A multivariate approach for defining fishing tactics from commercial catch and effort data

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3 Pelletier ad Ferraris 53 Fig. 1. Flowchart of the methodology used to obtai the fishig tactics i the two examples. I each example, two typologies are performed: (i) o catch data leadig to approachig the target species by a categorical variable, ad (ii) o both this categorical variable ad effort data to idetify fishig tactics. where m i ad m i are the weights of idividuals i ad i ad G is the ceter of gravity of the idividuals, i.e., the jth coordiate of G is g mσ m x, j = 1 i= 1 i ij m beig the sum of the idividual weights. The iertia of the data set may thus be see as a measure of the variability of the idividuals aroud G. Factorial aalyses yield the coordiates of the idividuals i the p-dimesioal space where axes are ordered accordig to decreasig cotributio to the iertia of the data set. These ordered axes are called factorial axes or sometimes ordiatio axes (e.g., see Rice 1985). The first axis is the oe alog which the idividuals are most scattered, i.e., they are best discrimiated. This amouts to maximizig the iertia of the projectios of the idividuals o this axis. The iertia ad thus the factorial axes deped o the way distaces betwee idividuals are computed, which differs accordig to the type of factorial aalysis (see Appedix). The spaig vectors of the factorial axes are the ormalized eigevectors of a square matrix A (see Appedix), called the iertia matrix because its trace (i.e., the sum of its diagoal terms) correspods to the iertia I of the data set defied i eq. 1. Diagoalizig A yields t () A = UΛU where U is the matrix of ormalized eigevectors ad Λ the diagoal matrix of eigevalues. Each p eigevector beig a liear combiatio of the iitial variables, it defies a ew variable, the variace of which is the correspodig eigevalue. The iertia of the data set is the the sum of the eigevalues. Oe may calculate the coordiates of the idividuals ad the p variables i the vector space spaed by the eigevectors (see Ap-

8 Table 1. Characterizatio of the tactics obtaied from the classificatio of fishig trips based o the four categorical variables. Catch profile (tactic ame i bold) Active variable Illustrative variable Cluster size Gear Locatio (Fig. ) Moth Catch per species (target species uderlied) Depth (m) Crew size 1. Sea bream 1490 (4) G, G3 L14, L6, L13, L1, L7 Feb., Ja., Mar., Dec., Pagellus bellottii , 3, 5 Nov., May Decapterus rhochus Brachydeuterus auritus Detex caariesis. Grouper 131 (15) G3 L, L4, L5, L8, L15, L17 Jue, July, Apr. Epiephelus aeeus 10 5 ad 3, Warmwater group Sparus caeruleostictus Pomadasys icisus Epiephelus goreesis Pomatomus saltator Plectorhychus mediterraeus Epiephelus gigas 3. Goatfish 339 () G1 L15, L40, L10, L11 July, Aug., Sept. Pseudupeeus prayesis , Diplodus vulgaris Pomadasys rogeri Sparus caeruleostictus Plectorhychus mediterraeus 4. Sailfish 449 (13) G L0, L13, L7 Aug., Sept., July, Oct. Istiophorus platypterus 5 75 Warmwater group Scyris alexadrius Coryphaea hippurus Brachydeuterus auritus 5. Octopus 111 (39) G1 L9, L11, L40, L10, L17 Mar., Oct., May, Octopus vulgaris <5 1 Warmwater group Nov., Apr. 6. Deepwater group 716 (1) G3 L16, L3, L1, L17 Mar., Dec., Apr., Oct., Detex spp. >75 4, 5 Sept., Feb., Ja. Brachiostegus semifasciatus Brotula barbata Scorpaea spp. Merluccius seegalesis Cetrophorus spp. Trachurus trachurus Note: Oly characteristic variables or categories are reported. All variables are raked by decreasig order of sigificace as give by their test value (ot reported). The tactic is amed after the most characteristic category of the variable catch profile (bold). The target species is assumed to be the most characteristic category of the variable catch per species (uderlied). I the secod colum, the umber of illustrative idividuals assiged to the cluster (i.e., the tactic) is reported i paretheses. I the gear colum, G1 correspods to o egie, G correspods to egie power <9 kw, ad G3 correspods to egie power >9 kw. Depth is coded i seve categories, but oly characteristic depth rages are reported for clarity. 58 Ca. J. Fish. Aquat. Sci. Vol. 57, 000

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