Cheikh Brahim

E L Vaigh

Martine Clouzot

Christophe Nicolle

Towards A Hybrid Approach for Medieval Illuminations Analysis

Keywords: Hybrid AI, Object Detection, Medieval illumination, Semantic Web, Ontology Identify

Medieval illuminations represent a system of graphic and visual information, based on metaphorical relationships whose meanings and messages are determined in a specific and evolving context. We consider an illumination as a knowledge graph used by certain elites during the Middle Ages to symbolize their social identity and convey events from their lives, along with their cultural values. This knowledge graph contains a set of entities connected through semantic relationships and was used to encode metaphors and impactful messages that can sometimes be challenging for non-experts to decipher. Our aim is to provide a straightforward approach to decoding those messages. Therefore, we first consider medieval illuminations as images and use YOLOv3 to identify the objects inside a given image using bounding boxes. Moreover, we retrieve the entities from the image, their relationships, and the implicit messages using logical inference. The ultimate aim is to simplify the interpretation of illuminations and provide in the future privacy tools for contemporary social media, such as a logical framework for encoding and transmitting information.

I. INTRODUCTION

Social networks encompass online platforms and applications that enable individuals and entities to establish connections, engage in communication, exchange information, and cultivate relationships. In the Middle Ages, social networks existed also but in a different manner, using different tools and representations. In fact, Medieval illuminations are systems of graphic and visual information-images painted on parchment-based on metaphorical relationships, whose meanings and messages are determined within a particular context [START_REF] Calkins | Illuminated books of the middle ages[END_REF], [START_REF] Sandler | A history of illuminated manuscripts[END_REF]. They were used by certain elites to share encrypted information. In Figure 1, we can see a medieval illumination that encodes very a particular message that we will elucidate hereunder.

The Illumination Project 1 is a knowledge engineering tool that aims to logically formalize human knowledge so that it can be manipulated by a computerized system. Within the project, we specifically focus on characterizing and formalizing symbolic relationships between concepts inside medieval illuminations. The project is driven by the appreciation of the cultural heritage of libraries and museums in Burgundy, by the semantic web as a tool for knowledge dissemination, and by the omnipresence of social networks in all areas of our lives.

In previous works [START_REF] Diarra | Causal reasoning and symbolic relationships in medieval illuminations[END_REF]- [START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF] authors studied medieval illuminations and created the ontology Medievelen [START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF] which allows to encode experts knowledge. Moreover, they highlighted the strong structural correlations between medieval illuminations and social networks which may help elucidate the processes through which illuminations served as visual means of communication in medieval times. In this work, we study how we can annotate the images that represent medieval illuminations and then use these annotations along with the experts' rules encoded with the ontology Medievelen to decode a given medieval illumination's message.

In this paper, we build a pipeline to automatically decode medieval illuminations. Our goal is to combine machine learning techniques and semantics ontology to retrieve the message of medieval illumination. Specifically, we combine computer vision models to extract objects from a given image using object detection algorithms and the Medievelen [START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF] ontology defined in semantic web standard OWL. Thus, we first use version 3 of the real-time object detection model YOLO [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF] to retrieve objects inside a given image. Then, we leverage SWLR rules [START_REF] Horrocks | Swrl: A semantic web rule language combining owl and ruleml[END_REF] to define the entities inside the image from the association of different objects. Finally, we make use of experts' SWLR rules to define the implicit message of medieval illuminations by looking at the set of entities found inside the images and their semantic relationships. These semantics rules are defined with the help of medievalist experts. The contribution of this paper is twofold. We built a pipeline combining machine learning for automatic image annotation and causal reasoning mechanisms to encode expert knowledge. Moreover, we conducted an experimental evaluation to show the effectiveness of our approach.

The rest of this paper presents our methodology for creating a pipeline to elucidate medieval illumination's content using both machine learning and semantics ontology. We first introduce the basic concepts relative to first-order logic ontologies and the used object detection model in the preliminaries (Section II). Then we review similar work in the domain of medieval illumination analysis in Section III. Our proposed pipeline is shown in Section IV. Finally, we conduct experiments (Section V) to show the effectiveness of our pipeline in extracting implicit messages from medieval illumination and conclude in (Section VI).

II. PRELIMINARIES

A. Ontology and Inference

We define an ontology (a.k.a. semantic knowledge graph or KG) as a deductive incomplete database that contains two elements: an assertion box or ABox which contains the facts similarly to any classical database and a terminological box or TBox that represents the background knowledge of the application domain and provides a way to reason about the data beyond what is explicitly stored in the ABox.

Ontologies are useful in designing semantics knowledge graphs that have a data component and a reasoning component which allow inference mechanism based on first order logic.

These ontologies can be expressed using description logic, which serves as the basis for the Web Ontology Language (OWL2) [START_REF]OWL 2 Web Ontology Language Profiles[END_REF] developed by the World Wide Web Consortium (W3C) 2 . Example 1 (Running example): Let us consider the simple KG K = (O, D) where

O = {r 0 = hasRightT oKill(X) → Knight(X), r 1 = hasRightT oKill(X) → P erson(X), W eapon(Y ), carry(X, Y ), r 2 = Duke(X) → Lord(X), r 3 = Duke(X) ∧ King(X) → ⊥ }, D = {Duke(a), Duke(b), Duke(g), Knight(c),
hasRightT oKill(g)}.

K is expressed using the DL-lite R fragment of datalog± and existential rules. O states that a knight has the right to kill with (r 0 ) someone carrying a weapon has the right to kill (r 1 ), A Duke is also a Lord (r 2 ), and a Duke can not be a King at the same time(r 3 ). D states that a, b, g, are dukes (Duke), c is a knight(Knight) and g has the right to kill. ⋄ Consistency. KB K is qualified as consistent if and only if it does not entail ⊥, i.e., K ̸ |= ⊥ where |= is the first order (FO) consequence relation. Inconsistency arises from the interaction between the negative rules in the ontology and the facts in the associated database to derive ⊥.

Example 2 (Cont.): K is consistent because ⊥ cannot be deduced from the unique negative rule r 3 and the (entailed) facts for the subClassOf relation: Duke ⊂ Lord and Duke(a), Duke(b), Duke(g) in D i.e., there is no Duke that is also a King. ⋄ Queries and answers. For query answering, FO queries are defined as q(x) = ϕ, where ϕ is an FO formula, and the set of free (non-quantified) variables in ϕ matches exactly the tuple x of answer variables. The arity of a query q(x) is the number of variables in x. If x is empty, the query q(x) is called Boolean. A certain answer to a query q(x) of arity n on a consistent KB K is a tuple of n constants t such that K satisfies the formula q( t), where q( t) is the Boolean query obtained by 2 https://www.w3.org/ substituting x with t in q. In the rest of this article, ans(q, K) denotes the set of answers of q in K.

