Empirical estimation of accumulation-induced change in gill net catchability: Mind the observation errors

Send O de s o Rep in s o ep in s@ben hamscience.ae The Open Fish Science Jou nal, 2015, 8, 13-22 13 1874-401X/15 2015 Ben ham Open Open Access Empi ical Es ima ion o Accumula ion-Induced Change in Gill Ne Ca ch- abili y: Mind he Obse a ion E o s Timo J. Ma jomäki1,*, Ma ko Paloniemi2, Tapio Keskinen3, Jonna Kuha1 and Juha Ka jalainen1 1Uni e si y o Jy äskylä, Depa men o Biological and En i onmen al Science, P.O.Box 35, 40014 Uni e si y o Jy äskylä, Finland; 2E elä-Pohjanmaan Kala alouskeskus y, Huh alan ie 2, 60220 Seinäjoki, Finland; 3Na u al Resou ces Ins i u e Finland; Su on ie 9 A, 40500 Jy äskylä, Finland Abs ac : We analyzed cumula i e ca ches o 24 h gill ne exposu es di ided in o 4*6 h, 2*12 h and 1*24 h soak ime ea men s o es ima e he educ ion in i s ca chabili y due o accumula ion o ish. The e ec s o loss o ca ch du ing ne li ing, dis u bance e ec and ouling we e elimina ed as a as possible o e eal he ue e ec o accumula ion. Fi s we applied simple nonpa ame ic and pa ame ic es s in compa ison o ea men s. As expec ed, conside able educ ion in ca chabili y ook place along wi h he inc ease in soak ime, indica ed by signi ican ly lowe o al 24 h ca ches om longe soaks in compa ison wi h sho e ones. The educ ion was mo e p onounced o oach han o pe ch. Fu he , we compa ed a unc ional ela ionship eg ession (FRR), admi ing co ec ly obse a ion e o a iance also in he x-axis a iable, wi h o dina y leas squa es eg ession (OLS) in modelling he ela ionship be ween cumula i e 24 h ca ches o di e en ea men s. We es ima ed he be ween- eplica es p opo ional obse a ion e o a iance wi hin a ea men and ound i o be simila in di e en ea men s. The e o e he a iance a io could be assumed o be close o 1 enabling he use o majo axis solu ion FRR. In his pa icula case he inco ec use o OLS ob iously gi es a se iously biased esul , exace ba ing he nega i e e ec o accumula ion o high x-axis alues in compa ison wi h FRR. We ecommend he use o FRR o any analysis compa ing di e en no o iously low p ecision ish abundance p oxies. Keywo ds: Accumula ion, bias, ca chabili y, e o in a iables, sa u a ion. INTRODUCTION In Eu ope, s anda dised gillne ing is a common me hod o moni o ing changes in abundance o ish popula ions and ish communi y s uc u e [1]. I is also a key me hod in he assessmen o he ecological s a us o lakes [2]. The basic assump ion o unbiased moni o ing o ela i e changes in popula ion abundance using ca ch pe uni e o (CPUE) is ha he ca chabili y o he gea is a densi y-independen con- s an , and con ains as li le as possible andom a ia ion due o o he densi y-independen ac o s [3, 4]. Thus, abundance and i s index should be di ec ly p opo ional o each o he . Un o una ely, his assump ion ypically does no hold o passi e gill ne s. Se e al s udies [5-10] ha e epo ed a nega- i e ela ionship be ween gill ne ca chabili y and abundance, and consequen ly CPUE may e en appea asymp o ically ela ed o abundance. One o he easons o his phenomenon is he e ec o ish accumula ion in a gill ne (see e iew [11] and e e - ences he ein). Many causal mechanisms, bo h biological and echnical, ha e been sugges ed: 1) ish a e epulsed a ound a cap u ed, possibly dead indi idual [12, 13]; 2) eas- ie isual de ec ion o he ne due o caugh ish [12]; 3) space limi a ion whe eby once a ish has been cap u ed, a ce ain a ea su ounding i is no longe capable o ca ching *Add ess co espondence o his au ho a he Uni e si y o Jy äskylä, Depa men o Biological and En i onmen al Science, P.O.Box 35, 40014 Uni e si y o Jy äskylä, Finland; Tel: +358 50 428 5274; E-mail: imo.j.ma jomaki@jyu. i ish [14]. Changes in he hanging a io and dec ease in lexi- bili y may also dec ease ca chabili y [15]. E en a small ca ch can educe he ca chabili y o a gill ne [15]. One consequence o ish accumula ion-induced dec ease in ca chabili y is ha he gill ne ca ch is no p opo ional o du a ion o ishing (se ime, soak ime) bu has been sug- ges ed o inc ease wi h dec easing a e [16, 12]. Kennedy [12] sugges ed ha i is possible o “sa u a e” ne s so ha hey will no ca ch ish any mo e, i.e. ca chabili y app oaches ze o (no e, howe e , ha pa o his dec ease may be due o ouling o ne wine wi h algae o sil [17, 18]). Sa u a ion is sugges ed o happen a a he low p opo ional ca ches, when only a ew pe cen o meshes a e occupied by ish [19, 