K Guizien
email: guizien@obs-banyuls.fr

M Belharet

P Marsaleix

J M Guarini

Using larval dispersal simulations for Marine Protected Area design: application to the Gulf of Lions (NW Mediterranean)

The design (location and size) of sustaining, no-take reserves was investigated by combining realistic numerical simulations of larval dispersal from a sedentary marine species with a population dynamics model. The method explored, a priori: (1) the Planktonic Larval Duration (PLD) of self-persistent populations within no-take reserves with radii from 1 to 20 kms, (2) the size of a no-take reserve reaching self-persistent recruitment of the reserve population, and (3) offspring spillover to adjacent fisheries for PLDs from one to six weeks. In the Gulf of Lions (NW Mediterranean), as the radius of a no-take reserve increased to 20 kms, the median PLD of a self-persistent species within the reserve increased from 2 to 6.5 days. No unique relation between PLD and sustaining no-take reserve size could be established due to large spatial and temporal variabilities, thus precluding any general guidelines for marine protected area sizes. For species with mass spawning lasting < 3 days, variability due to spawning timing yielded twice the spatial variability, reflecting strong wind variability. In contrast, when spawning lasted more than 10 days, the spawning location became more important. This pinpoints how a biological process (spawning duration) can trigger deterministic and stochastic effects of environmental variability. Finally, some unprotected areas (Narbonne to Agde and the Camargue) clearly appeared as better locations than the existing no-take reserves for maximizing biodiversity persistence within a reasonable no-take reserve size (10 to 20 kms), and for producing offspring spillover important for regional fisheries (80 %).

INTRODUCTION

During the 10 th meeting of the Conference of the Parties of United Nations Convention on Biological Diversity, held in October 2010 in Nagoya (Japan), the Strategic Plan for Biodiversity 2011-2020 formulated a conservation objective of 10% of coastal and marine areas by 2020. Such an objective clearly imposes a scientific basis for designing new Marine Protected Areas (MPAs) to sustain biodiversity and ecosystem services inside and outside the protected area (Palumbi, 2004). Most existing MPAs were not designed to fulfill these needs, but aimed instead at protecting habitats presumed to host high biodiversity and were created without any ecological foundation. Furthermore, the use of species surrogates measures to position an MPA is not supported by existing ecological theories that may be used to forecast the efficiency of protection measures for conservation of local and regional biodiversity [START_REF] Saetersdal | Prioritising conservation areas using species surrogate measures: consistent with ecological theory?[END_REF].

Amongst existing ecological theories, neutral theory (which ignores the role of biological constraints in biodiversity distribution) is a tempting scientific framework for MPA designers because its simplicity supports its operationality. According to neutral theory, local species richness S * has a power-law relationship with surface area A following S * ∝ A z with z > 0 at intermediate spatial scales [START_REF] Rosindell | The unified neutral theory of biodiversity and biogeography at age Ten[END_REF]. Taking z = 0.25, any MPA covering 10% of any region should thus protect 56% of its regional diversity.

Yet, a posteriori assessment of protection efficiency for some taxonomic groups showed that even if overall positive effects on both biomass and species diversity for fish in no-take reserves exist, protection efficiency is less clear for invertebrates and algae [START_REF] Lester | Biological effects within no-take marine reserves: a global synthesis[END_REF]. Differential effects of protection efficiency have been attributed to trophic cascade effects in relation to fish grazing pressure increase [START_REF] Halpern | The impact of marine reserves: do reserve work and does reserve size matter ?[END_REF][START_REF] Lester | Biological effects within no-take marine reserves: a global synthesis[END_REF], pinpointing the importance of species interactions in shaping local diversity. Conflicting results were also reported about the expected relation between biological response and no-take reserves size arising from the neutral theory [START_REF] Claudet | Marine reserves: size and age do matter[END_REF][START_REF] Lester | Biological effects within no-take marine reserves: a global synthesis[END_REF]. Reasons invoked to explain these discrepancies were either differences in statistical methods or shifts in Planktonic Larval Duration (PLD) range due to temperature differences between temperate and tropical regions that would affect dispersal distance.

Most marine sedentary species and particularly 70 % of invertebrates, [START_REF] Thorson | Reproduction and larval development of Danish marine bottom invertebrates, with special reference to the planktonic larvae in the Sound (Oresund). Medr.Komm[END_REF] exhibit a planktonic larval phase which can last from a few hours (ascidians, Olson, 1985) to several months or years [START_REF] Strathmann | An extraordinarily long larval duration of 4.5 years from hatching to metamorphosis for teleplanic veligers of Fusitrion oregonensis[END_REF]. Offspring released into the water column are transported and dispersed more or less passively by the flow due to limited motility ability compared to horizontal flow speed [START_REF] Chia | Locomotion of marine invertebrates larvae: a review[END_REF][START_REF] Scheltema | On dispersal and planktonic larvae of benthic invertebrates: an eclectic overview and summary of problems[END_REF]. Dispersal distance thus increases with the PLD because of both advection and diffusion processes when the current field is spatially uniform and permanent [START_REF] Siegel | Lagrangian descriptions of marine larval dispersion[END_REF]. This basic finding has been implicitly extended to the global scale (Kinlan & Gaines, 2003) with declarations like the larger the reserve, the broader range of PLDs, i.e. species, will be protected [START_REF] Gerber | Population models for marine reserve design: a retrospective and prospective synthesis[END_REF]. However, postulating hydrodynamic steadiness and spatial uniformity at a global scale is obviously incorrect. Dispersal distances differing by one order of magnitude for the same PLD were already related to hydrodynamic transport variability for the same species in different areas [START_REF] Shanks | Propagule dispersal distance and the size and spacing of marine reserves[END_REF]. Hydrodynamic variability, in both time and space, will easily blur any relationship between PLD and dispersal distance [START_REF] Siegel | The stochastic nature of larval connectivity among nearshore marine populations[END_REF], and may explain the absence of correlation between PLD and genetic connectivity as well (Weersing and Toonen, 2009). Hence, there is no reason for the biological response to protection and protected area size to be correlated at a global scale.

Ocean modelling works well for hindcasting realistic coastal circulation (Dufaud-Julliand et al., 2004;[START_REF] Estournel | Observation and modelisation of the winter coastal oceanic circulation in the Gulf of Lion under wind conditions influenced by the continental orography (FETCH experiment)[END_REF][START_REF] Leredde | Hydrodynamics in the Gulf of Aigues-mortes, NW Mediterranean Sea: In situ and modelling data[END_REF] and provides a comprehensive description of current variability useful for improving dispersal distribution and population connectivity estimates [START_REF] Treml | Modeling population connectivity by ocean currents, a graph-theoretic approach for marine conservation[END_REF]. Without overlooking the ultimate role of species' interaction to shape local diversity, ensuring marine sedentary species' self-persistence within a no-take MPA would require that the design accounts for a dispersion period during reproduction.

