RESEARCH ARTICLE
Me abolic size scaling e lec s g ow h
pe o mance e ec s on age-size ela ionships
in mussels (My ilus gallop o incialis)
I in zi Iba ola, K is ina A anz, Pablo Ma kaideID, En ique Na a o*
Depa amen o de Gene
´ ica, An opologı
´a Fı
´sica y Fisiologı
´a Animal, Facul ad de Ciencia y Tecnologı
´a,
Uni e sidad del Paı
´s Vasco/Euskal He iko Unibe si a ea (UPV/EHU), Bilbao, Spain
*en ique.na a [email protected]
Abs ac
Body-size scaling o me abolic a e in animals is ypically allome ic, wi h mass exponen s
ha a y o e lec di e ences in he physiological s a us o o ganisms o bo h endogenous
and en i onmen al o igin. Rega ding he in aspeci ic analysis o his ela ionship in bi al e
molluscs, one impo an sou ce o me abolic a ia ion comes om he la ge in e -indi idual
di e ences in g ow h pe o mance cha ac e is ic o his g oup. In he p esen s udy, we
aimed o add ess he associa ion o g ow h a e di e ences eco ded among indi idual mus-
sels (My ilus gallop o incialis) wi h a iable le els o he s anda d me abolic a e (SMR)
esul ing in g ow h-dependen shi in size scaling ela ionships. SMR was measu ed in mus-
sels o di e en sizes and allome ic unc ions i ing SMR s. body-mass ela ionships we e
compa ed bo h in e - and in a-indi idually. The esul s e ealed a me abolic componen
( he o e head o g ow h) a ibu able o he di e en ial cos s o main enance o eeding and
diges ion s uc u es be ween as and slow g owe s; hese cos s we e es ima ed o amoun
o a 3% inc ease in SMR pe uni o inc emen in he weigh speci ic g ow h a e. Scaling
exponen s compu ed o in aindi idual SMR s body-mass ela ionships had a common
alue b = 0.79 (~ ¾); howe e , when me abolic e ec s caused by di e en ial g ow h we e
discoun ed, his alue declined o 0.67 (= ⅔), cha ac e is ic o su ace dependen p o-
cesses. This las alue o he scaling exponen was also eco ded o he in e indi idual ela-
ionships o bo h s anda d and ou ine me abolic a es (SMR and RMR) a e long-las ing
main enance o mussels unde op imal uni o m condi ions in he labo a o y. The abo e
esul s we e in e p e ed based on he me abolic le el bounda ies (MLB) hypo hesis.
In oduc ion
Me abolism cons i u es an in eg a ed sys em o he ene gy yielding and u iliza ion p ocesses
in ol ed in suppo ing li e; and mos ac i i ies o o ganisms a e e lec ed in hei me abolic
a es. The ela ionship be ween me abolism and he size o indi iduals has been he subjec o
ho ough analysis o decades as a pa icula ly meaning ul case among he basic o ganismal
a ibu es s emming om s uc u al cons ain s se on unc ional p ope ies. Pa ly o his o i-
cal easons, mos o he s udies on his subjec ha e ocused on animals and hey ely on
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OPEN ACCESS
Ci a ion: Iba ola I, A anz K, Ma kaide P, Na a o
E (2022) Me abolic size scaling e lec s g ow h
pe o mance e ec s on age-size ela ionships in
mussels (My ilus gallop o incialis). PLoS ONE
17(9): e0268053. h ps://doi.o g/10.1371/jou nal.
pone.0268053
Edi o : E ik V. Thuesen, E e g een S a e College,
UNITED STATES
Recei ed: Ap il 20, 2022
Accep ed: Augus 8, 2022
Published: Sep embe 1, 2022
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esponses alongside inal, published a icles. The
edi o ial his o y o his a icle is a ailable he e:
h ps://doi.o g/10.1371/jou nal.pone.0268053
Copy igh : ©2022 Iba ola 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 ele an da a a e
wi hin he manusc ip and i s Suppo ing
In o ma ion iles.
de e mina ions o he s anda d me abolic le el based on oxygen consump ion eco ded unde
es ing pos -abso p i e condi ions, which is assumed o accoun o he ene gy equi emen s
o bo h issue main enance and basic p ocesses o homeos a ic egula ion [1]. As such, his
me abolic le el is conside ed as a s anda d o compa a i e pu poses in mul iple s udies
in ol ing bo h in e - and in a-speci ic analyses.
