Gabriel Facal

Religious Specificities in the Early Sultanate of Banten (Western Java, Indonesia)

Keywords: Islam, Banten, sultanate, initiation, commerce, cosmopolitism, brotherhoods

This article examines the religious specificities of Banten during the early Islamizing of the region. The main characteristics of this process reside in a link between commerce and Muslim networks, a strong cosmopolitism, a variety of the Islam practices, the large number of brotherhoods' followers and the popularity of esoteric practices. These specificities implicate that the Islamizing of the region was very progressive within period of time and the processes of conversion also generated inter-influence with local religious practices and cosmologies.

As a consequence, the widespread assertion that Banten is a bastion of religious orthodoxy and the image the region suffers today as hosting bases of rigorist movements may be nuanced by the variety of the forms that Islam took through history. The dominant mediacentered perspective also eludes the fact that cohabitation between religion and ritual initiation still composes the authority structure. This article aims to contribute to the knowledge of this phenomenon.

Banten is well-known by historians to have been, during the Dutch colonial period at the XIX th century, a region where the observance of religious duties, like charity (zakat) and the pilgrimage to Mecca (hajj), was stronger than elsewhere in Java 1 . In the Indonesian popular vision, it is also considered to have been a stronghold against the Dutch occupation, and the Bantenese have the reputation to be rougher than their neighbors, that is the Sundanese. This image is mainly linked to the extended practice of local martial arts (penca) and invulnerability (debus) which are widespread and still transmitted in a number of Islamic boarding schools (pesantren). Indeed, those ones concern almost fifty percent of the pupils registered in the educative institutions, which figure is particularly large, compared with the other Indonesian regions. As a matter of fact, the heads of martial arts schools (jawara) and the leaders of pesantren (ulama and kiai) play a prior role in Banten society.

A number of Bantenese consider that jawara and kiai have collaborated as representatives of authority since at least the XIX th century. Jawara benefited from kiai's esoteric knowledge and skills (ngelmu) and kiai used jawara's protection and service to organize and rule the locality [START_REF] Kartodirdjo | The Peasants Revolt of Banten in 1888[END_REF] . Although this singular vision is partly oriented by some politicians to favor cultural management, it is built on concrete basis, as it is shown by the fact that both jawara and kiai have been of main concerns for the successive central governments since the independence of Indonesia 3 . On another way, the political orientation of the Islamic religious discourse is also led by some formal religious leaders involved into political collaborations at both the regional and national levels [START_REF] Van Treche | Réseaux d'influence et politique locale en Indonésie. Les « hommes forts » de l'organisation Pendekar Banten[END_REF] . The slaughter of Ahmadiyah's members in 2011 in Cikeusik (South Banten) also influenced to the image of a regional rigorist practice of Islam.

However, these recent evolutions might be put in balance with the long history of the Islam's spreading in the region. Indeed, a diachronic perspective underlines that, during the early Islamizing, far from a unilateral ideological expansion, it is economic development and the integration of the merchants into international networks of commerce that constituted some of the main reasons of the success of Islam in Banten. As the historian Romain Bertrand underlined it in his recent study dedicated to the early contacts of the Archipelago with foreigners: "Islam did not arrive in Insulindia through a conquest way but through commerce's one" (« L'islam n'était en effet pas arrivé en Insulinde par voie de conquête mais de commerce ») [START_REF] Bertrand | L'Histoire à parts égales. Récits d'une rencontre Orient-Occident (XVI e -XVII e siècles)[END_REF] . The Muslim religion was integrated as a doctrine far later, when the sovereignty of the sultan and the religious officiates was threatened by colonial occupation.

Promiscuity between Islam and commerce as well as the strong religious and cultural influences that inflected on Banten far before the arriving of Islam influenced the long and slow process of the Muslim religion's integration into the local society [START_REF] Atsushi | intensively discussed the establishment of the kingdom and the rulers' attempts to reconcile with local Hindu traditions[END_REF] , starting with the northern coast and spreading progressively in the inlands to the South. We have to add that it was not a homogeneous movement of Islamizing but the progressive integration of several religious influences from diverse origins. It produced locally contrasted practices, which common point is probably a strong flexibility for interaction [START_REF]Romain Bertrand describes the plural and « mystic » dimension of the Islam which penetrated Banten[END_REF] .

The Islamizing of Banten: merchant networks and cosmopolitism

As soon as the VIII th century, the Muslim merchants of South China traveled across the maritime Silk Road through the straits of Malacca and Sunda. But the first Muslim States did not appear in the Malay world before the XIII th century, with the small Samudra-Pasai sultanate. The Muslim epigraphic studies indicate that the first Islamized regions were the Malay Peninsula and the East of Java (Gresik, Giri and Surabaya regions) [START_REF] Paterson | An Early Malay Inscription from Trengganu[END_REF] . Then, the Islamizing continued progressively until the West of Java, including Cirebon and Banten.

At this period, Islam, which brought an individualist conception of the social relations as well as the protection notion of interests through contract, tantalized the merchant spheres, the rulers and ruling classes of the Archipelago harbor cities to convert and integrate the Muslim networks 9 . Moreover, a number of the foreign merchants were linked to Sufi brotherhoods, which could easily integrate the local religious conceptions. The threat represented by Portuguese expansionism also favored the emergence of a common consciousness between the Muslim rulers 10 .

Those first generation Muslim States were constituted by a population of diverse origins, which used Malay as vehicular language. Malay spread synchronically with Islam in the harbors of the Archipelago. Those harbor States were centered on international commerce and only possessed few agricultural land. It were the property of Hindu-Buddhist kings who ruled upstream of the royal lands and had implemented the "Rule of upstream and downstream". This rule enabled the Muslim princes to commerce in the downstream coastal areas while staying under the federative rule of the Hindu-Buddhist dynasts. The sultanates spread in the XVI th century, with the Javanese kingdoms of Demak, Banten, Cirebon and Pajang in Sumatra (respectively founded in 1518, 1524, 1527 and 1568). The Javanese traditions that relate the Archipelago's Islamizing notably focus on the figure of a harbor chief or any pious figure from overseas that is reputed for having spread the new religion thanks to his virtues, his teachings or the miracles he has ever accomplished. Then, the local oral traditions gave to those more or less legendary heroes the title of "master" (guru) or "saint" (sunan, contraction of susuhunan: "which is carried on the head").

It is the case of Banten sultanate, which one was, according to the tradition, founded by Nurullah, better known by the Javanese sources under the name of Sunan Gunung Jati 11 .

He would have born in the late XV th century in Pasai, in North Sumatra. At the beginning of the 1520, when the Portuguese installed in Pasai, Sunan Gunung Jati would have gone to Mecca to deepen his religious learning. He is also told to have become an initiate in Medina in the Naqshabandiyah, Shattariyah and Shadiliyah brotherhoods.

When he came back to the Archipelago he married one of the sisters of the king Trenggana (1504-1546) in Demak [START_REF] Jati | 's wife was a Chinese from Cham and he originated from a North Chinese dynasty[END_REF] . There, he imposed himself in the political arena and with his son Hasanuddin he received the main task to lead a military expedition to conquer Banten harbor and the capital of Banten Girang. In their conquest, Gunung Jati and Hasanuddin got favor from Ki Jongjo, one of the main civil officers of the city, who was originated from China and had converted to Islam [START_REF] Jongjo | La principauté de Banten Girang[END_REF] . It is said that they began a journey to spread Islam across Banten, notably by forming Muslim bases against the Portuguese crusades.