In this study, we propose a methodology using larval dispersal simulations and population dynamics traits to design (in terms of location and size) sustainable no-take reserves for sedentary species with a planktonic larval stage. Offspring spillover from the no-take reserve to adjacent fished areas is also quantified and the best compromise between no take reserve size and maximum benefit for resources management solved for [START_REF] Pauly | Towards sustainability in world fisheries[END_REF][START_REF] Halpern | Matching marine reserve design to reserve objectives[END_REF]. The methodology was applied to the Gulf of Lions: a broad continental shelf in the NW Mediterranean Sea with high primary production (Chl a > 1 µ g L -1 ) compared to the generally oligotrophic Mediterranean sea [START_REF] Durrieu De Madron | Marine ecosystems responses to climatic and anthropogenic forcings in the Mediterranean by The MERMEX Group[END_REF] and intense fishery activities (40,000 tons per year, [START_REF] Demaneche | Méditerranée continentale, échantillonnage des marées au débarquement: Méthode d'élévation et évaluation des captures et de l'effort de pêche des flottilles de la façade Méditerranée continentale sur la période 2007-2008[END_REF] (16,000 km 2 , Fig. 1). Two MPAs with no-take zones were implemented 37 and 15 years ago in this region: the first is located at its southeastern and the second, at its western extremity (Mabile & Piante, 2005). These MPAs cover only 0.66% of the Gulf of Lion surface and include no-take areas with a maximum radius of 0.9 km. Recently, in October 2011, protection was dramatically increased by the creation of a Natural Marine Park 4,000 km 2 , representing about 25 % of the Gulf of Lions surface. Using our method, we selected locations optimizing both conservation potential and spillover benefit for adjacent fisheries along the 300-long coastline segement which remains unprotected.

MATERIAL AND METHODS

Methodology for No-Take reserve design based on larval dispersal simulations We consider the design of a no-take marine reserve ensuring the local persistence of a sedentary species with a pelagic larval stage and maximizing offspring spillover to adjacent fished area. Even if generally, the larger the no-take reserve, the higher the retention rate, such criteria are not acceptable to stakeholders. Thus, being able to determine the minimal dimensions of a sustainable no-take reserve and then follow how these minimal dimensions evolve at a regional scale appears crucial. Sustainability is taken here to mean that the reserve population is self-persistent.

Criteria for self-persistence of a population were derived from a simplified generic population dynamics model for a species with two sedentary stages (adult and juvenile) and a dispersive pelagic larval stage (Fig. 2). The time required by offspring to reach their first reproduction is ∆T and P LD is the pelagic larval stage duration. The sedentary population includes N 0 adults which reproduce at time t 0 . Sedentary reproducers abundance exponentially decays through time as a result of many loss processes (predation, starvation, ...) represented by a global mortality rate m. Reproducers' mortality rates can be related to life expectancy T 0.99 assuming cohort abundance had decreased by 99 % after T 0.99 , i.e. m = -ln(0.01)/T 0.99 . Losses of reproducers over the ∆T days are ∆N -= N 0 (1 -γ) where γ = exp(-m∆T ).

After each reproduction, the number of larvae N 1 released in the water reads:

N 1 = F S R f N 0 (1)
where F is female fertility (number of eggs per female), S R is the proportion of female within the sedentary population and f is the fertilization success rate. During the pelagic larval stage lasting P LD days, larvae are dispersed by currents and turbulence and some die as a result of biotic processes (predation, starvation, unsuccessful development, ...). The number of competent larvae remaining in the surroundings of the sedentary population after P LD days reads:

N 2 = R(x, P LD)MN 1 (2)
where R(x, P LD) is the retention rate of larvae after P LD days as a function of the distance x around the sedentary population and M = exp(-µP LD) where µ is the natural mortality rate during pelagic larval stage due to biotic processes, excluding dispersal.

At the end of larval stage, competent larvae settle as a benthic juvenile stage. Even if no recruitment failure due to substrate unsuitability occur in an area where adults already exist, young juveniles generally have higher mortality rates than adults due to enhanced competition and predation on smaller organisms. The number of benthic juveniles thus drastically decreases to N 3 during the growth period δt after settlement:

N 3 = N 2 exp(-m δt) (3)
where m is the enhanced mortality rate of post settlement juvenile stages.

Finally, the reproductive gain ∆N + reaching their first reproduction after ∆T days reads:

∆N + = exp(-m(∆T -P LD -δt))N 3 (4)
The population will be stable if the losses of sexually matured individuals between two reproductions ∆N -are compensated by the reproductive gains reaching their first reproduction ∆N + . Self-persistence condition describes the offspring retention rate R(x, P LD) within a distance x and after a pelagic larval duration P LD is larger than

R 0 (P LD): R 0 (P LD) = (1 -γ) γF S R f exp[-(µ -m)P LD] exp[-(m -m)δt] (5)
Offspring retention rate can be quantified using Lagrangian larval dispersal simulations.

Lagrangian larva track consists of the successive positions of one larva released at a

given time, at a given location accounting for current advection, turbulent dispersion and when relevant, specific swimming behaviour [START_REF] Guizien | Dispersal of Owenia fusiformis larvae by wind-driven currents: turbulence, swimming behaviour and mortality in a three-dimensional stochastic model[END_REF]. In the case no specific locomotion behaviour is accounted for (passive dispersal), the same track can be analysed for different PLDs. Lagrangian dispersal, as opposed to Eulerian dispersal, enables us to analyse independantly tracks originating from different locations at different times (even though they were computed in the same model run) and to account for age-varying motility of the larvae. However, in order to investigate tracks' sensitivity to the hydrodynamics variability, the Lagrangian approach requires computing a large number of tracks varying with the spawning location and timing, each of these being replicated thirty times to account for turbulent dispersion.

Larvae tracks were analyzed first for the offspring dispersal distance after PLD days.

For each spawning location assigned as the center of a no-take reserve and for the PLD of the species for which persistence is desireable, two cumulative frequency distributions of offspring dispersal distance (cumulative dispersal kernel) were built for the two half-planes defined by the right and the left sides of the spawning location in the along shore direction. Drift associated to directional dispersion was removed by ensuring that each larvae dispersed to the left was compensated by one larvae dispersed to the right.

