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Species’ ecological unc ionali y al e s he ou come o ish s ocking success p edic ed by
a ood-web model
© 2018 The Au ho s
Published e sion
Uusi-Heikkilä, Sil a; Pe älä, Tommi; Kupa inen, Anna
Uusi-Heikkilä, S., Pe älä, T., & Kupa inen, A. (2018). Species’ ecological unc ionali y al e s he
ou come o ish s ocking success p edic ed by a ood-web model. Royal Socie y Open Science,
2018(5), A icle 180465. h ps://doi.o g/10.1098/ sos.180465
2018
sos. oyalsocie ypublishing.o g
Resea ch
Ci e his a icle: Uusi-Heikkila
¨S, Pe a
¨la
¨T,
Kupa inen A. 2018 Species’ ecological
unc ionali y al e s he ou come o ish s ocking
success p edic ed by a ood-web model. R. Soc.
open sci. 5: 180465.
h p://dx.doi.o g/10.1098/ sos.180465
Recei ed: 24 Ma ch 2018
Accep ed: 9 July 2018
Subjec Ca ego y:
Biology (whole o ganism)
Subjec A ea:
ecology
Keywo ds:
ood-web dynamics, eeding in e ac ions,
allome ic ophic ne wo k model, ish s ocking,
ecosys em s abili y
Au ho o co espondence:
Sil a Uusi-Heikkila
¨
e-mail: [email p o ec ed]
Elec onic supplemen a y ma e ial is a ailable
online a h ps://dx.doi.o g/10.6084/m9. igsha e.
c.4180127.
Species’ ecological
unc ionali y al e s he
ou come o ish s ocking
success p edic ed by a
ood-web model
Sil a Uusi-Heikkila
¨, Tommi Pe a
¨la
¨and Anna Kupa inen
Depa men o Biological and En i onmen al Science, Uni e si y o Jy a
¨skyla
¨, PO Box 35,
40014 Jy a
¨skyla
¨, Finland
SU-H, 0000-0001-6503-455X; AK, 0000-0002-7807-8946
Fish s ocking is used wo ldwide in conse a ion and manage-
men , bu i s e ec s on ood-web dynamics and ecosys em
s abili y a e poo ly known. To be e unde s and hese e ec s
and p edic he ou comes o s ocking, we used an empi ically
alida ed ne wo k model o a well-s udied lake ecosys em.
We simula e wo s ocking scena ios wi h wo na i e ish species
aluable o ishing. In he i s scena io, we s ock plank i o ous
ish (whi e ish) la ae in he ecosys em. This leads o a 1%
inc ease in adul whi e ish biomasses and dec eases he
biomasses o he op p eda o (pe ch). In he second scena io,
we also s ock pe ch la ae in he ecosys em. This dec eases he
plank i o ous whi e ish and he oldes op p eda o age class
biomasses, and des abilizes he ecosys em. Ou esul s demon-
s a e ha he e ec s o s ocking depend on he species’
posi ion in he ood web and hus canno be assessed wi hou
conside ing in e ac ing species. We u he show ha s ocking
can lead o undesi ed ou comes om bo h managemen and
conse a ion pe spec i es. The gains o s ocking can emain
mino and ha e ad e se e ec s on he en i e ecosys em.
1. In oduc ion
In aqua ic en i onmen s, he elease o ha che y- ea ed ish (s ock-
ing) is one o he mos popula ools o es o a ion and main enance
o na i e ish popula ions. S ocking has ypically wo goals: conse -
a ion and enhancemen . Conse a ion aims o inc ease popula ion
sizes, which o en ha e been educed by ishing, h ough a di ec
con ibu ion o ha che y ju eniles in o he wild popula ion, and o
main ain hei abundances a sel -sus ainable le els [1]. The main
goal o s ocking, howe e , is enhancemen , i.e. he maximiza ion
&2018 The Au ho s. Published by he Royal Socie y unde he e ms o he C ea i e
Commons A ibu ion License h p://c ea i ecommons.o g/licenses/by/4.0/, which pe mi s
un es ic ed use, p o ided he o iginal au ho and sou ce a e c edi ed.
on Augus 19, 2018h p:// sos. oyalsocie ypublishing.o g/Downloaded om
o comme cial and ec ea ional ishe ies ca ches [2]. The gene ic isks associa ed wi h s ocking a e ela i ely
well documen ed [3,4], bu e y li le is known abou he consequences o s ocking o he ecosys em
(bu see [5]). S ocking o species ha a e impo an o ishing can change in e ac ions among o he species
which a e di ec ly o indi ec ly linked o he s ocked species. This aspec o s ocking has emained la gely
o e looked bo h wi hin he con ex s o conse a ion and ishe ies managemen .
