gy, Part B 145 (2006) 101–107www.elsevier.com/locate/cbpb

Comparative Biochemistry and Physiolo

Muscle δ13C change in Nile tilapia (Oreochromis niloticus):Effects of growth and carbon turnover

J.A.S. Zuanon a,⁎, A.C. Pezzato b, L.E. Pezzato b, J.R.S. Passos c,M.M. Barros b, C. Ducatti d

a Departamento de Biologia Animal, Universidade Federal de Viçosa, Viçosa, MG, Brazilb Departamento de Melhoramento e Nutrição Animal, Faculdade de Medicina Veterinária e Zootecnia, Universidade Estadual Paulista, Botucatu, SP, Brazil

c Departamento de Bioestatística do Instituto de Biologia, Universidade Estadual Paulista, Botucatu, SP, Brazild Centro de Isótopos Estáveis Ambientais, Unidade Auxiliar do Instituto de Biologia, Universidade Estadual Paulista, Botucatu, SP, Brazil

Received 21 November 2005; received in revised form 22 June 2006; accepted 23 June 2006Available online 29 June 2006

Abstract

The contribution of growth and turnover to the muscle δ13C change process was investigated using mathematical models which associate δ13Cchange to time of intake of a new diet or increase in body mass. Two groups of Nile tilapia (Oreochromis niloticus) were fed on diets based on C3(δ13C=−25.64±0.06‰) or C4 (δ13C=−16.01±0.06‰) photosynthetic cycle plants to standardize the muscle δ13C. After establishing the carbonisotopic equilibrium, fish (mean mass 24.12±6.79 g) then received the other treatment diet until a new carbon isotopic equilibrium could beestablished, characterizing T1 (C3–C4) and T2 (C4–C3) treatments. No significant differences were observed in fish productive performance.Good fits were obtained for the models that associated the δ13C change to time, resulting in carbon half-life values of 23.33 days for T1 and25.96 days for T2. Based on values found for the muscle δ13C change rate from growth (0.0263 day−1 and 0.0254 day−1) and turnover(0.0034 day−1 and 0.0013 day−1), our results indicate that most of the δ13C change could be attributed to growth. The application of model thatassociated the δ13C change to body mass increase seems to produce results with no apparent biological explanation. The δ13C change rate coulddirectly reflect the daily ration and growth rate, and consequently the isotopic change rates of carbon and other tissue elements can be properlyused to assess different factors that may interfere in nutrient utilization and growth.© 2006 Published by Elsevier Inc.

Keywords: carbon; fish; growth; isotopic change rate; mathematical models; Nile tilapia; stable isotopes; turnover

1. Introduction

A number of authors (Houlihan et al., 1988; Millward, 1989;Carter et al., 1993; Peragón et al., 1994; Hawkins and Day,1996; Conceição et al., 1998; Dobly et al., 2004) have sought torelate protein turnover in muscle tissue with growth efficiencyin fish and other species of interest to animal production.Peragón et al. (2001) stated that protein turnover rates determinethe tissue growth rate in fish. These authors pointed out that thenature of these relations is an important factor to be taken in toconsideration for protein turnover manipulation, and thereforebody growth control.

⁎ Corresponding author. Av. P. H. Rolfs s/n, 36571-000. Tel.: +55 3138991174; fax: 55 31 38992578.

E-mail address: zuanon@ufv.br (J.A.S. Zuanon).

1096-4959/$ - see front matter © 2006 Published by Elsevier Inc.doi:10.1016/j.cbpb.2006.06.009

Attempts to establish a correlation between turnover andgrowth have been concentrated on methodologies that involveradioactive or stable isotopes enriched tracers to measure bodyor tissue protein synthesis and degradation. However, using thenatural variation of carbon and/or nitrogen stable isotopes sim-ilar results have been observed, without the need to use enrichedand more expensive compounds.