For any given PLD, retention rate R P LD (x) was calculated as twice the minimum value of between larvae proportion dispersed within distance x from the spawning site, in one or the other half-plane. And finally, the radius b(P LD) of the smallest no-take reserve ensuring the persistence of a species with pelagic larval duration P LD was the distance at which retention rate R P LD (b) yielded the threshold value R 0 (P LD) defined by equation ( 5) for the species demographic parameters (Fig. 3a).

Larvae tracks were also analyzed for offspring age within a fixed distance around a spawning location in order to scan persistent species within an existing no-take reserve.

Two age frequency distributions were built up by counting the proportion of larvae of a given age remaining within the left or the right half part of a no-take reserve of radius b.

Again, care was taken to remove any drift and retention rate R b (t) as a function of larvae age t since spawning was twice the minimum value between larvae proportion of a given age t dispersed within the distance b in one or the other half plane. Persistent PLDs within a no-take reserve of radius b were identified when retention rate for the species PLD R b (P LD) was larger than the species persistence threshold R 0 (P LD) (Fig. 3b).

Finally, larvae tracks were also used to estimate the offspring spillover to adjacent fished area for any PLD, R s (P LD), that is, the proportion of larvae dispersed to fished areas.

Application to diversity conservation in the Gulf of Lions

The methodology described above was applied in the Gulf of Lions to design a no-take reserve fulfilling a double objective of global biodiversity conservation and fisheries support. The Gulf of Lions is a micro-tidal, wide continental shelf (< 200 m depth, Fig. 1), mainly covered by soft, sandy sediment down to 30 m depth. Hard-bottom substrates mostly occur at the very eastern (Marseille) and western (Banyuls) tips of the gulf. Two other small hard bottom locations exist in the central part of the Gulf of Lions (Leucate, Agde). Fisheries in the Gulf of Lions are divided between artisanal methods targeting demersal fishes and benthic invertebrates in the nearshore (up to three nautical miles from the coast) and intense benthic trawling targeting small pelagic and demersal fishes further offshore [START_REF] Demaneche | Méditerranée continentale, échantillonnage des marées au débarquement: Méthode d'élévation et évaluation des captures et de l'effort de pêche des flottilles de la façade Méditerranée continentale sur la période 2007-2008[END_REF].

We postulate that maximizing the number of self-persistent polychaete populations in a no-take reserve located anywhere along the coast and their corresponding offspring retention at the regional scale should contribute to global biodiversity conservation and fisheries support in the Gulf of Lions. Indeed, polychaetes dominate soft-bottom benthic invertebrates biomass and diversity in the Gulf of Lions [START_REF] Grémare | Long-term comparison of macrobenthos within the soft bottoms of the Bay of Banyuls-sur-mer (northwestern Mediterranean Sea)[END_REF], demersal fishes feed on them and the polychaetes suffer collateral damage during trawling activites. Moreover, other benthic invertebrate families and fish species will display life traits similar to polycheates and thus, our results should also be relevant for these species.

Realistic three-dimensional simulations of the Gulf of Lions circulation were carried out over two nested domains with increasing spatial resolution from 1500 m to 750 m (Fig. 1) and using meteorological forcings of the Météo-France weather forecast model [START_REF] Marsaleix | Marine reserves and ocean neighborhoods: the spatial scale of marine populations and their management[END_REF]. Simulations covered the reproductive period of most polychaetes and fish species in this area (January to June, Bhaud, 1972;[START_REF] Charles | Reproduction, recruitment and larval metamorphosis in the serpulid polychaete Ditrupa arietina (O.F. Müller)[END_REF]Macpherson & Raventos, 2006). The circulation in the Gulf of Lions results from the interaction between the large-scale northern current (1 to 2 10 6 m 3 s -1 ) flowing from east to west along a steep jagged shelf-break [START_REF] Petrenko | Circulation in a stratified and wind-forced Gulf of Lions, NW Mediterranean Sea: in situ and modeling data[END_REF] and local hydrology [START_REF] Reffray | Secondary flows induced by wind forcing in the Rhône region of freshwater influence[END_REF] and meteorology [START_REF] Petrenko | Barotropic eastward currents in the western Gulf of Lion, north-western Mediterranean Sea, during stratified conditions[END_REF]. Strong winds blow with speeds higher than 10 m s -1 and on average 30% of time from the North in the eastern part, and 60% of time from the North-West in the western part without a marked seasonal difference from January to June but showing strong daily to weekly variability (Millot, 1990;[START_REF] Guénard | An observational study of the mesoscale Mistral dynamics[END_REF]. The Rhône River flows at the eastern tip of the Gulf of Lions (average discharge is 1,700 m 3 s -1 , [START_REF] Ludwig | Riverine Transport of Water, Sediments and Pollutants to the Mediterranean Sea[END_REF] while the many Mediterranean rivers bordering the Gulf of Lions reach significant discharges of hundreds of m 3 s -1 only during flooding events [START_REF] Guizien | Nearshore dynamics of nutrients and chlorophyll during Mediterranean-type flash-floods[END_REF].

We considered two years with contrasted hydrological forcings. First, in 2004, the Rhône River discharge was high in January but remained lower than 1,000 m 3 s -1 from March to June while recurrent flooding of small rivers occurred. In 2006, flooding of small rivers was minimal and the Rhône River discharged more than 2,000 m 3 s -1 during most of January through June.

Simulations of Lagrangian larval dispersal in the Gulf of Lions used the three-dimensional currents and turbulent kinetic energy computed at a resolution of 750 m × 750 m after interpolation between hourly outputs [START_REF] Guizien | Dispersal of Owenia fusiformis larvae by wind-driven currents: turbulence, swimming behaviour and mortality in a three-dimensional stochastic model[END_REF]. As a Lagrangian dispersal track stops when the larva reach the domain boundary, computational domain design was of paramount importance to avoid any biases due to larvae returning into the domain. The offshore boundary was thus located in the large-scale northern current, ensuring an insignificant number of larvae could return [START_REF] Cianelli | Particle exchange and residence times in the North Western Mediterranean[END_REF]. Dispersal's role in conservation of polychaete populations was studied for two test cases: a generic passive species (neutrally buoyant, no locomotion behaviour) with PLD of one to six weeks (most frequently reported PLDs of temperate coastal species, [START_REF] Levin | Pattern and diversity in reproduction and development[END_REF]; and the annelid polychaete Owenia fusiformis (three week PLD, with settling behaviour, [START_REF] Guizien | Dispersal of Owenia fusiformis larvae by wind-driven currents: turbulence, swimming behaviour and mortality in a three-dimensional stochastic model[END_REF] which is the dominant species within the gulf's muddy sands [START_REF] Labrune | Assessment of soft-bottom polychaete assemblages in the Gulf of Lions (NW Mediterranean) based on a mesoscale survey[END_REF].

