on data in ; D, Atlantic cod (Gadus morhua), based on data in .

Thus, the transition from “energy” transferred from somatic growth to the elaboration of gonads is a case of the post hoc, ergo propter hoc fallacy that considers that an event (1) is the cause of an event (2) simply because event (1) occurred before event (2).

Earlier authors, notably Iles (1974)Iles T.D. 1974. The tactics and strategy of growth in fishes. In: Harden Jones E.R. (ed), Sea Fisheries Research. Elek Science, London, pp. 331-345., have also noted that the usual narrative does not make sense. Thus, he wrote, with regard to the age and size at first maturity of fish that “[d]espite the fact that at some time during this stage of the life history large quantities of protein, ultimately derived from the same food sources that sustain body growth, will be newly required for gonad development, there is no indication that the growth pattern is disrupted or disturbed. Indeed, under ‘normal’ conditions it appears that it is singularly unaffected by the new physiological and metabolic demands which the fish is called upon to meet. The fact that, for most species of fish, unlike those of mammals and birds, growth continues after the attainment of the adult stage is one of the most characteristic features of the growth of fishes”.

However, the “programme” that he then proposed as an alternative did not explain how fish manage to spawn at the “right” size, i.e. at the size that is a predictable fraction of the maximum size they can reach in a given environment. (Pauly 2019Pauly D. 2019. Gasping Fish and Panting Squids: Oxygen, Temperature and the Growth of Water-Breathing Animals - 2nd Edition. International Ecology Institute, Oldendorf/Luhe, Germany, 279 pp.).

In the following, we present a reconceptualization of spawning based on Pauly (2019Pauly D. 2019. Gasping Fish and Panting Squids: Oxygen, Temperature and the Growth of Water-Breathing Animals - 2nd Edition. International Ecology Institute, Oldendorf/Luhe, Germany, 279 pp., 2021aPauly D. 2021a. The Gill-Oxygen Limitation Theory (GOLT) and its critics. Sci. Adv. 7: 2. https://doi.org/10.1126/sciadv.abc6050 , 2019b)Pauly D. 2021b. Why do fish reach first maturity when they do? J. Fish Biol. https://doi.org/10.1111/jfb.14902 and evidence presented on Chen et al. (2022)Chen Z., Bigman J., Xian W., et al. 2022. The ratio of length at first maturity to maximum length in marine and freshwater fish. J. Fish Biol. https://doi.org/10.1111/jfb.14970 and other authors. However, before this can be presented, a brief review of fish growth and related matters is necessary.

MATERIALS AND METHODS

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Since Pütter (1920)Pütter A. 1920. Studien über physiologische Ähnlichkeit VI. Wachstumsähnlichkeiten. Pflüger‘s Archiv für die gesamte Physiologie des Menschen und der Tiere 180: 298-340. https://doi.org/10.1007/BF01755094 , the growth rate (dW/dt) in fish and other animals is often conceived as a differential equation

d W / d t = {H W}^{d} - k W

(1)

where W is the weight (i.e. mass), H is the rate of synthesis of body, 0<d<1 is the exponent of a relationship of the form $S = α \cdot W^{d}$ which limits protein synthesis, and k is the rate of protein denaturation, or, more precisely, the rate by which denaturation exceeds the refolding of spontaneously unfolding protein.

When $d = 2 / 3$ , corresponding to $S = α \cdot L^{2}$ and $W = a \cdot L^{3}$ , the integration of Equation 1 into a growth curve is the von Bertalanffy Growth Function (VBGF), which for growth in length has the form

L_{t} = L_{\infty} \cdot (1 - e^{- K \cdot (t - t_{0})})

(2)

where L_t is the mean length at age t of the animals in question, L_∞ is their asymptotic size, i.e. the mean size attained after an infinitely long time, K is a growth coefficient (here in year^-1; with $k = 3 K$ ) and t₀ is a parameter adjusting for the fact that the VBGF usually fails to describe the growth of the earliest (larval) stages of fish (see also Table 1).

For growth in weight, this becomes

W_{t} = W_{\infty} \cdot {(1 - e^{- K (t - t_{0})})}^{3}

(3)

Table 1. Definitions of the parameters (and their units), symbols and acronyms used in this contribution.