Ecosys em eedbacks o s ocking ha e been mos ly s udied in sys ems whe e he s ocked ish is an
exo ic game ish, ypically a op p eda o [6,7]. This can unde s andably ha e a ious d ama ic e ec s
on he ecosys ems and ood webs, such as eplacemen o he na i e p eda o , inc eased op-down con ol
and changes in ecosys em esilience ( e iewed in [5]). Howe e , when one o se e al na i e ish species
a e s ocked simul aneously in o he same sys em, i is no clea how s ocking species wi h di e en eco-
logical unc ionali ies a ec s he ecosys em. Fo example, s ocking a pisci o ous op p eda o can a ec
ecological dynamics di e en ly o s ocking a plank i o ous ish. These ou comes can be unexpec ed and
undesi able om he managemen and conse a ion pe spec i e.
He e, we explo e he ecological isks o s ocking (e.g. ecosys em ins abili y) and assess whe he s ock-
ing comp omises ecosys em-wide conse a ion and managemen objec i es (e.g. he inc ease in ishe ies
ca ches). We do his by mechanis ically simula ing how di e en s ocking scena ios al e he ood-web
dynamics in a na u al ecosys em. To his end, we use a li e-his o y s uc u ed, allome ic ophic ne wo k
(ATN) model pa ame ized and alida ed o he no h Eu opean alpine lake, Lake Cons ance (LC) [8,9].
Al hough he ood-web model is de e minis ic and simpli ied so ha i includes nei he all species
p esen in he LC sys em no abio ic in luences, i is based on well-measu ed plank on communi y
dynamics and, hus, can be used as a ealis ic scena io o he complex ish eeding en i onmen upon
which he ou comes o s ocking depend. We s udy he ecological consequences o s ocking wi h he
ocus on wo key species, which a e bo h impo an o ishe ies bu di e subs an ially in hei ecological
unc ionali y and posi ions in he ood web. We in es iga e he impac s o al e na i e s ocking scena ios
on (i) he abundances o he a ge species and (ii) in e ac ing species, as well as (iii) he ecosys em p o-
duc i i y and s abili y. We show ha in his pa icula ecosys em, he gains o s ocking can emain mino
and ha e ad e se e ec s on he en i e ecosys em.
2. Ma e ial and me hods
2.1. Food web and i s dynamics
The LC ood web con ains wo p eda o s, common whi e ish (Co egonus la a e us) and Eu asian pe ch
(Pe ca lu ia ilis) di ided in o i e li e-his o y s ages: la ae, ju enile (1-yea -old), 2-yea -old, 3-yea -old
and 4-yea -old and olde . While he whi e ish–pe ch species pai migh seem a a he speci ic pai o
compe i o s, hey highligh he species-speci ic di e ences in ecological unc ionali y and in hei
posi ions in he ood web as 2-yea -old and olde pe ch a e pisci o ous, whe eas whi e ish a e solely
plank i o ous. O he species in he ood web a e basal p oduce s, bac e ia and zooplank on. The LC
ood web consis s o 30 unc ional guilds (elec onic supplemen a y ma e ial, able S1) ha a e linked
h ough 133 eeding in e ac ions.
The dynamics o he ood web we e desc ibed h ough an ATN model pa ame ized and alida ed
o seasonal plank on dynamics [8], and u he expanded by ish li e-his o y s uc u e [9]. In his
model, biomasses a e desc ibed h ough ela i e ca bon densi ies (mgC m
23
). The daily biomass
dynamics ac oss an annual 90-day g ow h season a e modelled h ough a se o o dina y di e en ial
equa ions, which include sa u a ing unc ional esponses ha egula e p eda o –p ey in e ac ions and
in aspeci ic p eda o in e e ence. Basal p oduc ion is con olled by a logis ic g ow h model wi h a
sha ed communi y ca ying capaci y o all he p oduce s. A he end o each g ow h season, a ac ion
o adul ishes’ ne p oduc i i y becomes new la ae and he biomasses o younge ishes mo e om
hei cu en li e-his o y s age o he nex . Species’ body sizes de e mine hei me abolic a es and eeding
in e ac ions excep when mo e di ec ly measu ed a es a e a ailable [8]. See elec onic supplemen a y
ma e ial o he go e ning equa ions and u he in o ma ion on he pa ame e s.