Example 3 (Cont.): Let us consider the query asking for the dukes that are also knights: q(x) = Duke(?x) ∧ Knight(?x). Its answer set in K is ans(q, K) = {g}: g is obtained from Duke(g) ∈ D, hasRightT oKill(g) ∈ D and the fact Knight(g) ∈ D entailed from hasRightT oKill(g) ∈ D and r 0 . ⋄ From Example 3, even though there is nothing in KB D explicitly stating Knight(g) (g is a knight), this information can be inferred based on rule r 0 . In this case, the ontology is used to infer implicit facts using reasoning based on FO ontologies. In this work we use SWRL [START_REF] Horrocks | Swrl: A semantic web rule language combining owl and ruleml[END_REF] to write logical rules, and as stated in [START_REF] Horrocks | Swrl: A semantic web rule language combining owl and ruleml[END_REF] are equivalent to OWL assertions. The rule r 2 is equivalent to (Duke subClassOf Lord) in OWL language [START_REF]OWL 2 Web Ontology Language Profiles[END_REF]. The goal of this work is to bring high semantic reasoning capability to the field of medieval illumination analysis.

B. Object Detection

Object detection methods are a crucial component of computer vision and artificial intelligence, enabling machines to identify and locate objects within images or videos. These techniques have wide-ranging applications, from autonomous vehicles to surveillance systems, robotics, and image analysis. Several object detection methods have emerged over the years, each with its strengths and weaknesses. Besides the traditional approaches that relied on handcrafted features [START_REF] Soo | Object detection using haar-cascade classifier[END_REF]- [START_REF] Cole | Visual object recognition using template matching[END_REF], deep learning models such as R-CNN based models [START_REF] Xie | Oriented r-cnn for object detection[END_REF]- [START_REF] Girshick | Fast r-cnn[END_REF] first propose regions of interest and then classify and refine them. One-stage detectors perform detection in a single pass they are called two-stage detectors. Moreover, YOLO [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF] and SDD [START_REF] Liu | Ssd: Single shot multibox detector[END_REF] are one-stage detectors. SSD is known for its real-time object detection capabilities by combining multiple bounding box predictions at different scales. Similarly, YOLO is also a real-time object detection method that divides an image into a grid and predicts bounding boxes and class probabilities simultaneously. In this work, we use YOLO's ability to detect objects in different regions of an image in order to retrieve entities from medieval illumination. As part of our pipeline, YOLO is used with the ontology for medieval illumination decoding.

III. RELATED WORKS

Medieval Illumination Analysis is a multidisciplinary field that combines art history, computer science, and cultural studies to unlock the rich symbolism and cultural narratives embedded in illuminated manuscripts. The study of medieval illumination has a long history, but it has become increasingly sophisticated in recent years. Researchers use a variety of methods to analyze illuminated manuscripts, including: • Codicological analysis: They are based on the physical characteristics of the manuscripts, such as the materials used, the binding, and the scribal script [START_REF] Gulácsi | Mediaeval manichaean book art: A codicological study of iranian and turkic illuminated book fragments from 8th-11th century east central asia[END_REF]. • Paleographical analysis: They devise analysis based on the handwriting of the manuscripts to identify different scribes and to date the manuscripts [START_REF] De La Llave | Interdisciplinary exploration of medieval technical manuscripts from the iberian peninsula[END_REF]. • Machine learning based analysis: This type of analysis examines the visual aspects of the digital images associated with the medieval illuminations in order to facilitate their classification [START_REF] Meinecke | Labeling of cultural heritage collections on the intersection of visual analytics and digital humanities[END_REF], [START_REF] Meinecke | A visual analytics framework for composing a hierarchical classification for medieval illuminations[END_REF]. In [START_REF] Meinecke | Labeling of cultural heritage collections on the intersection of visual analytics and digital humanities[END_REF], [START_REF] Meinecke | A visual analytics framework for composing a hierarchical classification for medieval illuminations[END_REF] authors devised a framework that facilitates the creation of a hierarchical classification system for medieval illuminations through visual analytics, enabling researchers to organize and categorize these artworks effectively. • Ontology-based analysis: ontology-based approaches for medieval illumination analysis have gained prominence for their ability to provide structured and semantically rich insights into the symbolism, iconography, and cultural context of illuminated manuscripts and particularly medieval illumination [3]- [START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF], [START_REF] Diarra | Hybrid ai for medieval illuminations analysis[END_REF]. A medieval illumination can be considered as a knowledge graph which was used by some elites in the Middle Ages to represent themselves as a social group and exhibit the events in their lives and their cultural values. Authors in [START_REF] Diarra | Causal reasoning and symbolic relationships in medieval illuminations[END_REF] used this idea to describe the meaning of the elements of Fig. 2: Decoding the medieval illumination in Image 1 using our pipeline.

this knowledge graph through logical modeling using ontologies. Therefore, the authors built logical reasoning rules and used the inference mechanism to facilitate the interpretation of illuminations. Moreover, the Medievelen ontology was proposed in [START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF]. The goal of this work is to provide a formal ontology encoding the knowledge about medieval illuminations. An online annotation platform was proposed in [START_REF] Diarra | Illumination3. 0: A semantic annotation platform based on ontology for medieval illuminations[END_REF] to allow illumination annotation by users which creates a collaborative tool for knowledge sharing. These annotations are very basic they can be the type of the objects inside an image e.g., Person, Weapon, Bell... ) or a semantic relation from the ontology Medievelen between two entities e.g., holding (between a Peron and a Weapon). Our pipeline consists of using both causal reasoning (with an ontology such as Medievelen) and a computer vision model for object detection inside an image. An ontology makes it possible to define an entity from a set of different objects (see Example 4 for the definition of a Princess) using SWLR [START_REF] Horrocks | Swrl: A semantic web rule language combining owl and ruleml[END_REF] rules. In addition with the help of medieval experts, it allows us to represent and store the rules to decode illuminations. Our work includes an automatic annotation tool, it is similar to [START_REF] Diarra | Illumination3. 0: A semantic annotation platform based on ontology for medieval illuminations[END_REF], [START_REF] Meinecke | Labeling of cultural heritage collections on the intersection of visual analytics and digital humanities[END_REF], [START_REF] Meinecke | A visual analytics framework for composing a hierarchical classification for medieval illuminations[END_REF], but we do not need human annotation. Finally, the main contribution of our work is its ability to automatically decode the message of an illumination.

Example 4: Let us consider the illumination in Figure 1, with Yolo [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF], we can detect the objects Person, Dress, Tiara and from these objects we can define a Princess as fellow: P rincess(x) → P erson(x), Dress(d), has dress(x, d), T iara(t), has tiara(x, t)

This SWLR rule means that a princess is a person who has a dress and a tiara. ⋄

IV. MEDIEVAL ILLUMINATIONS DECODING PIPELINE

The objectives of the Illumination project are the characterization and formalization of symbolic relationships between concepts in a constantly evolving context for the case of medieval illuminations. In this regard, research has been conducted to identify the knowledge inside an image e.g., object inside the image, concepts that can be built by combining these objects, and finally the semantics relationships between these concepts.

The proposed pipeline contains a first machine learning model to identify objects inside an image IV-A, then an annotation step to identify concepts associated with a set of objects and their relationships IV-B and the concepts and their relationships are used to elucidate the message of the illuminations.

