Michel Marengo
email: marengo@univ-corse.fr

Jean-Michel Culioli

Marie-Catherine Santoni

Bernard Marchand

Eric D H Durieux

Comparative analysis between artisanal and recreational fisheries of Dentex dentex in a Marine Protected Area

Keywords: Small-scale fisheries, IUCN red list, fisheries management, marine reserve

The common dentex Dentex dentex (Linnaeus, 1758) is an iconic marine coastal fish in the Mediterranean Sea. This study was performed in the Bonifacio Strait Natural Reserve (BSNR), (NW Mediterranean Sea). The aims were to: (i) evaluate temporal variation of the artisanal fishing of common dentex (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012); (ii) compare and quantify (2006-08-11-12) catch rates, fishing techniques, catch composition , for artisanal and recreational fisheries and determine the influence of management measures by both activities; (iii) and estimate the production of both artisanal and recreational fisheries. Fishery data were collected from different artisanal fishing surveys (onboard fishing vessels and landings) and recreational fishing surveys (roving-roving). The gears with the highest rates of exploitation were Longline (3554.28 g.100 hooks -1 ±SE) and Trolling (358.50 g.boat -1 h -1 ±SE), respectively, for artisanal and recreational fishing. This study showed that catches obtained by both activities were quantitatively higher in partially protected areas than outside them. Production estimations suggest that recreational fishery contributes significantly to fishing mortality and that it can magnify the negative effects of artisanal fisheries. It is now necessary to implement specific measures to contribute to the sustainable fishery management of common dentex.

Introduction

The Mediterranean Sea is a marine biodiversity hot spot under intense pressure, where ecological and human influences meet and strongly interact [START_REF] Coll | The Biodiversity of the Mediterranean Sea: Estimates, Patterns, and Threats[END_REF][START_REF] Lejeusne | Climate change effects on a miniature ocean: the highly diverse, highly impacted Mediterranean Sea[END_REF]). Among ecological factors, such as direct habitat modification, species tropicalization, and seawater acidification, fishing represents the activity having the greatest impact because it has driven most stocks to overexploitation [START_REF] Quetglas | Synchronous combined effects of fishing and climate within a demersal community[END_REF].

To reduce such negative impacts, marine protected areas (MPAs) have been implemented as part of an ecosystem-based approach to coastal management [START_REF] Albouy | Simulation of the combined effects of artisanal and recreational fisheries on a Mediterranean MPA ecosystem using a trophic model[END_REF]. Multiple-use MPAs have been widely implemented due to their potential to achieve conservation objectives while allowing human uses and minimizing conflicts, by including some degree of protection for commercial species and important habitats as well as promoting the use of local fisheries and a range of recreational activities [START_REF] Lester | Biological effects within no-take marine reserves: a global synthesis[END_REF][START_REF] Rocklin | Spearfishing Regulation Benefits Artisanal Fisheries: The ReGS Indicator and Its Application to a Multiple-Use Mediterranean Marine Protected Area[END_REF][START_REF] Horta E Costa | Fishers' Behaviour in Response to the Implementation of a Marine Protected Area[END_REF].

More generally, MPAs are increasingly used as a tool for fishery management [START_REF] Rocklin | Spearfishing Regulation Benefits Artisanal Fisheries: The ReGS Indicator and Its Application to a Multiple-Use Mediterranean Marine Protected Area[END_REF]). They have the potential to sustain the fisheries adjacent to protected areas while safeguarding species and habitats within them [START_REF] Francour | A review of marine protected areas in the northwestern Mediterranean region: siting, usage, zonation and management[END_REF]. The expected benefits of MPAs for fishes include an increase in abundance (net emigration of adults and juveniles across borders, termed ''spillover"), biomass and fecundity (the increased production and exportation of pelagic eggs and larvae), as well as a potential benefit for biodiversity [START_REF] Francour | A review of marine protected areas in the northwestern Mediterranean region: siting, usage, zonation and management[END_REF][START_REF] Gell | Benefits beyond boundaries: the fishery effects of marine reserves[END_REF].

Artisanal fisheries or small-scale coastal fisheries are particularly important in the Mediterranean, where they constitute about 80% of the fishing fleet (European Commission 2004). Artisanal fishing is a complex system characterized by commercial fishers operating in small boats, exploiting areas near the coast, using a large number of gears and techniques, typically manned by a single fisherman or a pair of fishermen and targeting a high diversity of species [START_REF] Colloca | Structure and evolution of the artisanal fishery in a southern Italian coastal area[END_REF][START_REF] Gomez | The Decline of the Artisanal Fisheries in Mediterranean Coastal Areas: The Case of Cap de Creus (Cape Creus)[END_REF][START_REF] Lloret | A comparative analysis between recreational and artisanal fisheries in a Mediterranean coastal area[END_REF]). In the Mediterranean, fish are heavily exploited by commercial fishing but recreational fishing is also intensive along the Mediterranean coast [START_REF] Seytre | Assessment of commercial and recreational fishing effects on trophic interactions in the Cap Roux area (north-western Mediterranean)[END_REF]. Recreational fishing in the Mediterranean can be defined as follows: all non-commercial fishing carried out mainly for pleasure or sport, where the catch -the sale of which is illegal -is used for private consumption [START_REF] Font | Recreational fishing within Marine Protected Areas in the Mediterranean[END_REF].

Recreational fishing has economic, social, and cultural roles; it has been recognized as one of the most common leisure activities and is now a thriving activity in Mediterranean coastal areas [START_REF] Morales-Nin | The recreational fishery off Majorca Island (western Mediterranean): some implications for coastal resource management[END_REF][START_REF] Albouy | Simulation of the combined effects of artisanal and recreational fisheries on a Mediterranean MPA ecosystem using a trophic model[END_REF][START_REF] Font | Biological implications of recreational shore angling and harvest in a marine reserve: the case of Cape Creus[END_REF]). In the Mediterranean, recreational fishing is particularly important because it represents more than 10% of the total production of all fishing (European Commission 2004).

Recreational and artisanal sectors often compete for limited coastal resources and the intensification of recreational fishing magnifies pressure on species already in an advanced state of exploitation [START_REF] Diogo | Impact evaluation of spear fishing on fish communities in an urban area of São Miguel Island (Azores Archipelago)[END_REF][START_REF] Lloret | A comparative analysis between recreational and artisanal fisheries in a Mediterranean coastal area[END_REF]. Commercial and recreational fishing can have similar demographic and ecological consequences on fished populations and may provoke serious ecological and economic damage [START_REF] Coleman | The impact of United States recreational fisheries on marine fish populations[END_REF]. Despite this similarity, generating a variety of impacts on marine ecosystems, much less research is performed on recreational fishing compared to commercial fishing, due in part to the difficulties involved in collecting data on recreational fishing [START_REF] Font | Recreational fishing within Marine Protected Areas in the Mediterranean[END_REF]. There is an urgent need to evaluate the potential impact that the different types of fishing activities, alone and in combination, can have on the sustainability of coastal resources and on the general functioning of coastal ecosystems [START_REF] Albouy | Simulation of the combined effects of artisanal and recreational fisheries on a Mediterranean MPA ecosystem using a trophic model[END_REF].

The common dentex Dentex dentex (Linnaeus, 1758) is an iconic marine coastal fish in the Mediterranean Sea. It is a demersal sparid fish (0-200 m) that grows to a maximum length of 100 cm and weight of 13 kg, with a relatively long life span (more than 20 years) (Morales-Nin & Moranta 1997). As a high trophic level predator, it holds a key position in coastal marine food webs. The global commercial catch of common dentex has fluctuated over the last sixty years on a multidecadal time scale and declined significantly from a peak of ~7,000 tons in 1990 to less than 1,000 tons in 2005 (Abdul [START_REF] Malak | Overview of the Conservation Status of the Marine Fishes of the Mediterranean Sea[END_REF][START_REF] Marengo | A review of biology, fisheries and population structure of Dentex dentex (Sparidae)[END_REF]. D. dentex is now classified by the International Union for the Conservation of Nature (IUCN) as "vulnerable" on the Red List of Threatened Species in the Mediterranean Sea [START_REF] Malak | Overview of the Conservation Status of the Marine Fishes of the Mediterranean Sea[END_REF]. Despite this status, there is no Minimum Landing Size (MLS) to safeguard the reproductive potential for this species. D.dentex, due to its large size, flesh quality, and high commercial value is of great economic interest for both artisanal and recreational fisheries [START_REF] Morales-Nin | Life history and fishery of the common dentex (Dentex dentex) in Mallorca (Balearic Islands, western Mediterranean)[END_REF][START_REF] Loir | Sexuality and gonadal cycle of the common dentex (Dentex dentex) in intensive culture[END_REF]. The main fishing gears used by artisanal fishing, specifically targeting the common dentex are: bottom long-lines, trammel nets and medium-large mesh gillnets [START_REF] Morales-Nin | Life history and fishery of the common dentex (Dentex dentex) in Mallorca (Balearic Islands, western Mediterranean)[END_REF][START_REF] Sacchi | Report of the FAO EastMed Assessment of the Fishing Gears in Lebanon[END_REF]. The most common methods used in recreational fishing for D. dentex are boat fishing, spearfishing, line and shore fishing (Morales-Nin et al.

