RESEARCH ARTICLE
Rela ionship be ween weigh and linea
dimensions o Blue in una (Thunnus hynnus)
ollowing a ening on wes e n Medi e anean
a ms
Vicen e Puig-Pons
1
*, Vicen e Domingo Es uch
1
, Vı
´c o Espinosa
1
, Fe nando de la
Ga
´nda a
2
, Begonya Melich
3
, Jose
´Luis Co
4
1Ins i u d’In es igacio
´pe a la Ges io
´In eg ada de Zones Cos ane es, Uni e si a Poli ècnica de València,
G au de Gandia (Valencia), Spain, 2Ins i u o Español de Oceanog a ı
´a, Cen o Oceanog a
´ ico de Mu cia.
Plan a de Cul i os Ma inos, Pue o de Maza o
´n (Mu cia), Spain, 3G up Bal ego
´, L’Ame lla de Ma
(Ta agona), Spain, 4Fishe ies A ea, Ins i u o Español de Oceanog a ı
´a, Cen o Oceanog a
´ ico de
San ande , San ande (Can ab ia), Spain
*[email p o ec ed].es
Abs ac
This s udy p esen s a ious models based on o mulae ela ing weigh and dimensions
(leng h, heigh and wid h) o Blue in una, Thunnus hynnus (L.), a ened in cap i i y. The
main aim o es ablishing hese exp essions is o design ools o indi ec ly p edic ing he
weigh o a Blue in una om measu emen s o one o mo e dimensions ob ained using non-
in asi e me hods such as s e eoscopic came as. Measu emen s o maximum leng h, heigh
and wid h ollowing slaugh e we e aken o ish a ened in cap i i y (n = 2078). Di e en
ela ionships d awn om he dimensions o he una agains hei weigh a e i ed wi h pa
o he da a collec ion and la e checked agains a ese ed sample se . The esul ing o mu-
lae a e compa ed wi h he o mulae mos commonly used in he case o wild una. The
esul s o his s udy con i m ha , o una a ened in cages, he a ailabili y o mo e han one
dimension o es ima e weigh imp o es he p edic i e powe o he model and educes e o
in he es ima e.
In oduc ion
A lan ic Blue in Tuna—ABFT- is a highly mig a o y species. The In e na ional Commission
o he Conse a ion o A lan ic Tunas (ICCAT) is esponsible o managing ABFT, and as
pa o he managemen o his species, ICCAT spli he s ock managemen uni s in o wo
pa s, Wes s ock and Eas s ock (which includes he Medi e anean). The bounda y be ween
he wo s ocks is de ined as he 45˚ W me idian, hough in eali y high a es o mixing ha e
been ound, which a y om one yea o ano he [1,2]. Tuna a ming based on adul cap u e
in b eeding a eas has ecen ly been de eloped. In he Medi e anean Sea, ABFT is ished om
May o July by a pu se-seining lee . A e cap u e, una a e ans e ed in o owing cages (usu-
ally ci cula wi h a 50 m diame e ) and anspo ed o pe manen cages nea he coas . T ans-
po may ake se e al weeks because o dec ease s ess and mo ali ies una a e anspo ed a
PLOS ONE | h ps://doi.o g/10.1371/jou nal.pone.0200406 July 10, 2018 1 / 13
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OPEN ACCESS
Ci a ion: Puig-Pons V, Es uch VD, Espinosa V, de
la Ga
´nda a F, Melich B, Co JL (2018) Rela ionship
be ween weigh and linea dimensions o Blue in
una (Thunnus hynnus) ollowing a ening on
wes e n Medi e anean a ms. PLoS ONE 13(7):
e0200406. h ps://doi.o g/10.1371/jou nal.
pone.0200406
Edi o : Ma hew Lau e a, Na ional Oceanic and
A mosphe ic Adminis a ion, UNITED STATES
Recei ed: June 13, 2017
Accep ed: June 26, 2018
Published: July 10, 2018
Copy igh : ©2018 Puig-Pons e al. This is an open
access a icle dis ibu ed unde he e ms o he
C ea i e Commons A ibu ion License, which
pe mi s un es ic ed use, dis ibu ion, and
ep oduc ion in any medium, p o ided he o iginal
au ho and sou ce a e c edi ed.
