Time series modelling of landings in Northwest Mediterranean Sea

Transcription

1 ICES Journal of Marine Science, 57: doi:.6/jmsc.2.57, available online at on Time series modelling of landings in Northwest Mediterranean Sea Josep Lloret, Jordi Lleonart, and Ignasi Solé Lloret, J., Lleonart, J., and Solé, I. 2. Time series modelling of landings in Northwest Mediterranean Sea. ICES Journal of Marine Science, 57: Univariate seasonal ARIMA and intervention models were developed to forecast monthly catches of 53 commercial species in the northwestern Mediterranean Sea, up to one year in advance. In general terms, there was good agreement between forecasts and observed catches of target demersal species. By contrast, models fitted to non-target demersal species and pelagic species were unsatisfactory in terms of explained variability and predicting power. Large commercial size classes were better explained than the small size classes. Intervention analysis was used to identify the significance, magnitude and form of structural shifts (interventions) of the time series for each species. Most of the fitted interventions appeared in small commercial size classes and indicated a decrease in the mean level of the catch. Seasonality of demersal species, caught mainly by trawlers, was mainly attributed to changing availability and recruitment. By contrast, gear type explained the seasonal variation in landings of pelagic and some coastal species. Catch declines of two species were also compared with the variations of their respective seasonal patterns. 2 International Council for the Exploration of the Sea Key words: ARIMA/Box-Jenkins models, catch dynamics, fishery resources, forecasts, intervention analysis, northwestern Mediterranean, seasonal pattern, trend. Received 27 July 998; accepted January 2. Josep Lloret and Jordi Lleonart: Institute of Marine Sciences-CSIC, Passeig Joan de Borbó sn, E-839 Barcelona, Catalonia, Spain. Ignasi Solé: Polytechnical University of Catalonia, High School of Engineering, Department of Statistics, Avgda. Diagonal 647-6a, E-828 Barcelona, Catalonia, Spain. Correspondence to Josep Lloret: lloret@icm.csic.es Introduction The Mediterranean is a semi-enclosed sea, globally considered as oligotrophic (Margalef, 985). Its continental shelf is most frequently reduced to a narrow coastal fringe. From the fisheries biology point of view, two fundamental features are the presence of a large variety of species and the absence of large monospecific stocks such as those which inhabit some wide areas of the open oceans. The Gulf of Lions (Fig. ) is one of the most productive zones of the Mediterranean Sea because of hydrographic features such as a wide shelf, strong vertical mixing in winter, coastal upwelling and river runoff. The Gulf of Lions supports fisheries that use the bottom and pelagic trawl, the purse seine, the gill net and the long-line. Some of the species, due to their abundance and high economic value, can be regarded as target species, e.g. Merluccius merluccius, Mullus surmuletus and Mullus barbatus, Engraulis encrasicolus, Aristeus antennatus and Solea vulgaris (common names are shown in Table ). The Gulf of Roses is at the southern part of the Gulf of Lions, and supports a multispecific fishery exploited by bottom trawlers, purse seiners and by a small-scale fleet using long lines, gill nets and shellfish dredges. An artisanal gillnet fishery occurs around Cape Creus. The Mediterranean fishery is multispecific. Biological information is available for only the most important commercial species, e.g. Merluccius merluccius, Eledone cirrhosa and Engraulis encrasicolus. Time series analysis was used to forecast catch of 53 commercial species in the northwestern Mediterranean. A family of such techniques is the Box-Jenkins methodology (Box and Jenkins, 976), which concerns the building of linear and stochastic dynamic models with minimum data requirements, e.g. catch or catch per unit effort. This methodology has been also used to model //7+4 $3./ 2 International Council for the Exploration of the Sea

2 72 J. Lloret et al. 3 ' 3 3' 4 ' 4 3' 4 55' E 43 3' Rhone river 43 3' N m Gulf of Lions 43 ' 43 ' 4 m m 42 3' 42 3' Muga river Fluvia river Cape Creus Gulf of Roses 3 ' 3 3' 4 ' 4 55' Figure. Location of the study area: the Gulf of Lions and the Gulf of Roses-Cape Creus (NW Mediterranean). the dynamics of marine species in other areas (e.g. Fogarty, 988; Stergiou, 989; Hare and Francis, 995; Stergiou et al., 997; Downton and Miller, 998). In the present study, Box-Jenkins univariate time series and intervention models are used to model and forecast one year in advance the dynamics of the fishery resources of Gulf of Lions and Gulf of Roses-Cape Creus. Materials and methods A series of monthly catch records was available for 53 species or groups of species (henceforth called species) landed for different periods of time, In most cases, catch data were available from 99. Our time series span more than 5 months, which is adequate for a proper time-series analysis (Pankratz, 99). Catch was recorded in kg and for some species it was available by two commercial size classes, big and small. Most landings were from trawlers and seiners. Fishing effort for all gears remained stable during the study period (Confraria de Pescadors de Roses, 997). Univariate-ARIMA (autoregressive-integratedmoving-average) models (Box and Jenkins, 976) are constructed using only the information contained in the series itself. Thus, models are constructed as linear functions of past values of the series and/or previous random shocks (or errors). Forecasts are generated under the assumption that the past history can be