2005, Font & Lloret 2011

). There is an alteration and/or combined use of this gear, depending on the season, habitat and geographic area [START_REF] Marengo | A review of biology, fisheries and population structure of Dentex dentex (Sparidae)[END_REF]. Despite its economic and ecological importance, data on this species regarding fishing gear, seasonality, fishing effort, catches and the yields of the artisanal and recreational sector are still limited.

The aims of this study were to: (i) characterize the artisanal fishing of common dentex in the Bonifacio Strait Natural Reserve (BSNR, Corsica, NW Mediterranean Sea) in terms of temporal variability; (ii) compare and quantify, over a four year period, the catch rates, fishing techniques, catch composition of the artisanal and recreational common dentex fisheries and determine the influence of management measures (protected areas) on the captures by both activities; (iii) and estimate the production of the common dentex for both artisanal and recreational fishing.

Materials and methods

Study area

This study was performed in the Bonifacio Strait Natural Reserve (BSNR), located in southern Corsica (France; Mediterranean Sea, Fig. 1). Several activities take place in this MPA such as artisanal fishing (mainly trammel nets and longlines), recreational fishing (mainly longlines, hook fishing and spearfishing), diving and sailing.

It was created in September 1999 and encompasses the Lavezzi Islands Reserve created in 1982 [START_REF] Mouillot | Indicator species analysis as a test of non-random distribution of species in the context of marine protected areas[END_REF]. Its bottom substrate is predominantly covered by a mosaic habitat of rocks, sand and seagrass beds of Posidonia oceanica (L. Delile), and the maximum depth is 158 m. Its marine surface area of 79 640 ha includes four zones of Partially Protected Areas (PPA; 12 300 ha), where spearfishing is forbidden (artisanal fishing authorized), and six No-Take Zones (NTZ; 1130 ha) closed to all types of fishing activities (both artisanal and recreational) as well as diving [START_REF] Mouillot | Indicator species analysis as a test of non-random distribution of species in the context of marine protected areas[END_REF]. See http://www.rnbb.fr/ for more details about legislation.

Data collection

Fishery data were collected from different artisanal fishing surveys (from 2000 to 2012; except 2009) and recreational fishing surveys (2006,2008,2011,2012) carried out in BSNR (see Table 1 for a summary of the survey details). Over the study period, 962 commercial boats (= fishing parties) and 459 recreational boats (= fishing parties) were sampled.

Artisanal fishing surveys: the fishing catches were collected by BSNR scientists onboard fishing vessels or on landing, only on retained fish (see Table 1), in collaboration with fishermen of the prud'homie of Bonifacio, from four main ports (Pianottoli, Bonifacio, Sant'Amanza, Porto-Vecchio) and three shelter ports (Piantarella, Santa Giulia, La Chiappa). All the common dentex caught were measured and their total weight was estimated using size class correspondences: Small: 0-40 cm = 0.3828 kg; Medium: 40-60 cm = 2.1053 kg; Large: 60-80 cm =5.4653 kg; [START_REF] Marengo | A combined methodology for assessment of the common dentex (Dentex dentex) in the northern Corsica (France)[END_REF]. The fishing area, the duration, the type, the characteristics of the gear that were deployed and the fishing effort were recorded. To standardize the data collected, Catch Per Unit of Effort (CPUE) was expressed for nets, in grams by piece of net (50 m) (CPUE mass: g.50m -1 ), and per number of individual caught by piece of net (50 m) (CPUE num: ind.50m -1 ). In this study, the "Spiny Lobster net" is defined by duration of fishing operation of at least two days at a depth exceeding or equal to 50 m. The "Fish net" covers any type of net that does not correspond to the first definition. For longlines CPUE was expressed in grams per 100 hooks (CPUE mass: g.100 hooks -1 ) and per number of individuals caught per 100 hooks (CPUE num:

Ind.100 hooks -1 ). Fishing yield data is expressed in grams per day per boat.

Recreational fishing surveys: Surveys covered the summer (tourist) season. During fishing activity, a study on boat fishing was conducted at sea using a boat and several interviewers in the BSNR (roving-roving). For each fishing set, the data collected included type of fishing gear, the date, the duration of each fishing operation and the catch (only on retained fish). Weight estimates for common dentex were obtained with a spring balance (accuracy ± 20g) or were derived using length-weight relationships published in FISHBASE [http://www.fishbase.org/], based on Morales-Nin and Moranta 1997. CPUE mass was recorded per gram per boat per hour of fishing (g.boat -1 h -1 ) and CPUE num per number of individuals caught per boat per hour of fishing (ind.boat -1 h -1 ).

Estimation of fishing effort and production

Artisanal fishing: The fishing effort was expressed as the mean number of active fishing boats per day, and the mean number of trips performed during the whole fishing season [START_REF] Farrugio | A sampling strategy and methodology for assessment and monitoring of Mediterranean small-scale fisheries[END_REF]. The BSNR annual production was estimated using this previous information combined with the mean daily biomass caught per boat (yields data) for the years 2006, 2008, 2011, 2012. Recreational fishing: The BSNR annual production was estimated using several key assumptions; a heuristic approach was developed to estimate the fishing effort.

Information for the study was gleaned from a multiple approach based on fishing authorizations and roving-roving data, for more reliable assessments of the actual numbers of recreational anglers and their fishing effort and yields. The number of fishermen practicing in the RNBB was obtained from the number of declaration of intent of fishing made in 2013 within the BSNR. A new regulation (Arrété prefectoral n° 2013165-0001) requires all recreational fishermen to declare themselves to the managers. From this survey, the fishing effort was calculated based on: the number of fishermen, their profiles, the type of activity, the mean duration of fishing, the number of trips per year. The annual production value was estimated from the calculated average yield for Trolling (based on the study period 2006-2008-2011-2012) and the annual effort values, expressed as total catch per fisher and hour of fishing, and total number of fishing trips per fisher and year (2013), respectively.

Data analysis

Data-sets were not normally distributed; therefore assessments were tested for significance using non-parametric tests. Annual trends (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012) in the fishing yields were assessed using the Mann-Kendall test to test whether there was a trend in the time series and the Pettitt's test allowed identifying whether a shift occurred. A smoothing method was also used (Moving average) on these data sets. For artisanal fishing, differences in the CPUE between the sectors (PPA, GP, Out) was analyzed using the Kruskal-Wallis H test analysis of variance, with the Dunn post-hoc test and the Bonferroni correction. For recreational fishing, differences in the CPUE between sectors (PPA, GP) were analyzed using the Mann-Whitney U test. Analyses were performed using XLSTAT software (with the Time package).

Results

Time series analyses

The trend analysis of the fishing yield for artisanal fishery (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012) showed no significant temporal trends (Mann-Kendal test, p-value =0.86) and no shift was detected (Pettitt's test, pvalue =0.212). However, by segmenting the time series a significant increasing trend was detected between 2000 and 2006 (Mann-Kendal test, p-value ˂0.05) while no significant temporal trend was detected between 2007 and 2012 (Mann-Kendal test, p-value ˃0.05).

