Tiago Cyrille Mathieu
email: cyrille.mathieu@inserm.fr

Nascimento Figueira

Amanda R Decker

Marion Ferren

Tiziana F Bovier

Eric M Jurgens

Tara C Marcink

Anne Moscona

Matteo Porotto

Tiago Nascimento Figueira

Measles fusion complexes from central nervous system clinical isolates: decreased interaction between hemagglutinin and fusion proteins

Keywords: Viral fusion, CNS adaptation, viral infectivity

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction:

Despite the availability of an effective measles virus (MeV) vaccine and efforts to increase vaccine coverage by the WHO, UNICEF, and their partners, MeV has not been eradicated and the estimated global measles death toll rose from 89,780 in 2016 to 207,500 in 2019 [START_REF] Durrheim | A dangerous measles future looms beyond the COVID-19 pandemic[END_REF]. The SARS-CoV-2 pandemic and associated countermeasures reduced the incidence of other respiratory viral infections but also halted vaccination, increasing the risk of measles outbreaks in the future [START_REF] Durrheim | A dangerous measles future looms beyond the COVID-19 pandemic[END_REF].

MeV is the most infectious virus known to humans, transmits via the air, and causes systemic infection. The virus enters cells via two cellular receptors: CD150/SLAM expressed by subsets of immune cells [START_REF] Tatsuo | SLAM (CDw150) is a cellular receptor for measles virus[END_REF] and nectin-4 expressed by epithelial cells [START_REF] Noyce | Tumor cell marker PVRL4 (nectin 4) is an epithelial cell receptor for measles virus[END_REF][START_REF] Muhlebach | Adherens junction protein nectin-4 is the epithelial receptor for measles virus[END_REF]. Central nervous system (CNS) sequelae associated with active viral infection include subacute sclerosing panencephalitis (SSPE) and measles inclusion body encephalitis (MIBE) [START_REF] Griffin | Measles virus, immune control, and persistence[END_REF][START_REF] Rota | Measles[END_REF][START_REF] Kija | Subacute sclerosing panencephalitis in South African children following the measles outbreak between 2009 and 2011[END_REF][START_REF] Angius | Analysis of a Subacute Sclerosing Panencephalitis Genotype B3 Virus from the 2009-2010 South African Measles Epidemic Shows That Hyperfusogenic F Proteins Contribute to Measles Virus Infection in the Brain[END_REF][START_REF] Hardie | Molecular characterisation of virus in the brains of patients with measles inclusion body encephalitis (MIBE)[END_REF][START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF]. These CNS complications have been associated with viral evolution and specific CNS adaptation, specifically with alterations in the viral fusion mechanism [START_REF] Watanabe | New Insights into Measles Virus Brain Infections[END_REF][START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF].

MeV expresses two envelope glycoproteins that make up the fusion complex. The H protein mediates receptor binding, followed by triggering of the F protein, which leads to merger of the viral envelope with target cell membranes. We refer to the H/F pairs of MeV as the viral fusion complex, since these proteins act in concert. F is synthesized as a precursor (F 0 ) that is cleaved within the cell to yield the pre-fusion F complex comprising three C-terminal F 1 subunits associated non-covalently with three N-terminal F 2 subunits. This trimeric F structure is kinetically trapped in a metastable conformation, primed for fusion activation upon engagement of the H glycoprotein by the cell-surface receptor (either CD150/SLAM or nectin-4) [START_REF] Tatsuo | SLAM (CDw150) is a cellular receptor for measles virus[END_REF][START_REF] Noyce | Tumor cell marker PVRL4 (nectin 4) is an epithelial cell receptor for measles virus[END_REF][START_REF] Muhlebach | Adherens junction protein nectin-4 is the epithelial receptor for measles virus[END_REF][START_REF] Yanagi | Measles virus receptor SLAM (CD150)[END_REF][START_REF] Yanagi | Measles virus receptors[END_REF][START_REF] Hashiguchi | Measles virus hemagglutinin: structural insights into cell entry and measles vaccine[END_REF]. After receptor engagement by H, the pre-fusion F undergoes a structural transition, extending and inserting its hydrophobic "fusion peptide" into the target cell. During entry, F refolds into a so-called "trimer of hairpins" (or 6-helix bundle) post-fusion structure that brings together the N-terminal heptad repeat (HRN) and the C-terminal heptad repeat (HRC), and the viral and cell membranes fuse [START_REF] Yin | Structure of the uncleaved ectodomain of the paramyxovirus (hPIV3) fusion protein[END_REF][START_REF] Lamb | Paramyxovirus membrane fusion: lessons from the F and HN atomic structures[END_REF][START_REF] Yin | Structure of the parainfluenza virus 5 F protein in its metastable, prefusion conformation[END_REF][START_REF] Harrison | Viral membrane fusion[END_REF][START_REF] Chang | Paramyxovirus fusion and entry: multiple paths to a common end[END_REF][START_REF] Plemper | Structural and mechanistic studies of measles virus illuminate paramyxovirus entry[END_REF][START_REF] White | Structures and mechanisms of viral membrane fusion proteins: multiple variations on a common theme[END_REF][START_REF] Sapir | Viral and developmental cell fusion mechanisms: conservation and divergence[END_REF]. Peptides derived from the HRC region of the F 2 ectodomain inhibit paramyxovirus entry with varying activity [START_REF] Harrison | Viral membrane fusion[END_REF][START_REF] Eckert | Design of potent inhibitors of HIV-1 entry from the gp41 N-peptide region[END_REF][START_REF] Porotto | Molecular determinants of antiviral potency of paramyxovirus entry inhibitors[END_REF][START_REF] Schmidt | Peptide inhibitors of flavivirus entry derived from the E protein stem[END_REF][START_REF] Vigant | Hendra and nipah infection: pathology, models and potential therapies[END_REF][START_REF] Pessi | A general strategy to endow natural fusion-protein-derived peptides with potent antiviral activity[END_REF][START_REF] Steffen | Henipavirus mediated membrane fusion, virus entry and targeted therapeutics[END_REF][START_REF] Miyamoto | Novel HIV-1 fusion inhibition peptides: designing the next generation of drugs[END_REF][START_REF] Tan | The Current Status and Challenges in the Development of Fusion Inhibitors as Therapeutics for HIV-1 Infection[END_REF][START_REF] Lee | Capturing a fusion intermediate of influenza hemagglutinin with a cholesterolconjugated peptide, a new antiviral strategy for influenza virus[END_REF]. We and others have shown that fusion complexes from CNS isolated clinical samples are dysregulated and do not require H-receptor interaction for mediating fusion [START_REF] Angius | Analysis of a Subacute Sclerosing Panencephalitis Genotype B3 Virus from the 2009-2010 South African Measles Epidemic Shows That Hyperfusogenic F Proteins Contribute to Measles Virus Infection in the Brain[END_REF][START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF][START_REF] Sato | Cell-to-Cell Measles Virus Spread between Human Neurons Is Dependent on Hemagglutinin and Hyperfusogenic Fusion Protein[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF], and for a specific mutated F (L454W) even the presence of the H was dispensable for cell-to-cell fusion in transfected cells [START_REF] Angius | Analysis of a Subacute Sclerosing Panencephalitis Genotype B3 Virus from the 2009-2010 South African Measles Epidemic Shows That Hyperfusogenic F Proteins Contribute to Measles Virus Infection in the Brain[END_REF][START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF]. Here we investigated whether this phenotype was correlated with dimished H-F interaction and we highlight that fusion in the absence of receptor interaction is the combined effect of a decrease in the stability of F as well as a decrease in F's interaction with H.

Results:

Measles virus F glycoprotein from neuropathogenic viruses

MeV F glycoproteins with specific single residue alterations (S262R, L454W, T461I, and N462K) have been associated with neuropathogenic measles strains that were either isolated from patients or generated in laboratory settings [START_REF] Hardie | Molecular characterisation of virus in the brains of patients with measles inclusion body encephalitis (MIBE)[END_REF][START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF][START_REF] Watanabe | Mutant fusion proteins with enhanced fusion activity promote measles virus spread in human neuronal cells and brains of suckling hamsters[END_REF]. We mapped these mutations onto x-ray structures of the pre-fusion (36) conformations of F (Fig. 1A), highlighting the locations of these mutations in MeV F. The S262R mutation occurs at the interface of three protomers in the head region of the pre-fusion structure. The mutation from Ser to Arg at residue 262 results in a clash within each monomer in the existing crystal structure . These microenvironmental changes are likely to affect the conformational stability of the F. The other three mutations (L454W, T461I, and N462K) were located within the Cterminal heptad repeat domain (HRC). In the pre-fusion structure, the L454W mutation would also perturbs the current pre-fusion structure. The T461I and N462K mutations occur in a well-ordered α-helical region of the HRC domain. These three mutations (L454W, T461I, and N462K) occur in the portion of the HRC domain where the head and stalk regions of the prefusion conformation meet. Interactions at this region may be important for stabilizing the prefusion state and mutations in this junction would affect stability of the MeV-F prefusion structure, as our previous data have shown [START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF].

Impact of hyperfusogenic mutations in F on H-F interaction

We previously suggested that the ability of HRC mutants to fuse in the absence of known receptors could be at least partly due to reduced interaction between H and F [START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF]. The interaction between F and H and the impact of mutations in the HRC domain (i.e., L454W, T461I and N462 may be affected by thermal instabilityobscuring the effect of the specific mutations --we included the highly unstable mutant F-S262R [START_REF] Watanabe | New Insights into Measles Virus Brain Infections[END_REF][START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF][START_REF] Sato | Cell-to-Cell Measles Virus Spread between Human Neurons Is Dependent on Hemagglutinin and Hyperfusogenic Fusion Protein[END_REF][START_REF] Watanabe | Mutant fusion proteins with enhanced fusion activity promote measles virus spread in human neuronal cells and brains of suckling hamsters[END_REF] which interacts efficiently with H. H-F interaction was assessed with both the cleavable F proteins (Fig. 2A) and the cleavage site mutant (CSM) version of these F proteins (Fig. 2B), to distinguish between effects on the F 0 and the F 1 form of F. Results are presented as the average of 3 separate experiments ± SD (Fig. 2C). Densitometric analysis was used to normalize the results to total protein content and to convert the data to graphs (average of 3 separate experiments ± standard deviation; Fig. 2C). There is significant reduction in the amount of F 1 coimmunoprecipitated with H for the HRC hyperfusogenic mutants (i.e. , L454W, T461I and N462K) compared to the wt F (P = 0.0023, P = 0.0030 and P = 0.0014, respectively; two-way ANOVA with multiple comparisons against wt F, corrected with the Dunnett hypothesis test).

