J Garc

Ía-Meli Án

A Quaas

B Sirakov
email: bsirakov@mat.puc-rio.br

ELLIPTIC EQUATIONS WITH ABSORPTION IN A HALF-SPACE

We give a necessary and sufficient condition, in the spirit of the classical works by Keller and Osserman, for the elliptic equation ∆u = f (u) to have a solution in a half-space of R N . The function f is supposed to be nondecreasing and nonnegative, and we are interested in solutions whose range is where f > 0. The possibility of obtaining such a necessary and sufficient condition has been an open question for a long time.

Introduction and results

The aim of this work is to analyze the existence and nonexistence of solutions of the problem (P) ∆u = f (u) in R N + , where the function f is continuous, nonnegative and nondecreasing on R, and R N + denotes the half-space R N + = {x ∈ R N : x N > 0}. We also study the existence of subsolutions of this problem, that is, solutions of the inequality (P -) ∆u ≥ f (u) in R N + . The classical papers by Osserman [START_REF] Osserman | On the inequality ∆u ≥ f (u)[END_REF] and Keller [START_REF] Keller | On solutions of ∆u = f (u)[END_REF] have generated a tremendous amount of work on this type of equations, most of which has been devoted to the study of entire solutions or of explosive solutions in a bounded domain. As already explained in [START_REF] Osserman | On the inequality ∆u ≥ f (u)[END_REF] (see p. 1644 in that paper) it is meaningful to search for solutions whose range is in the set where f is strictly positive, since without this assumption the solution set can indeed be very large and variable. Thus, in the following we will consider such solutions only. Note that since f is nondecreasing and nonnegative, we have {t : f (t) > 0} = (t 0 , ∞) for some t 0 ≥ -∞. Up to a simple transformation we can assume that t 0 = 0 or t 0 = -∞, in other words, either f (t) > 0 for t > 0 and u > 0, or f > 0 on R and there is no sign restriction on u.

In particular, it is known from [START_REF] Osserman | On the inequality ∆u ≥ f (u)[END_REF] that the equation ∆u = f (u) does not have solutions in the whole space R N if and only if

(KO) ∞ 1 ds F (s) < ∞, where F (s) = s 0 f (t)
dt is a primitive of f (this condition is nowadays usually referred to as the Keller-Osserman condition). On the other hand, (explosive) solutions in a bounded domain exist if and only if (KO) holds. It is outside the scope of this short paper to attempt a reasonably full bibliography for the many developments that followed [START_REF] Osserman | On the inequality ∆u ≥ f (u)[END_REF] and [START_REF] Keller | On solutions of ∆u = f (u)[END_REF], we refer for instance to the surveys [START_REF] Farina | Liouville-type theorems for elliptic problems[END_REF] and [START_REF] Rǎdulescu | Singular phenomena in nonlinear elliptic problems: from boundary blow-up solutions to equations with singular nonlinearities[END_REF], where a large set of references can be found. However, to the best of our knowledge and maybe somewhat surprisingly, a study of the problem is not available for proper unbounded subdomains of R N such as a half-space (except for a comment on nonexistence of radial solutions in Remark 1.6 of [START_REF] Marcus | Existence and uniqueness results for large solutions of general nonlinear elliptic equations[END_REF]). Elliptic equations on a half-space are both intrinsically important and appear in the study of other problems, such as the study of existence of a priori bounds for solutions through the Gidas-Spruck blow-up method. Half-spaces and cones also naturally appear in the study of boundary behaviour of solutions of elliptic equations in Lipschitz domains.

We observe that the solvability of (P) has been extensively studied in the particular case when the function is supposed to satisfy a boundary condition at ∂R N + = {x ∈ R N : x N = 0}, such as u = 0 on this set. We refer for instance to [START_REF] Armstrong | Nonexistence of positive supersolutions of elliptic equations via the maximum principle[END_REF], [START_REF] Bandle | On positive solutions of Emden equations in cone-like domains[END_REF], [START_REF] Berestycki | Superlinear indefinite elliptic problems and nonlinear Liouville theorems[END_REF], [START_REF] Berestycki | Further qualitative properties for elliptic equations in unbounded domains[END_REF], [START_REF] Chen | Monotonicity and nonexistence results to cooperative systems in the half space[END_REF], [START_REF] Kondratiev | Positive solutions to superlinear second-order divergence type elliptic equations in cone-like domains[END_REF], and the references in these works.

In this paper we provide a necessary and sufficient condition for (P) to have a solution. This is the content of the following theorem. Throughout the paper, an existence statement will mean that (P) has a strong (or even classical, if f is supposed to be Hölder continuous) solution, whereas a non-existence statement will mean (P) does not even have solutions in any weak (such as weak-Sobolev or viscosity) sense which leaves valid the comparison principle.

Note that since the existence of a solution in R N implies existence in any subdomain of R N , we only need to study the problem under the hypothesis (KO).

           1 0 ds F (s) = ∞ if t 0 = 0, or -1 -∞ f (s) ds < ∞ if t 0 = -∞
If this hypothesis is not satisfied, even subsolutions do not exist.

We stress that this theorem completely characterizes the existence of solutions and subsolutions of (P), and thus represents a counterpart for a half-space of the results of Keller and Osserman for bounded domains or the whole space.

At this point a discussion on the possibility of extending the above theorem to more general unbounded domains is in order. The situation turns out to be very different depending on whether t 0 = 0 or t 0 = -∞.

First, if t 0 = 0 then the first condition in (HS) actually guarantees the existence of a positive solution in any subdomain of R N whose closure is not the whole space. Note that this condition is what ensures the validity of the strong maximum principle for nonnegative solutions of ∆u = f (u), by the well-known result of Vázquez ( [START_REF] Vázquez | A strong maximum principle for some quasilinear elliptic equations[END_REF], see also [START_REF] Pucci | The maximum principle[END_REF]). On the other hand, if (HS) fails when t 0 = 0 then positive solutions do not exist in any sufficiently "fat" subdomain of R N . Thus, the result in Theorem 1 remains the same if t 0 = 0 and the half-space is replaced by any strictly proper subdomain of R N which contains balls of arbitrary radius -such as, for instance, a nontrivial cone in R N (see Theorem 2 below).

Second, if t 0 = -∞ then the condition in (HS) appears strongly related to the specific geometry of the half-space. If a different cone in R N is considered, then this condition no longer characterizes the solvability of ∆u = f (u). For instance, the function u = -x α 1 x α 2 is a solution of the inequality ∆u ≥ c|u| β in the quarter-space {x 1 > 0, x 2 > 0} for any β ∈ (-1, 0) (and so f (u) = |u| β does not satisfy (HS)), provided α = 1 1-β and c = 2α(1 -α). Hence if f : R → (0, ∞) is increasing and f (u) ≤ |u| β for u < 0 then a solution of ∆u = f (u) in the quarterspace existssince u is a subsolution, ū = 0 is a supersolution, and they are ordered. Currently we do not know how to obtain a necessary and sufficient condition for existence of solutions of (P) in a cone different from R N or R N + , in the case t 0 = -∞. We believe this is an interesting open problem.

It is to be stressed that, while the existence and nonexistence of (sub-)solutions of (P) in the whole space depends only on the behavior at infinity of f , the result above shows that the behavior at t 0 = inf{ t : f (t) > 0} of f turns out to be important when a proper unbounded subdomain is considered.

Proofs

In this section we will prove Theorem 1. The proofs depend on the comparison principle, together with the resolution of some auxiliary problems. We recall that the monotonicity of f implies the equation is proper, thus satisfies the weak comparison principle, in the sense that a subsolution and a supersolution which are ordered on the boundary of any bounded domain are also ordered throughout the domain. Also, Perron's method applies and yields the existence of a solution between any given ordered subsolution and a supersolution (see for instance [START_REF] Du | Order structure and topological methods in nonlinear partial differential equations[END_REF] for classical or weak-Sobolev solutions and [START_REF] Crandall | User's guide to viscosity solutions of second-order partial differential equations[END_REF] for viscosity solutions).

Before giving the proof we briefly recall the construction of an entire (radial) solution of ∆u = f (u) when the condition (KO) is not satisfied. Fix a real number v 0 such that f (v 0 ) > 0 and consider the following ordinary differential equation for a function v = v(r), (2.1)

   v + N -1 r v = f (v), r > 0 v(0) = v 0 , v (0) = 0. Since f is continuous, problem (2.1) has at least one C 2 solution v defined in a maximal interval of existence [0, R) for some R > 0. Since (r N -1 v ) = r N -1 f (v) ≥ 0 we have r N -1 v ≥ 0 so that v is increasing and therefore v ≤ f (v)
, by (2.1). We can multiply this inequality by v , write the result as ((v ) 2 ) ≤ (2F (v)) , and integrate to get

v(r) v 0 dt 2F (t) ≤ r
for every r ∈ (0, R), which implies, since (KO) does not hold, that R is infinite. Thus for any

x 0 ∈ R N the function u(x) = v(|x -x 0 |) is a positive solution of ∆u = f (u) in R N .
The minimum of u is attained at x 0 and its value is v 0 .

On the other hand, when (KO) is satisfied, the solution of (2.1) blows up at a finite R; indeed, since the equation in (2.1) can also be written as

(2.2) v (r) = r 0 s r N -1 f (v(s))ds,
from the monotonicity of f and v we have v (r) ≤ r N f (v(r)), so that

v ≥ 1 N f (v).
Multiplying by v as above we get

v(r) v 0 dt F (t) -F (v 0 ) ≥ 1 √ N r
for every r ∈ (0, R), which implies that R is finite, by (KO). Thus

u(x) = v(|x -x 0 |) solves ∆u = f (u) in B R (x 0 ) with v = +∞ on ∂B R (x 0 ) (throughout the paper, B r (x 0
) stands for the ball with radius r centered at x 0 ; we write B r when x 0 = 0).

Proof of Theorem 1, case t 0 = 0. Existence. Assume that (HS) holds, that is, the Vázquez condition for the strong maximum principle 0 F -1/2 = ∞ is verified. Take any x 0 ∈ R N and r > 0 such that B r (x 0 ) ⊂ {x N < 0}. Since f (0) = 0 and f (δ) > 0 for some small δ > 0, the functions u = 0 and u = δ are respectively a subsolution and a supersolution for the problem

(2.3)    ∆u = f (u) in B R (x 0 ) \ B r (x 0 ) u = δ on ∂B r (x 0 ) u = 0 on ∂B R (x 0 ).
Hence there exists a solution u R of this problem such that 0 ≤ u R ≤ δ. By standard elliptic estimates (see for instance [START_REF] Gilbarg | Elliptic partial differential equations of second order[END_REF], Theorem 9.13) the sequence u R W 2,p (K) is bounded independently of R in any fixed compact set K of R N \ B r (x 0 ), for any p < ∞. Hence we can extract a subsequence which converges strongly in C 1,α (K) and weakly in W 2,p (K) to a function u. Thus, by a diagonal argument, taking larger and larger compacts K, we get a sequence R n → ∞ such that u Rn → u in W 2,p loc (R N \ B r (x 0 )). Passing to the limit we see that u is a nonnegative solution to the equation ∆u = f (u) in R N \ B r (x 0 ). This solution does not vanish identically by the boundary condition u = δ on ∂B r (x 0 ). Since the strong maximum principle holds (see [START_REF] Vázquez | A strong maximum principle for some quasilinear elliptic equations[END_REF]) we obtain that u is strictly positive in R N \ B r (x 0 ) ⊃ R N + . Nonexistence. As we recalled above, the Keller-Osserman condition (KO) implies that for each v 0 = ε > 0 there is a finite number R ε such that the problem ∆w = f (w) has a solution in each ball with radius R ε , which blows up at the boundary of the ball, and has value ε at the center of the ball.