Body-size scaling o me abolism in animals is ypically allome ic, exp essed by a powe
unc ion in he o m: R = a W
b
, whe e R is he me abolic a e, W is he body mass, ais he scal-
ing coe icien (o p opo ionali y cons an ), and bis he scaling exponen (o slope o he log-
log ela ionship). The as majo i y o hese scaling exponen s epo ed in animals in bo h
in e - and in a-speci ic compa isons is app oxima ely close o ⅔o ¾, bu is signi ican ly
lowe han 1, implying ha weigh -speci ic me abolic a e (i.e. pe uni o body mass) dec eases
wi h he inc easing body size ha encompasses bo h on ogene ic de elopmen and he e olu-
iona y p ocesses unde lying wide- ange specia ion. This me abolic es ic ion imposed by
size inc emen s is a undamen al ade-o in all biological p ocesses and is one o he opics o
he mos pe sis en and in ense deba es in he subjec . Ea lie s udies ha e conside ed b o
app oach he alue ¾in a a ie y o animals [2–5]; subsequen ly, his end was in e p e ed as
he exp ession o uni e sal p ope ies o esou ce- anspo ne wo ks unde lying a “¾powe
law” o me abolism ha is applicable o i ually all o ganisms [6–10]. Howe e , se e al s ud-
ies ha e ecen ly ques ioned he uni e sali y o he “¾powe law” based on ex ensi e su eys
o a ailable da a se s o me abolic size-scaling ha showed b alues o exhibi subs an ial a i-
a ion among axa and physiological s a es [11–14]. A po en ial app oach o add ess he a i-
abili y in scaling exponen s is o assume ha di e en cons ain s ac as bounda ies in he
a ious p ocesses ha make up he o ganism’s me abolic a e [13,15–17], which would hence
ha e di e en scaling cha ac e is ics. A de i a ion o he Dynamic Ene gy Budge (DEB) he-
o y [18] conside s ha he acquisi ion o bo h ene gy and esou ces is p opo ional o su ace
a ea, while ene gy demand is p opo ional o olume; hus, a iable scaling exponen s would
esul om he speci ic balances be ween bo h ypes o p ocesses achie ed unde he di e en
condi ions expe ienced by o ganisms. This iew is consis en wi h he obse a ion ha mos
me abolic scaling exponen s a e be ween ⅔and 1 acco ding o Glazie [13], who de eloped
he me abolic le el bounda ies (MLB) hypo hesis as an ex ension o his app oach o explo e
he dependence o scaling exponen s on he le el o me abolic ac i i y o o ganisms [13,16].
The MLB hypo hesis assumes he abo e di e en ial mass scaling o supply and demand p o-
cesses, and s a es ha he ela i e weigh o hese bounda y cons ain s depends on he me a-
bolic le el (L = me abolism pe uni mass) o p edic a complex (U-shaped) ela ionship
be ween he wo pa ame e s aand bo he allome ic equa ion o me abolism s. body mass.
The MLB app oach has p o en use ul in in e p e ing a ia ions in scaling exponen s associa ed
wi h a di e si y o condi ions ha shi me abolic ac i i y ac oss successi e le els o main e-
nance, es ing, ou ine, and ac i e s a es o me abolism [13,14,16,19].
In a-speci ic analysis o me abolic size scaling, eco ded in specimens co e ing an ample
size ange wi hin he popula ion, o ms he majo i y o cases in scaling exponen de e mina-
ion o wo easons: a) some o he explica i e causes o me abolic scaling a e be e
app oached h ough in a-speci ic analysis whe e, in opposi ion o in e -speci ic compa isons,
pa e s o body o ganiza ion a e conse ed, hus “a oiding he phylogene ic e ec s ha plague
in e -speci ic analysis” [13] and b) p ecise knowledge o allome ic scaling exponen s is
equi ed o size s anda disa ion in s udies o me abolism, allowing o “sub ac ” he e ec s o
body mass on me abolic a e in o de o disce n o he in luences such as g ow h a e. This
especially applies o hose s udies based on compa ing g oups o indi iduals ha may inhe -
en ly be size-he e ogeneous as a consequence o la ge in e -indi idual di e ences in g ow h
pe o mance.
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Funding: Funde 1 MINECO (h ps://sede.mineco.
gob.es) P ojec FIGEBIV (AGL2013-49144-C3-1-R)
Awa ded: E.N., I.I. and P.M. Funde 2 UPV/EHU
(www.ehu.es) P ojec : GIU20_064 Awa ded: I.I.
and K.A. The unde s had no ole in s udy design,
da a collec ion and 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 exis .
This is he case o bi al e molluscs, whe e ex emely high a es o endogenous a iabili y
in g ow h ha e been epo ed [20–26]. Fo ins ance, long-las ing main enance o spa s o di -
e en bi al e species unde homogenous condi ions in he labo a o y esul ed in he p og es-
si e size-di e en ia ion o he indi iduals spanning o e a ange o 5- o 10- old (e en ually up
o 30x) [25–31], hus e ealing a s ong g ow h componen o possible gene ic o igin. Pheno-
ypes ha a e seg ega ed as as and slow g owing, using ex eme g oups o such size dis ibu-
ion, exhibi no iceable di e ences in physiological beha iou ha accoun s o di e ences in
g ow h pe o mance [25,26,28,32].