3 Time series modelling of landings in Northwest Mediterranean Sea 73 Table.. Seasonal ARIMA models fitted to the monthly catches of 53 species (or groups of species) and commercial size classes, NW Mediterranean. N is the number of data points fitted. St. Dev., E.V. (%), U and Ct. are the standard deviation, the explained variance (in percent), the U-statistic and constant of the model, respectively. Coefficients of the models are also shown. AR, MA, ARS and MAS are the non-seasonal and seasonal autoregressive and moving average terms, respectively. Species names follow FAO notations (FAO, 997). Scientific name Common name Code N Method Fitted model St. Dev. E. V. (%) U Ct. AR- AR-2 ARS- ARS-2 MA- MA-2 MAS- MAS-2 Argentina sphyraena Argentine A 62 Tramo (,,) (,,) Aristeus antennatus (Big) Red shrimp (Big) B 89 Tramo (,,) (,,) Aristeus antennatus (Small) Red shrimp (Small) C 63 Tramo (,,) (,,) Boops boops Bogue D 8 Tramo (,,) Chamelea gallina Striped venus E 7 Tramo (,,) (,,) > Citharus linguatula+ Flounder+Megrim (Big) F 7 Tramo (,,) (,,) Lepidorhombus boscii (Big) Citharus linguatula+ Flounder+Megrim (Small) G 5 Tramo (,,) (,,) Lepidorhombus boscii (Small) Conger conger European conger H 89 Tramo (,,) Diplodus annularis+d. vulgaris Angular seabream I 69 SCA (2,,) Diplodus sargus White seabream J 59 Tramo (,,) (,,) Donax trunculus Donax clam K 5 Tramo (,,) (,,) Eledone cirrhosa (Big) Octopus (Big) L 8 Tramo (,,) (,,) Eledone cirrhosa (Small) Octopus (Small) M Tramo (,,) (,,) > Engraulis encrasicolus (Big) Anchovy (Big) N 87 SCA (,,) (,,2)2 > Engraulis encrasicolus (Small) Anchovy (Small) O 72 SCA (,,) (,,)2 > >. Epinephelus guaza Dusky grouper P 54 SCA (,,) (,,)2 >.5. Etmopterus spinax Lantern shark Q 54 Tramo (,,) (,,)2 > Helicolenus dactylopterus Rosefish R 77 Tramo (,,) (,,) Lichia amia Leerfish S 54 SCA (,,) > > Liocarcinus depurator Swimcrab T 77 Tramo (,,) (,,) Liza sp+mugil sp Mullet U 77 Tramo (,,) (,,) Loligo vulgaris (Big) Common squid (Big) V 8 Tramo (,,) (,,) Loligo vulgaris (Small)+ Alloteuthis media Common squid (Small) W 66 Tramo (,,) (,,) Lophius piscatorius+ Angler (Big) X 8 Tramo (,,) (,,) L. budegassa (Big) Lophius piscatorius+ Angler (Small) Y 72 Tramo (,,) (,,) L. budegassa (Small) Merluccius merluccius (Big) European hake (Big) Z 8 Tramo (,,) (,,) Merluccius merluccius (Small) European hake (Small) AA 82 Tramo (,,) (,,) Micromesistius poutassou (Big) Blue whiting (Big) AB 86 Tramo (,,) (,,) Micromesistius poutassou (Small) Blue whiting (Small) AC 92 Tramo (,,) (,,) >..645 Mullus barbatus+ Red mullet (Big) AD 74 Tramo (,,) (,,) M. surmuletus (Big) Mullus barbatus+ Red mullet (Small) AE 8 Tramo (,,) (,,) M. surmuletus (Small) Nephrops norvegicus (Big) Norway lobster (Big) AF 88 Tramo (,,) (,,) Nephrops norvegicus (Small) Norway lobster (Small) AG 64 Tramo (,,) (,,) Oblada melanura Saddled seabream AH 77 Tramo (,,) (,,)2 > > Pagellus acarne+p.bogaraveo Axillary seabream AI 8 Tramo (,,) (,,) Pagellus erythrinus Common pandora AJ 2 Tramo (,,2) (,,) Palinurus elephas Spiny lobster AK 7 Tramo (,,) (,,) Parapenaeus longirostris Rose shrimp AL 89 Tramo (,,) > Penaeus kerathurus Prawn AM 69 SCA (,,) (,,)2 > Phycis blennoides Greater forkbeard AN 69 Tramo (,,) (,,) Raja asterias+r. clavata Skates AO 69 Tramo (,,) Sardina pilchardus (Big) European pilchard (Big) AP 87 SCA (,,) (,,)2.89 >..967 Sardina pilchardus (Small) European pilchard (Small) AQ 79 SCA (,,) (,,)2 > > Continued over

4 74 J. Lloret et al. Table.. Continued. Scientific name Common name Code N Method Fitted model St. Dev. E. V. (%) U Ct. AR- AR-2 ARS- ARS-2 MA- MA-2 MAS- MAS-2 Sarpa salpa Salema AR 54 SCA (,,) > > 4.97 Scomber japonicus Chub mackerel AS 69 Tramo (,,) (,,)2 > Scomber scombrus (Big) Atlantic mackerel (Big) AT 8 Tramo (,,).9 > Scomber scombrus (Small) Atlantic mackerel (Small) AU 79 SCA (,,) (,,2)2 > > Scopthalmus rhombus+ Psetta maxima Brill+Turbot AV 89 Tramo (,,) (,,) Scorpaena porcus+s. scrofa Scorpionfish AW 76 Tramo (,,) (,,) Scyliorhinus canicula Catshark AX 87 SCA (2,,) Sepia officinalis Common cuttlefish AY 83 Tramo (,,) (,,) Sepiolidae Bobtail squid AZ 6 Tramo (,,) (,,) Serranus cabrilla+s. scriba Comber BA 69 Tramo (,,) Solea vulgaris Common sole BB 8 Tramo (,,2) (,,) Sparus aurata Gilthead seabream BC 2 SCA (,,) (,,) > Spondyliosoma cantharus Black seabream BD 69 Tramo (,,) (,,)2 > > Stichopus regalis Sea cucumber BE 77 Tramo (,,) (,,) Todarodes sagittatus+ Illex coindetii Flying squid+ Shortfin squid BF 78 Tramo (,,) (,,) Trachinus draco Weever BG 62 Tramo (,,) (,,) Trachurus trachurus (Big) Horse mackerel (Big) BH 8 Tramo (,,) (,,)2 > > Trachurus trachurus (Small) Horse mackerel (Small) BI 69 SCA (,,) (,,)2 > > Trichiurus lepturus+ Hairtail BJ 74 Tramo (,,) (,,) Lepidopus caudatus Trigla lucerna Gurnard BK 8 Tramo (,,) (,,) Trigla lyra Piper gurnard BL 69 SCA (,,) (2,,)2 > > Trisopterus minutus capelanus Poor cod BM 77 Tramo (,,) (,,) Zeus faber John dory BN 75 Tramo (,,) (,,)