Few studies have assessed the tissue elements turnover usingthe natural variation in stable isotope abundance (includingcarbon and nitrogen) in growing animals (Fry and Arnold,1982; Hesslein et al., 1993; Frazer et al., 1997; Cruz, 2002;Furuya et al., 2002). Similarly to adult animals, most studiescarried out with growing animals have presented first orderexponential equations of the y(t) =a+be

ct type, where y(t) rep-resent the element isotopic abundance, a and b the parametersdeterminated for the asymptotic and initial conditions,

Table 1Percentage composition of the ingredients used in the confection, chemicalcomposition and δ13C of the experimental diets (as fed)

Ingredient (%) C3 Diet C4 Diet

Soybean meal 62.63 24.00Corn gluten meal 5.00 28.70Cottonseed meal _ 13.00Corn 6.00 26.81Rice meal 20.00 _Soybean oil 2.13 _Corn oil _ 2.80Dicalcium phosphate 3.40 3.60Vit. min. supplement1 0.50 0.50DL-Methionine 0.07 _L-Lysine _ 0.32Salt (NaCl) 0.25 0.25Antioxidant2 0.02 0.02Total 100.00 100.00δ13C (‰) −25.64±0.06 −16.01±0.06

Calculated chemical compositionDigestible protein (%) 32.06 31.98Digestible energy (kJ/g) 13.41 13.34Ether extract (%) 5.55 4.45Crude fiber (%) 5.94 5.51Metionine (%) 0.60 0.68Lysine (%) 1.92 1.43Calcium (%) 1.00 0.95Available phosphorus (%) 0.77 0.771Vitamin and mineral supplement (Supremais): Levels of guarantee of theproduct: Vitamins: A=1,200,000 UI; D3=200,000UI; E=12,000 mg;K3=2400 mg; B1=4800 mg; B2=4800 mg; B6=4000 mg; B12=4800 mg;Folic Acid=1200 mg; Calcium pantothenate=12,000 mg; C=48,000 mg;biotin = 48 mg; choline = 65,000 mg; niacin = 24,000 mg; Minerals:iron=10,000 mg; copper=600 mg; manganese=4000 mg; zinc=6000 mg;iodine=20 mg; cobalt=2 mg e selenium=20 mg;2 Butyl hydroxide toluene.

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respectively, c represents the isotopic change rate and t the timeafter the diet change.

Fry and Arnold (1982) proposed a model to assess δ13C as afunction of body mass acquired during growth, and observedthat for Penaeus aztecus shrimp post-larvae, the δ13C changeoccurred mainly as a function of mass gain.

Depending on a new diet ingestion time, the isotopic com-position of the animal body is intermediary between the newand the old diet. These intermediary isotopic values, without theanimal growth history and rates of isotopic carbon and nitrogenturnover in its tissues, have limited value (Frazer et al., 1997).

Murchie and Power (2004) have observed in young-of-the-year yellow perch (Perca flavescens) that the rate and patternsof δ15N and δ13C changes depend on the timing of ontogeneticdietary shifts and growth rates.

Thus, this study aimed to investigate the contribution ofgrowth and carbon turnover to the muscle δ13C change processusing mathematical models which associate δ13C change to timeof intake of a new diet or increases in body mass in Nile tilapiafry.

2. Materials and methods

2.1. Experimental design, fish and culture facilities

A complete randomized design with two treatments was usedto evaluate the muscle δ13C change pattern in sex reversedmales of Nile tilapia (Oreochromis niloticus) fry. Treatment 1(C3–C4) was characterized by the supply of a diet formulatedbased on grains from C3 photosynthetic cycle plants until theestablishment of the carbon isotopic equilibrium in muscletissue and was later substituted by a diet based on grains fromC4 plants. Treatment 2 (C4–C3) used the same diets, but of-fered in the reverse order to Treatment 1.

Fry were sex reversed using 17α-methyltestosterone (60 mgkg−1 feed) as described by Guerrero III (1975). Fry weighing1.88±0.16 g for Treatment 1 and 2.12±0.16 g for Treatment 2were kept in 250 L fiberglass aquaria, in a water recirculationsystemwith filtering, and at a constant temperature (25±0.5 °C).Fish (480) were separated into two groups with 20 aquaria ineach group (12 fish/aquarium) in independent water recircula-tion systems.

Fish were fed to apparent satiation, four times a day, withdiets formulated to meet their nutritional requirements based onthe NRC (1993) and on the food composition according toRostagno (2000) (Table 1). Calculation of digestible protein anddigestible energy was based on apparent digestibility offeedstuffs by Nile tilapia, presented by Pezzato et al. (2002).