For the other hyperfusogenic mutant, F S262R, there was more co-immunoprecipitated F 1 protein when compared to the HRC mutants. There were no differences in coimmunoprecipitation of F 0 . Thus, mutations in HRC associated with a hyperfusogenic phenotype decrease the ability of H to interact with the active F 1 form of F.

Viral evolution leads to compensatory mutation

MeV bearing the L454W F protein, when grown at 37 o C in cell culture, acquired a compensatory mutation (E455G) that re-balanced F's stability and dependence on H and cellular receptor for mediating fusion [START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF]. The E455G mutation is shown in Fig. 3A, alone and in combination with L454W. Tryptophan (W454) contains a bulky aromatic sidechain when compared to leucine (L454), while glutamic acid (E455) is larger than glycine (G455).

We determined whether the E455G mutation restored H-F interaction (Fig. 3). H-F interaction for wt ,L454W, E455G, and L454W/E455G F proteins is shown in Fig. 3 . Densitometric analysis was used to normalize the results to total protein content and to convert the data to graphs (average of 3 separate experiments ± SD; Fig. 3C). The wt versus the L454W F was significantly different (as seen in Fig. 2), however the mutant E455G F and the double mutant L454W/E455G F co-immunoprecipitated similarly to the wt F. The E455G compensatory mutation in the HRC domain of the F resulted in a wt phenotype. We previously showed that E455G restored F's stability (as measured by sensitivity to thermal activation) and restored F's dependence on H-receptor interaction for fusion [START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF]. Fig. 3 reveals that E455G also reestablished interaction of H with the active F 1 form of F.

Loss of H-F interaction delays viral entry.

One of the consequences of the loss of interaction between F and H is the loss of protection of F from spontaneous triggering [START_REF] Porotto | Spring-loaded model revisited: paramyxovirus fusion requires engagement of a receptor binding protein beyond initial triggering of the fusion protein[END_REF]. Additionally, hyperfusogenic MeV F HRC mutants proteins are less stable in their pre-fusion state, as measured by their temperature sensitivity, compared to the wt F protein. The hyperfusogenic F proteins mediate fusion even in the absence of either CD150/SLAM or nectin-4 receptors [START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF]. We have shown that this decreased F stability, however, results in viruses that are inactivated at lower temperatures than wt virus [START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF], because F transitions to its post-fusion state more readily, rendering the viral particle non-infectious. We asked whether the destabilizing mutations in F of the neuropathogenic variants affect viral entry into SLAM-expressing cells [START_REF] Figueira | In Vivo Efficacy of Measles Virus Fusion Protein-Derived Peptides Is Modulated by the Properties of Self-Assembly and Membrane Residence[END_REF]. To do so, we used an assay developed for a related paramyxovirus, human parainfluenza virus 3 (HPIV3).

For HPIV3 we have shown that the kinetics of F protein activation and viral entry modulate the potency of HR derived peptides [START_REF] Porotto | Spring-loaded model revisited: paramyxovirus fusion requires engagement of a receptor binding protein beyond initial triggering of the fusion protein[END_REF][START_REF] Porotto | Kinetic dependence of paramyxovirus entry inhibition[END_REF], and therefore this modulation can be used as a tool to quantitate F activation and entry. Applying this strategy to MeV, we determined the sensitivity of MeV F to inhibition by MeV HR derived peptides, using a previously described dimeric HR lipopeptide, HRC4. In Fig. 4A, 1M of HRC4 peptide was added at time points from 0 to 2 hours during infection of Vero-SLAM cells. Peptide addition at time zero inhibited 100% of infection for all the viruses (wt and the three viruses bearing the mutated F proteins). Peptides added after 1 hour decreased inhibition to 30% for wt virus, meaning that most of the wt virus had already entered, while the mutants bearing F T461I and N462K were 50% inhibited and the mutant bearing F L454W was 70% inhibited. After 90 min, the peptide continued to inhibit the mutants (from 20 to 30% of viral entry). No inhibitory effect was observed after 2 hours. This experiment reveals that for wt viruses, the window of HRC4 inhibitor sensitivity is significantly shorter than that of the viruses bearing the mutated Fs. The longer time of inhibitor susceptibility of the HRC mutant Fs suggests that wt H-F is more efficient for entry in the presence of receptors.

Easier triggering of HRC hyperfusogenic mutants correlates with longer time to completion of fusion.

For HPIV3, fusion requires engagement of the receptor binding protein (the hemagglutinin neuraminidase, HN) beyond initial triggering of the F protein. This engagement of HN is essential for F's function until membrane merger [START_REF] Porotto | Spring-loaded model revisited: paramyxovirus fusion requires engagement of a receptor binding protein beyond initial triggering of the fusion protein[END_REF]. A similar mechanism of ongoing activation of the fusion process by receptor-engaged H could explain our observations for MeV. We showed that constant interaction with F by receptor-engaged H may allow wt H-F to fuse even in the presence of F-targeted anti-MeV peptides [START_REF] Mathieu | Prevention of measles virus infection by intranasal delivery of fusion inhibitor peptides[END_REF]. As above, we also previously showed that for HRC peptide fusion inhibitors, adding a lipid moiety improves antiviral potency over time [START_REF] Mathieu | Prevention of measles virus infection by intranasal delivery of fusion inhibitor peptides[END_REF]. In this case a cholesterol-conjugated dimeric peptide (HRC4) was inhibitory as long as 6h after in vitro [START_REF] Welsch | Fatal measles virus infection prevented by brain-penetrant fusion inhibitors[END_REF]. Without a lipid moiety (HRC1), peptide was effective only at early time points after infection.

We hypothesize that the loss of of H-F interaction affects both the triggering of HRC mutants and their ability to fuse in the presence of inhibitor. In Fig. 4B we assessed weak peptide inhibitor (HRC1) for inhibition of wt and mutant F fusion. The assay measures the fusion of cells that express viral envelope glycoproteins (MeV IC323 H/F) with cells that express the MeV receptor SLAM. HRC1 peptide inhibited fusion at early time points (1h, Fig. 4 B). As expected, this inhibition decreased below 70% after 3h and below 40% for the wt F and S262R F respectively after 6h. In contrast, for the H/L454W F fusion complex, HRC1 peptide inhibited over the time course of this fusion assay, significantly better than for the wt complex (**p value, Mann-Whitney U-Test). A parallel assay was performed with the HRC4 peptide, which completely inhibited fusion of all MeV Fs (Fig. S1).

HRC peptides are thought to stabilize F protein intermediates during the fusion process after insertion into the target cell membrane but before refolding to the post-fusion state. The stabilization of the transient intermediate state of F by HRC peptides was used to identify discrete steps in the fusion process [START_REF] Porotto | Spring-loaded model revisited: paramyxovirus fusion requires engagement of a receptor binding protein beyond initial triggering of the fusion protein[END_REF][START_REF] Mathieu | Broad spectrum antiviral activity for paramyxoviruses is modulated by biophysical properties of fusion inhibitory peptides[END_REF]. In Fig. 4C we determined whether the HRC1 fusion blockade for the HRC mutated F occurs at the same transitional state. Red blood cells (RBCs) were allowed to interact with cells expressing the MeV F hyperfusogenic mutants along with a chimeric receptor binding protein expressing the MeV H stalk and the globular head of HPIV3 HN. This chimeric protein can engage the sialic acid receptor on the RBCs and initiate MeV F-activation for the neuropathogenic F proteins [START_REF] Angius | Analysis of a Subacute Sclerosing Panencephalitis Genotype B3 Virus from the 2009-2010 South African Measles Epidemic Shows That Hyperfusogenic F Proteins Contribute to Measles Virus Infection in the Brain[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF][START_REF] Talekar | Measles virus fusion machinery activated by sialic acid binding globular domain[END_REF]. The read-out for peptide inhibition is irreversible binding of the RBCs to the F-expressing cells and/or fusion.

This assay provides a measure of the efficiency with which HRC1 binds and retains F in its transitional intermediate state, preventing membrane merger (Fig. 4C). 293T cells coexpressing the chimeric receptor binding protein MeV H-HN and MeV F (hyperfusogenic mutants) were incubated with RBCs at 4 °C, then transferred to 37 °C in the presence of HRC1 peptides (1M). Zanamivir, a small molecule sialic acid analog that blocks HNreceptor interaction was added after 1 h to disengage cells that were bound by HN-globular head engagement alone. Note that wt F was not used in this assay since it is too stable to be activated under these conditions. The proportion of RBCs either free, reversibly bound by HN-receptor interaction (and therefore released by zanamivir), irreversibly bound by F protein bridging (following insertion of the fusion peptide in the target cell membrane), or fused was quantified. For all three MeV F HRC mutants the larger majority of the cell population remained irreversibly bound and very little fusion was observed, confirming the ability of HRC1 to block F in its transitional state after insertion of the fusion peptide in the target cell membrane. In contrast, the percentage of irreversibly bound cells decreased to 30% concomitantly with an increase in fusion up to 50% for the S262R hyperfusogenic mutant, confirming that this F can "override" inhibition by the peptide. The HRC1 peptide stabilizes the intermediate fusion state for all the F proteins that bear mutations in the heptad repeat domain. Taken together, these results confirm that while the reduction in H-F interaction allows HRC hyperfusogenic mutants to fuse in the absence of receptorwhich seems to be a benefit in the CNS-it also decreases their fusion compared to wt virus in presence of receptor by reducing complete fusion after triggering. Outside the CNS, this reduced fusion is a disadvantage.