Thirty-three spawning locations, representing potential no-take reserve locations, were tested along the 20 m isobath (Fig. 1). Continuous spawning was simulated by releasing thirty eggs every hour from January 5 at 0h until April 13 at 23h and larvae positions were stored every thirty minutes (72000 tracks per spawning location). The dispersal of generic passive larvae was simulated over six week periods in 2004 and 2006, and for

Owenia fusiformis during three weeks in 2004.

Demographic parameters values for the seven test cases and corresponding retention rate threshold value within a no-take area are summarised in Table 1. Natural mortality rates during larval dispersal due to biological processes were the most difficult parameter to estimate. Values for mortality rates derived from monitoring larval cohorts in the plankton (thus including losses and gain through larval dispersa) have been reported as ranging from 0.016 up to 0.8 day -1 [START_REF] Rumrill | Natural mortality of marine invertebrate larvae[END_REF]. In our study, low larvae mortality rates were accounted for (m = 0.06 to 0.1 day -1 , Table 1), by assuming that larval losses measured in the field were mainly due to dispersal. This latter hypothesis leads to the minimal size for the sustainable Marine Protected Area as a higher larval mortality would increase the minimum retention rate required for local population sustainibility.

Statistical methods

For each of the thirty-three spawning locations (labeled i) and for four spawning durations (labeled j), descriptors of dispersal (regional retention rate R i,j,k s (P LD), retention rate after P LD days as a function of distance x R i,j,k P LD (x) and retention rate within a distance b as a function of larvae age R i,j,k b (t)) were computed for N j = 98, 91, 31 and 11 spawning periods (labeled k) of duration three, ten, thirty and ninety days, respectively. Thus, for each spawning duration j, each dispersal descriptor was an ensemble of thirty-three by N j values.

The potential for biodiversity conservation of a no-take reserve with radius b ranging from 1 to 20 kms was screened by seeking PLD for which retention rate within the no-take reserve R i,j,k b (P LD) was larger than the persistence retention rate R 0 (P LD).

Overall potential biodiversity conservation of the no-take reserve was indicated by the shortest non-persistent pelagic larval duration, P LD i,j,k SN P (b) defined as:

P LD i,j,k SN P (b) = min[t such as R i,j,k b (t) < R 0 (t)] (6)
The persistence probability P P (P LD, b) i,j of a species with a PLD and spawning duration j within the same no-take reserve centered on spawning site i and with radius b was computed as the proportion of spawning periods for which retention rate after PLD days exceeded the persistence condition:

P P (P LD, b) i,j = P rob[R i,j,k b (P LD) > R 0 (P LD), k ∈ (1, N j )] (7)
Persistent PLDs were defined as PLDs for which this probability was larger than 0.5.

For each spawning location i and and spawning period k of duration j, the minimum radius b(P LD) i,j,k of a sustainable no-take reserve for a generic species with a pelagic larval duration P LD or for Owenia fusiformis were computed. Regional retention rate R r (P LD) i,j,k defined as the number of larvae remaining over the Gulf of Lions continental shelf were also computed. The three quantities (shortest non-persistent PLD, minimum radius of sustainable no-take reserve, regional retention rate) were presented as boxplots for each spawning duration ensemble at the regional (whatever the reserve location) and local (for each reserve location) scales.

For each of the spawning durations (3, 10, 30 and 90 days) and each of the five reserve radii (1, 2, 5, 10 and 20 kms), the temporal variability of any quantity, X i,j,k , was computed by averaging over all reserve locations (labeled i) the coefficient of dispersion (variance-to-mean ratio) of the quantity between spawning periods (labeled k). Spatial variability was computed by averaging over all spawning periods, the coefficient of dispersion of the quantity between reserve locations.

RESULTS

Planktonic larval duration of persistent populations within no-take reserves

For all spawning durations and reserve locations studied, median values of shortest, non-persistent PLDs increased from 2 to 6.5 days when the radius of protection increased from 1 to 20 kms (Figure 4a). Concurrently, the variability of the shortest, non-sustainable PLD also increased with no-take reserve radius as the 25 % quantile increased less (from 1 to 2 days) than the 75 % quantile (from 2 to 20.5 days). This means that large no-take reserves can protect longer PLDs than shorter ones, but they can also have as low biodiversity conservation potential as a small reserve, depending on the location or on the spawning timing or duration. Median value of shortest non-persistent PLDs increased less for a short spawning duration (from 1 to 2 days, Fig. 4b), than for a long spawning duration (from 2 to 21.5 days, Fig. 4d) when no-take reserve radius increased, while the range of shortest non-persistent PLDs varied little with spawning duration. Thus, a no-take reserve's potential for conservation will be higher in the Gulf of Lions for species displaying long spawning duration compared to those having short spawning duration (Figure 4).

This property of conservation potential was not uniformly distributed along the Gulf of Lions coastline. Persistent PLDs within five no-take reserve sizes displayed large variability amongst the thirty-three reserve locations tested along the Gulf of Lions, and spatial variability increased with the spawning duration (Figure 5). In each location and for each spawning duration, the range of persistent PLDs increased with reserve size.

No-take reserves with radii of 2 km still have a very low potential for biodiversity conservation with persistent PLDs shorter than 3.5 days, whatever the location or the spawning duration. When reserve radius was increased to 5 km, persistent PLDs range increased only in a few locations for a spawning duration of three days (Figure 5a) while it increased everywhere for spawning duration larger than 10 days (Figure 5b). Spatial variability in conservation potential was further amplified when reserve radius increased from 5 to 10 kms and with spawning duration. Again using a three day spawning duration in the central part of the Gulf of Lions (position 16), the persistent PLDs range was already three times wider compared to locations in the western part of the Gulf of Lions (positions 3 to 8) and conservation potential increased not only for short but also for long PLDs (Fig. 5a). For spawning duration larger than 10 days, conservation potential increase was even more marked in the central part of Gulf of Lions (positions 12 to 20, Fig. 5b to d), up to six times larger than in the western part of the Gulf of Lions. Finally, it was necessary to increase the reserve radius to 20 kms to reach a persistence probability larger than 50 % for all PLDs from 0 to 6 weeks. Such wide conservation potential occurs in only a few locations (positions 14 and 24 to 26) when spawning duration lasted less than 10 days. For the same 10 day spawning duration and reserve radius of 20 kms, a no-take reserve in the western part of the Gulf of Lions would reach a similar probability of conservation potential only for species with PLDs less than 6 days. No-take reserve location became more important than spawning timing during the reproductive season in determining conservation potential only when spawning durations were longer than 30 days. This is because temporal variability of conservation potential was comparable to or dominated over spatial variability whatever the no-take reserve radius for spawning durations up to 10 days (Table 2).