2.2. Simula ion design
In LC, he whi e ish popula ion is dependen on s ocking and has i ually no na u al ep oduc ion.
Whi e ish s ocking has con inued o o e a cen u y [10]. Thus, in ou simula ion s udy, we conside
he s ocking o whi e ish la ae wi h 200 mgC m
23
as he baseline (Wh 200) [9]. This is equi alen o
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app oxima ely one la a pe 5 m
3
o wa e . The ealism o his numbe can be ques ioned, bu i should
be kep in mind ha he s ocking densi ies in he p esen s udy a e based on he lake p oduc i i y and
zooplank on densi ies and ou model igno es di e en mo ali y ac o s (o he han hose based on eed-
ing in e ac ions) and he quali y o s ocked la ae. The e o e, he ocus will be in he ela i e abundances
among species, no in he heo e ical numbe o la ae. S ocking occu ed a he beginning o he 90-day
g ow h season, he same ime when na u ally p oduced (pe ch) la ae we e in oduced o he ecosys em.
In he i s s ocking scena io, we inc eased he s ocking o plank i o ous whi e ish om 200 o
300 mgC m
23
o inc ease whi e ish abundances and ca ches. We call his scena io ‘Wh 300’. In he
second scena io, we also s ocked pisci o ous pe ch ( om 0 o 50 mgC m
23
) o inc ease bo h whi e ish
and pe ch abundances and o mimic a scena io whe e managemen a emp s o ‘ ec i y’ ecological
impac s o he i s s ocking scena io (see Resul s). We call his scena io ‘Wh 300 þPe 50’.
We in es iga ed he e ec s o he wo di e en s ocking p ac ices on he ecosys em in he absence (100
yea s) and p esence o ishing (100 yea s). Dynamic equilib ium (in he absence o ishing) e lec ed he
ood web’s in e nal de e minis ic dynamics. This pe iod ep esen s he conse a ion goal o inc ease
popula ion sizes. The simula ions conduc ed unde ishing ep esen he enhancemen goal o inc ease
abundances o he ish age classes a ge ed by ishing. Du ing he ishing pe iod, he maximum ins an-
aneous ishing mo ali y a e F
max
[9] was chosen o be 0.5/(90 þ1) and he ishing selec i i y S
age
was
1/3 o 2-yea -old ish, 2/3 o 3-yea -old ish and 1 o 4-yea -old and olde ish. These selec i i ies a e
ealis ic as ishing ends o a ge la ge (old) indi iduals, ye some ishing gea also ca ches smalle ish
(e.g. yke ne , small-mesh ne ).
Wi hin bo h pe iods (in he absence and p esence o ishing), we in es iga ed he ecological e ec s o
he wo s ocking p ac ices h ough (i) he s ocked ish species biomass densi ies (he ea e e e ed o as
densi ies), (ii) he ish zooplank on p ey densi ies (Daphnia,Cyclopoid and Lep odo a o adul s; see igu e 2
o la al p ey species), (iii) pe ch la ae p oduc ion, and (i ) he s abili y o o al ecosys em biomass. We
did his by compa ing he densi ies be ween he baseline (Wh 200) and he (inc eased) s ocking scena ios
(Wh 300 and Wh 300 þPe 50). Compa isons we e ca ied ou a he end o he 90-day g ow h season.
To es he obus ness o ou esul s, we simula ed scena ios whe e he densi ies o s ocked whi e-
ish and pe ch la ae we e inc eased and dec eased by 50 and 25 mgC m
23
, espec i ely. To u he
demons a e he obus ness o he esul s, we inc eased and dec eased he F
max o 0.6 and 0.4, espec i ely
.
3. Resul s
3.1. Inc eased whi e ish s ocking (Wh 300)
Al hough 50% mo e whi e ish la ae we e s ocked a he beginning o he g ow h season, he densi y o
whi e ish la ae a he end o he g ow h season was less han 1% highe compa ed o he baseline
(Wh 200). Consequen ly, ju enile whi e ish in he sys em inc eased by 2.3% and he adul whi e ish
only by 1% a each li e s age ( igu e 1). Pe ch la ae dec eased by 1.8% ela i e o he equilib ium abun-
dance esul ing in a dec ease in adul pe ch densi y ( igu e 1). Changes in ishe ies ca ches ollowed a
simila pa e n as changes in adul whi e ish and pe ch densi ies (elec onic supplemen a y ma e ial,
igu e S1).