Treatments consisted in two stages: a pre-experimental stageto ascertain that all fish presented similar δ13C (75 days), and thestage to assess the muscle δ13C change. After establishing thecarbon isotopic equilibrium in muscles, fish spent 24 h withoutfood. Then they were weighed and also had their standardlengths measured. At the beginning of the second experimentalstage, six fish/aquarium were selected in an attempt ofstandardizing fish mass in each aquarium, to minimize hierarchyproblems, resulting from disputes among fish of disproportional

sizes. Thus, at the beginning of this stage, the mean mass of fishwas 24.12±6.79 g. At this stage, the fish began to receive thediet of the other treatment until a new carbon isotopicequilibrium in the muscle tissue could be established(89 days), under the same feeding regime and rearing conditionsof the pre-experimental stage.

2.2. Productive performance

The productive performance of fishwas assessed at intervals ofapproximately 10 days, by weighting and measuring the standardlength of fish from five aquaria per treatment, alternating thesampled aquaria throughout the experimental period.

The mortality rate, apparent food intake, mass gain andapparent food conversion were assessed. The specific growthrate (SGR) was calculated according to the formula presentedby Ricker (1979):

SGR %d−1� � ¼ lnWf −lnWi

t

� �100 ð1Þ

Where: Wi = initial mass of the fish in g; Wf= final mass of thefish in g; and t=time in days.

Table 2Productive performance parameters of Nile tilapia during the assessment ofmuscle δ13C change

Treatment 1 Treatment 2

(C3–C4) (C4–C3)

Initial mass (g) 24.46±5.70 23.78±7.86Final mass (g) 91.40±16.65 95.77±17.11Mass gain (g) 67.16±12.16 72.02±14.47Food intake (g) 110.32±15.25 114.42±11.65Food conversion 1.68±0.24 1.64±0.30Standard length (cm) 13.36±1.97 13.34±1.65Specific growth rate (%/day) 1.46±0.87 1.54±0.87Mortality rate (%) 3.33±11.60 1.67±5.13

Mean values±SD.

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2.3. Isotopic analyzes

Three fillet samples were collected randomly from eachtreatment at variable time intervals throughout the experimentalperiod for the isotopic analyses. At the pre-experimental stage,the samples consisted of fillets from three to five fish and later,each fish represented one of the three replicates per collection.For this purpose, fish were anesthetized, killed by destroyingthe central nervous system and fillets without skin wereremoved. The muscle tissue samples were dried at 55±0.5 °Cuntil a constant mass could be obtained (about 24 h), ground in acryogenic grinder (−195 °C) and stored at −18 °C.

Fig. 1. Standardization of muscle δ13C in Nile tilapia fry submitted to treatments 1 (C3expression.

The 13C/12C ratio was measured using a mass spectrometer ofthe DELTA S type (Finningan Mat) coupled to an EA 1108 CHNElementar Analyzer. Values were expressed in δ13C notation andcalculated by δ13C=[(Rsample /Rstandard)−1]×103, where δ13C isthe enrichment of the sample in relation to the PeeDee Belmnitestandard (PDB) and R is the isotopic ratio 13C/12C of the sampleand of the standard. The instrumental precision was 0.2‰.

2.4. Muscle δ13C change

The muscle δ13C change process has been assessed by thegeneric expression presented by Ducatti et al. (2002), as afunction of a new diet intake time. This model has beenoriginally proposed to assess carbon turnover in adult animals,and is described by the following exponential model:

d13CðtiÞ ¼qkþ y0−

qk

� �exp −ktið Þ þ ei ð2Þ

Where: δ13C(ti) =carbon isotopic abundance in the tissue atany time i, in‰; y0= initial carbon isotopic abundance in thetissue (before diet change), in ‰; q=carbon compoundentrance rate in the tissue, in day−1; k=carbon turnover ratein the tissue, in day−1; ti = time in days; ei=error associated toeach observation i; and q/k=asymptotic of the expression, thatrepresents the δ13C value to reached in a infinite time of feedingwith the same diet, in ‰.

–C4) (A) and 2 (C4–C3) (B), n=24. Dotted line represents the asymptote of the

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However, in the present study, the constant k represents theδ13C change rate. In growing animals, the δ13C change rateincludes the effects of tissue mass increase (growth) that shouldreflect the isotopic composition of the new diet (Hesslein et al.,1993) and the metabolic turnover.