Minimum size of sustainable no-take reserve

Including all spawning durations and reserve locations, sustainable no-take reserve could only be defined in less than 10% of spawning periods (Figure 6). Radial median values of the smallest sustainable no-take reserve that could be defined increased from 5 to 20 kms when the targeted species' PLD increased from 1 to 4 weeks (Figure 6). The statistical distribution of smallest sustainable no-take reserve radius were comparable for species with five or six week PLDs and two week PLDs. Losses due to longer dispersal were compensated by lower persistence threshold due to the higher fertility attributed to species with large PLDs. The proportion of spawning periods for which a sustainable no-take reserve could be defined increase from 6 to 14 % when spawning duration increased from 3 to 90 days, whatever the species PLD. Smallest no-take reserve radii required to ensure species persistence were also more variable for shorter spawning durations than for a longer spawning duration (as shown for a species with a 3 week PLD in Fig. 7). Temporal variability due to spawning timing was larger than spatial variability due to spawning location for a spawning duration of 3 days (Fig. 7a), while it was reversed for the spawning duration of 30 days (Fig. 7c). Median values of the smallest sustainable no-take reserve radius displayed large variations along the Gulf of Lions. In the western part (positions 1 to 10) and the extreme eastern part (positions 31 to 33) of the Gulf of Lions, the self-persistence threshold for a neutrally buoyant larvae drifting passively during 3 weeks was not reached, whatever the no-take reserve size (Fig. 7).

In the eastern part of the Gulf of Lions (positions 21 to 30), sustainable no-take reserves could always be defined, while in the central part of the Gulf of Lions (positions 11 to 20), spawning duration triggered the probability to define a sustainable no-take reserve.

For example, a spawning duration of 3 days, this probability reached 50% in 5 locations and 25 % in others; durations longer than 30 days had a probability greater than 50 % in all locations. Including all spawning durations, median values of sustainable no-take reserve radius ranged from 9 to 40 km along the Gulf of Lions, while the same values only ranged from 5 to 20 km for PLDs ranging from one to four weeks for all spawning durations and locations (Fig. 6).

Conservation potential clearly varies with location in the Gulf of Lions. For a neutrally buoyant larvae drifting passively during 3 weeks, smallest values for sustainable no-take reserve radii were found between Narbonne and Agde (positions 12 to 16 for spawning duration larger than 10 days and only positions 13 and 14 for spawning duration of 3 days) and off the Camargue (positions 24 to 26) (Fig. 7). In these locations, median values of sustainable no-take reserve radii were about 10 km. For the same three week PLD, median values for the smallest no-take reserve radius required for Owenia fusiformis persistence were generally larger than the ones defined for passive drifting larvae in most locations along the Gulf of Lions. Larvae settling behaviour had the largest effect on sustainable no-take reserve radius in the central part of the Gulf of Lions, doubling its value in positions 11 to 13 and in positions 17 to 20. The settling larvae of O. fusiformis were only less far dispersed in the eastern part of the Gulf of Lions (positions 31 to 33) where the persistence threshold was reached in additional locations.

Spatial and temporal variability of regional retention rates

Including all spawning durations and reserve locations, median values of regional retention rate decreased from 100% to 38% when the targeted species PLD increased from 1 to 6 weeks. Yet, regional retention rates could vary from 0 to 100% whatever the species PLD, since spatial structure dominating over temporal variability or PLD biological constraints (Fig. 8). For neutrally buoyant larvae drifting passively during 3 weeks, median regional retention rate varied from less than 10% in the western part of the Gulf of Lions (positions 1 to 9, Fig. 8) to more than 90% in the eastern part of it (positions 20 to 28, Fig. 8), whatever the spawning duration. However, temporal variability due to spawning timing decreased when spawning duration increased. While temporal coefficient of dispersion was three times larger than spatial coefficient of dispersion for a spawning duration of 3 days (Fig. 8a), it had decreased to half the spatial coefficient of dispersion for a spawning duration of 90 days (Fig. 8d). Larvae settling behaviour increased retention rates by 10% on average, except at the western tip of the Gulf of Lions where regional retention rates were increased by 20 (35 %, respectively) in position 1 (2, respectively).

DISCUSSION

Dispersal simulations in the Gulf of Lions showed that on average at the regional scale, the longest persistent PLDs increased with no-take reserve size, and the smallest sustainable no-take reserve size increased with the PLD of the targeted species. This seemingly agrees with a dispersal distance increase with species PLD. However, both the shortest non-persistent PLD and smallest sustainable no-take reserve size had temporal and spatial variabilities of more than 300 %, ruling out any proportional relationship between dispersal distance and species PLD at the regional scale. This result weakens the argument about the presence or the absence of a relationship between reserve size and effects on biodiversity conservation at a global scale which are based on the existence of a proportional relationship between dispersal distance and species PLD [START_REF] Claudet | Marine reserves: size and age do matter[END_REF][START_REF] Lester | Biological effects within no-take marine reserves: a global synthesis[END_REF]. In fact, our results confirm that temporal and spatial variability of water circulation directly shapes dispersal kernels (Aiken et al., 2007), which in the general case are not gaussian as would arise from diffusion only [START_REF] Gerber | Population models for marine reserve design: a retrospective and prospective synthesis[END_REF]Moffitt et al., 2011). Dispersal distance strongly depends on the relative strength of advective and diffusive transport and on the permanence of its directionality which may also display spatial variability [START_REF] Gaines | Avoiding current oversights in marine reserve design[END_REF].

Temporal variability of circulation in the Gulf of Lions is mainly driven by the two regional winds (northerly Mistral and northewesterly Tramontane) which intensely blow, generally together, during repeated periods of one day to a week, whatever the season [START_REF] Guénard | An observational study of the mesoscale Mistral dynamics[END_REF]. This wind-induced temporal circulation dynamic explains how in our results, persistence conditions were triggered in dispersal kernels by spawning duration: transport drift dominated over diffusion in species dispersal for spawning durations less than 10 days and led to very low retention rates. For a spawning duration longer than 30 days it was reversed, except in the western part of the Gulf of Lions where directional transport prevailed. Thus, in most locations, the longer the spawning duration, the higher the probability to reach a persistent retention rate. These results also suggest that the probability to find a relationship between dispersal distance and PLD increases, when spawning duration is longer than the hydrodynamics' temporal stability scale.

Marine invertebrates are mostly free-spawning species (Barnes et al., 1988) which require reproduction synchronicity of neighbours to increase fertilization probability [START_REF] Levitan | The Ecology of fertilization in free-spawning invertebrates[END_REF]. Synchronized spawning seems to dominate among marine invertebrates species, presumably resulting from a fitness selective process (Barnes et al., 1988). In tropical regions, reduced spawning duration makes a relationship between dispersal distance and PLD not likely, considering the high stability of meteorological forcings in these regions.