They firstly visited places considered as sacred, because they wanted to conquer the country spiritually before than military. They would have meditated on the mounts Karang, Aseupan and Pulosari, where Pucuk Umun, the last ruler of Banten Girang kingdom would previously used to practice asceticism. They would have converted eight hundreds hermits (ajar) and during this spiritual retreat Gunung Jati initiated his son to a number of Islamic esoteric knowledge [START_REF] Djadjadiningrat | Tinjauan kritis sejarah Banten [Critical observation of Banten's history[END_REF] . Soon after he had successfully achieved all the religious concerns, he came back to North Banten to hold political functions, and gave his son the task of Islamizing the South of the region. The religion preached by Sunan Gunung Jati and his son was distinct from the early religion that had previously been developed in the region. Indeed, the first Muslims with whom the Bantenese were in contact were from Chinese descent, whereas the sunan brought an Islam originate from Arabia, which implicated a change of juridical school, with a passage from Hanafism to Chafiism. Sunan Gunung Jati ruled the power in Banten until 1552, then transferring the sovereignty to Hasanuddin. Himself installed in Cirebon, located at the border of the two politico-cultural areas of the island (the Javanese and Sundanese regions), to transform this city into a Muslim center. He died around 1570 and let as a successor Pangeran Ratu [START_REF] Graaf | De eerste moslimse vonsterdommen op Java[END_REF] . The sultanate lived his golden era under the reign of Sultan Ageng Tirtayasa (1650-1682), who stimulated the commerce and led great irrigation works 16 . The sultanate controlled a part of West Java and of what constitutes nowadays the province of Lampung, in South Sumatra. It played a major role in the Islamizing of Palembang and Bengkulu [START_REF] Cf | The Sultanate of Banten[END_REF] . At the XVII th century, Banten was a flourishing State, notably thanked to his strategic position as a merchant crossroads in the Archipelago. Among the multiple societies that were attracted by this position, the Chinese merchants were the more numerous.

The Great Banten's mosque, the regional religious centre (Serang, 2008)

The influence of the sea-cross Muslim Chinese

By their customs, believes and techniques, the overseas Chinese merchants durably marked the different coastal areas of Southeast Asia and the South sea. In Java and more particularly in Banten, they were the first to open plantations and mines [START_REF] Blussé | XVI th and XVII th centuries in Banten[END_REF] . By introducing new agricultural techniques, they played a major role in the production of rice for the city consumption. They cultivated groundnuts and indigo, monopolized the sugar cane alcohol and immediately developed a transformation crafts, where each plantation was linked to a factory which elaborated the finished product designed to be exported to China or Europe. They valorized new lands and dealt with the pepper commerce, cultivated in the backcountry and designed to exportation. Moreover, they imported an important number of plants as soya, tobacco, corn, tea, and they brought numerous innovations in the field of botany 19 .

Developing a type of agriculture where tools and animal force played a major role, they also imported metal and forging techniques 20 .

More importantly, at the XVII th century, the Javanized Chinese hold the sultanate secretary, played a role of intermediaries and occupied the functions of harbor chiefs (syahbandar), who were also the dignitaries in charge of the foreign merchants. They developed commerce associations, which functioned as insurance companies and banks by providing capitals for their members' business. In the years 1660, Kaytsu, the minister of commerce, managed the construction of a shipping float based on the European model to guarantee the competitiveness of Bantenese merchants [START_REF] Cf | Banten in times of revolution[END_REF] .

In the XVI th century, it is established that a Chinese neighborhood existed in Banten. It constituted a real city in the city; it possessed a market protected by an autonomous rampart and its own mosque, the Pacinan Tinggi of Banten Lama, which is nowadays one of the oldest Banten's mosques' minarets. The Chinese Banten communityas elsewhere in Javahas been strongly marked by the indigenous influences and a number of Chinese Muslims had Malay and Javanese titles. This influence was reciprocal, at the economic, religious, cultural and linguistic levels. Thus, in Banten language (basa Banten), we find numerous linguistic borrowings from the South China languages, which vocabularies have mainly been orally transmitted 22 .

The cultural inflexions were particularly strong concerning the ideals of the penca martial art. It prevails until today and the historian Denys Lombard has shown that the Chinese heterodoxy still inspires the ideology of the comics and novels that can be found in almost every local library. It conveyed values of independence, self-confidence, social rupture and secret quest 23 . Moreover, the historical sources show that in 1619, a number of the Chinese sent from Banten to build and populate Batavia city were sentinels or soldiers 24 . They practiced the Chinese martial art kuntao and deeply marked the local fighting techniques [START_REF] Cf | Pencak Silat in the Indonesian Archipelago[END_REF] .

The different influences notably originated from a Taoist China (rather than Confucius or mandarin's one) where the ancestors' cult prevailed, where a large place was provided to shamanism and where appeared the cult of historical semi-legendary heroes. The Chinese temples, which integrated local figures in their pantheon, functioned also for the surrounding population as spiritual and cultural points of bondage. The Chinese calendar gave rhythm to the festivities similar as the Muslim calendar did, and nowadays we still find influences in some barongsay (the local transposition of the Chinese lions) performances [START_REF] Cf | Survivance d'un rite bouddhique à Java: la cérémonie du Pu-du (Avalambana)[END_REF] , or in certain invulnerability practices as debus (notably in the practices of walking on fire). The influences were as important in the field of practices like medicine or mystic (kebatinan) as at the level of religion, as it is shown by the cult of the saints' practice.

Pacinan Tinggi minaret, minaret of one of the oldest Banten's mosques (Serang, 2010)

Cult of the saints and the reference to stranger descent

Differently from the historical studies which relate to the fact that Banten was conquered militarily, the popular Bantenese narratives argue that the Islamizing operated through persuasion and the demonstration that Islam permitted to realize miracles and to acquire supernatural powers superior to those obtained through other local religious practices.

It is also mentioned that to spread Islam Hasanuddin used a number of practices that were already popular, as cocks fighting or invulnerability performances. One of the local tales relates notably that Hasanuddin challenged the fighting cocks of the sovereign Prabu Pucuk Umun. This one created a cock of iron, steel and silver that he filled with a djinn, on the other side Hasanuddin created a cock of light (nur) that he filled with an angel. Hasanuddin's cock won the fight, forcing Pucuk Umun and his court to exile in the inlands of South Banten, where the legend tells that their descendants are nowadays known under the name of Baduy or Rawayan [START_REF] Cf | Tasbih dan golok [The rosary and the machete[END_REF] . This tale also reports that Gunung Jati and Hasanuddin could communicate between them through telepathy and that it is thanks to the esoteric practices kanuragan [START_REF]About this practice, notably in Central Java[END_REF] transmitted by his father that Hasanuddin was able to Islamize South Banten.