A. Object Detection in the Illuminations

The advent of machine learning techniques, particularly those employing pre-trained convolutional neural networks (CNNs) like ResNet [START_REF] He | Deep residual learning for image recognition[END_REF] or VGG [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF], has rendered the need for manually crafted features obsolete. These pre-trained CNNs have demonstrated their ability to effectively capture meaningful representations of various entities, including text, natural images, and art pieces, making them a widely adopted, ready-to-use approach for classifying artworks [START_REF] Vaigh | Gcnboost: Artwork classification by label propagation through a knowledge graph[END_REF], [START_REF] Wu | Not only generative art: Stable diffusion for content-style disentanglement in art analysis[END_REF]. CNNs are also used within deep learning models such as R-CNN, Fast R-CNN, and Faster R-CNN, to identify objects inside an image or object detection. In our study, we relied on the model YOLO [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF] (You Only Look Once). YOLO is an open-source object detection system that revolutionized the field of computer vision. It offers impressive speed and accuracy in identifying and locating objects in images or video frames. YOLO predicts bounding boxes around detected objects, providing precise location information for each object. Each bounding box is associated with a class label and a confidence score. The system has evolved over the years, introducing improvements in terms of accuracy, speed, and architecture. In our pipeline, we used YOLOv3 [START_REF] Redmon | Yolov3: An incremental improvement[END_REF] which implemented several minor design modifications to enhance YOLO's performance.

The YOLO [START_REF] Redmon | You only look once: Unified, real-time object detection[END_REF] detection network comprises 24 convolutional layers, followed by 2 fully connected layers. To reduce feature space, authors utilize alternating 1 × 1 convolutional layers. Initially, they pre-train the convolutional layers on the ImageNet classification task with a lower resolution (224 × 224 input image) and subsequently double the resolution for the detection task. Both YOLO and YOLOv3 are trained to predict bounding boxes that are responsible for each object inside the image. The model is evaluated in terms of IoU (Intersection over Union) which is defined as the ratio between the overlap of the predicted instance with the real one. It is highly valued for image segmentation problems.

Models like YOLO were trained on datasets with modern images such as the COCO dataset 3 . Meanwhile, we have old images obtained from scanned illumination manuscripts. In fact, we used Mandragore an API provided by the BnF (the French National Library) which serves as the iconographic indexing database for illuminations at the BnF. Continuously 3 https://cocodataset.org/ enriched since 1989, it currently describes 205,000 illuminations from nearly 7,000 manuscripts held in the Manuscripts Department and the Arsenal Library. Each identifiable element is indexed using a multilingual vocabulary of over 20,000 terms. The web application providing access to Mandragore since 2003 is now somewhat outdated and is the subject of a redesign project aimed at better showcasing the rich database content. As part of the Illumination project, more than 5,000 illumination images have been extracted from Mandragore, originating from various countries but primarily from France.

To conduct initial tests without annotating the entire dataset (which contains over 5000 complete illuminations and over 5000 illuminations manuscripts), we are limiting ourselves to detecting a minimum number of classes: Person, Animal, and Weapon. We have thus annotated approximately 300 images that may or may not contain these three classes. It is important to note that images without our classes are just as important as images containing our classes; this allows the neural network to identify what is not something. In addition, we used the Platform developed in [START_REF] Diarra | Illumination3. 0: A semantic annotation platform based on ontology for medieval illuminations[END_REF] which allows any user to annotate the objects inside the images by surrounding the objects with bounding boxes which can speed up the annotation processing and improve the quality of the detection model.

We take several precautions to ensure that the model is satisfactory:

• Images are resized before annotation, which allows the network to maintain the overall proportions of the objects to be annotated. • Images and annotations are placed in the same folder and saved in Yolo annotation format. • The configuration files provided for training the model are modified to match our dataset, GPU configuration, and the number of classes. This number of classes is updated after each modification of the dataset or the addition of a class to be detected. The off-the-shelf YOLOv3 model has poor accuracy on our images. In order to improve its accuracy, we fine-tuned YOLOv3 on our annotated images and tried two cases namely predicting only one class (Person) and predicting three classes (Person, Weapon, and Animals). The results for these experiments are shown in Section V.

B. Elucidating Medieval Illuminations

The automatic annotation of illumination has two parts: the object detection algorithm that yields the bounding boxes using YOLOv3 described in the previous section, and the reasoning mechanism that constructs a concept from a set of objects defined by their bounding boxes within the same image. In Example 4 the concept Princess is defined as a Person, with a Dress and a Tiara. We can define a set of SWRL rules defining all the concepts that are inside the ontology Medievelen [START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF]. We also make use of the inference mechanism to check the appropriate type of an object so the SWRL rules remain true. One can define the concept hasRightToKill as a Person carrying a Weapon: hasRightT oKill(X) → P erson(X), W eapon(Y ), carry(X, Y ) If we have in an image a Duke carrying a Sword (Duke(X), carry(X, Y ), Sword(Y )), the previous rule does not apply directly. But since in the Medievelen [START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF] and as shown in Image 3, we have Duke ⊂ Lord ⊂ P erson meaning that ∀XDuke(X) → P erson(X) and similarly if we have Sword ⊂ W eapon we can write it as ∀XSword(X) → W eapon(X). We can then use the inference mechanism to rewrite the previous facts (Duke(X), carry(X, Y ), Sword(Y )) as P erson(X), carry(X, Y ), W eapon(Y ) which means a Duke carrying a Sword has the right to kill. We define the rules for the most general concept and using the inference mechanism we can deduce implicit facts.

For example, there is no need to define the rule hasRightT oKill(X) → Duke(X), Sword(Y ), carry(X, Y )

In fact, as we show in the previous example, this rule can be deduced from the more general one:

hasRightT oKill(X) → P erson(X), W eapon(Y ), carry(X, Y )

For the relation between concepts we handle them partially by looking at a couple of concepts inside an image and we try to predict the most general relation from the ontology. Therefore relation detection inside the image is bound to the relationships defined inside the ontology Medievelen [START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF] The inference mechanism is performed based on the reasoning engine Pellet [START_REF] Sirin | Pellet: A practical owl-dl reasoner[END_REF]. Pellet is a popular reasoning engine used in the field of Semantic Web and ontology-based knowledge systems. It is known for its efficiency in performing Description Logic (DL) reasoning, which includes tasks such as ontology consistency checking, instance classification, and inferencing based on ontological knowledge. Pellet is often employed in applications that require automated reasoning to make logical inferences and deductions from complex knowledge structures, facilitating more intelligent and contextaware decision-making in various domains. Fig. 4: A woman touching a unicorn, but she is not looking for a husband obtained from this online catalogue https://www.bl.uk/catalogues/illuminatedmanuscripts/ ILLUMIN.ASP?Size=mid&IllID=47419

The process of elucidating medieval illuminations relies mainly on our annotation process, which enables concepts to be defined from the object detection stage. Once we define the concepts inside an image and their relationships, we define SWLR rules to elucidate the message of an illumination with the help of a medievalist expert. Inside the Image 2 after identifying all the objects, we will be able to define the concepts Princess and Unicorn but we also have a special expert rule stating that if a princess is shown inside an image touching a unicorn it means she is looking for a husband. We then devised the following rule: husband search(X) → P rincess(X), U nicorn(Y ), touch(X, Y )

These rules for elucidating medieval illumination are fixed by the expert and our contribution is to analyze the medieval images in order to find the best rule to use. We also make use of the inference mechanism with Pellet to reduce the quality of rules needed for illumination analysis.

For example, if we use our pipeline to understand the illumination in Image 4, we can see that we have a Woman touching the Unicorn. Can we deduce that the woman is looking for a husband? the answer is no. Actually, in Image 4 we have a Person who has the right to kill, and he is attacking the Unicron a Kinght then.