As sugges ed by hese cases, on ogene ic g ow h in bi al es would include wo di e en i-
a ed componen s: he sequen ial phases o on ogene ic de elopmen , oughly ela ed o age,
and he o e laid in e -indi idual a iabili y in g ow h a e ha is esponsible o size- o-age
di e ence be ween as and slow g owe s. One impo an poin is ha bo h sou ces o size a -
ia ion in he popula ion may gene a e di e en size cons ain s on s anda d me abolism and
hus con ibu e di e en ly o scaling e ec s. Consequen ly, an accu a e cha ac e isa ion o
in a-speci ic scaling ela ions would equi e an analy ical app oach in which mass exponen s
i ed o he ull size ange o he popula ion migh be compa ed wi h hose e lec ing pu e
on ogene ic e ec s as based on he in a-indi idual size a ia ion wi h age. Despi e ob ious
in e es [13], his ype o app oach has been add essed on e y ew occasions [33–35].
In his s udy, we analysed he size scaling o espi a o y me abolism in indi idual mussels—
My ilus gallop o incialis—o a popula ion. This s udy was mainly based on s anda d me abolic
a e (SMR) de e mina ions and aimed o di e en ia e wo sou ces o indi idual size a ia ion
( ime s. a e o g ow h) as ega d hei e ec s on me abolic size scaling. Mussels om a uni-
o mly-sized sample we e allowed o di e en ia e in size unde uni o m eeding and he mal
condi ions in he labo a o y, du ing which, hei SMR and indi idual g ow h a e we e
eco ded. On he o he hand, SMR was de e mined in a he e ogeneous sample o mussels co -
e ing he ull size ange ound in he popula ion. Pa ame e s o allome ic equa ions ela ing
me abolism o body mass we e hen compa ed o wo se s o da a: a) in aindi idual allome-
ies wi h size anges gi en by body-mass inc emen s achie ed du ing he g ow h pe iod and
b) in e -indi idual (in a-speci ic) allome ies wi h size anges gi en by na u al size dispe sion
wi hin he popula ion.
Ma e ial and me hods
Expe imen al design
O e 400 mussels we e collec ed om monolaye mussel beds g own in a ocky in e idal a ea
o An zo ape (Iba angelua, Bizkaia, Spain) on Feb ua y 2013. Mussels anged om app oxi-
ma ely 7–35 mm in shell leng h, ep esen ing he minimum and maximum sizes obse ed in
he bed, espec i ely. Mussels we e placed inside anks con aining seawa e se in a eci cula -
ing sys em egula ed a ambien empe a u e (15˚C) and salini y (34 psu), and ed a a ion o
Isoch ysis galbana in 2 mm
3
pa icula e olume pe li e (equi alen o 1.5 mg POM L
-1
) con-
inuously o wo weeks. Subsequen ly, wo expe imen al g oups o mussels we e c ea ed and
we e main ained in sepa a e anks o app oxima ely se en mon hs (Feb ua y–Augus ) unde
he abo e-men ioned empe a u e and eeding condi ions.
G oup 1. One hund ed ju enile mussels o uni o m size 10 mm (9.189 ±0.907) we e
a anged in indi idual numbe ed chambe s o six mon hs ( om Ma ch 5
h
o Augus 12
h
).
The Shell leng h (SL), li e weigh including shell mass (LW), and SMR o each indi idual we e
eco ded on eigh occasions (app oxima ely e e y h ee weeks). These measu emen s allowed
o he calcula ion o indi idual g ow h a es o selec ed mussels and es ablishmen o allome-
ic scaling o me abolic a e wi h body weigh a wo di e en le els:
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a. In a-indi idual allome y: The scaling o SMR wi h LW o each indi idual mussel was
de e mined by i ing powe unc ions o me abolism and body size da a eco ded on eigh
occasions (n = 8). As a esul , a se ies o 100 unc ions (k = 100) was ob ained.
b. In e -indi idual allome y: Simila ly, o each sampling occasion, powe unc ions we e i -
ed o he SMR s. LW da a o he ull sample. As a esul , a se ies o eigh powe unc ions
ela ing he me abolic a e o body size (k = 8) was ob ained o n = 100 mussels.
On he 7
h
sampling da e, addi ional measu emen s o ou ine me abolic a e (RMR) and
clea ance a e (CR) we e indi idually de e mined (n = 100), and allome ic scaling o hese
wo pa ame e s wi h LW was es ablished as desc ibed o SMR.
Subsequen ly, he gill su ace a ea was eco ded in 30 selec ed mussels co e ing an ample
ange o body sizes o es ablish he allome ic ela ionship o his pa ame e wi h he LW.
G oup 2. Fi y mussels co e ing he size ange obse ed in he sampled popula ion (7–35
mm SL) we e used o analyse he in a-speci ic allome ic ela ionship be ween SMR and LW.
Allome ic ela ionships we e analysed on wo occasions: a) immedia ely a e he g oup was
c ea ed (In a-speci ic 1: 18
h
o Feb ua y) and b) ou mon hs pos hei main enance in he
labo a o y unde cons an wa e empe a u e and con inuous ood supply (In a-speci ic 2:
17
h
o June).