The mausoleums of the saints who Islamized Java date from this era. Political power and religious authority are still linked in Banten, and as a result the cult of the dead rulers in Java is generally associated in the popular mind to the cult of the saints [START_REF] Loir | On this question in other parts of the Malay world[END_REF] . As soon as the XVII th century, their sepultures attracted pilgrimages (ziarah) from the Banten's great rulers and nobility. In Java and Banten, saints are individuals who, through their gifts and the virtue of a spiritual development have accumulated supernatural forces, a power concentrated in their person and which is now held in their sepulture, designed by the generic term kramat (from the Arabic karamat: "miracle ") 30 . The Banten great mosque was in this way sanctified by the sacred tombs of the buried sultans and the city and his suburbs were also marked by a number of individual kramat, as Maulana Yusuf, Pangeran Mas or Pangeran Astapati's ones.

It is also in the XVII th century that was born the literature about the deliberations of the "Nine saints" (Wali Songo)' Council. They were religious men, partly legendary, and the early Java's Islamizing is attributed to them. Until today, this cult stands a particular place in Javanese Islam because the tombs are object to a strong individual and collective frequentation. In the first case, pilgrims visit these tombs for instance before a wedding, the seventh month of a pregnancy or for revelations gains. Some sites, as Banten Girang's one are elected by pilgrims to get the lottery numbers, to win political elections or to succeed in business negotiations. In the second case, the sites are collectively visited, for example during annual ceremonies of "villages purifications" (bersih desa) and for the Muslim new year (lebaran) 31 .

The great Javanese saints are almost all considered as being from stranger descent, often from Middle East, sometimes from Champa or China. As underlined by the historians Claude Guillot and Henri Chambert-Loir, in contrast to a number of other countries of the Muslim world, in Java there is almost no martyr saints and, at the contrary, those ones are considered as invincible. Another important point is that the brotherhood tarekat [START_REF] On | Kitab kuning : pesantren dan tarekat, tradisi-tradisi Islam di Indonesia [The yellow books: boarding schools and brotherhoods, the Islamic traditions in Indonesia[END_REF] do not play any role in the control of the saints' cult practice, even if certain saints are reputed to have been initiated into brotherhoods. Also, even today, some brotherhoods masters are considers as saints while their living, as Kiai Asnawi from Caringin, who in the first mid of the XX th century was the master of Qadiriyah in Banten.

Ki Amuk cannon (Banten Lama, 2012)

Initiation into brotherhoods and the legitimating of politico-religious authority

In the first centuries of his implantation, Islam in Bantenas in the rest of Indonesiawas more dominated by mystic and metaphysic speculation than by the Muslim law (sharia) or legalism. It is essentially the development of the Sufi doctrine (tasawuf) 33 that enabled the inhabitants of the Archipelago to understand and integrate Islam into their practices [START_REF]It is also the hypothesis of Lombard[END_REF] . They also combined it with their spiritual needs and gave the rulers opportunities to legitimate their monarchic sovereignty, notably through the acquisition of extra mundane powers [START_REF] Cf | Islam and the Muslim State[END_REF] .

Moreover, in Banten, the brotherhoods were firstly associated to the sultans and that by the period of the XIX th century they became the privilege of independents religious leaders (ulama) and the agrarian bourgeoisie.

This initiation in a brotherhood consists in the dhikr practice (the recitation of the name of God) and of different prays' formulas (a. hizb ou salawat) and litanies (a. râtib, wirid). These recitations can be combined with breathing exercises, corporal postures and ascetic practices. The instruction (a. talqîn) is done after the initiate (a. mursyid) has pronounced the enthronization oath (a. bai'at) behind his master (a. sheikh) and after his exercising in different spiritual practices (a. sughul). If the sheikh gives the permission (a. ijâza) to the initiate to practice into the tarekat, he will name his disciple (a. khalîfa) and reveal to him his spiritual genealogy (a. silsilah), which goes back to the different sheikh who preceded him until Muhammad prophet.

In some versions of the chronicles Hikayat Hasanuddin and Sajarah Banten rantéranté, the link of Banten to brotherhoods is mentioned as soon as the Islamizing premise, when they report the journey of Sunan Gunung Jati and his son Hasanuddin in Mecca and Medina. The chronicles relate that during this pilgrimage, Gunung Jati was initiated in the Naqshbandiyah, Shattariyah, Syadiliyah and Kubrawiyah brotherhoods while Hasanuddin was receiving the Naqshbandiyah's teachings. When they returned to their native Banten, they initiated Naqshbandiyah members of the court and the qadi, the supreme religious judge and sultan counselor. The brotherhoods then appeared as a privileged way of introduction to mystic knowledge, secret and sources of power (s. kasekten), and the sovereign dynasty probably tried to control it [START_REF] Van Bruinessen | [END_REF] . However these chronicles and their interpretations are debated [START_REF]Sadjarah Banten: suntingan teks dan terjemahan disertai tinjauan aksara dan amanat[END_REF] (they tend to glorify the achievements of the early rulers), At the XVII th and XVIII th centuries, the first brotherhoods implanted in the region, and spread more largely in the following centuries, in a quite slow way 38 . In the second mid of the XVII th century, Syeikh Abdul Muhyi, whose tomb in Pamijahan is one of the most sacred sites visited in West Java, diffused in this region the Shattariyah. In the same period, Syeikh Yusuf introduced Khalwatiyah, one of the Suhrawardiyah branches. At the mid of the XVIII th century, Rifaiah and Qadiriyah developed. This last one spread largely under its fusion with Naqsbandiyah at the XIX th and XX th centuries 39 . It is also under this form Qadiriyah wa Naqsbandiyah that later, political and rebel networks which disrupted the regional history, created. Their success resided in two main factors: the congregational nature of their organization and the esoteric practices to which they initiated, among which the invulnerability techniques called debus.

The invulnerability practices debus and the expression of the link to divine

In the Islamic jurisprudence, the Quran contains a number of rules concerning the behavior that a Muslim has to respect. However, some subjects, religious and profanes, are not framed by the Quran rules. The exam of Muhammad prophet and his companions' way of life (a. sunna) provides indications on the behavior to adopt and to avoid. The example of the prophets also helps to find the way (a. sharia) which leads to God. The proofs that indicate that the faithful are on this way are extra-ordinary facts, miracles, which can be realized only in link to the divine. In Banten, the invulnerabilities called debus historically acquired an analogue status and they probably played an important role in the conversion processes.

We find quite similar exercises to debus in the Kurdish Qadiriyah and in a number of Middle East brotherhoods. The nail, the debus' central element, named almadad, is inherited from the Rifaiah brotherhood. Furthermore, the Rifaiah prays that are recited in Egypt, Turkish and India and that are attributed to the founder Ahmad ar-Rifaâi, often begin with the word madad, which means "help", "rescue", or "salvation" 40 . In the Archipelago, Rifaiah has spread until Minangkabau region, at the West of Sumatra, where it is also known under the name dabuih, the term that locally designates the invulnerability practices. We find this kind of practices in Aceh, the Malay Peninsula and the Moluccas. The Muslim of Malay descent in Cape Town (South Africa), also practice debus, which would have been spread by the Bantenese resistant to Dutch occupation, Syeikh Yusuf (originate from Makassar), when he was exiled in 1693.

The invocations and recitations used for debus vary locally. For example, in Pandeglang region, debus are explicitly associated to Rifaiah, whereas at the end of the XIX th century in North Banten and Cirebon was recited the Wawacan Sèh, the Javanese or Sundanese adaptation of the pious tales about Sheikh Abd al-Qadir Jilani's miraculous deeds (a. manâqib) 41 . Sheikh Samman 42 is also invoked in those two regions and the magical powers provided by its invocation can be reinforced by using the specific prays of the Shadiliyah brotherhood.