15]. Thus, in he case o a long soak ime, he ca ch may be a he cons an , and independen o abundance; only he a e o accumula ion, which canno be obse ed, a ies. The e o e, i is essen ial o use sho soak ime and sui able imes o day (e.g. [15]). The e a e di e en ways o s udying he e ec o soak ime on gill ne CPUE. A di ec app oach is o obse e CPUE as a unc ion o soak ime, ei he om ca ch s a is ics [12] o by mul iple inspec ions o ne s du ing he ca ching p ocess [10]. Howe e , a common app oach is o se s an- da d gill ne s simul aneously in o as homogenous as possible habi a o di e en soak imes wi h eplacemen , and hen calcula e he cumula i e ca ch o e a longe pe iod, e.g., compa ing soak imes 1*24 h s. 2*12 h s. 4*6 h e c. e.g., [15, 20]. I has ypically been obse ed in such expe imen s ha one longe soak yields lowe ca ches han se e al sho e 14 The Open Fish Science Jou nal, 2015, Volume 8 Ma jomäki e al. soaks o he same o al exposu e pe iod. A high ish densi y o ac i i y his phenomenon occu s wi hin a ew hou s o e en less. I he exposu es a e made in loca ions o di e en ish densi ies and/o ac i i y pe iods (e.g., daily, seasons wi h di e en empe a u es), he e ec o ish densi y on accumula ion e ec o , mo e p ecisely applying he e mi- nology o P chalo á e al. [10, 20], ish densi y a e can be es ima ed. Typically, hese ield expe imen da a om di e en soak imes ha e been s a is ically app oached by i ing a nonlin- ea eg ession model be ween cumula i e CPUE o sho e soak ime as “independen ” a iable (x-axis) and longe soak ime CPUE as “dependen ” a iable (y-axis) e.g., [15]. I is impo an o acknowledge in his eg ession app oach 1) ha he wo a iables a e “equal” and hus no in any sense “in- dependen ” and “dependen ” and 2) ha bo h a iables, as wi h ishe ies da a in gene al, a e es ima es ha may con ain conside able obse a ion e o due o andom a ia ion, ei- he measu emen e o o na u al a iabili y. This con a- dic s he undamen al assump ion o he o dina y leas squa es eg ession (OLS) ha he independen a iable is measu ed wi hou e o and hus all e o is a esul o ob- se ing he dependen a iable. In p ac ice, he OLS eg es- sion is a he obus o andom e o in x-axis a iable i i is low ela i e o he e o in y-axis a iable, bu his p econdi- ion is no me in he con ex o eg essing wo gill ne CPUEs, equally p one o high andom e o . The andom e o wi hin he measu emen s o he x-axis a iable dis ib- u es he obse a ions a i icially widely in he ho izon al scale. As a consequence, he i ed OLS eg ession cu es become biased; in he special case o linea eg ession he slope is biased owa ds ze o [21] and in he case o cu e i ing he endency o asymp o ical cu a u e is exace ba ed [22]. In he case o CPUEs, his may lead o sys ema ic unde - es ima ion o he le el o he asymp o e (y-axis) and he le el o he x-axis a iable a which his asymp o e (i.e. sa u a ion) is eached. To elimina e o a leas dec ease hese biases, measu emen e o models, such as unc ional ela ionship eg ession (FRR) models, should be applied, as ad oca ed by Kimu a [23]. Fi ing o a FRR model is a s aigh o wa d ask, bu o be success ul equi es ha he a iances o andom e - o s, a iances o indi idual obse a ions a ound some un- known ue alues o bo h a iables, o a leas he a io o hese a iances, is known. These a e ypically unknown bu can be assessed by eplica ed obse a ions co esponding o one o mo e alues o he a iables [24]. In his s udy, we analyse a da ase om a ield expe i- men applying di e en gill ne soak imes o es ima ing cumula i e ca ch pe uni e o (U) o 24 h exposu e. Fi s ly, we apply obus nonpa ame ic and pa ame ic es s o show he exis ence o a nega i e e ec o accumula ion on ca ch- abili y. Then we i unc ional ela ionship eg ession models in an a emp o quan i y he e ec o accumula ion wi hou much bias. To achie e his, we es ima e he a iances o an- dom e o s in ca ch pe uni e o obse a ions. MATERIALS AND METHODOLOGY S udy A ea The gill ne ing expe imen was ca ied ou in Lake Jy äsjä i, Finland (62° 14’ N, 25° 46’ E). The a ea o he lake is 3.4 km2, mean dep h 7 m and maximum dep h 25 m. L. Jy äsjä i is meso ophic wi h o al phospho us concen- a ion du ing summe ypically 25-30 g l-1, chlo ophyll a 10-13 g l-1 and o al ni ogen 700 g l-1. The Secchi dep h a ies du ing he open wa e season be ween 1.4 and 2 m and he wa e colou is a ound 80 mg P l-1. The dominan species in he ish assemblage a e pe ch (Pe ca lu ia ilis L.) and oach (Ru ilus