De e mina ion o SL, LW, and g ow h a e o ju enile mussels
On each sampling da e, mussels we e emo ed om he seawa e anks and ca e ully d ied
wi h issue pape . Indi idual LWs (g) we e de e mined in a 10
−4
g p ecision balance and SL
(mm) was measu ed using digi al callipe s. These measu emen s allowed he compu a ion o
indi idual g ow h a es o di e en ime in e als o e a 6-mon h pe iod. G ow h a e in
e ms o LW was exp essed as i) o al g ow h a e (GR
LW
: g day
-1
): indi idual LW inc emen
pe day and ii) size-speci ic g ow h a e (SGR
LW
: %): GR
LW
di ided by he ini ial LW o each
in e al, exp essed as a pe cen age.
Expe imen al de e mina ion o physiological pa ame e s
Clea ance a e (CR; L h
-1
). CR de e mina ions we e pe o med in a s a ic sys em by
eco ding he exponen ial decay in pa icle concen a ion o e ime [36]. Mussels we e indi-
idually placed in glass lasks ( olume a ied om 0.5 o 1.0 L acco ding o mussel size) con-
aining ae a ed sea wa e and pa icles o Isoch ysis galbana (�40 pa icles μl
-1
). Pa icle
concen a ion was measu ed e e y 10 minu es o 1–2 hou s wi h a Coul e Coun e Z1 analy-
se . A con ol chambe wi hou mussels was used o co ec ion o he sedimen a ion a e o
he pa icles.
Me abolic a es. Bo h SMR and RMR we e es ima ed as he a e o oxygen consump ion
(VO
2
:mlO
2
h
-1
). RMR was measu ed a e he ed mussels we e di ec ly ans e ed om he
eeding anks o espi ome e s. Fo SMR de e mina ions ( he majo i y o VO
2
eco dings in
his wo k), mussels we e ans e ed o anks illed wi h ae a ed il e ed (1 μm) sea wa e and
s a ed o h ee days be o e de e mina ion o oxygen consump ion. Indi idual mussels we e
con ined in chambe s ( he size o he chambe a ied be ween 30 and 150 ml acco ding o he
size o he mussel) sealed wi h luminescen dissol ed oxygen p obes connec ed o oxime e s
(HATCH HQ 40d); oxygen consump ion a es we e es ima ed om he dec ease in oxygen
concen a ion o e ime (4–8 h). Con ol chambe s wi hou mussels we e used o check he
s abili y o oxygen concen a ion du ing he measu emen pe iod. In cases whe e bo h me a-
bolic le els we e de e mined, he me abolic scope o eeding and g ow h (MSFG; [26]) was
calcula ed as he di e ence be ween RMR and SMR.
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De e mina ion o gill-su ace a ea (GA: mm
2
)
A he end o he expe imen s, 30 mussels om G oup 1, co e ing he en i e size ange o he
g oup, we e dissec ed by cu ing hei adduc o muscles o expose he gills. One ou e demi-
b anch o each indi idual was pho og aphed wi h a digi al came a placed nex o a piece o
g aph pape o se he scale, and he a ea o he demib anch was de e mined using ImageJ so -
wa e (Na ional Ins i u es o Heal h; Be hesda, MD, USA). The a eas es ima ed in his manne
we e doubled o accoun o each side o he demib anch and mul iplied by he numbe o
demib anchs (4) o es ima e he gill su ace a ea (GA; mm
2
).
S a is ical p ocedu es
One-way analysis o a iance (ANOVA) was pe o med o es signi icance o di e ences in
g ow h a e eco ded o he di e en ime in e als along he pe iod o s udy. Pos -hoc es
(Tukey) was hen applied o iden i y g ow h phases based on signi ican mean di e ences.
In e -indi idual and in a-indi idual allome ic ela ionships be ween he SMR and LW we e
exp essed acco ding o he exp ession SMR = LW
b
. The p opo ionali y cons an aand mass-
exponen s bwe e ob ained by i ing loga i hmically ans o med indi idual SMR and LW
da a wi h eg ession equa ions. Mass-exponen s (slopes) and p opo ionali y cons an s (ele a-
ions) ob ained in bo h he in a- and in e -indi idual ea men s we e compa ed using analy-
sis o co a iance (ANCOVA). The null hypo hesis (H
0
) wi h equal slopes (b
1
= b
2
= b
3
. . ..= b
k
)
we e es ed using he F-s a is ic alue. I H
0
was ejec ed, Tukey’s mul iple compa ison es was
pe o med o de e mine he signi ican di e ences be ween each pai o slopes. I H
0
is
accep ed, a common slope b
c
is compu ed and he null hypo hesis (H
0
) o equal ele a ions (a
1
= a
2
= a
3
. . ..= a
k
) we e subsequen ly es ed using he F-s a is ic alue. I H
0
was accep ed, hen
a common ele a ion a
c
and common eg ession we e compu ed. I H
0
was ejec ed, Tukey’s
mul iple compa ison es was pe o med o de e mine he signi icance be ween each pai o
ele a ions. All s a is ical analyses we e pe o med using a cus om R sc ip based on he p oce-
du es desc ibed by Za [37].