Furthermore, graphically, the moving average showed two main trends during these years. A first trend of increase between 2000 and 2006, with a yield in 2000 of 653.7 g day -1 boat -1 , reaching a peak exploitation in 2006 of 3750.2 g day -1 boat -1 . In the second phase, the results indicated a relatively stable yield (moving average), although highly variable with strong interannual fluctuations between 2007 and 2012. The yield varied from a minimum of 565.6 g day -1 boat -1 in 2007 to a maximum of 4720.9 g day -1 boat in 2011 (Fig. 2). The number of fishing vessels exploiting the MPA (an average of 13 boats per day) did not change between 2000 and 2012.

Catch composition

For artisanal fishing, the fishing method with the largest number of specimens caught was the Fish net (65% of catches) followed by the Longline (25% of catches) and the Spiny lobster net (10% of catches) (Fig. 3A). For recreational fishing, the fishing method with the largest number of specimens caught was (bottom) Trolling (90% of catches), followed by Spearfishing (6% of catches) and boat Angling (4% of catches) (Fig. 3A). As regards to size representativeness in the catch for artisanal fishing (Fig. 3B), it can be noted that Spiny Lobster nets (SL) and Fish nets (FI) have a broad spectrum of capture: the three size classes were well represented (SL, S: 24%, M: 48%, L: 28%; FI, S: 32% M: 46% L: 22%), with a predominance of the Medium size class.

Individuals caught using Longlines (LL) were essentially large specimens (LL, M: 22%, L: 78%). For recreational fishing, Trolling (TF= T in Fig. 3B) was the gear that captured the most large individuals (TF, S: 11%, M: 17%, L: 72%). For Spearfishing (SF= S Fig. 3B) and boat Angling (or handlining) BA= A Fig. 3B), the only size class found in the sample was the category Medium (SF and BA; M: 100%).

Fishing gears

In the study area for both artisanal and recreational fishing, six types of fishing gear targeting the common dentex were identified (Table 2). For artisanal fishing, the Longline had the highest rates of exploitation (3554.28 g.100 hooks -1 ) followed by the Fish net (69.53 g.50m of net -1 ) and the Spiny Lobster net (31.49 g.50m of net -1 ). Although these fishing gears were used in a wide range of depths, most of the effort was deployed between 48 and 68 m depth. For recreational fishing, Trolling reached the highest levels of exploitation (358.50 g.boat -1 h -1 ). By comparison, Spearfishing and boat Angling had much lower levels of exploitation (68.02 g.boat -1 h -1 and 12.73 g.boat -1 h -1 respectively).

Differences between protection levels

For artisanal fishing, the result indicated that there were significant differences between the CPUE values according to zone (Out of reserve = OUT, General Perimeter = GP, Partial Protected Area = PPA) (Kruskal-Wallis test, p < 0.0001). The multiple pairwise comparisons using Dunn's procedure showed that the CPUE values within the OUT were significantly higher than within the GP, and CPUE values within the PPA were significantly higher than within the GP. The mean CPUE was 26.3 g.50m of net -1 (±SE 6.6) in the OUT zone, 17.4 g.50m of net -1 (±SE 4.9) for GP and 98.6 g.50m of net -1 (±SE 17.4) for the PPA zone (Table 3).

For recreational fishing, data analysis showed that the CPUE values within the PPA were significantly higher than within the GP. The mean CPUE was 55.5 g.boat -1 h -1 (±SE 26.4) in the GP, and 355.1 g.boat -1 h -1 (±SE 87.1) in the PPA (Mann-Whitney test, p = 0.014) (Table 3).

Fishing Production

From the data collected, the estimated mean annual production (based on the study period) in BSNR was 5.8 and 3.4 tons for artisanal fisheries and for recreational fishing modalities considered in this study, respectively. Proportionally, recreational fishing represented 58% of the total captures of artisanal fisheries for this species. Recreational fishing amounts to 37% of the total catch (artisanal and recreational production combined) of the species in this MPA. The total annual fishing production estimated in the BSNR area for common dentex is 9.2 tons.

Discussion

The common dentex is considered as a trophy fish and it is therefore targeted by both artisanal and recreational fishing. Our time series results for artisanal fishing in the Bonifacio Strait Natural Reserve (BSNR) showed that despite strong intra and inter-annual variability two prominent periods (an increase from 2000-06 and relatively stable yield from 2007-12). Even if time series data of the present study started just after the creation of the BSNR, one possible explanation for the increased yield from 2000 till 2006 might be the direct effect of protection measures that first contributed to the increase of the common dentex and, second, to maintaining its exploitation. In the BSNR, a restrictive policy has been enforced on fishing activities since the creation of the Marine Protected Area (MPA) in 1999: the number of professional licenses and the minimum mesh size were controlled and various protected perimeters were delimited [START_REF] Albouy | Simulation of the combined effects of artisanal and recreational fisheries on a Mediterranean MPA ecosystem using a trophic model[END_REF]. These restrictions tend to decrease fishing pressure on the protected parts and increase catches in terms of CPUE in these areas [START_REF] Mouillot | Do we protect biological originality in protected areas? A new index and an application to the Bonifacio Strait Natural Reserve[END_REF]. The increase in the abundance of exploited species can be rapid, but the recovery of age-and size-structures might only occur after a longer period of protection [START_REF] Seytre | Assessment of commercial and recreational fishing effects on trophic interactions in the Cap Roux area (north-western Mediterranean)[END_REF]. A likely hypothesis is that a long term period (several decades) of fishing prohibition is necessary to reach a complete reserve effect that could lead to an increase in catches for fishermen outside the protected zone, as part of a density-dependent process [START_REF] Seytre | The Cap Roux MPA (Saint-Raphael, French Mediterranean): changes in fish assemblages within four years of protection[END_REF]. The stabilization of the yield for artisanal fishing , could be explained by the combined impact of recreational fishing and marine tourism. Technological advances for the recreational fishery has led to major advances in the ability to capture fish: (i) with equipment for traveling longer distances, e.g., more powerful motors; (ii) several gear modifications, e.g., using light, prey mimics, additional chemicals, motion and sound to increase bait attractiveness; (iii) the affordability of sophisticated fishing technologies, e.g. electric fishing reels [START_REF] Cooke | Contrasting recreational and commercial fishing: Searching for common issues to promote unified conservation of fisheries resources and aquatic environments[END_REF]. Progress has also been made in locating fish more rapidly and effectively: (i) e.g., global positioning systems and sonar and (ii) the improved transfer of knowledge, e.g. internet forums [START_REF] Cooke | Contrasting recreational and commercial fishing: Searching for common issues to promote unified conservation of fisheries resources and aquatic environments[END_REF]. Such investments generally result in increased capacity or efficiency (e.g., better access to current fishing grounds) and an extension to existing fishing strategies (e.g., access to new fishing grounds) (Torres-Irineo et al. 2014).

In addition, the large numbers of recreational boats that can be found in the MPA of BSNR during summer can have a number of effects on its coastal marine environment. In 2006, 14 003 boats visited the two main tourist ports of the BSNR (Bonifacio, Porto-Vecchio). The rapid growth in the numbers of recreational boats is causing stresses to the marine environment and to many aspects of the biology and ecology of fishes. These stresses include pollution (e.g. heavy metal deposits), habitat alteration (e.g. increased turbidity, physical damage to bottoms by anchoring); behavioral alteration due to pressure wave disturbance and sound disturbance (e.g., avoidance of boating traffic by fish) and invasive species propagation (e.g., direct and indirect introduction of invasive aquatic biota) (Whitfield & Becker 2014). The difficulty in controlling such an influx of tourists is a problem well recognized by the managers of all of those MPAs where marine tourism is practiced (e.g., Port-Cros, Bonifacio, Medes), and does not yet seem to have been resolved [START_REF] Francour | A review of marine protected areas in the northwestern Mediterranean region: siting, usage, zonation and management[END_REF]. However many other factors, such as biological interactions, variations in recruitment, and environmental variations can also influence ecosystem functioning and have impacts on fish stocks [START_REF] Pinnegar | Trophic cascades in benthic marine ecosystems: lessons for fisheries and protected-area management[END_REF][START_REF] Brander | Impacts of climate change on fisheries[END_REF].