To verify the establishment of carbon isotopic equilibrium,the simulation technique by Parametric Bootstrap (Efron, 1979)was used with the following steps:

(A) The regression model was fitted to the data set, obtainingthe estimate of the vector of the θ, parameter, or b� so thatθ=[k, q, y0] and the residual variance (�e

2);(B) 10,000 repetitions of the variable response δ13C were

generated from the regression model defined in (2), usingb�in the deterministic component and generating normalrandom variables for error (random component) consider-ing the values of time ti of the original sample (Ratkoswsky,1983):

d13C ðtÞij ¼q

kþ y0−

q

k

� �exp −ktij� �þ eij;

where: the j index refers to the repetitions ( j=1 until10,000) and the i index refers to time within each sample(i=1 until 89);

(C) The regression model was fitted for each one of the10,000 samples generated, obtaining new vector esti-mates of parameter θ that is b� so that θj= ⌊kj, qj, y0j⌋;

(D) A time data value (tw) was chosen to start the search forstabilization of the process. For each one of the j-ethsamples the values were obtained from the randomvariable Δ, defined as being the difference between theasymptotic value obtained previously in A and the valuesof the function for the time tw, that is:

Dj ¼ q

k−

qj

kjþ y0j−

qj

kj

!exp −kjtw� �" #

;

(E) Histograms and the corresponding empirical confidenceintervals of 90%were obtained for the random variableΔ,based on sample percentages of 5% and 95%;

(F) The first value for time tw where the approximateconfidence interval contained the zero value representedthe time when the tissue δ13C value no longer differedfrom the estimated asymptotic, indicating the timenecessary to establish the carbon isotopic equilibrium(stabilization time).

The tissue carbon half-life derived from the previous feedingwas calculated by the expression quoted by Ducatti et al. (2002):T=1n 2/k where: T is the time (days) to reach the condition inwhich 50% of tissue carbon is derived from the previous isotopicsource (old diet) and 50% from the new isotopic source (new diet).

Based on the development of the model proposed by Ducattiet al. (2002) for adult animals, we developed a model similar tothat proposed by Hesslein et al. (1993) for growing animals that

express the δ13C change pattern as a result of growth andmetabolic turnover, and also considers the entry of carboncompounds rate in the tissue:

d13CðtÞ ¼q

ðmþ gÞ þ Y0−q

ðmþ gÞ�

exp − mþ gð Þt½ � ð3Þ

where: m=tissue δ13C change rate derived from the turnover, inday−1; g=tissue δ13C change rate derived from growth, inday−1; and q/(m+g) = asymptotic of the expression, thatrepresents the δ13C value to be reached in an infinite time offeeding with the same diet, in ‰.

The model proposed by Fry and Arnold (1982) was used toassess the muscle δ13C change as a function of the increase inbody mass:

d13CðWtÞ ¼ df þ di−df� � Wt

Wi

� �c

ð4Þ

where: δ13C(Wt)=carbon isotopic abundance in the tissue duringgrowth, in ‰; δi= initial carbon isotopic abundance of the tissue(before diet change), in ‰; δf=carbon isotopic abundance afterestablishing the carbon isotopic equilibrium in the tissue (afterdiet change), in ‰; wi= initial body mass, in grams; wt=bodymass at collection, in grams; and c=tissue δ13C change rate thatincludes turnover and growth.

2.5. Statistical analyses

Parameters of productive performance of fish (final mass,mass gain, apparent food intake, apparent food conversion,standard length and specific growth rate) were compared byanalysis of variance using the GLM procedure with SASsoftware (1997). Muscle δ13C change was analyzed using theNLIN procedure of the SAS software (1997).

3. Results

3.1. Productive performance

No significant differences were observed between treatmentsfor final mass, mass gain, standard length, apparent food intake,apparent food conversion and specific growth rate (Table 2).