u ilus (L.)), comp ising >80 % o gillne ca ch pe uni e o [25]. Gillne s We used mul i mesh gillne s specially designed and s an- da dised o ish moni o ing. The leng h o he ne is 30 m (uppe ope 27 m, lowe 33 m) and heigh 1.5 m. The ne consis s o 9 panels o 3.3 m in leng h and a ea o 5 m2 wi h di e en mesh sizes om 10 o 55 mm om kno o kno (Table 1) in andomised o de . The mesh sizes closely obey a geome ic se ies p og ession ( a io be ween consecu i e mesh sizes cons an , in his case om 1.17 o 1.33) and hus i can be expec ed ha he ne is ai ly unselec i e owa ds ish leng h [26]. Table 1. P ope ies o mul imesh gill ne s used in expe imen in Lake Jy äsjä i. The numbe o meshes in each panel was calcula ed by: numbe o meshes ho izon- ally*numbe o meshes e ically * 2. Mesh Size, mm Twine Thickness, mm Numbe o Meshes 10 0.15 59940 12 0.15 41978 15 0.15 27084 20 0.15 15364 25 0.17 9443 30 0.17 6771 35 0.17 5130 45 0.20 2660 55 0.20 1891 Expe imen We ca ied ou 24 h ishing sessions epea ed 23 imes be ween June 28 and Sep embe 29 o s udy he e ec o accumula ion. We selec ed he loca ions o di e en ses- sions, based on he p e ious knowledge, o collec obse a- ions om di e en ish densi ies. Du ing e e y session, we se h ee ne s a noon wi hin one loca ion in he li o al zone ha was as homogenous as possible ega ding dep h and ege a ion. The ne s we e se in a ow pa allel o he sho e- line and 30-50 m apa . Based on p e ious expe ience, we conside ed his dis ance su icien o making he ca ches independen o each o he . A g ea e dis ance would ha e comp omised he assump ion o homogenei y o he habi a . One o he ne s was se o 24 h ( ea men 1*24 h), one was eplaced wi h a new one a e 12 h ( ea men 2*12 h) and one was eplaced a e e e y 6 hou s ( ea men 4*6 h). We Obse a ion E o s A ec Gill Ne Ca chabili y Es ima ion The Open Fish Science Jou nal, 2015, Volume 8 15 andomised he o de o ea men s in he ow o ne s o e e y session. Du ing e e y eplacemen , hus a 6 hou in- e als, we li ed e e y ne ha was no eplaced abo e he su ace and sunk again. This p ocedu e was ca ied ou be- cause: 1) I compensa es o he loss o caugh ish du ing li ing p ocess by making he numbe o li s o each ea - men equal du ing he 24 h pe iod; 2) I makes he amoun o dis u bance equal o e e y ea men ; and 3) I cleans he ne wines om deb is hus equalizing he loss o ca chabili y due o ouling o e e y ea men . Rega ding jus i ica ion 1) abo e we mus emphasise he ac ha al hough he ish ha we e caugh in he e y beginning o longe ea men s ob i- ously expe ienced se e al li ings, we assumed, based on ou p e ious obse a ions, ha he ish ha had been s uggling in he ne o longe han 6 hou s would ha e go en angled o an ex en ha hey would no ge eleased la e . Thus, we assume ha he ish ha ha e a chance o ge ing eleased mus ha e been caugh du ing he las 6 h pe iod be o e li - ing. Howe e , he numbe o ish escaping in li ing was so ma ginal ha his assump ion has no p ac ical e ec on he esul s. Bu see [10] o a p ope me hod o sho exposu es. Tempe a u e a ied be ween 12 and 25 °C du ing he s udy, he numbe o dayligh hou s om 19 o 11 h d-1 and wea he om sunny o ainy, so ha he ca ches ep esen no only he ac ual ish densi y bu he p oduc o densi y, empe a u e, illumina ion and wea he ela ed ac i i y. How- e e , i was assumed ha he p oduc , cumula i e ca ch in 24 h, esponded uni o mly o he accumula ion e ec despi e he uncon olled a ia ion in ac o s o he p oduc . No symp oms o di e en esponses (e.g. odd esidual co ela- ions wi h any o he abo e men ioned uncon olled ac o s) we e de ec ed in he analysis. We emo ed ca ches om he ne s immedia ely a e each gea eplacemen /main enance ip and eco ded he numbe and o al esh weigh o each species om e e y panel sepa a ely. We assessed he obse a ion e o a iance wi hin di e - en ea men s by eplica ing each soak ime ea men simul- aneously in a homogenous habi a o 24 h. The numbe s o eplica es we e 4 o ea men 1*24 h and 3 o 2*12 h and 4*6 h. S a is ical Analysis Va iables We calcula ed he o al numbe o ish caugh du ing he 24 h uni e o in each ea men sepa a ely o each panel o di e en mesh size and used his a iable in he u he analysis as a uni obse a ion. Una oidably, ca ches om di e en mesh sizes co ela ed wi h each o he wi hin ea - men be ween sessions; i.e. i he e was an excep ionally high ca ch in he 12 mm panel in he 1*24 h gillne in a ce - ain session, he 15 mm panel also yielded an excep ionally high