###################################################### ## Robin Cook ## ## University of Strathclyde ## ## Department of Mathematics and Statistics ## ## Livingstone Tower, 26 Richmond Street ## ## GLASGOW, G1 1XH, UK ## ## E-mail: robin.cook@strath.ac.uk ## ## ## ## Date: 25 November 2014 ## ## ## ## Reduced model bayesian estimation of fishery ## ## discard weights for a given species using input ## ## from demersal trawl survey biomass-at-length ## ## data. ## ## ## ## Requires OpneBUGS software package (v3.2.3) ## ## for performing Bayesian inference, which is ## ## available for download at www.openbugs.net ## ###################################################### ################################################## # nsp=number of reference species # B=fitted biomass # sigma.y=s.d. for biomass process error # dr= process error for catch ratio (estimated from reference species # r=catch ratio raising factor # q= "over-quota" or non-size selective discards # srd=selection range for size-discards # ld50=50% retention length for discards # sr=selectio range for commercial fleet # l50=50% selection length for commercial fleet # ret=proprtion of catch retained # sel=commercial selectivity # c=catch biomass at length # pb=biomass at length in the index # d=discard biomass at length # yld=total annual catch biomass # lan=total annual landings biomass # dis=total annual discard biomass # rmean=catch ratio for reference species k # p.ratio=weight given to rmean for reference species k # rfsum=weighted sum of reference species catch ratios # L=observed annual landings biomass # b.tot=log total annual biomass index # tau.l=precision of oberved landings # tau.b=precision of log biomass ################################################## model{ for( i in 1:l2){ len[i]<-i # sets up a length index } # set starting biomass as geometric mean sum of observed biomass at length B[1]~dnorm(b.tot[34],0.5) for(k in 1:nsp){ r[1,k]~dnorm(0,44.85) } # set up randon walk for biomass # fill time series for true biomass and catch ratio sigma.y~dunif(0,100) # uniform prior for process error tau.dy<-pow(sigma.y,-2) for(j in 2:y2){ dy[j]~dnorm(0,tau.dy) B[j]<-B[j-1]+(dy[j]) # note this is on a log scale for(k in 1:nsp){ dr[j,k]~dnorm(0,67.06) r[j,k]<-r[j-1,k]+dr[j,k] } } # fix values for q and priors for uncertain values of q for(j in y1:y2){ q[j]~dbeta(q1[1],q1[2]) # prior for over-quota discards based on distibution from reference species } # set discard retention ogive srd~dnorm(6,4)I(.1,10) # gives a range of about +- 3 cms bd<-(2.197225)/srd mls0<-0.874 # "h" paramterf or the model to account for negative bias in MLS estimates ld50<-mls*mls0 # scales MLS to virtual MLS ad<--bd*ld50 for(j in y1:y2){ for(i in l1:l2){ logit(ret[j,i])<-ad+bd*len[i] # fills discard retention ogive } } #set selectivity for commercial fleet sr~dnorm(6,2)I(1,10) l50~dnorm(l50.fleet,tau.fleet) bc<-(2.197225)/sr ac<--(bc*l50) for(j in y1:y2){ for(i in l1:l2){ logit(sel[j,i])<-ac+bc*len[i] } } # calculate mean discarded proportion for years of zeros in length distribution using an average size frequency q.mean<-q1[1]/(q1[1]+q1[2]) # expected value from beta