Da a A ailabili y S a emen : All xls iles a e
a ailable om he Ins i u o Español de
Oceanog a ı
´a da abase (h p://www. eposi o io.ieo.
es/e-ieo/bi s eam/handle/10508/10901/A ailable_
da a_VPuig_e al.xlsx?sequence=1&isAllowed=y).
Funding: This wo k was suppo ed by unding
om ACUSTUNA p ojec e . CTM2015-70446-R
(MINECO/ERDF, EU). The au ho s a e g a e ul o
he suppo p o ided by G up Bal ego
´. The unde s
had no ole in s udy design, da a collec ion and
e y low speed (1 kno ) [3,4]. Once he owing cage a i es a he ish a m, una a e ans-
e ed o he a ening cages and an e o is made o assess he biomass. As a ule, aquacul u e
a ms ca y ou manual sampling o ob ain mean weigh da a, howe e , in he case o ABFT
hese samplings a e e y cos ly and equi e e y di icul manoeu e s ha g ea ly s ess he ish
and lead o unwan ed dea hs. Fo his eason, samplings a e usually made wi h sys ems using
s e eoscopic came as, which p o ide eco dings o he ish om he side in a non-in asi e way
[5,6,7,8]. These eco dings pe mi ish leng hs o be e alua ed by measu ing hem om each
pai o s e eoscopic images. F om his in o ma ion, ma hema ical ela ionships a e applied o
es ima e weigh . ICCAT has es ablished his p ocedu e as an obliga o y measu emen o
ca ches aken by pu se seine s des ined o a ening in cages, wi h implemen a ion o ake
place du ing he p ocess o ans e ing una o he a ening cages [9]. In addi ion o leng h,
some o hese s e eoscopic sys ems pe mi maximum ish heigh o be used in he es ima ion
o weigh [10].
Fo a ming pu poses, ABFT a e housed in a ening cages ypically loca ed in close p ox-
imi y o he sho e. A a ge densi y in hese cages is 6 kg ish/m3 [4,11]. Fa ening pe iod in
he Medi e anean sea uns om July o Feb ua y, du ing he a ening pe iod ABFT a e ed a
a ie y o de os ed small pelagic ish (depending on a ailabili y and p ice): sa dinelle (Sa di-
nella au i a), pilcha d (Sa dina pilcha dus), he ing (Clupea ha engus), macke el (Scombe
scomb us), ho se macke el (T achu us sp.), chub macke el (Scombe japonicus), bogue
(Boops boops), and some cephalopods [12]. Usually ish a e o e ed 1–3 daily meals bu i may
inc ease u he (a ound six imes pe day) depending on wa e empe a u e, una size and
ish eeding esponses. Due o he a ming p ocedu e, ABFT mo phome ics a e modi ied. Fo
his eason, he use o biome ic ela ionships o wild ish o es ima e caged ish weigh s, o e a
me e app oxima ion a bes . Mo eo e , he p esence o la ge and small una in he caged ish
causes inaccu a e weigh es ima ions [4,13,14].
Puig e al. (2012) [15] p oposed he measu emen o una size om he en al pe spec i e
wi h a pai o s e eoscopic came as, s udying he co ela ion o ish leng h wi h measu emen s
o i s acous ical a ge s eng h. In ha expe imen , a synch onized sys em was se up in ol ing
a scien i ic echosounde and a pai o s e eoscopic came as placed in he bo om o he cage and
di ec ed upwa ds o collec images om unde nea h, unlike he usual con igu a ion in which
la e al images a e aken. This con igu a ion p o ides g ea e quali y images when isibili y is
poo , and has ecen ly been used o ob ain au oma ically accu a e leng h measu emen s using
s e eoscopic came as eco ding en al pe spec i e o una [16]. In ha s udy, a de o mable
model o he ish en al silhoue e was de eloped o measu e leng h and maximum wid h in a
pai o images. Va ia ion o maximum wid h was p oposed o moni o a ening p ocesses.