5 Time series modelling of landings in Northwest Mediterranean Sea 75 No of days at sea TR GN PS SD Month Figure 2. Distribution of fishing effort in 996 (monthly number of days at sea). Trawl (TR), Purse seine (PS), Gill net and other artisanal gears (GN) and Shellfish dredges (SD). September data was not available. translated into predictions for the future. To develop these univariate ARIMA models, the monthly catch for each species was used. The software package Force 4/R Research System (Prat et al., 998) developed by the Polytechnical University of Catalonia, was used. The software analyzes seasonality and trends by multiple moving averages. All remaining analyses were performed using Statistica for Windows 4.5 (Statsoft Inc., 993). Box and Jenkins (976) formalized the ARIMA modelling framework by defining three steps: identification of the model, estimation of the coefficients, and verification of the model. These procedures apply to stationary series (time series with no systematic change in mean and variance) whose data are normally distributed. First or second-order differencing (non-seasonal and/or seasonal) usually remedied non-stationary means, and logarithmic transformation remedied non-stationary variances and non-normal distributions of original data. Identification of the number of terms to be included in the model was based on the examination of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the differenced, log-transformed time series. Estimation of the model coefficients was achieved by means of the maximum likelihood method. Verification of the model was performed through diagnostic checks of residuals (histogram and normal probability plots of residuals and standardized residuals). The ability to forecast using ARIMA models was tested by applying the final fitted model to all available data excluding the monthly data of the last year, which was used to compare with forecasts obtained for that year. A detailed description of the non-seasonal and seasonal ARIMA models and the standardized notation used in this paper is provided in Appendix. The standard deviation and the Theil s U-statistic were used to measure the accuracy of the ARIMA models obtained. Theil s U-statistic indicates whether or not the improvement achieved by using a sophisticated technique such as ARIMA instead of a simple naïve model (a model 2 which uses as a forecast at time t+ the catch at time t) is worth it in terms of the time and cost involved (Makridakis et al., 983). U> indicates that there is no point in using ARIMA models, while U< indicates that the ARIMA approach is better than the naïve method. Some time series had one or two data points missing. As the Box-Jenkins (Box and Jenkins, 976) methodology requires complete data records and observations equally spaced in time, analyses were performed by filling gaps with extreme high and low values. The programme will consider this value as a punctual anomaly and if we intervene this value (Additive Outlier) we will correct the anomaly using the rest of the data, and will obtain an estimated value to replace the missing value in the original time series, which will be ready then for analyses. For all cases, and before fitting the models, it was necessary to transform logarithmically the raw data. Regular and seasonal differencing was usually required, because most of the series exhibited quite strong trends and seasonality. Thus, seasonal ARIMA models were fitted to nearly all data sets. Among the seasonal ARIMA models fitted, the (,,) (,,)2 was the most frequent. The forecasts obtained by such a model have a special interpretation: they are exponentially weighted moving averages of the available data. Thus, for example, the model (,,) (,,)2 fitted to big M. merluccius is represented by the following equation: ( B 2 )( B)lnZ t =(.426B)(.85B 2 )a t. By developing the equation, we obtain: lnz t =.6lnZ t +.24lnZ t 2 +.Z t 3 +.4lnZ t 4 +.2lnZ t 5 +.2lnZ t 2.2lnZ t 3.5lnZ t 4.2lnZ t 5 +.6lnZ t 24.lnZ t 25.4lnZ t 26.2lnZ t lnZ t a t. The ARIMA models provide additional information on fish catch time series structure and dynamics (Box and Jenkis, 976; Chatfield, 984; Pankratz, 99). It is often the case that a series contains a seasonal component and a non-seasonal component. It is necessary to distinguish between these two attributes in order to obtain an adequate representation of the series. Apart from seasonality, there is also the trend. Thus, all time series have been described by calculating the seasonal effect and the trend by means of multiple moving averages. As the time period under study is relatively short, cyclic changes have been disregarded. For each species, the time period when its catch typically peaked was compared with the time period of its reproduction and recruitment to the gear based on information provided elsewhere (Naef, 923; FAO, 973; Whitehead et al., 973; Armengol, 986; Sostoa, 99; Lleonart, 99; Cristian, 99).

6 76 J. Lloret et al (a) (b) Landings (t) (c) (e) (d) (f) (g) (h) Month/Year Observed Fitted St. Dev. of forecasts Forecasted Figure 3. Comparison between observed monthly catches of nine species or groups of species together with fits (for all months used to construct the models) and forecasts ( standard deviation with 75% probability) predicted from those models (for the 2 following months). (a) Trisopterus minutus capelanus, (b) Big Citharus linguatula and Lepidorhombus boscii, (c) Scorpaena porcus and S. scrofa, (d) Big Eledone cirrhosa, (e) Big Nephrops norvegicus, (f) Donax trunculus, (g) Big Merluccius merluccius, (h) Big Engraulis encrasicolus.

