# Road ecology: toward a predictive model of wildlife-vehicle collisions

Annaëlle Bénard

► To cite this version:

Annaëlle Bénard. Road ecology: toward a predictive model of wildlife-vehicle collisions. Biodiversity and Ecology. Université Claude Bernard Lyon 1, 2023. English. NNT: tel-04498498

HAL Id: tel-04498498

https://hal.science/tel-04498498

Submitted on 11 Mar 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# THESE de DOCTORAT DE L'UNIVERSITE CLAUDE BERNARD LYON 1

## Ecole Doctorale N° 341
## ÉVOLUTION, ÉCOSYSTÈMES, MICROBIOLOGIE ET MODÉLISATION (E2M2)

Discipline : Écologie

Soutenue publiquement le 01/12/2023, par :
**Annaëlle BÉNARD**

# Road ecology: toward a predictive model of wildlife-vehicle collisions

Devant le jury composé de :

GONZÁLEZ-SUÁREZ Manuela, Associate Professor, University of Reading

JULLIARD Romain, DR CNRS, CESCO UMR 7204

RODRIGUES Ana, DR CNRS, CEFE UMR 5175

DESOUHANT Emmanuel, PU, Université Lyon 1

LOISON Anne, DR CNRS, LECA UMR 5553

LENGAGNE Thierry, CR CNRS, LEHNA UMR 5023

BONENFANT Christophe, CR CNRS, LBBE UMR 5558

Rapportrice

Rapporteur

Rapportrice

Président du jury

Examinatrice

Directeur de thèse

Co-directeur de thèse
<figure><img src="image_2.png" /></figure>
# Table of Contents

<table><tr><td>REMERCIEMENTS</td><td>1</td></tr><tr><td>RÉSUMÉ</td><td>4</td></tr><tr><td>SUMMARY</td><td>8</td></tr><tr><td>Introduction</td><td>11</td></tr><tr><td>1. The importance of roads in ecology and conservation</td><td>13</td></tr><tr><td>2. A closer look at wildlife-vehicle collisions (WVC)</td><td>16</td></tr><tr><td>3. Toward a predictive model of WVC occurrences</td><td>20</td></tr><tr><td>4. The Faune-Auvergne-Rhône-Alpes roadkill dataset</td><td>32</td></tr><tr><td>5. Objectives and hypotheses</td><td>35</td></tr><tr><td>Chapter 1: Agent-based modelling of wildlife-vehicle collisions</td><td>39</td></tr><tr><td>A biologically realistic model to predict wildlife-vehicle collision risks (under review)</td><td>41</td></tr><tr><td>Chapter 2: Roadkill persistence on the road</td><td>79</td></tr><tr><td>Influence of traffic and weather on small wildlife carcass persistence time on roads (under review)</td><td>81</td></tr><tr><td>An experimental measurement of carcass persistence time and sources of removal as revealed by camera-traps (in preparation)</td><td>107</td></tr><tr><td>Case study: informing roadkill persistence time with citizen science</td><td>137</td></tr><tr><td>Chapter 3: Roadkill detection probabilities</td><td>149</td></tr><tr><td>Influence of animal size and driver attentiveness on roadkill detection rates (in preparation)</td><td>151</td></tr><tr><td>Chapter 4: Reporting probabilities in opportunistic roadkill monitoring</td><td>177</td></tr><tr><td>Case study: a methodology for estimating reporting probabilities in citizen science</td><td>179</td></tr><tr><td>General discussion and perspectives</td><td>197</td></tr><tr><td>1. On the value of citizen science for biodiversity monitoring</td><td>200</td></tr><tr><td>2. Toward a predictive model for WVC</td><td>213</td></tr><tr><td>3. General conclusions</td><td>217</td></tr></table>
REMERCIEMENTS

Après 3 années passées sur les routes d'Auvergne-Rhône-Alpes, à traquer le moindre animal écrasé, à grimper dans les arbres pour y poser des pièges photos, à transporter des chevreuils morts à travers le campus, je suis enfin en mesure de pouvoir me poser et faire le point. Ces années ont été formatrices, riches en rencontres, en science, et en découvertes.

Je remercie tout d'abord les rapporteurs qui a accepté de relire ce manuscrit : Drs. Julliard, González-Suárez et Rodrigues, mais aussi mes examinateurs, Drs. Desouhant et Loison. À l'heure où j'écris ces mots, nous ne nous sommes pas encore rencontrés, mais je tiens à vous remercier de l'intérêt que vous m'avez témoigné lorsque je vous ai contactés. J'espère que vous vous apprécierez ce manuscrit, et que vos rêves ne seront pas hantés par des visions d'animaux écrasés sur les routes.

*I would like to start by thanking the referees who agreed to review this manuscript: Drs. Julliard, González-Suárez and Rodrigues, but also my examiners, Drs. Desouhant and Loison. As I write these words, we haven't yet met, but I'd like to thank you for the interest you showed when I first contacted you. I hope you enjoy this manuscript, and that your future dreams aren't haunted by visions of animals crushed on roads.*

Je remercie infiniment mes directeurs de thèse qui m'ont encadrée et épaulée tout au long de cette thèse.

Thierry, pour ton enthousiasme débordant, ton savoir-faire et ta bonne humeur, je te remercie de m'avoir soutenue comme tu l'as fait. Je suis toujours époustouflée par ta capacité à imaginer des expériences et méthodologies qui ont rendu ce travail possible, et par ta volonté de m'accompagner sur le terrain par des températures négatives pour traîner des buses mortes sur la chaussée pendant plusieurs heures.

Christophe, pour ta rigueur scientifique, ton encadrement qui m'a beaucoup fait évoluer en tant que jeune chercheuse, et pour m'avoir aidée à surmonter bien des épreuves. Je te dois également beaucoup pour avoir impulsé plusieurs collaborations scientifiques, bien que celles-ci ne figurent pas dans ce manuscrit. Merci également de m'avoir accompagnée à la gendarmerie, ce qui m'a permis de repartir non seulement avec un piège photo mais aussi un casier judiciaire vierge.

Un immense merci également à toutes les personnes qui se sont impliquées de près ou de loin dans ce projet : Julien Girard-Claudon, pour ta réactivité et ta maîtrise sans faille de la base de données, je regrette que l'on n'ai pu se rencontrer face à face que si tard. Maudit Covid :) !

À l'ensemble de la LPO de l'Ain, et notamment son directeur Francisque Bulliffon, ainsi que Alexandre Roux et Emilie Müller qui se sont personnellement impliqués dans ce projet. Également, je remercie les LPO des autres départements, dont les présidents Louis Granier et Patrick Balluet, qui ont rendu possible certaines de ces expériences. Enfin, je remercie chaleureusement la LPO Auvergne-Rhône-Alpes, et en particulier Marie-Paule De Thiersant (présidente) ainsi que Sébastien Teyssier (directeur), qui se sont impliqués et s'impliquent encore pour m'aider à valoriser cette base de données unique et prometteuse. Merci d'avoir cru et de croire encore en ce projet !

Bien que je ne puisse pas vous citer pour des raisons éthiques, je remercie du fond du coeur tous les bénévoles qui ont répondu présent pour participer aux expériences de cette thèse. Ce sont des personnes comme vous, prêtes à donner de leur temps, qui rendent les sciences participatives possibles. Vous avez été nombreux à répondre à l'appel, et à vous déplacer, parfois plusieurs fois par jour, pour effectuer les différentes missions. Vos efforts sont précieux, et j'espère que ce manuscrit leur rendra justice. Je me permet tout de même de citer C. Guyard et O. Chevreuil qui ont fourni un effort remarquable, valorisé dans le second chapitre de ce manuscrit. Je remercie en particulier Maurice Benmergui, qui m'a en plus aidée à recruter des volontaires, toujours dans la bonne humeur !
Pour continuer sur le sujet du bénévolat, je remercie tout particulièrement l'équipe du Tichodrome, centre de soins pour faune sauvage de l'Isère, qui a accepté de collaborer avec nous sur ce projet. Vous avez répondu à l'appel et vous êtes pliés à nos exigeances pour trier les espèces, malgré la charge de travail que cela vous a demandé. Aucune des expériences de ce projet n'aurait été possible sans vous, et je reverserai une partie de la cagnotte de ma thèse à votre refuge.

Je remercie le SR3A, et en particulier Emilie Genelot, pour le soutien financier, mais aussi technique que vous m'avez apporté. Cette convention de recherche aura été longue à finaliser, mais nous y sommes arrivés !

