Sandrine Marquet

Bruno Bucheton

Camille Reymond

Laurent Argiro

Hassan Sayda

El-Safi

Mohamed Musa

Jean-Pierre Kheir

Christophe Desvignes

Adil Béroud

Awad Mergani

Hammad

Sayda Hassan El-Safi

Kheir

Jean-Pierre Desvignes

Christophe Béroud

Adil Mergani

Awad Hammad

Alain J Dessein

Exome Sequencing Identifies Two Variants of the Alkylglycerol Monooxygenase Gene as a Cause of Relapses in Visceral Leishmaniasis in Children, in Sudan

Keywords: AGMO, exome sequencing, genetic variants, haploinsufficiency, Kala-azar relapse F, female, KA, kala-azar, M, male

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Kala-azar (KA) or visceral leishmaniasis (VL) is the most severe form of leishmaniasis. It is caused by Leishmania donovani and is fatal without appropriate treatment. KA is a disseminated protozoan infection transmitted by sand fly bites, in which the macrophages of the liver, spleen, and bone marrow are preferentially parasitized and are the sites of intracellular parasite replication. KA is highly endemic in East Africa, with about 300 thousand cases reported annually (World Health Organization). The largest numbers of cases are reported in Sudan and in Ethiopia.

Most of subjects infected with L. donovani control the infection and remain asymptomatic. They may, however, be carrying the parasite for months or years. The spectrum of clinical disease is large, from mild fever to severe disease. The clinical features of KA include recurrent fever, weight loss, massive hepatosplenomegaly, general lymphadenopathy (which leads to severe pancytopenia), and anemia [START_REF] Pearson | Clinical spectrum of leishmaniasis[END_REF][START_REF] Zijlstra | Leishmaniasis in Sudan. Visceral leishmaniasis[END_REF]. In the absence of anti-Leishmania treatment, death occurs within a short period [START_REF] Chappuis | Visceral leishmaniasis: what are the needs for diagnosis, treatment and control?[END_REF]. Susceptibility to KA in Africa and South America is generally higher in children than in adults. It has been suggested that adults may develop cross-protective immunity after exposure to other Leishmania species [START_REF] Romano | Cutaneous infection with Leishmania major mediates heterologous protection against visceral infection with Leishmania infantum[END_REF].

We have performed a longitudinal study in a Sudanese village, Barbar El Fugara, during an outbreak of KA between 1995-2002 [START_REF] El-Safi | Epidemiology of visceral leishmaniasis in Atbara River area, eastern Sudan: the outbreak of Barbar El Fugara village (1996-1997)[END_REF][START_REF] Bucheton | The interplay between environmental and host factors during an outbreak of visceral leishmaniasis in eastern Sudan[END_REF][START_REF] Bucheton | A major susceptibility locus on chromosome 22q12 plays a critical role in the control of kala-azar[END_REF]. The population of Babar has migrated 30 years ago from regions where cutaneous leishmaniasis was endemic, then adults may have developed cross-protective immunity before reaching the village of Barbar. In East Africa, humans are the reservoir of L. donovani. In Barbar, the transmission was peridomiciliar, and all habitants of the village were exposed during the outbreak [START_REF] Bucheton | The interplay between environmental and host factors during an outbreak of visceral leishmaniasis in eastern Sudan[END_REF]. Overall, 29.2% of the villagers developed KA, with most cases (90%) occurring in subjects ≤30 years old. Most of the 575 subjects from this village who developed KA recovered from L. donovani infection after treatment with méglumine antimoniate (Glucantime), whereas 5.5% died. Incomplete treatment is associated with a reactivation within a few weeks of the infection. Complete treatment allows total disappearance of the clinical signs of KA. A few patients may, however, develop KA again 1 or 2 years later. These cases are referred here as "relapsing cases. " Relapses may be due to the reactivation of a latent infection or to a reinfection. Among subjects who developed KA in Babar, 5.7% suffered relapses corresponding to 1.7% of the total population.

Since relapsing KA affected 1.7% of the total population of the village (5.7% of the KA subjects), it was a rare and severe phenotype that was clustered in certain families in half of the cases. Among the relapsing KA, a quarter relapsed at least twice. These observations suggest that inherited factors may confer a predisposition to relapse. This is consistent with findings from Rijal et al. [START_REF] Rijal | Increasing failure of miltefosine in the treatment of Kala-azar in Nepal and the potential role of parasite drug resistance, reinfection, or noncompliance[END_REF], showing that clinical relapses are not due to reinfection with new strains of Leishmania and that there is no difference in drug-resistant parasites from cured and relapsed patients.

We tested here the hypothesis that rare genetic variants might confer a predisposition to KA relapse, by performing whole-exome sequencing (WES) on 5 families, each of which contained 2 children presenting KA relapse. We identified homozygous and heterozygous mutations of the alkylglycerol monooxygenase (AGMO) gene (MIM 613738) as the likely cause of relapse in 3 families.

METHODS

Ethics Statement

The study protocol was approved by both the federal and state Ministries of Health and by the Faculty of Medicine of Khartoum. Written informed consent was obtained from the district authorities, the village committee, all participating adults, and the parents of the children in the study.

Study Participants

The 5 families, 1 of which was consanguineous (family I), were recruited from the village of Barbar El Fugara [START_REF] El-Safi | Epidemiology of visceral leishmaniasis in Atbara River area, eastern Sudan: the outbreak of Barbar El Fugara village (1996-1997)[END_REF]. Clinical data for the 10 affected individuals are presented in Table 1. KA was diagnosed on the basis of the presence of the parasite in lymph node smears together with clinical presentation, through signs such as recurrent fever, splenomegaly, and/or lymphadenopathy. All individuals found to have KA were treated with Glucantime and recovered after treatment. However, 5.7% of the cured patients presented relapses within 1 to 3 years after treatment (Table 1). Mean age at VL onset was 9 years (5-12 years) for these patients. Six of the patients with relapsing VL were boys and 4 were girls. DNA was extracted from blood samples by a standard salting-out method.

Exome Sequencing and Data Analysis

High-quality DNA for WES was available for 10 individuals presenting relapses and 11 additional controls from the same families with no history of KA (n = 5) or with KA but no relapse (n = 6). Exome sequencing was performed on the Ion Proton Platform (Life Technologies), and the AmpliSeq Exome Kit (Life Technologies) was used for library preparation. For each individual, 100 ng of high-quality DNA was amplified with 12 primer pools of 200-base-pair amplicons and the AmpliSeq Exome library preparation kit, according to the manufacturer's protocol. Samples were barcoded with the Ion Xpress Barcode Adapter (Life Technologies) to allow the pooling of 2 exomes per chip. The libraries were purified with Agencourt AMPure beads and quantified with an ABI7900 machine and the Ion library Quantification Kit (Life Technologies). All libraries were diluted to 100 pM working solutions by multiplexing 2 barcoded samples, and were clonally amplified by emulsion polymerase chain reaction with the Ion PI HiQ Template OT2 200 Kit and the Ion OneTouch 2 System (Life Technologies). Finally, the positive spheres were sequenced with the Ion PI Hi-Q Sequencing 200 Kit and Ion PI Chip Kit v2. All procedures were carried out according to the kit manufacturer's instructions. We were able to generate a total of 18 gigabase of raw sequence, with a mean read length of 181 base pairs. Torrent Suite Software V3.0 was used to manage all experiment planning and data processing steps. Raw data were processed on the Ion Proton Sequencer and transferred to the Ion Proton Torrent Server for base and variant calling. The sequences were aligned with the human genome reference sequence (hg19), with TMAP4. When the alignment was complete, a BAM file and a Variant Call Format (VCF) file were generated for each individual. Exome analysis was performed with VarAFT software (http://varaft.eu). The sequences were annotated with Annovar [START_REF] Yang | Genomic variant annotation and prioritization with ANNOVAR and wANNOVAR[END_REF], dbSNP137 [START_REF]NCBI Resource Coordinators. Database resources of the National Center for Biotechnology Information[END_REF], and UMD-Predictor [START_REF] Salgado | UMD-predictor: a high-throughput sequencing compliant system for pathogenicity prediction of any human cDNA substitution[END_REF]. VarAFT software uses a series of filters that can be applied to ensure the rapid exclusion of common variants present in public databases (1000 Genomes Project, Exome Aggregation Consortium [ExAC], 6500 Exome Sequencing Project [ESP]) and nondeleterious variants. Using this software, we were also able to filter against a local database containing all the variants detected in our control samples. We selected the heterozygous or homozygous mutations identified in subjects with relapsing KA but not in control subjects. The filtering process is described in detail in Figure 1. We used UMD-Predictor, a mutation pathogenicity prediction system [START_REF] Salgado | UMD-predictor: a high-throughput sequencing compliant system for pathogenicity prediction of any human cDNA substitution[END_REF] to estimate the potential effects of the mutations. Follow-up analyses were carried out with Integrative Genome Viewer (IGV) software [START_REF] Thorvaldsdóttir | Integrative Genomics Viewer (IGV): high-performance genomics data visualization and exploration[END_REF],

to check the quality of the sequence alignment.

Sanger Sequencing

For validation and analysis of the segregation of the candidate mutations with KA relapse, we used specific primers designed with Primer3 software (V4.0.0) [START_REF] Untergasser | Primer3-new capabilities and interfaces[END_REF] to amplify DNA from all subjects with relapsing VL, their parents, and control family members for whom samples were available. The polymerase chain reaction products were purified with Agencourt AMPure beads and sequenced by Sanger sequencing.