Assume problem (P) has a positive solution u. Take a (small) number δ > 0 and fix any ball B = B Rε+δ (x 0 ) ⊂ R N + . We claim that u < 2ε in B δ (x 0 ). In fact, if we had u(x) ≥ 2ε for some x ∈ B δ (x 0 ), we could define w(x) = v(|x -x|), where v is the solution of (2.1) with v(0) = ε, and use the comparison principle in the ball B Rε (x) ⊂ R n + to get u ≤ w in this ball. However, this is a contradiction since u(x) ≥ 2ε while w(x) = v(0) = ε.

Finally, we claim that the failure of (HS) implies that there exists a supersolution z of (P) in B δ (x 0 ) with z = 2ε on ∂B δ (x 0 ) and z = 0 on B δ/2 (x 0 ) (a dead core). By using the comparison principle again, this time in B δ (x 0 ), we find that u ≤ 2ε = z on ∂B δ (x 0 ) implies u ≤ z = 0 in B δ/2 (x 0 ), contradicting the fact that u is positive.

Hence to conclude the proof of the theorem only this last claim remains to be proved. We will find a radial super-solution z such that z(x) = β(|x -x 0 |), and β is a real function which satisfies the ODE (2.4)

β + N -1 r β ≤ f (β) in (0, δ),
and is such that β = 0 on (0, δ/2) and β(δ) = 2ε. For this purpose it suffices to find a solution in (δ/2, δ) such that β(δ/2) = 0, β (δ/2) = 0 and β(δ) = 2ε, and then extend this solution as zero in (0, δ/2).

To find β we assume N ≥ 3 and perform the change of variables s = 1 N -2 r 2-N , β(s) = β(r) (a similar argument can be made in the case N = 2 with the change of variables s = log r; we will skip the details) and obtain the one-dimensional problem

(2.5) β ≤ cs -γ f ( β) in (s 0 , s 1 ) β(s 0 ) = ε, β(s 1 ) = β (s 1 ) = 0, where γ = 2(N -1) N -2 , c = (N -2) -γ , s 0 = δ 2-N /(N -2) and s 1 = 2 N -2 s 0 . Observe that γ > 2.
Since the integral 0 F -1/2 is convergent we can find adequately small ε > 0 and δ > 0 such that

ε 0 ds 2F (s) = cs -γ 1 (s 1 -s 0 ) = cδ γ .
where c, γ are positive constants which depend only on the dimension N . Thus we can define implicitly the function β through the equality

ε β(t) ds 2F (s) = cs -γ 1 (t -s 0 ) for t ∈ (s 0 , s 1 ). Therefore β satisfies β = cs -γ 1 f ( β), β(s 0 ) = ε, β(s 1 ) = β (s 1 ) = 0 and β ≤ ε. Using s -γ 1 ≤ s -γ
for s ∈ (s 0 , s 1 ) we infer (2.5) and the claim follows. This concludes the proof.

Observe that in the above proof we did not actually use the fact that the domain in which the equation ∆u = f (u) is set is a half-space. In the existence part of the proof we only used that we can find a ball outside the domain, whereas in the non-existence part we only used that the domain contains a sufficiently large ball. In other words, we have actually proved the following result.

Theorem 2. Suppose (KO) holds, and f (0) = 0, f (t) > 0 for t > 0 is monotone increasing. Assume Ω is such that Ω = R N and for each R > 0 there exists a ball with radius R included in Ω. Then the equation ∆u = f (u) has a positive solution in Ω if and only if Proof of Theorem 1, case t 0 = -∞.

Existence. Assume (HS) holds, that is, -∞ f is convergent. Fix a positive constant ∞). We define implicitly v as follows:

C * such that C * > 2 0 -∞ f (t)dt = -2F (-
0 v(t) ds 2F (s) + C * = t.
Observe that v is well defined by (HS) and the choice of C * . Moreover, by differentiating -v (t) = 2F (v(t)) + C * , and therefore v is strictly negative and bounded for t ≥ 0. By differentiating once more we see that v satisfies v = f (v) in (0, +∞) and thus u(x) = v(x N ) is a (one-dimensional and negative) solution of (P) in the half-space.

Nonexistence. Let us assume that (KO) holds, -∞ f is divergent and there exists a sub-solution u of (P) in R N + . First we observe that (2.6) lim

x N →+∞ u(x) = -∞ uniformly for x ∈ R N -1 ,
where x = (x , x N ).

In fact, if this were not the case, there would exist γ < 0 and a sequence x (n) with x (n) N → ∞ such that u(x (n) ) ≥ γ as n → ∞. As we observed before the proof of Theorem 1, we may use the condition (KO) to ensure that there exists a radial solution w n of the equation ∆w = f (w) in B R (x (n) ), with w n (x (n) ) = 2γ and w n = +∞ on ∂B R (x (n) ), for some sufficiently large and fixed R > 0. Observe that B R (x (n) ) ⊂ R N + for large n, therefore we can apply the comparison principle and deduce u(x) ≤ w n (x) in B R (x (n) ) for large n. We obtain a contradiction since

w n (x (n) ) = 2γ < γ ≤ u(x n ).
By the above argument, and replacing if necessary the half-space {x N > 0} by the half-space {x N > A} for some conveniently chosen A > 0, we can assume that u < 0 in R N + . Moreover, for a given M > 0 there exists

R = R(M ) > 0 such that u ≤ -M on R N -1 × {R} and R(M ) → +∞ as M → +∞.
For any R, T > 0 consider the finite cylinder

D T,R := {x = (x , x N ) ∈ R N + : |x | < T, x N < R}.
Let Ω n be a sequence of smooth bounded domains such that D n,R ⊂ Ω n ⊂ D n+1,R , and let h n be a continuous function defined on

∂Ω n such that -M ≤ h n ≤ 0 on ∂Ω n , h n = -M on ∂Ω n ∩ {|x | < n, x N = R} and h n = 0 on ∂Ω n ∩ {x N < R}. Consider the problem (2.7) ∆w = f (w) in Ω n w = h n on ∂Ω n .
By the construction of h n we see that u is a subsolution of this problem, while u = 0 is a supersolution (recall that f (0) > 0), and they are ordered. Therefore there exists a solution w n of (2.7) verifying u ≤ w n ≤ 0 in Ω n . Again by the usual elliptic estimates the sequence w n is bounded in W 2,p (K) for each compact K ⊂ {0 ≤ x N ≤ R}. Therefore we can pass to the limit by using a diagonal argument, to obtain a solution w M of the following problem in a strip (2.8)

   ∆w = f (w) in {0 ≤ x N ≤ R} w = 0 on x N = 0 w = -M on x N = R
Of course we also have u ≤ w M ≤ 0. We claim that actually w M is the maximal solution of (2.8) in the order interval [u, 0]. To show this, let w be any solution of (2.8) such that u ≤ w ≤ 0. Therefore w is a subsolution of (2.7), so by comparison w ≤ w n in Ω n for every n. At the limit w ≤ w M and maximality follows. By maximality, w M depends only on the variable x N (since any translation of w M in a direction parallel to {x N = 0} is still a solution of (2.8)). This means that v M (x N ) = w M (x) is a classical solution of v M = f (v M ) in (0, R) with v M (0) = 0 and v M (R) = -M . We can pass to the limit as M → +∞ as before to obtain that v Mn → v in C 2 loc [0, +∞) for some sequence M n → +∞, where v = f (v) in (0, +∞) with v(0) = 0. Now w(x) = v(x N ) is itself a solution of (P), and hence, by (2.6), we have v(x N ) → -∞ as x N → ∞. However, as we already observed, (v ) 2 = 2F (v) + v (0) 2 and so F (v(x N )) is bounded from below as x N → ∞, while on the other hand the failure of (HS) means precisely that F (t) = -0 t f tends to -∞ as t → -∞. The proof is concluded.

Theorem 1 .

 1 Suppose (KO) holds. Then equation (P) has a solution if and only if (HS)

  If this hypothesis is not satisfied, even positive subsolutions do not exist in Ω.

Acknowledgements. J. G-M and A. Q. were partially supported by Ministerio de Ciencia e Innovación under grant MTM2011-27998 (Spain), A. Q. was partially supported by Fondecyt Grant No. 1110210 and CAPDE, Anillo ACT-125 Chile). All three authors were partially supported by Programa Basal CMM, U. de Chile.


Camilla Liénart
email: camilla.lienart@gmail.com

Eric Feunteun

Michael J Miller

Jun Aoyama

Jean-Michel Mortillaro

Cédric Hubas

Mari Kuroki

Shun Watanabe

Christine Dupuy

Alexandre Carpentier

Tsuguo Otake

Katsumi Tsukamoto

Tarik Meziane

Geographic variation in stable isotopic and fatty acid composition of three families of anguilliform leptocephali and particulate organic matter (POM) in the western South Pacific

Keywords: Leptocephali, fatty acids, stable isotopes, biomarkers, trophic ecology, oceanic currents

The feeding ecology of leptocephali has remained poorly understood because they apparently feed on particulate organic matter (POM), which varies in composition, and it is unclear which components of the POM they assimilate. The δ 13 C and δ 15 N stable isotope (SI) and fatty acid (FA) compositions of 3 families of leptocephali and POM were compared in 3 latitudinal current zones of the western South Pacific. The δ 15 N signatures of both leptocephali and POM overlapped, with both having their lowest values in the southern current zone. POM contained 38 FAs and was rich in saturated FAs (SFA) (16:0, 18:0, 14:0), while leptocephali contained 50 FAs, with high proportions of 16:0, and higher contributions of 22:6ω3, 20:5ω3, 18:1ω9, 16:1ω7 and other FAs than the POM. Serrivomeridae leptocephali in the north had higher δ 15 N signatures and were also distinguished from Nemichthyidae and Muraenidae larvae by their FA compositions (higher SFAs, lower 22:6ω3 and 20:5ω3).

Although SI signatures of the Serrivomeridae larvae did not clearly vary with size, 16:0 and 18:0 FA proportions decreased with increasing larval size, and 22:6ω3 and 16:1ω7 increased in larger larvae. Correspondences between the latitudinal variations in nitrogen SI signatures and FA compositions of POM with those of leptocephali and the presence of FA markers of both autotrophic and heterotrophic organisms were consistent with leptocephali feeding on POM.

POM can contain various materials from primary producers and heterotrophic microorganisms, but differences in the SI signatures and FA compositions in leptocephali remain to be explained through further research.

INTRODUCTION

Leptocephali are the larvae of approximately 15 families of anguilliform fishes and their close relatives, which are widely distributed in the oceans from low-latitude temperate zones to tropical latitudes (Böhlke 1989[START_REF] Miller | An introduction to leptocephali: biology and identification[END_REF][START_REF] Miller | Ecology of anguilliform leptocephali: Remarkable transparent fish larvae of the ocean surface layer[END_REF]. They have highly laterally-compressed, transparent bodies and a unique physiology compared to other fish larvae [START_REF] Pfeiler | Developmental physiology of elopomorph leptocephali[END_REF], Bishop et al. 2000). All eel families except the Anguillidae are almost exclusively marine and live in habitats ranging from the meso-and bathy-pelagic zones (e.g., Nemichthyidae, Serrivomeridae) to coastal areas (e.g., Muraenidae) [START_REF] Miller | An introduction to leptocephali: biology and identification[END_REF]. All leptocephali however, are present together in the near the surface to 300 m depth zone of oceanic areas [START_REF] Castonguay | Vertical distributions, diel and ontogenetic vertical migrations and net avoidance of leptocephali of Anguilla and other common species in the Sargasso Sea[END_REF][START_REF] Miller | Ecology of anguilliform leptocephali: Remarkable transparent fish larvae of the ocean surface layer[END_REF]. Dependent on their taxa and adult habitats, the pelagic phase lasts for several months to more than a year before the larvae undergo metamorphosis into juveniles [START_REF] Marui | Comparison of early life history between New Zealand temperate eels and Pacific tropical eels revealed by otolith microstructure and microchemistry[END_REF].