7 Time series modelling of landings in Northwest Mediterranean Sea 77 Table 2. Interventions incorporated to the ARIMA models: LS (Level-Shifts), TC (Temporary-Change) and their respective values and significance (t-values). Δ% indicates the deviation (in percent) from the expected catch. Species Date LS TC Δ% Value t Δ% Value t Aristeus antennatus (Big) Oct Eledone cirrhosa (Small) Feb Feb Helicolenus dactylopterus Jul Loligo vulgaris (Small)+Alloteuthis media Jun Merluccius merluccius (Small) May Micromesistius poutassou (Small) May Jun Mullus barbatus+m. surmuletus (Small) Sep Raja asterias+r. clavata Oct Scomber scombrus (Big) Nov Jun Sepia officinalis Jul Solea vulgaris Apr Stichopus regalis Aug Todarodes sagittatus+illex coindetii Sep Trachurus trachurus (Big) Apr Landings (t) May 992 ( 55%) Mean landings Landings Effect of the intervention Month/Year Intervention Figure 4. Level-Shift (LS) intervention in May 992 for the small Merluccius merluccius. The effect of the intervention and the mean catch before and after it are shown by straight lines. Timing of the intervention and deviation from the expected values, i.e. the resultant change in mean (in percent), are also shown. Furthermore, to take into account the influence of seasonal fluctuations in effort on the seasonalities of catches, the monthly effort, (defined as the total number of days at sea per month) was calculated in 996 for the main gears used in the area: trawl, purse-seine, long-line, shellfish dredges and gill nets, including other artisanal gears (Fig. 2). Intervention analysis was used to detect and quantify non-random changes in variables (Box and Jenkins, 976; Chatfield, 984; Pankratz, 99). Owing to the lack of independence between successive observations, t-tests for equality of means could not be used to test production shifts. Therefore, intervention analysis was used here to identify the significance, magnitude, and form of structural shifts (interventions) of the time series for each species. While the input of an intervention represents a pulse shift in a given month, the output or Landings (t) Landings Effect of the 5 intervention.6 February February 992 ( 97%) ( 98%) Month/Year Intervention Figure 5. Temporary-Change (TC) interventions in February 99 and February 992 for the small Eledone cirrhosa. The effects of the interventions are shown by a straight line. Timing of the interventions and deviation from the expected value at the time of intervention are also shown. consequence of that event may be modelled in several ways. Thus, according to the output, two types of interventions are defined, pulse and step. A pulse intervention represents a temporary event that affects the level of the catch, and can be modelled as abrupt (i.e. a pulse intervention at t= shifts the level up or down only during period t=) or delayed (i.e. a pulse intervention at t= causes a decreasing or a increasing response during periods t+, t+2, t+3...). The first one is also called additive outlier (denoted AO), the second one is called the temporary-change intervention (denoted TC). Step interventions may be thought as a permanent change in the level of a time series. They are also called Level-shifts (denoted LS). What we are most interested in this analysis are regimes that define points in time where major delayed and permanent shifts occur in the catch history of a species. Thus, this paper concentrated in TC and LS interventions, meanwhile