Complemen a ily, SMR da a used in bo h he in a- and in e -indi idual analyses o G oup
1mussels we e plo ed agains mul iple ac o s, using LW, g ow h a e (SGR
LW
), and he in e -
ac ion e m as po en ial p edic o s, and a simul aneous unc ion was i ed by mul iple eg es-
sion p ocedu es using SPSS (IBM SPSS S a is ics V. 25).
Resul s
G oup 1: Mussels o ini ial uni o m size
G ow h and size dis ibu ion. The ime-cou se o size change o 100 mussels du ing 150
days o main enance in he labo a o y is shown in Fig 1A and 1B o bo h LW and SL. Di e -
en size ajec o ies we e illus a ed by he p og essi e di e gence o hese lines, accoun ing o
g ea di e ences in g ow h a es among indi iduals. An almos con inuous decline in alues
o condi ion index (CI: mg LW /mm SL
3
), om >0.1 o <0.1 (Fig 1C), indica ed ha LW
inc emen s a e majo ly d i en by shell g ow h.
Unde lying in e -indi idual a iabili y, sequen ial phases o as /slow g ow h we e eco ded
o g ow h a es compu ed o LW (Fig 2A), wi h a e age alues o 7 and 12 mg day
-1
o he
ea ly and la e phases o as g ow h, espec i ely, and a minimum a e age o 3 mg day
-1
in he
slow g ow h phases. Change in g ow h end was pa icula ly in ense om day 84 o 119, wi h
g ow h a es inc easing om 2.5 o 17 mg day
-1
. When g ow h is exp essed as a weigh -speci ic
a e (i.e., as a pe cen age o daily inc emen pe uni weigh o SGR
LW
) (Fig 2B), all indi idual
da a poin s can be i ed o a nega i e exponen ial unc ion wi h ime (cu e in Fig 2B),
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ep esen ing he na u al decline in he speci ic g ow h a e wi h size inc emen . Phases o as /
slow g ow h can be iden i ied by poin s depa ing om he o e all end desc ibed by he
cu e, especially hose co esponding o days 42 (4%), 84 (0.58%), and 119 (2.7%). A e 119
days ill he end o he expe imen , he e was a dec ease in g ow h a e (bo h in absolu e and
ela i e e ms) ha migh ep esen he onse o a subsequen pe iod o slow g ow h, in ag ee-
men wi h he obse ed ~ 6-week (40 days) sequence o di e en ial phases o g ow h.
The equency dis ibu ion o SGR
LW
calcula ed o he en i e g ow h pe iod ( om day 7 o
147) is plo ed in Fig 3 on a loga i hmic scale o no malisa ion pu poses, emo ing skewness.
Speci ic g ow h a es anged om app oxima ely 1–20% o ini ial LW inc emen pe day.
Fou een indi iduals (app oxima ely 15% o he g oup) displayed he lowes GRW
SPC
o 1.0–
3.4% LW day
-1
and we e conside ed a g oup o slow g owe s (S), whe eas he 11 o he mussels
achie ed he highes GRW
SPC
alues, om 11.5 o 21.0% LW day
-1
and we e conside ed a
Fig 1. G ow h ends o mussels (My ilus gallop o incialis) om G oup 1 du ing he main enance pe iod, gi en in e ms o : A) Shell leng h (SL: mm) and B)
Li e weigh (LW: g); C) mean alues o shell leng h (hollow symbols) and condi ion index (CI: LW / SL
3
) ( ull symbols). Ba s ep esen ±SE.
h ps://doi.o g/10.1371/jou nal.pone.0268053.g001
Fig 2. Mean a es o daily g ow h along he pe iod o s udy, gi en in bo h A) absolu e e ms (GR: mg LW day
-1
) and B) ela i e weigh speci ic e ms (SGR: %
day
-1
). E o ba s ep esen ±SE. Fo e e ence, an exponen ial unc ion was i ed o all indi idual da a o SGR s ime (line in B): SGR = 3.621 (±2.189) �e
(-0.008 ±0.006)
�
Time
. Resul s o pos -hoc es ollowing ANOVA: Di e en le e s deno a e signi ican mean di e ences.
h ps://doi.o g/10.1371/jou nal.pone.0268053.g002
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g oup o as g owe s (F). Thus, he same ange in e al (1.8x) was accomplished in he selec-
ion o ei he F o S g oups, and he compu ed g ow h a e di e ence be ween he wo g oups
was 8.5x on a e age. A compa ison o g ow h ends o bo h g oups (Fig 3) indica ed di e -
ences in he in ensi y o changes du ing he ansi ion be ween g ow h phases, wi h S indi idu-
als showing almos nil g ow h du ing he slow g ow h phase.
In a-indi idual allome ies o SMR. Allome ic equa ions ela ing SMR o LW o 100
indi iduals in G oup 1 we e i ed using linea eg ession a e log ans o ma ion o bo h a i-
ables (Fig 4). LW ange was achie ed h ough he g ow h o he indi iduals and a ied be ween
~ 400 mg in he S g oup (LW- ange o ~5x) and ~ 1800 mg in he F g oup (LW- ange o
~20x). Only 5 ou o he 100 indi idual eg essions we e ound no signi ican (P >0.05) and
we e excluded om u he analysis.