The invulnerability practices in Banten are probably anterior to the spreading of Islam, but the Bantenese Muslims report that it is thanks to such practices that Gunung Jati and Hasanuddin Islamized the region. The Bantenese notably relate that it is through debus that the brotherhoods gained popular audience and that they spread from the circles of the court to the rural populations. Johan Talens describes the enthronization ritual of the sovereign in 1691. The divine blessings received by the sultan through the intermediary of a priests' assembly founded his authority over the kingdom. The priests guarded the kingdom during the inter-reign, which one lasted forty days [START_REF] Talens | Ritual Power: the Installation of a king in Banten, West Java, in 1691[END_REF] . Among the powers obtained through religious practice, invulnerability seems to have been one of the most coveted, and it was used to instigate faith for the struggle against the Dutch colons until the national independence in 1945.

Formerly, debus performances possibly took place into a room located at the second floor of the Banten's mosque, a room called Tiama. All along its performing, it was led by one or two masters called khalifah or syeikh 44 . Almadad picks still can be found in the museum close to Banten Lama's mosque. Nowadays, even if the most reputed debus masters are not affiliated to brotherhoods, the practitioners often have the title designed to the brotherhoods' initiates (a. khalîfa) and a number of sheikh transmit these practices to their disciples through an initiate and secret way.

The specificity of Banten's debus, at the difference of the Central and East Indian practices, is that the picks do not stab the body. Thus, the miracle is linked to invulnerability, the mastering of a supernatural capacity, and not to an indifference to pain or the control of emotions (this one is just present during the process of formation to debus). This invulnerability is explicitly linked to martial arts and war, and some practitioners are reputed to be invincible to bullets. Therefore, debus are practiced to prevent harms and disasters. As protection practices, debus are inscribed into a wider set of esoteric techniques, designed under the generic term elmu hikmat ("supernatural practices") which take a specific local coloration in Banten.

The almadad pick used for debus (Serang, 2005)

The esoteric practices elmu hikmat

The brotherhoods techniques and prays have been integrated in different esoteric practices, eclectic and sometimes little formalized, which constitute a set classified as elmu hikmat (derived from the Arabic hikmah: "wisdom, magic") and which is largely spread in Java [START_REF] Athoullah | About Elmu hikmat in Banten[END_REF] . In the Muslim Arab countries, hikmah designates an aggregation of ancient practices to Islam, as Greek medicine and philosophy, or Babylonian magic [START_REF] Al-Nisa | There are several definitions of Al Hikmah in different surates of Curan[END_REF] , but in Indonesia the term designates the Islamic magic 47 , essentially of Sufi inspiration. Hikmat has different goals: to provide health, to cure, to increase the social status, to positively influence destiny, to gain money, to protect against misfortunes, to obtain invulnerability and to attract love 48 .

As in the brotherhoods, hikmat practice includes the training (a. riyadah), the struggle against passions (a. mujahadah), the commentaries about the "names of God" (a. asma alhusna), the secrets of the letters, verses and surates of the Quran. Hikmat specialists (ahli hikmat) who are often kiai, practice pray, intercession techniques to God (a. tawassul), Basmalah, Al Fatihah, Kaf Ha Ya 'Ain Shad, Ayat Kursi and Tahlil. According to the hikmat's specialists, each Quran verse is linked to a "servant" (a. khadam): a djinn 50 or an angel, with whom the disciple can associate or that can be invoked 51 .

Hikmat knowledge can be obtained through different ways. It can be transmitted through descent and the descendant has to pay attention to a number of divine signs (a. bakat) to conserve it. It can be obtained through the reading of the kitab texts. Finally, it can be provided by a master, who can be independent, the member of a Quran school or of a brotherhood. The so called kiai kitab and kiai hikmat often combine both roles, that is to say a teaching which is based on the text and which is associated with the magic or esoteric knowhow. This transmission is reserved to a small number of students (santri) 52 . Nowadays, certain pesantren, as Al Gazali's one (in the Petir district of Serang), offer intensive formations to hikmat during the month of Ramadhan. They provide licencia docenci (a. ijazah) of different levels classed between one and four. They propose formations to obtain supernatural capacities through a "filling of the body" (pengisian badan). The initiations called asma james and asma Sunan Kalijaga are presented as means to be invulnerable to fire, bullets and sharp weapons. Those are also used for neutralizing poison, giving lethal punches or paralyzing an opponent as well. Some formulas, like asma Suryani and asma Syeikh Khalil Madura, are meant to stronger bravery and to protect the initiates against harmful djinn. The pesantren also proposes magic and powerful objects (ajimat): rings, belts, rosaries, turbans, scarves, vests, and ritual oils 54 .

In Banten, most of the brotherhoods practice hikmat. Nevertheless, the practitioners tell that hikmat is just a sidewalk to influence God's ways, and as such it differs from the Sufi Way, which one is considered as a sinuous and demanding way. The disciple who follows this way has to purify his soul until he reaches the level called tabarruk, which enables him to receive the gifts of God 55 .

Conclusion: cosmopolitan culture and religious heterodoxy

To briefly summarize, since the XVI th century, in the sultanates of the Archipelago, new social groups were constituted, which based their fortune on movable goods. These maritime societies were characterized by the traditional role of the specialized merchant communities, often bonded by endogamy, as well as by affinity between Islam and commerce. According to Denys Lombard, these communities were from very diverse origins, comported Malay, Javanese, Bugis, Tamils, Bengalis, Guajarati and Chinese elements, while the Semitic influence was quite weak. They were neither from Islamic Arabia nor from imperial China, but nevertheless constituted a real "Islamic-Chinese stimulus" which provided the basis of a monetary economy in the same times than accordance with the concepts of individual, equality and an oriented time 56 .

These different ideals took time to penetrate Bantenese society and they long had an only limited influence upon the inside Javanese spaces, which were distant from the main commercial roads. Thus, at the period of Demak kingdom, Islam destabilized the ancient ideologies but did not supplant them. Notably marked by the Sufis' networks and the local ritual initiations, its character both mundane and supra-mundane opened the gate to multiples interpretations and provided the possibility to different groups to aggregate themselves under its name. This plurality of interpretations constitutes richness for the religious practices but it also brought up the possibility to rigorist discourses to find resonance among certain parts of Bantenese society, notably in the transmigration suburban areas, in which ritual initiations groups and authority structures have not been able to consolidate. However, as Claude Guillot insists, Banten cannot be considered as a bastion of orthodox Islam 57 . The rulers would have been perceived as heretic if they had self-proclaimed as representatives of divine on earth. Nevertheless, for the people they represented intermediaries with the divine and they were partially free from mundane limitations 58 .

Finally, according to Ota Atsushi, the expression of religious radicalism often originates from non-religious causes and it frequently followed a proportional way to the outside political pressures. For instance, the historian shows that Banten revolts of the years 1750-1752 were firstly motivated by ideals that were not formally Islamic but linked to succession conflicts for the throne [START_REF] Cf | Changes of regime and social dynamics in West Java: society, State, and the outer world of Banten, 1750-1830[END_REF] . It was the same in the XIX th century's anticolonial rebellions. Even if they were led by the religious leaders kiai and were catalyzed under the banner of a holy war jihad, in fact they were firstly and mainly caused by starvation resulting from natural disasters and by colonial socio-economic pressures. Then, the religious ideals converged with socio-economic and political regionalist ones.