Item (unit)	Definition
∝	Proportional to…
α	Multiplicative term in relationship linking gill surface and weight, i.e. $S = α \cdot W^{d}$
a	Multiplicative term of a length-weight relationship, i.e. $W = a \cdot L^{b}$
A	Threshold value of ${L_{m a x}}^{D} / {L_{m}}^{D} ~ 1.35$ , corresponding to $Q_{m} / Q_{m a i n t} ~ 1.35$
b	Exponent of a length-weight relationship, i.e. $W = a \cdot L^{b}$
d	Exponent in a relationship linking respiratory surface and weight, i.e. $S = α \cdot W^{d}$
D	$D = b (1 - d)$ , used to simplify some equations; note also $D ’ = 3 (1 - d)$
dW/dt	Growth rate
H	Coefficient of anabolism, i.e. of protein synthesis
k	Coefficient of catabolism; here: of protein denaturation. Note: $k = 3 K$
K (year^-1)	In the VBGF, the rate at which asymptotic size is approached
L (cm)	Any measure of length, with L_t the length at age t
L_∞ (cm)	Asymptotic length in the VBGF, as reached after an infinitely long time
L_m (cm)	Mean length at first maturity in a given population
L_m/L_∞	Reproductive load, usually close to L_m/L_max
L_m/L_max	Reproductive load, usually close to L_m/L_∞
L_max (cm)	Maximum length in a given population; generally close to L_∞
LWR	Length-weight relationship, of the form $W = a \cdot L^{b}$
Q_m	Weight-specific oxygen consumption at first maturity
Q_maint	Weight-specific oxygen consumption at maximum or asymptotic weight
RDH	Reproductive drain hypothesis
RL	Reproductive load, i.e. L_m/L_max or L_m/ L_∞
S (cm²)	A surface; here respiratory surface, i.e. gill surface area, as in $S = α \cdot W d$
t (year)	Absolute age; relative $a g e = t - t_{0}$
t₀ (year)	The usually negative “age” at L = 0 predicted by the VBGF
W (g)	Weight (or mass); W_t is weight at age; here fresh, or wet weight
W_∞ (g)	Asymptotic weight in the VBGF, as reached after an infinitely long time
W_i (g)	Inflexion point of a growth curve in weight, i.e. weight at which dw/dt is highest
W_m	Mean weight at first maturity; weight corresponding to L_m

where W_∞ is the weight corresponding to L_∞, all other parameters are defined as above and the exponent (b=3) at the right is justified by the fact that it is the most common exponent of the length-weight relationship (LWR) in fish (Froese 2006Froese R. 2006. Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations. J. Appl. Ichthyol. 22: 241-253. https://doi.org/10.1111/j.1439-0426.2006.00805.x , Hay et al. 2020Hay A., Xian W., BaillyN., Liang C. and Pauly D. 2020. The why and how of determining length-weight relationships of fish from preserved museum specimens. J. Appl. Ichthyol. 36: 373-379. https://doi.org/10.1111/jai.14014 , see also FishBase: www.fishbase.org).

Equation (2) $L_{t} = L_{\infty} \cdot (1 - e^{- K \cdot (t - t_{0})})$ has no inflexion point (dL/dt declines linearly with length), but Equation (3) $W_{t} = W_{\infty} \cdot {(1 - e^{- K (t - t_{0})})}^{3}$ has an inflexion point (W_i, where dW/dt is at a maximum) at $W_{i} = 0.296 \cdot W_{\infty}$ _.

Pauly (2019Pauly D. 2019. Gasping Fish and Panting Squids: Oxygen, Temperature and the Growth of Water-Breathing Animals - 2nd Edition. International Ecology Institute, Oldendorf/Luhe, Germany, 279 pp., 2021a)Pauly D. 2021a. The Gill-Oxygen Limitation Theory (GOLT) and its critics. Sci. Adv. 7: 2. https://doi.org/10.1126/sciadv.abc6050 interpreted Pütter’s equation in terms of the oxygen required for synthesis of native protein (the first term on the right side of Equation 1) and to replace denatured proteins (the second term on the right side of Equation 1). In this interpretation, d refers to the respiratory surface area of the gills or similar organs, i.e. 2-D structures whose growth cannot keep up with that of a 3-D body requiring oxygen. Hence, d<1 and generally ranges between 0.55 and 0.95 in fish and other metazoans that breathe water (De Jager and Dekker 1974De Jager S., Dekkers W.J. 1974. Relations Between Gill Structure and Activity in Fish. Neth. J. Zool. 25: 276-308. https://doi.org/10.1163/002829675X00290 , Pauly 1981Pauly D. 1981. The relationships between gill surface area and growth performance in fish: a generalization of von Bertalanffy’s theory of growth. Berichte der Deutschen wissenschaftlichen Kommission für Meeresforschung 28: 251-282.).