The inc ease in whi e ish and he dec ease in pe ch densi ies (compa ed wi h Wh 200) we e e iden
bo h in he absence and p esence o ishing, excep among he 4-yea -old and olde pe ch ( igu e 1). The
inc ease in la al and ju enile whi e ish was highe (less han 1% and 3%, espec i ely) and he dec ease
in la al and ju enile pe ch smalle (1.4% and less han 1%, espec i ely) in he p esence o ishing,
because ishing emo ed la ge amoun s o adul pe ch consuming he la ae and ju eniles.
Densi ies o he zooplank on p ey species o adul and ju enile whi e ish and (pa ly) pe ch
(Daphnia, Cyclopoid and Lep odo a) dec eased a e Wh 300 compa ed wi h Wh 200, while densi ies
o la al ish p ey species sligh ly inc eased ( igu e 2). These ends emained du ing ishing.
3.2. Pe ch s ocking (Wh 300 þPe 50)
As inc eased whi e ish s ocking dec eased he adul pe ch densi ies ela i e o he equilib ium abun-
dance, we simula ed ano he scena io whe e we ied o compensa e o he loss by also s ocking
pe ch. While his scena io inc eased la al pe ch densi y by 2.4%, ju enile pe ch by 2.2% and also
2- and 3-yea -old pe ch, i dec eased he densi y o he la ges and he mos aluable pe ch ( igu e 1).
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Fu he mo e, he densi y o la al whi e ish dec eased by 4.5%, ju enile whi e ish by 1.6% and adul
whi e ish by 4–5% a each li e s age compa ed wi h Wh 300 ( igu e 1).
The dec ease in adul whi e ish and he inc ease in adul pe ch biomasses be ween he wo s ocking
scena ios (Wh 300 e sus Wh 300 þPe 50) diminished in he p esence o ishing ( igu e 1). Simila ly, he
biomass dec eased less among he ju enile whi e ish (less han 1% e sus 3.3% be o e ishing) and
inc eased less among he la al (1.3% e sus 3.3% be o e ishing) and ju enile pe ch (0.7% e sus
3.7% be o e ishing) in he p esence o ishing because p eda o y pe ches we e emo ed by ishing.
Densi ies o he zooplank on p ey species o adul whi e ish and pe ch inc eased, while hose o la al
ish subs an ially dec eased a e pe ch s ocking ( igu e 2). Di e ences in he la e diminished in he
p esence o ishing ( igu e 2).
Finally, whi e ish s ocking educed, and pe ch s ocking subs an ially ampli ied, he luc ua ion o he
ish biomasses ( igu e 1) and he o al ecosys em biomass ( igu e 3). While he ins abili y o ish bio-
masses and he o al ecosys em biomass dec eased wi h ime, he sys em did no each an equilib ium
s a e e en a e 100 yea s o simula ed biomass dynamics, indica ing ha i akes a long ime o he
sys em o ind an equilib ium in changed s ocking condi ions.
13
14
15
16
17
−4.8%
+1.02%
−2.3%
+1.03%
whi e ish
Wh 200
Wh 300
Wh 300 + Pe 50 9.0
9.5
10.0
10.5
11.0
11.5
pe ch
+3.5%
−2.0%
+0.6%
−1.7%
2
y
ea old
6
7
8
9
10
11
12
−4.4%
+1.02%
−1.6%
+1.02%
5
6
7
8+2.5%
−1.8%
+0.2%
−1.4%
3
y
ea old
5
10
15
20
25
0 50 100 150 200
−3.9%
+1.01%
−1.0%
+1.01%
5
10
15
20
>4
y
ea old
−2.9%
−0.2%
−2.0%
+1.0%
ime (
y
ea )
0 50 100 150 200
ime (
y
ea )
biomass (µgC m−3 × 1000)biomass (µgC m−3 × 1000) biomass (µgC m−3 × 1000)
Figu e 1. Changes in he adul whi e ish and pe ch biomasses in esponse o inc eased whi e ish (Wh 300; black) and pe ch s ock-
ing (Wh 300 þPe 50; ed) compa ed wi h he whi e ish baseline (Wh 200; g ey). Pe cen ages in black e e o he Wh 200/Wh 300
and in ed o he Wh 300/Wh 300 þPe 50 compa ison. Dashed lines indica e he ime poin when ishing was in oduced o he
simula ions.