Ha ing new biome ic ela ionships in ol ing hese dimensions may acili a e a deepe unde -
s anding o he a ening p ocess o cap u ed una in a ms, bu also a be e de ini ion o he
physiological condi ion o wild una om biome ics. The alidi y o a speci ic equa ion ela ing
weigh and leng h o ABFT, depending on physiological condi ion associa ed o di e en ac-
o s (geog aphical loca ion, season, spawning pe iod, e c) has been a ma e o con o e sy
[17,18]. The idea o conside ing o he dimensions in addi ion o leng h is no new, since con-
e sion equa ions including leng h and heigh ha e been in oduced be o e [10]. Ne e heless i
is he i s ime o ou knowledge ha h ee dimensions ha e been conside ed wi h he objec i e
o educing es ima e e o . This s udy examines he ela ionships be ween weigh and di e en
biome ic measu emen s: leng h, maximum heigh and maximum wid h o una using s a is i-
cally signi ican i s wi h clea p edic i e alue. I is hoped he esul s will complemen he
knowledge om exis ing s udies cen e ed on ela ing ABFT weigh and leng h, which ha e no
p e iously conside ed any o he dimension o ish. The esul s could be o g ea ele ance in he
de ini ion o u u e ca ch con ol p ocedu es in di e en ishe ies and species.
Rela ionship be ween weigh and dimensions o Blue in una ollowing a ening on wes e n Medi e anean a ms
PLOS ONE | h ps://doi.o g/10.1371/jou nal.pone.0200406 July 10, 2018 2 / 13
analysis, decision o publish, o p epa a ion o he
manusc ip .
Compe ing in e es s: The au ho s ha e decla ed
ha no compe ing in e es s exis .
Ma e ial and me hods
Biome ic da a om una a ening we e p o ided by G up Bal ego
´. Da a we e aken a e una
ha es a a G up Bal ego
´ a m o he coas o l´Ame lla de Ma in Ta agona (Spain, 4˚052’11.7”
N and 0˚48’15.2” E). These biome ics we e ob ained in 2012 and 2013 and p o ided in o ma ion
om n = 2078 una. The in o ma ion included da a on leng h, g oss weigh , heigh and sex. Sizes
a y be ween 126 and 273 cm in leng h wi h a e age leng h o 207.17±17.61 cm (and a median o
207 cm). G oss weigh oscilla es be ween 46.29 and 457.14 kg wi h a mean alue o 197.44±54.76
Kg (191.65 kg median). Heigh measu emen s we e aken o all samples ob aining a ange o al-
ues be ween 33 and 79 cm (56.5±5.72 cm a e age alue). Fu he mo e, o 1067 o hese ish he
maximum wid h was known, wi h maximum wid h anging be ween 25 and 62 cm and an a e -
age alue o 43.27±6.74 cm.
A maximum leng h (Lmax) o ABFT o 331.2 cm (Lmax = 319.93±11.3 cm), es ablished by
he mos ecen ly published s udies, was applied as indica ed in he pape by Co e al. (2013)
[19]. Thus, he da a we e il e ed o elimina e all ishes whose leng hs exceeded he ex emal
alue, wi h he aim o ob aining a ep esen a i e and ealis ic popula ion sample and p e en -
ing undesi able e ec s on he end esul s due o ou lie s.
Using he il e ed da a, leas -squa es i ing was pe o med aking in o accoun di e se
ma hema ical models whose exp essions conside di e en ish dimensions o be p edic o
a iables. Thus, we ob ained ela ionships o he weigh o one o mo e dimensions conside -
ing heigh , leng h and maximum wid h. Wi h he aim o inding and e i ying ela ionships
be ween una linea dimensions, o he exp essions ela ing heigh o leng h and maximum
wid h o leng h we e also s udied. The equa ions o he ob ained biome ic models a e shown
in Tables 1and 2.
Table 1 shows models (M1-M13) whe e he independen a iable is weigh (W). Models
M1 and M2 es ablish ela ionships be ween weigh and leng h (L) and heigh (H) o he ishes.
Models M3, M4, M5 and M6 ela e weigh wi h L and maximum wid h (A). Models M7, M8,
M9, M10, and M11 ela e weigh o he h ee dimensions o he ishes: L, H A. Finally, models
M12 and M13 ela e weigh wi h L and A espec i ely, as usual. Models M6, M7 and M13 a e
di ec ly linea as a unc ion o he ans o ma ions o he p edic i e a iables.