When $d \neq ⅔$ , the VBGF is “generalized” and becomes

L_{t} = L_{\infty} ∙ {(1 - e^{- K ∙ D (t - t_{0})})}^{1 / D}

(4)

for length, and

W_{t} = W_{\infty} \cdot {(1 - e^{- K \cdot D (t - t_{0})})}^{b / D}

(5)

for weight, where $D = b (1 - d)$ and where b is the exponent of an LWR of the form $W = a \cdot L_{b}$ , with b generally 3, or near 3 (see above).

Equation 4 has an inflection point when $D \neq 1$ at age $t_{i} = t_{0} - (l n (D) / K \cdot D)$ and length $L_{i} = L_{\infty} ∙ {(1 - e^{- (l n (D))})}^{1 / D}$ , while Equation (5) has an inflection point at age $t_{i} = t_{0} - (l n (D / b) / K \cdot D)$ and weight $W_{i} = W_{\infty} \cdot {(1 - (D / b))}^{b / D}$ , which implies

W_{i} / W_{\infty} = {(1 - (D / b))}^{b / D}

(6)

In practice, the difference between the standard VBGF (Equations 2 $L_{t} = L_{\infty} \cdot (1 - e^{- K \cdot (t - t_{0})})$ and 3 $W_{t} = W_{\infty} \cdot {(1 - e^{- K (t - t_{0})})}^{3}$ ) and the generalized VBGF can be neglected when fitting a set of age-at-length, tagging-recapture, or length-frequency data with a growth curve, especially in fishes where the growth of gill surface area does not differ much from the ⅔ value assumed in the standard VBGF (i.e. up to d≈0.85). This is the case for small fishes, e.g. coral fishes and small pelagic fishes, such as herrings, sardines and anchovies, where d≈0.75, and medium-sized species, e.g. carp or cod, where d≈0.80 (De Jager and Dekker 1974De Jager S., Dekkers W.J. 1974. Relations Between Gill Structure and Activity in Fish. Neth. J. Zool. 25: 276-308. https://doi.org/10.1163/002829675X00290 ; see also Fig. 3). Only with higher value does the fit of the standard VBGF became problematic, e.g. in in the case of Atlantic bluefin tuna (Thunnus thynnus), where d=0.90 (Muir and Hughes 1969Muir B.S., Hughes G.M. 1969. Gill Dimensions for Three Species of Tunny. J. Exp. Biol. 51: 271-285. https://doi.org/10.1242/jeb.51.2.271b ), notably because the estimates of asymptotic length (L_∞) that are generated by fitting the equation to reliable age-at-length data tend to be much larger than the maximum length (L_max) in a given population, which is not the case when the special VBGF is used (Pauly 2021aPauly D. 2021a. The Gill-Oxygen Limitation Theory (GOLT) and its critics. Sci. Adv. 7: 2. https://doi.org/10.1126/sciadv.abc6050 ), As the overwhelming majority of applications of the VBGF are to species in which d is relatively close to ⅔ (see FishBase: www.fishbase.org), the fact that the standard VBGF differs slightly from a physiologically correct equation is usually ignored. This is also what was done here.

Fig. 3. - Showing that in fish, the parameter d and D are related to the maximum weight reached by various taxa (modified from in ); the straight line is based on the relations

d = 0.674 + 0.0357 (l o g (W_{m a x}))

, with live weight in g.