Bien sûr, que seraient les remerciements d'une thèse sans parler de mes collègues !
Caro, Loïc, Yann, Damien, FX, Nathalie, Adeline, Anne, Louise, l'ensemble de l'équipe E2C, pour votre bonne humeur, les conversations du midi, pour les boites de haribos qui apparaissent soudainement dans le bureau, pour les ballons, les croissants, les petits gâteaux, et le canapé ! Je remercie également Vanessa, qui a accepté de m'accompagner sur le terrain pour traîner des renards morts sur la route (vous remarquerez qu'il y a un thème dans ces remerciements). L'ensemble des membres du LEHNA, les doctorants, le secrétariat, et notamment Nadine qui a su d'un coup de téléphone régler ce sur quoi nous nous cassions les dents depuis des mois. J'ai également une pensée pour l'équipe pédagogique ainsi que Gisèle et Gaëlle qui m'ont épaulée lors de mes premiers pas en tant qu'enseignante.

Vous me voyez venir, je réserve une place toute particulière à vous, les andouilles du bureau. Julia et Chloé, j'espère que l'on aura l'occasion de continuer à cohabiter. Vous allez mener des thèses brillantes, et n'oubliez pas de vous amuser !

À Aude, que j'ai eu beaucoup de plaisir à rencontrer. Je te souhaite tout le meilleur pour la suite de ta vie professionnelle et personnelle, n'écoute que toi et trace ta route.

Julien, je regrette que tu n'aies pas commencé la thèse plus tôt car nous étions fais pour nous entendre. Ton enthousiasme est une bouée dans la tempête, contrebalancé seulement par tes capacités de survie en milieu urbain. Je sais que nous ne perdrons pas contact, mais au cas où, fais attention aux trams.

Jessica et Ambre, je n'ai rien à écrire que vous ne sachiez pas déjà. Je n'aurais pas pu traverser ces trois années sans vous à mes côtés, et je nous imagine ridées et cheveux gris dans un bois quelque part à faire brûler des sortilèges. Je n'ai pas les mots pour décrire à quel point je suis heureuse que le hasard nous ai fait nous rencontrer (pour la deuxième fois pour Ambre, comme quoi des fois, il faut insister).

Merci à ma famille, Baptiste, ma mère, et mon père sans qui ma petite voiture n'aurait jamais fait le trajet jusqu'à Lyon sans me lâcher sur l'autoroute. Merci de m'avoir encouragée à suivre mes envies et mes rêves, et de m'avoir apporté tout ce qu'il faut pour réussir. J'ai une pensée particulière pour mon défunt grand-père, Michel Bénard, pour les souvenirs, pour la passion et l'émerveillement constant du monde qui nous entoure que tu as su transmettre à ton fils, ainsi qu'à moi. Mamie, si tu lis ces mots, ce manuscrit de thèse vous est dédié.

Je termine ces remerciements en mentionnant Anna, Inès, Cécile, Marie et Héloïse, Edern, Léna, et tous tes ami.e.s que j'ai pu rencontrer au cours de ma vie et au détour de mes études.
J'espère que vous ferez toujours partie de ma vie.
Ligue de Protection des Oiseaux de la région Auvergne-Rhône-Alpes

<figure><img src="image_3.png" /></figure>

Agir pour
la biodiversité

Je remercie en particulier mon co-encadrant Julien GIRARD-CLAUDON pour le soutien apporté tout au long de cette thèse.

I would particularly like to thank my co-supervisor Julien GIRARD-CLAUDON for his unfailing support throughout this thesis.

<figure><img src="image_4.png" /></figure>

ÉCOLE
DOCTORALE

341

E2M2
ÉVOLUTION
ÉCOSYSTÈMES
MICROBIOLOGIE
MODÉLISATION
UNIVERSITÉ DE LYON

Le contrat doctoral ministériel à l'origine de ce projet a été accordé par l'École Doctorale E2M2.

This doctoral contract, funded by the ministry, was granted by the doctoral school E2M2.

SR3A
Ain Aval & Affluents

Les travaux présentés ici ont été en partie financés par le Syndicat de la Rivière d'Ain Aval et de ses Affluents

The work presented was partly funded by the Syndicat de la Rivière d'Ain Aval et de ses Affluents

<figure><img src="image_5.png" /></figure>

Ainsi que par le Centre de ressources pour les sciences de l'évolution de l'Université Claude Bernard Lyon 1.

As well as the Centre de ressources pour les sciences de l'évolution of the Claude Bernard Lyon 1 University.
# RÉSUMÉ

Les infrastructures linéaires de transport font peser de nombreuses pressions sur les écosystèmes. Selon le dernier rapport de l'IPBES, on peut attribuer le déclin actuel de la biodiversité à quatre grandes causes majeures : la destruction des habitats, leur dégradation par la pollution d'origine humaine, l'arrivée d'espèces étrangères invasives dans les milieux, et l'exploitation directe des espèces animales et végétales. Or, lorsque l'on étudie une route, chacune de ces causes est représentée. Bien sûr, la construction d'une route empiète sur les habitats naturels des espèces sauvages, mais au-delà du goudron, la présence d'une route a de nombreux impacts sur un écosystème : pollution aux métaux lourds, hydrocarbures, gaz à effet de serre, mais également pollution sonore et lumineuse. Cette pollution peut conduire les populations à éviter les bords de routes, laissant parfois jusqu'à plusieurs kilomètres de zone tampon. Les habitats proches des routes sont alors des habitats dégradés, qui ne sont propices ni à la présence, ni à la reproduction des espèces. La qualité amoindrie des habitats, en particulier des bords de routes, est en revanche profitable à l'établissement et la propagation d'espèces invasives, généralement plus résilientes que les espèces natives. Les véhicules eux-mêmes peuvent participer à la dispersion de graines ou d'espèces animales, et les routes sont des couloirs de dispersion parfaits pour des espèces invasives qui ont besoin de surfaces sans obstacles pour se déplacer. Pour finir, les collisions entre faune sauvage et véhicules sont une source de mortalité représentant un prélèvement direct d'individus dans les populations sauvages. Cette mortalité, en s'ajoutant au reste des pressions générées par l'activité humaine, peut mettre en péril la survie de nombreuses espèces.

Il apparaît donc crucial de pouvoir quantifier les pertes occasionnées par les collisions, ainsi que de savoir les prédire dans le temps et dans l'espace. Grâce à ces informations, il est possible de mettre en place des mesures de réduction, telles que des ponts, passages couverts, ou bien la fermeture temporaire de certains axes. De plus, il y a un intérêt scientifique à comprendre le fonctionnement du phénomène des collisions : les réseaux routiers sont de très bons modèles d'étude pour mieux comprendre les relations entre les activités humaines et la biodiversité, et notamment comment les nouvelles pressions évolutives générées peuvent modifier les écosystèmes sur le long terme. La communauté scientifique étudie depuis longtemps le phénomène des collisions. Cependant, devant la difficulté de surveiller l'ensemble des infrastructures de manière régulière, nous ne pouvons donner que quelques estimations de la mortalité, qui se chiffrerait à plusieurs centaines de millions d'écrasements annuellement à l'échelle européenne. Depuis une décennie, de nombreux projets collaboratifs de surveillance des collisions font leur apparition dans le monde : les utilisateurs de la route sont mis à contribution pour reporter eux-mêmes les animaux écrasés rencontrés sur les routes. Malgré cet engouement, les données collaboratives
sont plus difficiles à exploiter que celles générées lors d'expériences scientifiques protocolées, et leur
utilisation n'est pour le moment que marginale dans les publications scientifiques.

Cette thèse s'articule autour de trois grands axes. Tout d'abord, en partant du constat que la plupart des interactions identifiées entre les caractéristiques des paysages, la biologie des espèces, les facteurs temporels et la survenue de collisions, il apparaît que le déplacement des animaux est probablement le mécanisme sous-jacent le plus proéminent de la mortalité routière. Le premier axe de cette thèse (chapitre 1) propose un modèle mécaniste, c'est-à-dire basé sur une modélisation mathématique sans apport de données réelles, qui replace le mouvement des animaux et des véhicules au centre du système. Nous démontrons de manière formelle que certains prédicteurs pressentis, tels que le trafic routier ou le mode de déplacement des animaux, ont un réel lien de cause à effet avec les collisions. En revanche, d'autres prédicteurs, comme la vitesse des véhicules, n'impactent pas beaucoup les risques de collision. Pour finir, nous avons effectué une analyse de sensibilité du modèle, qui nous a permis d'identifier les paramètres clés pour lesquels de petites variations ont le pouvoir de réduire considérablement le nombre de morts sur les routes. Il ressort de cette analyse que toute la compréhension des collisions routières doit s'articuler autour de la question du déplacement des animaux, qui explique la majeure partie des variations dans les risques d'écrasement.