Table 1. Model iden i ie , equa ion o he p oposed models, and equa ion o he linea ised models and pa ame e s o calcula e.
Model iden i ie Equa ion Linea ised equa ion Pa ame e s
M1 W¼aL2H—a
M2 W¼aðLþHÞblogeðWÞ ¼ aþblogeðLþHÞa,b
M3 W¼aLbAlogeðWÞ logeðAÞ ¼ aþblogeðLÞa,b
M4 W¼aLAblogeðWÞ logeðLÞ ¼ aþblogeðAÞa,b
M5 W¼aðLþAÞblogeðWÞ ¼ aþblogeðLþAÞa,b
M6 W¼aL2:06 A—a
M7 W¼aLHA—a
M8 W¼aðLHAÞblogeðWÞ ¼ aþblogeðLHAÞa,b
M9 W¼aðLþHþAÞblogeðWÞ ¼ aþblogeðLþHþAÞa,b
M10 W¼aLHbAclogeðWÞ logeðLÞ ¼ aþblogeðHÞþclogeðAÞa,b,c
M11 W¼aLbHcAdlogeðWÞ ¼ aþblogeðLÞþclogeðHÞþdlogeðAÞa,b,c,d
M12 W¼aLblogeðWÞ ¼ aþblogeðLÞa,b
M13 W¼aA3—a
In all cases α= log
e
(a)
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Table 2 shows wo models conside ed o es ablish ela ionships be ween una dimensions,
heigh depending on leng h and maximum wid h (M14) and maximum wid h depending on
leng h (M15). To explo e he alidi y o all hese models, i s we e es ed using he da a sup-
plied by G up Bal ego
´.
To alida e he models ob ained om he i s, 500 andomly chosen indi iduals we e
ese ed a he s a o he s udy. The i s we e made using he da a co esponding o he
emaining indi iduals. The i o he linea ised models was made wi h he help o S a aphics
CENTURION XVI so wa e [20]
All he models conside ed can be linea ised and o a oid compu ing p oblems he i s we e
made using he models once linea ised. To de e mine whe he each o he models conside ed
was s a is ically signi ican , he F-s a is ic was calcula ed, which makes i possible o es he
hypo hesis ha he coe icien o de e mina ion, R
2
, is no equal o ze o, and he e o e he
model p o ides a s a is ically signi ican explana ion (p- alue<0.05) o he ela ionship
be ween a iables. The non-linea deg ee-o - eedom adjus ed (R
2
(d )) allows e alua ion o
he a iabili y o he dependen a iable explained by he model.
A e i ing each model, he deg ee-o - eedom adjus ed coe icien o de e mina ion and
he F-s a is ic alue(which enables he calcula ion o p- alue) we e compu ed. These indica o s
we e calcula ed on he linea ised models, and a e sui able o e alua ing he alidi y o each
model sepa a ely, bu hey canno de e mine he mos sui able model because he linea isa ion
p o ides non-compa able exp essions.
When alida ing he models, he one p oposed in [21] was also conside ed al hough his
model is used o es ima e weigh om leng h in wild ish.
Weigh was es ima ed using he di e en exp essions, and he alidi y o he models was
e alua ed by analysing he di e ence be ween he eal weigh alue and he weigh alue es i-
ma ed by each o he models. Goodness o i was analyzed wi h he non-linea deg ee-o - ee-
dom adjus ed coe icien o de e mina ion R
2
(d ):
R2¼1Piðp ipmiÞ2
Piðp i
p Þ2ð1Þ
R2ðd: :Þ ¼ R2 ð1R2Þp1
npð2Þ
whe e p is he eal weigh , pm is he es ima ed weigh , p is eal mean weigh , p is he num-
be o explana o y a iables and n is he sample size.
Mean absolu e e o was also calcula ed (Eam):
Eam ¼Pjp ipmij
nKg ð3Þ
Table 2. Models p oposed o he calcula ion o heigh om leng h and wid h, and he ela ionship be ween leng h and maximum wid h. The linea ised equa ion is
p esen ed o making he linea i using he leas squa es me hod.