ca ch. Thus, he obse a ions we e no comple ely inde- penden o each o he . This may lead in ce ain es s o a i i- cially high deg ee o eedom. To a oid his bias, we pe - o med se e al es s also o o al ca ch pe uni e o om all mesh sizes. We limi ed he mesh size speci ic s a is ical analysis o obse a ions om mesh sizes 10-30 mm. La ge meshes we e omi ed because hei cumula i e ca ches in 24 h we e e y low, wi h mo e han 50 % o he ca ches being 0, and a maximum o only 6 indi iduals. Ze o ca ches we e also omi ed om analysis o o he mesh sizes ( o 20 mm 1 ca ch ou o 69, 25 mm 2/69 and 30 mm 8/69, o ally 11/414, 2.7 %) because we conside ed hose cases o be below meas- u emen sensi i i y. To make all esul s compa able, we scaled he ca ches pe uni o e o (U) p opo ional o one million meshes in each panel by PUm, , i = Um, ,i / Nm *1 000 000, (1) whe e PUm, ,i = p opo ional ca ch pe uni o e o o mesh size m, ea men and session i, Um, ,i = numbe o ish caugh in 24 h and N m = numbe o meshes in panel o mesh size m ( om kno o kno ). We log10- ans o med all alues ou inely in o de o s anda dise and no malise e o a iance in model i ing. PUm, ,i is compa able o he commonly used index “pe cen - age o meshes occupied” so ha he alues o PUm, ,i = 1000 and logPUm, ,i = 3 co espond o 1 ‰ o meshes occupied. Whene e o al ca ch om all meshes (including all he mesh sizes and also ze o ca ches) was used in any analysis, i was calcula ed as an a e age pe cen age om he alues o di e en mesh sizes. To alPU ,i = sum(PUm, ,i)/9 A Nonpa ame ic Tes o Accumula ion E ec I accumula ion induces a nega i e e ec on ca chabili y, hen i can be hypo hesised (H1) ha longe con inuous soak ime yields ypically lowe ca ch han he equally long o al exposu e consis ing o se e al sho e soak imes. The pai s o obse a ions we e, he e o e, bina y coded: X = 1 i Um, ,i o longe soak ime ea men was lowe han ha om sho e soak ime ea men and X = 0 in opposi e case. Acco ding o he H0-hypo hesis o no e ec , he bina y obse a ions should obey an e en (50:50) dis ibu ion. We applied a simple 2- es o assess whe he he obse ed dis- ibu ion o ce ain pai o ea men s de ia ed signi ican ly om his. A Pa ame ic Tes o Accumula ion E ec We applied a pai wise - es wi h he session (da e) as he classi ying ac o o es he signi icance o di e ence in To alPU ,i om all pai s o ea men s. As abo e i accumula ion induces nega i e e ec on ca chabili y, hen i can be hypo hesised (H1) ha he a e age[log(To alPUY,i) – log(To alPUX,i)] < 0, whe e Y is longe exposu e ea men and X is sho e . We also es ed whe he he gene al esul was di e en o di e en mesh sizes (H1: in e ac ion e m o ea - men *mesh size signi ican ) using epea ed measu es ANOVA wi h mesh size as wi hin subjec ac o . Repea ed measu es and pai wise es s we e selec ed because he s udy desing was based on he idea o measu ing he same a i- 16 The Open Fish Science Jou nal, 2015, Volume 8 Ma jomäki e al. able, a e age densi y in pa icula si e in pa icula momen wi h h ee di e en “measu emen de ices” i.e., exposu e ea men s. Modelling We applied he powe unc ion, one o he simples non- linea unc ions, in model i ing be ween ea men s: PUm,Y,i = a * PUm,X,ib (2) whe e a and b a e eg ession coe icien s and subsc ip s Y and X deno e di e en ea men s. I accumula ion has no e ec a and b ha e a alue o 1and he unc ion simpli ies o PUm,Y,i = PUm,X,i (3) Taking he loga i hmic o m o equa ion 2, he model be- comes linea logPUm,Y,i = log(a) + b * logPUm,X,i (4) The pa ame e es ima es log(a) and b o OLS- eg ession we e es ima ed in a s anda d way. The pa ame e es ima es o linea unc ional ela ionship eg ession (FRR) a e [21, 23]: b = ((sy2 – sx2) + ((sy2 – sx2) + 4sxy2)0.5)/(2sxy), (5) whe e  = 2 / 2 (6) log(a) = Y – Xb (7) whe e sy2, sx2 and sxy a e sample a iances and co a iance o logPUm,Y,i and logPUm,X,i and Y and X a e hei sample means. 