We can write the facts inside the Image 4 as fellow:

hasRightT oKill(X), U nicorn(Y ), Attacking(Y, X), W oman(Z), touch(Z, Y )

This means the woman already found a husband and it is dangerous to come to make a proposal!

V. EXPERIMENTAL EVALUATION

We conducted a comprehensive experimental evaluation of our pipeline using the benchmarks that we created from BnF illuminations. To demonstrate the effectiveness of our proposed approach we finetuned the object detection model YOLOv3 [START_REF] Redmon | Yolov3: An incremental improvement[END_REF] to find objects in the illumination using bouding boxes. To evaluate our model we used the metric mAP, or mean Average Precision, which is a commonly used performance measure in object detection and information retrieval tasks. It evaluates the precision and recall of a model by calculating the average precision across various classes or queries. It provides a single number that quantifies the overall quality of the model's predictions, with higher mAP values indicating better performance in localizing and recognizing objects.

We first train the model to detect only the class Person. In any image, we will be looking for all the possible bounding boxes that contains a person. We observe a significant decrease in the loss function and a rapid increase in the mAP metric to around 97% (see Figure 7). It appears that object detection for the "Person" class is quite accurate. We can see that frontal faces are correctly detected, while profiles are detected less accurately as in Images 5b the model was not able to predict the last person in the image. Face detection via bounding boxes seems to work correctly with no false positives. Face detection appears to struggle or forget to detect individuals with darker skin tones. For example in Image 6, the model was not able to predict people with dark skin. We argue that the selection of illuminations plays a role; the choice of illuminations can influence the representation of people with different skin tones, and the dataset mainly consists of French illuminations where the majority of individuals are depicted as white. The number of annotations is also a major factor; it's easier for the model to develop biases when it has limited training data. It's important to note that only 300 images containing zero to multiple faces were annotated. The quality of illuminations varies; some illuminations are damaged, which may explain the model's difficulty in detecting certain faces affected by the aging of the document.

Impressed by the high accuracy of the model (97% in term of mAP), we increased the number of classes to 3 namely Person, Weapon and Animal.

In the same way as for the learning with one class, we observe a noticeable but slower decrease in the loss function (see Figure 8). However, it appears that the bounding box detection and the mAP calculation result in a lower percentage (67% in the best case). Nevertheless, certain results can still be discussed. We can see in Image 9 that faces still appear to be detected equally well. The detection of the Animal and Weapon classes is much less accurate. We can explain the decrease in accuracy with the fellowing reasons:

• The choice of our other two classes, Animal and Weapon, encompasses a wide range of vastly different shapes,

VI. CONCLUSION

Medieval illuminations serve as intricate systems of graphic and visual information, characterized by metaphorical relationships whose interpretations evolve within a specific context. These illuminations functioned as knowledge graphs employed by medieval elites to symbolize their social identity, depict life events, and convey cultural values. However, decoding these metaphors and messages can prove challenging, particularly for non-experts.

To address this challenge, we propose a systematic approach that treats medieval illuminations as images and employs YOLOv3 for object identification through bounding boxes. Additionally, we utilize ontology to extract entities, relationships, and implicit messages from these images, facilitated by logical inference. Our ultimate goal is to simplify the interpretation of illuminations and potentially provide privacy tools for contemporary social media platforms by establishing a logical framework for encoding and transmitting information. This approach offers a bridge between historical and modern communication methods, enabling a deeper understanding of the rich visual language of medieval illuminations.

In future work, we plan to improve the accuracy of our model by increasing the annotated images and the quality of the detection model. We also plan to devise logical communication tools based on the illumination idea where users can define a set of objects to encode a message. Finally, we plan to study how generative models such as Generative Adversarial Networks can be used to generate illumination from a plain text.

VII. ACKNOWLEDGMENT

Fig. 1 :

 1 Fig. 1: The Lady with the Unicorn at the Cluny Museum © Cluny Museum -National Museum of the Middle Ages.

Fig. 3 :

 3 Fig.3: The hierarchy of the classes inside the ontology Medievelen[START_REF] Diarra | Mediev'enl-a domain ontology for cultural heritage supports: Case of medieval illuminations of burgundy duke[END_REF]

  Fig. 5: Examples of objects detection using our finetuned YOLOv3 on the class Person.

Fig. 6 :

 6 Fig. 6: Examples of objects detection using our finetuned YOLOv3 on the class Person with white skin and dark skin.

Fig. 7 :

 7 Fig. 7: Accuracy and loss function associated to the detection and bounding box for the class Person.

Fig. 8 :

 8 Fig. 8: Accuracy and loss function associated to the detection and bounding box for the the classes Person, Weapon and Animal.

Fig. 9 :

 9 Fig. 9: Examples of objects detection using our finetuned YOLOv3 on the classes Person, Animal, Weapon.

• Art historical analysis: They consist in focusing on the formal elements of the illuminations, such as composition, style, and iconography[START_REF] Alexander | Art history, literary history, and the study of medieval illuminated manuscripts[END_REF].

The authors would like to express their deep gratitude to Nicolas Gros and Jonathan Martin-Maestre, engineers at the CIAD Laboratory, for their contributions to the development of our final tool. Their expertise and dedication were instrumental in bringing this project to fruition.

funding agency here. If none, delete this. 1 https://www.ciad-lab.fr/project/illumination-3-0/


Lokman Galal
email: lokmanmagalal@gmail.com

Claire Stragier

Farid Boumédiène

Azra Hamidović

Océane Maugrion

Marie-Laure Dardé

Aurélien Mercier

Marie- Laure Dardé

Combining spatial analysis and host population genetics to gain insights into the mode of transmission of a pathogen: The example of Toxoplasma gondii in mice

Keywords: Toxoplasma gondii, Mus musculus, spatial analysis, relatedness, transmission, vertical

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

Introduction

Toxoplasmosis is an ubiquitous parasitic zoonosis, caused by an obligate intracellular protozoan parasite Toxoplasma gondii. In humans, T. gondii infection is often subclinical, except in some risk groups like the developing foetus (in case of congenital infection) and immunocompromised patients, for which toxoplasmosis can have severe health consequences [START_REF] Montoya | Toxoplasmosis[END_REF]. Felids are the definitive hosts, with the domestic cat being the unique definitive host in the domestic environment, while all other warm-blooded animals are intermediate hosts for this parasite [START_REF] Frenkel | Toxoplasma gondii in cats: fecal stages identified as coccidian oocysts[END_REF][START_REF] Dubey | Toxoplasmosis in animals and humans[END_REF]. Birds and mammals, including humans, often develop dormant tissue cysts after ingestion of oocysts shed in the environment by cats in the form of contaminated faeces [START_REF] Dubey | Toxoplasmosis in animals and humans[END_REF]. Commensal rodents, being the main prey of cats [START_REF] Turner | The Domestic Cat: The Biology of its Behaviour[END_REF], are probably the most important reservoirs for T. gondii in the domestic environment [START_REF] Dubey | Sources and reservoirs of Toxoplasma gondii infection on 47 swine farms in Illinois[END_REF][START_REF] Hejlícek | Toxoplasmosis in wild mammals from the Czech Republic[END_REF].