RESULTS

The mean coverage of the 21 samples subjected to WES exceeded 100×. A summary of the variants detected by exome sequencing in the individuals with relapses is provided in Table 2. The mean number of variants detected in the subjects with relapse was 43 777, including 1502 variants with a mean frequency <1% in the general population that were nonsynonymous, stop loss, or stop gain, and 642 variants predicted to be pathogenic or probably pathogenic. The first step in the identification of potential causal mutations was the selection of all homozygous or heterozygous variants (n = 37 277) found in at least 50% of affected individuals (Figure 1). Assuming that relapse-associated mutations are rare, the next step was the exclusion of variants with an allele frequency >0.01 in the 1000 Genomes Project, ExAC, or 6500 ESP (n = 930). We then applied a filter, such that only nonsynonymous, frameshift, stop, and splice-site mutations were selected, whereas synonymous, 5'UTR, 3'UTR and intronic variants were removed. Additional filtering was performed on the basis of predicted deleterious effects (UMD-Predictor) and conservation (n = 109). Finally, variants that were found in the homozygous or heterozygous state in control individuals (either KA without relapse or no KA subjects) were also excluded. This filtering strategy revealed the presence of 2 mutations of AGMO gene encoding the alkylglycerol monooxygenase, also known as TMEM195, in subjects with KA relapse from 3 families (Figure 1 and Figure 2A). In families I and III, the 4 individuals displaying KA relapses were heterozygous for a missense mutation of exon 7 of AGMO: c.701A > G (rs143439626, p.Ly-s234Arg). In family II, the 2 individuals with KA relapse were homozygous for this mutation. None of the control subjects for whom exome sequencing was performed carried this mutation.

An additional nonsense mutation in exon 12 of AGMO, c.1213C > T (rs139309795, p.Arg405*), resulting in a premature stop codon (p.Arg405*) and early termination of the protein, was found to be homozygous in the 2 children with relapses from family II (Figure 2A). In families I and III, the children with KA displaying relapses after treatment were heterozygous, except for individual 5 of family I, who did not carry this mutation (Figure 2A). All the control individuals subjected to exome sequencing were homozygous wild-type.

Sanger sequencing validated the mutations identified for all WES samples (Figure 2B). The disease-associated variants of AGMO were then checked by direct sequencing of additional available DNA from family members (parents and controls). Sanger sequencing confirmed the cosegregation of the AGMO mutation (c.701A > G) with the disease phenotype in a dominant manner. Similar results were obtained for the second mutation (c.1213C > T), except for 1 affected child from family I who was wild-type homozygous. In family I, each parent (subjects 1 and 2) was a heterozygous carrier of both the c.701A > G (p.Lys234Arg) and c.1213C > T (p.Arg405*) mutations, and the siblings (subjects 3, 4, and 7) of the subjects Total variants (homozygous and heterozygous) common to at least 50% of cases: number of variants remaining after the filter employed at that step. We selected homozygous and heterozygous variants common to at least 50% of individuals presenting KA relapse. We selected rare variants with a MAF <0.01 in 1000 Genomes, the ExAC database, and 6500 Exome Sequencing Project. Rare nonsynonymous, stop-loss, or stop-gain variants and splice-site mutations with a probable pathogenic effect predicted by UMD-Predictor were retained. We excluded variants detected in the homozygous or heterozygous state in control individuals. This filtering strategy revealed 2 rare autosomal heterozygous or homozygous variants of the AGMO gene in 3 families. Abbreviations: AGMO, alkylglycerol monooxygenase gene; KA, kala-azar; MAF, minor allele frequency; WES, whole-exome sequencing.

presenting KA relapse were homozygous for the wild-type allele and carried neither of the 2 mutations (Figure 2A). In family II, each parent (subjects 1 and 2) was a heterozygous carrier of the c.701A > G and c.1213C > T mutations, whereas control sibling 5 was homozygous for the wild-type allele and carried neither of the 2 mutations. In family III, the father was a heterozygous carrier, and control sibling 4 was homozygous for the wild-type allele and carried neither of the 2 mutations. The c.704A > G variant results in the substitution of a lysine residue in position 234 by an arginine residue (p.Lys234Arg) predicted to be "probably deleterious" (UMD-Predictor score 66) as it is located in a highly conserved sequence (Genomic Evolutionary Rate Profiling [GERP]++ score >2) (Figure 2C). This mutation affects a residue located in the active site of AGMO [START_REF] Watschinger | Catalytic residues and a predicted structure of tetrahydrobiopterin-dependent alkylglycerol mono-oxygenase[END_REF], and a multiple sequence alignment for the AGMO protein confirmed that the strong conservation of the lysine residue across different species (Figure 2D). The nonsense mutation in exon 12 of AGMO, c.1213C > T, resulting in a premature stop codon p.Arg405* and early termination of the protein, affects a residue in transmembrane region 8 [START_REF] Watschinger | Catalytic residues and a predicted structure of tetrahydrobiopterin-dependent alkylglycerol mono-oxygenase[END_REF] (Figure 2C). The potential pathogenicity of the 2 variants, as predicted by bioinformatics tools, suggests that these variants are probably loss-of-function alleles responsible for the observed relapses.

These mutations were found with a frequency of <7 × 10 -4 in the 1000 genomes, ExAC and 6500 ESP databases. In addition, to confirm the rarity of these mutations in the population of Babar, we analyzed 100 unrelated ethnically matched individuals from the same village (200 chromosomes) who had KA but no relapse. Genotyping was performed with TaqMan assays, according to the manufacturer's instructions. We identified 2 individuals older than 14 years that were heterozygous for these mutations in this population.

DISCUSSION

Our results show that rare loss-of-function AGMO mutations were closely associated with relapse after KA treatment in 3 families. This conclusion is supported by several features:

(1) all individuals with relapses carried at least 1 mutation, and 5 of the 6 carried both mutations; (2) none of the control family members carried the susceptibility allele, and all were homozygous wild-type; (3) the mutations are located within AGMO, which encodes an enzyme that plays a critical role in macrophage-mediated immunity during leishmaniasis; and (4) the cosegregation of these AGMO mutations and the relapse phenotype is consistent with an autosomal dominant transmission. The parents responsible for transmitting the 2 mutations are both heterozygous carriers, although they are considered to be unaffected. Before settling in the village, they lived in Geneina (Western Sudan), where they probably have acquired immunity to L. major. Thus, they did not develop visceral leishmaniasis, probably due to cross-protection. It was not, therefore, possible to evaluate the likelihood of relapse in the parents, although they could, potentially, be susceptible.

An age-dependent incomplete penetrance of AGMO mutations may be another explanation as described in other diseases [START_REF] Auer-Grumbach | Rare variants in MME, encoding metalloprotease neprilysin, are linked to late-onset autosomal-dominant axonal polyneuropathies[END_REF][START_REF] Orr | A mutation in the atrial-specific myosin light chain gene (MYL4) causes familial atrial fibrillation[END_REF]. In our dataset for 10 familial cases of KA relapse, 1 AGMO mutation (701A > G) accounted for 60% of the relapse cases, and the other mutation (1213C > T) was found in 50% of the subjects with KA relapse. As both homozygous and heterozygous individuals have the same deleterious phenotype, AGMO deficiency probably involves a haploinsufficiency mechanism. This mechanism has frequently been reported to underlie autoimmune and autoinflammatory diseases [START_REF] Kuehn | Immune dysregulation in human subjects with heterozygous germline mutations in CTLA4[END_REF][START_REF] Zhou | Loss-of-function mutations in TNFAIP3 leading to A20 haploinsufficiency cause an early-onset autoinflammatory disease[END_REF]. Assuming this hypothesis to be correct, the single remaining functional copy of the AGMO gene would be unable to generate sufficient amounts of its product to preserve the wild-type phenotype, and this would result in KA relapse. Kuehn et al. [START_REF] Kuehn | Immune dysregulation in human subjects with heterozygous germline mutations in CTLA4[END_REF] reported that patients heterozygous for a loss-of-function CTLA4 allele had a phenotype similar to that of mice homozygous for a loss-of-function ctla4, whereas heterozygous mice have no detectable phenotype. Another example of haploinsufficiency has been reported for the human IFNGR2 locus, which has been implicated in mycobacterial disease [START_REF] Kong | Haploinsufficiency at the human IFNGR2 locus contributes to mycobacterial disease[END_REF]. Moreover, 2 of the 100 unrelated individuals with KA harbored AGMO heterozygous mutations and were not reported to have suffered relapses. This finding suggests that autosomal dominant AGMO deficiency may display incomplete penetrance. Autosomal-dominant CTLA4 deficiency provides another example of incomplete penetrance in haploinsufficiency conditions [START_REF] Kuehn | Immune dysregulation in human subjects with heterozygous germline mutations in CTLA4[END_REF]. Penetrance has been shown to be incomplete in most autosomal-dominant immunological disorders involving haploinsufficiency [START_REF] Rieux-Laucat | Immunology. Autoimmunity by haploinsufficiency[END_REF]. This incomplete penetrance in disease may also result from other genetic differences between individuals or may be age dependent because the 2 non-relapsing KA patients harboring AGMO heterozygous mutations were older than their relapsing counterparts.