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Inc eases and dec eases (o 50 mgC m
23
) in he biomass o s ocked whi e ish led o an ou come
analogous wi h he s ocking scena io in es iga ed in he p esen s udy (300 mgC m
23
; elec onic sup-
plemen a y ma e ial, igu e S2). Simila ly, ou esul s we e obus o a 25 mgC m
23
dec ease and
inc ease in pe ch s ocking (elec onic supplemen a y ma e ial, igu e S3), whe eas a 50 mgC m
23
inc ease
in pe ch s ocking g ea ly des abilized bo h he ish and he o al ecosys em biomasses. The esul s we e
obus o +0.1 changes in ishing p essu e (F
max
; elec onic supplemen a y ma e ial, igu e S4).
4. Discussion
Ou esul s demons a e ha s ocking al e s ecosys em dynamics and ha special a en ion should be
paid on species’ ecological unc ionali ies. We showed ha inc easing whi e ish s ocking by 50%
dec eased pe ch densi ies and inc eased whi e ish densi ies only by 1% a each adul li e s age. This is
a mino inc ease and he cos -e ec i eness o he s ocking p ac ice could be ques ionable. I should be
kep in mind, howe e , ha LC is an oligo ophic lake wi h low p ima y p oduc ion and his could
limi he p oduc ion o ish biomasses. Food-web models alida ed o lakes wi h medium o high p o-
duc i i y would inc ease ou unde s anding o he in e ac ion be ween lake ophic s a e and s ocking
p ac ices. E en hough ou esul s desc ibe ela i e biomass densi ies ins ead o absolu e popula ion bio-
masses, hey a e based on well-measu ed es ima es on ood-web dynamics and hus ha e a g ea
po en ial o inc ease ou unde s anding o he ecosys em-le el e ec s o ish s ocking.
0 50 100 150 200
200
300
400
500
600
700
800
Daphnia
Wh 200
Wh 300
Wh 300 + Pe 50
0 50 100 150 200
700
800
900
1000
1100
Cyclopoid
0 50 100 150 200
0.001
0.002
0.003
0.004
0.005
Lep odo a
0 50 100 150 200
1000
1200
1400
1600
1800
2000
ish la ae p ey species
ime (
y
ea ) ime (
y
ea )
biomass (µgC m−3)
biomass (µgC m−3)
Figu e 2. Changes in he biomasses o he zooplank on p ey species o adul and la al whi e ish and pe ch in esponse o inc eased
whi e ish s ocking (Wh 300; black cu e) and pe ch s ocking (Wh 300 þPe 50; ed cu e) compa ed wi h he whi e ish baseline
(Wh 200; g ey cu e). Dashed lines indica e he ime poin when ishing was in oduced o he simula ions. Adul zooplank on p ey
species consis ed o Daphnia,Cyclopoid and Lep odo a. La al zooplank on p ey species consis ed o small, medium-sized and la ge
Ro i e s,Daphnia and Cyclopoid.
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The eason behind he poo s ocking esul in his pa icula s udy was no he quali y o ha chlings,
because ou simula ions a e only a ec ed by he ood web’s in e nal dynamics. Thus, ou indings a e
op imis ic compa ed o ac ual s ocking, whe e low su i al o ha chlings is common [3]. A mo e
likely explana ion o ou inding is ood limi a ion. Whi e ish and pe ch la ae eed on he same p ey
species, and he inc eased compe i ion possibly led o he low s ocking success and o he dec ease in
he biomass o pe ch la ae. These changes u he ansla ed o he subsequen li e s ages. Whi e ish
and pe ch la ae only di e ed quan i a i ely (i.e. in hei densi ies), no quali a i ely (i.e. in hei
compe i i e abili ies) as hey ha e iden ical coe icien s o eeding in e e ence. The negligible esponse
in he biomass o 4-yea -old and olde pe ch sugges s ha he oldes li e s age in pe ch is be e bu e ed
agains dis u bances han he younge li e s ages [11], p obably because he oldes pe ch is solely pisci-
o ous and a be e compe i o o ood han he younge pe ch (i.e. has a highe coe icien o eeding
in e e ence).