Short mass spawning events of a few days have also been recorded for temperate gorgonians [START_REF] Coma | Reproduction and cycle of gonadal development in the Mediterranean gorgonian Paramuricea clavata[END_REF] and for the two dominant polychaetes species of the Gulf of Lions, Owenia fusiformis [START_REF] Koh | Le cycle de vie d'Owenia fusiformis(Annélide Polychète) en Méditerrannée: les processus locaux de recrutement et la distribution gégographique de l'espéce à l'échelle mondiale[END_REF] and Ditrupa arietina [START_REF] Charles | Reproduction, recruitment and larval metamorphosis in the serpulid polychaete Ditrupa arietina (O.F. Müller)[END_REF]. Yet, spawning duration tends to be longer due to synchronizing difficulty in a highly variable environment and may display large inter-annual variability (from a few days to a month for Owenia fusiformis, [START_REF] Koh | Le cycle de vie d'Owenia fusiformis(Annélide Polychète) en Méditerrannée: les processus locaux de recrutement et la distribution gégographique de l'espéce à l'échelle mondiale[END_REF]. Thus, the design of no-take reserves in the Gulf of Lions for protecting benthic invertebrates and particularly polychaetes, should account for short and long spawning durations with variable timing within the spawning season.

More generally, we know that spawning timing varies between species and within the same species, presumably due to complex interactions between ultimate (endogeneous cycle, food availability, temperature,...) and proximate (day/night, pressure, temperature,...) factors which are far from being elucidated (Morgan, 1995). As a result, spawning timing in temperate regions could be at best related to the season. In the present study, dispersal was only computed for spawning in late winter/spring, which is the main reproductive period in the Gulf of Lions, including temperate polychaetes species (Bhaud, 1972) and most labridae and sparidae fish species (Macpherson & Raventos, 2006). Moreover, as dispersal distance is expected to be larger in spring than in the summer (second most important reproductive period) when weaker wind speed favours higher retention (Millot, 1990), the present study analyzed the more constraining dispersal situation for no-take reserve design.

Despite the strong temporal variability for the short 3 days spawning duration, potential conservation requirement displayed a spatial structure with more favourable locations along the Gulf of Lions where sustainable no-take reserves could be defined with a median radius lower than 20 km and its temporal variability could be minimized. This contradicts one of the basic assumptions underlying the neutral theory which states that regional dispersal probability is spatially uniform. In the gulf, these sites are located between Narbonne and Agde and off the Camargue, in two of the six frequent upwelling areas (Millot, 1990). The existence of anticyclonic eddies between these upwelling areas was early suggested by Millot (1990) after he identified one large anticyclonic gyre in the southwestern part of the Gulf of Lions associated to the Tramontane upwelling between Narbonne and Agde. Such wind-driven spatial structures are well represented in circulation numerical simulations [START_REF] Estournel | Observation and modelisation of the winter coastal oceanic circulation in the Gulf of Lion under wind conditions influenced by the continental orography (FETCH experiment)[END_REF] and may potentially increase larvae retention. However, neither the locations nor the sizes of the best no-take reserves locations identified in the present study agreed with the location and size of mesoscale structures identified in a recent analysis of anticyclonic eddies of realistic numerical simulations of the Gulf of Lions hydrodynamics [START_REF] Hu | Numerical simulations of eddies in the Gulf of Lion[END_REF]. It is more probable that submesoscale eddies (smaller than 20 km) created by coastline promontories (Agde and Beauduc Cape) would explain the more favourable locations for biodiversity conservation identified between Narbonne and Agde and off the Camargue. Yet, the large mesoscale structures identified in the Gulf of Lions shelf may explain the strong regional retention rate of larvae released along the eastern and central parts of the Gulf of Lions shoreline [START_REF] Cianelli | Particle exchange and residence times in the North Western Mediterranean[END_REF].

Conversely, strong export through the canyons in the western part of the Gulf of Lions has been attributed to frequent cascading of negatively buoyant water formed after wind cooling (Dufaud-Julliand et al., 2004;[START_REF] Ulses | Suspended sediment transport in the Gulf of Lions (NW Mediterranean): Impact of extreme storms and oods[END_REF]. Climatic forecasts indicate a drastic reduction of dense water cascading in the region for the next century [START_REF] Herrmann | Dense water formation in the Gulf of Lions shelf: Impact of atmospheric interannual variability and climate change[END_REF]). The regional retention rate is thus likely to increase with probable positive consequence on regional fish populations' maintenance, even in the absence of any management measure.

Existing no-take reserves (Cerbére-Banyuls and Carry-le-Rouet, Fig. 1) are not located in the best locations identified and their radius (smaller than 1 km) is less than the smallest radius for a sustainable no-take reserve anywhere in the Gulf of Lions. Thus, these no-take reserves should not be very efficient for global biodiversity conservation.

For example, a protection effect of the Cerbére-Banyuls reserve has only been demonstrated for the emblematic dusky grouper Epinephelus marginatus [START_REF] Ludwig | Riverine Transport of Water, Sediments and Pollutants to the Mediterranean Sea[END_REF] and some commercial fish species (although not all, [START_REF] Dufour | Study of a Mediterranean reef fish assemblage. Comparisons of population distributions between depths in protected and unprotected areas over one decade[END_REF]. Habitat protection was clearly the primary motivation behind establishing these no-take reserves. The Cerbère-Banyuls reserve targeted rocky reefs, corraligenous habitats and the emblematic Posidonia oceanica beds, which are known to support higher fish diversity [START_REF] Guidetti | Differences among fish assemblages associated with nearshore Posidonia oceanica seagrass beds, rocky-algal reefs and unvegetated sand habitats in the Adriatic Sea[END_REF], while the more recent Carry-le-Rouet reserve also included sandy beds. Bearing in mind the interest for the specific habitats that motivated existing reserves establishment, it should be necessary to increase the reserve radius up to 20 kms to conserve efficiently species with larvae passively dispersed during three weeks in Carry-le-Rouet. In contrast, in Cerbère-Banyuls, no sustainable reserve could be defined for the same species. Moreover, even if a sustainable wider reserve could be settled there, impact on regional fisheries sustainability would be low due to current low regional retention rates. The recent creation of a Natural Marine Park extending the protection area around the Cerbère-Banyuls reserve in the western part of the Gulf of Lions highlights once again, the underappreciation for the dispersal process when planning marine protected areas.

Our results stress that marine protection spatial planning requires dedicated studies accounting for not only species biological traits but also local hydrodynamics.