As reviewed by Sakthianandeswaren et al. [START_REF] Sakthianandeswaren | The role of host genetics in leishmaniasis[END_REF], several loci and genes involved in host immune responses to infection (innate immunity, development and differentiation of immune cells, and T-cell immune response) have been involved in the development of KA. In particular, susceptibility to VL was shown to depend on loci located on chromosome 22q12 (IL2RB) [START_REF] Bucheton | A major susceptibility locus on chromosome 22q12 plays a critical role in the control of kala-azar[END_REF][START_REF] Bucheton | Identification of a novel G245R polymorphism in the IL-2 receptor beta membrane proximal domain associated with human visceral leishmaniasis[END_REF], 2q35 (NRAMP1) [START_REF] Bucheton | Genetic control of visceral leishmaniasis in a Sudanese population: candidate gene testing indicates a linkage to the NRAMP1 region[END_REF][START_REF] Mohamed | SLC11A1 (formerly NRAMP1) and susceptibility to visceral leishmaniasis in The Sudan[END_REF], 6p21 (HLA-DRB1 HLA-DQA1) [START_REF] Fakiola | Common variants in the HLA-DRB1-HLA-DQA1 HLA class II region are associated with susceptibility to visceral leishmaniasis[END_REF], and 17q12 (CCL1 and CCL16) [START_REF] Jamieson | Genome-wide scan for visceral leishmaniasis susceptibility genes in Brazil[END_REF]. Additional candidate genes such as DDL1 [START_REF] Fakiola | Genetic and functional evidence implicating DLL1 as the gene that influences susceptibility to visceral leishmaniasis at chromosome 6q27[END_REF], IL10 [START_REF] Mishra | IL10 Variant g.5311A is associated with visceral leishmaniasis in Indian population[END_REF], IL18 [START_REF] Kumar | Association of interleukin-18 gene polymorphism with susceptibility to visceral leishmaniasis in endemic area of Bihar, an Indian population[END_REF], IL4 [START_REF] Mohamed | Genetic susceptibility to visceral leishmaniasis in the Sudan: linkage and association with IL4 and IFNGR1[END_REF], TLR4 [START_REF] Rasouli | Toll-like receptor 4 (TLR4) polymorphisms in Iranian patients with visceral leishmaniasis[END_REF], CXR2 [START_REF] Mehrotra | Genetic and functional evaluation of the role of CXCR1 and CXCR2 in susceptibility to visceral leishmaniasis in north-east India[END_REF], and TGFB1 [START_REF] Frade | TGFB1 and IL8 gene polymorphisms and susceptibility to visceral leishmaniasis[END_REF] have also been associated with VL. No study has tested the hypothesis of genetic variants causing relapse of KA. An interesting question is whether AGMO mutations could increase susceptibility to KA in general. These mutations have not been associated with KA in previous studies, likely because of their rarity. The strategies used in previous genetic studies on KA (including genome-wide association studies) would not have detected such mutations. The identified AGMO variants were confirmed by Sanger sequencing, which was performed for all available individuals. Sanger sequencing confirmed these variants to be homozygous or heterozygous in subjects presenting relapses and absent from the controls. The parents, who did not develop KA, were either wild-type homozygous or were heterozygous carriers. C, Functional predictions for the 2 AGMO mutations. D, Interspecies alignment with Clustal Omega, showing complete conservation of the Lys234 residue, down to invertebrates. With a GERP++ score > 2, this amino acid may be considered highly conserved. Abbreviations: AGMO, alkylglycerol monooxygenase gene; GERP, Genomic Evolutionary Rate Profiling; KA, kala-azar; WT, wild-type.

It has recently been shown that a common single-nucleotide polymorphism (rs916943, minor allele frequency = 0.08) within the AGMO gene is associated with susceptibility to pulmonary tuberculosis [START_REF] Grant | A genome-wide association study of pulmonary tuberculosis in Morocco[END_REF]. The macrophages are the sites of human infection, latency, and reactivation of Mycobacterium tuberculosis, and pulmonary tuberculosis results from reactivation of the original infection or a new infectious episode [START_REF] Casanova | Genetic dissection of immunity to mycobacteria: the human model[END_REF]. A previous report based on site-directed mutagenesis showed that several point mutations of human AGMO reduced the activity of the encoded enzyme [START_REF] Watschinger | Catalytic residues and a predicted structure of tetrahydrobiopterin-dependent alkylglycerol mono-oxygenase[END_REF]. In particular, the Asp233, Asn235, and Tyr236 mutations located in the region of the active site caused a total loss of alkylglycerol monooxygenase activity when mutated to alanine. Moreover, plasmids encoding proteins with N235A and Y236A mutations produced half the amount of protein generated from the wild-type allele [START_REF] Watschinger | Catalytic residues and a predicted structure of tetrahydrobiopterin-dependent alkylglycerol mono-oxygenase[END_REF]. Our K234R AGMO mutation is located in the region of the active site, close to these 3 deleterious mutations. Thus, this mutation, which UMD-Predictor predicted to be pathogenic, may also affect the amount of AGMO protein and its activity. Moreover, the second mutation, c.1213C > T, may induce a complete loss of AGMO function due to premature protein truncation or mRNA decay.

The AGMO gene has 13 coding exons and encodes a 445-amino acid protein (Ensembl Genome BrowserID: ENSG00000187546) composed of 9 transmembrane domains. AGMO is widely expressed in human cells, particularly hematopoietic cells, and is strongly expressed in the liver, the organ in which the highest enzymatic activities have been reported [START_REF] Watschinger | Alkylglycerol monooxygenase[END_REF]. It functions in macrophages, the principal cells in humans in which Leishmania resides. The macrophages of the spleen are the principal sites of parasite multiplication. They play critical roles in mediating resistance and susceptibility during Leishmania infection. After phagocytosis, the parasite can proliferate into the macrophages, whereas upon activation, the macrophages kill the parasite. AGMO modulates platelet-activating factor (PAF) production by mouse macrophages [START_REF] Tokuoka | Alkylglycerol monooxygenase as a potential modulator for PAF synthesis in macrophages[END_REF], leading to effects on vascular permeability, the oxidative burst, leukocyte chemotaxis, inflammation, and increases in arachidonic acid metabolism in phagocytes [START_REF] Ishii | Platelet-activating factor (PAF) receptor and genetically engineered PAF receptor mutant mice[END_REF]. PAF regulates the ability of macrophages to control Leishmania infection [START_REF] Lonardoni | Essential role of platelet-activating factor in control of Leishmania (Leishmania) amazonensis infection[END_REF]. The addition of PAF to mouse macrophages has been shown to inhibit parasite growth significantly and to induce nitric oxide production [START_REF] Lonardoni | Essential role of platelet-activating factor in control of Leishmania (Leishmania) amazonensis infection[END_REF]. Moreover platelet activating factor receptor (PAFR -/-) mice are more susceptible to infection with Leishmania than wild-type controls [START_REF] Santiago | Platelet activating factor receptor-deficient mice present delayed interferon-gamma upregulation and high susceptibility to Leishmania amazonensis infection[END_REF]. The mechanisms by which AGMO causes relapse is unknown, but it may act through the PAF/PAF receptor pathway, causing a dysfunction in macrophage activation. PAF has a similar structure to miltefosine, a drug used to treat visceral leishmaniasis [START_REF] Das | Effectiveness of miltefosine treatment in targeting anti-leishmanial HO-1/Nrf-2-mediated oxidative responses in visceral leishmaniasis patients[END_REF] that induces the killing of intracellular Leishmania [START_REF] Gangalum | Platelet-activating factor receptor contributes to antileishmanial function of miltefosine[END_REF][START_REF] Wadhone | Miltefosine promotes IFN-gamma-dominated anti-leishmanial immune response[END_REF]. Miltefosine impairs parasite phospholipid synthesis [START_REF] Berkovic | Effects of hexadecylphosphocholine on membrane phospholipid metabolism in human tumour cells[END_REF][START_REF] Croft | Miltefosine-discovery of the antileishmanial activity of phospholipid derivatives[END_REF] and has immunomodulatory effects, promoting macrophage activation [START_REF] Hilgard | Investigation into the immunological effects of miltefosine, a new anticancer agent under development[END_REF][START_REF] Eue | Hexadecylphosphocholine selectively upregulates expression of intracellular adhesion molecule-1 and class I major histocompatibility complex antigen in human monocytes[END_REF]. The PAF receptor has been shown to contribute to the anti-Leishmania effects of miltefosine [START_REF] Gangalum | Platelet-activating factor receptor contributes to antileishmanial function of miltefosine[END_REF], and PAF receptor-deficient macrophages display lower levels of miltefosine-induced killing of L. donovani. Further functional studies may be useful to confirm the molecular mechanisms involving AGMO in relapses. However, we were unable to perform such studies for these patients because we had no access to cells from these individuals.

Overall, our results show that homozygous and heterozygous AGMO mutations in humans are associated with KA relapse. We suggest that AGMO deficiency involves haploinsufficiency with incomplete penetrance. AGMO mutations may exert their deleterious effects through the PAF/PAF receptor pathway, which plays an important role in the protective response of macrophages to Leishmania. For the first time, we have shown that the relapses of KA are, at least in part, the consequence of rare mutations in humans. It is an important finding that demonstrated that relapses can be due to host genetic factors rather than parasite virulence factors.

  loss or stop gain, splice-site mutations: UMD-Predictor: pathogenic or probably pathogenic: Not present in the homozygous state in any of the controls: Not present in the heterozygous state in any of the controls:

Figure 1 .

 1 Figure 1.Flowchart showing the WES variant filtering strategies used. The numbers indicated at each step indicate the number of variants remaining after the filter employed at that step. We selected homozygous and heterozygous variants common to at least 50% of individuals presenting KA relapse. We selected rare variants with a MAF <0.01 in 1000 Genomes, the ExAC database, and 6500 Exome Sequencing Project. Rare nonsynonymous, stop-loss, or stop-gain variants and splice-site mutations with a probable pathogenic effect predicted by UMD-Predictor were retained. We excluded variants detected in the homozygous or heterozygous state in control individuals. This filtering strategy revealed 2 rare autosomal heterozygous or homozygous variants of the AGMO gene in 3 families. Abbreviations: AGMO, alkylglycerol monooxygenase gene; KA, kala-azar; MAF, minor allele frequency; WES, whole-exome sequencing.

Figure 2 .

 2 Figure 2. Characteristics and predictions for the AGMO mutations. A, Pedigrees of the 3 families with AGMO mutations. Individuals for whom exome sequencing was performed are indicated by asterisks (*). Affected individuals are homozygous or compound heterozygous for the 2 causal variants (except for individual 5 in family I). B,The identified AGMO variants were confirmed by Sanger sequencing, which was performed for all available individuals. Sanger sequencing confirmed these variants to be homozygous or heterozygous in subjects presenting relapses and absent from the controls. The parents, who did not develop KA, were either wild-type homozygous or were heterozygous carriers. C, Functional predictions for the 2 AGMO mutations. D, Interspecies alignment with Clustal Omega, showing complete conservation of the Lys234 residue, down to invertebrates. With a GERP++ score > 2, this amino acid may be considered highly conserved. Abbreviations: AGMO, alkylglycerol monooxygenase gene; GERP, Genomic Evolutionary Rate Profiling; KA, kala-azar; WT, wild-type.