Discussion

The altered HRC region of the CNS-adapted MeV F proteins produced viruses that can fuse and infect without known receptors for H. While H-F interaction is essential for fusion and infection by wt MeV, these F proteins (L454W, T461I and N462K; fig 1A) interact less with H but nevertheless mediate infection in vitro (L454W, T461I and N462K) [START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF], in models of CNS infection (L454W, and T461I) [START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF] and in vivo (L454W) [START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF] more effectively than wt virus in the absence of SLAM or Nectin-4 receptors. As anticipated based on previous data [START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF][START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF], the hyperfusogenicity conferred by the alterations in the MeV F HRC region affects both functional and physical interactions with H. The E455G revertant restored wt-like properties in the context of the L454W-bearing F , and when introduced singly into the F protein led to an extremely stable F [START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF] . We speculate that introducing W454 into the prefusion F stalk results in local destabilization that enhances F activation, even in the absence of receptor. The nearby mutation G455 may alter the structure sufficiently to restore the "wt" properties. When the viral quasispecies formed by L454W and L454W/E455G F bearing viruses is cultivated in human brain organoids , the L454W/E455G F bearing virus is eliminated within 10 days confirming that the L454W F bearing virus is fit for growth in CNS tissues [START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF]. The virus bearing the S262R mutation in F is neuropathogenic in vivo [START_REF] Watanabe | New Insights into Measles Virus Brain Infections[END_REF][START_REF] Watanabe | Mutant fusion proteins with enhanced fusion activity promote measles virus spread in human neuronal cells and brains of suckling hamsters[END_REF], and we observed no significant differences in H-F interaction. A S262G mutation in F (along with several other mutations) was found in virus from a SSPE clinical case [START_REF] Angius | Analysis of a Subacute Sclerosing Panencephalitis Genotype B3 Virus from the 2009-2010 South African Measles Epidemic Shows That Hyperfusogenic F Proteins Contribute to Measles Virus Infection in the Brain[END_REF]. Thus, while destabilizing the F protein significantly improves MeV's ability to spread in the brain, the loss of H-F interaction may not be necessary for CNS adaptation.

MeV H-F interaction is key for the steps after F insertion in the target membrane, to complete fusion. The viruses bearing F mutations that lead to CNS spread are more susceptible to fusion inhibitory peptides [START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF]. We attribute this, at least in part, to the fact that the H does not continue to activate F after initial triggering.

In Fig. 5 we propose models of viral infection with wt MeV and the CNS adapted variants, incorporating the findings in this work as well as work from others. A common pattern for neuropathogenic F variants is decreased stability of F (as assessed by sensitivitiy to heat) and a fusion complex that mediates cell-to-cell fusion in the absence of either CD150/SLAM or nectin-4 [START_REF] Angius | Analysis of a Subacute Sclerosing Panencephalitis Genotype B3 Virus from the 2009-2010 South African Measles Epidemic Shows That Hyperfusogenic F Proteins Contribute to Measles Virus Infection in the Brain[END_REF][START_REF] Mathieu | Measles Virus Bearing Measles Inclusion Body Encephalitis-Derived Fusion Protein Is Pathogenic after Infection via the Respiratory Route[END_REF][START_REF] Mathieu | Molecular Features of the Measles Virus Viral Fusion Complex That Favor Infection and Spread in the Brain[END_REF][START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF][START_REF] Watanabe | Measles virus mutants possessing the fusion protein with enhanced fusion activity spread effectively in neuronal cells, but not in other cells, without causing strong cytopathology[END_REF]. These properties confer an infectivity cost, since they are significantly slower to complete the fusion process after inital triggering. These features together with lower viability (10) make these viruses adapt to cell-to cell transmission after initial infection but also likely mean that they are less transmissible.

Funding sources:

The work was supported by grant from NIH AI121349, NS091263, and NS105699 to MP, from French ANR NITRODEP (ANR-13-PDOC-0010-01) to CM. and non-cleavable (C) forms of F were included in the experiment. Precipitates were analyzed through western blotting using anti-MeV F HRC and anti-6xHis (top panels) while cell lysates were blotted using anti-MeV F HRC (bottom panels). (D) Densitometry measurements of coimmunoprecipitated MeV F protein detected by western blot analysis. Protein content was normalized for the total F protein in cell lysates and the immunoprecipitated H protein. There was no statistical difference (unpaired T-test) between the levels of F 0 that were coimmunoprecipitated for each allele. There was also no statistical difference between F(wt) and either allele that contained E455G (single and double mutant) for F 1 levels. However, the difference between the F(wt) and F(L454W) F 1 that co-immunoprecipitated with H was extremely statistically significant (P = 0.0007). Error equals +/-SEM. N = 3 biological replicates

Materials and Methods

Peptides: MeV F derived fusion inhibitor peptides HRC1 and HRC4 were previously described [START_REF] Mathieu | Prevention of measles virus infection by intranasal delivery of fusion inhibitor peptides[END_REF]. Briefly 36aa long peptides derived from the heptad repeat region at the Cterminal of the MeV F protein were synthesized (using the wt sequence or the L454W sequence). Monomeric unconjugated (HRC1) or dimeric cholesterol conjugated (HRC4) forms of the peptides were used in this study. MeV HRC4 dimeric fusion inhibitory peptide (1µM) was added to the medium at time points from 15 to 120 min after the beginning of infection. After 2h of incubation with the virus, medium was replaced with medium containing Avicel. Viral titers were assessed after 3 days of incubation at 32°C by immune staining.

Beta-Galactosidase (Beta-gal) complementation-based fusion assay.

The beta-gal complementation-based fusion assay was performed as described previously [START_REF] Jurgens | Measles fusion machinery is dysregulated in neuropathogenic variants[END_REF]. Briefly, 293T cells transiently transfected with the constructs indicated above and the omega reporter subunit were incubated for the indicated period with cells coexpressing viral glycoproteins and the alpha reporter subunit in presence or not of MeV F HRC derived peptide [START_REF] Mathieu | Prevention of measles virus infection by intranasal delivery of fusion inhibitor peptides[END_REF].

RBC fusion assay. RBC fusion assays were performed on HEK 293T cells transiently

expressing MV H_Y17H HPIV3_T193A chimerae [START_REF] Talekar | Measles virus fusion machinery activated by sialic acid binding globular domain[END_REF] and the indicated MeV Fs. Cell monolayers were washed three times with serum-free medium, placed at 4°C with 1% RBC in DMEM for 30 min, then treated with the indicated peptide and placed at 37°C. Zanamivir was added at a final concentration of 10 mM and the cells were incubated at 4°C, rocked, and the liquid phase was collected in V-bottomed 96-well plates for measurement of reversibly bound RBCs. The cells were then incubated at 4°C with ACK-Lysing buffer, and the liquid phase was collected in V-bottomed 96-well plates for measurement of irreversibly bound RBCs. The cells were then lysed in lysis buffer and transferred to flat-bottom 96 well plates for quantification of fused RBCs. The amount of RBCs in each of the four compartments (released, reversibly bound, irreversibly bound, and fused) was determined by measurement of absorption at 410 nm.

Co-Immunoprecipitation. 293T cells were seeded in biocoated 6-well plates (Corning) at 5x10 5 cells/well and incubated for 24h, at 37 o C. Cells were transfected with plasmid vectors encoding for MeV H-6xHis, MeV F (wt, L454W, T461I, N462K ,E455G, L454W/E455G and S262R) and mCherry (6:4:1 mixtures; 2.2 μg/well) using Lipofectamine® 2000 (Invitrogen), according to the manufacturer's recommendations. Transfected cultures were grown at 32 o C, overnight, in the presence of HRC1 peptide (1 M), to minimize cell-cell fusion. mCherry fluorescence was used to monitor cell transfection efficiency after 18h. Prior to cell lysis, cell protein expression was synchronized with cycloheximide (Sigma, 0.1 mg/mL), followed by membrane protein cross-linking with 3,3'-dithiobis(sulfosuccinimidyl propionate) (Sigma; 1 mM), at low temperature. The cross-linking reaction was quenched with 20 mM Tris, 150 mM NaCl, pH 7.5. Cells were lysed with 50 mM HEPES, 100 mM NaCl, 0.05 g/mL dodecyl maltoside, pH 7.5, supplemented with complete protease inhibitor cocktail (Roche). Lysates were centrifuged at 16000 g for 10 min to remove nuclei and cell debris, and the supernatant was collected for immunoprecipitation and total protein content analysis. MeV H-6xHis protein was immunoprecipitated from cell lysates using Dynabeads® (Thermo, 1 mg/mL) coated with a 6xHis tag-specific antibody (mouse monoclonal, Thermo, MA1-21315).

For Fig. 2: Co-immunoprecipitated and cell lysate proteins were analyzed by western blotting, using primary antibodies specific for MeV F HRC (rabbit polyclonal, Genscript, 503028-1) and 6xHis tag (rabbit polyclonal, Thermo, PA1-983B), followed by an HRP-conjugated antirabbit secondary antibody (Kindle Biosceiences, R1006). Western blots were developed using the SuperSignal West Femto substrate (Thermo) and imaged on a KwikQuant TM Imager UV (Kindle Biosciences).

For Fig. 3: Co-immunoprecipitated and cell lysate proteins were analyzed by western blotting, using primary antibodies specific for MeV F HRC (rabbit polyclonal, Genscript, 503028-1) and 6xHis tag (rabbit polyclonal, Thermo, PA1-983B), followed by WesternBreeze Chromogenic Immunodetection Protocol for detection.

Literature cited

Figure 1 -

 1 Figure 1 -Crystal structure of the trimeric measles F (PDBID:5YXW) in the prefusion state.

Figure 2 -

 2 Figure 2 -The effect of hyperfusogenic MeV F HRC domain mutations on MeV H

Figure 3 -

 3 Figure 3 -The effect of F protein's E455G compensatory mutation on H protein's

Figure 4 -

 4 Figure 4 -HRC hyperfusogenic mutants fuse less in presence of entry receptor-(A)

Figure 5 -

 5 Figure 5 -Model for the hyperfusogenic entry mechanism of neuropathogenic MeV

  Plasmids and reagent. The genes of MeV IC323 H and F proteins were codon optimized, synthesized, and sub cloned into the mammalian expression vector pCAGGS. Plasmids encoding nectin 4 and CD150/SLAM were commercially acquired.Cells. 293T (human kidney epithelial) and Vero-SLAM (African green monkey kidney) cellswere grown in Dulbecco's modified Eagle's medium (DMEM; Gibco, Invitrogen) supplemented with 10% fetal bovine serum (FBS) and antibiotics in 5% CO 2 . The Vero-SLAM culture medium was supplemented with Geneticin. HRC4 Peptide time addition related inhibition. Dulbecco's Modified Eagle's medium (DMEM) containing the indicated viruses (MeV IC323-EGFP, MeV IC323-EGFP-F L454W, MeV IC323-EGFP-F T461I, MeV IC323-EGFP-F N462K all these viruses are from(34)) was used to infect sub-confluent VERO-SLAM cells in 6 well plates (100pfu/well) for 2h at 32°C.