Guidelines for MPA size and spacing established in one area should not be transposed to other places. For example, in California (USA), a pioneering American state in terms of MPA implementation, the design of MPA network was recommended. Current guidelines describe recommendations for size (5 to 20 kms along shore) and spacing (50 to 100 km apart, CDFG, 2009). These recommendations are based on dispersal distance estimates ranging from 50 to 100 kms and yielding unacceptable size for isolated sustainable no-take reserve. Yet, spatially explicit population dynamics have shown that these recommendations would not guarantee persistence of targeted species along the California coast when exploitation pressure was high outside the MPAs and that a large MPA of the size of the dispersal distance would be preferable (Moffitt et al., 2011).

Returning to the Gulf of Lions, the reasonable radius (10 to 20 kms, compared to dispersal distance of hundreds of kms estimated from [START_REF] Shanks | Propagule dispersal distance and the size and spacing of marine reserves[END_REF] ) of sustainable no-take reserve for species with the most frequent PLD (3 weeks) is encouraging for the implantation of reserves. Moreover, extension of protection measures targeting the central or the eastern part of the Gulf of Lions would combine benefits for both biodiversity conservation and fisheries sustainability. However, it is clear that convincing fishermen that protection measures in this part of the Gulf of Lions will benefit them will not be easy as these areas are currently supporting 45% of the regional fishing effort [START_REF] Demaneche | Méditerranée continentale, échantillonnage des marées au débarquement: Méthode d'élévation et évaluation des captures et de l'effort de pêche des flottilles de la façade Méditerranée continentale sur la période 2007-2008[END_REF]. From the dispersal point of view, implementing conservation measures off the Camargue would have the largest effect on fisheries while conservation measures between Narbonne and Agde would probably contribute more to regional biodiversity conservation as these areas include diverse habitats, including rock reefs, Posidonia oceanica beds and sandy beds. Next step will be to discuss MPA design as a framework for optimizing the potential for biodiversity conservation in an ecosystem-based approach.

The importance of using a methodology like that proposed in this paper is that it enables pre-screening of locations at a regional scale. Our estimates showed discrepant values for both passive drifting and settling larvae in upwelling areas, highlighting the interaction between three dimensional physical structure and biological traits. Our approach offers a scientific basis for decision-making using the dispersal process, and a reasonable no-take reserve size (about 300 km 2 , 2 % of the Gulf of Lions surface) could become a reality under the new marine park and existing Natura 2000 initiatives.

However, even if the approach presented in this paper allowed us to detect best locations for protection implementation at the regional scale, it should be complemented by local dispersal studies accounting for more detailed hydrodynamic features and species motility behaviour [START_REF] Guizien | Dispersal of Owenia fusiformis larvae by wind-driven currents: turbulence, swimming behaviour and mortality in a three-dimensional stochastic model[END_REF] between January and June (in 2004 and 2006) versus no-take reserve radius for four spawning durations of (a) 3 days, (b) 10 days, (c) 30 days and (d) 90 days, whatever the reserve locations along the Gulf of Lions (see Figure 1). 43

Persistent PLDs (see definition in the text, displayed with grey shading)

between January and June 2004 within no-take reserves of increasing radius , 2002). Female fertility in the oligotrophic Mediterranean sea was taken in the lower part of female fertility range [START_REF] Charles | Reproduction, recruitment and larval metamorphosis in the serpulid polychaete Ditrupa arietina (O.F. Müller)[END_REF][START_REF] Koh | Le cycle de vie d'Owenia fusiformis(Annélide Polychète) en Méditerrannée: les processus locaux de recrutement et la distribution gégographique de l'espéce à l'échelle mondiale[END_REF] and was assumed to increase with species PLD (McHugh & Fong, 2002). Sex ratio S R in the adult population and fertilization success rate f were taken equal to 0.5 and 0.1 respectively, for all species [START_REF] Eckman | Closing the larval loop: linking larval ecology to the population dynamics of marine benthic invertebrates[END_REF]. The mortality rate of young, small juveniles was one order of magnitude greater than the adult mortality rate and applied during one-tenth of the time between two reproduction events (m = 0.042 day -1 during δt = 36 days).

No-take reserve radius 1 kms 2 kms 5 kms 10 kms 20 kms Spawning duration 3 days 1.5 2: Ratio of the averaged coefficient of dispersion between different spawning events to the averaged coefficient of dispersion between spawning location of the shorstest sustainable PLD for no-take reserve radii increasing from 1 to 20 kms and spawning durations increasing from 3 to 90 days. Fig. 6: Boxplots of minimum radius of sustainable no-take reserve when it could be defined versus Planktonic larval duration (PLD) whatever the spawning duration between January and June (2004 and2006) and the reserve locations along the Gulf of Lions (see Figure 1). The proportion of spawning periods for which a sustainable no-take reserve could be defined is reported above each boxplot. Fig. 8: Boxplots of regional retention rate versus no-take reserve locations computed for four spawning durations of (a) 3 days, (b) 10 days, (c) 30 days and (d) 90 days between January and June 2004 for a neutrally buoyant passive larvae and Owenia fusiformis larvae(both 3 weeks PLD). No-take reserves were centered on the 33 spawning locations shown on Figure 1 and numbered from the west (Banyuls) to the East (Marseille).

b678

  from 2 kms to 20 kms (see greyscale on plot) along the Gulf of Lions and for four spawning durations of (a) 3 days, (b) 10 days, (c) 30 days and (d) 90 days. No-take reserves were centered on the 33 spawning locations shown on Figure1and numbered from the west (Banyuls) to the East (Marseille). 44 Boxplots of minimum radius of sustainable no-take reserve when it could be defined versus Planktonic larval duration (PLD) whatever the spawning duration between January andJune (2004 and 2006) and the reserve locations along the Gulf of Lions (see Figure1). The proportion of spawning periods for which a sustainable no-take reserve could be defined is reported above each boxplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Boxplots of minimum radius of sustainable no-take reserve versus no-take reserve location computed for four spawning durations of (a) 3 days, (b) 10 days, (c) 30 days and (d) 90 days between January and June 2004 for a neutrally buoyant passive larvae and Owenia fusiformis larvae(both 3 weeks PLD). No-take reserves were centered on the 33 spawning locations shown on Figure1and numbered from the west (Banyuls) to the East (Marseille). 46 Boxplots of regional retention rate versus no-take reserve locations computed for four spawning durations of (a) 3 days, (b) 10 days, (c) 30 days and (d) 90 days between January and June 2004 for a neutrally buoyant passive larvae and Owenia fusiformis larvae(both 3 weeks PLD). No-take reserves were centered on the 33 spawning locations shown on Figure1and numbered from the west (Banyuls) to the East (Marseille

Fig. 4 :

 4 Fig. 1: Gulf of Lions (NW Mediterranean Sea) bathymetric map with depth contour in meters (depth contour spacing is 200 m below 200m deep). Locations for potential notake reserves are shown as filled circles. Arrows indicate the location of existing no-take reserve, CR stands for Carry-le-Rouet and BC stands for Cerbère-Banyuls. Boxes show the extension of the two nested computational domains (1500 m and 750 m resolution grids).