La seconde partie de cette thèse (chapitres 2, 3 et 4) se penche sur la question de la collecte des données de collision. Nous avons travaillé à partir d'un modèle conceptuel représentant les différentes étapes du signalement d'un animal écrasé dans un projet collaboratif : l'animal écrasé doit rester en place assez longtemps pour permettre le passage d'une personne qui participe au projet collaboratif, puis doit être détecté par cette personne, et enfin, doit être effectivement signalé. Le chapitre 2 se penche sur la question du temps de persistance des carcasses animales sur les routes, qui est un aspect crucial des projets de report collaboratifs aussi bien que des comptages protocolés plus traditionnels. Nous avons estimé, par intervalles de deux heures, le temps de disparition des petites carcasses d'amphibiens et de passereaux. Si le temps de disparition d'un passereau, estimé à environ 20 minutes, n'est pas modifié par la pluie ou par le trafic de la route, la disparition des amphibiens est largement dépendante du nombre de véhicules passant sur la route : la disparition moyenne peut survenir entre 1h et 18h après la collision. Au cours d'une seconde expérience, nous avons suivi la disparition d'un grand nombre d'oiseaux et de mammifères, au moyen de pièges photographiques qui se déclenchent au mouvement. Nous étudions en particulier les interactions entre la cause de la disparition et deux prédicteurs potentiels du temps de persistance : le poids de l'espèce et le volume de trafic. Les animaux disparaissaient de la route selon deux mécanismes principaux, soit l'écrasement répété par les pneus (plutôt lié aux petites espèces tuées sur des axes avec un fort trafic), soit le déplacement volontaire de l'animal par une personne (plutôt lié
aux gros animaux sur les petites routes). Il apparaît cependant que le temps de disparation n'est pas dépendant du poids de l'animal, ou du trafic, ce qui nous permet de tirer un seul et unique estimateur de la persistance pour ces espèces : suivant la collision, l'animal ne restera visible qu'en moyenne 10 heures. Un cas d'étude est également présenté à la fin de ce chapitre. Nous y expérimentons une nouvelle méthodologie pour étudier la disparition des animaux suite à la collision, en se reposant sur la participation de collaborateurs volontaires. Cette expérience permet de confirmer les résultats obtenus précédemment, et nous encourageons les scientifiques à développer ce type d'approche pour améliorer la précision des estimateurs de persistance, qui sont nécessaires pour développer ensuite des estimations de la mortalité routière.

Les chapitres 3 et 4 se penchent sur les sciences participatives et en particulier la base de données de collisions constituée via le portail Faune-Auvergne-Rhône-Alpes, qui compte près de 100 000 signalements d'animaux retrouvés morts sur les routes de la région. De part sa taille, cette base est l'une des plus importantes au niveau mondial. Nous étudions d'abord l'efficacité de détection des conducteurs, en comparant notamment la probabilité de détection d'un animal mort lorsque le conducteur est activement à la recherche de carcasses à celle d'un conducteur qui ne l'est pas. Nous démontrons que la détection d'un animal est conditionnelle à sa taille, son espèce, mais aussi que les conducteurs qui ne sont pas en recherche active détectent 34 fois moins de carcasses. Ces résultats ont de fortes implications pour les projets collaboratifs : en effet, dans ces projets, les contributeurs ne conduisent pas uniquement pour relever les écrasements, à la différence des comptages routiers menés par des chercheurs. Pour finir, nous proposons dans le chapitre 4 une méthodologie innovante pour calculer le taux de signalement des animaux repérés dans le projet Faune-Auvergne-Rhône-Alpes. À l'aide de fausses carcasses placées sur les routes, de questionnaires semi-dirigés, et d'un modèle mathématique basé sur une chaine de Markov, nous démontrons formellement et pour la première fois dans la littérature que l'effort de signalement dans les projets collaboratifs n'est pas égal au nombre d'animaux détectés. Ce résultat, obtenu ici dans la cadre du signalement collaboratif des collisions routières, s'étend probablement à l'ensemble des projets collaboratifs pour reporter la présence de tous types d'espèces animales. Cependant, s'agissant d'une expérience préliminaire, nous ne sommes pas en mesure de fournir des estimations très précises de ce taux de signalement : il pourrait se situer entre 5 % et 72 % pour Faune-Auvergne-Rhône-Alpes, avec une proportion moyenne estimée à 33 %. L'amélioration du traitement mathématique des données devrait permettre de fournir des résultats plus précis.

Le dernier axe de cette thèse se penche sur l'application directe des résultats obtenus pour transformer les signalements d'écrasements de la faune présents dans Faune-Auvergne-Rhône-Alpes en estimations de la mortalité réelle dans la région. À titre d'exemple, nous estimons le nombre de collisions pour certaines
espèces : la buse variable *Buteo buteo*, le renard roux *Vulpes vulpes*, l'écureuil roux *Sciurus vulgaris*, et enfin, les petits passereaux (mésanges, moineaux...). Grâce aux estimateurs obtenus précédemment, nous estimons que 800 000 passereaux sont morts sur les routes de la région en 2022, soit un taux de 10 collisions par km² et par an. Pour le renard, ce serait 6500 cas de collisions en 2022, soit 0,1 renard par km². Les populations d'écureuils auraient perdu 9000 individus sous les roues des voitures (0,13/km²/an) et les buses, 1600 individus (soit 0,02/km²/an). Cette mortalité, qui est entièrement d'origine humaine, vient s'additionner à la mortalité naturelle ainsi qu'aux autres pressions anthropiques qui pèsent sur les populations. Elle peut donc avoir des conséquences catastrophiques sur la survie à long terme des populations sauvages de la région.

Les travaux présentés sont innovants par biens des points : nous proposons de nouvelles méthodologies pour étudier les collisions, et pour mettre en valeur les base de données de signalements participatifs des collisions existantes. L'étude et la valorisation des projets de sciences participatives est un cercle vertueux, car la valorisation rigoureuse de ces données contribue à l'avancement de l'état des connaissances scientifiques, ce qui valorise le travail des contributeurs bénévoles et permet d'impulser de nouveaux projets touchant à d'autres domaines des sciences. Le cadre théorique apporté par le premier chapitre de cette thèse permet d'orienter les futurs efforts de recherche dans le domaine de l'écologie des routes. En effet, le modèle mécaniste que nous avons construit fournit une base de travail pour comprendre le phénomène des collisions, et donne des pistes concrètes pour modéliser de manière efficace les données de collisions telles que celles présentes sur le portail Faune-Auvergne-Rhône-Alpes. La synergie de ces deux approches, l'une basée sur la théorie et l'autre sur les données empiriques, est la piste la plus prometteuse pour arriver, à terme, à un modèle prédictif des risques de collision entre véhicules et faune sauvage.
SUMMARY

Linear transport infrastructures have substantial effects on ecosystems. According to the latest IPBES report, the current decline in biodiversity can be attributed to four major causes: habitat loss, their decline in quality, invasive alien species, and the direct exploitation of animals and plants. Roads represent each of these causes. This thesis focuses specifically on collisions between wildlife and vehicles, which is a direct source of mortality for wildlife. This mortality, in addition to other pressures generated by human activity, can jeopardize the survival of many species. It is therefore crucial to be able to quantify the losses caused by collisions, and predict them both in time and space. Beyond the pragmatic need to reduce these collisions through means such as wildlife crossing structures, there is scientific value in understanding how the wildlife-vehicle collision system works: road networks are excellent models for studying the relationship between human activities and biodiversity, and in particular how the new evolutionary pressures generated can modify ecosystems in the long term. Given the difficulty of monitoring all roads on a regular basis, there are few estimates available for the magnitude of this mortality which is nevertheless estimated at several hundred million deaths per year in Europe. Collision monitoring projects based on citizen science are gaining traction in many countries: road users are asked to contribute their own reports of animal carcasses encountered on roads. However, citizen science data is more difficult to exploit than data generated through standardized scientific surveys, and is currently under-exploited in scientific publications.