Fre Borea

Charlotte Chazeau

Guy Duhamel

Johanna Faure

Andréa Filippo

Nicolas Gasco

Alexis Martin

Félix Massiot-Granier

Clara Péron

Patrice Pruvost

Jules Selles
email: jules.selles@mnhn.fr

Clara Js

Péron

Félix

STOCK ASSESSMENT OF THE SOUTHERN INDIAN OCEAN ST. PAUL AND AMSTERDAM ROCK LOBSTER STOCKS USING STATISTICAL CATCH AT AGE Fishing campaign 2020-2021

Keywords: Jasus paulensis, Rock lobster, Saint Paul and Amsterdam islands, Statistical catch at age, Assessment, Population dynamic

This report presents new stock assessments for the rock lobster (Jasus paulensis) fishery of the Saint Paul and Amsterdam islands with data up to the last fishing campaign of 2020/21. These new assessments are based on statistical catch at age models using all available data except tagging program data.

Stock status trajectories for both stocks start from a period of unsustainable fishing in the 1980s and recovered in the 1990s. The assessment results indicate that exploitable biomass in 2020 is likely to be well above BMSY, biomass status (B/BMSY) are 1.09 (0.86 -1.50) and 2.12 (1.66 -2.92) for Saint Paul and Amsterdam stocks respectively, and that fishing mortality is well below FMSY. These estimates are consistent with the results of preliminary assessment from biomass dynamic models.

The short-term projection scenarios that were tested show that current catch levels are compatible with the sustainability of the rock lobster stocks.

Introduction

St. Paul and Amsterdam (SPA) islands are part of the French Southern and Antarctic Territories (TAAF) and are located in the subtropical zone of the South Indian Ocean. Initially focused on the exploitation of fur seals (Arctocephalus tropicalis) and demersal fishes, these islands have been exploited annually for rock lobsters (Jasus paulensis) since 1948.

Since 1995, the fishery has been managed by setting annual total allowable catches (TAC) for the rock lobster as well as technical prescriptions to control the fishing effort (e.g. fishing period, authorized fishing gear, mandatory fishing logbook, trap mesh size, legal-size of first catch, control of discards). Fishery observers are present on all fishing trips to collect biological and statistical data and complete logbooks. They monitor and transmit every week the catch data and the biological data collected onboard. Landings are controlled by an independent company and are matched with the observer data.

The key indicator for setting TAC is the Catch per Unit Effort (CPUE) trend, based on data of lobster catches per pot (by weight) and the numbers of pots recorded. Until now, the nominal CPUE was used directly without standardization based on the rationale that the fishing period, area and method have been kept throughout the time series. Until 2020, the fishery was managed to maintain the CPUE at the level of the long-term average and total catches have historically fluctuated between 350 and 400 tons per year. In 2020, a harvest control rule was set with a CPUE target corresponding to a reference period (2001 -2010).

The stock assessment was performed over the period 1986-2020 using a4a model [START_REF] Jardim | What if stock assessment is as simple as a linear model? The a4a initiative[END_REF], over age classes ranging from 3 to 9+. The a4a model is a statistical catch at age model (SCA), allowing flexibility to fit a wide range of models to the data.

Methodology Description of the fleet

Since 1980 and the introduction of fisheries monitoring, the fishing fleet is composed of a single mother ship, the "Austral", which targets and lands mainly rock lobster fished from 4 coastal (operating in-depth inferior to 50 m) canots (''doris'') setting wooden pots in the kelp zone and 2 pilothouse fishing boats (''caseyeurs'') in the deepest area (operating in depth from 70 to 400 m) with lines of 20 steel pots. Rock lobsters are transshipped and weighted to the mother ship where catches are processed on the onboard factory. Fishing takes place during the austral summer between the end of November of the year t and May of the year t + 1 during which the vessel makes two fishing trips of approximately the same duration (two and a half months).

Before this period, the fishery suffered from the reckless fishing effort (legal and illegal) of the 1970s with catches reaching over 1 100 tons per year [START_REF] Pruvost | La pêche aux îles Saint Paul et Amsterdam[END_REF].

Fishery data

All the fishery data gathered by observers aboard is stored in the "Pecheker" database host at MNHN Paris [START_REF] Martin | Data Curation, Fisheries, and Ecosystem-based Management: the Case Study of the Pecheker Database[END_REF]. Catch and effort data from commercial fisheries in SPA French EEZ are available for the period 1980-2020.

The daily data on pot fishing operations include information such as fishing date, area, number of traps deployed and total catches per species in numbers and weight and biological data.

Biological data

High densities of rock lobsters, J. paulensis, have only been observed off St. Paul and Amsterdam. Lower numbers have been reported on seamounts along the South West Indian Ridge [START_REF] Romanov | Summary and review of Soviet and Ukrainian scientific and commercial fishing operations on the deepwater ridges of the southern Indian Ocean[END_REF]. The population in SPA is thought to form a single genetic stock, exchanging by larval dispersal between the two islands. A similar pattern was observed in J. tristani, synonymized species [START_REF] Groeneveld | High connectivity and lack of mtDNA differentiation among two previously recognized spiny lobster species in the southern Atlantic and Indian Oceans[END_REF], in the Tristan da Cunha archipelago. No genetic differentiation could be found between rock lobsters caught on the four islands separated by distances of up to 400 km, and depths that form a barrier to inter-island benthic migration of adults (von der [START_REF] Heyden | Long current to nowhere? Genetic connectivity of Jasus tristani populations in the southern Atlantic Ocean[END_REF]. However, based on the different patterns in growth and demographic structures each island is used as an individualized area for the assessment of J.

paulensis.

The sampling program collects biological data on a daily basis after transhipment from the small operating fishing vessels to the mother ship. It includes carapace length (CL), sex and weight of all sampled rock lobsters from 1986-2020. Ovigerous females are not present during the fishing season but are found throughout the austral winter and immature individuals below the legal size of 5.6 cm CL are released alive directly from small operating fishing vessels.

Input data

Growth and maturity

The only available information on the growth of St Paul rock lobster is found in Grua (1960).

Females reach sexual maturity at 6.5-7.5 cm CL (Grua, 1960), which would be equivalent to about 5-7 years after post-larval settlement. Other information from J. tristani (Tristan rock lobsters) can be found in Pollock and Roscoe (1977) and Pollock (1981) and have been used by [START_REF] Johnston | The Age-structured Production Modelling approach for assessment of the Rock Lobster Resources at the Tristan da Cunha group of islands[END_REF] for the assessment of Tristan rock lobster. Females reach 50% maturity at 5.6 cm CL at Inaccessible Is. and 5.9 cm CL at Nightingale Is. [START_REF] Pollock | Spiny lobsters at Tristan da Cunha, South Atlantic: Inter-island variations in growth and population structure[END_REF]Roscoe, 1987, Pollock 1991). This information is based on tagging studies conducted in the 1970s.

In order to calculate length at age, parameters values for the von Bertalanffy growth function are presented in Table 1. Pollock and Roscoe (1977) and [START_REF] Pollock | Spiny lobsters at Tristan da Cunha, South Atlantic: Inter-island variations in growth and population structure[END_REF] ** 90% of the maximum CL observed in SPA (including outer banks)

The growth curve parameters above are based on mature lobsters (5.6 cm and larger). The growth of immature male and female spiny lobsters is similar, and it is only at maturity that the growth rate slows *for females. The growth of immature individuals is assumed to be identical for males and females and the t0 parameter for males is assumed to be 0 and for females is adjusted to -6 as we only consider mature female in the catch.

Weight at length relationship Length-weight relationship was estimated using 𝑊 = 𝑎𝐶𝐿 𝑏 , based on carapace length (CL) and whole weight (g) data collected in the vicinity of the SPA islands for both sexes since 1986. The parameter estimates are presented in Table 2.

The weight at length by sex and stock was weighted by the catch of the fishing trip. All size classes from 3.3 cm to 14.3 cm CL were pooled in 4 mm intervals. Rock lobsters smaller than the legal size of 5.6 cm have been removed from the CAS as they are sorted and released with sorting errors of less than 0.1% per fishing trip with very high survival.

The CAS by sex (estimated on a subset of total catch) was scaled using the total catch of the fishing trip. The resulting CAA matrices for males and females were scaled using the total catch of the fishing trip and then merged into a single CAA matrix. Age plus groups were set to 8+.

Natural mortality

The natural mortality M was set at 0.15 (𝑦𝑒𝑎𝑟 -1) and constant for all age classes. Average M for main rock lobster stocks ranged from 0.1 to 0.3 (RAM legacy database 2020).

Abundance index CPUE time series were available from 1980 to 2020 for both stocks. Relative abundance indices were used in the form of standardized CPUE time series [START_REF] Selles | CPUE standardisation of the rock lobster fishery in St Paul & Amsterdam Island. 19[END_REF] which were assumed to be proportional to biomass. Standardized CPUE indices were calculated from a GLM model integrated effects of the fishing year, fishing period, fishing area, proxy of octopus abundance (CPUE) and fishing year-area interactions which correspond strictly to the operation of two fleets.

Statistical catch at age

The a4a stock assessment implements a statistical catch-at-age model in R, making use of the FLR platform (Kell et al., 2007), and using automatic differentiation implemented in ADMB as the optimization engine [START_REF] Fournier | AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models[END_REF]. To fit this model to data, there are certain components (submodels) that need to be given structure: fishing mortality (fmodel), survey catchability (qmodel), recruitment (srmodel), variance (vmodel) and first year's age structure (n1model). In the a4a framework, these submodels can incorporate linear functions of age and year, as well as fixed degrees of freedom splines which can vary with age, year, or both age and year.