For the first time, our results characterize all fishing boat activities targeting the common dentex within an MPA, with an inventory of the fishing gear used, their selectivity and their rates of exploitation. Our study showed that in the BSNR, common dentex were targeted by both artisanal and recreational fishing using a wide variety of gears. In the BSNR, for common dentex fishing, Longline fishing essentially targets large specimens, whereas the composition by size class for Fish net and Spiny lobster net fishing shows broad variations in terms of catches. The catch by Fish net mainly corresponds to a peak of exploitation, with maximum efficiency in May during the spawning period when individuals aggregate or during seasonal migration. The catch by "Spiny lobster net" is low and mainly corresponds to a bycatch. These results are in agreement with previous studies conducted in the Mediterranean Sea for common dentex (reviewed by [START_REF] Marengo | A review of biology, fisheries and population structure of Dentex dentex (Sparidae)[END_REF].

The gears used most frequently for recreational fisheries in this area are Trolling, followed by Spearfishing and boat Angling. Trolling clearly has the greatest impact in terms of biomass removed, targeting essentially large specimens. Spear fishing might have a relatively minor impact compared to trolling. These results do not agree with the conclusions of Abdul [START_REF] Malak | Overview of the Conservation Status of the Marine Fishes of the Mediterranean Sea[END_REF], who identified spearfishing as the main threat to the exploitation of the common dentex in the Mediterranean.

The combined impact of artisanal and recreational fishing (e.g Longline, Trolling), targeting large specimens can have serious consequences on the state of stocks of D. dentex.

The removal of large individuals can adversely affect the reproductive potential of vulnerable fish populations because larger females are proportionally more fecund, reproduce over an extended period, and spawn better quality eggs and larvae with better survival rates [START_REF] Birkeland | The importance in fishery management of leaving the big ones[END_REF]. Size selective fishing may not only reduce the biomass but may induce: depensatory mechanisms, truncation of age and size structure, loss of genetic variability, and evolutionary changes [START_REF] Lewin | Documented and potential biological impacts of recreational fishing: insights for management and conservation[END_REF].

CPUE data have been evaluated inside and outside the MPA using the same gear. This allows the use of CPUE as an indicator of population abundance of fish communities according to protection levels [START_REF] Guidetti | Assessing the potential of an artisanal fishing co-management in the Marine Protected Area of Torre Guaceto (southern Adriatic Sea, SE Italy)[END_REF]. This study showed that catches obtained by artisanal and recreational fishermen inside the PPA and outside these areas were consistently different. On average, catches were quantitatively higher in PPA relative to GP and OUT. This effect has been described previously and was consistent with the results of previous studies, which show a higher increase in the biomass and density of common dentex inside the MPAs than outside them [START_REF] Guidetti | Assessing the potential of an artisanal fishing co-management in the Marine Protected Area of Torre Guaceto (southern Adriatic Sea, SE Italy)[END_REF][START_REF] Forcada | Structure and spatio-temporal dynamics of artisanal fisheries around a Mediterranean marine protected area[END_REF]. There is a body of evidence suggesting that the differences observed between average CPUEs inside and outside the MPA are likely due to different fishery managements [START_REF] Guidetti | Assessing the potential of an artisanal fishing co-management in the Marine Protected Area of Torre Guaceto (southern Adriatic Sea, SE Italy)[END_REF]. The higher trophic levels tend to show greater responses to protection, likely because higher predators tend to be targeted by fisheries [START_REF] Lester | Biological effects within no-take marine reserves: a global synthesis[END_REF]. Other factors can explain a substantial proportion of the variation observed in the abundance of fish species such as habitat structure [START_REF] Lizaso | Density dependence in marine protected populations: a review[END_REF][START_REF] Miller | Studies of no-take marine reserves: Methods for differentiating reserve and habitat effects[END_REF][START_REF] Harasti | Does a No-Take Marine Protected Area Benefit Seahorses?[END_REF]. In this case, two main hypotheses could explain the high catch rates of common dentex in the PPA: (i) the banning of spearfishing in the PPA and (ii) the "refuge effect".

Firstly, [START_REF] Rocklin | Spearfishing Regulation Benefits Artisanal Fisheries: The ReGS Indicator and Its Application to a Multiple-Use Mediterranean Marine Protected Area[END_REF] demonstrated in the BSNR that spearfishing can modify species assemblage structure. The dramatic effects of spearfishing on some of these species have been well established [START_REF] Coll | Spear fishing in the Balearic Islands (west central Mediterranean): species affected and catch evolution during the period 1975-2001[END_REF]). Secondly, one of the most important benefits to marine coastal species is that MPAs can act as refuges into which fish move to escape fishing [START_REF] Lester | Biological effects within no-take marine reserves: a global synthesis[END_REF]. The common dentex is one of those species that benefit from this protection measure, as it is especially targeted by both recreational and artisanal fishing. The trophic balance of an aquatic ecosystem can be disrupted by the direct and indirect effects of commercial and recreational fishing [START_REF] Cooke | Contrasting recreational and commercial fishing: Searching for common issues to promote unified conservation of fisheries resources and aquatic environments[END_REF]. Depending on role and dominance within the ecosystem, the removal of a substantial part of a population can significantly affect the trophic process and the community structure [START_REF] Lewin | Documented and potential biological impacts of recreational fishing: insights for management and conservation[END_REF]. Cascade processes concern interconnected changes in predation interactions involving keystone species at different trophic levels, which are induced by modifications affecting the identity or the activity rate of toppredators [START_REF] Francour | A review of marine protected areas in the northwestern Mediterranean region: siting, usage, zonation and management[END_REF]. The abatement of their stocks in overfished areas and, conversely, their replenishment in protected areas may thus trigger cascade processes [START_REF] Steneck | Human influences on coastal ecosystems: does overfishing create trophic cascades?[END_REF]. In Port de la Selva (Spain), the proportion of a top predator such as Dentex dentex in total landings increased after the establishment of the MPA to the detriment of Octopus vulgaris (Cuvier, 1797), Diplodus sargus (Linnaeus, 1758), Scorpaena sp (Linnaeus, 1758), and Palinurus elephas (Fabricius, 1787) [START_REF] Gomez | The Decline of the Artisanal Fisheries in Mediterranean Coastal Areas: The Case of Cap de Creus (Cape Creus)[END_REF]. For example, in the Bonifacio straits (France) the significant decrease of Serranus cabrilla (Linnaeus, 1758) could be explained by the significant increase of D. dentex [START_REF] Rocklin | Spearfishing Regulation Benefits Artisanal Fisheries: The ReGS Indicator and Its Application to a Multiple-Use Mediterranean Marine Protected Area[END_REF]). The explanation for this difference was based on increased predation within the reserve due to a number of larger predators such as Dentex dentex [START_REF] Francour | Mediterranean marine protected areas and nonindigenous fish spreading[END_REF]. Such a trend is generally not expected after the implementation of an MPA, but can be explained by trophic interactions between species through the top-down effect, by which an increase of predators would lead to a decrease of its preys [START_REF] Pinnegar | Trophic cascades in benthic marine ecosystems: lessons for fisheries and protected-area management[END_REF][START_REF] Seytre | The Cap Roux MPA (Saint-Raphael, French Mediterranean): changes in fish assemblages within four years of protection[END_REF]. However, the role of these keystone species is fundamental to ecosystem functioning and their protection is an insurance against the erosion of functional diversity [START_REF] Caro | Top predators as conservation tools: ecological rationale, assumptions, and efficacy[END_REF].

The recreational fishing modalities considered in this study catch around 3.4 tons of common dentex per year, which is equivalent to 58% of the artisanal fishery production in the MPA (artisanal fisheries catch 5.8 tons.year -1 of common dentex). The comparison of recreational catch estimates from this study with artisanal catch estimates of common dentex in the MPA suggests that recreational fishing (i) contributes significantly to fishing mortality, (ii) and it can exacerbate the magnitude of the negative effects of artisanal fisheries on the common dentex. However, it is noteworthy that the recreational and artisanal fishing catches reported in this study were probably underestimates. Recreational catches have a degree of imprecision due to the constraints associated with onsite survey methods [START_REF] Lockwood | Conducting roving and access site angler surveys[END_REF], and discards and illegal catches were not estimated in this study.

It is becoming increasingly apparent that recreational fishing is contributing significantly to the total fishing mortality of some species in certain regions [START_REF] Coleman | The impact of United States recreational fisheries on marine fish populations[END_REF].