Despite their wide distributions and the extensive literature on their morphology (e.g., Böhlke 1989), the feeding ecology of leptocephali is still poorly resolved. During their larval feeding and growth period, leptocephali accumulate energy storage compounds such as lipids and glycosaminoglycans (GAG) in a gelatinous body matrix, which are then used for building new tissues during metamorphosis [START_REF] Padrón | Changes in lipid composition during metamorphosis of bonefish (Albula sp.) leptocephali[END_REF][START_REF] Pfeiler | Developmental physiology of elopomorph leptocephali[END_REF][START_REF] Pfeiler | Identification, structural analysis and function of hyaluronan in developing fish larvae (leptocephali)[END_REF]. A few studies have examined the gut contents of leptocephali and have observed materials that resemble particulate organic matter (POM) such as marine snow, discarded appendicularian houses or faecal pellets [START_REF] Otake | Dissolved and particulate organic matter as possible food sources for eel leptocephali[END_REF][START_REF] Mochioka | Diet of anguillid larvae: leptocephali feed selectively on larvacean houses and fecal pellets[END_REF], Miller et al. 2011).

Carbon and nitrogen stable isotope studies of leptocephali indicate they feed at a low trophic level [START_REF] Otake | Dissolved and particulate organic matter as possible food sources for eel leptocephali[END_REF][START_REF] Miyazaki | Stable isotope analysis of two species of anguilliform leptocephali (Anguilla japonica and Ariosoma major) relative to their feeding depth in the North Equatorial Current region[END_REF], Feunteun et al. 2015), which was confirmed using amino acid nitrogen isotopes [START_REF] Miller | A low trophic position of Japanese eel larvae indicates feeding on marine snow[END_REF].

Other observations have suggested that leptocephali might also feed on microplanktonic organisms such as protozoans [START_REF] Tanaka | The first report of eel larvae ingesting rotifers[END_REF], Govoni 2010) and the DNA sequences of various organisms including gelatinous zooplankton have been detected in leptocephalus stomach contents [START_REF] Riemann | Qualitative assessment of the diet of European eel larvae in the Sargasso Sea resolved by DNA barcoding[END_REF]. Marine snow however, can be composed of multiple materials and/or organisms, due to both aggregation and colonization processes (Alldredge & Silver 1988[START_REF] Shanks | Holoplankton, meroplankton, and meiofauna associated with marine snow[END_REF][START_REF] Kiørboe | Colonization of marine snow aggregates by invertebrate zooplankton: abundance, scaling, and possible role[END_REF]. Therefore, the hypothesis that leptocephali feed on POM and assimilate some of the components of marine snow, including colonising microorganisms, appears most likely [START_REF] Deibel | Lipid class and fatty acid content of the leptocephalus larva of tropical eels[END_REF][START_REF] Miller | A low trophic position of Japanese eel larvae indicates feeding on marine snow[END_REF], Feunteun et al. 2015). Differences in the isotopic compositions of leptocephali taxa have been detected and clear correspondences between POM signatures and expected enrichment values in leptocephali have not always been observed [START_REF] Miyazaki | Stable isotope analysis of two species of anguilliform leptocephali (Anguilla japonica and Ariosoma major) relative to their feeding depth in the North Equatorial Current region[END_REF], Feunteun et al. 2015).

Thus, it is unclear if leptocephali feed on POM opportunistically or if there are selective differences in the types of POM consumed and/or the types of compounds assimilated from ingested POM between different taxa.

An important component of the POM and organisms that potentially contribute to the diet of leptocephali are lipids, but only a few studies have examined the lipid content of leptocephali [START_REF] Padrón | Changes in lipid composition during metamorphosis of bonefish (Albula sp.) leptocephali[END_REF][START_REF] Deibel | Lipid class and fatty acid content of the leptocephalus larva of tropical eels[END_REF]. Lipids are important for marine organisms because they are their major metabolic energy reserves (Falk-Petersen et al. 2000[START_REF] Lee | Lipid storage in marine zooplankton -a review[END_REF]) and play key roles in cell structure and metabolism [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF].

Fatty acids (FAs) are a specific class of lipids that are energy rich molecules [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF]. Most consumers are unable to synthetize essential FAs (EFAs: 20:4ω6,20:5ω3,22:6ω3), which are polyunsaturated FAs (PUFAs) with a terminal end omega-3 (ω3) or omega-6 (ω6), due to their lack of specific enzymes and therefore they acquire these EFA molecules exclusively from the food they eat (Canuel et al. 1995[START_REF] Styrishave | Seasonal variations in hepatopancreas fatty acid profiles of two colour forms of shore crabs, Carcinus maenas[END_REF][START_REF] Meziane | Role of fiddler crabs of a subtropical intertidal flat on the fate of sedimentary fatty acids[END_REF][START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF].

Biochemical tracers such as FAs and stable isotope ratios (SI) are commonly used in trophic ecology studies because they provide information about the food sources that are assimilated by the organism over time [START_REF] Pitt | Stable isotope and fatty acid tracers in energy and nutrient studies of jellyfish: a review[END_REF]. SI ratios of carbon (δ 13 C) and nitrogen (δ 15 N) are used to evaluate the food sources of organisms (Fry & Sherr 1984, Canuel et al. 1995) and to characterize organic matter transfer through food webs (Fry & Sherr 1984, Canuel et al. 1995, Abrantes & Sheaves 2009). FAs can be used as biomarkers of specific organisms [START_REF] Meziane | Inter-specific and geographical variations in the fatty acid composition of mangrove leaves: implications for using fatty acids as a taxonomic tool and tracers of organic matter[END_REF], or to determine the food sources exploited by consumer organisms [START_REF] Meziane | The use of lipid markers to examine sources of organic matter and its incorporation into food web of the intertidal salt marshflat ecosystem, Mont Saint Michel Bay, France[END_REF][START_REF] Meziane | Fatty acids as tracers of organic matter in the sediment and web of a mangrove/intertidal flat ecosystem, Okinawa, Japan[END_REF][START_REF] Mortillaro | Trophic opportunism of central Amazon floodplain fish[END_REF]. They can also be used to follow organic matter transfer through food webs [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF], Budge et al. 2006, Hall et al. 2006) and can provide information on larval ontogenetic changes [START_REF] Plante | Ontogenetic variations in lipid class and fatty acid composition of haddock larvae Melanogrammus aeglefinus in relation to changes in diet and microbial environment[END_REF]).

This study used bulk SI and FA composition to provide information on the possible food sources of leptocephali and was specifically intended to investigate: (1) How leptocephali, belonging to three families, may assimilate POM and the associated microorganisms colonizing POM (protozoa, microalgae, bacteria, etc.) (2) Whether the diet of leptocephali changes with size and/or with latitude and/or current systems in the western South Pacific Ocean?

MATERIALS AND METHODS

Study area and sample collection

Leptocephali were collected in the western South Pacific (WSP) during Leg 1 of the KH-13-2 research cruise of the research vessel (R/V) Hakuho Maru from 4-24 February 2013.

Thirty-four stations were sampled at every 2° of latitude/longitude between 5°S-30°S and 165°E-175°W, in the region that includes New Caledonia, Fiji and Samoa (Figure 1A).

Leptocephali were collected using an Isaacs-Kidd midwater trawl (IKMT) with an 8.7 m 2 mouth opening and 0.5 mm mesh. Sampling at each station was conducted following two strategies: during the night a step tow fished in the upper 120 m (10 min. steps at 120 m, 70 m and 50 m), and during the day an oblique tow fished from the surface to 200 m, with both types of tows taking less than 1 hour. Temperature, conductivity, depth (CTD) profiles were made at 21 of the stations to a depth of 500 m.

Leptocephali from each IKMT sample were sorted fresh, measured and identified to the lowest possible taxonomic level according to [START_REF] Miller | An introduction to leptocephali: biology and identification[END_REF]. A total of 538 leptocephali from 13 families were collected, but only the 3 most abundant families were analysed in this study. After identification and measurement, specimens to be used for SI and FA analyses were stored at -80°C. In this study, family is the only taxonomic level considered, and 101 leptocephali from the 3 most abundant families; Muraenidae (n=27; length 25.3-83.0 mm, mean±S.D.= 50.1±13.4 mm), Nemichthyidae (n=28; length 30.0-259.0 mm, 122.0±60.5) and Serrivomeridae (n=46; length 9.2-62.0 mm, 28.4±14.4 mm) were analysed for SI and FA composition (Figure 1). Five samples of the Serrivomeridae larvae samples consisted of 2 of the smallest larvae (< 10 mm) pooled together to obtain enough tissue for analysis. Each leptocephalus specimen or pooled sample was used for both SI and FA analyses.

Serrivomeridae larvae were used to examine differences in SI and FA composition in relation to leptocephalus size, because of the insufficient specimens of different sizes of Muraenidae and Nemichthyidae larvae, and the Serrivomeridae larvae were mostly from the same current zone.

Seawater samples were collected in triplicate at 13 stations (Figure 1A) in 12 L Niskin bottles attached to the CTD rosette multisampler at the depth of the chlorophyll maximum as measured by a fluorometer on the CTD were used for POM analyses. The depth of the chlorophyll maximum differed depending on the station, and was chosen because it is likely to have high concentrations of particulate material that may be suitable for feeding by leptocephali. No POM was sampled at the first CTD station in the southwest due to its proximity to the start of the cruise. POM was collected by filtering each 12 L of seawater sample through separate pre-combusted glass fibre filters (GF/F, 47 mm diameter, 0.7 μm mesh). Large organisms such as copepods were removed manually and filters were immediately stored frozen at -80°C until analysed.

Stable isotopes analysis

All samples were lyophilised before analysis. GF/F filters were fumigated with 10% HCl for 4 h to remove inorganic carbon [START_REF] Lorrain | Decarbonation and preservation method for the analysis of organic C and N contents and stable isotope ratios of low-carbonated suspended particulate material[END_REF]. Leptocephali samples were weighed. Carbon ( 13 C/ 12 C) and nitrogen ( 15 N/ 14 N) SI analysis were performed by the UC Davis Stable Isotope Facility (Department of Plant Sciences, University of California at Davis, Davis, California) using a PDZ Europa ANCA-GSL elemental analyser for leptocephali analysis (half body, excluding the head region except for the smallest larvae) and an Elementar Vario EL Cube or Micro Cube elemental analyser (Elementar Analysensysteme GmbH, Hanau, Germany) for the GF/F filter POM samples (half filter). Each elemental analyser was interfaced to a PDZ Europa 20-20 isotope ratio mass spectrometer (Sercon Ltd., Cheshire, UK). Isotopic data are reported using standard delta notation (δ 13 C or δ 15 N), defined as parts per thousand deviation (‰) from an international standard (Vienna Peedee belemnite for δ 13 C and atmospheric N 2 for δ 15 N) as defined by the equation:

δ 13 C or δ 15 N =[(R sample /R standard )-1]x1000
Where R = 15 N/ 14 N or 13 C/ 12 C of the sample or standard [START_REF] Peterson | Stable isotopes in ecosystem studies[END_REF]. The analytical precision (standard deviation for repeated measurements of internal standards) was ±0.2‰ and ±0.3‰ for δ 13 C and δ 15 N, respectively. All mean values of SI and FA data are expressed as mean ± standard deviation (S.D.).

Fatty acid analysis

Lipids were extracted following [START_REF] Meziane | Inter-specific and geographical variations in the fatty acid composition of mangrove leaves: implications for using fatty acids as a taxonomic tool and tracers of organic matter[END_REF]. Briefly, lipid samples (half bodies or filters) were extracted twice with a mixture of distilled water, MeOH and CHCl 3

(1:2:1, v:v:v). Saponification and methylation were performed successively under reflux according to [START_REF] Meziane | Fatty acids as tracers of organic matter in the sediment and web of a mangrove/intertidal flat ecosystem, Okinawa, Japan[END_REF]. Saponification was achieved using a 2 M NaOH:MeOH solution (1:2, v:v) and methylation with 1 ml of 14% BF 3 -MeOH. The fatty acid methyl esters (FAMEs) were separated and quantified by Gas Chromatography (Varian CP-3800) using a flame ionisation detector at the National Museum of Natural History (MNHN-Paris, Resaqua Laboratory). Separation was performed with an Agilent J&W GC VF-WAXms column (30 m x 0.25 mm i.d.; 0.25 μm film thickness) with He as carrier gas.