Experimental studies have shown that rodents are able to get infected by T. gondii through several routes [START_REF] Dubey | Toxoplasmosis in animals and humans[END_REF]. Infection through oocyst ingestion is universally admitted as a conventional infection route for most of intermediate host species including rodents, although a high inoculum dose can be fatal in some susceptible hosts such as the house mouse Mus musculus [START_REF] Owen | Vertical transmission of Toxoplasma gondii from chronically infected house (Mus musculus) and field (Apodemus sylvaticus) mice determined by polymerase chain reaction[END_REF]). In addition, several studies have shown that an infected female rodent can vertically transmit the parasite to her offspring, during pregnancy due to transplacental passage of parasites to foetuses, or to neonates during lactation [START_REF] Dubey | Rat model of congenital toxoplasmosis[END_REF][START_REF] Roberts | Studies on a murine model of congenital toxoplasmosis: vertical disease transmission only occurs in BALB/c mice infected for the first time during pregnancy[END_REF][START_REF] Zenner | Rat model of congenital toxoplasmosis: rate of transmission of three Toxoplasma gondii strains to fetuses and protective effect of a chronic infection[END_REF][START_REF] Dubey | Toxoplasmosis in rats (Rattus norvegicus): congenital transmission to first and second generation offspring and isolation of Toxoplasma gondii from seronegative rats[END_REF][START_REF] Owen | Vertical transmission of Toxoplasma gondii from chronically infected house (Mus musculus) and field (Apodemus sylvaticus) mice determined by polymerase chain reaction[END_REF][START_REF] Paulino | Experimental congenital toxoplasmosis in Wistar and Holtzman rats[END_REF][START_REF] Marshall | Detection of high levels of congenital transmission of Toxoplasma gondii in natural urban populations of Mus domesticus[END_REF][START_REF] Freyre | Toxoplasma gondii: congenital transmission in a hamster model[END_REF]. Vertical transmission of T. gondii through successive generations of chronically infected rodents without exogenous reinfection was demonstrated only in outbred laboratory mice [START_REF] Beverley | Congenital Transmission of Toxoplasmosis through Successive Generations of Mice[END_REF] and wild mice Mus musculus from the United Kingdom [START_REF] Owen | Vertical transmission of Toxoplasma gondii from chronically infected house (Mus musculus) and field (Apodemus sylvaticus) mice determined by polymerase chain reaction[END_REF]. Infected mothers transmitted the infection to the majority of their offspring from each litter [START_REF] Owen | Vertical transmission of Toxoplasma gondii from chronically infected house (Mus musculus) and field (Apodemus sylvaticus) mice determined by polymerase chain reaction[END_REF][START_REF] Marshall | Detection of high levels of congenital transmission of Toxoplasma gondii in natural urban populations of Mus domesticus[END_REF]. In contrast, in BALB / c mice, hamsters, and in most of the laboratory rat lineages, vertical transmission was noticed mainly when the infection occured during pregnancy, but seldom in individuals with a chronic infection [START_REF] Dubey | Experimental Toxoplasma Infection in Mice with Strains Producing Oocysts[END_REF][START_REF] Dubey | Rat model of congenital toxoplasmosis[END_REF][START_REF] Roberts | Studies on a murine model of congenital toxoplasmosis: vertical disease transmission only occurs in BALB/c mice infected for the first time during pregnancy[END_REF][START_REF] Zenner | Rat model of congenital toxoplasmosis: rate of transmission of three Toxoplasma gondii strains to fetuses and protective effect of a chronic infection[END_REF][START_REF] Dubey | Toxoplasmosis in rats (Rattus norvegicus): congenital transmission to first and second generation offspring and isolation of Toxoplasma gondii from seronegative rats[END_REF][START_REF] Paulino | Experimental congenital toxoplasmosis in Wistar and Holtzman rats[END_REF][START_REF] Freyre | Toxoplasma gondii: congenital transmission in a hamster model[END_REF][START_REF] Hide | Role of vertical transmission of Toxoplasma gondii in prevalence of infection[END_REF]. Hence, the modes of transmission of T. gondii in natural populations of rodents are still unresolved and are a matter of debate [START_REF] Dubey | Toxoplasmosis in animals and humans[END_REF].

Vertical transmission in intermediate hosts, bypassing sexual multiplication in the definitive host, was proposed as a possible explanation for the clonal structure of most T. gondii populations [START_REF] Johnson | Speculation on possible life cycles for the clonal lineages in the genus Toxoplasma[END_REF][START_REF] Worth | Adaptive host manipulation by Toxoplasma gondii: fact or fiction?[END_REF]. However, oral transmission could also sustain the clonality of T. gondii populations, as cats simultaneously infected with different strains of T. gondii are likely to be very rare events in nature [START_REF] Howe | Toxoplasma gondii comprises three clonal lineages: correlation of parasite genotype with human disease[END_REF], and hence only selfing of the infecting strain usually occurs in the cat's gut. In addition, the ability of T. gondii to modify the behaviour of rodents to presumably facilitate their predation and its trophic transmission to cats [START_REF] Webster | Effect of Toxoplasma gondii upon neophobic behaviour in wild brown rats, Rattus norvegicus[END_REF][START_REF] Berdoy | Fatal attraction in rats infected with Toxoplasma gondii[END_REF][START_REF] Gonzalez | Toxoplasma gondii infection lower anxiety as measured in the plus-maze and social interaction tests in rats A behavioral analysis[END_REF][START_REF] Vyas | Behavioral changes induced by Toxoplasma infection of rodents are highly specific to aversion of cat odors[END_REF] suggests that oral transmission is of key importance in this current pattern of host-parasite coevolution. Evaluating the relative frequency of vertical transmission over oral transmission in rodents in natural settings may help in the understanding of the mechanisms underlying the clonality of T. gondii populations. A previous study relied on comprehensive lambing records to define families within a flock of sheep, in order to test the hypothesis of possible successive vertical transmission of T. gondii within families [START_REF] Morley | Significant familial differences in the frequency of abortion and Toxoplasma gondii infection within a flock of Charollais sheep[END_REF]. However, investigating an association between families and infection occurrence may be much more challenging to test in wild species given the difficulty of reconstructing families a posteriori, using molecular techniques for example [START_REF] Jones | A practical guide to methods of parentage analysis[END_REF].

In the present study, the objective was to provide insight into the transmission pathways of T. gondii within wild populations of house mice (Mus musculus domesticus) from Dakar, Senegal (West Africa). In Senegal, and more widely in West Africa, the genetic structure of T. gondii populations was shown to be strongly clonal, with few clonal lineages representing the majority of parasitic strains [START_REF] Galal | Toxoplasma and Africa: One Parasite, Two Opposite Population Structures[END_REF](Galal et al., , 2019a)). Here, we relied on data on trapping location, microsatellite genotypes and infectious status for T. gondii for mice from several sites in Dakar. The spatial heterogeneity of infected cases was investigated to test if the occurrence of T. gondii infection could be associated to putative foci of environmental contamination within the population home range. To this end, the occurrence of possible over-prevalence zones of T. gondii infection among mice was investigated within each site. In addition, the genetic structure of local mice populations was analysed and the degree of relatedness between mice was calculated, in order to test if the infected individuals were more related to each other than to non-infected mice. We hypothesized that relationships between genetic structure or relatedness and infection could be expected in the case of vertical transmission of T. gondii.