Iden i ie o models Equa ion Linea ised equa ion Pa ame e s
M14 H¼ ðLAÞblogeðHÞ ¼ blogeðLAÞb
M15 A¼aL— a
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he s anda d e o o he absolu e e o s (eEa):
eEa ¼s anda d de ia ion o he absolu e e o s
i i in
pð4Þ
he mean o ela i e e o s (E m):
E m ¼Pjp ipmij
pmi
nð5Þ
and he s anda d e o o he ela i e e o s (e
E
)
eE ¼s anda d de ia ion o he ela i e e o s
i i in
pð6Þ
To e alua e whe he he p edic ions o he abo e exp essions and hose used o wild ishes
unde o o e es ima e weigh , he mean alue o he esiduals was calcula ed ( esm):
esm ¼Pp pm
nð7Þ
To es ablish whe he he e a e s a is ically signi ican di e ences be ween he p edic i e
powe o he di e en models, ANOVA analysis [22] was pe o med on mean absolu e e o ,
mean ela i e e o and mean o he esiduals, conside ing he model as a ac o in he h ee
cases. The mul iple ange es e ealed he models be ween which s a is ically signi ican di e -
ences a e de ec ed (p- alue<0.05).
Resul s
The esul s o he i o he di e en models conside ed, ob ained om he da a acili a ed by
G up Bal ego
´a e ha es ing una a ened a hei ins alla ions in 2012 and 2013, a e shown
in Table 3. The able (Table 3) con ains he alues o he pa ame e s calcula ed o each model.
The alues o R
2
(d. .) co espond o he linea ised models and so hey a e no mu ually compa-
able. The able also includes he deg ees o eedom o each model and he alue o F, which is
Table 3. Coe icien s and alues o R
2
( i ed o deg ees o eedom o each i ). All wi h a p- alue unde 0.05.
models R
2
(d. .) a B c d d F
M1 99.73 8.0563610–5 — — — 1 215961.39
M2 95.14 4.5610–6 3.15114 — — 1 11102.06
M3 97.24 7.2171910–5 2.07092 — — 1 2086.06
M4 62.40 7.5788810–5 1.28121 — — 1 937.82
M5 89.19 1.4598510–5 2.96853 — — 1 4662.33
M6 97.25 7.4531310–5 — — — 1 20047.43
M7 97.23 3.731310–4 — — — 1 19909.76
M8 90.74 1.5605710–4 0.916383 — — 1 5555.33
M9 92.05 7.808510–6 2.97397 — — 1 6558.30
M10 91.08 4.958410–5 1.74506 0.133815 — 2 2892.20
M11 95.99 1.077510–5 1.67757 1.26742 0.091396 3 4515.77
M12 92.70 7.2167910–6 3.20805 1 7178.54
M13 99.00 2.51296110–3 — — — 1 4857921.92
M14 99.98 — 0.443762 1 56262.90
M15 97.28 0.209187 — — — 1 20362.75
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used o calcula e he p- alue associa ed wi h he es o check whe he he model is s a is ically
signi ican (R
2
(d. .) 6¼0). The esul s indica e ha , in all cases he models a e s a is ically signi -
ican o a con idence le el o 95%.
Valida ion o he models wi h he ese ed da a also in ol ed he calcula ion o se e al indi-
ca o s: he non-linea coe icien o de e mina ion i ed o deg ees o eedom, mean absolu e
e o , mean ela i e e o and hei co esponding s anda d e o s, and las ly he mean alue
o he esiduals. This las indica o es ablishes whe he he es ima ed alues adap o he alues
obse ed o , i no , whe he hey unde o o e es ima e hese alues (Table 4). Table 4 is com-
ple ed wi h he esul s o a e e ence model o he ela ionships be ween una leng h and
weigh published ecen ly. The model p oposed in [21] is a conc e ion o Eq (8) and has he
coe icien s a = 0.0000287 and b = 2.9076 [21].
W¼aLbð8Þ
Table 4 shows he goodness o i indica o s ha ela e weigh o one o mo e han one
dimension o una. Fig 1 shows he cu es o all he i s conside ed o be a single dimension o
es ima ing weigh : he model in [21] and models M12 and M13 p esen ed in his s udy.
Fig 2 shows he obse ed alues agains he p edic ed alues wi h he i made by all he
models ela ing weigh and a leas wo una dimensions (L, H and A).