It is well-established that the mean length at first maturity (L_m) of the individual in a given population of iteroparous fish is a predicable ratio of the asymptotic length (L_∞) or maximum length (L_max) and generally ranges from 0.4 to 0.6 in fish that reach larger sizes and from 0.6 to 0.8 in fish that remain small (Beverton and Holt 1959Beverton R.J.H., Holt S.J. 1959. A Review of the Lifespans and Mortality Rates of Fish in Nature, and Their Relation to Growth and Other Physiological Characteristics. In: Wolstenhome G.E.W., Maeve O’Oconner B.A. (eds), Ciba Foundation Symposium - The Lifespan of Animals (Colloquia on Ageing). John Wiley & Sons Ltd, pp. 142-180. https://doi.org/10.1002/9780470715253.ch10 , Pauly 2021aPauly D. 2021b. Why do fish reach first maturity when they do? J. Fish Biol. https://doi.org/10.1111/jfb.14902 ). Thus, this ratio does not deserve the name “Beverton and Holt invariant” that Charnov (2008)Charnov E. 2008. Fish growth: Bertalanffy k is proportional to reproductive effort. Environ. Biol. Fishes. 83: 185-187. https://doi.org/10.1007/s10641-007-9315-5 gave it. Rather, we use here the term “reproductive load” for the L_m/L_∞ (or the similar L_m/L_max) ratio as used by Cushing (1981)Cushing D.H. 1981. Fisheries Biology: as Study in Population Dynamics, 2nd edition. University of Wisconsin Press, Madison, 295 pp., which resonates with the RDH mentioned above.

That reproductive loads are not invariant, but vary systematically among fishes of widely different sizes was demonstrated by Froese and Binohlan (2000)Froese R., Binohlan C. 2000. Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes, with a simple method to evaluate length frequency data. J. Fish Biol. 56: 758-773. https://doi.org/10.1111/j.1095-8649.2000.tb00870.x who, based on data from 265 fish species from 88 Families and 27 Orders in FishBase (www.fishbase.org), derived the relationships:

\log (L_{m}) = 0.898 \cdot \log (L_{\infty}) - 0.0782

(7)

where L_m and L_∞ are in cm.

This model expresses that fish with L_∞≈10 cm will have L_m values of 6 to 7 cm, while fish of L_∞≈100 and 1000 cm will have L_m values near 50 and 400 cm, respectively.

In the following, we present corroborations of the gill-oxygen limitation theory (GOLT; Pauly 2019Pauly D. 2019. Gasping Fish and Panting Squids: Oxygen, Temperature and the Growth of Water-Breathing Animals - 2nd Edition. International Ecology Institute, Oldendorf/Luhe, Germany, 279 pp., 2021aPauly D. 2021a. The Gill-Oxygen Limitation Theory (GOLT) and its critics. Sci. Adv. 7: 2. https://doi.org/10.1126/sciadv.abc6050 ) that result from following up on these considerations.

RESULTS

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Because their gill surface area, with d<1, which supplies oxygen to their growing bodies, cannot keep up with their weight, and hence with their oxygen demand, relative oxygen supply declines with body weight. This decline of relative oxygen supply has its limit when ${H W}^{d} - k W = 0$ , i.e. when the oxygen supply meets only the requirements for maintenance (Q_maint), with nothing left for further somatic growth. Pauly (2019)Pauly D. 2019. Gasping Fish and Panting Squids: Oxygen, Temperature and the Growth of Water-Breathing Animals - 2nd Edition. International Ecology Institute, Oldendorf/Luhe, Germany, 279 pp. and Pauly and Liang (2022)Pauly D., Liang C. 2022. Temperature and the early maturation of fish: a simple sine-wave model for predicting spring spawning. Environ. Biol. Fish. https://doi.org/10.1007/s10641-022-01212-0 elaborate on the seasonal trade-off allowing the elaboration and release of reproductive products under these conditions.

It is evident that gonads, which require oxygen for their synthesis, will have to be elaborated when fish are smaller than L_max and hence their relative oxygen supply higher, i.e. $Q_{m} > Q_{m a i n t}$ , where Q_m is the relative oxygen supply at first maturity. Also, it can be shown that, given LWR of the form $W = a \cdot L^{b}$ and gill surface area-body weight relationship of the form $S = α \cdot W^{d}$ , the ratio ${L_{m a x}}^{D} / {L_{m}}^{D}$ is equivalent to the ratio $Q_{m} / Q_{m a i n t}$ (Pauly 1984Pauly D. 1984. A mechanism for the juvenile-to-adult transition in fishes. J. Cons. Int. Explor. Mer 41: 280-284. https://doi.org/10.1093/icesjms/41.3.280 ).