2 and 2 a e he es ima es o obse a ion e o a i- ances o Y- and X-axis a iables, espec i ely. These we e es ima ed om he da a o simul aneous eplica es o e e y ea men by  2 = (logPUm, ,j – logPUm, )2/(n – 1) (8) whe e logPUm, ,j is he j: h eplica e obse a ion o mesh m and ea men and logPUm, is he sample mean o all eplica es o ea men . To illus a e he e ec o unc ional o m on he di e - ence be ween OLS and FRR we i ed also an asymp o ic model logPUm,Y,i = log(1/(1/a+b/PUm,X,i) (9) o di e en alues o  using he i e a i e me hod de- sc ibed by Kimu a (2000) [23]. RESULTS To al Ca ch and Species Dis ibu ion Al oge he 10428 indi iduals, 296 kg and 12 species we e caugh du ing he 23 ishing sessions o 24 h wi h h ee ea men s (Table 2). The majo i y o he ca ch (indi iduals) consis ed o pe ch, wi h oach he second mos common spe- cies. Toge he hese species o med o e 90 % o he ca ch. Rega ding yield (ca ch in mass uni s), oach was he mos abundan species and pe ch second, oge he cons i u ing almos 90 % o o al yield. Nonpa ame ic F equency Di e ence App oach In compa ison o e en dis ibu ion o anks, he 24 h ca ches pe uni e o om he 1*24 h and 2*12 h soak ime ea men s we e signi ican ly mo e o en lowe han ha o he 4*6 h ea men (Table 3, Figs. (1-3) di ision o obse a- ion on di e en sides o Y = X line), showing ha ish ac- cumula ion clea ly educed gill ne ca chabili y. The esul was consis en o bo h indi idual 10-30 mm panels and he a e age o he whole gillne . The ea men 1*24 h ypically also yielded lowe ca ches han 2*12 h bu he esul was no as p onounced as o he compa ison wi h 4*6 h. Table 2. The ca ch (indi iduals), yield (kg) and mean mass o di e en ish species caugh om Lake Jy äsjä i du ing he ex- pe imen . Common Name Scien i ic Name Ca ch % Yield % Mean Mass, g Pe ch Pe ca lu ia ilis L. 6955 66.7 108.1 36.5 16 Roach Ru ilus u ilus (L.) 2844 27.3 148.9 50.3 52 Bleak Albu nus albu nus (L.) 218 2.1 3.6 1.2 17 Ru Gymnocephalus ge nuus (L.) 153 1.5 1.4 0.5 9 B eam Ab amis b ama (L.) 91 0.9 12.0 4.1 132 Pike-pe ch Sande luciope ca (L.) 84 0.8 13.6 4.6 162 Sil e b eam Ab amis bjoe kna (L.) 43 0.4 1.7 0.6 40 Whi e ish Co egonus la a e us (L.) 25 0.2 2.6 0.9 104 Smel Osme us epe lanus (L.) 9 0.1 0.1 < 0.1 11 Pike Esox lucius L. 4 < 0.1 2.4 0.8 600 Rudd Sca dinius e y h op halmus (L.) 1 < 0.1 0.1 < 0.1 100 B own ou Salmo u a L. 1 < 0.1 1.6 0.5 1600 To al 10428 296.1 28 Obse a ion E o s A ec Gill Ne Ca chabili y Es ima ion The Open Fish Science Jou nal, 2015, Volume 8 17 Table 3. Resul s o he 2- es o H1: he p opo ional cumula i e 24 h ca ch pe uni e o o a longe soak ime ea men is lowe han ha o a sho e one. Roman nume als e e o ea men s. Da a T ea men I s. II I < II I > II n 2 p 1*24 h s. 4*6 h 83 49 132 8.76 0.003 1*24 h s. 2*12 h 71 56 127 1.77 0.183 10–30 mm meshes indi idually 2*12 h s. 4*6 h 75 54 129 3.42 0.064 1*24 h s. 4*6 h 17 6 23 5.26 0.022 1*24 h s. 2*12 h 14 9 23 1.09 0.297 To al ca ch 2*12 h s. 4*6 h 17 6 23 5.26 0.022 Table 4. Resul s o he pai wise - es o one- ailed H1: he mean di e ence be ween log o ca ch pe uni e o (logPU) o he 24 h ishing pe iod o longe soak imes and sho e ones is nega i e. Mean a io is he geome ic mean o he a io be ween longe and sho e soak ime U:s (no e: di e ence log(y)-log(x) = log(y/x) and hus Mean a io = 10mean(log(y/x))). Da a T ea men s Mean Di e ence S.E. d p Mean Ra io 1*24 h s. 4*6 h -.111 .034 -3.264 131 0.001 .775 1*24 h s 2*12 h -.065 .031 -2.087 126 0.019 .861 10–30 mm meshes indi idually 2*12 h s. 4*6 h -.039 .030 -1.310 128 0.096 .914 1*24 h s. 4*6 h -.158 .040 -3.933 22 < 0.001 .695 1*24 h s. 2*12 h -.078 .038 -2.040 22 0.027 .835 To al ca ch 2*12 h s. 4*6 h -.080 .026 -3.100 22 0.003 .832 Table 5. The o al ca ches o pe ch and oach du ing he 24 h ishing pe iod and hei p opo ions o o al ca ch om di e en soak ime ea men s is shown below. Species Indi iduals Ca ch % 4*6 h 2*12 h 1*24 h 4*6 h 2*12 h 1*24 h Pe ch 2493 2422 2040 65.9 69.4 73.1 Roach 1221 937 686 27.8 24.5 22.5 Pa ame ic Quan i a i e Di e ence App oach Quan i a i e pai wise compa ison o he logPU alues be ween longe and sho e soak ime ea men s indica ed ha he longe soak gillne s yielded lowe ca ches han sho e soak ones (all one- ailed p- alues < 0.1, Table 4). The ca ches o he longes 1*24 h soak ea men we e on a e age 20-30 % lowe han ha o he sho es 4*6 h soak ea men . The di e ence be ween 1*24 h and 2*12 h and be ween 2*12 h and 4*6 h was ypically less, as expec ed, bu was s ill signi ican . The highes ca ches o he longes soak ime (1*24 h) we e also clea ly lowe han hose o sho e soak imes (Figs. 1-3). The epea ed measu es ANOVA wi h mesh size as wi hin-subjec ac o e ealed ha he gene al esul was no di e en o di e en mesh sizes, because in e ac ion ea - men o he*mesh size was no signi ican (p > 0.1). The soak ime ea men had a signi ican e ec on he p opo ions o he wo mos common species (Table 5) (Re- pea ed measu es ANOVA: Pe ch F = 6.48, d = 2, p = 0.003; Roach F = 4.29, d = 2, p = 0.02). The p opo ion o pe ch inc