Table 1 . Clinical Details of the Individuals With Relapses Subjected to Exome Sequencing

 1

		Family I		Family II		Family III		Family IV		Family V
	Subject, no.	5	6	3	4	2	3	5	6	4	5
	Sex	M	M	F	M	F	F	M	F	M	M
	Age at first KA	11	10	12	10	9	10	11	6	7	5
	Age at relapse I	12	12	13	12	10

Table 2 . Summary of Variants Detected by Exome Sequencing in Individuals With Relapses

 2

		Family I	Family II	Family III	Family IV	Family V
	Subject, no.	5	6	3	4	2	3	5	6	4	5
	No. variants	43 097	44 688	42 556	43 739	42 947	43 869	44 086	44 933	44 000	43 853
	No. variants with	6177	6351	4529	4455	6516	6919	5091	4904	4777	6768
	MAF <1%
	Coding and splicing	3853	4013	2572	2639	4122	4247	2909	2867	2740	4334
	nonSyn, stop-loss,	1558	1738	1112	1231	1791	1832	1248	1327	1264	1920
	stop-gain, splicing
	UMD-Predictor:	722	819	417	452	850	860	457	503	459	882
	Patho or PPatho
	Abbreviations: No., number; nonSyn, nonsynonymous; MAF, minor allele frequency; Patho, pathogenic; PPatho, probably pathogenic.


Delphine Lautier
email: delphine.lautier@dauphine.fr.

Franck Raynaud
email: franck.raynaud@unil.ch

Michel A Robe
email: mrobe@american.edu

Scott Mixon

Casey Petro

Jonathan Wallen

Information Flows across the Futures Term Structure: Evidence from Crude Oil Prices

Keywords: Mutual information, Market integration, Information flows, Shocks Propagation, Directed graphs, Term structure, Futures, WTI JEL Classification Codes: G10, G13, G14, Q49

We apply the concepts of mutual information and information flows and we built directed graphs to investigate empirically the propagation of price fluctuations across a futures term structure. We focus on price relationships for North American crude oil futures because this key market experienced several structural shocks between 2000 and 2014: financialization (starting in 2003), infrastructure limitations (in 2008-2011) and regulatory changes (in 2012-2014). We find large variations over time in the amount of information shared by contracts with di erent maturities. The mutual information increased substantially starting in 2004 but fell back sharply in 2012-2014. In the crude oil space, our findings point to a possible re-segmentation of the futures market by maturity in 2012-2014. This raises questions about the causes of market segmentation. In addition, although on average short-dated contracts (up to 6 months) emit more information than backdated ones, a dynamic analysis reveals that, after 2012, similar amounts of information flow backward as flow forward along the futures maturity curve. Moreover, the directions of the transfers between pairs of maturities become drastically di erent. This has implications for the Samuelson e ect.

Introduction

Commodity futures markets fulfill the key economic functions of allowing for hedging and price discovery. In these markets, two important questions arise.

First, are futures prices interconnected across the maturity curve? Theory suggests that they should be linked through the cost-of-carry relationship. In practice, however, such market integration requires cross-maturity arbitrage. Büyük ahin, Harris, Overdahl and [START_REF] Büyük Ahin | The Changing Structure of Energy Futures Markets[END_REF] document that even the three largest U.S. commodity futures markets did not witness substantial activity in longer-dated derivatives until 2003 (crude oil) or later (corn and natural gas). This empirical reality suggests the possibility of changes in cross-maturity informational linkages in the past decade.

Second, assuming that di erent-maturity futures prices are interconnected, where in the term structure do prices shocks originate, and which other parts of the term structure do they reach? Is the direction of the shocks' propagation stable over time? Theoretically, the physical market is the place for the absolute price to emerge as a function of the supply and demand for the underlying asset. In turn, the derivative market allows for relative pricing: futures prices derive from the spot price. Under normal circumstances, the prices shocks should thus spread from the underlying asset to the derivative instrument. Yet, amid a massive increase in far-dated commodity futures trading after 2003, might one not expect to also observe prices shocks spreading from the far end to the short (physical) end of the futures curve?

We apply concepts derived from the theory of information of [START_REF] Shannon | A Mathematical Theory of Communication[END_REF] and we built directed graphs to answer these questions empirically. The New York Mercantile Exchange's (Nymex) West Texas Intermediate (WTI) sweet crude oil futures market provides an ideal setting for our analysis. Among all commodity markets, the WTI futures market boasts the highest level of activity together with the greatest number of far-out delivery dates (up to seven years).

The theory of information, first proposed by [START_REF] Shannon | A Mathematical Theory of Communication[END_REF], aims at quantifying information. In this article, we associate information to unexpected futures prices' returns. Mutual information is a key concept in this context. Given that two variables are interdependent (as is the case, for example, for two times series of futures prices' return for two di erent maturities), the mutual information gives the amount of uncertainty that is reduced, compared to the case where the two variables are independent. The mutual information can thus be used as a proxy for market integration.

Compared with correlations, this probabilistic approach does not depend on any assumption on the variables under consideration. We find substantial variations over time in the amount of mutual information shared by futures contracts with di erent delivery dates. Intermediate-maturity contracts (6 months to 2 years) share relatively more mutual information than other contracts. For all contracts, cross-maturity integration increased dramatically after 2003 (amid tight oil supply conditions and the onset of commodity markets' financialization) but fell back sharply in 2012 (to pre-2005 levels) and fell further in 2013 and 2014 (to pre-2002 levels).Taken together, our term structure findings point to a possible re-segmentation of the futures market by maturity in [2012][2013][2014] To investigate the propagations of prices shocks, we then rely on the concept of transfer entropy.

Such measures allows for dynamic analyses and introduce directions. They allows to answer the following question: does a shock on the return of a given maturity • at time t create a shock at time t+1 on an another maturity? Directions are important to know whether prices shocks evolve from short-term to long-term maturities, or vice and versa. This idea is closely linked to the Granger causality, in a non parametric world.

On average across our 2000-2014 sample period, we find that the nearby contract sends more information than any other maturity and that short-dated contracts (maturities up to 6 months) emit more information than backdated ones -a pattern consistent with the typical functioning of futures market. A dynamic analysis, however, reveals that the amount of information flows originating in the far end of the curve increased as cross-maturity integration progressed. Nowadays, similar amounts of information flow from the near and far ends of the maturity curve but the directions of the shocks (from near-to far-dated contracts or vice-versa) is less stable.

Finally, using these non parametric measures in the framework of the graph theory gives us the possibility to sort among futures contracts, according to their maturity. A key reason underlying our choice of graph theory is that, insofar as all the futures prices that we are studying create a system, then this system is a complex one: it is made of many components that may interact in various ways through time. On any sample day year, after having discarded illiquid maturities, there remain 33 di erent delivery dates in the crude oil market, so we have 1056 pairs of maturities to examine after accounting for directionality. Moreover, such linkages may change through time as a result of evolving trading practices in the past 15 years. Finally, chances are few that the relationships between di erent maturities are always linear.

A graph gives a representation of pairwise relationships within a collection of discrete entities.

Each point of the graph constitutes a node (or vertex). In the present article, a node corresponds to the time series of prices returns of a futures contract for a given maturity. The links (or edges) of the graph can then be used in order to describe the relationships between the nodes. More precisely, the graph can be weighted in order to take into account the intensities and/or the directions of the connections. We do both on the basis of information theory.

There are several ways to enrich the information contained in a graph through its links. In finance, for example, the connections between the nodes can be related to the correlations of price returns or to the positions of market operators. Here, we rely on the theory of information in order to enrich the links of the graph in two ways: first, to determine the intensities of the links; second, to obtain their direction. To the best of our knowledge, such an application is unprecedented in studies of futures term structures and of commodity markets.

The use of the graph theory in this context allows us to examine precisely where the entropy is transferred in the prices system. Even more, we are able like to know whether or not a prices shock hitting the first-month maturity has a chance to propagate along the whole prices curve, up to the last maturity, or if is gradually amortized before reaching that point.

We show that on average on the period, the directed graphs support the conventional view of how a futures markets operates: specifically that prices shocks are thought to form in the physical market, here represented by the short maturities, and transmit to the paper market, here made up of further-out maturities. Moreover, transfers from the shortest maturities along the whole prices curve are far from negligible. The same is not true for shocks born in the far end extremity of the curve: they are amortized more rapidly. Finally, we underline that this behavior changes in the end of the period. These results have implications for Samuelson's (1965) hypothesis regarding the term structure of futures volatilities The paper proceeds as follows. Section 2 summarizes our contribution to the literature. Section 3 outlines our methodology, which is based on mutual information and transfer entropy. Section 4 presents the data and our empirical results. Section 5 concludes.

Literature

The present paper contributes to three literatures: on term structures and market segmentation, on causality, and on the use of graph theory in the context of financial markets.

The theoretical literature on the term structure of futures prices for commodities in general, and crude oil in particular, includes many distinguished contributions such as those of [START_REF] Schwartz | The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging[END_REF] [START_REF] Baker | The Financialization of Storable Commodities[END_REF]. The models proposed in those papers, however, do not deal with the possibility that market frictions may prevent di erent parts of the price curve from moving in sync. 1Questions related to the information contained in a term structure of prices and the possible implications of market imperfections for segmentation date back to the works of [START_REF] Culbertson | The Term Structure of Interest Rates[END_REF] and [START_REF] Modigliani | Innovations in Interest Rate Policy[END_REF] on "preferred habitats" in bond markets. Spurred in part by interest rate behaviors during the 2008-2011 financial crisis and the so-called Great Recession, the past ten years have seen a resurgence of theoretical and empirical work on segmentation. The latter is defined as a situation in which di erent parts of the price curve are disconnected from each other. [START_REF] Gürkaynak | Macroeconomics and the Term Structure[END_REF], who review this still-growing literature, conclude that "the preferred habitat approach (has) value, especially at times of unusual financial market turmoil" (p. 360). For example, D'Amico and King (2013) document the existence of a "local supply" e ect in the yield curve in 2009 during the U.S. Federal Reserve's unprecedented program to purchase $300 billion of U.S. Treasury securities.