This thesis is structured around three main objectives. Chapter 1 presents a mechanistic model that places animal and vehicle movement at the center of the wildlife-vehicle collisions system. We formally demonstrate causal links between certain predictors, such as road traffic or animal movement, and collision risks. A sensitivity analysis shows that wildlife-vehicle collisions research should center around movement ecology paradigms, as animal trajectories explained the major part of the variations in collision risks. Chapters 2, 3 and 4 contain an in-depth analysis of the roadkill data collection process. Each of the steps involved in reporting roadkill is addressed: roadkill persistence on road, detection rates by drivers, and reporting rates of detected roadkill in the context of citizen sciences. Carcass persistence, crucial to both citizen science projects and standardized surveys, was estimated for amphibians, birds, and mammals. In, addition, we investigated the effects of rainfall, traffic volume and body mass on persistence. A case study is also included at the conclusion of this chapter, where we introduce a novel approach for conducting roadkill persistence studies using citizen science, and validate prior findings.
Chapters 3 and 4 look at citizen science through the Faune-Auvergne-Rhône-Alpes reporting project, which has currently accumulated over 100 000 reports. We first study the search efficiency of drivers in the context of opportunistic reporting of roadkill, and find it to be 34 times less than during standardized surveys, which has major implications for citizen science projects. Chapter 4 presents an innovative methodology for estimating the reporting rate of animals spotted on the road to Faune-Auvergne-Rhône-Alpes. Using roadkill decoys, semi-directed interviews, and a Markov chain model, we demonstrate formally and for the first time in the literature that the reporting effort in opportunistic monitoring projects is not equal to the number of animals detected. This result has major implications for all biodiversity monitoring projects based on citizen science. The final objective of this thesis was to provide direct applications of the results obtained, and convert Faune-Auvergne-Rhône-Alpes reports of wildlife mortality on roads into estimates of the number of collisions in the region for select species.

This manuscript contains new methodologies for studying wildlife-vehicle collisions and leveraging existing databases of collision reports. The rigorous use of citizen science data contributes to advancing scientific knowledge, which in turn recognizes the valuable work of volunteer contributors, and drives new projects in other scientific fields. The theoretical framework presented in the first chapter of this thesis provides guidance for future research efforts in the field of road ecology: the mechanistic model we have developed serves as a foundation for understanding the collision system and offers practical approaches for statistical modelling of collision data, such as citizen science data. The combination of these two approaches, one rooted in theory and the other relying on robust empirical data, holds great promise for ultimately developing a comprehensive predictive model of the risk of collision between vehicles and wildlife.
Introduction

<figure><img src="image_6.png" /></figure>
> **“ IN PUSHING OTHER SPECIES TO EXTINCTION, HUMANITY IS BUSY SAWING OFF THE LIMB ON WHICH IT PERCHES.”** Paul Ehrlich<fnref n="1" />

# 1. The importance of roads in ecology and conservation

As I write these words, the world is experiencing its hottest month ever at the global scale (Copernicus, 2023). Human activities have significantly impacted the Earth's ecosystem, limiting the ability of ecosystems to provide services that are essential to our survival (Lafortezza & Chen, 2016). One major consequence of humanity's actions is the Holocene extinction, a mass extinction event projected to lead to the extinction of approximately one million species within the next decade (IPBES, 2019). The IPBES has identified the global factors contributing to the current loss of biodiversity: changes in land use, pollution of the air, water, and soil, invasions by non-native species, and the direct exploitation of wildlife. These factors are all notably embodied by the terrestrial transportation network, comprising both roads and railroads.

Our transportation systems have a significant impact on greenhouse gas emissions, accounting for 25% of overall emissions in Europe (European Environment Agency, 2019). However, it is important to recognize that roads themselves also have pervasive effects on the surrounding natural environment: they have numerous impacts on ecosystems, spanning from altering erosion patterns to directly influencing the behaviour of species (Spellerberg, 1998). In France, roads cover over 1 million kilometers, occupying 2% of the total area and are used in 72% of travels (Ministère de la Transition Écologique, 2020). Globally, the estimated length of roads, which currently stands at 21 million kilometers, is projected to increase by up to 23% in the next two decades (Meijer et al., 2018). With roads being so prevalent, and their significant influence on our ecosystems, it is not surprising that Harvard landscape ecologist Richard Forman referred to them as the “sleeping giants” of environmental sciences. The term “Road Ecology<fnref n="2" />” was therefore proposed to unify the previously disconnected understanding of the various ecological effects of roads into a cohesive framework (Forman & Alexander, 1998).

<footnote n="1">1 This quote appears in the Hall of Biodiversity of the American Museum of Natural History, NYC, USA.</footnote>

<footnote n="2">2 Often attributed to Forman, the first mention of this term in the literature can be found in Walper *et al.* (1981) according to van der Ree *et al.* (2011)</footnote>
Ecological effects of the road network

In the last global assessment report on biodiversity and ecosystem services (2019), the IPBES lists changes in land use, pollution, invasive alien species and direct exploitation of the natural resources as major drivers of the current decline in biodiversity. By demonstrating each of these drivers, the road network serves as an exemplary representation of anthropogenic change (Spellerberg, 1998). Naturally, a road's surface does not provide a hospitable habitat for species. Although the construction of a road leads to a seemingly small loss of square footage, a highway can still occupy up to 0.1km² per kilometer of road (Seiler, 2001). As a point of reference, the French road network covers a total of 10,300 km², and this network covers 81,000km² in the United States (Carr et al., 2002). However, it would be incorrect to assume that the loss and degradation of habitats is only limited to the physical presence of roads. For example, the presence of roads affects the patterns of soil erosion and thus modifies the geomorphic and hydrological settings of landscapes (Shi et al., 2008; Valentin et al., 2005). Unpaved roads in particular erode at a faster rate than the surrounding areas, and the eroded materials can directly enter water streams (Fu et al., 2010; Reid & Dunne, 1984), posing a threat to the persistence of wildlife by altering the physical and chemical properties of the water column (Ellis, 1936). Wind erosion of roads also leads to the release of dust into the atmosphere (Středová et al., 2021; Yulevitch et al., 2020), causing significant negative impacts on human health, climate, and ecosystems (Walker & Everett, 1987).

Furthermore, road traffic generates both acoustic and light pollution, significantly diminishing the overall quality of the surrounding habitats (Seiler, 2001). Road surfaces often contain residues of gasoline, oil, and heavy metals all stemming from engines, fuel consumption, brake pads and tires. These substances are then deposited on the sides of roads and can be transported to the surrounding habitat through water runoff (Deletic & Orr, 2005). Consequently, the physico-chemical properties of road-adjacent habitats are altered, usually exhibiting elevated levels of lead, cadmium, copper, zinc, and nickel, all of which originate from vehicular traffic (Timothy & Tagui Williams, 2019). Additionally, polluted road water runoff can enter nearby freshwater systems with devastating impacts on the organisms (Dugan & Arnott, 2023).

Multiple authors have explored the concept of “road-effect zones”, which refers to the area of the habitat that is directly ecologically impacted by the presence of a road (Forman & Alexander, 1998). Early research has shown that the density and reproductive success of bird populations can be negatively affected up to 3km on both sides of major roads, likely due to the noise and pollution generated by traffic (Forman et al., 2002; Reijnen et al., 1995). In general, the destruction and degradation of habitats contribute to a decrease in species richness, reproductive success, immunity, and genetic diversity in populations and communities of amphibians (Eigenbrod et al., 2009; Lesbarrères et al., 2003; Semlitsch
et al., 2007; Tennessen et al., 2014), large mammals (Newmark et al., 1996; Shanley & Pyare, 2011), birds (Crino et al., 2013; Kroeger et al., 2022) and reptiles (Boarman & Sazaki, 2006) in proximity to roads.

Roads are also perhaps the most compelling visual representation of landscape fragmentation (fig. 1). The fragmentation of landscapes has been identified as one of the most significant drivers of biodiversity loss and poses a significant threat to the survival of plant and animal communities alike (Aguilar et al., 2019; Kuipers et al., 2019). Roads fragment landscapes by creating barriers to movement and dispersal. This barrier effect can be attributed to the inhospitable nature of road surfaces, fencing, the volume of traffic leading to high levels of noise and disturbance, light and chemical pollution, as well as the direct mortality caused by animal-vehicle collisions (Jacobson et al., 2016; Jaeger et al., 2005; Lesbarrères & Fahrig, 2012). Consequently, the presence of roads has the potential to diminish the connectivity of landscapes, thus impeding gene flows between populations (Garcia-Gonzalez et al., 2012; Keller & Largiadèr, 2003; Riley et al., 2006; but see Prunier et al., 2014) and compromising their persistence (Couvet, 2002).

<figure><img src="image_7.png" /><figcaption>Fig. 1: Roads provide compelling visual representations of landscape fragmentation, which is recognized as one of the major contributors to the current decline in biodiversity.</figcaption></figure>

Credit: Deva Darshan.