3.2. Muscle δ13C change

Using themodel presented byDucatti et al. (2002),δ13C results ofthe pre-experimental stage of fish that received the C3 diet (treatment1) followed the expression: δ13C(t)=−23.63+2.21exp–0.0643t withstabilization time equal to 52.5 days. For Treatment 2, fish receivingthe C4 diet, the expression obtainedwas δ13C(t)=−15.33−3.59exp–0.0471t with stabilization time equal to 66.5 days (Fig. 1). Thefollowing expressions were obtained in the second experimentalstage: δ13C=− 16.36−7.21exp–0.0297t, with half-life (T) equaling23.33 days and stabilization time equaling 120 days for treatment 1(C3–C4), and δ13C = − 23.80 + 9.12exp–0.0267t, with

Fig. 2. Muscle δ13C change in juvenile Nile tilapia submitted to treatments 1 (C3–C4) (A) and 2 (C4–C3) (B), n=51. Solid line corresponds to the change in muscleδ13C as a function of growth and metabolic turnover together, obtained by the model presented by Ducatti et al. (2002). Dashed line corresponds to the muscle δ13Cchange as a function of growth alone, obtained by the model adapted from Hesslein et al. (1993). Dotted line represents the asymptote of the expressions.

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T=25.96 days and stabilization time equal to 120 days for treatment2 (C4–C3) (Fig. 2).

The use of the model adapted from Hesslein et al. (1993) toassess the muscle δ13C change fitted both treatments well. Theexpression obtained for treatment 1 (C3–C4) was δ13C=−16.36−7.21exp− (0.0034+0.0263)t and for treatment 2 (C4–C3) was δ13C=−23.80+9.12exp− (0.0013+0.0254)t (Fig. 2).

In the present study, the assessment of the muscle δ13C data as afunction of increases in bodymass (Fry andArnold, 1982model) didnot produce reliable results, since δf values were not compatible toδ13C values from C4 and C3 diets (δ13C(wt)=553,786−553,808.21(Wt/Wi)

−0.00000551 and δ13C(wt) =−675,683+675,666.46(Wt/Wi)

−0.00000527, respectively).

4. Discussion

4.1. Productive performance

Findings of productive performance were as expected, sinceall fish in both treatments were submitted to the same feedmanagement, with diets formulated to be similar in protein,energy, fiber and fat content. Thus, fish were expected tometabolize these diets with the same efficiency, while pre-senting differences in the 13C/12C ratios only.

4.2. Muscle δ13C change

The model proposed by Ducatti et al. (2002) was adequatefor growing animals, because the δ13C change rate (k) obtainedintegrates the effect of the addition of new tissue (growth) andthe metabolic turnover. Cruz (2002), who worked with growingpoultry, and Furuya et al. (2002), studying juvenile specimensof a catfish (Pseudoplatystoma corruscans) also obtainedsimilar results.

During the pre-experimental stage, we observed a largervariation in δ13C at one sample time. These probably havehappened due to the amount of diet consumed, because fishwere fed in groups. The increase in δ13C on day 75 for C3 groupmight have happened due to the same problem. However, theresults of the stabilization time in the pre-experimental stageshowed that 75 days of feeding were sufficient to prepare thefish for the assessment of muscle δ13C change, when the tissueδ13C had already reached the carbon isotopic equilibrium.

Expressions of muscle δ13C changes obtained by Ducatti et al.(2002) model were coherent with fish productive performancefindings, which do not differ among treatments. As growth is thepreponderant factor in the tissue isotopic change rate (Hessleinet al., 1993; Maruyama et al., 2001; Tominaga et al., 2003), it wasexpected that muscle δ13C change rate would also be similar

106 J.A.S. Zuanon et al. / Comparative Biochemistry and Physiology, Part B 145 (2006) 101–107

between treatments, as the muscle carbon half-lives valuesindicated. The stabilization time for muscle δ13C equal to120 days for both treatments confirms the results for δ13C changeand productive performance.

Results for muscle δ13C change rate (g) derived from growth(0.0263 day−1 and 0.0254 day−1), using the model adapted fromHesslein et al. (1993) were greater than those derived fromturnover (m=0.0034 day−1 and 0.0013 day−1) and are in linewithFry and Arnold (1982), Hesslein et al. (1993) and Herzka et al.(2001), who stated that the tissue mass increase resulting fromgrowth is the main factor in determining the isotopic change rateof tissue carbon in young animals. Vander Zanden et al. (1998)have observed that 86% of change in δ15N of juvenile smallmouthbass, Micropterus dolomieu was explained by the accretion ofnew tissue (growth). These findings are similar to those observedin this study (91.84±4.65%).