8 78 J. Lloret et al. Table 3. Seasonal pattern against time of reproduction and recruitment (// denotes the absence of seasonality), and main gear responsible for the catch of each of the species (or groups of species) and commercial size classes (TR, Trawl; PS, Purse seine; SD, Shellfish dredges; GN, Gill net and other artisanal gears). Species High Season Reproduction Season Recruitment Season (Gear) Main Gear Argentina sphyraena May Jul. Apr. Jul. Unknown TR Aristeus antennatus (Big) May Aug. May Sep. Unknown TR Aristeus antennatus (Small) May Aug. May Sep. Unknown TR Boops boops // Apr. May Unknown TR Chamelea gallina Jul. Nov. May Jul. Unknown SD Citharus linguatula+lepidorhombus boscii (Big) Jul. Oct. Mar. Jun. Unknown TR Citharus linguatula+l. boscii (Small) May Jul. Mar. Jun. Unknown TR Conger conger // Jun. Jul. Unknown TR Diplodus annularis+d. vulgaris // Apr. Jun. Unknown TR Diplodus sargus Mar. Apr. Mar. Jun. Unknown TR Donax trunculus Mar. Apr. and Jul. Aug. May Jul. May Jul. SD Eledone cirrhosa (Big) Jan. Mar. Jan. May Jul. Sep. TR Eledone cirrhosa (Small) Jul. Nov. Jan. May Jul. Sep. TR Engraulis encrasicolus (Big) May Jul. May Aug. Nov. Dec. PS Engraulis encrasicolus (Small) Mar. May May Aug. Nov. Dec. PS Epinephelus guaza Feb. Mar. Jul. Aug. Unknown GN Etmopterus spinax Apr. Jul. Jan. Dec. Unknown TR Helicolenus dactylopterus May Jul. Apr. Aug. Unknown TR Lichia amia // Apr. Jun. Unknown PS+GN Liocarcinus depurator Jun. Oct. Jan. Mar. Aug. Oct. TR Liza sp+mugil sp Sep. Oct. Jul. Oct. Jun. Sep. TR Loligo vulgaris (Big) Sep. Dec. Mar. Jul. Oct. Dec. TR Loligo vulgaris (Small)+Alloteuthis media Dec. Jan. Mar. Jul. Oct. Dec. TR Lophius piscatorius+l. budegassa (Big) Mar. Jul. Apr. Jul. Unknown TR Lophius piscatorius+l. budegassa (Small) Mar. Jul. Apr. Jul. Unknown TR Merluccius merluccius (Big) May Jul. Oct. Feb. Jul Sep. TR Merluccius merluccius (Small) Sep. Nov. Oct. Feb. Jul Sep. TR Micromesistius poutassou (Big) Mar. Jul. Feb. May Jun. Nov. TR Micromesistius poutassou (Small) Sep. Jan. Feb. May Jun. Nov. TR Mullus barbatus+m. surmuletus (Big) Sep. Nov. May Jul. Oct. Dec. TR Mullus barbatus+m. surmuletus (Small) Oct. Dec. May Jul. Oct. Dec. TR Nephrops norvegicus (Big) May Jul. Aug. Jan. May Jul. TR Nephrops norvegicus (Small) May Aug. Aug. Jan. May Jul. TR Oblada melanura Jun. Sep. Apr. Jun. Unknown PS Pagellus acarne+p. bogaraveo Sep. Oct. Jul. Sep. Unknown TR Pagellus erythrinus Oct. Nov. Apr. Sep. Unknown TR Palinurus elephas Jun. Sep. Oct. Feb. Unknown TR Parapenaus longirostris // Jun. Aug. Unknown TR Penaeus kerathurus Jun. Aug. Jun. Aug. Unknown GN Phycis blennoides May Jul. Apr. Jul. Apr. Jul. TR Raja asterias+r. clavata // Jan. Dec. Unknown TR Sardina pilchardus (Big) Apr. Aug. Nov. Mar. Unknown PS Sardina pilchardus (Small) Oct. Nov. Nov. Mar. Unknown PS Sarpa salpa // Mar. Apr. and Sep. Oct. Unknown TR Scomber japonicus Jul. Sep. Jun. Sep. Unknown PS Scomber scombrus (Big) // Jan. Apr. Unknown PS Scomber scombrus (Small) Jul. Aug. Jan. Apr. Unknown PS Scophtalmus rhombus+psetta maxima Sep. Nov. Mar. Aug. Unknown TR Scorpaena porcus+s. scrofa May Aug. May Aug. Unknown TR Scyliorhinus canicula // Jan. Dec. Unknown TR Sepia officinalis Mar. May and Oct. Dec. Mar. Aug. Unknown TR+GN Sepiolidae Apr. Sep. Mar. Nov. Unknown TR Serranus cabrilla+s. scriba // Apr. Jul. Unknown TR Solea vulgaris Nov. Feb. Dec. Mar. Unknown TR Sparus aurata Oct. Nov. Oct. Dec. Unknown TR Spondyliosoma cantharus May Jun. Mar. May Unknown TR Stichopus regalis May Aug. May Jun. Unknown TR Todarodes sagittatus+illex coindetii May and Sep. May Jun. and Oct. Nov. Unknown TR Continued

9 Time series modelling of landings in Northwest Mediterranean Sea 79 Table 3. Continued. Species High Season Reproduction Season Recruitment Season (Gear) Main Gear Trachinus draco Jul. Dec. Jun. Aug. Unknown TR Trachurus trachurus (Big) May Nov. Jul. Sep. Unknown PS+TR Trachurus trachurus (Small) Jul. Nov. Jul. Sep. Unknown PS+TR Trichiurus lepturus+lepidopus caudatus May Aug. Jul. Sep. Unknown TR Trigla lucerna Sep. Nov. May Jul. Unknown TR Trigla lyra May Jul. Jun. Aug. Unknown TR Trisopterus minutus capelanus Sep. Dec. Feb. May Unknown TR Zeus faber Apr. Jun. Mar. Jun. Unknown TR AO interventions will not be considered because they could be a direct consequence of recording errors or anomalous fishing effort (e.g. an anomalous windy or stormy month that prevents fishing). By carrying out the intervention analysis, we will not only obtain better models (estimated parameters will improve) and better forecasts (in case that the invention occurs in the last values used to model the series), but also it will be possible to learn more about the time series under study (i.e. detect possible external events and try to explain them). To evaluate the catch variation for each species from October 99 onwards (in order to define patterns of similar trends), a comparison of trends for all species was carried out by classification methods. Thus, the matrix of species trends during that period was classified using cluster analysis using the -Pearson r as a measure of distance and the unweighted pair group average (UPGMA) as the linkage rule, and by principal components analysis with 2 factors, using VARIMAX normalized as a rotational strategy. Results The final ARIMA models fitted to the monthly catches of the 53 species (desegregated by commercial size class when possible) are presented in Table. Overall, 27 general ARIMA models were identified. In general terms, the ARIMA models fitted to target demersal, benthic and semi-pelagic species explained a reasonable amount of the variability observed. The amount of variability explained by the models ranged from 79% for big M. merluccius, to% fore. encrasicolus, whereas ARIMA models explained more than 5% of the variance for 28 species (Table ). Landings of big M. merluccius at month Z t depend on the landings at months (t ) to (t 5), (t 2) to (t 5), (t 24) to (t 27), and so on. Non-seasonal ARIMA models were restricted to a small number of species, e.g. Boops boops, Conger conger and Parapenaeus longirostris, with the (,,) model being the most frequently used. The within-species comparisons indicated that the large commercial size classes were generally better explained than the small size classes (Table ). An important check of any model is to compare predicted with observed values. Figure 3 shows some examples of these comparisons and show the predictive ability of the ARIMA models. Significant interventions (p<.5, t>3. or t< 3.) are shown in Table 2. Many of these interventions were for small commercial size classes and indicated a decrease in the mean catch, e.g. small M. merluccius (Fig. 4), small E. cirrhosa (Fig. 5) and small Micromesistius poutassou. Most of the anomalies were found during the period of smallest catches. Cephalopod species where particularly affected by them (e.g. Todarodes sagittatus and Illex coindetii, and Sepia officinalis). The monthly catches of nearly all species exhibited a seasonal cycle (Table 3). In most cases winter was the low season. Important catch declines of Solea vulgaris and Sparus aurata were preceded and followed by a strong variation of their respective seasonal patterns (Fig. 6). In contrast, the landings of the remaining species (e.g. big Loligo vulgaris, Fig. 6) showed a constant seasonal pattern over time. Classification of trends from October 99 onwards by cluster analysis (Fig. 7) indicated five clusters. The same pattern also emerged from the use of principal component analysis (Fig. 8), although the total variance explained by the two factors was low (45.4%). Table 4 displays the typical trend profile for each of the species, while Figure 9 shows the mean shape of each profile. There were five profiles. The first profile, which encompassed species such as small M. merluccius, big Loligo vulgaris and Sparus aurata, had a main peak at the end of 99. The second profile refers to species whose catches peaked in 992 (e.g. big M. merluccius, big and small Lophius piscatorius and L. budegassa and Conger conger). The third profile refers to species whose catches peaked in 994 (e.g. Scophtalmus rhombus and Psetta maxima, Liocarcinus depurator, Donax trunculus and big Citharus linguatula and Lepidorhombus boscii). The