Most of FAs peaks were identified by comparing their retention times with those of known standards (Supelco TM 37 FAME mix; Sigma-Aldrich ® ) and confirmed with a GC-mass spectrometer (Varian 450-GC 220-Ion Trap MS; He as carrier gas). FAs are designated as X:YωZ, where X is number of carbon atoms, Y is number of double bonds and Z is the position of the ultimate double bond with respect to the terminal methyl group. The concentration of each FA was calculated using 23:0 as an internal standard according to [START_REF] Schomburg | Gaschromatographie[END_REF]: C FA =A S /A IS x C IS /W S , where A S is the peak area of the FA, A IS the peak area of the internal standard, C IS the concentration of the standard and W S the dry weight of sample.

Latitudinal regions of the study area

The study area was located within the northwestern part of the WSP subtropical gyre [START_REF] Qiu | Seasonal modulations in the eddy field of the South Pacific Ocean[END_REF]. The water temperature in this region decreases from the north to south [START_REF] Miller | Geographic variation in the assemblages of leptocephali in the western South Pacific[END_REF] and during the survey it ranged from 29°C (surface) and 21-23°C (200 m) at northern stations (8°N) to 25°C and 18°C respectively in the south (24°S). This region includes 3 main surface currents at different latitudes, which are the westward South Equatorial Current (SEC, Equator to 20°S), the narrow eastward South Equatorial Countercurrent (SECC) at 5 to 10°S (between two branches of the SEC), and the eastward South Tropical Countercurrent (STCC) at latitudes south of Fiji and north of New Zealand [START_REF] Qiu | Seasonal modulations in the eddy field of the South Pacific Ocean[END_REF]Ganachaud et al. 2014).

The SECC was present north of 10°S according to ADCP observations made during the cruise, with mixed westward flow at central latitudes and mixed eastward flow in the south (Otake et al. unpubl. cruise report). The assemblages of leptocephali vary latitudinally in this region, with Serrivomeridae larvae being most abundant in the north, species such as Muraenidae being abundant at central latitudes, and Nemichthyidae being more equally distributed across latitudes [START_REF] Miller | Geographic variation in the assemblages of leptocephali in the western South Pacific[END_REF] as they were during the present survey (Figure 1B-D). According to the general pattern of currents, the cruise stations were separated into 3 latitudinal zones for analyses of SI and FA compositions of leptocephali and POM, which generally correspond with the SECC, SEC, and STCC current systems (Figure 1B).

Data analysis

All SI and FA data are expressed as mean values ± standard deviation (S.D. All FAs were used in the analyses and no transformations were performed on the dataset to prevent excessive weighting of low proportion FAs. Data matrices (% TFA per sample) were used to create triangular dissimilarity matrices with the Bray-Curtis dissimilarity coefficient, followed by non-metric multidimensional scaling (n-MDS). Stress values < 0.2 were considered robust [START_REF] Clarke | Non-parametric multivariate analyses of changes in community structure[END_REF]. Groups used as factors for the analysis were family (Muraenidae, Nemichthyidae, Serrivomeridae) and size groups (≤10.0, 10.1-20.0, 20.1-40.0, 40.1-60.0 mm, Serrivomeridae only), as well as current zones (SEC, SEC, STCC) for both leptocephali and POM. Differences in FAs composition among groups was statistically tested using separate one-way analysis of similarity (ANOSIM) computed after 5000 permutations.

Average dissimilarity (AD) between groups was determined by SIMilarity of PERcentage (SIMPER) analysis (PRIMER ® 5 software module) was used to identify which fatty acids determine the observed differences within or between groups.

Multivariate analyses were performed with PRIMER ® 5 software [START_REF] Clarke | Change in marine communities: An approach to statistical analysis and interpretation[END_REF]) and univariate tests using R software (R development Core Team 2014, Vegan package, [START_REF] Oksanen | Package 'vegan': Community Ecology Package[END_REF]. For all univariate tests, the probability α was set at 0.05.

RESULTS

Isotopic and fatty acids composition of Particulate organic matter and leptocephali

Particulate organic matter (POM). SI values of POM (Figure 2) ranged from -27.8‰

to -25.0‰ for δ 13 C (mean±S.D. = -26.6±0.7‰) and from 2.5‰ to 10‰ for δ 15 N (6.1±2.3‰) (Table 1). A total of 38 FAs were identified in the POM (Table 1). Average saturated fatty acid (SFAs) contribution to POM was 75.2±4.6% of total FAs, with 16:0 showing the highest contribution (35.9±2.3%). The main monounsaturated fatty acids (MUFAs) were 18:1ω9

(5.3±1.1%) and 16:1ω7 (4.4±0.9%). All relative contributions of polyunsaturated fatty acids (PUFAs) were low with maximum values of 1.7±0.4% for 16:2ω4, 1.7±0.8% for 22:6ω3 and 1.7±0.5% for 18:4ω3. Similarly, EFAs 20:5ω3 and 20:4ω6 had low contributions to TFAs (about or ≤ 1%). Contributions of branched-chain fatty acid (BrFAs) were 2.4±0.4% of TFAs.

Leptocephali. For the 3 families of leptocephali (Figure 2), δ 13 C stable isotope values ranged from -23.1‰ to -18.8‰ and from 0.7‰ to 14.5‰ for δ 15 N (Table 1). There was a significant difference in δ 13 C composition between Serrivomeridae (-21.0±0.8‰) and Nemichthyidae (-19.9±0.8‰) leptocephali (KW: p<0.001; followed by MWW: p<0.001).

δ 15 N signatures were significantly different among each of the 3 families (KW: p<0.001; MWW: p<0.01) with an average δ 15 N of 4.7±3.3‰ for Nemichthyidae, 6.7±2.7‰ for Muraenidae and 10.9±1.9‰ for Serrivomeridae.

A total of 50 FAs was identified in leptocephali (Table 1), with a large contribution of SFAs, MUFAs, and PUFAs to TFAs. The same 6 FAs (16:0, 16:1ω7, 18:0, 18:1ω9, 20:5ω3 and 22:6ω3) were most abundant in all 3 families, with all the other FAs each contributing less than about 4% to the TFAs. Muraenidae had higher levels of FAs by weight (11.7±7.4 mg g -1 )

than Nemichthyidae (5.2±2.5 mg g -1 ) and Serrivomeridae (5.4±4.0 mg g -1 ).

The 3 families also showed differences regarding their FAs compositions (ANOSIM: p<0.001), with Muraenidae showing no overlap with the Serrivomeridae and Nemichthyidae, which overlapped to some degree in the n-MDS plot (Figure 3). FAs profiles of leptocephali exhibited average dissimilarity values (AD; SIMPER analysis) that were more similar between Muraenidae and Serrivomeridae (16.6%) than between Muraenidae and Nemichthyidae (14.3%) and between Nemichthyidae and Serrivomeridae (14.6%). The observed differences were mostly due to the relative contributions of 16:0, 16:1ω7, 18:0, 18:1ω9, 20:5ω3 and 22:6ω3 to TFAs (Table 1). SFAs contributed a higher proportion of TFAs in Serrivomeridae leptocephali (44.8±7.5%) than PUFAs (33.8±5.7%), whereas the PUFAs contribution was slightly higher in Muraenidae and Nemichthyidae (42.3±3.7% and 39.4±4.2%, respectively)

than SFAs contribution (38.5±3.7% and 37.4±4.2%, respectively) (Figure 4A,B). The total ω3

FAs contribution were significantly different (KW: p<0.001; MWW: p<0.05) for the 3 families, ranging from 23.7±5.5% for Serrivomeridae to 32.5±3.8% for Muraenidae (Figure 4C). BrFAs contributed less than 1% of TFAs, but differed significantly in their contribution to TFAs (KW: p<0.001; MWW: p<0.001) between Muraenidae (0.5±0.1%) and the other families (Nemichthyidae: 0.8±0.1% and Serrivomeridae: 0.9±0.2%) (Figure 4D).

Fatty acid trophic markers (FATMs) of the leptocephali included two predominant 16:0 and 22:6ω3 FAs, which contributed on average 40% of the TFAs (Table 1). Proportions of the PUFAs 20:5ω3 and 22:6ω3 were lower for Serrivomeridae (5.1±2.1% and 14.8±3.2%, respectively) than for the two other families (KW p<0.001; MWW: p<0.001). Muraenidae had the highest percentage of 22:6ω3 of the 3 families. The contribution of 18:1ω9 to TFAs was lower for Muraenidae (5.8±0.9%; KW: p<0.001; MWW: p<0.001) than Nemichthyidae and Serrivomeridae (8.3±1.7% and 8.8±1.3%, respectively).

FA compositions and SI signatures of Serrivomeridae size groups

The 4 size groups of Serrivomeridae leptocephali were compared for their FAs and SI signatures. No significant differences were found between size groups for δ 15 N (Table 2) and δ 13 C values were only significantly different for ≤10 mm larvae (-19.9±0.6‰) and 40-60 mm larvae (-21.4±0.5‰) (KW: p<0.01; MWW: p<0.05).

The FA compositions of the Serrivomeridae leptocephali showed various percentage changes with increasing size, with SFAs and BrFAs tending to decrease, and MUFAs and PUFAs tending to increase with increasing leptocephali size (Table 2). The total weight of FA in the body of the leptocephali tended to decrease only slightly from the smallest to largest size classes (5.8 to 4.4 mg g -1 ) but differences were not significant. The 40-60 mm and ≤10 mm sizes classes were significantly different in FA composition (ANOSIM: p<0.05; n-MDS),

Figure 5) with an AD of 23.2%. The SFAs contribution to ≤10 mm larvae was higher (56.7±0.9%) and PUFAs contribution was lower (25.2±0.6%) than in 40-60 mm larvae (37.1±0.3% for SFAs and 39.0±0.4% for PUFAs) mainly due to the contribution of the SFAs 16:0 and 18:0, the MUFA 16:1ω7 and the PUFAs 22:6ω3 and 20:5ω3 (Table 2). The contribution of ω3 FAs increased with size, from 16.4±1.0% for ≤10 mm to 30.0±0.7% for 40-60 mm larvae.

POM and leptocephali SI signatures in current zones

The POM exhibited variation in δ 15 N values, which ranged from 7.7±2.3‰ in the SECC in the north, to 4.1±1.0‰ in the STCC in the southeast (Table 3), although the SEC values overlapped with those of the other zones (Figure 6D). The δ 13 C values showed less variation with mean values that ranged from -27.0±0.2‰ to -26.2±0.9‰, but some of the SECC values were lower (Figure 6D). When FA compositions of POM were separated according to the 3 current zones, samples from the SECC (5-15°S) were significantly different (ANOSIM: p<0.05) from those of both the SEC (15-20°S) and STCC (20-30°S) with an AD of 12.5% between the SECC and SEC, and 13.2% between SECC and STCC. These differences mostly resulted from variations in the proportions of the SFAs 18:0, 16:0 and 14:0 (AD between 1.4 and 2.6%), the MUFAs 18:1ω9 and 16:1ω7 (AD between 0.9 and 0.7%) and

PUFAs 22:6ω3 and 18:4ω3 (AD between 0.8 and 0.5%). In the SECC, the SFA contribution was higher (78.8±3.9%) and MUFA and PUFA contributions lower (11.7±2.9% and 7.1±1.4%) than in the other zones (Table 3).

Leptocephali also showed differences in isotopic signatures between the 3 current zones, with δ 15 N values being different (KW and MWW: p<0.05). Some separation of the δ 15 N signatures in the 3 zones was also seen within families, except there was only one Serrivomeridae larva analysed from the STCC (Figure 6A-C). For Serrivomeridae leptocephali there was no significant difference in δ 13 C values between larvae caught in the different current zones, whereas δ 15 N signatures were different between larvae from the SECC and SEC (t-test: p<0.05) (Figure 6C). Muraenidae from the SEC and SECC had different in both their δ 13 C and δ 15 N values (KW and MWW: p<0.05) (Figure 6B). There were also differences in the δ 13 C and δ 15 N signatures of Nemichthyidae found in the STCC and those in the SECC and SEC, respectively (KW and MWW: p<0.05) (Figure 6A). FA profiles for the leptocephali caught in the three different currents were not significantly different (KW and MWW: p>0.1).