The minimum and maximum alues o he scaling exponen s o he SMR we e
0.570 ±0.080 and 1.171 ±0.127, espec i ely. Possible signi ican di e ences among he slopes
and ele a ions o he 95 in a-indi idual allome ies we e analysed using ANCOVA. No signi -
ican di e ences in ei he he slopes o ele a ions we e ound (Table 1), indica ing ha all indi-
iduals sha e a common mass-exponen and p opo ionali y cons an .
Resul s o ANCOVA analysis o es ing signi ican di e ences be ween slopes and ele a-
ions o he 95 in a-indi idual allome ic ela ionship (on log-log scale) be ween s anda d
me abolic a e (VO
2
: ml O
2
h
-1
) and body weigh (LW: g). Size anges a ied be ween a mini-
mum 5x o a maximum 30x. Fo abou hal hese ela ionships, anges a ied be ween 10 and
20x.
The e o e, a common equa ion accoun ing o in a-indi idual scaling o SMR o body
weigh was calcula ed as ollows:
Fig 3. F equency dis ibu ion s g ow h in e als. Fo no mali y, SGR alues we e loga i hmically ans o med. Two g oups
o slow (S) and as (F) g owe s we e c ea ed wi h he ex emes o he dis ibu ion. Inse : G ow h ends o seg ega ed g oups
o as (F) and slow (S) g owing mussels. Da a a e mean li e weigh (LW) alues ±SE.
h ps://doi.o g/10.1371/jou nal.pone.0268053.g003
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Fig 4. Reg ession lines i ed o log-log ans o med da a o SMR (ml O
2
h
-1
) s LW (g) in 100 indi iduals. Size anges co espond o he weigh inc emen
expe ienced by each indi idual mussel. Only 5 o hese eg essions we e no signi ican (P >0.05).
h ps://doi.o g/10.1371/jou nal.pone.0268053.g004
Table 1. Analysis o co a iance (ANCOVA) o in a-indi idual SMR s LW ela ionships.
Te m o compa ison Slopes Ele a ions
Hypo hesis H
0
= b
1
= b
2
=. . . = b
95
H
0
= a
1
= a
2
=. . . = a
95
F ab 1.278 (0.05, (1), 94, 579) 1.275 (0.05, (1), 94, 673)
F0.752 1.257
P0.956 0.063
Conclusion Do NOT ejec H
0
Do NOT ejec H
0
Common alue b
c
= 0.789 a
c
= -1.331
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• Log SMR = 0.789 (±0.013) ×Log W– 1.331 (±0.007);
R2¼0:824; P<0:0001 ð1Þ
The mean alues (±SD) o he slopes band ele a ions log a a e plo ed in Fig 5. A signi ican
co ela ion (R
2
= 0.61; P <0.001) was ound be ween hese wo pa ame e s (Fig 5A), indica -
ing a posi i e e ec o me abolic le el on he s eepness o he lines scaling SMR o body size.
Howe e , nei he o he wo pa ame e s co ela ed wi h indi idual g ow h a es (weigh -spe-
ci ic alues) (Fig 5B and 5C), e y likely due o he e oskedas ic dis ibu ion o a iances along
he SGR axis, whe e la ge a iances in slow g owe s (low SGR) can be a ibu ed o he na -
owe size- anges o e which eg ession analysis we e deployed compa ed wi h as g owe s
(high SGR). This poses a me hodological cons ain on he a emp o explo ing he e ec s o
indi idual g ow h a es on a es o me abolism.
Thus, a u he a emp was made by i ing a mul iple eg ession model in which he SMR
o each indi idual on a gi en sampling da e was gi en as a simul aneous unc ion o bo h he
body weigh and he weigh -speci ic g ow h a e (SGR
LW
) eco ded on ha da e. Toge he
wi h hese independen a iables, po en ial p edic o s in he model also included he combina-
ion o body weigh and g ow h a e, al hough his in e ac ion e m did no signi ican ly a ec
he SMR. The i ed equa ion (n = 665) wi h he wo emaining a iables is:
• Log SMR = 0.677 (±0.016) ×Log W + 0.014 (±0.003) ×SGRLW−1.382 (±0.009)
R2¼0:745; F: 921:3; P<0:0001 ð2Þ
The weigh -spec(3)i ic g ow h a e exhibi ed by indi iduals exe ed, along wi h body size,
highly signi ican posi i e e ec s on SMR, and hus con ibu ed o a mo e de ailed desc ip ion
o ac o s a ec ing SMR. Pa icula ly, his model accoun s o he inding ha , a e he me a-
bolic e ec s o g ow h we e subsumed in he co esponding coe icien , body size scaling expo-
nen s we e ound o dec ease om 0.79 (1) o 0.68 (2).