The statistical catch at age model is based on the Baranov catch equation:

𝑒 𝐸[𝑙𝑜𝑔𝐶 𝑎,𝑦 ] = 𝐹 𝑎,𝑦 𝐹 𝑎,𝑦 + 𝑀 𝑎,𝑦 [1 -𝑒 (𝐹 𝑎,𝑦 +𝑀 𝑎,𝑦 ) ]𝑅 𝑦 𝑒 -∑(𝐹 𝑎,𝑦 +𝑀 𝑎,𝑦 )

Vmodel: For the observation variance σ² of the CAA, the default spline through ages was selected and assumed no year effect, while the observation variances τ² of the tuning indices were all assumed constant throughout the years.

• V_mod1 <-list(~s(age, k = 3), ~ 1)

• V_mod2 <-list(~s(age, k = 3), ~ s(year k = 5))

All the combinations of the sub-models were tested using maximum likelihood estimation (MLE), compared using BIC criterion and evaluated according to the quality of residuals. The best fits were selected based on BIC criterion.

Model fitting and Diagnostics

The best models were then fitted using Markov Chains Monte Carlo (MCMC) sampling. For the MCMCs, the first 500 000 iterations are dismissed (burn-in), and every 100th sample is taken from the 1000000 iterations (thin). Diagnostics of model convergence included visualization of the MCMC chains throughout trace-plots as well as Heidelberger and Welch [START_REF] Heidelberger | Simulation run length control in the presence of an initial transient[END_REF] and [START_REF] Geweke | Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments[END_REF] diagnostics as implemented in the coda package.

To evaluate CPUE fits, predicted CPUE indices were compared to the observed CPUE. Residual plots were also examined, and the randomness of model residuals was evaluated by means of the Root-Mean-Squared-Error (RMSE).

Biological reference points, projection and phase plots

The best-fit model runs of the a4a model were used to calculate reference points based on yield per recruit analysis. A Ricker Stock Recruitment relationship was assumed and harvest management measures have been derived including Maximum Sustainable Yield (MSY), F0.1 (proxy of FMSY, fishing mortality that corresponds to a point on the yield per recruit curve where the slope is 10% of that at the origin) the fishing mortality corresponding to MSY (FMSY). The ratio of the spawning stock biomass (SSB) to MSY (SSB/SSBMSY) and the ratio of the fishing mortality to MSY (F/FMSY) were used for determining stock status trajectories using ''Kobe plots".

To explore potential Total Allowable Catch (TAC) levels, the model was used to predict stock status for different TACs over a 10-year period assuming a constant recruitment level equal to its averages over the last 5 years.

Results

Model fit and convergence

The best fit specification of the models were the following:

Saint Paul rock lobster stock :

• F submodel: ~~ s(age, k = 4) + s(year, k = 7) + te(age, year)

• Sr submodel: ~ricker(CV=0.2)

• V submodel : ~ list(~s(age, k = 3), ~ 1)
Amsterdam rock lobster stock :

• F submodel: ~ s(age, k = 4) + s(year, k = 9) + te(age, year)

• Sr submodel ~ ricker(CV=0.2)

• V submodel : ~ list(~s(age, k = 3), ~ s(year k = 4))
The model allowed for an effect of time and age and a combined effect of both these variables on the fishing mortality estimates (submodel fmod). The stock-recruitment was modelled as a Ricker function (submodel sr mod). Finally, a submodel for the model variance was specified so that more flexibility, particularly for the last years, could be allowed to fit.

The best models selected by the procedure displayed consistent residuals for both the catch and the CPUE indices, with no obvious trend detected (Figure 1). The models were able to predict both the CPUE indices and CAA although some extreme years were less accurately predicted resulting in systematic positive or negative residuals.

The CPUE indices predicted from the model fit were compared to the observed CPUE and indicated a lack of fit for peak years and the end of the time series where variance increases. This pattern is most prevalent for the Amsterdam rock lobster stock, but the overall fits of the abundance indices were good (Figure 2, Figure 3).

The visual inspection of trace plots for the model parameters showed adequate mixing (i.e., moving around the parameter space), which is indicative of convergence of the MCMC chains (Annex 5, Annex 6).

Exploitation status

For both stocks, the estimated SSB shows an increase in recent years, with the current values being the highest in the time series (Figure 4). This increase in SSB is related to the steady decline in catches since the beginning of the time series for the Amsterdam stock and a relatively constant catch level for the St. Paul stock. 3, Table 4).

The exploitable biomass of both rock lobster stocks has increased since the 2000s. The harvest rate fluctuated for much above FMSY over the beginning of the time series followed by an overall decrease trend below of FMSY (Figure 5). Models indicated that the Saint Paul rock lobster stock was not overfished1 (B > BMSY) and not subject to overfishing2 (F < FMSY ). The current biomass state B2020 over BMSY was 9% above BMSY (0.86 -1.50; 95% C.I.) and the current fishing mortality F2020

over FMSY is 27% below FMSY (0.54 -0.98; 95% C.I.). The situation is better for the Amsterdam rock lobster stock with a current biomass state 112% above BMSY (1.65 -2.92; 95% C.I.) and the current fishing mortality was 57% below FMSY (0.31 -0.62, 95% C.I.).

Kobe phase plots showed that rock lobster stocks do not appear to be overfished (𝐵>𝐵 𝑀𝑆𝑌 ) and that there is no overfishing (green phase 𝐹<𝐹 𝑀𝑆𝑌 ) except in the late 1980s (Figure 6).

Projections based on a range of alternative constant TAC for the period 2021-2030 showed that the current exploitation levels are consistent with the MSY management objective (Figure 7).

Discussion

SCA assessments of SPA rock lobsters suggest that the biomass of both stocks experienced a period of overexploitation prior to the start of the CAA series, followed by a relatively stable period from 1986 to 2000. Since 2000, have increased steadily with an acceleration over the last decade. The analysis shows that the status of both lobster stocks in 2020 is likely to be well above BMSY and that fishing mortality is below FMSY.

The short-term projection scenarios that were tested show that current catch levels are consistent with the sustainability of the rock lobster stocks.

The model presented here is an age-based model assuming a continuous growth of rock lobster which grows through a succession of moults. Very little information is available on age length keys of crustaceans, as they are hard to age, and the primary source of data is the size composition of catches. Transitioning into an fully integrated age-based model is a priority especially to model size-based processes such as selectivity that is particularly important for SPA rock lobster stocks which are managed using minimum legal size. An integrated model would allow efficient use of data from the tagging program and corroborate trends in CPUE indices.

Annexes Annex 1

Length distribution of total catch for Amsterdam rock lobster stock.

Amsterdam -Male

Amsterdam -Female

  Annex 3...................................................................................................................................26 Annex 4...................................................................................................................................26 Annex 5...................................................................................................................................27 Annex 6...................................................................................................................................28

FIGURE 1 :

 1 FIGURE 1 : LOG RESIDUALS OF CATCH AND CATCH PER UNIT EFFORT (CPUE) OF THE SPA ROCK LOBSTER.

Amsterdam

FIGURE

  FIGURE 2 : OBSERVED (BLUE) AND PREDICTED (RED) CATCH PER UNIT EFFORT (CPUE) INDEX AND CATCH AT AGE OF THE AMSTERDAM ROCK LOBSTER.

FIGURE 3 :

 3 FIGURE 3 : OBSERVED (BLUE) AND PREDICTED (RED) CATCH PER UNIT EFFORT (CPUE) INDEX AND CATCH AT AGE OF THE SAINT PAUL ROCK LOBSTER.

FIGURE 4 :

 4 FIGURE 4 : TIME-SERIES OF FITTED CATCH (TONS), FISHING MORTALITY (F), RECRUITMENT (1000) AND SPAWNING STOCK BIOMASS (SSB TONS) OF THE SPA ROCK LOBSTER. SHADED AREAS INDICATE THE 95% CREDIBLE INTERVAL Biological reference points, phase plots and projection The standard biological reference points were close for the two rock lobster stocks. MSY estimates was centered around 188 tons (167 -214; 95% C.I.) and 235 tons (165 -399, 95% C.I.) resulting in FMSY median estimates of 0.49 (0.46 -0.53; 95% C.I.) and 0.25 (0.23 -0.27; 95% C.I.) for Amsterdam and St. Paul rock lobster stock respectively. BMSY estimates varied from 448 tons (404 -503; 95% C.I.) for Amsterdam to 1157 tons (811 -1926; 95% C.I.) for St. Paul (Table3, Table 4).

FIGURE 5 :

 5 FIGURE 5:TRENDS IN HARVEST RATE RELATIVE TO FMSY AND BIOMASS RELATIVE TO BMSY FOR THE SPA ROCK LOBSTER. LIGHT AND DARK SHADED GREY AREAS INDICATE 95% AND 50% CREDIBLE INTERVAL RESPECTIVELY.

FIGURE 7 :

 7 FIGURE 7: SHORT TERM PROJECTIONS (2021-2030) FOR SPA ROCK LOBSTER STOCKS OVER A SEQUENCE OF FUTURE TAC BASED ON CATCH MULTIPLIER (0, 0.4, 0.8, 1.8 CATCH IN 2020), STATUS QUO (SQ), F0.1 AND FMSY SCENARIOS. SHADED AREAS INDICATE 95% CREDIBLE INTERVAL.

TABLE 1 : ESTIMATED GROWTH PARAMETERS FROM THE SP AND AM FISHERY AND LITTERATURE.

 1

	Stock	Sex	k	L∞
		Males	0.11*	15.9**
	Amsterdam	Females	0.06*	12.7**
		Males	0.11*	15.9**
	Saint Paul	Females	0.06*	12.7**

* estimates from

TABLE 2 : WEIGHT AT LENGTH PARAMETERS DERIVED FROM THE SP AND AM FISHERY.