Paradoxically, while roads hinder the dispersal of many species, they can also facilitate the dispersal of others. The vegetation along road verges can support biodiversity (Rotholz & Mandelik, 2013), but these habitats are polluted by heavy metals and gasoline residue and tend to be particularly favorable to invasive and non-native species, which use roads as corridors for dispersal (Nunes et al., 2020; Padmanaba & Sheil, 2014). This dispersal is further enhanced by seeds hitching a ride on car tires and exteriors (Ansong & Pickering, 2013). This phenomenon is not exclusive to flora, as invasive animal species also use roads and road verges as dispersal corridors, taking advantage of the low or lack of vegetation to move freely (e.g., cane toad *Rhinella marina*: Brown et al., 2006) or being transported by
vehicles (e.g., ant *Lasius neglectus*: Gippet et al., 2015; Asian tiger mosquito *Aedes albopictus*: Miller & Loaiza, 2015).

Roads also have documented positive impacts, such as providing shelter for various species of small mammals and arthropods, leading to the formation of unique communities at the road level (Rotholz & Mandelik, 2013). Road surfaces can also serve as basking areas for reptiles (Meek, 2009), and as foraging grounds for carrion-feeders consuming roadkill (Schwartz et al., 2018). However, the occurrence of wildlife in close proximity to roads as well as behaviours that result in animals coming into contact with the road surface, such as basking and scavenging, have the potential to increase the risks of collisions between wildlife and vehicles (Coleman et al., 2008; González-Suárez et al., 2018; Meek, 2009; Slater et al., 2022).

## 2. A closer look at wildlife-vehicle collisions (WVC)

### 2.1. The toll of road traffic collisions with wildlife

Encountering animal carcasses resulting from collisions with vehicles is a universal experience among car drivers, but the ecological consequences of this anthropogenic source of mortality remain uncertain. Road mortality is established as a significant source of mortality for many terrestrial species (amphibians: Hels & Buchwald, 2001; Schmidt & Zumbach, 2008; mammals: Moore et al., 2020, Seiler 2004, reptiles: Selvan, 2012; birds: Loss et al., 2014; see Hill et al., 2019 for a comprehensive review). Current large-scale estimates for road mortality in birds and mammals stand at respectively 29 million and 192 million each year on European roads (Grilo et al., 2020), 8 million and 2 million in Brazil (González-Suárez et al., 2018). Loss et al. (2014) estimated between 89 and 340 million annual bird roadkill for the United States. In addition, an estimated 0.2 million reptiles and 1 million amphibians die in road traffic annually in Finland (Manneri, 2002). Although the magnitude of these estimates is substantial, their relevance to the long-term survival of populations requires to take into consideration the populations' sizes, which may not always be known at such large scales.
At smaller scales, studies using bio-logging to follow the movements of select individuals in a population can help provide figures regarding the relative impact of road mortality within wild populations. The proportion of the population lost to road mortality over the course of a study ranged from less than 1% in the Eurasian otter *Lutra lutra* (Balčiauskas, 2012) and least weasel *Mustela nivalis* (Sidorovich, 2020), to 1%-10% in the amphibians *Rana temporaria*, *Rana arvalis* and *Pelobates fuscus* (Hels & Buchwald, 2001), and the European polecat *Mustela putorius* (Sidorovich, 2020), red squirrel *Sciurus vulgaris* (Fey et al., 2016), European hedgehog *Erinaceus europaeus* (Bearman-Brown et al., 2020) and elk *Cervus canadensis* (DeVivo et al., 2011). In some studies, the estimated proportion of the population lost to road collisions even climbed over 10% of the study sample: coyotes *Canis latrans* (Stevenson et al., 2016), woodchucks *Marmota monax* (Lehrer et al., 2012), European hares *Lepus europaeus* (Cukor et al., 2018) and bobcats *Lynx rufus* (Serieys et al., 2021).

Yet, despite these sometimes alarming numbers, the implications of road mortality on the demography of populations are still in question. Recently published reviews highlight the current lack of knowledge surrounding the long-term effects of roadkill on wild species (Barrientos et al., 2021; Moore et al., 2023). Moreover, roadkill can be selective, with dispersing or less experienced individuals being often more vulnerable to collisions. For example, Burgstahler et al. (2023) found higher incidences of road mortality among female ground squirrels *Callospermophilus lateralis*, which may be attributed to their heightened activity levels during the summer season, and inexperienced juvenile Florida scrub jays *Aphelocoma coeruleescens* were also more often killed by vehicles than adults in Mumme et al. (2000). In consequence, sex ratios and age structures found in roadkill may differ from the general population (Moore et al., 2023), with possible detrimental effects on the persistence of populations even when the overall road mortality rate is low (Baker et al., 2007; Burgstahler et al., 2023; Ryu & Kim, 2021).
## 2.2. Is roadkill inevitable?

When confronted with the ecological consequences of wildlife mortality caused by vehicle collisions, the next natural steps are to attempt to minimize this issue. There is an extensive literature dedicated to exploring and evaluating roadkill mitigation measures. Among the commonly employed approaches, we find non-disruptive and seemingly cost-effective methods such as wildlife warning reflectors and repellents (Gladfelter, 1984). Reflectors are designed to reflect the headlights of approaching vehicles, thus scaring animals away from the road. However, several studies have indicated that these reflectors are not associated to decreased roadkill rates (Benten et al., 2018; Brieger et al., 2022). Acoustic and olfactory repellents are sometimes placed in the vicinity of roads, but also demonstrate little effectiveness in mitigating road mortality (Bíl, Kušta, et al., 2020; Coulson et al., 2019; Grilo et al., 2010, but see Balčiauskas & Jasiulionis, 2012).

Traffic-calming refers to a collection of techniques primarily aimed at decreasing traffic speeds and volumes through strategies such as urban planning, strict speed limits, and the use of various devices such as chicanes, signage, and rumble strips. The implementation of traffic-calming measures has been suggested in the context of roadkill prevention (Jaarsma, 1997). Road signage for the presence of wildlife, occasionally augmented with flashing lights, may have limited effectiveness in altering driver behaviour and reducing roadkill incidents (Pojar et al., 1975; Seburn & McCurdy-Adams, 2019, but see Collinson et al., 2019). The other traffic-calming measures can however be effective in reducing roadkill (Farmer & Brooks, 2012; Hobday & Minstrell, 2008; Jones et al., 2014). However, these approaches are not well-suited for long-term and extensive mitigation measures, and are instead best for temporary or targeted mitigation in strategic locations and during roadkill peaks (Ascensão et al., 2022).

Finally, road crossing structures, often accompanied by road fencing, can help prevent animals from accessing roads while also preserving or restoring landscape connectivity (Glista et al., 2009). Crossing structures include overpasses and underpasses (fig. 2), and their efficiency is only achieved through careful planning as they must ensure successful use by wildlife (Denneboom et al., 2021; Mata et al., 2008; Testud et al., 2020; Woltz et al., 2008). These structures must be placed in strategical locations in order to efficiently mitigate roadkill and restore ecological continuities (Loraamm & Downs, 2016). When implemented correctly, the combination of fencing and crossing structures has proven to be highly effective in reducing roadkill by up to 83% (Rytwinski et al., 2016; Villalobos-Hoffman et al., 2022). However, it is important to note that these structures are associated with significant costs of construction
and maintenance, ranging from tens of thousands of euros to several millions<fnref n="3" /> (Helldin, 2022; Sijtsma et al., 2020).

In recent years, the rise of self-driving cars has led to advancements in automatic collision avoidance systems that can be fitted on autonomous and semi-autonomous vehicles (Riaz & Niazi, 2016.). These systems, which detect and avoid obstacles present on road lanes, have been extended to the avoidance of collisions with wildlife (Gupta et al., 2021; Saad & Alsayyari, 2020; Saxena et al., 2021; Sharma & Shah, 2017). Although not yet widely implemented, such advances deserve to be mentioned in this section, as they may become more significant in the near future. However, these approaches primarily focus on ensuring public safety, and therefore put an emphasis on collisions with large wildlife species which can pose significant threats to human lives (Al-Zahrani et al., 2011), such as ungulates (Sharma & Shah, 2017). In addition, the ‘avoidance’ aspect of the systems, often left to the drivers as the systems only alerts of the presence of an animal, may not always be achievable, especially for vehicles moving at high speeds (Sharma & Shah, 2017).

<figure><img src="image_8.png" /><figcaption>Fig. 2: Example of wildlife crossing structures: the Varennes overpass on highway A89, Puy-de-Dôme, France (top) and an amphibian underpass on road D14 (bottom, located in Doubs, France).</figcaption></figure>

Photo credits: ASF, FNTP.