In e -indi idual allome ies o s anda d me abolic a es. In e -indi idual allome ic
ela ionships be ween SMR and LW we e i ed using he size dis ibu ion o 95 mussels in
G oup 1 on he eigh sampling da es du ing he g ow h pe iod. The pa ame e s o he i ed
log- ans o med equa ions a e p esen ed in Table 2, oge he wi h size anges ha a ied
be ween a minimum (3.3x) on day 7 and a maximum (18.1x) on day 147. ANCOVA esul s
Fig 5. A) Rela ionship be ween p opo ionali y cons an (log a) and mass exponen s (b) o indi idual allome ic ela ionships o s anda d oxygen consump ion
and li e weigh . B) Mass-exponen s b(±SD) and C) P opo ionali y cons an , log a (±SD) o in a-indi idual allome ic ela ionships o s anda d oxygen
consump ion and li e weigh plo ed as a unc ion o speci ic g ow h a e o li e weigh (SGR
LW
).
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he alues o g ow h coe icien s o me abolism in o he empo al phases, such F s. S di e -
ences ended o lessen as g ow h ac i i y was esumed. A simila beha iou o me abolic scal-
ing along phases o on ogene ic g ow h ha e been epo ed o e es ial gas opods, wi h
slope alues declining be ween ju enile ( as g ow h) and adul (slow g ow h) s ages o de el-
opmen [55,56].
Second, mussels in G oup 2 belonged o di e en coho s o he popula ion; he e o e, he
size a ia ion in he allome ic ela ionships (Fig 7) was mainly caused by age di e ences
be ween indi iduals. In G oup 2, he scaling exponen dec eased signi ican ly om 0.813 wi h
mussels ecen ly ans e ed o he labo a o y om he na u al in e idal en i onmen (in a-
speci ic1) o 0.709 wi h mussels acclima ed o ou mon hs in he labo a o y (in aspeci ic2).
Such a shi in he scaling exponen migh e lec he ac ha in e -indi idual di e ences in
g ow h condi ions due o en i onmen al ac o s ( e y likely associa ed wi h he ophic and
he mal he e ogenei y cha ac e is ic o he in e idal habi a ) we e a enua ed a e he
4-mon h main enance o indi iduals unde he op imal and s able condi ions in he labo a-
o y, hus educing he o iginal g ow h a iabili y wi hin his g oup, along wi h he al eady dis-
cussed e ec o his a iabili y on he size exponen . This in e p e a ion is consis en wi h he
hypo hesis pos ula ed by Glazie and collabo a o s [13,54,57,58] ha ecological ac o s such
as he p esence o p eda o s o changes in a ailable die o he mal en i onmen a ec he scal-
ing exponen o in a-speci ic allome y o SMR.
This scaling exponen o G oup 2 (di e en ially aged mussels) a e acclima ion o labo a-
o y condi ions (b= 0.709) di e ed signi ican ly om he common exponen o lines i ed o
in a-indi idual SMR alues (b= 0.79) o he a e age alue o slopes eco ded in he in e -
indi idual analysis o G oup 1 mussels in he ini ial pe iod (2 mon hs) o g ow h unde labo a-
o y condi ions (Table 2), when endogenous in e -indi idual di e ences in g ow h a e we e
conside ed o g ea ly con ibu e o he size a ia ion o his single coho o mussels. Howe e ,
i espec i e o some i egula i ies ep esen ed by g ow h phases, hese di e en ial g ow h
e ec s ended o decline wi h he age o mussels, as indica ed by he gene al beha iou o
weigh -speci ic g ow h a es du ing he main enance pe iod (Fig 2B), wi h a co esponding
decline in he slope om day 63 onwa ds o alues (a e age b= 0.68) ha we e no signi i-
can ly di e en om hose o G oup 2 mussels (b= 0.709) o o he epo ed alues (b= 0.71)
o a simila size ange o he species [46].
Concluding ema ks
The scheme shown in Fig 8 was elabo a ed o help summa ise some concluding poin s con-
ce ning size-scaling dependence on he a iable le els o s anda d me abolism achie ed by
mussels exhibi ing di e ences in g ow h condi ions.
These conclusions ha e been mainly in e ed om he esul s o he p esen analysis o
in a-indi idual SMR s. body weigh ela ionships in 95 ju enile indi iduals, al hough hey
we e also suppo ed by di e en app oaches o he in a-speci ic (in e -indi idual) ela ion-
ships epo ed he ein. Fo a gumen a i e con enience, he ull size- ange in his scheme has
been plo ed as he addi ion o wo componen s: he i s componen is s ic ly dependen on
he ime o g ow h (age) and he second componen is associa ed wi h di e en ial g ow h
accoun ing o size di e ences among indi iduals o he same age. Cu es o SMR s. body
size we e hen plo ed o he wo ca ego ies o F and S g oup indi iduals, whe e he le el o
demand o issue main enance cons i u es he speci ic di e ence ega ding es ing me abo-
lism, acco ding o easons ha ha e al eady been discussed. The assump ion is ha o he S
g oup indi iduals, me abolic demands o he homeos a ic egula ion o body unc ions (e.g.,
su ace- ela ed p ocesses o esou ce supply and was e disposal) a e a p e alen componen o
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SMR o e issue main enance, esul ing in me abolic scaling o body size acco ding o a su -
ace/ olume exponen (b=⅔). Con e sely, in he F g oup indi iduals, SMR inc emen
esul ed om he highe demands o issue main enance. These demands a e assumed o
scale isome ically (b= 1) he size span achie ed h ough di e en ial g ow h, hus imposing a
shi (as indica ed by he a ow) in he weigh exponen o alues close o b=¾. This shi was
obse ed i espec i e o he o igin o di e ences in g ow h condi ions, ei he endogenous
(G oup 1 expe imen s) o exogenous (when main enance in he labo a o y o G oup 2 mussels
ended o smoo h he o iginal a iabili y in g ow h condi ions o eshly collec ed specimens),
indica ing ha a iable demands o issue main enance cons i u e a basic ea u e inhe en o
di e ences in g ow h pe o mance.