DISCUSSION

FA and SI signatures of leptocephali and POM

This study examined the variation of the FA profiles and SI signatures of 3 families of leptocephali and their likely food source of POM. Samples were collected across a wide range of latitudes and longitudes of the WSP. Previous studies in the western North Pacific [START_REF] Miyazaki | Stable isotope analysis of two species of anguilliform leptocephali (Anguilla japonica and Ariosoma major) relative to their feeding depth in the North Equatorial Current region[END_REF]) and western Indian Ocean (Feunteun et al. 2015) analysed leptocephali and POM from much more limited areas of the ocean.

The chemical composition of the different taxa of leptocephali is generally comparable [START_REF] Pfeiler | Developmental physiology of elopomorph leptocephali[END_REF], Bishop et al. 2000) as confirmed by the FA profiles of the 3 families of leptocephali studied in the WSP that show many similarities. There were however, also some differences. The Nemichthyidae, Muraenidae, and Serrivomeridae larvae had the same number of major FAs and categories of FAs markers showed similar proportions. [START_REF] Deibel | Lipid class and fatty acid content of the leptocephalus larva of tropical eels[END_REF] also found similar FA compositions for 6 other taxa of leptocephali (Congridae, Muraenesocidae, Ophichthidae) from coastal, shelf or deep slope habitats off northwest Australia. However, despite these overall similarities, the present study found small but significant differences between the FA profiles of Muraenidae larvae and those of Nemichthyidae and Serrivomeridae. The similarities in FAs compositions of the 3 families were largely due to the FAs that were present in large proportions: 16:0, 18:0, 22:6ω3, 20:5ω3, 16:1ω7, and 18:1ω9. The same 6 FAs also had the highest proportions in leptocephali from northwestern Australia [START_REF] Deibel | Lipid class and fatty acid content of the leptocephalus larva of tropical eels[END_REF].

SFAs 16:0 and 18:0 (mean 24% and 8% of TFAs in all 3 families of leptocephali) are the most abundant FAs in nature as they are products of lipogenesis in all organisms [START_REF] Dewick | The Acetate Pathway: Fatty Acids and Polyketides[END_REF]. Similarly, ω3 FAs are abundant in marine zooplankton [START_REF] Lee | Lipid storage in marine zooplankton -a review[END_REF]) and fish larvae (Grote et al. 2011), as they were in the leptocephali, where they represented 24 to 33% of total FAs depending on family. Amongst ω3, the EFAs 20:5ω3 and 22:6ω3 are major components of cell membrane phospholipids [START_REF] Sargent | The metabolism of phospholipids and polyunsaturated fatty acids in fish[END_REF]) and are also important for larval growth and development [START_REF] Sargent | The metabolism of phospholipids and polyunsaturated fatty acids in fish[END_REF], Furuita et al. 2006, Grote et al. 2011). Marine consumers however, cannot synthetize essential ω3 and ω6 PUFAs [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF][START_REF] Lee | Lipid storage in marine zooplankton -a review[END_REF][START_REF] Kattner | Perspectives on marine zooplankton lipids[END_REF]) so they need to obtain them through feeding (Canuel et al. 1995[START_REF] Styrishave | Seasonal variations in hepatopancreas fatty acid profiles of two colour forms of shore crabs, Carcinus maenas[END_REF][START_REF] Meziane | Role of fiddler crabs of a subtropical intertidal flat on the fate of sedimentary fatty acids[END_REF]. Thus, high proportions of ω3 and ω6 in leptocephali suggest that leptocephali feed on material containing or originating from autotrophic organisms or primary consumers in which ω3 and ω6 are abundantly present [START_REF] Scott | Species differences, origins and functions of fatty alcohols and fatty acids in the wax esters and phospholipids of Calanus hyperboreus, C. glacialis and C. finmarchicus from Arctic waters[END_REF][START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF][START_REF] Lee | Lipid storage in marine zooplankton -a review[END_REF]. There is also the possibility that leptocephali, as do some heterotrophic organisms [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF], Canuel et al. 1995), synthesize these FAs from a precursor such as 18:1ω9. This MUFA is abundant in leptocephali (mean of 7.6±1.6% for the 3 families combined in this study, and 6.4±1.3% in [START_REF] Deibel | Lipid class and fatty acid content of the leptocephalus larva of tropical eels[END_REF]) and can be obtained from feeding on zooplankton or other heterotrophic sources in pelagic food webs [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF][START_REF] Lee | Lipid storage in marine zooplankton -a review[END_REF].

In this study, POM was characterized by a strong contribution of SFAs (75% of TFAs)

and a low contribution of ω3 (5%), MUFAs (13%) and PUFAs (9%), which typically indicates a low nutritional quality for the bulk organic matter, as suggested by other studies in diverse aquatic systems (e.g., North Sea, Boon & Duineveld 1996; Amazon River, [START_REF] Mortillaro | Fatty acid and stable isotope (δ13C, δ15N) signatures of particulate organic matter in the lower Amazon River: Seasonal contrasts and connectivity between floodplain lakes and the mainstem[END_REF]. Interestingly, the important FATMs 18:1ω9 and 16:1ω7 (markers of heterotrophs and autotrophic microplankton, respectively) were the main unsaturated FAs that contributed to the TFAs of POM (5 and 4%, respectively). Also, BrFA markers made a low contribution to TFAs (2%) in POM. Most of these FATMs are typically biosynthesized in large amounts by bacteria [START_REF] Kaneda | iso-and anteiso-fatty acids in bacteria: Biosynthesis, function and taxonomic significance[END_REF][START_REF] Ederington | Trophic transfer of fatty acids, sterols, and a triterpenoid alcohol between bacteria, a ciliate, and the copepod Acartia tonsa[END_REF][START_REF] Meziane | Fatty acids as tracers of organic matter in the sediment and web of a mangrove/intertidal flat ecosystem, Okinawa, Japan[END_REF] and because decaying bulk POM is rapidly colonised by bacteria [START_REF] Skerratt | Seasonal and inter-annual changes in planktonic biomass and community structure in eastern Antarctica using signature lipids[END_REF][START_REF] Najdek | Fatty acid and phytoplankton compositions of different types of mucilaginous aggregates in thenorthern Adriatic[END_REF], it would be expected to be rich in these BrFAs. Thus, the FA composition may indicate that the POM sampled within the chlorophyll maximum layer during this study is likely to be composed of a large non-living POM fraction (detritus, faecal pellets, etc.) with a low bacterial influence and to a lesser extent of living organic material (autotrophic and heterotrophic microplankton) that leptocephali would preferentially assimilate.

The diet of an organism can usually be examined by assuming a mean isotopic trophic enrichment of 1‰ in δ 13 C [START_REF] Deniro | Influence of diet on the distribution of carbon isotopes in animals[END_REF][START_REF] Rau | Animal 13 C/ 12 C correlates with trophic level in pelagic food webs[END_REF]) and of 3.4‰ in δ 15 N [START_REF] Deniro | Influence of diet on the distribution of nitrogen isotopes in animals[END_REF][START_REF] Minagawa | Stepwise enrichment of δ 15 N along food chains: Further evidence and the relation between δ 15 N and animal age[END_REF] from food source to consumer. The δ 15 N values of POM (2.5 to 12‰) and leptocephali (0.5 to 13‰) in the present study heavily overlapped, so no clear trophic enrichment between δ 15 N signatures of POM and leptocephali was evident, except perhaps for Serrivomeridae. One explanation for this is that there could be a mismatch between the POM sampled on the filters and the types of POM that leptocephali consume and what they assimilate from this, as mentioned above and described further below.

A similar result was also described by [START_REF] Otake | Dissolved and particulate organic matter as possible food sources for eel leptocephali[END_REF] found similarly high values of δ 15 N for POM [START_REF] Waite | Food web structure in two counter-rotating eddies based on δ 15N and δ 13C isotopic analyses[END_REF], Lorrain et al. 2015). This is presumably a result of regional variations that occur globally in the δ 15 N values of primary producers that contribute to POM, with some areas such as parts of the South Pacific likely having higher values than other regions of the world [START_REF] Somes | Simulating the global distribution of nitrogen isotopes in the ocean[END_REF]). The δ 13 C gap of about 7‰ between mean values (2‰ gap for closest values) of POM and leptocephali is also clearly larger than the expected 1‰ gap if leptocephali were consuming POM within the chlorophyll maximum and assimilating all of it. The values of δ 13 C of the POM we collected within the chlorophyll maximum (about -25 to -27‰) were lower than those usually reported for oceanic environments (e.g. [START_REF] Waite | Food web structure in two counter-rotating eddies based on δ 15N and δ 13C isotopic analyses[END_REF][START_REF] Hwang | Molecular and isotopic constraints on the sources of suspended particulate organic carbon on the northwestern Atlantic margin[END_REF], Miyazki et al. 2011).

However, values of δ 13 C of bulk POM as low as -25 to -29‰ have been reported at similar depths in several offshore areas [START_REF] Jeffrey | Vertical trends in particulate organic carbon 13C:12C ratios in the upper water column[END_REF], Durffel et al. 2003, Feunteun et al. 2015[START_REF] Soares | Latitudinal δ 13 C and δ 15 N variations in particulate organic matter (POM) in surface waters from the Indian ocean sector of Southern Ocean and the Tropical Indian Ocean in 2012[END_REF]. These low δ 13 C bulk POM values are measured within or just below the depth of the chlorophyll maximum and this may be a common pattern in the open ocean [START_REF] Jeffrey | Vertical trends in particulate organic carbon 13C:12C ratios in the upper water column[END_REF], Durffel et al. 1998[START_REF] Hwang | Molecular and isotopic constraints on the sources of suspended particulate organic carbon on the northwestern Atlantic margin[END_REF][START_REF] Close | Lipid and 13C signatures of submicron and suspended particulate organic matter in the Eastern Tropical North Pacific: Implications for the contribution of Bacteria[END_REF]. Moreover, POM is considered to be organic material that usually forms bigger particles commonly called "marine snow" that contains various living organisms (Alldredge & Silver 1988[START_REF] Shanks | Holoplankton, meroplankton, and meiofauna associated with marine snow[END_REF][START_REF] Kiørboe | Colonization of marine snow aggregates by invertebrate zooplankton: abundance, scaling, and possible role[END_REF]. Therefore, bulk POM composition in the open ocean likely depends on plankton communities but also on the non-living degraded part of the organic matter as well as bacterial communities. Isotopic fractionation and thus the signature of the bulk POM can differ due to variations in physiological processes between phytoplanktonic groups (metabolic 13 C enrichment, C-fixation) that are related to cell size, physiology and growth rate (Goericke & Fry 1994[START_REF] Popp | Effect of phytoplankton cell geometry on carbon isotopic fractionation[END_REF]. POM with widely varying δ 13 C and δ 15 N signatures can be found at different depths [START_REF] Jeffrey | Vertical trends in particulate organic carbon 13C:12C ratios in the upper water column[END_REF][START_REF] Waite | Food web structure in two counter-rotating eddies based on δ 15N and δ 13C isotopic analyses[END_REF], Miyazki et al. 2011, Feunteun et al. 2015), so our POM isotopic values may be related to the specific signatures within the chlorophyll maximum, which is not targeted in studies that only sample at particular depths. Or they could be partly related to aspects of the biological communities in our study area, which have not yet been studied. These factors might explain the large range of values in carbon and nitrogen signatures of POM in the WSP.