 2 The available catch-at-size (CAS, Annex 1 and Annex 2) data covered the period 1986-2020 and the catch at age (CAA, Annex 3, Annex 4) data were generated by age slicing the catch based on the Von Bertalanffy growth function. These data were available for SP and AM on both sexes.

	Stock	Sex	a	b
	Amsterdam	Males (n= 358 579) Females (n= 131 061)	0.0011. 0.0019	2.84 2.53
	Saint Paul	Males (n= 339 089) Females (n= 180 169)	0.00084 0.0012	2.97 2.79

TABLE 3 : SUMMARY OF POSTERIOR QUANTILES OF REFERENCE POINTS INDICATING THE MEDIAN AND THE 95% CREDIBLE INTERVAL FOR THE REFERENCE CASE MODEL FOR SAINT PAUL ROCK LOBSTER. B/BMSY AND F/FMSY ARE PRESENTED FOR THE FINAL ASSESSMENT YEAR.

 3

		Values
	𝐵 0	2 573 t (1802 -4282)
	𝐵 𝑀𝑆𝑌	1 157 t (811 -1926)
	𝐹 𝑀𝑆𝑌	0.26 (0.24 -0.28)
	𝑀𝑆𝑌	235 t (165 -399)
	𝐵	1.09 (0.86 -1.50)
	𝐵 𝑀𝑆𝑌
	𝐵	0.49 (0.39 -0.67)
	𝐵 0
	𝐹	0.73 (0.54 -0.98)
	𝐹 𝑀𝑆𝑌

TABLE 4 : SUMMARY OF POSTERIOR QUANTILES OF REFERENCE POINTS INDICATING THE MEDIAN AND THE 95% CREDIBLE INTERVAL FOR THE REFERENCE CASE MODEL FOR AMSTERDAM ROCK LOBSTER. B/BMSY AND F/FMSY ARE PRESENTED FOR THE FINAL ASSESSMENT YEAR.

 4

		Values
	𝐵 0	984 t (884 -1 098)
	𝐵 𝑀𝑆𝑌	597 t (516 -708)
	𝐹 𝑀𝑆𝑌	0.39 (0.37 -0.40)
	𝑀𝑆𝑌	187 t (161 -224)
	𝐵	2.12 1.65 -2.92)
	𝐵 𝑀𝑆𝑌
	𝐵	0.97 (0.76 -1.33)
	𝐵 0
	𝐹	0.43 (0.31 -0.62)
	𝐹 𝑀𝑆𝑌

September 2021

Overfished refers to the biomass of a stock (B), the state upon which overfishing has occurred. The stock is no longer able to produce at a maximum sustainable yield.

Overfishing refers to the fishing mortality (F), the fishing mortality rate is higher than the rate that produces its maximum sustainable yield.

Acknowledgements

This work was conducted using data collected from the rock lobster fishery observer program (COPEC) supported by the Museum National d'Histoire Naturelle (MNHN) and funded by the French Southern Territories (TAAF). The author wishes to thank all fishery observers who collected data onboard fishing vessels, the Museum national d'Histoire naturelle team in charge of the scientific assessment of the French southern fisheries Guy Duhamel, Patrice Pruvost, Clara Péron, Charlotte Chazeau, Nicolas Gasco, Alexis Martin and especially Félix Massiot-Granier for his support conducting analysis.

And the survey catchability:

𝑒 𝐸[𝑙𝑜𝑔𝐼 𝑦 ] = 𝑄 𝑦 𝑅 𝑦 𝑒 -∑(𝐹 𝑎,𝑦 +𝑀 In order to reduce the number of parameters, M is assumed known, and the remaining parameters are written in terms of a linear combination of covariates described in submodels.

Candidate models

For the assessment purposes, the following a4a submodels were tested:

F submodel : For the fishing mortality F, a separable submodel has been used, in which age and year effects are modelled by using thin plate regression splines (smoothers) provided by the package mgcv (Wood, 2003). The combined effect of both age and year is also tested on the fishing mortality with tensor products.

• With Y [7; 15] and A [2; 5] Q submodel: For the catchability of the biomass index Q, a constant model (∼ 1) was assumed.

• Q_mod1 <-list(~1) SR submodel : For the recruitment R, a factor effect for years and a ricker model have been tested.

• Sr_mod1 <-~ factor(year)

N1 submodel : For the initial age structure N1 a smoother was also applied. Annex 3

Age distribution of total catch for Saint Paul rock lobster stock.

Annex 4

Age distribution of total catch for Amsterdam rock lobster stock.


Fre Borea

Charlotte Chazeau

Guy Duhamel

Johanna Faure

Andréa Filippo

Nicolas Gasco

Alexis Martin

Félix Massiot-Granier

Clara Péron

Patrice Pruvost

Jules 1 Selles
email: jules.selles@mnhn.fr

STOCK ASSESSMENT OF THE SOUTHERN INDIAN OCEAN ST. PAUL AND AMSTERDAM ROCK LOBSTER STOCKS USING BAYESIAN STATE SPACE SURPLUS PRODUCTION MODEL Fishing campaign 2020-2021

Bayesian state-space surplus production models were fitted to Amsterdam and St. Paul rock lobster (Jasus paulensis) catch and CPUE data using the open-source stock assessment tool JABBA. The results of the reference case models indicated that MSY estimates lied between 182 and 258 tons for Amsterdam and 208 and 352 tons for St. Paul rock lobster. Stock status trajectories for both rock lobster stocks started from an underexploited state and moved from of a period of unsustainable fishing in the beginning of the 1980s. Both stocks recovered in the 1990s leading to a > 95% and > 85% probability of stocks biomass in 2019/2020 being above level that produce MSY and fishing mortality rates below sustainable exploitation levels for Amsterdam and St. Paul respectively. Finally, based on the sensitivity analysis, all alternative scenarios combined lead to a 95% and 89% probability that the stock of Amsterdam and St. Paul were below sustainable bounds.

Introduction

St. Paul and Amsterdam (SPA) islands are part of the French Southern and Antarctic Territories (TAAF) and are located in the subtropical zone of the South Indian Ocean (Figure 1). Initially focused on the exploitation of fur seals (Arctocephalus tropicalis) and demersal fishes, these islands have been exploited annually for rock lobsters (Jasus paulensis) since 1948.

In the recent year, the fishing fleet is composed of a single mother ship, the "Austral 2", which targets and lands mainly rock lobster fished from 4 coastal (operating in depth inferior to 50 m) canots (doris) setting wooden traps in the kelp zone and 2 pilothouse fishing boats (''caseyeurs '') in the deepest area (operating in depth from 70 to 400 m) with line of 20 steel traps. Rock lobsters are transhipped and weighted to the mother ship where catches are proceeded on the on-board factory. Fishing takes place during the austral summer between the end of November of the year t and May of the year t + 1 during which time the vessel makes two fishing trips of approximately the same duration (less than 2 months).

The fishery is managed by setting annual total allowable catches (TAC) for the rock lobster as well as technical prescriptions to control the fishing effort (e.g. fishing period, authorized fishing gear, mandatory fishing logbook, trap mesh size, legal size of first catch, control of discards) with the support of onboard fishing controllers on 100% of the fishing trips and landing controls.

The key indicator for setting TAC is the Catch per Unit Effort (CPUE) trend, based on data of lobster catches per trap set (by weight) and the numbers of traps set recorded. Until now, the nominal CPUE was used directly without standardisation based on the rationale that the fishing period, area and method have been kept throughout the time series. The fishery is managed to maintain the CPUE at the level of the long-term average leading to TAC which has historically fluctuated between 350 and 400 tons per year. This document presents the first stock assessment results for Amsterdam and St. Paul rock lobster stocks based on the Bayesian state-space Surplus Production Model (SPM) framework, JABBA (Just Another Bayesian Biomass Assessment; Winker et al., 2018a) using long catch and standardized CPUE time series from 1981 to 2019.

Methodology Fishery data

Catch and CPUE time series were available from 1981 to 2019. Relative abundance indices were used in the form of standardized CPUE time series for each Island [START_REF] Selles | CPUE standardisation of the rock lobster fishery in St Paul & Amsterdam Island. 19[END_REF] which were assumed to be proportional to biomass. The standardizing CPUE series was based on fishing year, fishing period, fishing area and fishing year-area interactions which corresponds strictly to the operation of two fleets (Figure 2, 3).

State-space surplus production model

The stock assessment was implemented using the Bayesian state-space surplus production model framework JABBA (Winker et al., 2018a) and based on the generalized Pella-Tomlinson surplus production function of the form:

𝑔(𝐵 𝑡 ) = 𝑟 𝑚 -1 𝐵 𝑡 [1 -( 𝐵 𝑡 𝐾 ) 𝑚-1 ]
where 𝑟 is the intrinsic rate of population increase at time 𝑡, 𝐾 is the carrying capacity or the unfished (virgin) biomass level at equilibrium and 𝑚 is a shape parameter that determines at which 𝐵/𝐾 ratio the maximum surplus production is attained.

Based on the parameterization by [START_REF] Meyer | BUGS in Bayesian stock assessments[END_REF], the process equation was rewritten into a stochastic population model with population state variables expressed as a depletion biomass formulated as the proportion of the virgin biomass (𝑃𝑡 = 𝐵 𝑡

𝐾

). The initial biomass depletion level was estimated by introducing model parameter (𝜑). The stochastic form of the state process equation is given by:

𝑃 1 = 𝜑𝑒 𝜂 𝑡 ; 𝑓𝑜𝑟 𝑡 = 1 𝑃 𝑡 = [𝑃 𝑡-1 + 𝑟𝑃 𝑡-1 (1 -𝑃 𝑡-1 𝑚 ) - 𝐶 𝑡 𝐾 ] 𝑒 𝜂 𝑡 ; 𝑓𝑜𝑟 𝑡 = 2, . . . , 𝑛
where 𝜂 𝑡 is the process error, with 𝜂 𝑡 ~𝑁𝑜𝑟𝑚𝑎𝑙(0, 𝜎 𝜂 2 ), 𝑟 is the intrinsic rate of population increase, 𝐾 denotes the unfished biomass at theoretical carrying capacity, 𝐶 𝑡 is the catch in year 𝑡 and 𝜑 is the initial biomass depletion.