distribution for(i in 1:l2){ pb.sum[i]<-sum(pb[,i]) c.mean[i]<-pb.sum[i]*sel[1,i] dis.mean[i]<-c.mean[i]*(q.mean+(1-q.mean)*(1-ret[1,i])) } yld.mean<-sum(c.mean[])/sum(pb.sum[]) # mean proportion of index biomass that is discounted by selectivity p.mean<-sum(dis.mean[])/sum(c.mean[]) # mean proportion discarded # calculate total catch, landings and discards for(j in y1:y2){ for(i in l1:l2){ c[j,i]<-pb[j,i]*sel[j,i]*exp(B[j]-b.tot[j]) # correct biomass at length to fitted biomass scale d[j,i]<-c[j,i]*(q[j]+(1-q[j])*(1-ret[j,i])) # this is already corrected for biomass in above eqn } yld[j]<-sum(c[j,])+equals(sum(c[j,]),0)*yld.mean*exp(B[j]) # use mean values when zero data dis[j]<-sum(d[j,])+equals(sum(d[j,]),0)*p.mean*yld[j] # use mean vlaues when zero data lan[j]<-yld[j]-dis[j] p[j]<-dis[j]/yld[j] } # estimate total catch # prior for catch ratio weights (dirichlet distribution derived from uniform) for(k in 1:(nsp-1)){ c.ratio[k]~dunif(0.0,alpha[1]) } p.r[nsp]<-1 p.r[1:(nsp-1)]<-sort(c.ratio[]) p.ratio[1]<-p.r[1] for(k in 2:nsp){ p.ratio[k]<-p.r[k]-p.r[k-1] } for (j in y1:y2){ for(k in 1:nsp){ rf[j,k]<-p.ratio[k]*(rmean[j,k]+r[j,k]) } rfsum[j]<-sum(rf[j,]) Y[j]<-yld[j]*exp(rfsum[j]) log.Y[j]<-log(Y[j]) L.fit[j]<-Y[j]*(1-p[j])+.1 l.fit[j]<-log(L.fit[j]) D[j]<-Y[j]-L.fit[j] dis.q[j]<-Y[j]*q[j] # get q related discards dis.s[j]<-Y[j]*(p[j])-dis.q[j] # get size related discards } # likelihoods tau.l~dgamma(.01,.01) # gamma prior on landings precision tau.b~dgamma(.01,.01) # gamma prior on biomass precision for(j in y1:y2){ L[j]~dlnorm(l.fit[j],tau.l)#landings data b.tot[j]~dnorm(B[j],tau.b) #survey data } } #end model # data file for lemon sole list(l1=1,l2=60, # length range for biomass index y1=1,y2=33, # year range for data mls=25, # minimum landing size l50.fleet=15.08, # L50 for commercial selectivity estimated from reference species tau.fleet=.156, # precision of L50 estimate nsp=5, # number of reference species alpha=c(1,1,1,1,1), # default weighting for catch ratio q1=c(1.4,12), # parameters for beta prior on q from refefence species pb=structure(.Data=c( # matrix of biomass at length by year 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000259936,0.000353291,0.000466945,0.001205930,0.000763430,0.007603444,0.00233213,0.01271201,0.03214211,0.04212442,0.06836128,0.11266455,0.12401865,0.1498793,0.1503705,0.2325655,0.2092584,0.2294148,0.2299530,0.2414740,0.2516295,0.2972894,0.3692230,0.4289277,0.3220526,0.3388905,0.3255284,0.1933469,0.4026000,0.3225801,0.2052734,0.2437900,0.1433022,0.0770775,0.0275914,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000423297,0.000546602,0.001384135,0.001723176,0.00317120,0.01024333,0.01533557,0.01091051,0.04060177,0.06227627,0.07495056,0.1358691,0.1098088,0.1247747,0.1605134,0.1204037,0.2084578,0.2189019,0.2661262,0.3705623,0.2510320,0.2148814,0.2694907,0.2089044,0.3219264,0.2921226,0.3808345,0.2408218,0.1116511,0.0602731,0.0433023,0.0931635,0.1000491,0.0268174,0.0287083,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000998444,0.000000000,0.001632403,0.001016128,0.00748001,0.01359072,0.02532076,0.03216873,0.04788437,0.10576304,0.08839420,0.1446064,0.1250392,0.1116