Materials and methods

We took advantage of an extensive survey of urban rodents in the city of Dakar [START_REF] Stragier | Impact of historical and current features of the cityscape on the genetic structure of the house mouse (Mus musculus domesticus) in Dakar (Senegal, West Africa)[END_REF]. Briefly, sampling was carried out in 12 sites of the Cape Verde Peninsula and in the Goree Island (Figure 1), each site being separated from each other by a minimum distance of 600 m and covering a median surface of 0.04 km². Two traps (one wire mesh trap and one Sherman trap) were set per room or courtyard in buildings such as dwelling houses, boutiques, workshops, offices or warehouses, and locations were precisely recorded with a GPS device. This survey led to the sampling of 473 mice, which were genotyped using a set of 15 microsatellite markers. Details about genotyping methodology and basic analysis of genetic data (allelic richness, genotypic differentiation between sampling sites, deviation from Hardy-Weinberg equilibrium) are reported elsewhere [START_REF] Stragier | Impact of historical and current features of the cityscape on the genetic structure of the house mouse (Mus musculus domesticus) in Dakar (Senegal, West Africa)[END_REF]. Mice were previously screened for chronic infection with T. gondii using a real-time PCR assay that target the 529 bp repeat region of T. gondii genome (Galal et al., 2019b). Among the 13 sampled sites considered for this study, four were excluded from the analysis. In the first two sites (Hann-Pecheur and Yoff), the single PCR-positive mouse detected did not enable to investigate the spatial heterogeneity of infected cases. In the two other sites (International Port of Dakar and Parc de Hann), the sampling coverage of the site was highly unbalanced, with important distances (> 500 meters) between the sampled sectors within the site. Sampling size, number of infected individuals and prevalence data per site are summarized in Table S1.

Spatial clustering analysis

Within each of the 9 sites included in this study, purely spatial cluster analysis was performed to test whether the infected mice were distributed randomly over space and, if not, to identify significant over-prevalence zones using Kulldorf's statistic. An over-prevalence zone was defined as a circular geographic area within a site in which the number of observed cases was significantly higher than the number expected if cases were randomly distributed in space. Building units where rodent traps were set during the survey were considered as the smallest spatial unit in this study. 'Spatial scan statistics' which relies on Kulldorf's statistic was used to test the null hypothesis that the relative risk (RR) of T.

gondii infection was the same between any building groups (or collection of building groups) and the remaining building groups of a sampling site. SaTScan software version 9.4.4 [START_REF] Kulldorff | A spatial scan statistic[END_REF][START_REF] Kulldorff | SaTScan-Software for the spatial, temporal, and space-time scan statistics[END_REF], designed specifically to implement this test and using a Bernoulli model, imposed a circular scanning window on the map that moves across space. The area within the circular window, centered on the centroid of each building unit, varied in size from zero to a maximum radius never including more than 50% of the total population within a given site. The SaTScan software tested for possible overprevalence zones within the variable window around the centroid of each building group. The number of Monte Carlo replications for statistical inference was set to 999, and over-prevalence zones with statistical significance of p <0.05 were reported.

Genetic structure and relatedness within over-prevalence zones

Within each site exhibiting an over-prevalence zone, analyses of genetic structure and relatedness were performed in relation to T. gondii infection.

The possible occurrence of distinct genetic groups of mice was investigated using Discriminant Analysis on Principal Components (DAPC) [START_REF] Jombart | Discriminant analysis of principal components: a new method for the analysis of genetically structured populations[END_REF]. DAPC was performed using the adegenet package [START_REF] Jombart | adegenet: a R package for the multivariate analysis of genetic markers[END_REF] for the R 3.4.0 software (R Development Core Team, 2009). This Bayesian clustering method is not based on a predefined population genetics model and is thus free from Hardy-Weinberg equilibrium assumptions. Prior clusters were defined by sequential Kmeans and a range of appropriate clustering solutions based on the Bayesian information criterion (BIC) was defined. The optimal number of clusters selected was the one for which the BIC showed the lowest value and after which BIC increased or decreased by the least amount. Individuals were considered having an admixed genotype when they exhibited no more than 90% of probability of membership in a single cluster [START_REF] Jombart | A tutorial for discriminant analysis of principal components (DAPC) using adegenet 2.0[END_REF]. Relatedness (r) for all pairs of mice within each site was estimated through maximum-likelihood methods using ML-Relate [START_REF] Kalinowski | ML-Relate: a computer program for maximum likelihood estimation of relatedness and relationship[END_REF]. ML-Relate uses the downhill simplex routine to find the maximum likelihood estimate of r. The r values of pairs composed of two infected mice (named group A) were compared to those of pairs composed of an infected mouse and a non-infected mouse (named group B). The Mann-Whitney U test was used to determine statistical significant difference between the two groups in XLSTAT 2017 for Windows.

Concordance between DAPC clustering and relatedness

To evaluate the concordance between DAPC clustering and relatedness, we compared the r values of pairs of mice from identical DAPC clusters (intra-cluster pairs) to those obtained for pairs of mice from distinct DAPC clusters (inter-cluster pairs). Therefore, the r values were organized in groups defined according to the DAPC cluster to which belongs each of the two mice composing a pair (DAPC1/DAPC1, DAPC1/DAPC2, DAPC2/DAPC2, etc.). The distribution of r values between groups was compared using the Kruskal-Wallis test. Post hoc pairwise comparisons of the distributions of r values between groups were performed using the Dunn's procedure, which applies the Bonferroni's correction of p-values. This analysis was performed using XLSTAT 2017 for Windows.

Results

Spatial clustering analysis

Purely spatial cluster analysis revealed the occurrence of over-prevalence zones in four sites (Table 1): Goree Island (Fig. S2), Grand Dakar (Fig. S3), Ouakam (Fig. S5) and Plateau Reubeuss (Fig. S7).

Genetic structure and relatedness

The occurrence of more than one genetic group was detected in seven of the nine sites included in this study using DAPC (Table 2). In the seven sites where genetic structure was found, most individuals showed clear assignment to a single DAPC cluster, as the percentage of individuals with an admixed DAPC genotype was 18.30% on average (ranged from 0.00% to 36.36% according to site). A more or less marked spatial aggregation of mice of the same DAPC cluster was noticed in most sites (Fig. S1-S7). This pattern of spatial aggregation by DAPC cluster was strong in Colobane, Grand Dakar, Ouakam and Gueule Tapée and less pronounced in Goree Island, Patte d'oie and Plateau Reubeuss (Fig. S1-S7). Within the four over-prevalence zones previously identified, more than one DAPC cluster was found, and infected individuals also belonged to more than one DAPC cluster (Table 2; Fig. S2,S3, S5 and S7).

In two of the four over-prevalence zones previously identified (in Grand Dakar and Ouakam), only infected mice were found. We therefore could not compare the r values of pairs composed of two infected mice (group A) to the r values of pairs of mice composed of an infected mouse and non-infected mouse (group B) within these two over-prevalence zones. In the over-prevalence zone occurring in Goree Island, r values ranged from 0 to 0.62 for group A (n=42), with an average of 0.13 and from 0 to 0.91 for group B (n=196), with an average of 0.09. In the over-prevalence zone occurring in Plateau Reubeuss, r values ranged from 0 to 0.37 for group A (n=30), with an average of 0.06 and from 0 to 0.25 for group B (n=132), with an average of 0.03. Mann-Whitney test showed no significant difference between group A and group B in both Goree Island and Plateau Reubeuss, with p-values of 0.202 and 0.267, respectively.