Wildlife mortality resulting from collisions with vehicles is a pervasive source of mortality. To effectively address this potential threat to biodiversity, two key elements are essential. First, it is crucial to recognize and evaluate the impact of roadkill on populations, as this information should be integrated into species conservation planning efforts (Grilo et al., 2021). Generating awareness about the significance of this issue can also help secure adequate funding for research efforts and the implementation of appropriate mitigation measures. Secondly, as discussed previously, a comprehensive understanding of where and when roadkill incidents occur, as well as the vulnerability of each species, is vital for targeted and efficient interventions (Teixeira et al., 2017). Beyond the pragmatic focus on

<footnote n="3">3 Wildlife underpasses, e.g. to allow amphibian movement during breeding migrations, range from 30 000€ to over 600 000€ depending on the location (France 3 régions). The construction of wildlife overpasses on french highways can cost 3-10 million of euros (APRR, 2023), and a crossing structure is reportedly under development in California, United States with a projected budget of $90 million (20 minutes).</footnote>
roadkill mitigation, there is value in the comprehension of the ecological significance of road mortality as an anthropogenic pressure in the larger context of global change. In particular, the relatively recent threat of vehicles has the potential to induce notable changes in evolutionary pressures, an aspect that currently lacks sufficient attention from the scientific community (Brady & Richardson, 2017).

## 3. Toward a predictive model of WVC occurrences

Predictive modelling in the field of ecology can be categorized into two approaches: statistical (or phenomenological) and mechanistic (Robertson et al., 2003), which are not necessarily mutually exclusive (e.g., Louvrier et al., 2020). When studying a biological system, statistical models rely on describing samples of the observed outcomes to predict future outcomes of the system. In ecology, this process often takes the form of delineating correlative patterns between the sampled outcomes and a set of predictors (Freedman, 2009). On the other hand, mechanistic modelling does not rely on empirical observations of the system's outcomes, but instead employs mathematical models to simulate the underlying mechanisms at play within the system (Rastetter et al., 2003). The validity of a mechanistic model can be explored by comparing the predictions it yields to the actual outcomes of the system (e.g., Nathan et al., 2001).

In other words, statistical models describe the outcomes of a system, and mechanistic models describe the system itself, each approach with its own merits and limits. Statistical models, for instance, often make assumptions about the potential predictors involved and the nature of the relationships with the sampled outcomes (e.g., assuming linear relations). Moreover, the accuracy of a statistical model is closely tied to the quality of the data sample (Baguley, 2004). Mechanistic models, however, require a precise comprehension of the underlying processes operating within a system, which are frequently simplified to enable their description (Batty & Torrens, 2001). The representation of reality through models is inherently flawed as they solely provide an approximation rather than an exact depiction, as stated in the famous maxim "*all models are wrong, but some are useful*" (Box, 1979).

Mechanistic approaches to WVC prediction are not frequent, although mechanistic modelling is well-developed in other areas of ecology, such as species distribution modelling (Peterson et al., 2015). In contrast, statistical modelling, often in the form of linear regression models, has been extensively employed to explore roadkill datasets. They often utilize predictors such as landscape features, temporal
variables and species' life-history traits to identify high-risk species and predict potential hotspots and peaks of roadkill (e.g., Chyn et al., 2021; Farmer & Brooks, 2012; Santos et al., 2018).

**3.1. Identified factors influencing the distributions of collisions**

Several key conclusions arise from the examination of the literature focused on modelling wildlife-vehicle collisions with statistical models: (1) collisions are not randomly distributed, but instead tend to occur in specific areas and at certain times, respectively known as collision hotspots and collision peaks, (2) the rates of collision vary between species, and (3) there are interactions among the spatial, temporal and biological predictors of roadkill. Comprehensive reviews and meta-analyses of the documented factors correlated to the observed distributions of WVC help provide a global overview of the state of the literature in this field (e.g., Grilo et al., 2020; Gunson et al., 2011; Litvaitis & Tash, 2008; Pagany, 2020). As such, the following section is not intended to serve as a comprehensive review of all the predictors of roadkill that have been identified, but instead aims at introducing the reader to select examples including some widely accepted factors influencing collisions, and others that are still debated as repeated studies tend to yield conflicting outcomes.

*Spatial factors*

Land use and habitat features are frequently examined as potential indicators of hotspots for wildlife-vehicle collisions (Pagany, 2020). Research indicates that roads passing through forested habitats are often associated with higher occurrences of WVC (Gunson et al., 2011), although some studies found that the reverse was true (Grilo et al., 2015; Saint-Andrieux et al., 2020; Tatewaki & Koike, 2018). Similarly, grassland and other open areas are associated with both increased or decreased WVC risks (Pagany, 2020). Collisions with birds, amphibians, and reptiles are generally more likely to occur near open water bodies (Gunson et al., 2011). Roadside characteristics also influence WVC, with general increases in collisions when road verges are planted with vegetation (Pagany, 2020), although the opposite has also been evidenced (Hoermann et al., 2020; Skórka et al., 2015). On a larger scale, the diversity and connectivity of landscapes can also be linked to the occurrence of WVC in both positive and negative ways (Pagany, 2020).
The characteristics of the road itself can also indicate the probability of WVC. Collisions can increase (Barrientos & Bolonio, 2009; Seiler, 2005) or decrease with increasing speeds of traffic (Bashore et al., 1985; Murphy & Xia, 2016). The relation between road traffic volume and WVC risk has been theorized to be non-linear (fig. 3). In this conceptual model, the probability of collision first increases and then decreases (or stagnates) with increasing volumes of road traffic: the road becomes progressively less traversable when it gets more and more frequented by vehicles (e.g., noise and disturbance generated by traffic), which may deter animals from crossing (Seiler, 2001). Although there is some empirical support for this model (Clarke et al., 1998; Oxley et al., 1974), some dispute its validity (Bright et al., 2015; Grilo et al., 2015).

Other road characteristics have received less attention in comparison, such as the width and number of lanes, the presence of embankments, fences, the use of de-icing salt, and the slope and sinuosity of the road. Although these have been linked to WVC occurrences, there are once again conflicting findings in this regard (Gunson et al., 2011; Pagany, 2020). Some authors have pointed out an “end of fence” effect, in which roadkill hotspots are artificially created by fences positioned along roads: while fenced sections contain little roadkill, both ends of the fence, which allow wildlife to cross roads again, coincide with increased collision numbers (Helldin & Petrovan, 2019; Huijser et al., 2016; Plante et al., 2019).

<figure><img src="image_9.png" /><figcaption>Fig. 3: Adapted from Seiler & Helldin (2006). Conceptual model: wildlife attempts at crossing roads decrease with the volume of traffic, because highly frequented roads generate noise and disturbance that deter animals from approaching. In result, there is a predicted non-linear relation between traffic volume and the number of WVC.</figcaption></figure>

## Temporal factors

Wildlife collisions vary throughout the year: mammal, bird and amphibian collisions are usually highest in the spring according to Pagany (2020), although Bullock et al. (2011) found higher rates of bird-vehicle collisions during the summer in Kalahari, South Africa, and Kreling et al. (2019) found the highest rates of large mammal collisions during the fall season in California, United States. In general, authors recognize that seasonal peaks in WVC could be explained by levels of activity or specific
behaviours of species, e.g., breeding migrations in amphibians generating high WVC probabilities (Zhang et al., 2018), and deer rutting seasons coinciding with periods of high road mortality (Steiner et al., 2014). Collision risks also vary throughout the day, and depending on the day of the week (Steiner et al., 2014), which could be theorized as the result of changes in traffic volumes (Van Langevelde & Jaarsma, 2005), wildlife activity, and driver visibility (Pagany, 2020).

Finally, some studies have evidenced correlations between the phases of the moon and roadkill occurrences: deer-vehicle collisions peak during full moons (Colino-Rabanal et al., 2018; Steiner et al., 2021), while darker nights account for most of the mortality in the Iberian ribbed newt *Pleurodeles waltl* (Mestre et al., 2019). However, other authors detected no correlation between WVC and lunar phases across several mammalian species (Kreling et al., 2019), which hints once again at a complex relationship between this predictor and road mortality. Recently, the COVID-19 pandemic and its associated lock-downs (i.e., significant and sudden drops in traffic volumes) have granted a reprieve to wildlife (Driessen, 2021), although reductions in roadkill have not been observed for all species and locations (Asari, 2022; Pokorny et al., 2021) which may serve as evidence that road traffic volume alone cannot predict the occurrence of collisions.