Thus, historical insights may enrich our perspective of Banten's Islam, its diversity over time, its capacity of integration of local religious specificities and the political bias that inflected its development.

  recitations of Quran formulas (a. zikir and wirid) and fast. The hikmat teachings are contained in certain texts (a. kitab), as Manba Ushul Al Hikmah and Syams al Ma-arif al Kubru, the books Fath al Malik al Majidou Mujarrabatal Dairabi al Kubra or Khzinah Al Asrar, which are linked to the writings of the Quran or the name of God 49 . The most used prays are

Several

  kiai are reputed to be hikmat experts, like Syeikh Yusuf or Ki Abd al Karim al Tanari al Jawi, a master of Qadiriyah wa Naqsbandiyah, whom most well-known disciple was the rebel Syeikh Muhammad Asnawi from Caringin 53 . A number of those kiai were the instigators of great historical revolts: they mobilized the crowds against the Dutch colons and transmitted to their disciples debus and martial arts penca techniques. In the second mid of the XX th century, the most well-known expert was K.H. Armin from Cibuntu in Pandeglang, the nephew of Ki Asnawi from Caringin, who received the visit of high foreign and State political representatives who wanted to receive his benedictions. Others kiai, like K.H. Khalil Pani'is from Pandeglang and K.H. Dimyati from Cidahu in Cadasari (Pandeglang), were Syadiliya's initiates.


Florent Le Moël

Antoine Wystrach

Towards a multi-level understanding in insect navigation

Keywords: insects, navigation, modelling, neuroethology

Towards a multi-level understanding in insect navigation

Florent Le Moël, Antoine Wystrach

Introduction

Behaviour, like any natural phenomena, is entwined in the universe. To 'explain' behaviour, an arbitrary amount of levels (or scales) of explanation may be invoked, from the interactions between atoms to long-term influences of the surrounding ecosystems. The choice of levels of course depends on one's question. The typical neuroscience approach tries to establish direct causal links between the level of 'neurons' and the level of the 'individual's behaviour'. This endeavour can be quite problematic, as understanding 'how brain produces behaviour' cannot be achieved by solely studying the neural circuitry [START_REF] Jonas | Could a Neuroscientist Understand a Microprocessor?[END_REF], but requires first a good understanding of the animal's behaviour itself, which, most of the time, is lacking [START_REF] Gomez-Marin | The Life of Behavior[END_REF], [START_REF] Krakauer | Neuroscience Needs Behavior: Correcting a Reductionist Bias[END_REF]. In response to this problem, Marr has suggested that one should consider a third, intermediate, level between neurons and behaviour: the 'computational level [START_REF] Krakauer | Neuroscience Needs Behavior: Correcting a Reductionist Bias[END_REF], [START_REF] Marr | Vision: A computational investigation into the human representation and processing of visual information, henry holt and co[END_REF]. Considering three levels implies understanding two transitions: from neurons to computation, and from computation to behaviour.

Here, we show that the field of insect navigation, with its strong ethological background, has naturally implemented this three-level approach while seeking how brains relate to behaviour. Neural mappings in various insect species have been vital in developing recent computational models and behavioural data from other species have been vital in linking them to ecologically-relevant behaviour. This combination of approaches makes the field of insect navigation an interesting example case to help us identifying the possible difficulties and solutions towards a multi-level understanding from neurons to behaviour.

Three levels to bridge neurons and behaviour

The variety of approaches to insect navigation can be mapped to Marr's proposed three levels [START_REF] Marr | Vision: A computational investigation into the human representation and processing of visual information, henry holt and co[END_REF].

Level 3: Behaviour

The level 3 corresponds to the ecologically relevant behaviour itself. Thanks to its ethological background [START_REF] Wehner | Early ant trajectories: spatial behaviour before behaviourism[END_REF]- [START_REF] Wystrach | What can we learn from studies of insect navigation?[END_REF], the field of insect navigation is rich in such examples: the long-range migrating prowess of Monarch butterflies; the efficient visit of multiple flower patches by bumblebees; or the impressive homing abilities of desert ants after kilometre-long foraging bouts, are few examples. The key is here that the behaviour is observed in the field and interpreted in the light of the species natural tasks.

Level 2: Computation

The 'computation level' comprises the relationship between 'computational modules', which may (or may not) be mapped to brain areas. These functional modules interact together with the body and environment to extract information, to store it, and to produce motor outputs. The computation level can be used to explain behaviour, without the need to consider the neural implementation level. For instance, homing behaviour may result from a process of path integration (reviewed in [START_REF] Heinze | Principles of Insect Path Integration[END_REF]), which requires computational modules such as an internal compass, an odometer, and the integration of both into a homing vector to influence the animal's course. Often, if not always, interactions between computational modules, the body and the environment, show emergent properties: meaning that behaviour cannot be reduced to the understanding of a single module studied in isolation.

Level 1: Neurons

The neural implementation level refers to the actual connectivity at the scale of neurons or groups of neurons. The aim being to explain 'computational module' rather than behaviour. For instance, the insects' internal compass (i.e., a computational module) has been shown to emerge from a subset of neurons organised into what is called a ring attractor [START_REF] Honkanen | The insect central complex and the neural basis of navigational strategies[END_REF]. Here again, groups of neurons typically show emergent properties -which cannot be grasped when looking at single neurons only-that allow the above level ('computation') to emerge.

The need for models

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Three levels imply two transitions (level 3 <-> level 2 <-> level 1), and understanding a transition requires a so-called 'model' [START_REF] Webb | Can robots make good models of biological behaviour?[END_REF]. A model, as we mean here, is not necessarily an algorithm run by a computer (computational model), it can simply use words. However, as we will see, computational models are key to explore the non-linear dynamics of brain-body-environment interactions. In any case, to provide a cross-level 'understanding', the model must establish and clearly state rules that explain how the desired proprieties at a given level emerge from the assumptions at the level below. We next provide examples of how models can help us understand both types of transitions.

Models from 'Behaviour' to 'Computation' (level 3 <-> level 2)

Understanding behaviour is far from trivial, as it is not merely a consequence of brain activity, but emerges from a complex system forming a closed loop involving dynamics between the animals' brain, body and environment, a phenomenon that is crucial yet often overlooked [START_REF] Beer | 6 -The Dynamics of Brain-Body-Environment Systems: A Status Report[END_REF], [START_REF] Clark | Being There: Putting Brain, Body, and World Together Again[END_REF]. These processes are hard to intuit because the interactions usually happen in parallel and are typically nonlinear. In addition, each element of the system (i.e. the brain, body posture and perceived environment) is constantly changing, adding in complexity. Understanding behaviour also requires consideration of the individuals' Umwelts, that is, their personal experience through their specific sensory (e.g., polarised light sensing, panoramic vision or chemosensing) and motor (e.g., crawling, running or flying) systems, as well as the natural environment in which they have evolved [START_REF] Gomez-Marin | The Life of Behavior[END_REF], [START_REF] Wystrach | What can we learn from studies of insect navigation?[END_REF], [START_REF] Uexküll | Umwelt und Innenwelt der Tiere[END_REF].