349,0.0917838,0.0774546,0.1301549,0.1048798,0.1255441,0.1390546,0.1644771,0.0482712,0.1986428,0.1304337,0.2214737,0.1722598,0.1497145,0.1622956,0.0658388,0.0473894,0.0255346,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0386311,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000841448,0.000000000,0.000000000,0.00162727,0.01379765,0.01888626,0.02239442,0.02960670,0.01533906,0.09319165,0.1326375,0.1224094,0.1390926,0.2470970,0.1600762,0.2076434,0.3791039,0.4682046,0.3630135,0.3148794,0.4883121,0.7260024,0.4540106,0.4542806,0.6070928,0.5618354,0.2383233,0.4583403,0.2783563,0.4332916,0.1792718,0.1155130,0.0000000,0.0441941,0.0472402,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000442343,0.000000000,0.002264855,0.006691052,0.009520008,0.01459990,0.03183254,0.04448023,0.03013858,0.05902951,0.08945481,0.09953810,0.1556193,0.1830439,0.1604501,0.1813882,0.2267703,0.3133205,0.3306857,0.3255585,0.2210090,0.3724013,0.4239832,0.4342486,0.3903680,0.5187417,0.3631244,0.5040815,0.5464412,0.2313142,0.2774918,0.2392316,0.1608435,0.0345463,0.0000000,0.0396512,0.0423842,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000483469,0.000624303,0.002371341,0.000984065,0.02052463,0.01169944,0.05604981,0.06438426,0.11715393,0.14794837,0.23376752,0.2346674,0.3200334,0.5405619,0.5166598,0.5938339,0.7002668,0.6484880,0.5644912,0.7887632,0.5840531,0.6194122,0.7438492,0.7719435,0.6740969,0.6672974,0.5074665,0.5697576,0.5525983,0.5966229,0.5193071,0.2128139,0.1999750,0.1531480,0.1311573,0.1752469,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000183118,0.000000000,0.000700049,0.000462628,0.001792171,0.002269116,0.007533145,0.01732927,0.05037793,0.07542220,0.18283881,0.29193635,0.37570629,0.34026095,0.5794869,0.4221106,0.5736871,0.6379189,0.7177697,0.5762680,0.7326768,0.6066374,1.2149804,0.9653300,0.7940078,0.9449529,0.5640722,0.6010575,0.4469717,0.4162202,0.3007978,0.3660760,0.5050298,0.1656401,0.3054596,0.1913543,0.0879276,0.0313758,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000158835,0.000000000,0.000303608,0.000401279,0.000000000,0.001968210,0.007350952,0.01202500,0.04369734,0.06105914,0.06895333,0.10331492,0.14168874,0.18582836,0.2230472,0.3553661,0.2447266,0.3781053,0.4098696,0.4591641,0.4863651,0.5478159,0.5269313,0.5464603,0.6887149,0.4364334,0.5591667,0.4832040,0.4984702,0.5716237,0.3098296,0.2293279,0.2666440,0.5541738,0.2428734,0.0474225,0.1016901,0.0000000,0.0000000,0.0621040,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000446180,0.000303212,0.000400755,0.002587473,0.003931283,0.011419893,0.03802947,0.05576264,0.11034381,0.12567564,0.25086930,0.29244132,0.32477530,0.3200159,0.3549024,0.3421702,0.5479979,0.5181453,0.5050019,0.5375417,0.5111076,0.7176051,0.6161663,0.7168789,0.7228963,0.8027534,0.9016504,0.7605580,0.3605544,0.6677074,0.2994990,0.1711904,0.2459781,0.1764047,0.3315246,0.1777254,0.0271796,0.0290530,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000103547,0.000151985,0.000000000,0.000000000,0.000000000,0.000000000,0.000627775,0.002344642,0.00575320,0.01277613,0.04868820,0.07257754,0.08335192,0.11976067,0.26149136,0.1983977,0.3400402,0.3200355,0.4191571,0.3872286,0.4449