It is also possible that leptocephali do not feed exclusively within the chlorophyll maximum or consume every type of POM. It is more likely that leptocephali select specific types of POM particles to eat, such as some types of marine snow or the appendicularian houses that have been directly observed in the intestines of leptocephali (Mochioka andIwamizu 1996, Miller et al. 2011). In addition, some materials such as zooplankton faecal pellets observed in gut contents [START_REF] Otake | Dissolved and particulate organic matter as possible food sources for eel leptocephali[END_REF], Miller et al. 2011) are unlikely to be digested. Further differences between the SI signatures of the POM sample collected on a filter and those that leptocephali consume and assimilate might be related to the transparent exopolymer particles (i.e. TEP; Passow 2002) produced by microorganisms (phytoplankton, bacteria) that aggregate within POM. TEPs are mainly composed of carbohydrate molecules that aggregate into marine snow (Holloway and Cowen 1997, [START_REF] Skoog | Neutral aldoses as source indicators for marine snow[END_REF], Engel et al. 2012) and are at the interface between dissolved and particulate organic carbon [START_REF] Passow | Transparent exopolymer particles (TEP) in aquatic environments[END_REF].

Therefore, a significant fraction of TEP is likely not retained on the GF/F filters used to collect POM from the water samples, leading to these compounds being only partially included in POM carbon measurements; whereas they would have been present in the POM materials assimilated by leptocephali. In addition, carbohydrates are molecules having no nitrogen, only the δ 13 C signature of these compounds would be reflected in leptocephali if they were assimilated (Feunteun et al. 2015). Also, leptocephali have a long larval duration, so as previous studies have pointed out, larger larvae could be transported into collection areas after originating from other areas where they have fed on POM with different isotopic signatures (Myazaki et al. 2011, Feunteun et al. 2015).

Feeding ecology of leptocephali

Considering the various possible factors discussed above, the SI and FA analyses of this study may still be generally consistent with the hypothesis that leptocephali feed on POM, which has been indicated by direct observations of their gut contents [START_REF] Otake | Dissolved and particulate organic matter as possible food sources for eel leptocephali[END_REF], Miller et al. 2011) and an analysis of their trophic position [START_REF] Miller | A low trophic position of Japanese eel larvae indicates feeding on marine snow[END_REF]. The observational studies of the gut contents of leptocephali that have found POM components such as amorphous materials, appendicularian and other zooplankton fecal pellets, and discarded appendicularian houses [START_REF] Otake | Dissolved and particulate organic matter as possible food sources for eel leptocephali[END_REF][START_REF] Mochioka | Diet of anguillid larvae: leptocephali feed selectively on larvacean houses and fecal pellets[END_REF], Miller et al. 2011), provide direct evidence of POM consumption by a variety of eel larvae taxa. Also, Feunteun et al. ( 2015) characterised SI signatures of many taxa of zooplankton along with 12 taxa of leptocephali and POM and did not find evidence of leptocephali feeding on zooplankton.

However, as in previous SI studies [START_REF] Miyazaki | Stable isotope analysis of two species of anguilliform leptocephali (Anguilla japonica and Ariosoma major) relative to their feeding depth in the North Equatorial Current region[END_REF], Feunteun et al. 2015) it remains unclear what types and components of POM are used by various taxa of leptocephali, and methodological issues related to the filtration and analysis of POM may make it difficult to see clear linkages using SI analyses.

The FATM compositions determined in the present study and those of [START_REF] Deibel | Lipid class and fatty acid content of the leptocephalus larva of tropical eels[END_REF] indicate that leptocephali obtain their nutrition from various sources that include both phytoplankton (16:1ω7, 20:5ω3), dinoflagellates (22:6ω3) and heterotrophic microorganisms such as bacteria and protozoans (18:1ω9) [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF], all of which are likely to contribute to POM composition (Alldredge & Silver 1988[START_REF] Shanks | Holoplankton, meroplankton, and meiofauna associated with marine snow[END_REF][START_REF] Kiørboe | Colonization of marine snow aggregates by invertebrate zooplankton: abundance, scaling, and possible role[END_REF]. As explained above and also suggested in other studies [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF], Pitt el al. 2009), the composition of the food contents in the intestines of leptocephali could be different from what they assimilate from ingested food. Our FA results suggest that it is the materials from living organisms associated with POM that are mainly assimilated by leptocephali (e.g.

FATM of autotrophic and heterotrophic organisms). Indeed, Muraenidae larvae were rich in PUFAs and ω3 meaning even they feed on FA poor food source, they are able to preferentially assimilate and store FAs-rich components of the POM. Conversely, Serrivomeridae larvae had the highest SFA and lowest PUFAs and ω3 proportions, which suggests that they may feed on POM opportunistically, with no selective assimilation or FA storage.

FA and SI composition of Serrivomeridae size classes

Although no major differences were found in the isotopic compositions of the 4 size classes of Serrivomeridae leptocephali, clear changes in their FA composition were detected.

The only significant SI differences were that δ 13 C values differed between the largest (-21.4‰) and smallest (-19.9‰) size classes, but no significant differences were found in δ15N values.

In contrast, all the major categories of FAs showed at least minor changes with size, either increasing MUFA and PUFA or decreasing SFA contributions to TFAs.

The dynamic nature of lipid metabolism and the influence of dietary lipids when larvae first feed can cause FA composition shifts during ontogeny [START_REF] Wiegand | Composition, accumulation and utilization of yolk lipids in teleost fish[END_REF][START_REF] Rainuzzo | The significance of lipids at early stages of marine fish: a review[END_REF][START_REF] Plante | Ontogenetic variations in lipid class and fatty acid composition of haddock larvae Melanogrammus aeglefinus in relation to changes in diet and microbial environment[END_REF], Grote et al. 2011), and shifts in the growth strategies of leptocephali when they reach large sizes may result in physiological changes [START_REF] Pfeiler | Developmental physiology of elopomorph leptocephali[END_REF], Bishop et al. 2000). The decrease in percentage of SFAs in larger Serrivomeridae larvae might be caused by 16:0 and 18:0 being used as a major substrates for energy production [START_REF] Sargent | Origin and functions of egg lipids: nutritional implications[END_REF]. MUFAs and PUFAs are energy sources for development and growth especially during the larval stage when fish need energy for organogenesis, fast growth and basal metabolism (Abi-ayad et al. 2004[START_REF] Plante | Ontogenetic variations in lipid class and fatty acid composition of haddock larvae Melanogrammus aeglefinus in relation to changes in diet and microbial environment[END_REF]) and these tended to increase in proportion in the leptocephali.

Moreover, the PUFA 20:5ω3 is an important energy substrate, as well as the 22:6ω3, which is also one of the principal components of cell membranes [START_REF] Dalsgaard | Fatty acid trophic markers in the pelagic marine environment[END_REF]. In Serrivomeridae, the increase of MUFAs and PUFAs percentages with size suggest that these energetically rich FAs are not preferentially used to provide energy during larval growth. Thus, larvae may be preferentially storing energy dense FAs such as long chain FAs and PUFAs that they cannot synthesize and which are in low concentrations in POM, to support the later highenergy requirements of metamorphosis or to use during the early juvenile stage, when food availability may be uncertain. In bonefish leptocephali, SFA, MUFA, and PUFA FAs were used during metamorphosis (e.g., 30% use of 16:0, 12% of 16:1ω7, 7% of 18:5ω3), but most of 22:6ω3 was conserved [START_REF] Padrón | Changes in lipid composition during metamorphosis of bonefish (Albula sp.) leptocephali[END_REF]. More species of leptocephali including those that reach larger sizes than the Serrivomeridae should be examined to further evaluate how FA compositions changes during growth and metamorphosis.

Regional differences in leptocephali and POM

The isotopic signatures of leptocephali in the 3 current zones showed variations that appeared to be related to the POM signatures in each zone. Both δ 15 N and δ 13 C values of Nemichthyidae and Muraenidae larvae decreased to some extent from north (SECC) to south (STCC) and the same pattern was seen in POM signatures, especially for δ 15 N. The compositions of the FAs of POM and leptocephali also varied significantly among the current zones. This suggests there is regional variability in the nutritional quality (SFA and 22:6ω3 contributions) and availability (18:1ω9, 16:1ω7 and 18:4ω3) of POM. For example, the SECC POM had the highest percentage of SFAs and the lowest percentage of MUFAs and PUFAs, which indicates a lower nutritional quality. This may be reflected in the FA compositions of Serrivomeridae larvae that were mostly collected in the SECC, since they also had high SFA contents and low contents of PUFAs compared to the other more widely distributed families.

In contrast, the SEC and STCC tended to have POM with higher nutritional quality with larger PUFA and ω3 contributions.

These observed differences in POM may have affected the composition of the leptocephali, because many studies indicate that diversity and bioavailability of POM plays a key role in ecosystem functioning by supporting the trophic network (Grémare et al. 1997, Carlier et al. 2007), with regional variability in trophic resources being reflected in the consumers (Cartes et al. 2014[START_REF] Chouvelon | Trophic ecology of European sardine Sardina pilchardus and European anchovy Engraulis encrasicolus in the Bay of Biscay (north-east Atlantic) inferred from δ13C and δ15N values of fish and identified mesozooplanktonic organisms[END_REF]. Our sampling was spread across 20 degrees of latitude and crossed 3 current systems, so it is not surprising that geographic variations were observed in both the SI signatures and FA compositions of POM and leptocephali. This variation was likely due to latitudinal differences in planktonic community structure in the different current systems and temperature regimes, because differences in the δ 15 N of primary producers can cause variations in the δ 15 N values of POM and organisms between regions [START_REF] Somes | Simulating the global distribution of nitrogen isotopes in the ocean[END_REF], Cartes et al. 2014, Lorrain et al. 2015[START_REF] Soares | Latitudinal δ 13 C and δ 15 N variations in particulate organic matter (POM) in surface waters from the Indian ocean sector of Southern Ocean and the Tropical Indian Ocean in 2012[END_REF].

Longitudinal differences in the δ 15 N of mesozooplankton have also been observed around New Caledonia [START_REF] Hunt | A coupled stable isotope-size spectrum approach to understanding pelagic food-web dynamics: A case study from the southwest sub-tropical Pacific[END_REF].

It is clear though, that questions remain about the feeding ecology of leptocephali, because this study and the study in the western Indian Ocean (Feunteun et al. 2015) have found differences in the compositions of other taxa of leptocephali collected from the same area. Similar δ 15 N differences were also seen between Anguilla japonica and Congridae larvae of the genus Ariosoma [START_REF] Miyazaki | Stable isotope analysis of two species of anguilliform leptocephali (Anguilla japonica and Ariosoma major) relative to their feeding depth in the North Equatorial Current region[END_REF] in the western North Pacific. Possible reasons proposed for these differences are similar to those already discussed above, such as different types of POM being selected, the taxa feeding at different depths where the POM is slightly different, differences in assimilation of materials from the POM, or physiological differences among leptocephalus taxa [START_REF] Miyazaki | Stable isotope analysis of two species of anguilliform leptocephali (Anguilla japonica and Ariosoma major) relative to their feeding depth in the North Equatorial Current region[END_REF], Feunteun et al. 2015). To begin to evaluate these possibilities, more research is needed using SI and FA analyses of leptocephali and other food web components in a wider range of areas to gain a better understanding of the feeding ecology of these fish larvae.

Thanks also to Régis Gallon, Anthony Acou and Emmanuelle Sultan (MNHN, station marine de Dinard), to Christel Lefrançois (University of La Rochelle, LIENs, DYFEA Team), Thierry

Wirth (MNHN -EPHE, France) as well as Paco Rodriguez Tress for helping on the project and Dave T. Welsh (Griffith University) for a final editing.

LITERATURE CITED

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Feunteun

  et al. (2015) found that Nemichthyidae leptocephali had lower δ 15 N values than Muraenidae and Serrivomeridae leptocephali (and other families), and similar differences were seen between Nemichthyidae and Muraenidae larvae in the STCC zone in the present study.