The best way to understand how a behaviour is produced is therefore to start with a question stemming from the observation of the animal's behaviour in its natural environment. Once the ecological task of the animals defined, one can try to characterise what types of computations can explain such a behaviour, with an emphasis on its sensory-motor systems (its specific Umwelt). Such an approach has motivated more than 100 years of behavioural experimentation in insect navigation, literally decomposing the insects' impressive navigational feats into ever finer and more powerful mechanistic 'models'. Importantly, because of the endorsement of a naturalistic approach and the lack of neural data, the vast majority of these models was not neuroanatomically constrained. We believe this was a blessing rather than a problem because it led the field to focus on the level 3 <-> level 2 transition without being burdened by too many neural data. As we will see, the level 3 <-> level 2 transitions typically invoke explanations and rules that are entirely different from the ones at the levels below.

Various insect navigational behaviour have been investigated with such an approach: path integration [START_REF] Collett | Path integration: how details of the honeybee waggle dance and the foraging strategies of desert ants might help in understanding its mechanisms[END_REF], the use of learnt terrestrial cues [START_REF] Graham | Vision for navigation: What can we learn from ants?[END_REF], wind and olfaction [START_REF] Buehlmann | Desert ants use olfactory scenes for navigation[END_REF], [START_REF] Wolf | Pinpointing food sources: Olfactory and anemotactic orientation in desert ants, Cataglyphis fortis[END_REF], obstacle avoidance [START_REF] Baba | Collision avoidance by running insects: antennal guidance in cockroaches[END_REF], route optimisation [START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF], [START_REF] Wystrach | Rapid Aversive and Memory Trace Learning during Route Navigation in Desert Ants[END_REF], sequence learning [START_REF] Collett | Sequence learning by honeybees[END_REF], [START_REF] Macquart | Sensorimotor sequence learning in the ant Gigantiops destructor[END_REF] or navigation backwards [START_REF] Collett | Insect Navigation: What Backward Walking Reveals about the Control of Movement[END_REF], [START_REF] Schwarz | How do backward walking ants ( Cataglyphis velox ) cope with navigational uncertainty?[END_REF]. Below, we focus on behavioural models of route following and visual homing in ants and bees, because these illustrate well the importance of considering the 'brain-body-environment' dynamics at play.

Using views to navigate: modelling the brain-body-environment loop

Ants and bees are known to use learnt visual cues to follow routes and return to places of interest [START_REF] Kohler | Idiosyncratic route-based memories in desert ants, Melophorus bagoti: How do they interact with path-integration vectors?[END_REF]- [START_REF] Collett | Spatial memory in insect navigation[END_REF]. Seminal behavioural experiments demonstrated the use of egocentric views in bees and ants, and suggested models for how movement towards the goal could be achieved using egocentric visual memories [START_REF] Cartwright | Landmark learning in bees: Experiments and models[END_REF], [START_REF] Wehner | Visual spatial memory in desert ants, Cataglyphis bicoior (Hymenoptera: Formicidae)[END_REF]. Later on, a key piece of information was brought by studying the natural environment through low-resolution panoramic pictures with the attempt to approximate the J o u r n a l P r e -p r o o f insect's point of view (approaching its Umwelt): natural scenes, when compared as a whole through the insect eyes' low-resolution insect, provide remarkably robust directional information, which can be obtained by simply rotating on the spot [START_REF] Zeil | Catchment areas of panoramic snapshots in outdoor scenes[END_REF]. Subsequent behavioural experiments quickly confirmed that ants just do so: they use panoramic visual cues [START_REF] Graham | Ants use the panoramic skyline as a visual cue during navigation[END_REF]- [START_REF] Wystrach | Landmarks or panoramas: what do navigating ants attend to for guidance?[END_REF], and display physical rotations -such as saccades and scanning-to recover directions [START_REF] Collett | Scene perception and the visual control of travel direction in navigating wood ants[END_REF]- [START_REF] Wystrach | Visual scanning behaviours and their role in the navigation of the Australian desert ant Melophorus bagoti[END_REF]. Computational models implementing these ideas revealed that route following would spontaneously emerge in complex environments given remarkably simple guidance rules and little memory space [START_REF] Baddeley | A Model of Ant Route Navigation Driven by Scene Familiarity[END_REF]. But what about pinpointing the nest? Here again, a solution came from observations of the insect's body rather than the brain. Detailed studies of the choreographies displayed by ants, bees and wasps when leaving their nest -so called 'learning walks' or 'learning flights'-revealed that insects position their body in specific orientations relative to the nest for learning [START_REF] Fleischmann | Species-specific differences in the fine structure of learning walk elements in Cataglyphis ants[END_REF]- [START_REF] Zeil | Structure and function of learning flights in ground-nesting bees and wasps[END_REF]. Adding these behavioural routines to the previously mentioned route-following models was enough for a pinpointed nest search to emerge. Additional motor routines, such as the continuous lateral oscillations observed in insects [START_REF] Collett | Scene perception and the visual control of travel direction in navigating wood ants[END_REF], [START_REF] Stürzl | How Wasps Acquire and Use Views for Homing[END_REF], [START_REF] Kuenen | A non-anemotactic mechanism used in pheromone source location by flying moths[END_REF]- [START_REF] Wystrach | Continuous lateral oscillations as a core mechanism for taxis in Drosophila larvae[END_REF], or the fact that ants look regularly away from the nest [START_REF] Jayatilaka | The choreography of learning walks in the Australian jack jumper ant Myrmecia croslandi[END_REF] enabled further improvement of the navigational efficiency [START_REF] Kodzhabashev | Route Following Without Scanning[END_REF], [START_REF] Prescott | Opponent processes in visual memories: A model of attraction and repulsion in navigating insects' mushroom bodies[END_REF]. The viability of these models was further strengthened by the fact that they equally captured a range of insect behavioural signatures, even though they were not designed to do so [START_REF] Wystrach | Continuous lateral oscillations as a core mechanism for taxis in Drosophila larvae[END_REF], [START_REF] Kodzhabashev | Route Following Without Scanning[END_REF], [START_REF] Murray | The role of attractive and repellent scene memories in ant homing (Myrmecia croslandi)[END_REF].

Taken together these various models led to an understanding of behaviour that arose from the study of the animals' movements and environment, rather than from looking at the brain. The simple rules identified lead to the emergence of impressive navigational feats only when embedded in an agent in closed loop with its environment and displaying the appropriate motor routines during learning (which is absolutely not trivial without computer simulations) [START_REF] Webb | The internal maps of insects[END_REF]. Whether one could have reached such an understanding by focusing on the brain's circuitry -or by identifying direct causal links between brain activity and behaviour-is very unlikely, if not fundamentally impossible [START_REF] Jonas | Could a Neuroscientist Understand a Microprocessor?[END_REF], [START_REF] Webb | The internal maps of insects[END_REF]. In any case, we are now left with clear computational requirements for the brain. How can neurons achieve these requirements has not much to do with the above understanding, and requires an entirely different explanation at the level below.