Other studies have also shown that recreational fishing can represent a significant part of total landings [START_REF] Cooke | The Role of Recreational Fishing in Global Fish Crises[END_REF]. Overall, recreational fishing's share of total catches ranges by as much as 10% to 50% of the total commercial fishing catch (European Commission 2004[START_REF] Morales-Nin | The recreational fishery off Majorca Island (western Mediterranean): some implications for coastal resource management[END_REF][START_REF] Lloret | A comparative analysis between recreational and artisanal fisheries in a Mediterranean coastal area[END_REF]. However, for specific species recreational catches may often be equal to, or exceed, commercial catches (Zischke et al. 2012).

This activity may challenge the sustainability of artisanal fisheries sharing the same areas and the same resources [START_REF] Rocklin | Spearfishing Regulation Benefits Artisanal Fisheries: The ReGS Indicator and Its Application to a Multiple-Use Mediterranean Marine Protected Area[END_REF]. Within the BSNR, artisanal and recreational fishing activities generate combined pressure on the ecosystem [START_REF] Albouy | Simulation of the combined effects of artisanal and recreational fisheries on a Mediterranean MPA ecosystem using a trophic model[END_REF]. Although rarely considered to be an important factor, the result of recreational fishing has the potential to produce effects that parallel those of commercial fisheries (e.g., reduced stock size, decreasing mean size, genetic changes, ecosystem level changes and habitat degradation) [START_REF] Cooke | Contrasting recreational and commercial fishing: Searching for common issues to promote unified conservation of fisheries resources and aquatic environments[END_REF]. D. dentex is a vulnerable species included on the red list of the IUCN and also a highly important target of artisanal fishing and recreational boat fishing in the BSNR. The data collected and the results presented in this study make a significant contribution to knowledge on several aspects of the artisanal and recreational fishing of common dentex in the Mediterranean, providing an overview of the pressure levels and catches arising from these practices. In this work, we showed that the common dentex was favored by protection measures in Western Mediterranean MPAs.

In brief, MPAs are an essential tool for protecting overexploited populations and threatened species [START_REF] Hackradt | Response of Rocky Reef Top Predators (Serranidae: Epinephelinae) in and Around Marine Protected Areas in the Western Mediterranean Sea[END_REF]. Managers of the BNSR predict an increase in recreational fishing activities while the fishing effort from artisanal fisheries may stabilize [START_REF] Albouy | Simulation of the combined effects of artisanal and recreational fisheries on a Mediterranean MPA ecosystem using a trophic model[END_REF].

Considering the effect of recreational fishing, it seems important to formulate new regulation policies for recreational activities [START_REF] Albouy | Simulation of the combined effects of artisanal and recreational fisheries on a Mediterranean MPA ecosystem using a trophic model[END_REF]. It should be noted that since June 2012, new management tools have been tested by managers within the BSNR to limit the impact of recreational fishing (e.g. daily bag limitations, the restriction of recreational fishing in the PPA).

For the common dentex in the BSNR, managers should consider the implementation of specific measures to safeguard its reproductive potential, such as the establishment of Minimum landing sizes (MLS). It is essential to adjust MLS values so that they are larger than size at maturity, especially for the most vulnerable species [START_REF] Font | Biological and Ecological Impacts Derived from Recreational Fishing in Mediterranean Coastal Areas[END_REF]. Based on the size at first maturity and life history traits of the common dentex (Morales-Nin & Moranta 1997), it would be necessary to establish an MLS of 40 cm.

Common efforts devoted to educating fishers would be also necessary, especially to develop the practice of "catch-and-release". Unlike in other parts of the world where catch and release is common practice [START_REF] Cooke | The Role of Recreational Fishing in Global Fish Crises[END_REF][START_REF] Cooke | Contrasting recreational and commercial fishing: Searching for common issues to promote unified conservation of fisheries resources and aquatic environments[END_REF], it is not widespread in the Mediterranean.

Fish mortality after catch-and-release is an essential element to evaluate in order to adapt fishing regulations; however, it is highly dependent on variables such as the species considered, the gear used [START_REF] Bartholomew | A review of catch-and-release angling mortality with implications for no-take reserves[END_REF] and seawater temperature [START_REF] Gale | The role of temperature in the capture and release of fish[END_REF]. Thus, it is recommended that the factors influencing the post-release mortality of released fish be studied to allow accounting for post-release mortalities when estimating fishing mortalities and to assist in the development of best-practice guidelines [START_REF] Ferter | Unexpectedly high catch-and-release rates in European marine recreational fisheries: implications for science and management[END_REF].

Table captions

Table 1. Information on the different recreational and artisanal fishing surveys in which data were collected. The years and months when surveys were conducted, the survey type, and the number of boats sampled are shown.

Table 2. Characterization of fishing gear used by artisanal and recreational fishing (2006-08-11-12) with their catch per unit effort (CPUE).

Table 3. Mean values (±SE) of CPUE by artisanal fishery (g.50m -1 of net) and recreational fishery (g.boat -1 h -1 ) in the BSNR (2011-12), according to zone (PPA: Partial Protected Area, GP: General Perimeter, OUT: Out of reserve.

Figure caption Fig. 1

 caption1 Figure caption

Fig. 2

 2 Fig.2The mean fishing yield (g.day -1 boat -1 ) (±SE) and moving average for artisanal fishing

Fig. 3

 3 Fig.3Catch representativeness in % according to the total number (A) of individuals (n)

Fig. 1

 1 Fig. 1

Fig. 2

 2 Fig. 2

Fig. 3

 3 Fig. 3

Table 3

 3

	Zone	CPUE Artisanal Fishery		CPUE Recreational Fishery
	OUT	26,2 (±6,6) g.50m of net	-1	˗
	GP	17,4 (±4,9) g.50m of net	-1	55,5 (±26,3) g.boat	-1 h -1
	PPA	98,6 (±17,4) g.50m of net	-1	355,1 (±87,1) g.boat	-1 h -1

Acknowledgements

This research was funded by the ''Contrat de Plan Etat Région'' (CPER, PhD grant to M. Marengo), the ''Fonds Européen de Développement Régional'' (FEDER), the ''Collectivité Territorial de Corse'' (CTC), and the ''Università di Corsica Pasquale Paoli (UCPP). We thank Dr Jean-José Filippi (UCPP) for making the map. Special thanks are extended to the team of the ''Office de l'Environnement de la Corse'' (OEC) for collecting data and the effective collaboration of the fishermen of the BSNR.


Ph. D Jacques Rivoirard
email: jacques.rivoirard@mines-paristech.fr

Renard Didier

Didier Renard

A specific volume to measure the spatial sampling of deposits 1

Keywords: spatial sampling density, mineral resource classification, geostatistics, sampling grid, estimation variance spatial sampling density, mineral resource classification, geostatistics, sampling grid, estimation variance

A concept is proposed, that allows measuring the density of the spatial sampling of a regionalized variable in a domain. This "spatial sampling density variance" possesses an additivity property, that enables combining the values from different parts of a domain. In the case of a regular sampling pattern, the spatial sampling density variance is constant throughout the domain. It depends on the sampling grid and on the variogram, not on the extension of the domain. It can also simply be expressed as a "specific volume", similar to the inverse density of sample points in space, but taking into account the spatial structure. This can be used to compare different sampling patterns in a domain, as well as sampling patterns in different domains. In case of irregular sampling pattern, this can be mapped (like a density of points) using a moving window. The resulting map can be used to make the distinction between areas with different sampling densities. In the context of mineral resources, the concept can provide a description of the level of sampling for a deposit, or for parts of deposits sampled with different densities. This can be further used for classification, given expected production volumes.

Introduction

The concepts developed in this paper originate from mineral resources classification. This classification is based essentially on the geological model of the deposit, the sampling quality and the data spacing, and a key point for classifying resources (into inferred, indicated, measured resources) is the confidence which can be associated to these (eg Jorc 2012). From a geostatistical point of view, the confidence in estimated resources is closely linked to the data spacing or to the proximity of data. Purely geometric methods are often used to classify resources (search neighborhoods, drill-hole spacing), but do not take into account the spatial continuity of the variables nor the redundancy between data. By contrast geostatistics account for these and is capable to provide confidence or precision on estimated resources, whether derived from conditional simulations, or more simply expressed as estimation variances (eg kriging variance) (Emery and others, 2006;[START_REF] Silva | Mineral resource classification: a comparison of new and existing techniques[END_REF].