## Life-history traits

The correlation between abundance and roadkill has long been noted (D'Amico et al., 2015; George et al., 2011), although some species are found on road more (or less) often than expected based on their abundance (Quiles, 2018). Life-history traits can predict the probability of road mortality. Grilo et al. (2020) provided a handy meta-analysis of European species traits associated with higher WVC risks: they conclude that species characterized by high population density, small body mass and early maturity are the most often killed by traffic. Additional ecological traits have been shown to impact the relative risks of WVC, such as moving speeds and flying abilities (González-Suárez et al., 2018).

Some species-specific behaviours can increase the risk of roadkill, such as basking on roads in reptiles (Meek, 2009) or salt licking in cervids (Grosman et al., 2009). As vehicles constitute recently appeared threats in the evolutionary sense, some species may also be unable to detect them or exhibit maladaptive responses, such as freezing in front of oncoming cars (Lima et al., 2015). In contrast, some species may have the cognitive ability to actively avoid collisions: several bird species have been shown to adapt their flight initiation distance to the speed limit of the road (DeVault et al., 2014; Legagneux & Ducatez, 2013), and it has been suggested that black bears *Ursus americanus* can learn to avoid vehicles while crossing (Jaeger et al., 2005). Therefore, the cognitive and learning abilities of a species may help predict
their tendency to get killed on roads, and it has been suggested that individual personality traits may also
induce differences in collision risks within a population (Lima et al., 2015).

These findings indicate that roads and the associated risk of mortality may lead to rapid adaptations through changes in behaviour, but they may also exert unique evolutionary pressures on species, thereby altering both wildlife and ecosystems in ways extending well beyond the mere loss of individuals to human transportation. For example, Brown & Bomberger Brown (2013) have found that the wing length of cliff swallow *Petrochelidon pyrrhonota* showed a general decrease over 30 years, while road-killed individuals consistently had longer wings than the population average. They proposed that the length of the wing may predict the ability to avoid an oncoming vehicle through a vertical take-off, such that the threat of roadkill selects for shorter wings. The evolutionary changes brought about by the road network have yet to receive significant attention from the scientific community (Brady & Richardson, 2017).

Conclusion

This section offers a concise overview of the identified factors influencing WVC, and emphasizes the discrepancies in findings in the literature (fig 4). WVC hotspots can potentially be forecasted based on spatial predictors at both broad scales (such as land use patterns) and localized scales (such as fencing and roadside vegetation). Likewise, some temporal patterns in roadkill have been described, encompassing variations occurring within a day as well as seasonal differences. Finally, the risks of WVC are influenced by species and individual characteristics, and therefore extend beyond a mere reflection of species abundance.

All of these predictors appear intricately linked, which may explain why correlations identified in one
study may not be repeatable in other contexts. For example, temporal predictors of roadkill often find
likely explanations in changes in the species' abundance and behaviour, or in traffic volume. Similarly,
patterns of land use, roadside vegetation or the use of de-icing salt most likely directly affect the presence
of wildlife in proximity of the road, which in turn drives collision risks. Teixeira et al. (2013) revealed
that the spatial distribution of roadkill hotspots was not coincidental across taxa, and temporal patterns of
WVC also vary depending on the species (Raymond et al., 2021). As previously discussed, if statistical
models highlight correlative patterns between WVC occurrences and its predictors, they are not best-
suited for causal inference. Discerning the individual effects of the identified predictors can be difficult
with statistical modelling, due to the potential high degree of correlation among them. For instance, there
is a likely consistent correlation between certain road characteristics, such as width, number of lanes,
traffic volume and speed limits. In addition, we can cite the well-described allometric relationship
between body mass and population density (Peters & Wassenberg, 1983; White et al., 2007), which may
play a role in some of the identified patterns of correlation.

In conclusion, the use of observed distributions of roadkill is a commonly employed approach for identifying predictors of WVC, and although the predictors of roadkill identified in studies are pertinent within the specific scope of the investigation, scaling up to comprehensive predictive models of WVC is not straightforward due to the inherent complexity of the wildlife-vehicle collision system. Beyond the prediction of WVC, there is also a heuristic value in comprehending the causal relationships between anthropogenic pressures such as road mortality and various other factors.

<figure><img src="image_10.png" /><figcaption>Fig. 4: Interdependencies of the currently identified wildlife-vehicle collision predictors (Pagany, 2020; Gunson et al., 2011; Grilo et al., 2020).</figcaption></figure>
## 3.2. Challenges in WVC data collection

As described earlier, the observed outcomes of a system (in this case, wildlife-vehicle collisions) are central to statistical modelling approaches. Ideally, comprehensive models of WVC should incorporate large-scale dataset to obtain reliable predictions (Denny & Benedetti-Cecchi, 2012). However, while I have so far used *roadkill* and *collisions* interchangeably, it is important to recognize the distinction: roadkill is the observable consequence of an animal-vehicle collision. Ideally, we should rely upon the latter, as the ultimate goal is to understand and predict the mortality generated by road traffic on wild populations. For example, analyses such as fine-scale analysis of the temporal distribution of WVC are not possible with roadkill data, because there is no information available on the time of the collision, and instead only the time of discovery of the carcass is known. In practice however, *roadkill* is often the only accessible data to study WVC, while the collisions themselves are seldom witnessed

Roadkill is often gathered through periodic road surveys, generally performed by research teams, which makes data gathering costly and often limits its scale. Roadkill data can also be provided through opportunistic reporting by road maintenance crews (e.g., Williams et al., 2019) or volunteers (e.g., Swinnen et al., 2022). In contrast, collision data can be obtained from insurance companies or police reports (subsequent to insurance claims from drivers involved in WVC, e.g., dos Santos et al., 2017). However, such data is difficult to assess as it may suffer from over or under-reporting (e.g., insurance fraud, Inbar et al., 2002), and it will logically only represent the limited set of large-bodied species which cause damages to vehicles upon impact. Roadkill data differs from collision data because (1) not all carcasses persist on roads long enough to be detected during surveys, (2) not all carcasses present on the road are successfully detected and (3) in the case of opportunistic sampling by volunteers or maintenance crews, it is possible that not all detected carcasses will be reported. In addition, an unknown percentage of animals involved in collisions may not immediately perish on the road. Instead, they may ultimately succumb shortly after leaving the road, be ejected due to the force of the impact, or become trapped in the front grill of vehicles (Glista, 2008; fig. 5). Beyond mere underestimations of the road mortality due to

<figure><img src="image_11.png" /><figcaption>Fig. 5: Pheasant trapped in a front grill following a collision.</figcaption></figure>

Photo credit: Julien Bouvet (2023)
overlooked animal carcasses, there is evidence that the persistence of carcasses on roads (Henry et al., 2021; Santos et al., 2016) and the rates of their detection (Collinson et al., 2014; Teixeira et al., 2013) are contingent upon biological and contextual factors. As a result, there likely are biases in roadkill datasets, with inevitable repercussions on the outcomes and predictions derived from statistical models.

In recent years, there has been growing attention ported to the biases present in roadkill datasets (Guinard et al., 2023; Santos et al., 2016; Teixeira et al., 2013). In general, improving the accuracy of roadkill carcasses requires more frequent road surveys (up to several times a day, Antworth et al., 2005) to counter the high rates of carcass disappearance from roads, as well as conducting surveys on foot or bike rather than from cars to improve the detection rates (Gerow et al., 2010). The sampling efforts required to detect all carcasses are however often incompatible with the human and financial resources available to research projects (Henry et al., 2021), which limits the scope and feasibility of these studies. In consequence, post-hoc corrections of the datasets (e.g., accounting for the number of roadkill missed during surveys with estimations of the persistence of carcasses on roads and of the detection rates by observers) have been developed and applied as alternative solutions (González-Suárez et al., 2018; Grilo et al., 2020; Teixeira et al., 2013). Consequently, there is a growing need in WVC research for identifying, understanding and providing estimates of the biases in roadkill data collection, such as the persistence of carcasses on roads or the detection rates of carcasses by observers during surveys.