232,0.5956986,0.5310875,0.5576827,0.5903631,0.6404489,0.6722524,0.6799613,0.7908871,0.7419574,0.4750013,0.4681067,0.2700771,0.1457968,0.1178386,0.1056359,0.0453773,0.0486522,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.002087716,0.00640345,0.02016677,0.04644959,0.18065484,0.18899757,0.29878567,0.38418131,0.3733892,0.4312302,0.3596827,0.3712616,0.4376259,0.5496839,0.4806950,0.5527297,0.6836367,0.5068972,0.6446514,0.6530040,0.5508613,0.8125636,0.4247060,0.4614008,0.2084058,0.2029067,0.2190720,0.2623147,0.1975267,0.0000000,0.0974721,0.0695633,0.0743580,0.0396853,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000630269,0.003990000,0.006954275,0.02193962,0.05167415,0.07250001,0.17403082,0.28336324,0.25851122,0.34236794,0.4394293,0.4977353,0.5258824,0.5888993,0.6184399,0.8130017,0.6783477,0.7189318,0.8934098,0.9648554,0.8613047,0.8156944,0.8076585,0.8661392,0.9768266,0.5123154,0.4760290,0.5364216,0.1853304,0.2246868,0.1611355,0.1153633,0.0309223,0.0000000,0.0000000,0.0000000,0.0402609,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.001415425,0.009856590,0.020079712,0.01231772,0.04641886,0.12111981,0.20483230,0.37905075,0.40316055,0.57105564,0.5792367,0.7255819,0.6183536,0.6234736,0.6306560,0.8811456,0.7528422,0.8564938,0.6978691,0.6018951,0.7684101,1.1485374,0.6841518,0.7294241,0.4160478,0.3287233,0.2449886,0.2891203,0.1560770,0.0280328,0.0301558,0.1295385,0.1041655,0.0000000,0.0000000,0.0424105,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000802935,0.000249032,0.000365524,0.000771098,0.000349345,0.002770376,0.002384921,0.001509806,0.003759259,0.01614258,0.02514006,0.02676471,0.06545614,0.14451927,0.20107450,0.18552237,0.2638775,0.4502031,0.3848443,0.4615932,0.4596746,0.4213301,0.4999391,0.5059319,0.3674610,0.4462321,0.5580747,0.5144280,0.4825516,0.6145219,0.3983069,0.4673385,0.3752671,0.3856632,0.2410670,0.0472339,0.0254055,0.0272832,0.0292523,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000149360,0.000000000,0.000308316,0.000419046,0.000553854,0.000715191,0.003622088,0.012400599,0.03042814,0.04355869,0.08026207,0.14275636,0.20131415,0.35853017,0.44884766,0.6764129,0.7827928,0.6361468,0.6173332,0.9380777,0.6738590,0.5370334,0.6964149,0.8154376,0.7785667,1.0576870,0.6905274,0.6753024,0.7371317,0.5733329,0.3944838,0.2250703,0.1947836,0.0525754,0.0566580,0.1523723,0.0000000,0.0350887,0.0751257,0.2409116,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000444096,0.000312283,0.000000000,0.003926863,0.001448786,0.000917173,0.005709163,0.03362144,0.04242227,0.14429828,0.23616891,0.34267280,0.45227860,0.52720988,0.6543740,1.0738806,0.8610102,0.8960147,0.8993768,0.9100394,0.7161922,0.9169884,1.0156705,0.9857307,0.6237928,0.4613146,0.6677061,0.7643930,0.8129940,0.5467658,0.1139832,0.2712736,0.2396336,0.1434675,0.1234663,0.0994437,0.0000000,0.0760924,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000985861,0.000458651,0.000000000,0.000315591,0.000857867,0.000000000,0.002196195,0.001853774,0.004615702,0.02406741,0.02743780,0.08010189,0.13151212,0.20606399,0.28358272,0.32430908,0.3728159,0.4665577,0.5359073,0.5016103,0.5570689,0.3859361,0.3939547,0.4480748,0.3835003,0.4980852,0.5070