The observation model connects the state process to abundance index 𝐼 𝑡 (CPUE series) for year 𝑡, assuming 𝐼 𝑡 is proportional to biomass. The observation equation is given by:

𝐼 𝑡 = 𝑞𝐵 𝑡 𝑒 𝜖 𝑡
where, 𝑞 is the catchability coefficient and 𝜖 𝑡 is the observation error, with 𝜀 𝑡 ~𝑁𝑜𝑟𝑚𝑎𝑙(0, 𝜎 𝜀 2 ).

The full Bayesian state-space model specification requires a joint probability distribution over all unobservable hyper-parameters 𝜃(𝐾, 𝑟, 𝑞, 𝜑, 𝜎 𝜂 2 , 𝜎 𝜖 2 ) assuming independent priors and the 𝑛 process errors relating to the vector of unobserved states 𝜂(𝜂 1 , . . . , 𝜂 𝑛 ) , together with all observable data in the form of the relative abundance indices 𝐼 = (𝐼 1 , . . . , 𝐼 𝑛 ).

Priors

For the reference case model (Table 1) priors for 𝑟 and 𝐾 were kept uninformative to convey minimal prior information on the parameter estimates. For 𝐾, a lognormal was implemented as ranges of minimum and maximum of plausible values for a uniform distribution [START_REF] Froese | Estimating fisheries reference points from catch and resilience[END_REF] for each island. A virgin biomass between 500 t and 10,000 tons was selected and is equivalent to a mean value of 5250 t and a CV of 118%. The lower limit was set above the maximum observed catch since the beginning of the time series.

For 𝑟 the minimum and maximum values were set to 0.1 and 1 to approximate prior ranges of medium resilience species [START_REF] Froese | Estimating fisheries reference points from catch and resilience[END_REF] which resulted in a mean of 0.55 and a CV of 85%.

The initial depletion biomass (𝜑) was defined by a lognormal prior with a mean of 0.6 and a CV of 83% assuming a lower exploitation rate before 1981 based on the reconstruction of the catch series made by [START_REF] Pruvost | La pêche aux îles Saint Paul et Amsterdam[END_REF].

The total observation variance 𝜎 𝜖 2 were separated into two components1 to distinguish between fixed observation error 𝜎 𝑠𝑒,𝑡 2 estimated from standardised CPUE [START_REF] Selles | CPUE standardisation of the rock lobster fishery in St Paul & Amsterdam Island. 19[END_REF] and estimable variance 𝜎 𝑒𝑠𝑡 2 where the prior was kept uninformative with an inverse-gamma distribution with both gamma scaling parameters set to 0.001. Similarly, catchability parameters were formulated as uninformative uniform priors with an inverse-gamma distribution.

Process error (𝜎 𝜂 2 ) was freely estimated using a non-informative inverse-gamma distribution with gamma scaling parameters set to 0.001.

Sensitivity analysis

SPMs structural and biological uncertainty are represented in the form of parameters 𝐾, 𝑟 and the shape 𝑚 of the production function, where Schaefer (𝑚 = 2) and Fox (𝑚-> 1) formulations are the most common choices. Given that K was estimated with priors which convey very little information, we assumed that the main source biological uncertainty is linked to 𝑟 and structural uncertainty of the model can be attributed to the choice of 𝑚.

To capture this uncertainty, we fitted the reference case model over a range of informative priors for 𝑟 which assume low and high resilience hypotheses [START_REF] Froese | Estimating fisheries reference points from catch and resilience[END_REF] and fixed values for 𝐵𝑀𝑆𝑌/𝐾 which cover Fox and Schaefer models (Table 2).

Model fitting and Diagnostics

The Bayesian State-space surplus production model JABBA is implemented in R (R Development Core Team, https://www.r-project.org/) with JAGS interface [START_REF] Plummer | JAGS: A Program for Analysis of Bayesian Graphical Models using Gibbs Sampling[END_REF] through ''r2jags'' library [START_REF] Su | R2jags: A Package for Running jags from R[END_REF] to estimate the Bayesian posterior distributions of all quantities of interest by means of a Markov Chains Monte Carlo (MCMC) simulation. In this study, two MCMC chains were used. The model was run for 30,000 iterations, sampled with a burn-in period of 5,000 for each chain. Basic diagnostics of model convergence included visualization of the MCMC chains throughout trace-plots as well as Heidelberger and Welch [START_REF] Heidelberger | Simulation run length control in the presence of an initial transient[END_REF] and [START_REF] Geweke | Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments[END_REF] and [START_REF] Gelman | lnference from Iterative Simulation Using Multiple Sequences[END_REF] diagnostics as implemented in the coda package.

To evaluate CPUE fits, the model predicted CPUE indices were compared to the observed CPUE. Residual plots were also examined, and the randomness of model residuals was evaluated by means of the Root-Mean-Squared-Error (RMSE). The different models run for the sensitivity analysis were compared using the Deviance Information Criterion (DIC).

Biological reference points, projection and phase plots

For SPM, harvest management measures can be derived directly from the expression of g(Bt)

(see [START_REF] Winker | Unifying parameterizations between age-structured and surplus production models: an application to Atlantic blue marlin (Makaira nigricans)[END_REF], including Maximum Sustainable Yield (MSY), the fishing mortality corresponding to MSY (FMSY); the ratio of the spawning stock biomass to MSY (B/BMSY) and the ratio of the fishing mortality to MSY (F/FMSY). These parameters were used for determining stock status trajectories using ''Kobe plots".

To explore the potential total allowable catch (TAC) levels, the model was used to predict the stock status in the form of biomass depletion (B/K) for different TAC over a period of 10 years.

Results

Catch and CPUE

For both islands, catches decreased rapidly in the beginning of the time series starting from approximatively 300 tons and reaching 159 tons in 1990 and 152 tons in 1989 for Amsterdam and St. Paul respectively (Figure 2, 3). This period was followed by gradual increases (with

Model convergence and fits

The predicted CPUE indices from model fit were compared to the observed CPUE and indicated a lack of fit of the two periods of sharp variations in the beginning and end of the series resulting in systematic positive residuals for Amsterdam island (Figure 6, 7). This pattern was still present for St. Paul rock lobster, but the overall fit of the abundance index was greater judging by the RMSE as a goodness-of-fit criterion (0.212, Figure 8,9).

The visual inspection of trace plots for the key model parameters showed adequate mixing of the two chains (i.e., moving around the parameter space), which is indicative for convergence of the MCMC chains (Annex 1, 2). All key parameter MCMC chains passed both Heidelberger and

Welch [START_REF] Heidelberger | Simulation run length control in the presence of an initial transient[END_REF] and Geweke [START_REF] Geweke | Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments[END_REF] test diagnostics further providing evidence for adequate model convergence (Table 3, 4).

Posteriors distribution

Plots of posterior densities together with prior densities are depicted in Figure 10, and 11.

Summaries of posterior quantiles of parameters and quantities of management interest are provided in Table 3 and4 Kobe phase plots showed that the rock lobster stocks appear to be no overfished (𝐵>𝐵 𝑀𝑆𝑌 ) and no overfishing is occurring (green phase 𝐹<𝐹 𝑀𝑆𝑌 ) except in the beginning of the 1980s (Figure 14, 15).

Projections based on a range of alternative constant TAC for the period 2020-2029 showed that the current exploitation levels are consistent with the MSY management objective (Figure 16, 17).

Sensitivity analysis

All scenarios produce similar trends in relative stock status 𝐵/𝐵 𝑀𝑆𝑌 and 𝐹/𝐹 𝑀𝑆𝑌 for both rock lobster stocks (Figure 18,19,20,21). However, absolute stock status and parameter estimates were sensitive to the choice of the shape parameter (𝑚, 𝐵 𝑀𝑆𝑌 /𝐾) of the Pella-Tomlinson surplus production (Figure 22,23,24,25).

Kobe phase plots were similar among all scenarios indicated that the rock lobster stocks were not overfished and not subjected to overfishing with 94% probability for both stocks (Figure 26, 27).

Discussion

The results of the first assessment of St. Paul and Amsterdam rock lobster suggest that the two stocks biomass have experienced a period of sharply declined following by a period of steady increase. The analysis shows that the 2019 status of both rock lobster stocks is likely above 𝐵 𝑀𝑆𝑌 and that fishing mortality is below 𝐹 𝑀𝑆𝑌 .

However, it is important to highlight that there is uncertainty in estimated quantities of stock biomass as well as the estimated harvest rates, since that 95% credibility intervals are somewhat high.

Larger indices and variability observed at the beginning and the end of the observed standardized CPUEs time-series were poorly fitted by the model. Several explanations for the poor fit to the complete data set could be raised including the assumption of a linear relationship between the CPUE and abundance is invalid, the oversimplification of the surplus production models which do not consider changes in the size, age or sex structure of the population.

Sensitivity analysis for alternative structural models and biological which includes different 𝐵 𝑀𝑆𝑌 /𝐾 shows that the reference points 𝐵/𝐵 𝑀𝑆𝑌 and 𝐹/𝐹 𝑀𝑆𝑌 estimates were fairly robust to the choice of 𝐵 𝑀𝑆𝑌 /𝐾. Furthermore, varying intrinsic growth rates suggests that high resilience for St. Paul and Amsterdam might be the best hypothesis given the abundance index data.

Acknowledgments

This work was conducted using data collected from the rock lobster fishery observer program (COPEC) supported by the Museum National d'Histoire Naturelle (MNHN) and funded by the French Southern Territories (TAAF). The author wishes to thank all fishery observers who collected data onboard fishing vessels, the Museum national d'Histoire naturelle team in charge 7. Tables Table 1:

Figures

Annexes Annex 1

Annex 1: Trace plots for the reference case model parameter drawn from MCMC samples in the Bayesian state-surplus production model for Amsterdam rock lobster.