Research on possible term structure segmentation in commodity futures markets deals almost exclusively with the crude oil market, which boasts the highest trading volumes and (in the United States) contract maturities extending up to seven years. In contrast to interest rate markets, prior work in the WTI futures space suggests that the Lehman crisis and its direct aftermath did not witness an increase in market segmentation. Granted, on the basis of the informational value of futures prices, Lautier (2005) finds cross-maturity segmentation during the 1990's. She argues, however, that this phenomenon had become less strong by the end of her sample period in 2002. Indeed, using recursive cointegration techniques, Büyük ahin et al. (2011) document that WTI cross-maturity linkages became statistically significant in 2003-2004 and remained so through at least May 2011 (the end of their sample period). 2 We complement this prior work in several ways: we quantify the information shared by different contracts according to their maturity, assess the direction of the information flows between maturities, and document how these measures have evolved through time. Our analysis, based on di erent techniques, confirms the prior finding of increasing market integration until 2011. We show, however, that when discussing market segmentation one must distinguish between forward vs. backward flows of information, as both types of flows are not equally impacted by segmentation. Furthermore, in sharp contrast to the cross-maturity integration that characterized the 2004-2011 period, we show that di erent parts of the WTI term structure became much less integrated in 2012-2014.

Insofar as it focuses on price relationships, the present paper belongs to a vast literature on prices linkages. If the spatial dimension of market integration has been analyzed in depth elsewhere for equities and currencies as well as for commodities, cross-maturity linkages have not. Other than the two articles discussed above, prior work on information flows in the crude oil market abstracts from term structure issues and investigates instead the relationship between spot and futures prices. 3 In that context, a central empirical question is whether price discovery takes place on the futures or the spot market [START_REF] Garbade | Price Movements and Price Discovery in Futures and Cash Markets[END_REF]. While early studies tend to rely on Granger causality to provide an answer, a number of papers apply other techniques in an attempt to tease out causality when the relationship between prices might be non-linear. 4 The methodological choices in the present paper are likewise motivated not only by concerns 2 Using a comprehensive, trader-level dataset of end-of-day futures positions and trader type, Büyük ahin et al.

document that this market development can be attributed to what has been dubbed the "financialization" of commodity markets (specifically, the increased market activity by commodity swap dealers, hedge funds and other financial traders). See Büyük ahin and Robe (2011[START_REF] Büyük Ahin | Speculators, Commodities and Cross-Market Linkages[END_REF] for further evidence regarding the financialization of energy (2011) and other (2014) commodity markets; see [START_REF] Cheng | The Financialization of Commodity Markets[END_REF] for a review of the financialization literature. 3 Kawamoto and Hamori (2011) are an exception. These authors look at WTI futures contracts with maturities up to nine months. Their focus, however, is on market e ciency and unbiasedness. 4 See, e.g., [START_REF] Silvapulle | The Relationship Between Spot and Futures Prices: Evidence from the Crude Oil Market[END_REF] This allows us to study all the possible connections between the di erent maturities of the North American crude oil market, in a non parametric world.

Methodology

In order to study the interdependence of, and the directionality of price movements for di erent futures contracts, we rely on the theory of information based on the notion of entropy proposed by [START_REF] Shannon | A Mathematical Theory of Communication[END_REF]. This Section first presents the concept of "mutual information" that quantifies the dependency between two random variables and that we use as a proxy for market integration. Unlike correlations, the mutual information measure captures non-linear relationships between variables; however, it does not allow for studying the propagation of information. On that purpose, we rely on measures of transfer entropy.

Mutual information

In what follows, we consider a time series of a futures prices' returns for a given maturity • as a discrete random variable R • with a probability distribution p(r • ). Before enlarging to a large scale study, we first want to study the interdependence of two series corresponding to the maturities • 1 and • 2 . This measure of the interdependence, also called "mutual information", rely on the use of several quantities: the "information entropy" of one variable, as well as the conditional and joint entropies of two variables. These di erent measures are linked to each others.

A first step is to consider the "information entropy" H(R • ) of the futures prices' return. This quantity captures the degree of uncertainty associated to the variable R • . In other words, it measures how much we ignore about the futures prices' returns for a given maturity. To illustrate this idea, let us omit temporarily the maturity dimension • and assume that we can observe all the possible values of the variable R: r 1 , r 2 , r 3 , ...r n . Let us denote by p(r i ) the probability that R is equal to r i :

P (R = r i ) = p(r i ).
If the probabilities associated with all realizations are such as p(r 1 ) = p(r 2 ) = p(r 3 ) = ... = p(r n ) = 1 n , then all realizations are equally likely and H(R) is maximum.

Formally, the information entropy H(R • ) is defined as:

H(R • ) = ≠r • ÿ p (r • ) log p(r • ) (1)
where q p is the sum over all the possible values of R • .Note that this quantity increases with the number of possible values for the random variable.

Next let us consider the case of two maturities • 1 and • 2 , and the interdependency between

R • 1 and R • 2 . Let us denote by p(r • 1 , r • 2 ) the joint probability distribution of the two variables. What remains unknown of R • 1 if the values of R • 2 are known is captured by the notion "conditional entropy", ie the entropy of R • 1 conditionally on R • 2 : H(R • 1 |R • 2 ) = ≠ ÿ r• 1 ,r• 2 p(r • 1 , r • 2 ) log p(r • 2 ) p(r • 1 , r • 2 ) (2)
Using the conditional probability distribution of the two variables p(r

• 1 |r • 2 )
, the conditional entropy can be rewritten:

H(R • 1 |R • 2 ) = ≠ ÿ r• 1 ,r• 2 p(r • 1 , r • 2 ) log p(r • 1 |r • 2 ) (3)
Another interesting quantity directly linked to the preceding one is the joint information en-

tropy H(R • 1 , R • 2 ).
It quantifies the amount of information revealed by evaluating R • 1 and R • 2 simultaneously. This symmetric measure is related to the conditional entropy as follows:

H(R • 1 , R • 2 )) = H(R • 1 |R • 2 )) + H(R • 2 )) = H(R • 2 |R • 1 )) + H(R • 1 ) = H(R • 2 |R • 1 )) (4)
On the basis of these definitions, it is now possible to express the mutual information

M (R • 2 , R • 1 )).
This quantity measures the amount of information obtained about one variable through the other.

Given that the two variables are interdependent, the mutual information gives the amount of uncertainty that is reduced, compared to the case where the two variables are independent. There are two (equivalent ways) to compute the mutual information

M (R • 2 , R • 1 )).
One possibility is to rely on equation 4:

M (R • 1 , R • 2 ) = H(R • 1 , R • 2 ) ≠ H(R • 1 |R • 2 ) ≠ H(R • 2 |R • 1 ) (5)
This expression shows intuitively that the mutual information is a symmetric quantity. Moreover, as a consequence of the properties of the joint entropy, it is equivalently possible to write:

M (R • 1 , R • 2 ) = H(R • 1 ) ≠ H(R • 1 |R • 2 ) = H(R • 1 ) + (H(R • 2 ) ≠ H(R • 1 , R • 2 ))
Relying on equations 1 and 2, another possible expression is:

M (R • 1 , R • 2 ) = ÿ r• 1 ,r• 2 p(r • 1 , r • 2 ) log p(r • 1 , r • 2 ) p(r • 1 )p(r • 2 ) (6)
In this article, we use the mutual information as a measure of the integration of the crude oil futures market in the maturity dimension. This quantity indeed includes synchronous correlations between pairs of futures prices' return, due to the common history of the returns, and/or to common shocks.

Compared with correlations however, this probabilistic approach does not rely on any assumption regarding the behavior of futures returns.

Transfer entropy

If we are now interested in the propagation of shocks along the futures prices curve, there is a need first for dynamic measures, second for directions. Dynamic measures aim to answer the question: does a shock on the return of a given maturity • at time t create a shock at time t + 1 on an another maturity? Directions are important to know whether prices shocks evolve from short-term to long-term maturities, or vice and versa. This idea is closely linked to the Granger causality, in a non parametric world.

Starting from information entropy, one natural way to proceed is to rely on the notion of transfer entropy [START_REF] Schreiber | Measuring Information Transfer[END_REF]. This measure quantifies how much information entropy (or uncertainty) is transported between dates t and t + 1 from one variable to another (in our case, from one futures maturity to another). It relies on transition probabilities rather than on static probabilities.

Relying on the definition of conditional entropy as described by equation

h(R • 1 ) = ≠ ÿ p(r t+1 • 1 , r t • 1 , r t • 2 ) log p(r t+1 • 1 |r t • 1 ) (7)
The entropy rate h(R

h(R • 1 |R • 2 ) = ≠ ÿ p(r t+1 • 1 , r t • 1 , r t • 2 ) log p(r t+1 • 1 |r t • 1 , r t • 2 ) (8)
Once these dynamic measures defined, it is possible to introduce directions in the analysis: the "transfer entropy" T from R • 2 to R • 1 is the di erence between the two rates:

T R• 2 aeR• 1 = h(R • 1 ) ≠ h(R • 1 |R • 2 ) = ÿ p(r t+1 • 1 , r t • 1 , r t • 2 ) log p(r t+1 • 1 |r t • 1 , r t • 2 ) p(r t+1 • 1 |r t • 1 ) (9)
Likewise, the transfer from R • 1 to R • 2 can be written as follows:

T R• 1 aeR• 2 = h(R • 2 ) ≠ h(R • 2 |R • 1 ) = ÿ p(r t+1 • 2 , r t • 1 , r t • 2 ) log p(r t+1 • 2 |r t • 1 , r t • 2 ) p(r t+1 • 2 |r t • 2 ) (10)
This transfer entropy measure is equivalent to Granger causality in the case of a linear dependency between two Gaussian random variables [START_REF] Barnett | Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables[END_REF]. Transfer entropy presents however the advantages of being model-free and of holding in the case of non-linearity.