Concordance between DAPC clustering and relatedness

As r values were only calculated between pairs of mice from Goree Island and Plateau Reubeuss, the comparison between DAPC and relatedness was only possible for these two sites.

In Goree Island, 15 groups were defined for r values according to the DAPC cluster to which belongs each of the two mice composing a pair. Five groups were composed of intra-cluster pairs of mice (which correspond to the five DAPC clusters identified in this site) and 10 groups were composed of inter-cluster pairs of mice. The distribution of r values between groups was significantly different using the Kruskal-Wallis test (p-value < 0.0001). The distribution of r values in groups composed of intra-cluster pairs of mice stochastically dominated (significance threshold of 0.0005 after Bonferroni's correction) groups composed of inter-cluster pairs in all pairwise comparisons, with the exception of an absence of significant difference between group 1 and group 3 (Table S2).

In Plateau Reubeuss, six groups were defined for r values according to the DAPC cluster to which belongs each of the two mice composing a pair. Three groups were composed of intra-cluster pairs of mice (which correspond to the three DAPC clusters identified in this site) and three groups were composed of inter-cluster pairs of mice. The distribution of r values between groups was significantly different using the Kruskal-Wallis test (p-value < 0.0001). The distribution of r values in groups composed of intra-cluster pairs of mice stochastically dominated (significance threshold of 0.003 after Bonferroni's correction) groups composed of inter-cluster pairs in all pairwise comparisons (Table S3).

Discussion

In this study, we aimed to evaluate whether spatial patterns of T. gondii infection in mice may be related or not to the genetic structure of hosts, giving clues about the mode of transmission.

A previous study investigating oocyst spatial distribution in an urban area has demonstrated highly localized foci of oocysts' occurrence, associated with cats' defecation sites [START_REF] Afonso | Spatial distribution of soil contamination by Toxoplasma gondii in relation to cat defecation behaviour in an urban area[END_REF]. Therefore, we hypothesized that mice living on areas of recent oocyst shedding would be predominantly exposed to the oocysts found on the soil, resulting in a spatial aggregation of infected mice. We evaluated whether or not the spatial distribution of infected cases was random, by investigating if infected mice gathered in over-prevalence zones of T. gondii infection. Our results showed that the spatial distribution of mice infected with T. gondii was not random within several sites in Dakar, as over-prevalence zones of T. gondii infection could be identified in four sites. Such a pattern may correspond to (1) an environmental source of infection for mice associated to localized putative foci of environmental contamination, but also to (2) vertical transmission, given that mice are known to live in extended family groups occupying a small territory [START_REF] Berry | Life history and bioeconomy of the house mouse[END_REF][START_REF] Pocock | Adaptations of animals to commensal habitats: population dynamics of house mice Mus musculus domesticus on farms[END_REF]. The analyses of genetic clustering using DAPC showed that mice within overprevalence zones belonged to more than one genetic group. This pattern observed in all the four overprevalence zones identified in this study suggests that infected mice within an over-prevalence zone can exhibit some degree of genetic distance, and that genetic proximity (according to DAPC clustering) is not associated with T. gondii infection in mice. In the two sites (Goree Island and Plateau Reubeuss) having over-prevalence zones with infected and non-infected mice, we also showed that relatedness was not higher in pairs of infected mice than in pairs involving infected and noninfected mice. This result suggests no effect of the relatedness on mice infection. In these two sites, the r values of pairs of mice from identical DAPC clusters (intra-cluster pairs) were generally significantly higher than those obtained for pairs of mice from distinct DAPC clusters (inter-cluster pairs). This comparison enabled to verify the concordance between the two types of genetic analysis. Finally, no clues supporting an association between T. gondii infection and genetic structure could be found, suggesting that vertical transmission has no significant role in T. gondii infection and that infection occurrence can only be associated to the location.

However, the approach used in this study, combining host genetics and spatial analysis of T. gondii prevalence, faced some limitations in several sites. In five sites, no over-prevalence zones could be detected, which may be attributed to gaps in sampling, the spatial overlapping (partial or total) of several contamination foci within a siteif we assume a predominant role of oral transmissionor the movements of infected individuals within the site. In addition, no genetic structure could be identified using DAPC in two of these sites to test the effect of genetic structure on the distribution of infected individuals. Furthermore, DAPC is known to group together individuals with similar genetic profiles in terms of allele frequencies, but inferred groups do not necessarily correspond to family groups. Studies in the lab or in the wild have shown that mice populations are subdivided into social breeding groups, termed demes, where gene flow is restricted by behavioural barriers [START_REF] Petras | Studies of Natural Populations of Mus. II. Polymorphism at the T Locus[END_REF][START_REF] Anderson | Ecological structure and gene flow in small mammals[END_REF][START_REF] Selander | Behavior and genetic variation in natural populations[END_REF][START_REF] De Fries | Behavioural genetics and the fine structure of mouse population: a study in microevolution[END_REF][START_REF] Berry | Ecological genetics of an island population of the house mouse (Mus musculus)[END_REF][START_REF] Singleton | The social and genetic structure of a natural colony of house mice, Mus musculus, at Healesville WildlifeSanctuary[END_REF]. This social organisation may contribute to the occurrence of a genetic structure within populations of mice.

Although populations inferred from DAPC could be composed of related individuals, they may also be composed of unrelated individuals with close genetic profiles. Finally, the significance of relatedness inferences could have been affected by the small sampling from each site when larger sample sizes are usually required to infer relatedness from wild populations [START_REF] Jones | A practical guide to methods of parentage analysis[END_REF].

Overall, despite the limitations that we have pointed out, the results provided by this study suggest that T. gondii infection in mice may be more associated to location than to genetic proximity or degree of relatedness between mice. Transmission is hence more likely to occur through an oral route than by vertical transmission in mice from Dakar.

This conclusion appears to be in contradiction with a number of field studies in which the results supported a vertical transmission of T. gondii in several species of rodents [START_REF] Murphy | The urban house mouse (Mus domesticus) as a reservoir of infection for the human parasite Toxoplasma gondii: an unrecognised public health issue?[END_REF][START_REF] Thomasson | Prevalence and coinfection of Toxoplasma gondii and Neospora caninum in Apodemus sylvaticus in an area relatively free of cats[END_REF][START_REF] Webster | Prevalence and transmission of Toxoplasma gondii in wild brown rats, Rattus norvegicus[END_REF]. In those previous studies, high prevalence levels of T. gondii infection were reported among rodents in areas that appear to be relatively free of cats. These findings provide indirect evidence that vertical transmission can be sufficient to the perpetuation of transmission.

In line with this, a field study was performed on wood mice Apodemus sylvaticus in a location where low a cat density [START_REF] Bajnok | Prevalence of Toxoplasma gondii in localized populations of Apodemus sylvaticus is linked to population genotype not to population location[END_REF]. The wood mice from this location were found to belong to four genetically distinct subpopulations defined with STRUCTURE [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF], distributed in different parts of the study zone. The prevalence of infection was found to be significantly different in each of the subpopulations and was linked to host genotype rather than location of capture. This suggested that parasite infection was associated to subpopulations and non-randomly distributed throughout the populations, which is in accordance with a predominantly vertical route of transmission.