Numerous studies covering hundreds of species suggest that in growing iteroparous bony fishes maturation and spawning is initiated when a threshold ratio ${L_{m a x}}^{D} / {L_{m}}^{D} ~ 1.35$ is reached, as was first demonstrated for 56 populations of marine fish in 34 species by Pauly (1984)Pauly D. 1984. A mechanism for the juvenile-to-adult transition in fishes. J. Cons. Int. Explor. Mer 41: 280-284. https://doi.org/10.1093/icesjms/41.3.280 and confirmed for 51 populations in 3 freshwater salmonid species by Meyer and Schill (2021)Meyer K.A., Schill D.J. 2021. The Gill-Oxygen Limitation Theory and size at maturity/maximum size relationships for salmonid populations occupying flowing waters. J. Fish Biol. 98: 44-49. https://doi.org/10.1111/jfb.14555 , for 41 populations in 7 species of cichlids by Amarasinghe and Pauly (2021)Amarasinghe U.S., Pauly D. 2021. The relationship between size at maturity and maximum size in cichlid populations corroborates the Gill- Oxygen Limitation Theory (GOLT). Asian Fish. Sci. 34: 14-22. https://doi.org/10.33997/j.afs.2021.34.1.002 and for 241 populations in 132 freshwater and marine species by Chen et al. (2022)Chen Z., Bigman J., Xian W., et al. 2022. The ratio of length at first maturity to maximum length in marine and freshwater fish. J. Fish Biol. https://doi.org/10.1111/jfb.14970 . This established that the threshold ratio ${L_{m a x}}^{D} / {L_{m}}^{D} ~ 1.35$ acts as a heuristic (sensu Budaev et al. 2019Budaev S., Jørgensen C., Mangel M., et al. 2019. Decision-making from the animal perspective: bridging ecology and subjective cognition. Front. Ecol. Evol. 7: 164. https://doi.org/10.3389/fevo.2019.00164 ) which individual fish can rely on (Pauly 2021bPauly D. 2021b. Why do fish reach first maturity when they do? J. Fish Biol. https://doi.org/10.1111/jfb.14902 ) and which is compatible with life-history theory (Morbey and Pauly 2022Morbey Y.E. and D. Pauly. 2022. Juvenile-to-adult transition invariances in fishes: perspectives on proximate and ultimate causation. J. Fish Biol. 1-11. https://doi.org/10.1111/jfb.15146 ). We shall use the label $A = {L_{m a x}}^{D} / {L_{m}}^{D} ~ 1.35$ because it signifies a beginning (in German Anfang-the letters of the English alphabet are exhausted).

Given its definition and LWRs, $A = {({W_{m}}^{1 / b} / {W_{\infty}}^{1 / b})}^{D}$ and its inverse A^-1 is:

A^{- 1} = {({W_{m}}^{1 / b} / {W_{\infty}}^{1 / b})}^{D}

(8)

Thus, $A^{- 1} = {(W_{m} / W_{\infty})}^{D / b}$ > or

W_{m} = W_{\infty} {(1 / A)}^{b / D}

(9)

By combining equation (6) and (9), we obtain

W_{i} / W_{m} = {(1 - (D / b))}^{b / D} / A^{- b / D}

(10)

When $W_{i} > W_{m}$ , we also have:

{(1 - (D / b))}^{b / D} > A^{- b / D}

(11)

which implies $(1 - (D / b)) > A^{- 1}$ . Now, given the definition of $D = b \cdot (1 - d)$ , we have

d > A^{- 1} i m p l i e s W_{i} > W_{m}

(12a)

d \approx A^{- 1} i m p l i e s W_{i} \approx W_{m}

(12b)

d < A^{- 1} i m p l i e s W_{i} < W_{m}

(12c)

Thus, while for d<1/1.35 (i.e. 0.74, generally occurring in small, short-lived and often semelparous fishes; see Fig. 3) spawning occurs after their growth rate (dW/dt) has started to decline, this is not the case in larger iteroparous, longer-lived fish in which d>0.75. This explains why, e.g., the maturity of cod and similarly large species occurs well before these fish have spawned (Fig. 2), thus refuting the RDH.