eased wi h he inc ease in soak ime (pai wise compa i- son 4*6 h s. 1*24 h p = 0.003) and ha o oach dec eased (pai wise compa ison 4*6 h s. 1*24 h p = 0.012). Al hough he ca ch in numbe o bo h species declined wi h he in- c ease in soak ime, he dec ease was mo e ma ked o oach han o pe ch. Thus, he ca chabili y o oach seems o be mo e sensi i e o he accumula ion han ha o pe ch. Modelling App oach Fo he applica ion o a unc ional ela ionship eg ession (FRR), we i s es ima ed he obse a ion e o a iances o di e en ea men s. The coe icien o a ia ion o logPU be ween simul aneous eplica es om one si e a ied consid- e ably o di e en mesh sizes bu wi hou any end ela ed o mesh size (Table 6), e en hough he geome ic means o di e en ea men s we e almos iden ical a 5 – 6 %. This co esponds o a pe cen ile de ia ion om he mean in he 18 The Open Fish Science Jou nal, 2015, Volume 8 Ma jomäki e al. o iginal U-da a o -24 % o +32 %; hus assuming a log o no mal dis ibu ion o measu emen s, 66 % o U- obse a ions we e wi hin he ange and 76 – 132 % o he mean. Table 6. The coe icien o a ia ion (C.V. = S.D./mean) o logPU be ween eplica es o di e en soak ime ea men s. Mesh Size C.V. o T ea men mm 1*24 h 2*12 h 4*6 h n=4 n=3 n=3 10 0.17 0.15 0.03 12 0.04 0.02 0.05 15 0.02 0.01 0.05 20 0.03 0.08 0.06 25 0.12 0.06 0.07 30 0.10 0.12 0.06 GM 0.06 0.05 0.05 The a iance a ios  o di e en mesh sizes and pai s o ea men s also a ied conside ably (Table 7). Howe e , he geome ic mean o e e y pai was e y close o uni y, indi- ca ing ha he ela i e obse a ion e o was a he simila o e e y ea men . Due o he low numbe o eplica es and he e o e high andom a iabili y in a io es ima es, conside able unce - ain y abou he ue alue o  emains. The e o e, we i ed a unc ional ela ionship eg ession o se e al - alues (Figs. 1-4, Table 8). Based on he esul ha obse a ion e o a iances o di e en soak ime ea men s a e a he equal, he mos likely unc ional ela ionship is he cu e o  = 1. The cu e o  = 2 ep esen s an assump ion ha he obse a ion e o a iance o he y-axis a iable is 2- imes ha o he x-axis a iable, and o  = 0.5 he opposi e. The ue a io o a iances is no likely o be ou side ha ange. In con as , he o dina y leas squa es (OLS) solu ion assum- ing no obse a ion e o o he x-axis a iable gi es a se i- ously biased esul , exace ba ing he nega i e e ec o ac- cumula ion o high x-axis alues. Mo eo e , i p edic s ha a low alues o he x-axis a iable (sho e soak imes), he ypical ca ch o longe soak ime is highe . This is clea ly no logical, bu a highly expec ed bias which can be ex- plained simply by measu emen e o s in he x-axis a iable (in his pa icula case unde es ima ion o he ue alue). Fo FRR wi h  = 1 he esiduals be ween obse ed and p edic ed alues we e no signi ican ly di e en o di e en mesh sizes (ANOVA, all p > 0.05) in any pai o soak ime ea men s. The accumula ion e ec was s onges when compa ing he pai o longes and sho es ea men s, 1*24 h s. 4*6 h, (Fig. 1) bu could be de ec ed also o o he pai s o less di - e ence in soak ime (Figs. 2 & 3). Thus, he accumula ion e ec was e iden al eady wi h a 12 h soak ime. Assuming an asymp o ic ela ionship be ween he soak ime ea men U:s (wi h log-no mal e o s uc u e) leads o e en mo e biased in e p e a ion in he OLS solu ion in com- pa ison wi h FRR wi h  = 1 (Fig. 4, Table 8). Fo OLS, he ne appea s sa u a ed when U is abou 1 ‰, whe eas o  = 1 he sa u a ion appea s a abou 2 ‰ (Table 8). DISCUSSION The simple nonpa ame ic and pa ame ic es s indica ed clea ly ha he accumula ion o ish nega i ely a ec s he ca chabili y al eady be ween 6 and 12 h soak imes a he ish densi y a e, sensu [10, 20], occu ing in Lake Jy äs- jä i. Impo an ly, in ou ield es he e ec s o loss o some ca ch due o ne li ing, dis u bance and ouling we e elimi- na ed as a as possible o e eal he ue e ec o accumula- ion. In he cases o highes ish densi y a e he ne s may ha e al eady los conside able ca chabili y wi hin 6 h and he e- o e he ca ch pe uni e o migh no be p opo ional o densi y e en o his sho soak ime. When compa ing 1*4 h wi h 4*1 h ea men s, signi ican accumula ion e ec has been de ec ed e en wi hin he i s 4 hou s [15]. When Table 7. The es ima ed obse a ion e o a iances o logPU o di e en mesh sizes and ea men s and a iance a io . Mesh Size Va iance o T ea men  o Pai mm 1*24 h 2*12 h 4*6 h 1*24 h 4*6 h 1*24 h 2*12 h 2*12 h 4*6 h 10 0.1988 0.2060 0.0068 29.23 0.96 30.30 12 0.0194 0.0048 0.0272 0.72 4.01 