10 8 J. Lloret et al. 2 (a) Trend January Seasonality July Trend (t).5 5 Seasonality Date (months).5 (b) Trend October Seasonality June 35 3 Trend (t) Seasonality Date (months) 7 6 Trend May Seasonality October (c) 3 25 Trend (t) Seasonality Date (months) Figure 6. Seasonal pattern and trend of catches of (a) Solea vulgaris, (b) Sparus aurata and (c) Big Loligo vulgaris, January 98 August 997. and indicate the evolution of the January and July, the June and October and the May and October catch data at their respective seasonal pattern. fourth was represented by species whose catches peaked in 995 (e.g. big Sardina pilchardus, small Eledone cirrhosa, Oblada melanura and Scomber japonicus). Finally, the fifth profile refers to species whose catches peaked late in 996 (e.g. Diplodus sargus, small Engraulis encrasicolus, small Sardina pilchardus and big Scomber scombrus). While the first three profiles included mostly demersal species, the last two included nearly all pelagic species. Discussion Univariate ARIMA models predicted the catches of target demersal and benthic species, especially those of the long-lived species. ARIMA models for pelagic and non-target species had little forecasting power. For those cases, using a simple naïve method would have been enough, as the U-statistic was greater than. Catch data from target species probably represented stock dynamics

11 Time series modelling of landings in Northwest Mediterranean Sea Linkage distance AU AJ BA L AH Q AD AE AP AG BD AC BI M AS BG ATCJ G BHAI AF AQ PO AA SW BC BFV AL AV AZB ABFK E T AO BEU BL BM RX AN AY AK Y AX BN AW BB AM BKD ARAZ I H BJN Figure 7. UPGMA clustering of trend data for all species and commercial size groups (alphabetical codes listed in Table ) from October 99 to August 997, with the resulting five main clusters..2 Factor BK 2 AN BN D AW AR Z A Y X H AX BB AM N S W BJ BF V R I AA K E AY AK AA AB BM AL AV 3 T AZ BL U BE AC AJ AF O F AQ AS BG AH BI B AO M AU AT L 4 P G 5 AD BA AI C BD G BH AP AG J AE Factor Figure 8. Bi-dimensional projection of trend data of all species and commercial size groups (alphabetical codes listed in Table ) onto the first two principal components, from October 99 to August 997. The five clusters obtained in Figure 7 are also indicated. better than from non-target species. Models fitted to pelagic species were poor because of high temporal and spatial variability in landings and daily fishing effort. The fact that the seasonal ARIMA model (,,) (,,)2 was appropriate for the majority of the species suggested that the catch of these species had a similar statistical structure. The majority of the interventions appeared in small commercial size classes and showed a decrease in catches. High catches typically occurred during the time period of reproduction or recruitment to the gear (Table 3). Based on the 996 monthly effort values (Fig. 2), it seems evident that seasonal fluctuations in effort of