Since he p esen in e p e a ion was based on assump ions unde lying he MLB hypo hesis
[16] i is necessa y o discuss how he p esen analysis suppo s he inding o a posi i e depen-
dence in he ela ionship be ween he mass exponen and he le el o es ing me abolism (as
ep esen ed by he slope and ele a ion o allome ic unc ions in he in a-indi idual analysis;
Fig 5A); while he opposi e endency (see Fig 2 in [16]) cons i u es he co e o MLB hypo hesis
p edic ions o es ing me abolism, suppo ed by empi ical obse a ions pe o med on a wide
ange o animal species, bo h ec o he ms and endo he ms [13,16,52]. The conside a ion o
some dis inc i e ea u es o bi al e molluscs, pa ly sha ed by o he ma ine in e eb a es o
inde e mina e g ow h, migh help explain he abo e disag eemen based on di e ences in he
na u e o a ia ions in me abolic es ing le els be ween he p esen case and he mo e gene al
case p esen ed by Glazie [13,16]. In he la e , minimum alues a e assumed o ep esen
Fig 8. P oposed scheme accoun ing o a shi in he scaling exponen o he s anda d me abolic a e s body size ela ionship, be ween slow g owe s
(low main enance demands) and as g owe s (high main enance demands). See ex o de ails.
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cons an issue main enance equi emen s (b= 1); he addi ion o egula o y demands (includ-
ing expensi e homeo he my, when applicable) sa is ied h ough luxes o me abolic esou ces,
was es, and (o ) hea , which a e su ace-a ea-limi ed (b=⅔), o his minimum alue would
esul in inc eased le els o he es ing me abolism [16]. This is seen o di e in bi al e mol-
luscs, whose g ow h he e osis has been a ed among he highes in he animal kingdom [59],
esul ing in la ge in e -indi idual di e ences in g ow h a e, ypically eaching up o 10- old in
he mussels o ou s udy. He e, a iable le els o es ing me abolism would s em om g ow h-
ela ed di e ences in issue main enance equi emen s supe imposed on he a he weak egu-
la o y demands ha is cha ac e is ic o con o ming o ganisms. Isome ic size dependence o
his me abolic componen will hus p e ail in as e g owe s, accoun ing o highe mass expo-
nen s when SMR scales he size anges ha a e mos ly dependen on g ow h a e di e ences
among indi iduals, as in he case o in a-indi idual analysis o a single coho o ju eniles sub-
jec ed o p og essi e size di e en ia ion in he labo a o y. The p og essi e decline o his di -
e en ial ac o in SMR wi h he aging o mussels would esul in mass exponen s app oaching
he ⅔ alue cha ac e is ic o me abolic demands d i en by su ace- o- olume-dependen p o-
cesses. This also applies o addi ional demands se o ac i i y, as in he me abolic scope o
eeding and g ow h (MSFG) and is consis en wi h he b alue o 0.65 eco ded o he RMR.
Suppo ing in o ma ion
S1 Da a.
(XLSX)
Acknowledgmen s
Au ho s a e indeb ed o Douglas S. Glazie and one anonymous e iewe o aluable com-
men s and sugges ions ha g ea ly con ibu ed o imp o e he manusc ip in he phase o
e ision.
Au ho Con ibu ions
Concep ualiza ion: I in zi Iba ola, En ique Na a o.
Da a cu a ion: K is ina A anz, Pablo Ma kaide.
Fo mal analysis: I in zi Iba ola, K is ina A anz, Pablo Ma kaide.
Funding acquisi ion: I in zi Iba ola, En ique Na a o.
In es iga ion: I in zi Iba ola, K is ina A anz, En ique Na a o.
Me hodology: I in zi Iba ola, K is ina A anz, Pablo Ma kaide.
P ojec adminis a ion: En ique Na a o.
Resou ces: K is ina A anz, En ique Na a o.
So wa e: Pablo Ma kaide.
Supe ision: K is ina A anz, Pablo Ma kaide, En ique Na a o.
W i ing – o iginal d a : I in zi Iba ola.
W i ing – e iew & edi ing: En ique Na a o.
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