Equipped with the above definitions, we are able to provide an insightful analysis of the propagation of prices shocks along the term structure, for all maturities and all directions. In what follows, we first present the data and the way they are manipulated. Then we present our empirical results.

Data

Our dataset consists of the daily settlement prices for Nymex's WTI light, sweet crude oil futures contracts from the 21 st of January 2000 to the 25 th of February 2014. We construct 33 time series of futures prices. The first 28 are for the 28 shortest-dated contract maturities (i.e., contracts with 1 to 28 months until expiration). The last five time series correspond, respectively, to contract maturities of 30, 36, 48, 60 or 72 months. Futures roll dates are calendar-based. 5 Our empirical analyses use daily futures returns. We compute daily futures returns as the logarithm of the price di erence:

r • = (ln F • (t) ≠ ln F • (t ≠ t)) / t, where F • (t)
is the price of the futures contract with maturity • at t and t is the time interval between consecutive sample days.

Figure 1 depicts the evolution of WTI futures prices and returns in our sample period. For readability, we focus on the nearby, one-and two-year contracts. The right panel of the figure

shows that the returns' volatility is lower for the two backdated contracts than for the nearby futures, an empirical fact consistent with the Samuleson (1965) hypothesis that volatility should increase as a futures contract's maturity nears. 6 Quite obvious in the left panel of Figure 1 period, Figure 1 shows that the one-year (two-year) futures prices did not move in sync with the nearby price prior to 2003 (2004) but started doing so soon thereafter. Figure 1 extends these prior empirical findings by showing that, starting in late 2011 and accelerating in 2012, a disconnect has reappeared between short-and further-dated WTI futures.

All dynamic analyses are made on the basis of rolling windows having a length of 500 trading days. 5 That is, we use the Nymex calendar to determine which contract has (for example) a one-vs. two-month maturity and when the first-deferred contract becomes the nearby contract. 6 We obtain the same volatility ranking with futures rolled based on the preponderance of the open interest rather than calendar dates. Bessembinder, Coughenour, Seguin and Monroe Smoller (1996) give an elegant theoretical analysis of conditions under which the Samuelson (1965) e ect holds, such as asset markets in which spot price changes include a temporary component (so that investors expect mean-reversion) or, alternatively, the assumption that information revelation about spot prices is systematically clustered around futures expiration dates (as in [START_REF] Anderson | The Time Pattern of Hedging and the Volatility of Futures Prices[END_REF]. For more recent analyses of the Samuelson e ect, see Jaeck and Lautier (2016).

Empirical Results

We present empirical evidence on the information shared by futures contracts of di erent maturities and its evolution through time. Next, we introduce directionality and examine information flows.

Finally, we study the stability of the directions of transfer entropy.

Mutual Information: A Proxy for Market Integration

Changes in the WTI market during the period under consideration can be characterized through the lens of mutual information. Recall the mutual information measure quantifies how much we know about the return R • 1 once the return R • 1 is known. In other words, this quantity captures the synchronous moves in prices. In what follows, we distinguish between the mutual information shared by all the futures contracts under consideration, and the mutual information attached to one specific maturity.

Mutual information shared by all maturities

On the basis of equation 6, that defines the mutual information for a pair of maturities

• 1 and • 2 ,
we can extend the analysis to the case of the average mutual information shared at date t by all T futures prices' returns, M T t :

M T t =< M t (R • i , R • j ) > i,i>j (11)
where i) T is the total number of maturities, ii) the M t (R • i , R • j ) are the elements of the (T ◊ T ) matrix of mutual information computed on day t using daily returns for the Two prior years (500 trading days), iii) <> i,i>j denotes the averaging operator over the relevant contract maturities i.

Figure 2 depicts the dynamic behavior of the mutual information shared by all maturities over the period. The high values of M T t between 2004 and the beginning of 2011 are evidence of strong cross-maturity linkages. 7 As an increase in M T t can be interpreted in terms of greater integration of the futures market for crude oil during that period, this finding complements the cointegration- 7 To provide a visual reference for the statistical significance of the measure, we generate a benchmark by "shu ing" (i.e., using permutations of) the time index of each analyzed dataset. The resulting "shu ed" time series have the same statistical properties (mean, variance and higher moments) as the original ones but temporal relationships are removed. The resulting benchmark (i.e., the "shu ed" mutual information) is plotted in red in Figure 2. Unlike the actual series (M T t , left-hand scale in black), the counterfactual (right-hand scale) is close to 0 and does not display any systematic pattern over time.

Mutual information for each contract maturity

Figure 3 gives more insight into the developments identified in Figure 2 by depicting the mutual information for each contract maturity over the course of our sample period. For each maturity • i and each day of the sample period t, the level of mutual information that a maturity shares with all others is as follows:

M t (R • i ) =< M t (R • i , R • j ) > j,j" =i
This measure is plotted in a color ranging from blue (very low) to green, yellow, orange or red (very high).

Figure 3 shows that, for all maturities, the mutual information is much higher in 2004 ≠ 2011 than at other times. Figure 3 also provides evidence that all futures prices do not have the same level of mutual information with the others. To wit, at each point in time, the graph "temperature"

is typically cooler at the short end of the term structure (situated on the top of the plot) than at the far end of the curve (on the bottom of the graph), showing that near-dated contracts usually contain less mutual information. This finding is consistent with the notion that short-dated crude oil futures prices are more volatile. 8 In contrast, there is a lot of mutual information for middle maturities: at any given time, the two extremities of the futures maturity curve share less mutual information with the others than the intermediate one. Overall, these results suggest that the WTI futures term structure consists of three main segments: from the first to the third months, from the 4th to the 30th months, and finally the furthest-out delivery dates (those beyond the 30th month). An important development took place in 2012 ≠ 2014, a period when the graph temperature becomes much cooler across the entire spectrum and is coolest for backdated contracts (those with maturities greater than three years). Figure 3 shows that the middle part of the maturity curve,

where the amount of mutual information is the highest, is also larger in 2004-2011 than before or after. In other words, Figure 3 establishes that the integration phenomenon observed in Figure 2 comes principally from what happens at intermediate maturities.

Figure 4 provides additional evidence of this fact by averaging, over the sample period, the information that a specific maturity shares with all others. Each point on the curve gives the average mutual information for each maturity. The bars around each point show the average variance of the measure over the sample period.

Figure 4 shows that the average mutual information is a hump-shaped function of contract maturity. It reaches its maximum near the 18 months maturity. Again, there is more mutual information at the back end of the curve (which we capture up to 6 years out) than at the front end (up to 3 months out). Whereas the shortest maturities are mostly influenced by shocks emerging in the physical market, the behavior of the longest maturities might be related to other factors such as expectations of future supply and demand for the commodity, technological changes, future discoveries, or possibly a lack of liquidity in the WTI futures markets. 9

Transfer entropy between maturities

A key component of the analysis of cross-maturity linkages is the examination of transfer entropy between di erent maturities. To answer the question of which side of the term structure is the shock transmitter and which one is the receiver, we first perform a static analysis across the whole sample period and then carry out a dynamic analysis using rolling windows of two years (500 trading days).

Static analysis: the average transfer entropy associated to each maturity

We start by computing the transfer entropy over the entire sample period. This approach gives us a picture of the "average" behavior of the system, i.e., if one maturity sends on average more than what it receives, and vice-versa. Starting from equation [START_REF] Büyük Ahin | Physical Markets, Paper Markets and the WTI-Brent Spread[END_REF], that focuses on the pairwise transfer between maturities • 1 and • 2 , we can extend this measure and compute the total amount of entropy sent, on average on the period, from the futures prices' return with maturity i to all other maturities j " = i:

T S R• i =< T R• i aeR• j > j,j" =i (12)
Similarly the quantity received on average by the maturity i from all others is:

T R R• i =< T R• i ΩR• j > j,j" =i (13)
where <> j,j" =i denotes the average over all the contract maturities other than i.

Figure 5 depicts the average transfer entropy associated to each maturity for our entire 2000-2014 sample period. The black line corresponds to the total amount of information entropy emitted by each maturity on average over the period, given by Equation 12; the red line shows the total amount of information entropy received by each contract on average over the period, computed using Equation 13. The bars represent, for each maturity, the average variance recorded for the measure; they are particularly large for the entropy received on the long-term maturities.

Figure 5 shows that maturities up to one and one half years (precisely up to and including the 19-month contract) emit more than they receive. Most of the information entropy is sent to 9 For a discussion of these likely explanatory factors, see e.g. Cortazar and Schwartz (2003).

the far-out maturities. Once contract maturities extend beyond 6 months, the information entropy emitted decreases with the maturity although the pattern levels o beyond the two-year mark. The information entropy received exhibits a di erent pattern: it is high for the first three maturities, lowest for maturities ranging from 6 to 18 months and highest for maturities of 27 months and beyond (with the maximum value reached at the back end of the term structure). Intuitively, these static results imply that market participants whose "preferred habitat" [START_REF] Modigliani | Innovations in Interest Rate Policy[END_REF] is the back end of the maturity curve are more likely to be the object of a shock than to be the source of one.

Dynamic analysis: forward and backward information flows

In what follows, we propose an analysis of the way the transfer entropy has changed over time. To link the analysis with the Samuelson e ect, we restrain our focus on two sub-sets of the transfer entropy. The later indeed measures the entropy emitted (received) by one maturity, whatever the direction of this emission (reception). If we want to have insight into prices shocks propagation and the direction of these propagations from the short to the long term (or vice and versa), then we want to restrain ourselves to what is emitted in one direction only, but from any maturity. To this end, we propose the notions of "forward" and "backward information flows".