However, as for the DAPC is the present study, it is unknown whether or not these populations defined by STRUCTURE truly correspond to family groups. In addition, an important aspect to point out is that all these studies were conducted in the United Kingdom and in areas free (or nearly free) of cats, limiting the diversity of epidemiological situations in the exploration of this issue. Indeed, in situations where cats densely populate an areaas it is the case in Dakar, Senegal [START_REF] Lahamdi | Etude Comparative de deux Techniques Serologiques: ELISA et IFI appliquées au Serodiagnostic de la Toxoplasmose ovine dans les quartiers de Dakar et Banlieue[END_REF][START_REF] Bend | Enquête coprologique sur la toxoplasmose dans la population des chats de la ville de Dakar[END_REF] and in which rodents are therefore heavily exposed to oocysts, the high predation pressure could reduce the rodents' overall lifespan and the likelihood of reaching sexual maturity to transmit the infection to offspring through vertical transmission (Turner et al., 2013). In particular, assuming a role of parasitic manipulation in facilitating the predation of rodents by cats, a primary involvement of vertical transmission could be detrimental for the sustainability of the cycle, as infected individuals would be less likely to reach sexual maturity and reproduce compared to non-infected individuals as they would die earlier in age.

Conclusions and perspectives

Altogether, the factors quoted above emphasize on the importance of considering the specificities of each epidemiological situation in inferring on transmission dynamics from empirical data. Cat and rodent density, rodent host and parasite genetic determinants probably influence the mode of transmission of T. gondii, by favouringor notvertical transmission [START_REF] Lélu | When should a trophically and vertically transmitted parasite manipulate its intermediate host? The case of Toxoplasma gondii[END_REF]Turner et al., 2013). The absence of a validated and standardized methodology to evaluate the relative epidemiological importance of vertical transmission over oral transmission in rodents in natural settings may also explain the inconsistencies between the results of different studies. The findings of the present study provide interesting insights into the transmission routes of T. gondii in natural populations of mice, although the approach we used showed certain limitations in a number of situations.

Estimating the epidemiological importance of vertical transmission based on the levels of prevalence in embryos collected from pregnant dams may not necessarily be the most appropriate approach to address this question. Although a high frequency of T. gondii transmission from infected females to foetuses is observed [START_REF] Beverley | Congenital Transmission of Toxoplasmosis through Successive Generations of Mice[END_REF][START_REF] Owen | Vertical transmission of Toxoplasma gondii from chronically infected house (Mus musculus) and field (Apodemus sylvaticus) mice determined by polymerase chain reaction[END_REF][START_REF] Marshall | Detection of high levels of congenital transmission of Toxoplasma gondii in natural urban populations of Mus domesticus[END_REF], experimental congenital infection in mice was shown to be associated with heavy mortalities among the offspring and does significantly reduce the number reared to maturity in each litter [START_REF] Beverley | Congenital Transmission of Toxoplasmosis through Successive Generations of Mice[END_REF]. This may limit the transmission of the parasite between generations of mice. Another appealing approach could be the genotyping of T. gondii strains infecting mice of distinct family groups which do not segregate in space to see if they are infected by different strains or not. The limited sensitivity of the available genotyping techniques would probably hamper the application of this approach at the present time as the tissue burden of T. gondii is too low for genotyping in most individuals (Galal et al., 2019b). Indeed, among 89 PCR-positive mice (from a total of 671 mice), only 6 T. gondii genotypes could be obtained (refer to Supplementary Fig. S1 in Galal et al., 2019b).

Future field studies should rely on a denser sampling in smaller spatial scales, which could allow a more accurate determination of parenthood between trapped individuals. A two steps sampling approach could be followed: the first step would be to conduct an extensive sampling (density of traps similar to the one followed in this study) to detect areas where infected mice appear to aggregate, and the second step would be to maximize the sampling efforts on those areas in order to obtain a robust sampling for kinship analyses in relation to infection. In parallel, fine-scale environmental specificities that could explain the spatial heterogeneity in the distribution of infected cases should be thoroughly investigated. This part of the survey should include an estimation of the spatial variability in cat density and the identification of cat defection sites as possible foci of environmental contamination with oocysts.

Another important aspect is the social organization of wild mice populations and their spatiotemporal evolution which are still poorly understood. A better understanding of the family structure of mice and the interactions between family groups would be useful to validate kinship analysis and to understand how T. gondii and other pathogens may spread between mice. DAPC was performed for each sampling site included in this study (n=9). S3. Pairwise comparisons of the distribution of r values between groups of mice pairs 4 from Plateau Reubeuss defined according to their DAPC clusters of belonging. 5

Pairwise comparisons between the mean ranks of the different groups and their p-values (in italics) 6 using the Dunn's procedure (Bonferroni corrected significance level: 0.003). 7 8 9 10

Fig

  Fig. S 1

Table 1 . Over-prevalence zones of infected mice.

 1

	sites	number of over-prevalence zones (p < 0.05)	p-value	SIR (95% CI)	number of mice within the over-prevalence zone	number of infected mice within the over-prevalence zone	total number of building units within the over-prevalence	number of building units with infected mice	radius of the over-prevalence zone (in meters)
	Colobane	0
	Goree	1	0.007	2.71 (1.09 -	21	7	9	6	97
	Island			5.59)
	Grand	1	0.027	5.77 (1.16 -	3	3	3	3	40
	Dakar			16.86)
	Ngor	0
	Ouakam	1	0.003 10.71 (2.15 -	3	3	3	3	18
				31.31)
	Patte	0
	d'oie
	Plateau	0
	Faidherbe
	Plateau	1	0.014	2.89 (1.06 -	17	6	10	5	55
	Rebeuss			6.31)
	Gueule Tapée	0
	For each sampling site included in this study (n=9), purely spatial cluster analysis was conducted to
	identify significant over-prevalence zones using Kulldorf's statistic.

Table 2 . Genetic clustering of mice populations using discriminant analysis of principal components (DAPC).

 2

Table S1 . Sampling size, number of infected individuals and prevalence data per site.

 S1

		group 1	group 2	group 3	group 4	group 5	group 6
		DAPC1/DAPC1 DAPC1/DAPC2 DAPC1/DAPC3 DAPC2/DAPC2 DAPC2/DAPC3 DAPC3/DAPC3
	group 1 DAPC1/DAPC1	*	520.718	466.945	-846.943	350.128	99.000
	group 2 DAPC1/DAPC2	< 0.0001	*	-53.774	-1367.661	-170.591	-421.719
	group 3 DAPC1/DAPC3	< 0.0001	0.240	*	-1313.887	-116.817	-367.945
	group 4 DAPC2/DAPC2	< 0.0001	< 0.0001	< 0.0001	*	1197.070	945.942
	group 5 DAPC2/DAPC3	< 0.0001	0.001	0.003	< 0.0001	*	-251.128
	group 6 DAPC3/DAPC3	0.030	< 0.0001	< 0.0001	< 0.0001	< 0.0001	*
	3

Table

Acknowledgements

We thank Karine Berthier and Carine Brouat for her methodological advices. We thank the French Agence Nationale de la Recherche (ANR project IntroTox 17-CE35-0004) and the Nouvelle-Aquitaine region for funding this research.

 S2. Pairwise comparisons of the distribution of r values between groups of mice pairs from Goree Island defined according to their DAPC 0 clusters of belonging. Pairwise comparisons between the mean ranks of the different groups and their p-values (in italics) using the Dunn's procedure 1 (Bonferroni corrected significance level: 0.0005). 2