In the present study, the muscle δ13C change rates derivedfrom growth (g) and from the metabolic turnover (m) wereobtained by fitting observed δ13C data, by interactive searchesfor these parameters, using the NLIN procedure in SAS (SAS,1997). However, Hesslein et al. (1993) and Sakano et al. (2005)have calculated the mean growth rate taking the values of fishbody mass at collection as a function of time, and obtained themetabolic turnover change rate by δ13C data fit. Growth ratesobtained here by fit of fish mass data as a function of time,0.0180 day−1 for treatment 1 and 0.0179 day−1 for treatment 2,were different from isotopic change rates derived from growthobserved by fit of muscle δ13C values (0.0263 day−1 and0.0254 day−1). This suggests that body growth rates cannot beused as element isotopic change rates (carbon, nitrogen, etc.) intissues of growing fish, possibly because they are not elementmass in tissues, but rather a total mass of the organismconsisting of various elements mixture.

Fry and Arnold (1982) stated that slower growth rates shouldproduce high turnover rates. The authors argued that this is thebase of the turnover studies in adult animals, as turnover isobserved when there is no growth. However, in these studies, thegrowth stage is avoided to prevent errors in interpretation, sinceturnover occurs with or without growth (Jardine et al., 2003) andshould be the function of genetic and environmental factors. Onthe other hand, Herzka et al. (2001) expect that fast growing fishshould present higher turnover rates because they have highmetabolic rates.

By comparing half-life values or δ13C change rates amongdifferent tissues in the same species or one tissue among differentspecies we might presume the tissues relative metabolic activity.The δ13C change rates derived from metabolic turnover (m) andderived from growth (g) are both consideredmore appropriated toevaluate the nutrient utilization from the diet. The observedincreased values on tissue δ13C change rate derived frommetabolic turnover (m) in fish fed C4 diet show a highercatabolism activity than in those fed on C3 diet, since the tissuedegradation rate is equal to the metabolic turnover in growinganimals (Weisner and Zak, 1991).

From muscle δ13C change rate (growth+turnover) of Corego-nus nasus, reported by Hesslein et al. (1993), a half-life of101.93 days can be expected for muscle carbon. This value is

different from those obtained in this study with Nile tilapia fry(23.33 and 25.96 days). According to Fauconneau (1985),interspecific variation in the muscle protein synthesis could beexplained by differences in the rearing temperature and in thegrowth rates. As temperature influences the general metabolism infish and growth results mainly from protein addition, but also fromother carbon compounds (lipids, nucleic acids etc), the interspecificvariation in the muscle δ13C change process can probably also beexplained by the same factors.

Hesslein et al. (1993)speculated that isotopic differences amongindividuals in groups of fast-growing fish exposed to a change inisotope compositions in their diets could be due to different growthrates. Thus, the increased scattering observed in muscle δ13C at theend of the experimental period could be attributed to individualdifferences in growth rates that only become evident as smalldifferences in muscle tissue have been accumulated through time.

Tominaga et al. (2003) have studied the relation between therelative growth of otolith and δ13C in dorsal muscles ofindividual juvenile Japanese flounders (Paralichthys olivaceus)at 14 days after the diet shift. The regression line between bothvariables was significant (R=0.83; Pb0.001), and δ13C changewas found to be larger for fish with a rapid growth rate. Theauthors also observed that the δ13C change rate in dorsal muscleof fish fed on 4.4% BW/day was larger (0.05) than observed infish fed on 2.2% BW/day (0.04). These results show that δ13Cchange rate could directly reflect the daily ration and growthrate. Therefore, the isotopic change rates of carbon and othertissue elements can be properly used to assess the diet-nutrientefficiency retention and growth rates of different lineages offish, or even the effect of energy/protein ratio, growthpromoters, environmental, and other factors that may interferein growth.

Acknowledgement

This study was carried out at the Laboratory of AquaticOrganisms Nutrition-AquaNutri, of the São Paulo StateUniversity (UNESP), Botucatu, São Paulo, Brazil, unitintegrated into the Aquaculture Center of UNESP-CAUNESPand supported by Environmental Stable Isotopes Center,auxiliary unit of the Biology Institute of UNESP, Botucatu,São Paulo, Brazil. We are thankful to the Federal University ofViçosa for issuing the license for the 1st author's Doctorate,which resulted in this study as part of the thesis, and to the“Coordenação de Aperfeiçoamento de Pessoal de Nível Su-perior” (CAPES) for the financial support.

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