The forward flow " f is the sum of the transfers of entropy from any maturity • i to all higher maturities • j :

" f = ÿ i<j T R• i aeR• j ( 14
)
Similarly the backward flow " b is given by the sum of the transfers of entropy from any maturity

• i to all smaller maturities • j :

" b = ÿ i>j T R• i aeR• j ( 15
)
In other words, the forward flows capture the propagation of shocks in the direction of the long-term maturities, whereas the backward flows measure the propagations in the direction of the short-term maturities. Thereafter, however, the amplitude of the two information flows is comparable. Put di erently, whereas in the beginning of our sample period, the term structure of futures prices was generally more prone to influence from shocks arising at the near end of the maturity curve, this is not true after 2010: the short-term prices (and, hence, physical prices) can be influenced by price fluctuations moving backward from far-dated contracts. In other words, the driving forces of price movements seem to have become comparable all along the term structure, and prices shocks nowadays propagate as easily in the forward direction as in the backward direction.

These findings raise questions regarding the Samuelson e ect. Samuelson (1965) hypothesized that futures prices volatility should increase as futures contracts approach their maturity. In theoretical models of the Samuelson e ect, such as [START_REF] Bessembinder | Is There a Term Structure of Futures Volatilities? Reevaluating the Samuelson Hypothesis[END_REF], the volatility of futures prices stems from shocks that arise in the physical market and are transmitted to the paper market.

The term structure of volatilities is therefore downward-sloping: the direction for the propagation of shocks is forward (i.e. from short to long-term maturities) with a progressive absorption as contract maturity increase. However, our empirical results show that, in the later part of our sample period, there are price shocks coming from the far end of the futures term structure that spread to shorter maturities (and hence, arguably, to the physical market). In other words, it is nowadays possible to have backward propagation of prices shocks from the far end of the prices curve to the physical market. This results strongly contrasts what is usually said about the Samuelson e ect in commodity markets. 10 To provide a visual benchmark for the statistical significance of the changes depicted by the red and black curves, we generate benchmark counterfactual forward and backward flow measures, " f,shuf f le and " b,shuf f le , by permutating ("shu ing") the time index of each analyzed dataset. The resulting time series have the same statistical properties (mean, variance and higher moments) as the original ones but temporal relationships are removed. The resulting information flows are shown in green (forward flow " f,shuf f le ) and blue (backward flow " b,shuf f le ). Unlike the actual forward and backward flows (depicted in black and red, respectively), the counterfactual information flows fluctuate very little. Crucially, "(t) f,shuf f le and "(t) b,shuf f le are almost equal for all t

Pair-wise analysis: the net transfer entropy between two maturities

The notion of transfer entropy shows that certain maturities send more than the others. As exhibited by Figure 5, this is the case, on average over the study period, for the first-month futures contract. To go further in this direction, it would be interesting to see precisely where the entropy is transferred. Even more, we would like to know whether or not a prices shock hitting the first-month maturity has a chance to propagate along the whole prices curve, up to the 72 th maturity, or if is gradually amortized before reaching that point.

In order to investigate such questions, we propose a pairwise analysis of the directions of prices shocks. The direction is determined by the net amount of entropy transported from one maturity to one other 11 . Such a pairwise study however requires the examination of 1056 links. This leads us to rely on the graph theory, that is especially suited for large scale analyses.

In what follows, we exploit the non parametric measures presented before in the framework of the graph theory. We first built a filtered directed graph that exhibits not only the directions of the pairwise transfer entropy, but also their strength. This filtered graph retains only the most important connections between maturities. We then analyze the direction of the net transfer entropy, expressed in percentage, maturity by maturity, in a static as well as in a dynamic way. Finally we assess the stability of the directions in the whole prices system.

The directionality index

A graph is defined by its nodes and links. Quite intuitively, we attribute one time series of futures prices' returns to each node of the graph (i.e., one node per maturity, with a total of 33 nodes).

In order to enrich the links of the graph with directions as well as with an information about the importance of the connection between two nodes, we construct an index of directionality D R• i R• j that combines equations ( 9) and (10):

D R• i R• j = T R• i aeR• j ≠ T R• j aeR• i T R• i aeR• j + T R• j aeR• i (16) D R• i R• j
gives first the direction between two nodes. It is bounded by ≠1 and 1.

When D R• i R• j
is greater than 0, the net transfer entropy is positive and the link is directed from

R • i to R • j ;
connection between the two returns. This expression first divides by two the dimensionality of the graph: we are left with 528 connections instead of 1056. Second, it allows for comparison between all contracts.

The filtered directed graph

We rely on this index to built a directed a graph. We first retain a static and full connected graph:

we compute the values of the index over the entire 2000 ≠ 2014 sample period and generate the

(T ◊ T ) matrix of directionality DR• i R• j .
Such graph, with its 528 connections, is however di cult to read. Hence we filter it according to the strength of the connection between to nodes. As depicted by Figure 7, we distinguish between four level of strength: directionality indexes lower than 0.3 are not exhibited; the black arrows stand for indexes between 0.3 and 0.4, the blue for the range 0.5 to 0.6, and the red for values between 0.6 and 0.7 (there are no values higher than 0.7 in our graph).

Let us come back to the question of the extent of shocks propagation raised by Figure 5. As depicted by Figure 7, shocks arising at the very short end of the curve, on the first-month maturity, go up to the far end extremity of the curve, on the 72 th maturity. More importantly, as illustrated by the red color of the link connecting the two nodes, such transfers are far from negligible on average on the period. The same is true for the 6th, 9th and 10th months. Conversily, what is received from the short-term maturities, as illustrated by maturities 1 to 3, does not come from far end maturities, and is not very strong. So it seems that forward shocks propagate themselves on the whole term structure, whereas backward shocks are amortized more rapidly.

More generally, this figure shows that on average over the period, the far-out maturities, which for readability we have positioned at the center of the graph, are those to which the links point.

The most important nodes, in terms of information received, are the 48th and 60th. So this filtered graph provides us with a reference case, not only in that it represents what happens over the entire sample period but also in that it appears to support the conventional view of how a futures markets operates (specifically that prices shocks are thought to form in the physical market, here represented by the short maturities, and transmit to the paper market, here made up of further-out maturities).

Outgoing links associated to each maturity

The directionality index also allows for dynamic analyses. On the basis of on one-year rolling windows, we compute, at each date t, the instantaneous directionality matrix D R• i R• j (t). This allows to built daily directed graphs, to examine their properties and their evolution over time.

Figure 8 exhibits the relative proportion, for each maturity, of outgoing and ongoing links, on average and on the sample period. It shows, for example, that approximately 60% of the links attached to the one-month maturity are outgoing links (40% are ongoing). The same observation can be done for the six-months maturity. However, the dispersion around this average, measured through the variance, is strong for the first month maturity, and low for the six-months;

More generally, this analysis shows that: i) the proportion of outgoing links is a decreasing function of the maturities; ii) the first 18 maturities are characterized by a proportion of outgoing links that is higher than 50%. This figure is stable, except for the three first maturities; iii) in contrast, the deferred maturities are characterized by a large proportion of ongoing links (up to 80% on average on the sample for certain ones), with quite large deviations around the average. This result is consistent with the conventional view of the functioning of a futures market, as with the conclusions drawn through Figures 5 and7. Up to now however, the specific behavior of the one-, two-and three-month maturities was not observable.

Stability and survival ratios

A second point of interest regarding the properties of daily directed graphs is their stability: do the directions in the graph evolve during the period? How? To answer these questions, we rely on the reference case: the static full directed graph built on the basis of the matrix of directionality

DR• i R• j .
We then compare the directions of the links in the reference case and in the daily directed graphs.

In order to give evidence of the distance between the static and the daily graph, we compute survival ratios, ratio SR (t), as follows:

SR (t) = 1 N D R• i R• j (t) fl DR• i R• j ( 17
)
This ratio quantifies the similarities in the two directionality matrices, and express them as a percentage of the total number of elements. If SR (t) = 1, the two matrices are identical, the two graphs are the same. At the other extreme, if SR (t) = 0, then the set of directed links is totally di erent.

Figure 9 shows that, from 2000 until the end of 2010 and with the exception of a six-month period at the end of 2005, the survival ratio is generally higher than 70%. This results indicates that during this period, day after days, most of the directed links remained in the same state as in the benchmark case. Thereafter, the ratio displays some variations but generally decreases, sometimes up to 30%-a finding suggesting a profound change in the pattern of shocks propagation in recent years.

Conclusion

We apply the notions of mutual information and transfer entropy to empirically investigate the nature of price relationships across a futures term structure. The Nymex's WTI crude oil futures market, a large market that experienced a number of participatory and regulatory changes between

• = (ln F • (t) ≠ ln F • (t ≠ t)) / t,
where F • (t) is the price of the futures contract with maturity • at time t and t is the time interval between two consecutive sample days.