Fig. 5 :

 5 Fig.5: Persistent PLDs (see definition in the text, displayed with grey shading) between January and June 2004 within no-take reserves of increasing radius b from 2 kms to 20 kms (see greyscale on plot) along the Gulf of Lions and for four spawning durations of (a) 3 days, (b) 10 days, (c) 30 days and (d) 90 days. No-take reserves were centered on the 33 spawning locations shown on Figure1and numbered from the west (Banyuls) to the East (Marseille).

Fig. 7 :

 7 Fig.7: Boxplots of minimum radius of sustainable no-take reserve versus no-take reserve location computed for four spawning durations of (a) 3 days, (b) 10 days, (c) 30 days and (d) 90 days between January and June 2004 for a neutrally buoyant passive larvae and Owenia fusiformis larvae(both 3 weeks PLD). No-take reserves were centered on the 33 spawning locations shown on Figure1and numbered from the west (Banyuls) to the East (Marseille).

  and species interactions, which can potentially reshape diversity patterns within communities (Moriz et al., 2009), should not be overlooked. Simple population dynamics model for benthic species with a pelagic larval stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

	conditions for regional and coastal ocean models. Journal of Atmospherical and Ocean 1 Gulf of Lions (NW Mediterranean Sea) bathymetric map with depth contour
	Technology 23:1604-1613 in marine systems. Marine Ecology Progress series 393:1-12 in meters (depth contour spacing is 200 m below 200m deep). Locations for
	Mabile, S., Piante, C. 2005. Global Directory of Mediterranean Marine Protected Areas. potential no-take reserves are shown as filled circles. Arrows indicate the
	WWF-France. Foundation Paris, France xii +132 pp location of existing no-take reserve, CR stands for Carry-le-Rouet and BC
	stands for Cerbère-Banyuls. Boxes show the extension of the two nested
	Acknowledgments: This work was partly funded by the Fondation pour la Macpherson, E., Raventos, N. 2006. Relationship between pelagic larval duration and computational domains (1500 m and 750 m resolution grids). . . . . . . . 40
	Recherche sur la Biodiversité within program "Modélisation et scénario pour la geographic distribution of Mediterranean littoral fishes. Marine Ecology Progress 2
	biodiversité" under pre-project Q-MBC. We also thank METEO FRANCE for series 327:257-265
	supplying the atmospheric forcings and the Banque Hydro for supplying rivers discharge
	McHugh, D., Fong, P.P. 2002. Do life history traits account for diversity of polychaete
	data. Many thanks to Jennifer Coston-Guarini for English language corrections.
	annelids ?. Invertebrate Biology. 121:325-338
	Millot, C. 1990. The Gulf of Lion's hydrodynamics. Continental Shelf Research
	10(9-11):885-894
	LITERATURE CITED Moffitt, E.A., White J.W., Botsford, L.W. 2011. The utility and limitations of size and
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3

(a) Definition of the minimum size b(P LD) of sustainable no-take area for a species with pelagic larval duration equal to PLD days based on retention rate R P LD (x) after transport drift has been removed from dispersal kernels; (b) Exploration of the pelagic larval duration P LD of persistent populations within a no-take area with radius b defined as pelagic larvae age t for which retention rate R b (t) after transport drift has been removed from age frequency distribution is larger than population persistence retention rate R 0 (P LD). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4 Boxplots of shortest non-persistent Planktonic larval duration (P LD SN P )

Table 1 :

 1 Demographic parameters (female fertility F and larval mortality rate m ) and subsequent minimum retention rate for population persistence R 0 for Owenia fusiformis and generic species with passive larval dispersal durations increasing from one to six weeks. Most restrictive condition on adult mortality rate m = 0.0042 day -1 for population stability was applied based on shortest life expectancy (three years,McHugh & Fong

			Generic passive species		Owenia
	PLD (weeks)	1	2	3	4	5	6	fusiformis
	F	10 4 10 4 10 4 10 4 10 5 10 5	10 4
	m (% day -1 ) 10 10	6	6	6	6	6
	R 0 (%)	5.9 6.6 9.8 14.4 2.1 3.15	9.8

). . . . . . . . . . 47

List of Tables 1

Demographic parameters (female fertility F and larval mortality rate m ) and subsequent minimum retention rate for population persistence R 0 for Owenia fusiformis and generic species with passive larval dispersal durations increasing from one to six weeks. Most restrictive condition on adult mortality rate m = 0.0042 day -1 for population stability was applied based on shortest life expectancy (three years, McHugh & Fong, 2002). Female fertility in the oligotrophic Mediterranean sea was taken in the lower part of female fertility range [START_REF] Charles | Reproduction, recruitment and larval metamorphosis in the serpulid polychaete Ditrupa arietina (O.F. Müller)[END_REF][START_REF] Koh | Le cycle de vie d'Owenia fusiformis(Annélide Polychète) en Méditerrannée: les processus locaux de recrutement et la distribution gégographique de l'espéce à l'échelle mondiale[END_REF] and was assumed to increase with species PLD (McHugh & Fong, 2002). Sex ratio S R in the adult population and fertilization success rate f were taken equal to 0.5 and 0.1 respectively, for all species [START_REF] Eckman | Closing the larval loop: linking larval ecology to the population dynamics of marine benthic invertebrates[END_REF]. The mortality rate of young, small juveniles was one order of magnitude greater than the adult mortality rate and applied during one-tenth of the time between two reproduction events (m = 0.042 day -1 during δt = 36 days). . . . . . . . . 39 2 Ratio of the averaged coefficient of dispersion between different spawning events to the averaged coefficient of dispersion between spawning location of the shorstest sustainable PLD for no-take reserve radii increasing from 1 to 20 kms and spawning durations increasing from 3 to 90 days. . . . . . 39 ) of sustainable no-take area for a species with pelagic larval duration equal to PLD days based on retention rate R P LD (x) after transport drift has been removed from dispersal kernels; (b) Exploration of the pelagic larval duration P LD of persistent populations within a no-take area with radius b defined as pelagic larvae age t for which retention rate R b (t) after transport drift has been removed from age frequency distribution is larger than population persistence retention rate R 0 (P LD).

List of Figures