Such a geostatistical confidence is attached to a particular volume. For instance the classical global estimation variance (Matheron 1971, Chilès and[START_REF] Chilès | Geostatistics: Modeling Spatial Uncertainty[END_REF] is a way to express the precision attached to a whole domain when regularly sampled. It can also be used to choose the drill hole spacing required for a given precision on a production volume [START_REF] Sans | Resource risk characterisation, technical paper[END_REF][START_REF] Geovariances | Drill Hole Spacing Analysis, white paper[END_REF]). Kriging variance is often used in block-by-block classification, but making the classification dependent on the size of the blocks (Emery and others, 2006).

Hence it is not consistent from one deposit to the other, and do not allow comparison. Block kriging variances also present artifacts (e.g., lower variance around each hole) and require smoothing. Such effects can be reduced by excluding the hole having the largest weight in kriging (the "cross validation variance" proposed by [START_REF] Silva | Mineral resource classification: a comparison of new and existing techniques[END_REF]). Variants of variance (relative variance, conditional variance, variance efficiency...) can be used, while still being dependent on the block size. Concerning the choice of the criteria, it is advised to prefer a "neutral" criteria, that is, a criteria which does not penalize higher (or lower) grades (Emery and others, 2006). For instance using a conditional variance in presence of a proportional effect penalizes high grades and should be avoided. This makes sense, but then the question remains open, whether taking or not into account local proportional effects, as in conditional simulation. On the other hand, conditional simulation can provide the uncertainty on whatever volume is considered (and can include SMU's and cutoff).

In any case, a statement of confidence should specify whether it relates to global or local estimates, include the relevant tonnages, and be compared to production if available (Jorc 2012). Volumes are thus to be related to production scale. A global variance over the deposit is often insufficient, while conversely the actual precision of each individual block is much too detailed in the view of the classification of the resources of the deposit. In addition, it is not possible to combine kriging variances directly over a set of blocks, because common data are used when kriging neighboring blocks, leading to correlated errors.

The present paper develops a concept to measure the level of sampling of a regionalized variable, bridging the gap between the classical global estimation variance and the block-byblock classification. This concept, introduced as the "spatial sampling density variance" in [START_REF] Rivoirard | A geostatistical measure for the spatial sampling of a deposit[END_REF], was derived from the global estimation variance. A variant, the "specific volume", is introduced further to facilitate the use of the concept. The paper is organized as follows. After reminders on global estimation variance, the spatial sampling density variance is introduced, in a more general way as it was before. Then the specific volume is presented.

Mapping these quantities in the case of an irregular sampling is considered after that. The paper ends with discussion and conclusion.

Sampling density variance and specific volume

Estimation variances

A basic concept of linear geostatistics is that of estimation variance. Let Z(x) be an intrinsic random function representing an additive regionalized variable, with variogram γ(h). Suppose we want to estimate the value on a set V from the value on another set v:

* ( ) ( ) Z V Z v  Then the estimation error ( ) ( ) Z V Z v
 has a zero expectation, and its variance (the estimation variance) is given by the formula [START_REF] Matheron | The theory of regionalized variables and its applications[END_REF][START_REF] Journel | Mining geostatistics[END_REF][START_REF] Chilès | Geostatistics: Modeling Spatial Uncertainty[END_REF]:

22 E ( ) [ ( ) ( )] 2 ( , ) ( , ) ( , ) V E Z V Z v v V V V v v         
where for instance ( , ) vV  designates the mean variogram between a first point describing v and another point describing V independently. This formula is general: for instance V can be a block or a domain, and v a point or a set of points (e.g., datapoints). The formula can also be extended to a set of weighted points ( * () ZV being a weighted average of the points values), as in the case of ordinary kriging. For the time being we will consider the case of the global estimation of V from datapoints i x that are located on a regular centered grid within V. In this case V can be estimated from a simple average of data:

* 1 ( ) ( ) i i Z V Z x N  
and the main issue is the precision of this estimator, for instance its estimation variance. This can be obtained by:

2 2 2 1 1 1 ( ) ( ) ( ) 2 ( , ) ( , ) ( , )
E i i i j i i i j V E Z V Z x x V x x V V N N N               
Unfortunately such a variance is numerically sensitive and its computation is not so easy, as it appears as a small difference between two similarly small differences:

2 2 1 1 1 ( ) ( , ) ( , ) ( , ) ( , ) E i i j i i i j i V x V x x V V x V N N N                  
A long time ago, [START_REF] Matheron | The theory of regionalized variables and its applications[END_REF] had developed approximation principles to compute such global estimation variances from regular grids and with usual variogram models. One consists in combining estimation variances of parts of V, when parts are estimated by their inner samples, with negligible correlations between their errors. In two dimensions for instance, with an isotropic variogram and a square grid (or a rectangular grid based on a geometrical anisotropy), V is divided into N parts i v (i = 1, ..., N) equal to the grid mesh and centered on datapoints. The estimation error can be written as the average of the errors i  's on parts:

  * 1 1 ( ) ( ) ( ) ( ) i i i i i Z V Z V N N Z v Z x       
The global estimation variance:

2 2 2 2 2 2 1 1 2 ( ) ( ) ( ( ) ( 2 1 ( ) , ) ,
) ,

E i j E i i j i j i i j i E i j i j i V Cov v Cov N N N v N N                            reduces to: 2 2 ( () ) E E v V N    (1)
when the correlations ( ) , i j    between the errors can be neglected. In practice, a further advantage of such an approximation principle is that it uses the variogram model at short distances, not at longer distances for which the variogram is less well known.

In the case of a square grid (Fig. 1A), the correlation between the errors is indeed negligible with current variogram models. However this may be different with a rectangular grid corresponding to elongated blocks (under isotropy or after transformation into an isotropic space). For instance, with a linear variogram the error correlation between two 100 m × 100 m adjacent centered blocks is actually negligible, but is 0.18 between two adjacent 33 m × 100 m centered blocks. Of course this is due to the relative closeness between the samples caused by the elongation. To illustrate the effect of errors correlations, consider a simple example. Take a 100 m × 200 m big block subdivided into six 100 m × 33 m small blocks with one sample at their center (Fig. 1B). This big block can also be subdivided into three 100 m × 67 m blocks with two samples each, and into two 100 m × 100 m blocks with three samples each. For each case, consider the estimation variances that would be obtained by combination (1) when neglecting the errors correlations (Table 1). The estimation variance appears to be largely underestimated when subdividing the block into thin blocks. For the division into two 100 m × 100 m blocks, the estimation variance is still smaller than the global variance by 9% (which is the correlation between the errors on the two 100 m × 100 m blocks). Here the variogram was linear and isotropic. Things are expected to be better with current variogram models used for variables such as concentrations and accumulations, which are less continuous than a linear variogram, but this shows the risk of underestimating the estimation variance when combining error variances from too elongated blocks (after correction of a possible anisotropy). A similar configuration exists in three dimensions with a two-dimensional regular grid of vertical holes defining piles of blocks, each block being estimated from its samples. Thin blocks estimated from their samples may present correlations between their errors, and thicker blocks must be used to reduce these correlations.

When the correlations between errors are negligible, the global estimation variance of V (1) simply depends on the number of blocks: the larger this number, the smaller the variance.

However it is worth noticing that, due to (1) and since the number of blocks

N is | | / | | Vv , the quantity 2 ( ) | | E VV  is equal to 2 ( ) | | E vv
 and does not depend on this number. This observation is the origin of the concept of spatial sampling density variance developed in the next paragraph [START_REF] Rivoirard | A geostatistical measure for the spatial sampling of a deposit[END_REF].

The spatial sampling density variance

Here Z(x) still represents an additive regionalized variable, but is not necessarily an intrinsic RF, and it is sampled at datapoints

i x . Let * ()
ZV be an estimator of Z over a block or domain V (typically a linear estimator based on an average of its inner samples) and let 2 E () V  be its estimation variance. The corresponding "spatial sampling density variance" of V (or more simply its "sampling density variance") is defined as:

Spatial sampling density variance = 2 E () VV  (2)
(it is a variance, since it corresponds to the estimation variance of () Z V V ).