603,0.5714714,0.4937398,0.5030158,0.4499262,0.5950609,0.2303807,0.2492242,0.2959874,0.1159896,0.2183544,0.0334990,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000171527,0.000000000,0.001062227,0.000962481,0.001908168,0.001642675,0.004159671,0.010357142,0.01429536,0.03270773,0.08295696,0.15574677,0.18944964,0.28073352,0.34219927,0.3435867,0.4267279,0.4137699,0.5116181,0.4194089,0.4329997,0.5653439,0.4113130,0.4555767,0.5448544,0.7687764,0.5736698,0.3139048,0.4635789,0.3292129,0.4530323,0.3618648,0.2236930,0.1509464,0.0325335,0.0699949,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0004672284,0.000000000,0.000265874,0.000373919,0.002541051,0.002686807,0.003469469,0.005490985,0.012304776,0.02851562,0.05892243,0.08760604,0.25681207,0.39335168,0.54154532,0.65413782,0.6573225,0.8472081,0.7851596,0.7872801,0.8424041,0.6810343,0.5644618,0.5308892,0.4811081,0.4278535,0.5195906,0.2494551,0.3704963,0.4044181,0.3244852,0.3525208,0.3002563,0.2362292,0.0956435,0.0343568,0.0739175,0.0396904,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000157835,0,0.0000631018,0.0008425037,0.000163315,0.001677977,0.001685622,0.002291004,0.003633627,0.008602175,0.002970394,0.025885889,0.03024659,0.04396494,0.12944824,0.21593155,0.30878556,0.38490237,0.56914759,0.6447925,0.5200616,0.4924506,0.8768236,0.5324395,0.4561282,0.4599829,0.4568915,0.3614715,0.3990533,0.3074278,0.3212971,0.5098481,0.4797662,0.2925550,0.1816182,0.2214902,0.2396066,0.0862319,0.0929279,0.0000000,0.0357847,0.0000000,0.0000000,0.0439036,0.0468632,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000307384,0.000417779,0.001656536,0.004278164,0.007222266,0.016858762,0.03998850,0.12192949,0.27606660,0.45069449,0.71361869,1.01384616,1.23717845,1.2147252,1.3089410,1.1225181,0.9898216,0.9566582,0.7358037,0.6335674,0.7042272,0.4724022,0.5579023,0.6006577,0.4833720,0.7053199,0.2799627,0.4953856,0.2483941,0.3814623,0.1456458,0.1834574,0.0000000,0.0911469,0.0000000,0.0699652,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0001210174,0.000000000,0.000275457,0.001549587,0.000526529,0.000695913,0.000898631,0.007964470,0.008498868,0.02780561,0.05683620,0.20421856,0.32287008,0.67453249,0.69211708,0.89572284,0.8662520,1.1578773,1.2095807,1.2234864,0.7468020,0.9071771,0.5060837,0.6750308,0.5122955,0.5044169,0.6560766,0.3322886,0.2626348,0.4410478,0.5522978,0.3391398,0.3393590,0.1835581,0.1321212,0.0355952,0.0000000,0.0000000,0.0440887,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000696941,0.0001163151,0.000541132,0.000794262,0.001489376,0.001012139,0.000668873,0.000863714,0.009842144,0.016337268,0.04843941,0.10925553,0.14781836,0.36779209,0.54026893,0.86990836,1.09322978,1.2515073,1.2564848,1.2441656,1.2066901,0.8734481,0.9009919,0.7134149,0.8530540,0.7186227,0.5142000,0.3395452,0.3548634,0.5436949,0.3179328,0.2077190,0.2758141,0.1902675,0.2646385,0.1587344,0.0000000,0.0000000,0.0000000,0.0423756,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000492989,0.002079988,0.002827005,0.002490970,0.008041462,0.017308570,0.032956158,0.04820894,0.09230193,0.19853920,0.28624718,0.39297512,0.59735688,0.68279624,0.7995477,0.9915691,0.8228781,0.9588837,0.9581373,0