As, an alternative, we propose a new framework for understanding the concept of a “spawning season”. For simplicity’s sake, we shall here assume one spawning season per year, occurring in the spring (Pauly and Liang 2022Pauly D., Liang C. 2022. Temperature and the early maturation of fish: a simple sine-wave model for predicting spring spawning. Environ. Biol. Fish. https://doi.org/10.1007/s10641-022-01212-0 ), as the extension of the conceptualization presented would here would require further elaboration to account for autumn spawning in temperate fish (Warlen and Burke 1990Warlen S.M., Burke J.S. 1990. Immigration of larvae of fall/winter spawning marine fishes into a North Carolina estuary. Estuaries 13: 453-461. https://doi.org/10.2307/1351789 ) or monsoonal spawning in fishes of the Indo-Pacific (Longhurst and Pauly 1987Longhurst A., Pauly D. 1987. Ecology of Tropical Oceans. Academic Press, San Diego, 407 pp. https://doi.org/10.1016/B978-0-12-455562-4.50010-0 ).

This new framework should explain the processes taking place such that various aspects of fish spawning, which had remained unexplained or been treated as anomalies, can be straightforwardly accounted for, i.e. without ad hoc hypotheses. This requires a second heuristic, the “cusp catastrophe”.

The cusp catastrophe, or “cusp”, is one of the seven topological entities which, as shown by Thom (1975)Thom R. 1975. Structural stability and morphogenesis: an outline of a general theory of models. Translated by D.H. Fowler. Benjamin-Cummings, Reading, MA, 348 pp., are sufficient to describe qualitatively the transitions among a maximum of four “control factors”, and to distinguish areas where the transitions would be smooth from areas where they would be sudden (thus the term “catastrophe”, the cause of many misunderstanding). With its two control factors, the cusp can easily be used to represent sudden transitions between, e.g., two biologically relevant variables (Woodcock and Davis 1980Woodcock A., Davis M. 1980. Catastrophe theory: a new way of understanding how things change. Penguin Books, Harmondworth, 152 pp.). Our use of the cusp is illustrated by the example of a growth curve in Figure 4, whose insert represents a cusp and the two control factors that adapt it to maturation and spawning events. Thus, our cusps have body size and time (here one year, given one spring spawning season per year) as control factors.

Fig. 4. – A representation of fish growth as a succession of cusps, with the young fish being too small to enter the region (shaded grey) where spawning occurs. This region is approached in pre-adults which may undergo an (abortive) maturation, but fail to spawn. In the year following, however, their size will be higher that than that associated with

Q_{m} / Q_{m a i n t} ~ 1.35

, and maturation and spawning can proceed. In the following years, size increases are associated with a spawning season that starts earlier and ends later, until maximum size is approached, when spawning often occurs repeatedly, and the body weight is reset at a lower value, which allows growth to be re-initiated.

Young fish (age 1 and 2 in Fig. 4) are too small for their A-ratio to have fallen to 1.35, so they entirely avoid the region of the cusp where maturation and spawning occurs. At 3 years, the largest fish of a cohort will mature and spawn, the smallest will not, and the fish of intermediate size may undergo an abortive maturation, i.e. elaborate production of gonads which, however, are resorbed and not shed (Iles 1974Iles T.D. 1974. The tactics and strategy of growth in fishes. In: Harden Jones E.R. (ed), Sea Fisheries Research. Elek Science, London, pp. 331-345.; review in Rideout et al. 2005Rideout R.M., Rose G.A., Burton M. 2005. Skipped spawning in female iteroparous fish. Fish Fish. 6: 50-62. https://doi.org/10.1111/j.1467-2679.2005.00174.x ).

This “skipped spawning”, performed “more often by young and small fish” and often when food is scarce (Jørgensen et al. 2006Jørgensen C., Ernande B., Fiksen Ø., Dieckman U. 2006. The logic of skipped spawning in fish. Can. J. Fish. Aquat. Sci. 63: 200-211. https://doi.org/10.1139/f05-210 ), is therefore neatly explained without requiring elaborate models of trade-offs between reproductive output, growth and survival, which individual fish could not use as heuristic to “decide” whether to spawn or not.

Subsequent growth in year 4 and beyond pushes the fish deeper onto the shaded areas of the cusps in Figure 4, implying that the maturation of larger (older) fish should start earlier than that of smaller fish, and end later in the season, while smaller (younger) fish mature (and spawn) only during the peak of the season. This is confirmed by numerous authors, such as Rijnsdorp (1989)Rijnsdorp A.D. 1989. Maturation of male and female North Sea plaice (Pleuronectes platessa L.). ICES J. Mar. Sci. 46: 35-51. https://doi.org/10.1093/icesjms/46.1.35 for plaice Pleuronectes platessa in the North Sea, and Trippel et al. (1997)Trippel E.A., Kjesbu O.S., Solemdial P. 1997. Effects of adult age and size structure on reproductive output in marine fishes. In: Chambers R.C., Trippel E.A. (eds), Early life history in fish populations. Chapman & Hall-Kluwer, Dordrecht, pp. 31-61. https://doi.org/10.1007/978-94-009-1439-1_2 , who summarized their review by stating that “[t]he importance of female size to recruitment success is reinforced by the observation that large females commonly start spawning earlier in the season […], continue for longer and produce larger eggs with higher viability than smaller females.”