0.18 15 0.0045 0.0015 0.0307 0.15 2.99 0.05 20 0.0058 0.0624 0.0395 0.15 0.09 1.58 25 0.1103 0.0297 0.0443 2.49 3.72 0.67 30 0.0398 0.0906 0.0244 1.63 0.44 3.72 GM 1.10 1.10 1.01 Obse a ion E o s A ec Gill Ne Ca chabili y Es ima ion The Open Fish Science Jou nal, 2015, Volume 8 19 Fig. (1). The unc ional ela ionship eg ession powe unc ions o di e en alues o obse a ion e o a iance a io  i ed o mesh size speci ic pai s o p opo ional ca ch pe uni e o du ing 24 h pe iod om soak ime ea men 1*24 h and 4*6 h. OLS is o dina y leas squa es solu ion ( = ), Y = X is he line o equal alues indica ing no accumula ion induced e ec on ca chabili y. Linea models we e i ed o log-da a. Pa ame e es ima es a e gi en in Table 8. Fig. (2). The unc ional ela ionship eg ession powe unc ions o di e en alues o obse a ion e o a iance a io  i ed o mesh size speci ic pai s o p opo ional ca ch pe uni e o du ing 24 h pe iod om soak ime ea men 1*24 h and 2*12 h. OLS is o dina y leas squa es solu ion ( = ), Y = X is he line o equal alues indica ing no accumula ion induced e ec on ca chabili y. Linea models we e i ed along wi h log-da a. Pa ame e es ima es a e gi en in Table 8. compa ing he esul s wi h o he expe imen s i mus be no ed ha di e en densi y a es, o al ishing pe iods and soak imes yield quan i a i ely di e en p o iles. Also bo h he wa e colou [15] and he species composi ion (as shown in his s udy) a ec he accumula ion e ec . Howe e , a e compensa ing o he di e en soak imes and o he me h- odological di e ences, he ela i e ca ches in his s udy a e compa able wi h hose in [15]. The use o FRR, assuming equal p opo ional obse a- ion (es ima ed o log-obse a ions) e o in bo h a iables wi h  = 1, yielded e y di e en cu es in modelling in compa ison o OLS- eg ession, which as expec ed exagge - a ed he accumula ion e ec . Thus, FRR can be ecom- mended as a wo king s anda d o his so o modelling ap- p oach. Howe e , i mus be emphasized ha he co ec ness (accu acy) o he es ima ed model depends on he 0 1000 2000 3000 4000 0 1000 2000 3000 4000 P opo ional ca ch pe uni e o o 1*24 h soak ime P opo ional ca ch pe uni e o o 4*6 h soak ime 10 mm 12 mm 15 mm 20 mm 25 mm 30 mm Y = X λ = 0.5 λ = 1 λ = 2 OLS 0 1000 2000 3000 4000 0 1000 2000 3000 4000 P opo ional ca ch pe uni e o o 1*24 h soak ime P opo ional ca ch pe uni e o o 2*12 h soak ime 10 mm 12 mm 15 mm 20 mm 25 mm 30 mm Y = X λ = 0.5 λ = 1 λ = 2 OLS 20 The Open Fish Science Jou nal, 2015, Volume 8 Ma jomäki e al. Fig. (3). The unc ional ela ionship eg ession powe unc ions o di e en alues o obse a ion e o a iance a io  i ed o mesh size speci ic pai s o p opo ional ca ch pe uni e o du ing 24 h pe iod om soak ime ea men 2*12 h and 4*6 h. OLS is o dina y leas squa es solu ion ( = ), Y = X is he line o equal alues indica ing no accumula ion induced e ec on ca chabili y. Linea models we e i ed o log-da a. Pa ame e es ima es a e gi en in Table 8. Fig. (4). The unc ional ela ionship eg ession solu ion wi h  =1 o an asymp o ic unc ion in compa ison wi h he OLS solu ion o powe unc ion o 1*24 h and 4*6 h ea men s. Fo compa ison o models, he powe unc ion solu ions om Fig. (1) a e also gi en. OLS is o di- na y leas squa es solu ion ( = ), Y = X is he line o equal alues indica ing no accumula ion induced e ec on ca chabili y. Models we e i ed along wi h log-da a. Pa ame e es ima es a e gi en in Table 8. co ec ness o he es ima e o he a iance a io . To ou knowledge, no es ima es o obse a ion e o a iance, le alone a iance a ios , o gill ne s ha e been published p e- iously. The p esen s udy did no yield e y p ecise es i- ma es ei he , e en hough we ied o es ima e i in as ho- mogenous as possible habi a . The numbe o eplica es was un o una ely a he low due o he limi ed a ailable a eas judged as homogenous. Despi e hese sho comings he e- sul ha he ela i e a iances o di e en soak imes we e o he same o de o magni ude sounds logical and acco ds wi h expec a ions, and hus o assume  = 1 (a so-called ma- jo axis solu ion) may be a easonable a p io i assump ion i he obse a ion e o a iance is unknown. Impo an ly also, he FRR mus be ecommended as a s anda d o any eg ession app oach s udy compa ing meas- u emen s om di e en densi y es ima ion me hods, such as CPUEs om di e en gea , ma k- ecap u e, emo al, echo sounding and isual coun s. Typical ish densi y p oxies, whe he ela i e o absolu e, a e es ima es con aining 0 1000 2000 3000 4000 0 1000 2000 3000 