12 82 J. Lloret et al. Table 4. List of species (or group of species) classified according to their trend profiles (October 99 August 997) obtained from cluster analysis (Figures 6 8). Alphabetical codes listed in Table. Species Code Species Code Profile (cluster ) Lichia amia Loligo vulgaris (Big) Loligo vulgaris (Small)+Alloteuthis media Merluccius merluccius (Small) Sparus aurata Todarodes sagittatus+illex coindetii Profile 2 (cluster 2) Argentina sphyraena Boops boops Conger conger Diplodus annularis+d. vulgaris Engraulis encrasicolus (Big) Helicolenus dactylopterus Lophius piscatorius+l. budegassa (Big) Lophius piscatorius+l. budegassa (Small) Merluccius merluccius (Big) Palinurus elephas Penaeus kerathurus Phycis blennoides Sarpa salpa Scorpaena porcus+s. scrofa Scyliorhinus canicula Sepia officinalis Solea vulgaris Trichiurus lepturus+lepidopus caudatus Trigla lucerna Zeus faber Profile 3 (cluster 3) Aristeus antennatus (Big) Chamelea gallina Citharus linguatula+lepidorhombus boscii (Big) Donax trunculus Liocarcinus depurator Liza sp+mugil sp Micromesistius poutassou (Big) S V W AA BC BF A D H I N R X Y Z AK AM AN AR AW AX AY BB BJ BK BN B E F K T U AB Profile 3 (cluster 3) continued Parapenaus longirostris Raja asterias+r. clavata Scophtalmus rhombus+psetta maxima Sepiolidae Stichopus regalis Trigla lyra Trisopterus minutus capelanus Profile 4 (cluster 4) Eledone cirrhosa (Big) Eledone cirrhosa (Small) Etmopterus spinax Micromesistius poutassou (Small) Mullus barbatus+m. surmuletus (Big) Mullus barbatus+m. surmuletus (Small) Nephrops norvegicus (Small) Oblada melanura Pagellus erythrinus Sardina pilchardus (Big) Scomber japonicus Scomber scombrus (Small) Serranus cabrilla+s. scriba Spondyliosoma cantharus Trachinus draco Trachurus trachurus (Small) Profile 5 (cluster 5) Aristeus antennatus (Small) Citharus linguatula+l. boscii (Small) Diplodus sargus Engraulis encrasicolus (Small) Epinephelus guaza Nephrops norvegicus (Big) Pagellus acarne+p. bogaraveo Sardina pilchardus (Small) Scomber scombrus (Big) Trachurus trachurus (Big) AL AO AV AZ BE BL BM L M Q AC AD AE AG AH AJ AP AS AU BA BD BG BI C G J O P AF AI AQ AT BH purse seiners and small-scale artisanal gears (gill neters and shellfish dredgers) are responsible for the seasonality of landings of pelagic species and a few coastal species, Trend (standardized) Profile 5 Profile 4 Profile 3 Profile Month/Year Profile 2.96 Figure 9. Typical shape of trend profiles 5 corresponding to species of clusters 5, respectively. Trend data has been scaled from to, and represent the mean trend of all species of a given cluster. respectively. This would reflect the adaptation of fishermen s strategy either to species biology (e.g. E. encrasicolus), or to the market needs (D. trunculus). In contrast, since trawl effort does not fluctuate seasonally, seasonal fluctuations in the landings of trawlable species (e.g. L. piscatorius and L. budegassa, C. conger, M. merluccius and M. poutassou), can probably be attributed to their changing availability to the gear and/or recruitment processes, thus supporting the results of Martín (989) for Catalan trawl dynamics. The comparison between the seasonal patterns and trends in landings might be of interest in trying to identify important events at the level of the catch. As it is seen in Figure 6, important catch declines of S. vulgaris and S. aurata were preceded and followed by a strong variation of their respective seasonal patterns, and thus might be used as a tool for predicting important negative changes in landings of a species.

13 Time series modelling of landings in Northwest Mediterranean Sea 83 The factors responsible for trends in landings will be the object of further analyses. Long-term changes in landings of some target species in the NW Mediterranean have been also observed by Bas and Calderon (989), Lleonart (993), Oliver (993) and Fiorentini and Caddy (997). The fact that fishing effort in Roses Harbor remained stable during the study period suggests that the catches reported in this paper might be considered as a raw measure of abundance. The five groups of species trends (profiles) might suggest large-scale events that had an impact on a wide variety of marine species. The first three profiles (corresponding to those species whose catches peaked in 99, 992 and 994, respectively) included mostly demersal species and large commercial size-groups. The last two profiles were pelagic and small commercial size groups. Catches of most demersal species and large commercial size groups diminished from 99 onwards, while those of pelagic species and small commercial size-classes increased. Acknowledgements Our sincere thanks to many people of the Polytechnical University of Catalonia and the Institute of Marine Sciences-CSIC which contributed to the elaboration of this paper, and to the Organization of Fishermen of Roses fish market for providing the data. We are indebted to Dr Michael Chadwick and Dr Konstantinos I. Stergiou for reviewing the manuscript. Josep Lloret was financially supported by the D.G. Research of the Government of Catalonia. Appendix : standardized ARIMA notation The simple non-seasonal ARIMA model has a general form of (p,d,q) where p is the order of the non-seasonal autoregressive term (AR), q is the order of the nonseasonal moving average term (MA) and d is the order of non-seasonal differencing. AR describes how a variable Zt depends on some well-defined previous catch values Z t (AR-), Z t 2 (AR-2)..., while MA describes how this variable Z t depends on a weighted moving average of the available data Z t to Z t n. For example, for a one-step ahead forecast (say, for period t, an October), with an AR-, all weight is given to the catch of the immediately previous month (September), and with an AR-2 the weight is given to the catch of the two immediately previous months (September and August). By contrast, with an MA- or MA-2, a certain weight is given to the catch of the immediately previous month (September), a smaller weight is given to the catch obtained two months ago (August) and so forth, i.e. the weights decline in value exponentially. The seasonality exhibited by many catch time series renders simple ARIMA modelling inadequate. In the case of a seasonal time series, there is a relationship between months Z t and Z t s, where s is the seasonal timespan. The multiplicative, seasonal modelling approach which has a general form of ARIMA (p,d,q) (P,D,Q)s is used herein for species whose catch dynamics shows seasonal behavior. In this general form, P is order of the seasonal autoregressive term (ARS), Q is the order of the seasonal moving average term (MAS), D is the order of seasonal differencing and s is the seasonal span (e.g. s=2 for an annual trend in monthly data). Thus, ARS is describing how a variable Z depends on some and well defined previous values Z t 2 (ARS- ), Z t 24 (ARS-2)... while MAS describes how this variable Z depends on a weighted moving average of the available data Z t 2 to Z t 2n. For example, for a one-step ahead forecast (say, for period t, an October) and with an ARS-, all weight is given to the catch of the same season (October) year ago while with an ARS-2 the weight is given to October catch one and two years ago. By contrast, with an MAS- or MAS-2, the model gives a certain weight to October catch one year ago, to the October catch two years ago, and so on. These weights also decline exponentially. The standardized notation used in this paper to represent ARIMA (p,d,q) (P,D,Q)s models is φ p (B)Φ P (B s )] D s ] d Z t =C+θ q (B)Θ Q (B s )a t, where: φ p (B)= φ B φ 2 B 2...φ p B p is the non-seasonal autoregressive operator of order p. Φ P (B s )= Φ B s Φ 2 B 2s...Φ P B Ps is the seasonal autoregressive operator of order P. ] D s is the seasonal differencing operator of order D. ] d is the non-seasonal differencing operator of order d. Z t is the value of the variable of interest at time t. C=μφ p (B) Φ P (B s ) is a constant term, where μ is the true mean of the stationary time series being modelled. It was estimated from sample data using the approximate likelihood estimator approach. θ q (B)= θ B θ 2 B 2...θ q B q is the nonseasonal moving average operator of order q. Θ Q (B s )= Θ B s Θ 2 B 2s...Θ Q B Qs is the seasonal moving average operator of order Q. φ, φ 2,..., φ p ; Φ, Φ 2,..., Φ P ; θ,θ 2,...θ q ; Θ, Θ 2,..., Θ Q are unknown coefficients that were estimated from sample data using the approximate likelihood estimator approach. a t is the error term at time t. s is the seasonal span. When modelling, two different options have been used: tramo-seats and SCA options (Gómez and Maravall, 997). Tramo-seats is able to construct good models in a reasonable time for time series whose structure is relatively simple. The second option, SCA, is especially useful to model complex time series, although it takes