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Figure 1 :

 1 Figure 1: Maps of the KH-13-2 sampling survey of the R/V Hakuho Maru showing (A) the IKMT stations for collecting leptocephali (St. 32-65) and stations where particulate organic matter (POM) was analyzed (black circles) and where other CTD casts were made (shaded circles). The number of leptocephali caught per station of (B) Muraenidae (C) Nemichthyidae, and (D) Serrivomeridae are represented by the relative sizes of the shaded circles. The general locations of the South Equatorial Current (SEC), South Equatorial Countercurrent (SECC) and South Tropical Countercurrent (STCC) are shown with arrows, and the dotted lines separate the 3 current zones used for analyzing latitudinal differences in SI and FA compositions of leptocephali and POM.

Figure 2 .

 2 Figure 2. Carbon and nitrogen stable isotope values of particulate organic matter (POM) and the leptocephali of the Muraenidae (MR), Serrivomeridae (SR) and Nemichthyidae (NM).

Figure 3 .

 3 Figure 3. Non-metric multi-dimensional scaling (n-MDS) based on Bray-Curtis similarity distance of total fatty acid composition for leptocephali of the Muraenidae (MR), Serrivomeridae (SR) and Nemichthyidae (NM). Stress = 0.12.

Figure 4 .

 4 Figure 4. Fatty acids proportions (median, first and third quartiles) of (a) Polyunsatured Fatty Acids (PUFAs), (b) Saturated Fatty Acids (SFAs), (c) sum of ω3 Fatty Acids (Σω3), (d) Branched-chain Fatty Acides (BrFAs), for the leptocephali of the Muraenidae (MR), Serrivomeridae (SR) and Nemichthyidae (NM).

Figure 5 .

 5 Figure 5. Non-metric MultiDimensional Scaling (n-MDS) based on Bray-Curtis similarity distance of total fatty acid concentration (mg g -1 ) of Serrivomeridae leptocephali for 4 different size groups (see methods for exact size ranges). Stress = 0.08.

Figure 6 .

 6 Figure 6. Carbon and nitrogen stable isotope values of (A) Nemichthyidae, (B) Muraenidae, (C) Serrivomeridae leptocephali and (D) POM from the 3 current zones of the South Equatorial Countercurrent (SECC), South Equatorial Current (SEC), and South Tropical Countercurrent (STCC).

Table 1 .

 1 Fatty acid relative contribution (%) and Carbon (δ 13 C) and Nitrogen (δ 15 N) mean isotopic signature of Particulate Organic Matter (POM) for 13 stations (3 replicates per station) and all leptocephali tissues for the three families Muraenidae (MR), Nemichthyidae (NM) and Serrivomeridae (SR). All values are mean ± S.D. n is the number of samples.

	Isotopes/ FA	POM (n=39)	MR (n=27)	NM (n=28)	SR (n=41)		POM (stn=13)	MR (n=27)	NM (n=28)	SR (n=41)
	Stable Isotopes					Polyunsat.
	δ 15 N	6.1 ± 2.3	6.7 ± 2.7	4.7 ± 3.3	10.9 ± 1.9	16:2ω4	1.7 ± 0.41 0.57 ± 0.19 0.61 ± 0.17 0.72 ± 0.33
	δ 13 C	-26.6 ± 0.7	-20.5 ± 1.1	-19.9 ± 0.8	-21.0 ± 0.8	16:2ω6	-± -	0.05 ± 0.02 0.09 ± 0.02 0.04 ± 0.02
	Saturated					16:4ω3	0.22 ± 0.06 0.05 ± 0.05 0.02 ± 0.03 0.05 ± 0.04
	12:0	0.51 ± 0.25	0.08 ± 0.12	0.04 ± 0.06	0.07 ± 0.1	18:2ω6	1.21 ± 0.26 2.76 ± 0.47 2.97 ± 0.44 2.55 ± 0.6
	13:0	0.11 ± 0.03	0.02 ± 0.02	0.02 ± 0.01	0.03 ± 0.1	18:3ω3	0.45 ± 0.09 1.15 ± 0.33 1.17 ± 0.56	0.8 ± 0.28
	14:0	14.05 ± 1.71	3.99 ± 1.32	4.63 ± 0.86	4.12 ± 0.6	18:3ω6	0.42 ± 0.08 0.28 ± 0.06 0.23 ± 0.06 0.39 ± 0.1
	15:0	1.7 ± 0.22	1.52 ± 0.23	1.71 ± 0.37	2.1 ± 0.2	18:4ω3	1.69 ± 0.52 1.24 ± 0.26 1.37 ± 0.44 1.16 ± 0.37
	16:0	35.91 ± 2.28 20.94 ± 2.44	24.04 ± 2.64 26.63 ± 4.3	20:2ω6	-± -	0.24 ± 0.1	0.11 ± 0.05 0.08 ± 0.05
	17:0	0.67 ± 0.11	1.73 ± 0.18	1.26 ± 0.18	1.75 ± 0.3	20:3	-± -	0.15 ± 0.04 0.15 ± 0.04 0.09 ± 0.03
	18:0	19.47 ± 2.31	9.32 ± 1.25	5.14 ± 1.7	9.1 ± 2.9	20:3ω6	-± -	0.37 ± 0.08 0.24 ± 0.06 0.27 ± 0.1
	19:0	0.46 ± 0.09	0.31 ± 0.1	0.2 ± 0.09	0.34 ± 0.2	20:4ω3	0.09 ± 0.02	1.4 ± 0.77 0.86 ± 0.3	0.96 ± 0.69
	20:0	0.85 ± 0.1	0.27 ± 0.07	0.14 ± 0.03	0.35 ± 0.2	20:4ω6	0.13 ± 0.04 2.82 ± 0.79 2.81 ± 0.51 3.49 ± 0.96
	21:0	0.06 ± 0.02	0.04 ± 0.01	0.03 ± 0.05	0.03 ± 0	20:5ω3	1.02 ± 0.22 7.85 ± 0.97 8.52 ± 1.22 5.05 ± 2.07
	22:0	0.58 ± 0.13	0.19 ± 0.04	0.14 ± 0.03	0.17 ± 0.1	22:2ω6	0.27 ± 0.14	-± -	-± -	-± -
	24:0	0.58 ± 0.25	0.08 ± 0.06	0.04 ± 0.03	0.09 ± 0.1	22:4ω6	-± -	0.36 ± 0.15 0.27 ± 0.21 0.12 ± 0.13
	Σ SFA (%)	75.23 ± 4.58	38.5 ± 3.65	37.41 ± 4.2	44.79 ± 7.5	22:5ω3	-± -	2.79 ± 1.58 0.95 ± 0.51 0.93 ± 0.59
	Monounsat.					22:5ω6	0.19 ± 0.11 2.18 ± 0.65 2.24 ± 0.37 2.34 ± 0.63
	16:1ω5	0.07 ± 0.03	0.14 ± 0.03	0.15 ± 0.03	0.13 ± 0	22:6ω3	1.67 ± 0.79 18.1 ± 2.13 16.8 ± 2.58 14.8 ± 3.16
	16:1ω7	4.42 ± 0.88	5.71 ± 1.14	7.6 ± 1.77	6.59 ± 1.3	Σ PUFA (%)	9.1 ± 2.1	42 ± 3.7	39 ± 4.2	34 ± 5.7
	16:1ω9	2.07 ± 0.5	0.54 ± 0.09	0.66 ± 0.13	0.63 ± 0.1	Branched-chain
	17:1ω7	0.37 ± 0.08	0.45 ± 0.12	0.49 ± 0.11	0.32 ± 0.1	14:0iso	0.35 ± 0.1	0.01 ± 0.01 0.22 ± 0.01 0.03 ± 0.01
	17:1ω9	-± -	0.45 ± 0.1	0.73 ± 0.15	0.75 ± 0.1	15:0anteiso	0.45 ± 0.06 0.03 ± 0.01 0.04 ± 0.02 0.05 ± 0.03
	18:1ω5	-± -	0.1 ± 0.03	0.1 ± 0.03	0.11 ± 0	15:0iso	0.37 ± 0.05 0.12 ± 0.03 0.14 ± 0.03 0.17 ± 0.05
	18:1ω7	0.71 ± 0.16	4.18 ± 0.77	3.93 ± 0.63	2.82 ± 0.7	16:0iso	0.22 ± 0.04 0.08 ± 0.02	0.1 ± 0.04 0.13 ± 0.04
	18:1ω9	5.3 ± 1.06	5.84 ± 0.94	8.33 ± 1.72	8.77 ± 1.3	17:0anteiso	0.68 ± 0.17 0.08 ± 0.02	0.1 ± 0.03 0.11 ± 0.04
	19:1ω9	-± -	0.03 ± 0.02	0.02 ± 0.02	0.03 ± 0	17:0iso	0.05 ± 0.01 0.12 ± 0.03 0.26 ± 0.05 0.27 ± 0.06
	20:1ω7	-± -	0.18 ± 0.08	0.12 ± 0.04	0.09 ± 0.1	18:0iso	0.26 ± 0.09 0.07 ± 0.05 0.16 ± 0.06 0.13 ± 0.05
	20:1ω9	-± -	0.22 ± 0.21	0.13 ± 0.07	0.1 ± 0.1	Σ BrFA (%)	2.38 ± 0.3	0.5 ± 0.1	0.8 ± 0.1	0.9 ± 0.2
	22:1ω11	0.38 ± 0.13	0.09 ± 0.1	0.03 ± 0.02	0.06 ± 0	Total FA (mg.g-1)	3.6 ± 0.97 11.7 ± 7.44 5.22 ± 2.51 5.41 ± 3.99
	22:1ω9	-± -	0.05 ± 0.02	0.01 ± 0.01	0.02 ± 0	Σ ω3	5.14 ± 1.46 32.5 ± 3.77 29.7 ± 3.84 23.7 ± 5.51
	24:1ω9	-± -	0.08 ± 0.05	0.06 ± 0.05	0.07 ± 0.1	Σ ω6	1.95 ± 0.12 9.06 ± 1.44 8.96 ± 0.83 9.28 ± 1.62
	Σ MUFA (%)	13.33 ± 2.66 18.69 ± 1.15	22.38 ± 2.9	20.49 ± 2.5	Σ EFA	2.82 ± 0.35 28.7 ± 1.3	28.1 ± 1.44 23.3 ± 2.06

Table 2 .

 2 Fatty acid relative contribution (%) and Carbon (δ 13 C) and nitrogen (δ 15 N) mean isotopic signature of Serrivomeridae leptocephali from four different size groups (≤10, 10.1-20.0, 20.1-40.0 and 40.1-60.0 mm). The 5 samples of ≤ 10 mm larvae each include 2 larvae pooled together. All values are mean ± S.D. n is the number of samples.