.5231557,0.5937659,0.5816833,0.6566714,0.4650589,0.4666648,0.3799480,0.3615699,0.4933431,0.4082747,0.1867578,0.3289841,0.1095054,0.0591148,0.0637051,0.0685298,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0001252973,0.0000000000,0.000648571,0.001903917,0.009036995,0.012737498,0.009620093,0.013975209,0.017694387,0.024476200,0.07056909,0.12367285,0.25268086,0.37452104,0.63438382,0.79966018,1.10145889,1.1720622,1.2908180,1.4484091,1.3057911,0.8706620,1.0885885,0.6801615,0.6372150,0.6699016,0.6603130,0.5959062,0.3987375,0.5061871,0.4001097,0.1659738,0.3155496,0.2198998,0.1057271,0.0570751,0.0615071,0.0000000,0.0710555,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000674674,0.002475681,0.005222617,0.005678635,0.001250910,0.003230594,0.016361369,0.030553563,0.04373321,0.14756953,0.27191441,0.41646311,0.64097115,0.94226623,1.27357297,1.2975790,1.3595546,1.4749168,1.3655327,1.2129962,0.7700329,0.7681822,0.5954516,0.6221995,0.3983956,0.3326239,0.3152371,0.1815723,0.2576557,0.4100529,0.1406784,0.1016667,0.0824868,0.0296861,0.0959739,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.001599876,0.002250030,0.002038745,0.000673653,0.000869887,0.006608321,0.008227011,0.03532749,0.07131984,0.12935019,0.25466410,0.40469665,0.45986659,0.61474874,0.7858043,0.8858250,1.0476378,1.2772405,1.6635726,1.2001504,0.6640805,0.8833518,0.6165349,0.8729889,0.2931186,0.3395295,0.3520160,0.2134699,0.4184070,0.2525320,0.3558791,0.1184577,0.0639475,0.0344566,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000736007,0.000000000,0.000661075,0.003414580,0.002161646,0.010764539,0.02806448,0.07398755,0.13891010,0.23286999,0.38712861,0.60300400,0.66629905,0.7142033,0.7273615,0.7592990,0.7976138,0.4871894,0.4691819,0.7478311,0.4631163,0.5787182,0.3339636,0.2077442,0.3507265,0.4797826,0.3561232,0.2965408,0.0991268,0.1611851,0.0290615,0.1255071,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000730309,0.000000000,0.001311914,0.000847036,0.003217366,0.005340602,0.02457108,0.05952549,0.11169364,0.16625567,0.28478722,0.40532422,0.55839594,0.6162384,0.5339633,0.6667440,0.6859137,0.6445571,0.5700608,0.5512310,0.4241825,0.4437293,0.2449317,0.3329888,0.4698152,0.2856410,0.2078625,0.2489766,0.0737695,0.1066249,0.0288365,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0003723869,0.000962473,0.006498409,0.008741864,0.008100996,0.004996644,0.000000000,0.000000000,0.005811591,0.02317294,0.05182004,0.16292059,0.26371069,0.35674844,0.62589917,0.73889150,0.8885247,0.9386251,0.8851641,1.1319104,0.7198586,0.7754183,0.8305535,0.6410990,0.6106784,0.5173862,0.4141202,0.3218971,0.3729981,0.4523878,0.3448250,0.0802753,0.1740422,0.2196572,0.0677591,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.000000000,0.000000000,0.000680482,0.000000000,0.008900411,0.040166969,0.09516161,0.13791050,0.19229413,0.34201972,0.39505787,0.56864660,0.83878693,0.7724607,0.8217592,1.1066746,0.8601251,0.8358190,0.6997923,0.6378214,0.4889349,0.8123278,0.5679636,0.3454383,0.6678914,0.5728859,0.4312677,0.4461288,0.1530551,0.2765282,0.0299146,0.0322979,0.0348058,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0000000000,0.000000000,0.000000000,0.001495232,0.001016119,0.000000000,0.000000000,0.001097871,0.005467167,0.02179959,0.04671772,0.07298338,0.13846430,0.29492624,0.32008874,0.54419096,0.5993003,0.7027939,0.7098468,0.6558721,0.5296021,0.4765826,0.4015172,0.3136142,0.2805632,0.3097330,0.2272534,0.2315681,0.2144342,0.1489520,0.2317064,0.1762081,0.0545759,0.0295199,0.0318717,0.0343466,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0, 