0 1 -2 0 0 2 0 1 -2 0 0 4 0 1 -2 0 0 6 0 1 -2 0 0 8 0 1 -2 0 1 0 0 1 -2 0 1 2 0 1 -2 0 1 4 Time 0,7 0,8 0,9 1 1,1 1,2 M
T t =< M t (R • i , R • j ) > i,i>j where the M t (R • i , R • j )
are the elements of the (T ◊ T ) matrix of mutual information computed on day t using daily returns for the prior two years (500 trading days) and <> i,i>j denotes the averaging operator over the relevant contract maturities i. The increase of M T from 2004 until the end of 2010 shows that cross-maturity linkages are becoming more and more intense and can be interpreted as a higher integration of the futures market for crude oil. To provide a visual reference for the statistical significance of the changes depicted by the black curve, we generate a benchmark by "shu ing" (i.e., using permutations of) the time index of each analyzed dataset. The resulting "shu ed" time series have the same statistical properties (mean, variance and higher moments) as the original ones but temporal relationships are removed. The resulting benchmark (i.e., the "shu ed" mutual information) is plotted in red. Unlike the actual series (M T t , left-hand scale in black), the counterfactual (right-hand scale in red) is close to 0 and does not display any systematic pattern over time. Note: Figure 5 depicts the average transfer entropy associated to each maturity for our entire 2000-2014 sample period. The black line corresponds to the total amount of information entropy emitted by each maturity on average over the period, given by Equation 12; the red line shows the total amount of information entropy received by each contract on average over the period, computed using Equation 13. The bars represent, for each maturity, the variance recorded for the measure. Note: Figure 6 illustrates what is emitted, daily, by all maturities in the direction of longer maturities (forward flows " f , black curve) and what is received by all of them from shorter maturities (backward flows " b , red curve). On each day from February 2002 to February 2014, we compute the values of " f and " b applying, respectively, Equations 14 or 15 to daily futures returns for the prior year ( 500 trading days). To provide a visual benchmark for the statistical significance of the changes depicted by the red and black curves, we generate two benchmarks, " f,shuf f le and " b,shuf f le , by "shu ing" (i.e., using permutations of) the time index of each analyzed dataset. The resulting "shu ed" time series have the same statistical properties (mean, variance and higher moments) as the original ones but temporal relationships are removed. The resulting benchmarks (i.e., the "shu ed" information flows) are plotted in green (forward flow " f,shuf f le ) and blue (backward flow " b,shuf f le ). Unlike the actual forward and backward flows, the counterfactual flows fluctuate very little and are very close. Note: Figure 7 presents the filtered directed graph extracted from the directionality matrix DR• i R• j computed in the static case (i.e., for the entire 2000 ≠ 2014 sample period). The graph's links are oriented according to DR• i R• j , which measures the strength of the net transfer entropy: for a couple of nodes (R • i , R • j ), if the transfer entropy T R• i aeR• j is greater than T R• j aeR• i , then the edge is oriented from maturity • i to maturity • j , otherwise from • j to • i . The graph is filtered: only directionality indexes higher that 0.3 are retained. Besides, the color of the links indicates intensity with colors ranging from black (directionality index between 0.3 and 0.4), to green (0.4 to 0.5), to blue (0.5 to 0.6) to red (0.6 to 0.7). Note: Figure 9 provides insight into the distance between the static directed graph, used as a reference, and daily directed graphs, by plotting the survival ratio SR (t). We measure SR (t) as the number of element of same sign in 1

N D R• 1 R• 2 (t) fl DR• 1 R• 2 .
On each day t from February 2001 to February 2014, the values are computed using daily returns from the prior year (N = 500 trading days). At one extreme, if SR (t) = 1, then the two graphs are identical, the pattern of shocks propagation has remained stable. At the other extreme, if SR (t) = 0, then the set of directed links has been completely rearranged.

  , Routledge, Seppi and Spatt (2000), Casassus and Collin-Dufresne (2005), Casassus, Collin-Dufresne and Routledge (2007), Carlson, Khokher and Titman (2007), Kogan, Livdan and Yaron (2009), Liu and Tang (2010) and

  are the sharp oil price rise in 2007-2008 and the consequent precipitous price decrease after August 2008. Equally notable, and especially relevant to the present study, is the di erence in the relative behaviors of nearby vs. longer-dated contracts at the beginning (before 2004) and at the end (2012-2014) of our sample. As previously documented in Lautier (2005) for pre-2002 data and Büyük ahin et al. (2011) for the May 2000 to May 2011

  based study of this phenomemon by Büyük ahin et al.(2011).Figure 2, however, also shows that the mutual information M T t decreases sharply after 2011 and drops further, to a very low level, in 2013-2014. This finding is novel. It provides formal support for our interpretation of Figure 1 in the previous subsection: starting in 2012, di erent parts of the term structure of WTI futures prices have become much less integrated. This apparent re-segmentation of the WTI market across futures delivery dates follows a partial geographic segmentation of world crude oil markets after the Summer of 2008 as evidenced by the emergence of a large di erential between the prices of North American (WTI) and world (Brent) benchmark crudes. This large Brent-WTI price di erential has been linked by Fattouh (2010), Pirrong (2010) and Büyük ahin et al. (2013) to two developments in the physical market for crude oil: infrastructure constraints at the delivery point for WTI futures in Cushing, OK, and a divergence in supply-side conditions in North America vs. the rest of the world. In contrast, rather than physical-oil market fundamentals, Büyük ahin et al. (2011) show that the WTI futures market's cross-maturity integration in 2004-2011 stemmed from a large increase in (cross-maturity) spread trading by hedge funds and other financial institutions amid what has been dubbed the "financialization of commodities." Intriguingly, the 2012-2014 re-segmentation apparent in Figure 2 itself has been taking place amid a massive growth in North American oil production, export restrictions and transportation constraints, as well as new derivatives regulations in the United States. Interdependency, though, need not imply causation. Our findings therefore raise the important question of the respective roles played by fundamentals vs. trading activity and (dis)incentives in the WTI market's re-segmentation.

Figures 6

 6 Figures 6 exhibits the forward and backward flows on each day from February 2002 to February 2014. The values of " f and " b are computed using daily futures returns for the prior two years (500 trading days). This figure highlights big changes. Both forward and backward flows decrease

February 2000 and

 2000 February 2014, provides an ideal setting for our analysis. We find substantial variations over time in the amount of information shared by futures with di erent delivery dates. The common share increased dramatically starting in 2004 (amid tight oil supply conditions and the onset of commodity markets' financialization) but fell back sharply in 2012 (to pre-2005 levels) and fell further in 2013 and 2014 (to pre-2002 levels). On average over the entire sample period, short-dated contracts (maturities up to 3 months) emit more information than longer-dated ones. While this pattern seems consistent with the typical functioning of futures market, a dynamic analysis using rolling windows reveals that the information flows originating at the back end of the maturity curve have increased over time. Nowadays, similar amounts of information flow from both ends of the curve. Notably, the directionality of information flows (from near-to far-dated contracts or vice-versa) is less stable after 2005. These results suggest two natural venues for further research.First, our term structure findings raise a theoretical question regarding the Samuelson(1965) hypothesis that a futures contract price's volatility should be inversely related with the contract's time to maturity. A theoretical model is needed to determine whether physical fundamentals or paper market conditions may be responsible for such a pattern of information flows in a term structure.Second, our analysis establishes that the WTI market was segmented until 2003, integrated between 2004 and 2011, and segmented once more in 2012-2014. Questions regarding the possible presence of a market segmentation a ecting di erent parts of a term structure date back to[START_REF] Modigliani | Innovations in Interest Rate Policy[END_REF]. In the present paper we document, that the WTI market has since 2011 once again become segmented -a calamity for market participants who use backdated futures to hedge long-term price risk. The analysis of Büyük ahin et al.(2011) suggests that the unprecedented WTI market integration across the term structure in 2003-2011 was due to a combination of tight oil supply conditions and the onset of commodity markets' financialization. One therefore wonders if, in a similar vein, physical-market developments or a pullback by financial institutions from participating at the far end of the WTI futures term structure explains the apparent post-2011 re-segmentation of the market. Answering this question requires access to non-public trader-level trading data: we therefore leave it for further research.

Figure 1 :

 1 Figure 1: WTI crude oil futures prices and returns, 2000-2014

Figure 2 :

 2 Figure 2: Average mutual information M T t shared at date t by all maturities, 2000-2014

Figure 3 :

 3 Figure 3: Mutual information shared at date t by each contract with all others, 2000-2014

1 AFigure 4 :Figure 5 :

 145 Figure 4: Mutual information shared by one maturity with all others averaged over the period, 2000-2014 Note: Figure 4 shows the average A, computed over the entire 2000-2014 sample period, of the mutual information that a specific maturity shares with all others. Each point on the curve gives the average mutual information for each maturity. The bars around each point show the average variance of the measure over the whole sample period.

Figure 6 :

 6 Figure 6: Daily forward and backward information flows between maturities, 2000-2014

Figure 7 :

 7 Figure 7: Pair-wise analysis -filtered directed graph, benchmark case, 2000-2014

Figure 8 :

 8 Figure 8: Mean and variance of outflows, static analysis

Figure 9 :

 9 Figure 9: Survival ratios

  3, and introducing time in the analysis allows for defining a new quantity: the entropy rate h. Two kind of rates can be distinguished, according to the type of dependance under consideration. The entropy rate h(R • 1 ) quantifies the uncertainty on the next value of R • 1 , if only the previous state of R • 1 matters:

  • 1 |R • 2 ) quantifies the uncertainty on the next value of R • 1 , if both the previous states of R • 1 and R • 2 have an influence:

A di erent part of the literature on commodity price formation analyzes the role of spot markets in revealing trader information. That body of work comprises theoretical work by[START_REF] Stein | Informational Externalities and Welfare-reducing Speculation[END_REF] and Smith, Thompson and Lee (2014), as well as empirical work by Ederington, Fernando, Holland and Lee in the specific case of crude oil. We focus instead on information flows across the futures term structure. Those papers highlight the role played by inventories. Our paper instead contributes to the literature investigating the extent to which, or the potential mechanisms through which, information travels within futures markets.

See, e.g.,Robe and Wallen (2014) for evidence on the term structure of WTI implied volatilities in 2000-2014.

Figure 5 shows that the first month futures contracts sends a lot; but it receives also a large amount.

comments on an early draft. Thanks also go to the participants at the seminar at the Department of Energy (December 2016), and to Gautier Boucher and Pierre-Alain Reigneron for research assistance. Lautier and Raynaud gratefully acknowledge support from the Chair Finance and Sustainable Development and the FIME Research Initiative. Robe contributed to this project during a period when he was also doing consulting work for the U.S. Department of Energy (DOE) and for the U.S. Commodity Futures Trading Commission (CFTC). No compensation was received from, and no resources were used at, either the DOE or the CFTC for this project.