When pe ch was s ocked o ec i y he losses caused by whi e ish s ocking, whi e ish densi ies
dec eased. This was p obably due o a combined e ec o inc eased compe i ion among la ae and ju en-
iles, and p eda ion. An undesi ed ou come o pe ch s ocking was he dec ease in he densi y o he
4-yea -old and olde pe ch. This was possibly caused by he dec ease o la al and ju enile whi e ish,
which oge he wi h la al and ju enile pe ch cons i u e he die o he la ge pe ch. Inc eased whi e ish
s ocking (Wh 300) did no al e he abundance o he la ges pe ch because la al and ju enile whi e ish
(p ey o he la ges pe ch) densi ies inc eased du ing he g ow h season. In Wh 300 þPe 50, on he o he
hand, he densi ies o la al and ju enile pe ch inc eased sligh ly bu he densi ies o whi e ish la ae
and ju eniles dec eased.
Whi e ish s ocking inc eased ecosys em s abili y, while pe ch s ocking dec eased i . Pe ch as a pisci-
o ous ish media e he abundances o la al and ju enile ish. Changes in pe ch biomasses cascade
apidly h ough he LC ood web, des abilizing he ecosys em. Whi e ish depends solely on zooplank on
420
440
460
480
500
Wh 200
Wh 300
Wh 300
Wh 300 + Pe 50
middle o he
g
ow h season
0 50 100 150 200
580
590
600
610
620
630
Wh 200
Wh 300
end o he
g
ow h season
Wh 300
Wh 300 + Pe 50
ime (
y
ea )
0 50 100 150 200
ime (
y
ea )
biomass (µgC m−3 × 1000) biomass (µgC m−3 × 1000)
Figu e 3. Fluc ua ions in he o al ecosys em biomass a e inc eased whi e ish s ocking (Wh 300) compa ed wi h he whi e ish
baseline (Wh 200) and a e pe ch s ocking (Wh 300 þPe 50) compa ed wi h inc eased whi e ish s ocking (Wh 300) in he
middle and a end o he g ow h season. The o me is shown due o seasonal cyclici y in plank on biomasses.
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whose densi ies espond less d ama ically o inc eased p eda ion, po en ially because hey ha e mo e
eeding links han ish. This inc eased connec i i y can bu e agains changes in ish densi ies and s abil-
ize he species [12]. Fishing inc eases luc ua ions in he ecosys em [13] because i dec eases he a e age
body size o adul s and hus he body-size a ios be ween p eda o s and p ey [9]. This is a classical eco-
sys em and a popula ion-des abilizing ac o [14]. En i onmen al s ochas ici y would u he magni y he
luc ua ions a ising om in insic ood-web dynamics. Des abilized ecosys em is an undesi ed ou come
o bo h managemen and conse a ion: inc eased luc ua ions (pa icula ly among la ae) lead o
inc eased unce ain ies in s ock assessmen s, educed p edic abili y o popula ion and ecosys em
dynamics, and inc eases he isk o a ca as ophic popula ion collapse [15].
I he complex species in e ac ions and di e ences in species ecological unc ionali y a e igno ed
when planning s ocking p ac ices, s ocking can lead o undesi ed ou comes, such as dec eased adul
ish abundances and s abili y. Using a ood-web model o s udy he ou comes o s ocking can help o
o e come his. The s ocking p ac ices in ou s udy did no c ea e con lic s be ween he managemen
and conse a ion goals: nei he o hem was eached as s ocking did no subs an ially inc ease abun-
dances o ishes impo an o ishing bu al e ed he ecosys em dynamics and inc eased ins abili y.
In es iga ing closely how di e ences in lake ophic s a es and in species pai s in e ac wi h s ocking
p ac ices would be e allow gene aliza ion o ou esul s and c ea es a enues o u u e esea ch.
Da a accessibili y. Da a and codes a e deposi ed in D yad: h p://dx.doi.o g/10.5061/d yad.q53g43n [16].
Au ho s’ con ibu ions. A.K. and T.P. concei ed he s udy. S.U.-H., T.P. and A.K. did he simula ions and analysed he
esul s. S.U.-H. w o e he pape .
Compe ing in e es s. The au ho s do no ha e any compe ing in e es s.
Funding. This s udy was unded by he Academy o Finland and Na u al Sciences and Enginee ing Resea ch Council o
Canada (A.K.).
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