The compa a i e analysis o models ela ing weigh wi h ish dimensions was comple ed
wi h he esul s o he ANOVA un on mean absolu e e o , mean ela i e e o and mean o
he esiduals, co esponding o he di e en models analyzed (Tables 5–7). To es ablish he
homogenei y o he g oups Fishe ’s LSD me hod was used, wi h a 95% con idence in e al.
Ob aining biome ic da a o una in he wild is complica ed. Ne e heless, when he ishes
a e held in cages o a ening he da a can be ob ained using di e en echniques. Some o
hem ha e been es ed and alida ed o his species such as, o example, s e eoscopic ision
sys ems [5,6,7,10,16]. Table 8 summa izes he goodness o i indica o s used o alida e he
models ela ing heigh o leng h, and maximum wid h, and leng h o maximum wid h. Tables
4and 8also include he mean alue o he esiduals.
To comple e he ep esen a ion o he esul s, Fig 3 shows he g aphs o obse ed alues e -
sus p edic ed alues o models M14 and M15.
Table 4. Values o he pa ame e s de ining he goodness o i , which ela e weigh o una dimensions; calcula ed om he da a ese ed o he alida ion.
Model R
2
(d. .) Eam (kg) e-Eam(kg) E m (%) e-E m (%) Resm (Kg)
Degua a e al (2016) 24.31 42.30 0.91 25.68 0.43 42.11
M1 95.17 8.77 0.36 4.57 0.21 0.16
M2 94.94 9.41 0.34 4.85 0.19 0.95
M3 94.98 9.36 0.34 4.88 0.18 1.88
M4 88.04 14.84 0.51 7.43 0.23 4.73
M5 93.19 11.47 0.37 5.99 0.19 7.08
M6 93.66 10.84 0.37 5.51 0.19 2.49
M7 93.19 10.88 0.40 5.93 0.25 7.76
M8 95.21 9.23 0.33 4.74 0.17 2.04
M9 94.58 9.11 0.39 4.70 0.22 2.36
M10 94.16 8.44 0.44 4.56 0.32 1.04
M11 95.26 8.24 0.38 4.36 0.24 0.92
M12 86.27 15.19 0.58 7.17 0.26 -13.05
M13 87.60 13.31 0.61 6.36 0.30 -4.24
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Discussion
Table 4 shows he alues o he goodness o i indica o s ha ela e weigh wi h one o mo e
han one dimension o he una. The esul s indica e ha he a ailabili y o a ened una heigh
o wid h imp o es he p edic i e powe o he models, gi en ha he alues o he coe icien o
de e mina ion inc ease a he same ime as bo h mean absolu e e o and mean ela i e e o
dec ease. The same hing happens i we conside he h ee dimensions (leng h, heigh and
wid h). In he case o conside ing maximum wid h and leng h, coe icien o de e mina ion al-
ues a e sligh ly lowe bu so a e he co esponding mean absolu e e o and mean ela i e e o
alues in ela ion o hose ob ained when jus one dimension is used in he model. Model 13
(M13) p o ides a good i be ween una weigh and maximum wid h. Re iewing he goodness
o i alues shows low absolu e e o s and low ela i e e o s, compa able wi h hose ob ained
when conside ing leng h as he only dimension in he i .
I we look a Table 5, showing he ANOVA analysis on mean absolu e e o alues o all
he i ed models and hose o e e ence [21], i can be seen ha he in oduc ion o mo e han
one dimension in he i educes he mean absolu e e o alue. Clea ly he in oduc ion o
h ee dimensions p o ides he lowes absolu e e o s (as is he case o M10 and M11). The
same able shows how models M11, M10, M1, M8, M9, M3 and M2 p o ide absolu e e o s
lowe han 10 Kg. I we look a Table.6, which p esen s he alues o he ANOVA analysis on
Fig 1. G aph o he i ed model M12, and he e e ence model o Degua a e al. (2016). G aph o he i ed model
M13 (bo om).