14 84 J. Lloret et al. longer because of the strict rules for model verification. Thus, the option tramo-seats has been used here as a first attempt to model time series of catches for each species. The SCA option has only been used in those cases when, due to the complex structure of the catch series, the tramo-seats option totally failed in producing models and predictions. References Armengol, J Artròpodes I. In Història Natural dels Països Catalans, 9. Ed. by R. Folch. Enciclopèdia Catalana. 437 pp. Bas, C., and Calderon, L. E Effect of anthropogenic and environmental factors on the blue whiting Micromesistius poutassou off the Catalonian Coast, Marine Ecology Progress Series, 54: Box, G. E. P., and Jenkins, G. M Time Series Analysis: Forecasting and Control. Prentice Hall, Inc., New York. 575 pp. Chatfield, C The analysis of time series: an introduction. Chapman & Hall, New York. 286 pp. Confraria de Pescadors de Roses 997. Estadístiques internes, 3 pp. Cristian, R. 99. Invertebrats no artròpodes. In Història Natural dels Països Catalans, 8. Ed. by R. Folch. Enciclopèdia Catalana. 598 pp. Downton, M. W., and Miller, K. A Relationships between Alaskan salmon catch and North Pacific climate on interannual and interdecadal time scales. Canadian Journal of Fisheries and Aquatic Sciences, 55: FAO 973. FAO Species identification sheets for fishery purposes: Mediterranean and Black Sea. Ed. by W. Fischer. FAO 997. FAO Standard Common Names and Scientific Names of Commercial Species. Fiorentini, L., and Caddy, J. F Long and short-term trends of Mediterranean fishery resources in the Western Mediterranean. GFCM Studies and Reviews, 69: 72. Fogarty, M. J Time series models of the maine lobster fishery: the effect of temperature. Canadian Journal of Fisheries and Aquatic Sciences, 45: Gómez, V., and Maravall, A Tramo-Seats-SCA. Polytechnical University of Catalonia, Department of Statistics, High School of Engineering, Barcelona. Hare, S. R., and Francis, R. C Climate change and salmon production in the Northeast Pacific Ocean. In Climate Change and Northern Fish Populations, pp Ed. by R. J. Beamish. Canadian Special Publication of Fisheries and Aquatic Sciences, 2. Lleonart, J. 99. La pesquería en Cataluña y Valencia. Descripción global y planteamiento de bases para su seguimiento. Informe Projecte EEC DG XIV. 634 pp. Lleonart, J Trends in Mediterranean fisheries yields. In Pollution of the Mediterranean Sea. Pollution Research and Environmental Monitoring. Analyses, recommendations and assesment of the scientific and technological options, pp Ed. by F. Briand. STOA Repport EC. 2 pp. Makridakis, S., Wheelwright, S., and McGee, V Forecasting: methods and applications. John Wiley & Sons, Inc., New York. 926 pp. Martín, P Dinámica de la pesquería de arrastre en Cataluña. Ph.D. Thesis. University of Barcelona. 358 pp. Margalef, R Introduction to the Mediterranean. In Key Environments: Western Mediterranean, pp. 6. Ed. by R. Margalef. 363 pp. Naef, A Die Cephalopoden. Fauna, Flora Golf Neapel, 35(): 863. Oliver, P Analysis of fluctuations observed in the trawl fleet landings of the Balearic Islands. Scientia Marina, 57(2 3): Pankratz, A. 99. Forecasting with Univariate Box-Jenkins Models. John Wiley & Sons, Inc., New York. 562 pp. Prat, A., Catot, J. M., and Solé, I Force 4/R Research System. Polytechnical University of Catalonia, Dpts. of Statistics, High School of Engineering, Barcelona. Sostoa, A. 99. Peixos. In Història Natural dels Països Catalans,. Ed. by R. Folch. Enciclopèdia Catalana. 487 pp. StatSoft Inc Statistica for Windows, 4.5. Stergiou, K. I Modelling and forecasting the fishery for pilchard (Sardina pilchardus) in Greek waters using ARIMA time-series models. ICES Journal of Marine Science, 46: Stergiou, K. I., Christou, E. D., and Petrakis, G Modelling and Forecasting monthly fisheries catches: comparison of regression, univariate and multivariate time series methods. Fisheries Research, 29: Whitehead, P. J., Bauchot, M.-L., Hureau, J.-C., Nielsen, J., and Tortonese, E Fishes of the North-eastern Atlantic and the Mediterranean. Unesco, Vol., 2, and pp.