0,0,0.0000000000,0,0.0000000000,0.0002225078,0.000172528,0.002025868,0.013533402,0.011133124,0.008316982,0.002478393,0.013597826,0.018230775,0.06869866,0.08321412,0.10430136,0.16764908,0.32620477,0.50073943,0.62303890,0.5809950,0.6466888,0.7348259,0.6616335,0.6038339,0.6115906,0.5066094,0.5171418,0.4582354,0.3513039,0.3711662,0.2885088,0.2043002,0.1824591,0.3090586,0.0959318,0.0779950,0.0281248,0.0303655,0.0327234,0.0000000,0.0378034,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0,0,0.0000000,0,0,0,0,0,0,0,0,0 ), .Dim=c( 33 ,60)), L=c( # landings data 6306.146252, 6563.394703, 6520.643185, 6084.036162, 7215.017536, 8402.808817, 6965.588629, 6579.962964, 5061.379803, 5530.907658, 5916.498574, 5994.610456, 6225.402783, 6673.226602, 6176.762062, 5873.857309, 5281.754272, 4731.78768, 4756.478301, 4750.331845, 6502.363121, 6348.996542, 6077.976765, 5457.377873, 3846.578237, 3699.978835, 3556.116883, 3452.422884, 3637.61937, 3899.609786, 3471.126647, 2695.262766, 2626.302149 ), rmean=structure(.Data=c( # catch ratio values estimated for reference species 6.778,5.883,5.743,8.862,11.92, 6.851,5.769,5.641,8.897,11.9, 6.881,5.771,5.542,8.834,12.03, 6.909,5.669,5.429,8.824,12.06, 6.909,5.64,5.332,8.764,12.02, 6.848,5.652,5.303,8.738,11.88, 6.801,5.677,5.218,8.74,11.85, 6.78,5.699,5.141,8.705,11.76, 6.782,5.673,5.103,8.723,11.62, 6.826,5.622,4.999,8.74,11.52, 6.79,5.572,4.766,8.704,11.46, 6.735,5.439,4.68,8.662,11.42, 6.688,5.412,4.639,8.642,11.5, 6.707,5.423,4.568,8.677,11.5, 6.788,5.439,4.528,8.651,11.49, 6.831,5.425,4.535,8.624,11.44, 6.844,5.376,4.525,8.61,11.38, 6.859,5.333,4.472,8.593,11.31, 6.911,5.238,4.404,8.585,11.21, 6.98,5.145,4.308,8.578,11.12, 6.934,5.087,4.239,8.531,11.1, 6.801,5.005,4.247,8.486,11.07, 6.698,4.97,4.174,8.403,11.02, 6.571,4.838,4.047,8.388,10.95, 6.542,4.634,3.968,8.294,10.88, 6.33,4.499,3.929,8.246,10.87, 6.319,4.503,3.886,8.118,10.84, 6.331,4.534,3.866,8.011,10.74, 6.321,4.591,3.93,7.903,10.66, 6.328,4.533,3.873,7.728,10.65, 6.308,4.472,3.862,7.617,10.62, 6.294,4.452,3.761,7.566,10.63, 6.304,4.43,3.716,7.547,10.65 ), .Dim=c(33,5)), b.tot=c( # total biomass index by year 1.75734508422038 , 1.52190926451675 , 1.0293921181949 , 2.05616095516523 , 1.95510914313233 , 2.58343152412285 , 2.64579323253214 , 2.2881087480487 , 2.53204419546951 , 2.3218223008699 , 2.37890247541194 , 2.67862019336332 , 2.62732003872305 , 2.20875125230743 , 2.61278606071169 , 2.75143113715695 , 2.29199846815605 , 2.23908706630298 , 2.45567282279567 , 2.28132816403502 , 2.78904013266779 , 2.67565393799266 , 2.73674211391142 , 2.53705396323078 , 2.78308441332132 , 2.74819443704869 , 2.66244188345668 , 2.33527274098504 , 2.16997524606469 , 2.53732736561141 , 2.5812403634615 , 2.05516279072083 , 2.22730672079983 , 2.42604241295961 ) )