	Isotopes/ FA	≤ 10 mm (n=5)	10-20 mm (n=6)	20-40 mm (n=20)	40-60 mm (n=10)		≤ 10 mm (n=5)	10-20 mm (n=6)	20-40 mm (n=20)	40-60 mm (n=10)
	Stable Isotopes					Polyunsat.
	δ 15 N	11.1 ± 1.4	11.8 ± 0.8	10.6 ± 1.9	10.0 ± 2.3	16:2ω4	0.36 ± 0.21	0.83 ± 0.39	0.68 ± 0.3	0.94 ± 0.24
	δ 13 C	-19.9 ± 0.57	-21.3 ± 1.0	-20.6 ± 0.8	-21.4 ± 0.5	16:2ω6	0.01 ± 0.01	0.04 ± 0.02	0.04 ± 0.02	0.05 ± 0.03
	Saturated					16:4ω3	0.05 ± 0.05	0.07 ± 0.04	0.05 ± 0.04	0.03 ± 0.02
	12:0	0.13 ± 0.11	0.06 ± 0.06	0.07 ± 0.05	0.04 ± 0.02	18:2ω6	1.93 ± 0.73	2.81 ± 0.3	2.78 ± 0.26	2.25 ± 0.82
	13:0	0.05 ± 0.02	0.04 ± 0.03	0.03 ± 0.01	0.03 ± 0.01	18:3ω3	0.48 ± 0.3	0.76 ± 0.2	0.79 ± 0.26	1.1 ± 0.2
	14:0	4.5 ± 0.54	3.84 ± 0.88	3.99 ± 0.55	4.35 ± 0.61	18:3ω6	0.32 ± 0.05	0.43 ± 0.06	0.42 ± 0.1	0.37 ± 0.14
	15:0	2.25 ± 0.29	2.07 ± 0.27	2.16 ± 0.16	1.95 ± 0.12	18:4ω3	0.69 ± 0.41	1.17 ± 0.29	1.23 ± 0.32	1.24 ± 0.34
	16:0	33.23 ± 5.29	27.01 ± 1.33 27.22 ± 2.67 21.95 ± 1.67	20:2ω6	0.1 ± 0.12	0.06 ± 0.02	0.07 ± 0.02	0.12 ± 0.03
	17:0	1.79 ± 0.14	1.76 ± 0.24	1.83 ± 0.27	1.56 ± 0.21	20:3	0.07 ± 0.04	0.07 ± 0.02	0.09 ± 0.02	0.12 ± 0.02
	18:0	13.18 ± 3.9	9.9 ± 2.25	9.17 ± 2.13	6.42 ± 0.62	20:3ω6	0.16 ± 0.05	0.25 ± 0.05	0.25 ± 0.06	0.4 ± 0.08
	19:0	0.69 ± 0.24	0.32 ± 0.14	0.3 ± 0.09	0.24 ± 0.08	20:4ω3	0.41 ± 0.24	0.69 ± 0.22	0.67 ± 0.16	1.96 ± 0.7
	20:0	0.46 ± 0.15	0.48 ± 0.39	0.31 ± 0.07	0.32 ± 0.09	20:4ω6	3.73 ± 1.25	3.69 ± 0.77	3.89 ± 0.66	2.46 ± 0.74
	21:0	0.04 ± 0.02	0.03 ± 0.01	0.04 ± 0.01	0.03 ± 0.01	20:5ω3	4.04 ± 1.55	5.02 ± 0.69	4.47 ± 2.42	6.75 ± 0.98
	22:0	0.24 ± 0.07	0.16 ± 0.03	0.17 ± 0.03	0.14 ± 0.03	22:4ω6	0.03 ± 0.06	0.11 ± 0.11	0.09 ± 0.12	0.22 ± 0.13
	24:0	0.18 ± 0.08	0.13 ± 0.11	0.07 ± 0.06	0.08 ± 0.07	22:5ω3	0.44 ± 0.17	0.66 ± 0.1	0.77 ± 0.19	1.67 ± 0.77
	Σ SFA (%)	56.73 ± 0.91	45.79 ± 0.48 45.36 ± 0.51 37.09 ± 0.3	22:5ω6	2.12 ± 0.68	2.36 ± 0.4	2.51 ± 0.75	2.08 ± 0.3
	Monounsat.					22:6ω3	10.25 ± 4.35	13.54 ± 1.81	14.99 ± 2.22	17.36 ± 1.95
	16:1ω5	0.08 ± 0.04	0.13 ± 0.02	0.14 ± 0.03	0.13 ± 0.02	Σ PUFA	25.17 ± 0.6	32.55 ± 0.32	33.78 ± 0.47	39.01 ± 0.44
	16:1ω7	4.95 ± 0.81	6.54 ± 1.14	6.31 ± 0.68	8.01 ± 1.24	Branched-chain
	16:1ω9	0.49 ± 0.14	0.63 ± 0.05	0.65 ± 0.08	0.67 ± 0.06	14:0iso	0.04 ± 0.01	0.02 ± 0.01	0.03 ± 0.01	0.02 ± 0.01
	17:1ω7	0.3 ± 0.03	0.27 ± 0.07	0.34 ± 0.1	0.33 ± 0.08	15:0anteiso	0.11 ± 0.02	0.05 ± 0.02	0.05 ± 0.02	0.03 ± 0.01
	17:1ω9	0.6 ± 0.15	0.77 ± 0.08	0.73 ± 0.11	0.84 ± 0.09	15:0iso	0.21 ± 0.07	0.15 ± 0.02	0.17 ± 0.04	0.18 ± 0.04
	18:1ω5	0.05 ± 0.03	0.11 ± 0.01	0.11 ± 0.03	0.13 ± 0.02	16:0iso	0.17 ± 0.07	0.12 ± 0.02	0.13 ± 0.04	0.14 ± 0.03
	18:1ω7	2.4 ± 0.3	2.77 ± 0.32	2.63 ± 0.78	3.47 ± 0.38	17:0anteiso	0.15 ± 0.09	0.11 ± 0.03	0.1 ± 0.02	0.08 ± 0.02
	18:1ω9	7.81 ± 2.11	9.33 ± 0.64	8.76 ± 1.23	8.92 ± 0.94	17:0iso	0.27 ± 0.05	0.25 ± 0.04	0.27 ± 0.07	0.29 ± 0.05
	19:1ω9	0.02 ± 0.02	0.03 ± 0.03	0.01 ± 0.02	0.06 ± 0.04	18:0iso	0.13 ± 0.05	0.12 ± 0.09	0.13 ± 0.05	0.14 ± 0.03
	20:1ω7	0.06 ± 0.02	0.06 ± 0.03	0.07 ± 0.02	0.15 ± 0.07	Σ BrFA (%)	1.07 ± 0.05	0.82 ± 0.03	0.88 ± 0.04	0.88 ± 0.03
	20:1ω9	0.07 ± 0.03	0.07 ± 0.04	0.08 ± 0.03	0.19 ± 0.12	Total FA (mg.g-1)	5.82 ± 1.08	5.19 ± 1.92	4.62 ± 1.41	4.36 ± 1.54
	22:1ω11	0.08 ± 0.05	0.06 ± 0.03	0.06 ± 0.03	0.05 ± 0.02	Σ ω3	16.36 ± 1.01	21.9 ± 0.48	22.97 ± 0.8	30.01 ± 0.71
	22:1ω9	0.02 ± 0.01	0.02 ± 0.01	0.02 ± 0.02	0.02 ± 0.01	Σ ω6	8.39 ± 0.37	9.74 ± 0.22	10.05 ± 0.25	7.95 ± 0.28
	24:1ω9	0.1 ± 0.03	0.05 ± 0.04	0.07 ± 0.05	0.07 ± 0.07	Σ EFA	18.02 ± 2.38	22.25 ± 1.09	23.35 ± 1.77	26.57 ± 1.20
	Σ MUFA (%)	17.03 ± 0.27	20.84 ± 0.18 19.98 ± 0.23 23.02 ± 0.23

Table 3 :

 3 Fatty acid relative contribution (%) of particulate organic matter (POM) from three different currents (South Equatorial Countercurrent (SECC), South Equatorial Current (SEC) and Sub-Tropical Countercurrent (STCC). All values are mean ± S.D. n is the number of samples.

	Isotopes/ FA	POM in SECC (n=15)	POM in SEC (n=15)	POM in STCC (n=9)		POM in SECC (n=15)	POM in SEC (n=15)	POM in STCC (n=9)
	Stable Isotopes				Polyunsat.
	δ 15 N	7.7 ± 2.3	6.1 ± 2.2	4.1 ± 1.0	16:2ω4	0.97 ± 0.32 1.98 ± 0.4	2.45 ± 0.56
	δ 13 C	-26.2 ± 0.9	-26.6 ± 0.5	-27.0 ± 0.2	16:4ω3	0.26 ± 0.08 0.22 ± 0.04 0.18 ± 0.07
	Saturated FA				18:2ω6	1.1 ± 0.21 1.24 ± 0.21 1.34 ± 0.45
	12:0	0.48 ± 0.19	0.6 ± 0.32	0.41 ± 0.23	18:3ω3	0.44 ± 0.07 0.44 ± 0.08 0.49 ± 0.14
	13:0	0.1 ± 0.03	0.13 ± 0.03	0.07 ± 0.01	18:3ω6	0.4 ± 0.09 0.43 ± 0.07 0.42 ± 0.06
	14:0	14.05 ± 1.48	14.6 ± 1.74 13.14 ± 2.03	18:4ω3	1.16 ± 0.24 1.93 ± 0.55 2.16 ± 0.92
	15:0	1.71 ± 0.25	1.64 ± 0.25	1.8 ± 0.11	20:4ω3	0.09 ± 0.03 0.08 ± 0.01	0.1 ± 0.03
	16:0	37.75 ± 1.9	34.87 ± 2.43 34.59 ± 2.63	20:4ω6	0.11 ± 0.03 0.14 ± 0.05 0.16 ± 0.04
	17:0	0.74 ± 0.11	0.64 ± 0.13	0.61 ± 0.06	20:5ω3	0.88 ± 0.21	0.9 ± 0.18 1.43 ± 0.3
	18:0	21.31 ± 2.2	18.29 ± 2.56 19.53 ± 2.08	22:2ω6	0.31 ± 0.2	0.32 ± 0.13 0.13 ± 0.05
	19:0	0.45 ± 0.08	0.42 ± 0.08	0.54 ± 0.12	22:5ω6	0.21 ± 0.15 0.15 ± 0.08 0.21 ± 0.11
	20:0	0.94 ± 0.13	0.79 ± 0.08	0.79 ± 0.08	22:6ω3	1.17 ± 0.51 1.71 ± 0.76 2.43 ± 1.31
	21:0	0.06 ± 0.02	0.07 ± 0.02	0.05 ± 0.02	Σ PUFA (%)	7.11 ± 1.44 9.53 ± 1.96 11.5 ± 3.47
	22:0	0.62 ± 0.17	0.56 ± 0.11	0.55 ± 0.11	Branched-chain
	24:0	0.6 ± 0.26	0.56 ± 0.2	0.59 ± 0.3	14:0iso	0.34 ± 0.12 0.35 ± 0.08 0.37 ± 0.09
	Σ SFA (%)	78.83 ± 3.86	73.16 ± 4	72.7 ± 6.72	15:0anteiso	0.46 ± 0.08	0.4 ± 0.05	0.5 ± 0.06
	Monounsat.				15:0iso	0.39 ± 0.06 0.34 ± 0.04 0.37 ± 0.04
	16:1ω5	0.08 ± 0.04	0.08 ± 0.03	0.07 ± 0.03	16:0iso	0.21 ± 0.06 0.21 ± 0.04 0.23 ± 0.02
	16:1ω7	3.62 ± 0.73	5.62 ± 1.1	3.76 ± 0.75	17:0anteiso	0.64 ± 0.18 0.99 ± 0.26 0.23 ± 0.02
	16:1ω9	1.99 ± 0.49	2.2 ± 0.46	1.99 ± 0.57	17:0iso	0.06 ± 0.01 0.05 ± 0.02 0.04 ± 0.01
	17:1ω7	0.39 ± 0.1	0.34 ± 0.04	0.37 ± 0.12	18:0iso	0.23 ± 0.09 0.28 ± 0.06 0.29 ± 0.13
	18:1ω7	0.65 ± 0.16	0.73 ± 0.14	0.8 ± 0.2	Σ BrFA (%)	2.34 ± 0.46 2.62 ± 0.36 2.03 ± 0.08
	18:1ω9	4.63 ± 0.91	5.32 ± 0.71	6.36 ± 1.9	Total FA (mg.g-1) 2.86 ± 0.83 4.49 ± 0.77 3.33 ± 1.53
	22:1ω11	0.36 ± 0.11	0.39 ± 0.12	0.42 ± 0.17	Σ ω3	4.00 ± 0.87 5.27 ± 1.49 6.81 ± 2.4
	Σ MUFA (%)	11.71 ± 2.87	14.68 ± 2.1	13.8 ± 3.32	Σ ω6	2.14 ± 0.14 2.28 ± 0.11 2.26 ± 0.14
					Σ EFA	2.16 ± 0.25 2.75 ± 0.33 4.02 ± 0.55

Acknowledgements. This project was realized thanks to the help of the captain, crew and technicians of the R/V Hakuo Maru. We also thank the other scientific members for assistance with sampling and plankton sorting. Fatty acid analyses were performed at the French National History Museum of Paris (MNHN-ResAqua), especially with help from Najet Thiney.