Because of the additivity of Z, if V can be divided into N parts ( 1,..., )

i v i N  , we have: | | ( ) ( | | ) i i i v Z V Z V v   Suppose that * ()
ZV can be expressed as the corresponding average of estimates of such

v : * * | | ( ) ( | | ) i i i v Z V Z V v   and that errors * ( ) ( ) Z v Z v  are uncorrelated. Then we have: 2 2 | | ( ) | | ( ) | | | | i E E i i i v V V v v V    
so that the involved spatial sampling density variances are additive. More generally if a whole domain is divided into parts, the estimation errors of which being uncorrelated, then the resulting spatial sampling density variance of all i v and all the possible unions V of these are additive. This makes the combination of variances possible, a highly desirable property when one wishes to combine uncertainties over larger sets.

Of course the key assumption for this additivity is the lack of correlation between the errors of the different parts, in addition to the additivity of the estimates. This assumption can result from the sampling design. This is the case in particular when the domain is divided into parts, and when sample points are tossed randomly, independently and uniformly within each part.

Then each part is estimated by its own samples, and the errors are uncorrelated. This corresponds to the stratified random sampling used in fisheries, with limits of strata corresponding for instance to thresholds on sea floor depth or latitudes (the spatial variability may differ from one strata to the other). In mining the lack of correlation between estimation errors of the different parts is essentially the consequence of each part being estimated by its inner samples. However dividing a domain into parts informed by inner samples is not sufficient. In particular, as seen above, considering too thin blocks with a regular sampling grid can lead to an underestimation of the spatial sampling density variance.

In the case of a regular grid and a given variogram, and when the approximation principle applies, we have:

2 2 ( ) | | ( ) | | E E V V v v   
The spatial sampling density variance of a set of N blocks does not depend on N. So it characterizes the density of the sampling pattern (hence the name), irrespective of the size of the area. Moreover it can be obtained from the estimation variance of each part, which can be computed from the variogram. This allows to compare the efficiency of different spatial sampling patterns within an area, or within areas having different variograms.

The specific volume

By definition, the unit of spatial sampling density variance is z 2 *volume unit, that is, z 2 *m 3 in three dimensions, or z 2 *m 2 in two dimensions (z being the unit of Z). Just as variances in general, it is suitable to develop calculations but not directly understandable. In the stationary case, a way to make it more understandable is to consider it relatively to the variance of the variable, typically the sill of the variogram. The sampling density variance, divided by this variance, becomes a volume: it is a specific volume, measuring the density of the spatial density relatively to the variance of the variable (as can be typically obtained from a normalized variogram with unit sill). Such a specific volume may be interesting in applications where the variable under study Z is defined up to a constant and is not necessarily positive (e.g., the elevation of a geological horizon, counted from a conventional reference). Of course the additivity of the sampling density variance over a set of i v extends to the specific volume only when the dividing variance remains constant.

Still in a stationary case, when working with a positive (or non-negative) variable (such as a concentration, thickness, accumulation), a better solution is to take into account the mean of the variable, say M. A given sampling density variance may represent a small or a large uncertainty depending on whether the mean is large or small. The solution is to consider the volume obtained by dividing the sampling density variance by the square of the mean:

Specific volume : 2 2 ( ) | | E o VV V M   (3)
This specific volume (the one which will be used from now on) measures the density of a spatial sampling of the variable, relatively to its mean: the smaller the specific volume, the more precise the sampling pattern. Here too, the additivity of the specific volume over the i v is only applicable when the dividing mean remains constant.

To fix ideas, consider the simple case of a regular grid and a pure nugget effect 2  . The specific volume then equals  

2 * mesh M



. In case of a sample coefficient of variation

CoV M   equal to 1, the specific volume coincides with the size of the mesh, and so with the inverse of the classical density of points in space, that is 1 point per mesh. A smaller sample CoV makes it smaller, a larger sample CoV makes it larger. In Table 2, we can see that the specific volume (in two dimensions) is the same with a sample CoV of 1 and a grid of 100 × 100, a CoV of 0.5 and a grid of 200 × 200 or a CoV of 2 and a grid of 50 × 50.

In the particular case of a grid which is large compared to the structure, a simple formula also exists for the specific volume. Following [START_REF] Matheron | The theory of regionalized variables and its applications[END_REF], the estimation variance of a domain V estimated by N datapoints can be approximated by:

2 2 () || 1 () E V V C h dh N     
where C(h) is the covariance function with

A toy example

The following toy example illustrates the interest of the concept of sampling density variance and of specific volume, in the context of optimal sampling. Consider a deposit with constant rock density, subdivided into different zones i = 1, …, n, each having its own volume , the sampling density variance (2) within zone i is

2 i i i V N 
, so is proportional to

2 i i i T N  , while the estimation variance of i Q is 2 2 i i i T N  . Hence the estimation variance of i i QQ   is 22 2 ii eQ i i T N    
The minimum of this quantity, with respect to the i N given that their sum is N, gives the optimal i N as the solution of the system:

ii i T i N   
where µ is a Lagrange parameter. The optimal i N is found to be proportional to i i T : the larger the zone and the higher the standard deviation of the grade in this zone, the larger the number of samples in it. The optimal estimation variance of As could be expected, sampling density variance and specific volume do not depend on the zone extension. Classification of resources based on sampling density variance would ignore the level of the grades and would favor parts with lower variability (even if these are poorer due to a global proportional effect). In the current case of a proportional effect of the type

" i i m 
constant", the optimal specific volume is proportional to 1 i m : the classification based on specific volume will favor parts where the mean is larger, which is satisfactory.

Example (regular sampling pattern)

The thickness of a mineralized layer has a mean of 10 m, a sample point variance of 10, and a variogram equal to 1 nugget(h) + 9 spherical (h/200 m). The extension variance of a 100 m × 100 m block by its center equals 2.69, so that for a 100 m × 100 m grid, the sampling density variance (2) is 26,900 m 4 , and the specific area (specific volume (3) in two dimensions) 269 m 2 . A similar computation shows that the specific area would be reduced to Page 14

Now another issue is whether this 100 m × 100 m sampling is better, or not, than a 70 m × 70 m sampling in a similar deposit, where the thickness has a mean of 8 and a variogram equal to 6 nugget(h) + 6 spherical (h/200 m) (Fig. 2). Hence the nugget is higher, but the sampling is finer. Interestingly the sampling density variances (2) derived from the normalized variogram (sill set to 1) are quite close: 2690 in the first case, 2680 in the second one. However the sill is higher in the second case, so that the sampling density variance ( 2) is slightly higher (32,100 m 4 against 26,900 m 4 ). If additionally we take into account the means, the sampling is nearly twice less good in the second case, with a specific area (3) of 502 m 2 against 269 m 2 . The finer sampling is not sufficient to compensate for the larger nugget component and, above all, the lower mean. As will be seen in the next paragraph (Eq. 5), we can deduce that, for instance, the 5% CoV area (area over which the mean thickness has a coefficient of variation of 5%) must practically reach 200,000 m 2 , while it is only108,000 m 2 in the first case.

Use of specific volume

The sampling density variance, or its simpler version the specific volume, can be used to characterize a regular sampling pattern with respect to the variogram. After that, the sampling density variance can be used to approximate the estimation variance of the regionalized variable over a volume V, typically a multiple of the mesh: Here it is useful to make a parallel between the spatial sampling density variance, or even more the specific volume, and the inverse of the classical density of points in space, which is also a volume. From a simple physical point of view, the density of points in a given volume is the number of points within it, divided by the volume. So its inverse is the average volume occupied by one point. It is equal to the mesh size in the case of a regular grid. This physical point of view can be adopted for each part of a domain, in particular when the density of the points varies from one part to the other. However things are different when the density of points varies within the domain but without any a priori partitioning.