Models from neurons to computational modules (level 2 <-> level 1)

An alternative -but complementary path to the one mentioned above can be followed, one that takes an opposite stance and is constrained by the lower levels: one may wonder how the identified 'computational modules' are implemented within the brain, being less concerned with behaviour. This is actually a quite different question from the daunting "How do neurons drive behaviour?". Understanding this transition, from neurons to computational modules, also requires models, especially when one considers the overwhelming amount of connectivity data available [box 1].

How to obtain the current view's familiarity?

Let us pursue with the example of route following and homing. One of the computational modules identified at the above level require to enable to memorise visual information from the scene experienced, as well as to output the familiarity of a current view. A solution at the neural level came from a model of the flies and honeybees' brain structure called Mushroom Bodies (MB). This model was originally designed to explain how neurons in this structure could support the learning and memories of odours [START_REF] Heisenberg | Mushroom body memoir: from maps to models[END_REF], [START_REF] Smith | A model of associative learning in the mushroom body[END_REF], but researchers in insect navigation realised that this neural model, provided with visual input, could equally explain the learning and memories of panoramic visual scenes, as well as how memorised and currently perceived scenes are compared to output a familiarity signal [START_REF] Ardin | Using an Insect Mushroom Body Circuit to Encode Route Memory in Complex Natural Environments[END_REF], [START_REF] Webb | Neural mechanisms of insect navigation[END_REF]. In other words, the circuitry of the MB naturally achieves the desired J o u r n a l P r e -p r o o f computational function identified by behavioural research on route following and homing. Establishing a direct link between MB and route following, without prior knowledge that such computational functions are sufficient for the navigational behaviour to emerge could have probably been achieved by direct neurobiological manipulation, however, in no case the knowledge of such a causal link would have brought understanding of the mechanism at play.

Together, this provides us with a truly multi-level understanding, from neurons to computation, and from computation to behaviour. Whether this understanding is correct regarding insects can be tested. Then comes the time for an experimental demonstration of a causal link from neurons to behavior (this being only achieved post-hoc and based on a prediction drawn from this understanding of the intermediary computational level, [box 3]). It turned out, while we wrote this review, two studies did indeed test and support these models' predictions by using pharmaceutical injections in ant's MB to demonstrate the expected roles of this brain area in ant visual navigation [START_REF] Kamhi | Vertical Lobes of the Mushroom Bodies Are Essential for View-Based Navigation in Australian Myrmecia Ants[END_REF], [START_REF] Buehlmann | Mushroom Bodies Are Required for Learned Visual Navigation, but Not for Innate Visual Behavior, in Ants[END_REF].

How to build a good internal compass?

The behavioural approach has demonstrated that multiple behaviours such as path integration in ants and bees [START_REF] Collett | Path integration: how details of the honeybee waggle dance and the foraging strategies of desert ants might help in understanding its mechanisms[END_REF], [START_REF] Cheung | Animal path integration: A model of positional uncertainty along tortuous paths[END_REF] -or walking in a straight direction as observed when dung beetles try to run away with their ball of dung [START_REF] Dacke | The Dung Beetle Compass[END_REF] -result from the integration of multiple directional cues, such as terrestrial, celestial, wind-based and self-motion cues, into a single but remarkably robust sense of direction [START_REF] Dacke | Multimodal cue integration in the dung beetle compass[END_REF]- [START_REF] Wystrach | Ants use a predictive mechanism to compensate for passive displacements by wind[END_REF]. Now that the need for such a computational feat has been behaviorally demonstrated, the question of how it can be implemented in an insect brain arises.

The insects Central Complex (CX), a central neuropil well conserved across arthropods species, had long been known for being implicated in navigation, but it is only recently that details on the compass implementation have been revealed [START_REF] Pfeiffer | Organization and Functional Roles of the Central Complex in the Insect Brain[END_REF]. Seelig and Jayaraman [START_REF] Seelig | Neural dynamics for landmark orientation and angular path integration[END_REF] showed with neuroimagery that a bump of neural activity shifting around a toroidal structure (the Ellipsoid Body of the CX) could encode and track the individual's current direction, not without recalling older theoretical models of 'ring-attractor' networks [START_REF] Sun | An Analysis of a Ring Attractor Model for Cue Integration[END_REF]- [START_REF] Song | Angular Path Integration by Moving "Hill of Activity": A Spiking Neuron Model without Recurrent Excitation of the Head-Direction System[END_REF]. We now understand how a stable heading emerges in this brain structure from multi-modal neural signals [70, p. 201], [START_REF] Green | A neural circuit architecture for angular integration in Drosophila[END_REF]- [START_REF] Turner-Evans | Angular velocity integration in a fly heading circuit[END_REF]. Here again, this example shows how multi-level understanding arises from entirely different research approaches united by the identification of the intermediate computation module: how various natural behaviours emerge from an internal compass (in interaction with other computational modules) on one hand, and how such an internal compass representation emerges from a neural population on the other hand.

Closing the loop: Models from neurons to behaviour (level 3 <-> level 2 <-> level 1)

Considering nowadays' computing power, the idea of a fully functional simulation of a whole brain is considered as a next step for many [START_REF] Collins | The case for emulating insect brains using anatomical "wiring diagrams" equipped with biophysical models of neuronal activity[END_REF]. However, we argue that this view is still far from realistic [box 3]. In many situations one should restrain a given model to the transition between two levels only. Indeed, adding levels complexifies the modelling effort, while not necessarily bringing additional insights, and may also result in a 'black box' effect [boxes 1, 2 and 3]. If not for additional insights, is it useful to design computational models from neurons to behaviour? So long as one has acquired a multi-level understanding through models at both transitions 1 <-> 2 and 2 <-> 3, it can be useful to try and see if the neuron-to-behaviour model (1-2-3) works, as a proof J o u r n a l P r e -p r o o f of concept. For instance, Stone et al. [START_REF] Stone | An Anatomically Constrained Model for Path Integration in the Bee Brain[END_REF] successfully modelled path integration by embedding a biologically constrained neural model combining compass and distance information in a navigating agent. This proof of concept is important, as unexpected phenomena may emerge when complex neural dynamics are integrated to the complex brain-body-environment dynamics. Sometimes this is good news. In the case of this Path integration model, the authors were surprised to see that path integration worked irrespectively of the relation between the insect body orientation and direction of movement; a phenomenon that was actually reported in insects [START_REF] Pfeffer | How to find home backwards? Navigation during rearward homing of Cataglyphis fortis desert ants[END_REF], [START_REF] Riley | Compensation for wind drift by bumble-bees[END_REF].

Another advantage of such integrative models is that, if the model does work, it can then be used to make predictions about the neural activity in relation to specific behavioural situations [START_REF] Stone | An Anatomically Constrained Model for Path Integration in the Bee Brain[END_REF], something which would be difficult to obtain without an integrative model. Similarly, it becomes possible to predict the emergence of specific behaviours given specific neural signatures. Both types of predictions can then be tested by respectively recording and stimulating neurons of navigating animals.

Multi-level models can also be of interest for predicting how differences in neural connectivity between species may explain respective behavioural optimisations to their ecological needs [START_REF] Webb | Neural mechanisms of insect navigation[END_REF]. For example [START_REF] Pisokas | The head direction circuit of two insect species[END_REF] show how slight differences in the Central Complex connectivity between locusts and fruit flies, and may gift the first with a compass more resilient to noise (i.e. suitable for long-distance migration) and the second with a compass that is faster in responding to changes in direction (i.e. allowing fast body saccades).