4000 P opo ional ca ch pe uni e o o 2*12 h soak ime P opo ional ca ch pe uni e o o 4*6 h soak ime 10 mm 12 mm 15 mm 20 mm 25 mm 30 mm Y = X λ = 0.5 λ = 1 λ = 2 OLS 0 1000 2000 3000 4000 0 1000 2000 3000 4000 P opo ional ca ch pe uni e o o 1*24 h soak ime P opo ional ca ch pe uni e o o 4*6 h soak ime 10 mm 12 mm 15 mm 20 mm 25 mm 30 mm Y = X λ = 1 asymp . OLS asymp . λ = 1 powe OLS powe Obse a ion E o s A ec Gill Ne Ca chabili y Es ima ion The Open Fish Science Jou nal, 2015, Volume 8 21 Table 8. The pa ame e es ima es o he models gi en in igu es 1 – 4. Models we e i ed along wi h log-da a consis en ly. OLS = O dina y Leas Squa es. Fig. Model T ea men s  a b 0.5 2.7 0.81 1 7.9 0.65 2 14.8 0.55 Fig. (1) Powe y=a xb 1*24 h s. 4*6 h  OLS 27.2 0.43 0.5 0.8 1.02 1 3.2 0.80 2 8.4 0.65 Fig. (2) Powe y=a xb 1*24 h s. 2*12 h  OLS 21.2 0.51 0.5 1.8 0.90 1 3.7 0.79 2 6.5 0.70 Fig. (3) Powe y=a xb 2*12 h s. 4*6 h  OLS 12.5 0.60 1 2200 0.87 Fig. (4) Asymp o ic y=1/(1/a+b/x) 1*24 h s. 4*6 h  OLS 974 0.39 conside able obse a ion e o . No aking hese in o accoun in he analysis may lead o se iously biased unde s anding o he co espondence be ween di e en me hods. Ano he cause o unce ain y in he eg ession app oach is unce ain y abou he co ec model unc ional o m. In ou analysis we used a simple powe unc ion, which does no each any asymp o e, ull sa u a ion, al hough admi edly ha mus s ill be assumed possible, a leas heo e ically, wi h e y long soak ime and/o high densi y a e. Howe e , he a iabili y o he da a is high which ende s i di icul o de e mine any “co ec ” o m o he ela ionship. One bene- i o he powe unc ion is ha i is easy o apply in p ac ice because i can be educed o a linea model assuming log- no mali y o e o . Ano he bene i is ha i is a bijec i e unc ion o any posi i e X-axis a iable alue and he e o e i s ans e unc ion is a bijec ion as well. The ans e unc- ion is needed whene e a emp ing o elimina e he accumu- la ion e ec bias in CPUE induced by long soak ime. The a iabili y induced by obse a ion e o and ue spa ial a ia ion in densi y in CPUE es ima es om e e y indi idual gill ne is oo high o p ac ical applica ion o a ans e unc- ion bu he annual whole lake a e age could be ea ed wi h i , as when ying o make esul s om a 24 h soak ime mo e compa able wi h a 4*6 h soak ime and hus mo e p opo - ional o he ue densi y a e. Fo example, he annual a e - age o 20 gill ne s using 24 h soak ime which has been he s anda d o Lake Jy äsjä i could be ans o med o 4*6 h es ima es whene e he 1*24 h ca ch is highe han he poin o in e sec ion be ween he model and line y=x, oughly abo e he le el o 500 in Fig. (1). Fo he Wa e F amewo k Di ec i e [2], he assessmen o ecological s a us o lakes based on ish assemblages is accomplished by expe imen al gill ne ishing. In he Eu o- pean s anda d [1] he ecommended sampling pe iod is 12 h. Acco ding o he s anda d, bias induced by accumula ion will occu when he 19 mm panel yield exceeds 120 g m-2 o he yield o he whole gill ne exceeds 6 kg. In hose cases soak ime should be educed. Accumula ion is measu ed by mass which does no ake in o accoun he numbe o ish o numbe o meshes occupied. Based on ou and ea lie s udies he bias should be assessed based on he numbe o ish in he ca ch o he numbe o meshes used. An in e es ing, ye o p ac ical applica ions complica - ing, esul was he inding ha pe ch and oach had di e en accumula ion e ec esponses, oach being mo e sensi i e o accumula ion. I his is ue i mus be aken in o accoun when applying indices o lake ecological s a us based on ish assemblages e.g., EQR4 [27]. Mo eo e , gillne sampling o e es ima es he p opo ion o pe cids in ela ion o cyp- inids [28] inc easing he bias. The species-speci ic ea u es can be complica ed o model, as he accumula ion e ec migh be a unc ion o densi y and ac i i y o he species i sel o a ec ed also by se e al o he species wi h di e en e ec sizes and, he e o e, beyond he scope o his s udy. O he compa able s udies [15, 20] did no epo any symp- oms o p ominen changes in species p opo ions when compa ing da a o 1*12 h s. 3*4 h ea men s and o e - nigh s. 1 h ea men s, espec i ely. Con a y o ou ind- ings, e en dec easing ca chabili y wi h inc easing densi y pa icula ly o pe ch and o a lesse ex en wi h oach has been ound [9]. These species-speci ic di e ences de ini ely equi e u he s udy. CONFLICT OF INTEREST The au ho s con i m ha his a icle con en has no con- lic o in e es .