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he ela i e e o s, we can see ha hese same models (M11, M10, M1, M8, M9, M3 and M2)
gi e weigh es ima es wi h e o s o less han 5%, accep able alues in he same ange as hose
o e ed by indi ec sys ems o leng h es ima ion such as hose in ol ing s e eoscopic came as
[5,6,7]. Fu he mo e, bo h in he Tables 5and 6is con i med ha using a single dimension
inc eases e o in he p edic ion o weigh , hough i should be poin ed ou ha using he max-
imum wid h ins ead o leng h does no signi ican ly inc ease he e o , as e ealed by he mean
absolu e and ela i e e o alues o M12, M13 and he e e ence model o [21]. Ne e heless,
i is e y impo an o emembe ha he e e ence model [21] was ob ained o he weigh o
wild ishes, usually be o e o du ing he spawn, a he han ishes la e caugh and a ened in
cap i i y. In addi ion, i is mo e han plausible o assume ha , in he case o wild ishes, leng h
is he mos de e minan dimension o p edic ing weigh . Fu he mo e, in ishes a ened in
cap i i y, dimensions a e a ec ed by li e condi ions, such ha he emaining dimensions, in
pa icula wid h, gain ele ance as p edic i e a iables o weigh .
In he same way, Table 7 e lec s he esul o he ANOVA analysis o he mean alue o he
esiduals. In his case as in he p e ious ones, he smalles de ia ions occu in he i s M1, M11,
M2, M10, M3, M9, M2 and M5, all o which ha e alues o less han 3, wi h alues excep ion-
ally low and less han 1 o i s M1, M11 and M2. This con i ms ha inc easing he numbe o
dimensions in he weigh de e mina ion imp o es he p edic ions o e ed by he models. Fu -
he mo e, he mo e usual exp essions o he es ima es o he weigh o ishes in he wild
Fig 2. G aphs o obse ed weigh e sus p edic ed alues o models 1 o 11.
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equi e an adap a ion o i he alues ob ained wi h ishes a ened in cap i i y, since hey end
o o e es ima e weigh . On he o he hand, when he da a a e i ed o a single dimension
(leng h, L, o wid h, A) as M12 and M13 show, mean weigh p edic ion end o unde es ima e
mean weigh in p edic ions.
As al eady indica ed, om he analysis o he mean alues o he esiduals i is in e ed ha
mos o he models o e es ima e he weigh o he una, howe e , his o e es ima ion dimin-
ishes when mo e han one dimension o una is included, and is close o ze o o M1, which
only includes heigh . Models M12 and M13 unde es ima e weigh . M12 only uses leng h as an
Table 5. Resul s o applying he mul iple ange es o mean absolu e e o . The F- alue co esponds o he
ANOVA, which checks he equali y o all he means. Also indica ed is mean absolu e e o (in ascending o de ) o
each model. The las column indica es he p edic i e a iables and when a be ween-b acke s le e coincides in conse-
cu i e wo ows, i indica es ha he e a e no s a is ically signi ican di e ences (95%) be ween he means.
F= 299.64, p<0.000
Model
Mean P edic i e Va iables
M11 8,23629 LHA (a)
M10 8,43998 LHA (a)
M1 8,76972 LH (a)
M8 9,11387 LHA (a)
M9 9,22796 LHA (a)
M3 9,35717 LA (a)
M2 9,40722 LH (a)
M5 10,8446 LA (b)
M7 10,8837 LHA (b)
M6 11,466 LA (b)
M13 13,3114 A (c)
M4 14,8372 LA (d)
M12 15,1931 L (d)
Degua a 42,1138 L (e)
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Table 6. Resul s o applying he mul iple ange es o mean ela i e e o . F- alue co esponds o he ANOVA
which checks he equali y o all he means. Also gi en is mean ela i e e o (in ascending o de ) o each model. The
las column shows he p edic i e a iables and when a be ween-b acke s le e coincides in wo consecu i e ows, i
indica es ha he e a e no s a is ically signi ican di e ences (95%) be ween he means.
F= 690.45, p<0.000
Models
Mean P edic i e Va iables
M11 4,35771 LHA (a)
M10 4,55862 LHA (ab)
M1 4,56925 LH (ab)
M8 4,70279 LHA (ab)
M9 4,74283 LHA (ab)
M2 4,85382 LH (ab)
M3 4,8763 LA (ab)
M5 5,5126 LA (bc)
M7 5,9294 LHA (c)
M6 5,9944 LA (c)
M12 7,17349 L (d)
M4 7,42609 LA (d)
M13 13,3114 A ( )
Degua a 25,6784 A (g)
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