Finally, combination of behavioural, computational and neural models enables to understand how same brain structures can be implicated in drastically different navigational behaviours and as a corollary, how the stunning variety of behaviours observed across species can arise from very similar brains [START_REF] Honkanen | The insect central complex and the neural basis of navigational strategies[END_REF], [START_REF] Webb | Neural mechanisms of insect navigation[END_REF], [START_REF] Wystrach | Insect spatial learning, a stroll through Tinbergen's four questions[END_REF]. The fact that neural data from different insect species converges makes sense in this light: switching from one behaviour to another can be achieved by changing the body, the sensory system or how brain modules interact, and does not necessarily requires additional computational modules.

Conclusion

The current tools of neurobiology are undeniably useful, but their usefulness appears sublimed when exploited as a second step, after one has achieved a good understanding of how computational modules might interact to produce a given behaviour. We think that the study of navigation in insects still benefits from the advantage of its rich naturalistic background which pervades today's behavioural, computational and neuroscience research, and we hope that this ecological relevance will survive the modern upsurge of neurobiological data.

Declarations of interest: none [BOX 1: 'Why we cannot be purely bottom up']

One might expect to be able to extrapolate a fully functional model from full-brain connectomics only, 'ideally' by feeding all the lower level data to a computer, press 'play', and being able to observe the emerging behaviour. This kind of approach may appear as the perfectly objective, purely bottom-up model, but it turns out not to be that practical, and perhaps fundamentally impossible. First, we still lack key information about neurons (synapse gain, plasticity rules, etc.); and to model neurons perfectly accurately, we would need equally accurate models of the underlying molecular interactions, and so on, leading an impossible reduction. Second, for behaviours to emerge one would also need to model the body and the environment experienced, although this can be bypassed by embedding the model in a robot exposed to the real environment. But let us imagine our description of a given bee's body and brain circuits is exhaustive and perfectly accurate and our robotic technology advanced enough to make this approach possible. A robot-bee based on these data is constructed, the experimenter presses 'play' and it works, navigating and reacting just as well as a bee would… Now, question about the usefulness of such an approach arise: what understanding did we actually gain? Not much. We could then tweak the robot using diverse interventionist approaches in order to understand it better, but we would find ourselves basically right back where we were initially with the real bee. "The best material model for a cat is another, or preferably the same cat" [START_REF] Rosenblueth | The Role of Models in Science[END_REF] but then the model, because it does not bring any simplification of the object, brings no understanding. We thus need to concentrate our efforts towards achieving models that are simple enough to allow us to understand the rules at play. But if the model is a simplification, it should concern only a 'subset of the animal', a specific function, at a specific level of explanation. We therefore should always have an a-priori idea of the specific function we want to explain. In other words, a pinch of top-down thinking will always be necessary.

[BOX 2: 'What about Artificial Neural Networks?']

Models taking biological constraints at both the higher level and the lower level are best exemplified by ANNs: the goal function (the behaviour) is constrained at one end, the cells activity is constrained at the other, but the connectivity in between is not; these provide a sort of direct neuron-tobehaviour links (levels 1-3). The work is then to understand the type of computation (level 2) that might have emerged from various learning rules. Even though machine learning can be thought unsuited to study network structure of biological systems (only the cell-level response properties are similar to biology), such explorations have proven insightful. First, the emergence of computational modules can still bring insights on how the original complex behaviour may be decomposed into subcomponents. Second, one can observe the emergence of elements otherwise observed in real biological systems such as ring-like organization and existence of shifter neurons for compass orientation [START_REF] Cueva | Emergence of functional and structural properties of the head direction system by optimization of recurrent neural networks[END_REF], or neurons reminiscent of grid cells for navigation tasks [START_REF] Banino | Vector-based navigation using grid-like representations in artificial agents[END_REF].

Why does it work? Is it on the idea that both evolution and the ANNs should converge on the best connectivity? If that is so, one should keep in mind the constraints that are at play with evolution and not with ANN: the historical constraints. Evolution does not start from scratch, but modifies previously existing brains. Also, contrary to ANN, animals need to maintain a vast amount of functions simultaneously, and the resulting solution for the animal may well be different than the simple pooling of several functions optimised independently.

J o u r n a l P r e -p r o o f [BOX 3: 'About modelling multiple levels…']

If one should stick to model transitions between two levels only, should we ever model how fullfledged behaviours in the world emerge from neurons? Modelling through multiple levels at once can drastically increase the number of parameters. Such increased complexity, on top of exposing to a higher risk of biases and errors, bears one fundamental pitfall: it makes the modelling effort drift away from the possible insights it should bring. What good is a model that is as complex as the organism it is supposed to explain? [box 1]. To our opinion, modelling through multiple levels at once should be achieved only 'when needed'. For example, when modelling the transition from neurons to 'brain computation', lower levels such as ions movement that generate action potentials might preferably be abstracted if simpler 'spiking rates' values are good enough for the desired brain computation to emerge. However, there might be a 'need' to model single spikes if for instance, spike-timing dependant processes are key for the brain computation to emerge. This simplification step enables to identify the key elements for the desired process to emerge, that is, to understand well the transition. To sum up, if the lower level can be approximated by an existing assumption, this assumption should be preferred: the lower-level axioms of one field are the upper-level research goals of others.

[BOX 4: 'Integrating multiple cues']

Some models have focused on the integration of multiple cues or multiple navigation strategies such as path integration and learnt views into a single motor output. Behavioural experiments have shown that this integration is achieved continuously and optimally based on the relative certainty of the cues [START_REF] Collett | How Navigational Guidance Systems Are Combined in a Desert Ant[END_REF]- [START_REF] Buehlmann | Multimodal interactions in insect navigation[END_REF], and subsequent mathematical formalisation of the suggested computation have demonstrated that it could indeed fit the various observed data [START_REF] Cruse | No Need for a Cognitive Map: Decentralized Memory for Insect Navigation[END_REF]- [START_REF] Hoinville | Optimal multiguidance integration in insect navigation[END_REF], as well as suggested how this type of computation could be implemented in the insect's brain [START_REF] Sun | A Decentralised Neural Model Explaining Optimal Integration Of Navigational Strategies in Insects[END_REF]. Within Marr's 3 level framework, this endeavour stands clearly as an attempt to explain behaviour from the interaction between computational modules, that is, the transition between level 3 and 2. However, while other work aimed at identifying the computational modules underlying the emergence of a given navigational strategy (i.e., path integration or the use learnt view), here the computational modules are the navigational strategies per se (i.e., path integration and learn view). Therefore, the explanatory framework of this line of work can be viewed as standing one hierarchical level above. Even though biological relevance of the implementation (level 1 <-> level 2) is disregarded, these models, taken together, provide a good example of the complexity of the transition from computation to behaviour, and explain how behaviours can be decomposed into several levels of computations.

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Acknowledgements / Funding

This work was funded by the European Research Council: ERCstg EMERG-ANT 759817 attributed to Antoine Wystrach. The funders had no role in decision to publish or preparation of the manuscript. J o u r n a l P r e -p r o o f J o u r n a l P r e -p r o o f