Annex 2

Annex 2: Trace plots for the reference case model parameter drawn from MCMC samples in the Bayesian state-surplus production model for St. Paul rock lobster.

  peaks and troughs) between approximately 1990 and the early 2000s for Amsterdam and 2015 for St. Paul. For Amsterdam island the total catch showed an overall decrease during the last decade with a slight increase in the last year reaching 151 tons in 2019. Since 2010 annual catches were 144 and 222 tons in average for Amsterdam and St. Paul respectively. Standardized CPUE (Figure 4, 5) followed in average the same trend that the nominal CPUE showing a sharply decrease of the abundance until 1989 and a gradual increase with (with peaks) until 2015. The last years series showed a dissimilarity between the two series with the standardized CPUE well above approaching the highest recorded level of abundance since 1980.

  Summary of prior for the reference case Bayesian state-space surplus production model for St. Paul and Amsterdam rock lobster. Table 2: Summary of uncertainty grid model specifications for St. Paul and Amsterdam rock lobster. Table 3: Summary of posteriors quantiles indicating the median and the 95% credible interval and the Geweke and Heidel p-value of the convergence diagnostics for the reference case model for Amsterdam rock lobster. Table 4: Summary of posteriors quantiles indicating the median and the 95% credible interval and the Geweke and Heidel p-value of the convergence diagnostics for the reference case model for St. Paul rock lobster. Table 5: Summary of posteriors quantiles of reference points indicating the median and the 95% credible interval for the reference case model for Amsterdam rock lobster. B/BMSY and F/FMSY are presented for the final assessment year. Table 6: Summary of posteriors quantiles of reference points indicating the median and the 95% credible interval for the reference case model for St. Paul rock lobster. B/BMSY and F/FMSY are presented for the final assessment year.

Figure 1 :

 1 Figure 1: Location of Saint Paul and Amsterdam within the French EEZ in the South Indian Ocean. The French EEZ is delineated by a grey dashed line.

Figure 2 :

 2 Figure 2: Time-series of catch in metric tons (t) for Amsterdam rock lobster.

Figure 3 :

 3 Figure 3: Time-series of catch in metric tons (t) for St. Paul rock lobster.

Figure 4 :

 4 Figure 4: Comparative plot of the relative nominal CPUE (red) and GLM standardised CPUE series (black) for Amsterdam with the 95% credible interval (dashed lines).

Figure 5 :

 5 Figure 5: Comparative plot of the relative nominal CPUE (red) and GLM standardised CPUE series (black) for St. Paul with the 95% credible interval (dashed lines).

Figure 6 :

 6 Figure 6: Time-series of observed (circle) and predicted (solid line) catch per unit effort (CPUE) of the Amsterdam rock lobster for the Bayesian state-space surplus production model. Shaded area indicates the 95% credible interval.

Figure 7 :

 7 Figure 7: Residual diagnostic plots for the reference case model for Amsterdam rock lobster. The solid black line indicates a loess smoother through all residuals.

Figure 8 :

 8 Figure 8: Time-series of observed (circle) and predicted (solid line) catch per unit effort (CPUE) of the St Paul rock lobster for the Bayesian state-space surplus production model. Shaded area indicates the 95% credible interval.

Figure 9 :

 9 Figure 9: Residual diagnostic plots for the reference case model for St. Paul rock lobster. The solid black line indicates a loess smoother through all residuals.

Figure 10 :

 10 Figure 10: Prior and posterior distributions for the reference case model for Amsterdam rock lobster. Posteriors distributions are plotted using kernel densities estimates (black lines).

Figure 11 :

 11 Figure 11: Prior and posterior distributions of the reference case model for St. Paul rock lobster. Posteriors distributions are plotted using kernel densities estimates (black lines).

Figure 12 :

 12 Figure 12: Trends in harvest rate relative to FMSY and biomass relative to BMSY for the reference case model for Amsterdam rock lobster. Shaded grey area indicates the 95% credible intervals.

Figure 13 :

 13 Figure 13: Trends in harvest rate relative to FMSY and biomass relative to BMSY for the reference case model for St. Paul rock lobster. Shaded grey area indicates 95% credible interval.

Figure 14 :

 14 Figure 14: Kobe phase plot showing estimated trajectories (1980-2019) of B/BMSY and F/FMSY for the reference case mode for Amsterdam rock lobster. Different grey shaded areas denote the 50, 80 and 95 % credible interval for the terminal assessment year. The probability of terminal year points falling within each quadrant is indicated in the figure legend.

Figure 15 :

 15 Figure 15: Kobe phase plot showing estimated trajectories (1980-2019) of B/BMSY and F/FMSY for the reference case model for St. Paul rock lobster. Different grey shaded areas denote the 50, 80 and 95% credible interval for the terminal assessment year. The probability of terminal year points falling within each quadrant is indicated in the figure legend.

Figure 16 :

 16 Figure 16: Projections (2020-2029) based on the reference case model over a sequence of future TAC from 50 to 550 tons for Amsterdam rock lobster. The initial catch for the years 2020-2021 was set to the 2020 TAC. The dashed line denotes BMSY.

Figure 17 :

 17 Figure 17: Projections (2020-2029) based on the reference case model over a sequence of future TAC from 50 to 550 tons. The initial catch for the years 2020-2021 was set to the 2019 TAC. The dashed line denotes BMSY.

Figure 18 :

 18 Figure 18: Time series of B/Bmsy for the different sensitivity analysis scenarios for Amsterdam rock lobster.

Figure 19 :

 19 Figure 19: Time series of F/Fmsy for the different sensitivity analysis scenarios for Amsterdam rock lobster.

Figure 20 :

 20 Figure 20: Time series of B/Bmsy for the different sensitivity analysis scenarios for St. Paul rock lobster.

Figure 21 :

 21 Figure 21: Time series of F/Fmsy for the different sensitivity analysis scenarios for St. Paul rock lobster.

Figure 22 :

 22 Figure 22: Surplus Production functions for the different sensitivity analysis scenarios for Amsterdam rock lobster.

Figure 23 :

 23 Figure 23: Surplus Production functions for St. Paul rock lobster.

Figure 24 :

 24 Figure 24: Boxplots of the posteriors distributions for the different sensitivity analysis scenarios for Amsterdam rock lobster where B/BMSY and F/FMSY are presented for the final assessment year. Dashed lines denote means across all of the scenarios.

Figure 25 :

 25 Figure 25: Boxplots of the posteriors distributions for the different sensitivity analysis scenarios for St. Paul rock lobster where B/BMSY and F/FMSY are presented for the final assessment year. Dashed lines denote means across all of the scenarios.

Figure 26 :

 26 Figure 26: Kobe phase plot showing estimated terminal B/BMSY and F/FMSY for different sensitivity analysis scenarios for Amsterdam rock lobster. The probability of terminal year points falling within each quadrant is indicated in the figure legend.

Figure 27 :

 27 Figure 27: Kobe phase plot showing estimated terminal B/BMSY and F/FMSY for different sensitivity analysis scenarios for St. Paul rock lobster. The probability of terminal year points falling within each quadrant is indicated in the figure legend.

  . The marginal posterior for r has similar values for both Amsterdam and St. Paul rock lobster with a median of about 0.45 (0.27 -0.62; 95% C.I.) upper than the prior for Amsterdam and 0.43 (0.26 -0.61; 95% C.I.) for St. Paul. The posterior for K has a median

	of 1,452 tons (1,024 -2,465; 95% C.I.) and 1,585 tons (1,154 -2,642; 95% C.I.) for Amsterdam
	and St. Paul rock lobster respectively.
	Biological reference points, phase plots and projection
	The standard biological reference points were close for the two rock lobster stocks. MSY
	estimates was centered around 198 tons (182 -228; 95% C.I.) and 227 tons (212 -246; 95%
	C.I.) resulting in FMSY median estimates of 0.36 (0.08 -0.55; 95% C.I.) and 0.29 (0.16 -0.67; 95%
	C.I.) for Amsterdam and St. Paul rock lobster respectively. BMSY estimates varied from 610 tons
	(430 -1,035; 95% C.I.) for Amsterdam to 665 tons (484 -1109; 95% C.I.) for St. Paul (Table 5,

6

). The BMSY posterior distribution was positively skewed with a long tail of distribution.

The exploitable biomass of both rock lobster stocks has decreased until the end of the 1980s followed by an increasing trend until 2019. The harvest rate fluctuated for much above FMSY over the period 1981-1988 followed by an overall decrease trend below of FMSY since the end of the 1990s (Figure

12

, 13).

Models indicated that Amsterdam rock lobster was no overfished 2 (B > BMSY) and was no subject to overfishing 3 (F < FMSY ). The current biomass state B2019 over BMSY was 53% above BMSY (1.09 -2.01; 95% C.I.) and the current fishing mortality F2019 over FMSY is 50% below FMSY (0.38 -0.66; 95% C.I.). The situation was less evident for St. Paul rock lobster with a current biomass state 24% above BMSY (0.98 -1.61; 95% C.I.) and the current fishing mortality was 26% below FMSY (0.57 -0.93, 95% C.I.).

Table 7 :

 7 Summary of model diagnostics for the different sensitivity analysis scenarios for Amsterdam rock lobster. Nobs, Parameters, DF, RMSE and DIC stands for number of observations, number of parameters, degree of freedom, root mean squared error and deviance information criterion respectively.

Table 8 :

 8 Summary of model diagnostics for the different sensitivity analysis scenarios for St. Paul rock lobster. Nobs, Parameters, DF, RMSE and DIC stands for number of observations, number of parameters, degree of freedom, root mean squared error and deviance information criterion respectively.

September 2020

Fixed input variance was set to 0.

Overfished refers to the state of a stock upon which overfishing has occurred. The stock is no longer able to produce at a maximum sustainable yield.

Overfished refers to the state of a stock upon which overfishing has occurred. The stock is no longer able to produce at a maximum sustainable yield.

Annex 4 Annex 4: Equilibrium yield (t) and CPUE (kg/trap) for the reference case model for St. Paul rock lobster. Grey shaded area indicates the 75% credible interval.

of the scientific assessment of the French southern fisheries Guy Duhamel, Patrice Pruvost, Clara Péron, Charlotte Chazeau, Nicolas Gasco, Alexis Martin and especially Félix Massiot-Granier for his support conducting Bayesian analysis.

Annex 3

Annex 3: Equilibrium yield (t) and CPUE (kg/trap) for the reference case model for Amsterdam rock lobster. Grey shaded area indicates the 75% credible interval.