In that case, the density of points, supposed to vary within the domain, will rather be subject of local estimation, using a moving window or a more sophisticated kernel function (of course there is a question of scale here, as the result depends on the chosen window size). The situation is very similar in our case, with the main difference that our sample points are associated with values of the regionalized variable, so that their influence in the spatial density should depend on the variogram. For instance, two close sample points should count differently whether the variogram contains a nugget effect or not. Hence it is proposed to measure the local density of sample points using the previously developed spatial sampling density variance (and the associated specific volume). This requires choosing a moving window that will capture inner samples. In mining exploration, even when the sampling pattern is irregular, holes are drilled in a systematical way, respecting directionality of sections and lines, and the use of parallelepiped windows, i.e. superblocks, is appropriate. The size of the window must be chosen so that it includes a local but representative distribution of inner samples. Having chosen the superblock, one must compute its estimation variance when estimated by its inner samples. This can be done using a "superkriging", i.e. a kriging of superblocks. Multiplying by the superblock volume gives the sampling density variance, and a further division by the squared mean gives the specific volume.

The superblock (the moving window) in the case of an irregular sampling pattern has the same role as big blocks set on the mesh, in the case of regular sampling. Both are usually much bigger than the usual blocks of the block model of the deposit. These smaller blocks are more appropriate to follow bodies with irregular geometries and to design mining projects.

Moving the superblock window at the center of each block of the block model results in a map at this resolution (but the result at one location does not depend on the size of the small block). Having mapped the sampling density (or the specific volume), it is possible to make the distinction between more homogeneous domains that are sampled with different sampling densities, i.e. different levels of confidence. An average sampling density may then be computed within such a domain, as the mean of the sampling density variances.

Example (irregular sampling pattern)

The concept is illustrated here on a porphyry copper deposit. This deposit has been sampled with fans of holes located within parallel sections spaced every 50 m. Superkriging was performed for each of the 10 m × 10 m × 10 m blocks of the block model. First, 50 m × 50 m × 50 m superblocks were used. However this resulted into envelops around each hole, since the distance between holes often exceeds 50 m (Fig. 3A). Satisfying results were obtained with 150 m × 150 m × 50 m superblocks, without any smoothing post-process (Fig. 3B). Homogeneously sampled domains can be drawn from such a map.

Having characterized in this way the spatial sampling within the deposit, this can be exploited to characterize resources given an assumption on the production volume (or more exactly the ore + waste volume to be extracted). For instance, using (4), a specific volume (3) of 6000 m 3 gives a grade CoV of 4.7% for an annual production of 2.7 Mm 3 (i.e. 7 Mt at 2.6 density), or a twice larger CoV (9.4%) on the corresponding quarterly production.

Discussion

The aim of this paper was to propose a concept to measure the spatial sampling density of a regionalized variable. The proposed spatial sampling density variance, derived from the concept of estimation variance, is additive, in the sense that its value for a big volume is the average of its values over parts dividing the volume. This requires parts having uncorrelated errors when estimating each of these by its inner samples. In the case of a regular sampling pattern within a big volume, this sampling density variance is constant and characterizes the pattern, depending on the variogram, not on the big volume. It thus allows comparing different sampling patterns within a given domain, or even sampling patterns on domains having different variograms. A variant of the sampling density variance, the specific volume, facilitates the measure and the comparison, by taking into account the mean of the variable in addition to its variogram.

The sampling density variance can be computed from big blocks corresponding to the mesh in the case of a regular grid. In the case of an irregular pattern, it can be computed from a moving superblock, and then be mapped in order to make the distinction between domains with different spatial sampling densities. Compared to the common tools of geostatistics, the sampling density variance (and the associated specific volume) is a flexible substitute for the classical global estimation variance in the case of a regular grid, and otherwise provides a local measure of estimation variance that is not be dependent on the size of the block from the block model (but it depends on the moving superblock, just like the estimation of a local density of points in space depends on the moving window used). It proposes a description of the sampling efficiency of a deposit, or within a deposit, which only depends on the spatial distribution of sample points, and on the mean and variogram of the variable. This description can be used as an input for mineral resources classification in a geostatistical perspective. In particular the specific volume can be used to make a direct link between a nominal volume to be mined in a given period and its coefficient of variation. While conditional simulation is able to provide the uncertainty within a given delineated volume, taking into account the particularities of local data and local proportional effects, our concept only requires nominal volumes. It cannot replace conditional simulation to assess the uncertainty of next quarterly production, but appears as a simple and flexible way to measure objectively the level of sampling within a deposit, even at the first stage of systematic sampling (inferred resources).

As mentioned at the beginning, the concepts developed in this paper originated from mineral resources classification. However, the spatial sampling density variance proposed here appears as a new concept in geostatistics in general, not only in mining geostatistics. By measuring the level of sampling of a regionalized variable per se rather than at a given support, it enables to assess, map, and combine uncertainties over space.

Conclusion

The spatial sampling density variance of a regionalized variable in a domain is a measure of the spatial sampling density in this domain. When the domain is divided into parts, estimated from inner samples and having uncorrelated errors, the sampling density variance over the domain is the average of its values on the different parts. Thanks to this additivity property, the sampling density variance offers a way to combine uncertainties in space. In the case of a homogeneous sampling pattern, the spatial sampling density variance is constant within the domain. In the case of an intrinsic variable, it depends on the variogram and on the sampling pattern, not on the domain extension. The spatial sampling density variance, or its variant, the specific volume, allows comparing different sampling patterns, in one domain or in several domains, having possibly different spatial structures. In case of an irregular sampling pattern, it can be mapped and allows distinguishing areas having a different sampling density. The specific volume is very similar to the inverse of the classical density of points in space, but depending on the spatial structure.

While common tools of geostatistics can provide the confidence on the estimation of a sampled variable on defined volumes, the present concept provides the level of confidence due to the density of spatial sampling. In the context of mineral resources classification, it can be used as a first step, to provide an objective description of the sampling effort throughout a deposit, enabling comparison between different domains or deposits. This first step may be further used to classify resources based on expected production volumes.

Tables captions

Table 1: Approximation of the estimation variance of a block subdivided into sub-blocks, each informed by 1, 2 or 3 samples (linear variogram γ(h) = |h|).

Table 2: Specific volume in the case of a square grid and a pure nugget effect.

Figures captions

  i

  e. the volume characterizing the spatial structure[START_REF] Chilès | Geostatistics: Modeling Spatial Uncertainty[END_REF].

  variogram of the point support grade within zone i is assumed to be a pure nugget effect i  2 ). How to allocate a given number N of samples at best, i.e. minimizing the global metal estimation variance?

Figure 1 .

 1 Figure 1. (A) square grid; (B) a big 100 m × 200 m block, divided into six 100 m × 33 m

Figure 2 .

 2 Figure 2. Which is better: (A) a 100 m × 100 m sampling of a thickness with mean 10 m and

Fig1

  Fig1

Fig3

  Fig3

Table 1

 1

	estimation variance
	from six 100 m × 33 m blocks	2.97
	from three 100 m × 67 m blocks 3.51
	from two 100 m × 100 m blocks 3.80
	of the 100 m × 200 m block	4.15
	(true)

Table 2

 2

		Sample CoV = σ/m
		0.5	1	2
	50 × 50	625	2500	10000
	Grid 100 × 100	2500 10000	40000
	200 × 200 10000 40000 160000

Acknowledgements

The authors are grateful to Codelco (Felipe Celhay) and Vale (in particular Celeste Queiroz and Leandro Jose Oliveira) for their support in this research. Mapping the specific volume has been made possible thanks to a "Superkriging" plugin developed for Geovariances Isatis software.

or to determine |V| corresponding to a given CoV:

Hence, having characterized the sampling pattern by its specific volume, it is possible to relate volumes to their CoV. In term of mineral resource classification, V could be chosen as the volume to be mined in order to ensure the production in a given period, while thresholds on CoV would be used to categorize the resources. Note that the CoV used here is a nominal CoV, computed from the global mean M and the mean variogram. In practice the global mean M should be computed from the same data that are used to compute the variogram.

Case of an irregular sampling pattern

In the previous cases, the grid was supposed to be regular, either over the whole deposit, or over a part of deposit. But there are situations where the sampling pattern is not regular, typically when exploration is made by fans of holes. Often fans of holes are drilled within regularly spaced vertical sections, but the spatial density of data within each section is higher where the holes are close together, and smaller away from this. Then it may be important to make the distinction into parts that are more or less densely explored.