The cusp often implies that once a phase transition has occurred, the system displays “hysteresis”, wherein the behaviour in question (in this case spawning) loops repeatedly at the highest age in Figure 4, above the ∞ symbol. As it happens, this is precisely the behaviour of large, old fish, which may spawn repeatedly during a spawning season, while small adults usually spawn only once, or even skip spawning. The interpretation of this behaviour is as follows: once a large fish has spawned, i.e., lost some of the tissues that it has to supply with oxygen, it has a higher gill area/body weight than before spawning, and hence it can in principle return to its usual activities, including feeding. This leads to increased body weight, and thus renewed lowering of the gill area/body weight ratio, which can (at least in large individuals) cause rapid re-maturation and repeated spawning (Trippel et al. 1997Trippel E.A., Kjesbu O.S., Solemdial P. 1997. Effects of adult age and size structure on reproductive output in marine fishes. In: Chambers R.C., Trippel E.A. (eds), Early life history in fish populations. Chapman & Hall-Kluwer, Dordrecht, pp. 31-61. https://doi.org/10.1007/978-94-009-1439-1_2 ). This cycle can repeat itself within a spawning season until the temperatures drops and the respiratory stress declines, at which point the reproductive season ends.

DISCUSSION

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The case made above was that a heuristic determines the overall readiness of fish to mature and spawn as a function of their metabolic rate (Q) relative to their maintenance metabolism (Q_maint). Specifically, in longer-lived iteroparous fish this heuristic readies them to perceive seasonal (i.e. within-year) environmental maturation and spawning stimuli only when the threshold A is reached (see Table 1 and the above equation for the definition and properties of A) and not earlier (Pauly 2021bPauly D. 2021b. Why do fish reach first maturity when they do? J. Fish Biol. https://doi.org/10.1111/jfb.14902 ).

Another heuristic, the cusp, then provides a graphic metaphor for spawning. Indeed, the cusp links three phenomena which to date had not been tied to a common explanatory framework (skipped spawning, size-dependent reproductive seasons and spawning hysteresis). Figure 4 thus represents an integrated view of the life of a long-lived fish as a succession of cusps, each “entered” at another size (corresponding to successive ages), thus implying a different set of responses by the individual fish.

Obviously, maturation and spawning are more complicated than is presented in this account. Notably, these processes involve the release of numerous hormones in response to environmental stimuli (Pankhurst 2016Pankhurst N.W. 2016. Reproduction and development. In: Schreck C.B., Tort L., Farrell A.P., Brauner C.J. (eds), Fish Physiology Vol. 35. Elsevier, Amsterdam, pp. 295-331. https://doi.org/10.1016/B978-0-12-802728-8.00008-4 ). However, as shown in Pauly (2021b)Pauly D. 2021b. Why do fish reach first maturity when they do? J. Fish Biol. https://doi.org/10.1111/jfb.14902 , based on multiple long-lived fish species that fail to respond to such seasonal stimuli during many years (even decades) of pre-adulthood during which they could perceive these stimuli, the “hormonal cascade” leading to maturation and spawning is not self-starting. What is required for such maturation and spawning is an internal state that is related to the size of the fish (Fig. 4), i.e. to their relative oxygen supply.

Finally, the reconceptualization presented here implies that, rather than being, in analogy to humans, the life-threatening and often debilitating event that giving birth is, spawning in fish is a seasonally liberating event, which frees females from a quivering mass of eggs that must be supplied with scarce oxygen and thus enables them to grow again.

A reconceptualization of the interactions between spawning and growth in bony fish

Reconceptualización de la interacción entre desove y crecimiento en peces óseos

INTRODUCTION

MATERIALS AND METHODS

RESULTS

DISCUSSION

ACKNOWLEDGEMENTS

REFERENCES