Even with the help of post-hoc corrections, the cost (both financial and in man-hours) of “professional” roadkill monitoring (i.e., conducted by research teams with a rigorous sampling protocol) is nonetheless considerably high. Consequently, its implementation at extensive spatial or temporal scales is infrequent, thus reducing the relevance of the predictive models that can be produced (Denny & Benedetti-Cecchi, 2012). Similar limitations are present in biodiversity monitoring in general (Proença et al., 2017), which has in consequence led to the rise of citizen sciences as a valuable tool for collecting extensive ecological datasets (Deguines et al., 2012; J. L. Dickinson et al., 2010; Thel et al., 2021). In WVC research, citizen science datasets cover large temporal and spatial scales, usually by taking advantage of smartphone apps from which volunteers can report observed roadkill from anywhere at anytime (Vercayie & Herremans, 2015). In the last decade, several roadkill monitoring schemes using volunteer contributors have emerged around the globe, often covering entire countries at a time (South Africa: Périquet et al., 2018; UK: Petrovan et al., 2020; US: Shilling & Waetjen, 2015; Korea: Shin, Kim, Groffen, Woo, Song, & Borzée, 2022; Belgium: Swinnen et al., 2022; Taiwan: Yue et al., 2019), with some projects achieving upwards of 90 000 roadkill observations in over a decade (e.g., Faune-Auvergne-Rhône-Alpes). Therefore, they represent a promising avenue for large-scale predictive modelling of WVC (Shilling & Waetjen, 2015).
However, in addition to the sources of biases presented above, citizen science projects also suffer from their opportunistic nature, meaning that sampling effort is likely to be unevenly distributed across time and space (Petrovan et al., 2020). In WVC research, some projects have attempted to standardize sampling effort by adding the possibility to report the presence and absence of roadkill during itineraries (i.e., sampling along transects, Swinnen et al., 2022), but the vast majority of datasets mostly contain opportunistic reporting of roadkill. Furthermore, in addition to issues with carcass persistence and carcass detection rates, there is currently no research on the rates of the willingness to report<sup>4</sup> roadkill from contributors, or whether this reporting is selective toward more charismatic species. Indeed, it is important to consider that reports in unstructured citizen science biodiversity monitoring—including but not limited to roadkill reporting—may represent only a subset of the detected animals, that could potentially be influenced by observers’ biases (Callaghan et al., 2021; Koch et al., 2022).

<footnote n="4">4 Throughout the course of this work, I will be using the term "roadkill reporting probability" to encompass the concept of willingness to report roadkill in citizen science projects. This is not to be confused with the term "reporting rate" which is sometimes used to signify the rate at which new roadkill is reported in a database.</footnote>
### 3.3. Mechanistic approaches to WVC prediction

Although statistical methods are more commonly used for predicting wildlife-vehicle collisions, there are also authors who have employed mechanistic approaches. In a formal sense, the probability of a WVC can be described as the combination of three probabilities: the probability of coming across a road, of stepping onto the road surface, and the probability of being struck by a vehicle while on the road (fig. 6).

<figure><img src="image_12.png" /><figcaption>Fig. 6: Conceptual model of a wildlife-vehicle collision model. The probability of collision is the result of three consecutive steps: the probability to encounter a road, the decision to step on the road surface, and finally, the probability of a collision with a vehicle while on the road surface.</figcaption></figure>
Some authors have developed mechanistic models of road traversability, i.e. the collision probability for an animal crossing the road (Hels & Buchwald, 2001; Jaarsma et al., 2006; Van Langevelde & Jaarsma, 2005). Assuming that the number of vehicles passing a given point, denoted *X*, follows a Poisson distribution (Breiman, 1963; Oliver, 1961), then the probability for an animal on the road to encounter at least one vehicle is given by $P(X \ge 1)=1-e^{-\lambda \cdot \delta T}$, where $\lambda$ is the volume of traffic of the road and $\delta T$ is the time the animal spends on the road (defined as the time to cross the road perpendicularly, Van Langevelde & Jaarsma, 2005). This model has direct practical uses to predict the proportion of a population killed during road-crossing events, for example in conjunction with metapopulation models (e.g., breeding migrations in amphibians, Hels & Buchwald, 2001). The significant advantage of this model lies in its ability to predict collision probabilities by considering only two variables: traffic, and the time required to cross the road. However, this approach is limited to the scale of a road and is therefore not designed for large-scale predictions, as it does not incorporate road encounter probabilities, and does not consider animal behaviours other than road crossing (e.g., consumption of roadkill, basking on the asphalt, salt licking...). Furthermore, there may be a difference between encountering a vehicle while on the road surface, and getting hit by said vehicle.

The probability of crossing a road, especially at large scales, can be explored through the lens of landscape connectivity, or “the degree to which a landscape facilitates or impedes movement” (Taylor et al., 1993). Previous studies have found that well-connected landscapes tend to have higher occurrences of roadkill (Grilo et al., 2011; Kang et al., 2016; Santos et al., 2013). Landscape connectivity models, drawing for example from concepts in electrical circuits theory, can help identify the most likely locations where the paths of wildlife intersect with roads, and therefore the sections of roads that pose the greatest risk (Girardet et al., 2015; Swanson et al., 2008). This information is particularly valuable in cases where, for example, there is a need to strategically place wildlife crossing structures (Downs & Horner, 2012; Gurrutxaga et al., 2010), or other mitigation measures. However, it should be noted that these approaches do not consider the probability of animals colliding with vehicles while on the road, only the most likely crossing points based on the characteristics of the landscape. In addition, as previously discussed, some characteristics such as high road traffic volume can modify the traversability of roads for many species (Seiler, 2005). Connectivity metrics can be used as covariates in statistical models of roadkill, in addition to road characteristics that are often found to be associated with WVC (e.g., road traffic volume, width or elevation, Girardet et al., 2015).

In summary, existing mechanistic models describe the probability of wildlife-road encounters, or the probability of wildlife-vehicle collisions during the time the animal is on the road surface. To the author's best understanding, there is currently no all-encompassing framework that combines both road encounter
and collision probabilities to mechanistically generate dependable estimates of road mortality within a given landscape. One avenue to successfully combine all the steps presented in figure 6 would be to put an emphasis on modelling the movement and trajectories of animals through the habitats, and on the road surface. There is some empirical support for the importance of animal (and vehicle) movement in understanding the WVC system, such as correlation patterns between roadkill and the presence of specific patches of habitats (in which animal may move differently, Saint-Andrieux et al., 2020), the level of activity of the animals (Steiner et al., 2014), their space-use behaviour (Meek, 2009) and their travel speed (González-Suárez et al., 2018), as well as the speed and density of road traffic (Pagany, 2020).

In movement ecology, the individual trajectories of animals can be described through stochastic equations of two or three-dimensional random walks, such as the Brownian motion (initially describing the motion of particles suspended in a liquid or gas), or correlated random walks (Fagan & Calabrese, 2014). Modelling individual trajectories and behaviour (*agent-based modelling*) can help explain patterns observed at larger scales (e.g., the group behaviour of starling murmurations is modelled with individual trajectories, Reynolds, 1987, the same is true for groups' responses to predators, Viscido et al., 2001). Agent-based models focusing on individual movement and trajectories have also been applied in the context of wildlife management, to help understand the responses of animals to changing environments (McLane et al., 2011). In road ecology, agent-based approaches have been used to explore the costs and benefits of road fencing on population genetics and roadkill risk (Ascensão et al., 2013), and, more specifically, movement-oriented agent-based models have been applied to moose-vehicle collisions mitigation (Grosman et al., 2009) or to model the temporal dynamics of roadkill hotspots by introducing population depletion mechanisms (Teixeira et al., 2017). Although the animal trajectories are simulated, none of these example also considered vehicles as agents, i.e., as entities with their own movement and trajectories. In consequence, collision risks were treated input parameters: animals stepping on the road had a pre-established probability of dying. To the author's best knowledge, no agent-based model has been developed to model the WVC system at large scales to explore the causal relations between spatial, temporal or biological factors and the risk of roadkill for an individual and a population.
4. The Faune-Auvergne-Rhône-Alpes roadkill dataset

The Faune-Auvergne-Rhône-Alpes (thereafter: Faune-AuRA) project is a citizen science initiative focused on biodiversity monitoring, involving both systematic and opportunistic monitoring of all terrestrial species in the Auvergne-Rhône-Alpes region (fig. 7). This regional database is integrated into the Faune-France national database. The monitoring project is overseen by the Ligue de Protection des Oiseaux (translation: Bird Protection League, thereafter: LPO).

<figure><img src="image_13.png" /><figcaption>Fig. 7: Map of the Auvergne-Rhône-Alpes (AuRA) region, France and its 12 departments. It covers an area of about 70 000 km².</figcaption></figure>

Since 2010, Faune-AuRA has integrated the possibility to report incidents of animal mortality on roads. As of July 27th, 2023, the roadkill dataset includes a total of 95,610 reports covering 589 species of reptiles, amphibians, mammals, birds, and insects (fig. 8). Reporting roadkill incidents can be done through a web interface or via the *Naturalist* mobile app, which is available for all Android devices. The roadkill reports include the following information: date, time, location, species, number of carcasses, photograph (optional) and contributor's comment (optional). The project currently involves 4059
contributors, among which many are LPO members. About 15% of the contributors are professionals (LPO technical staff, naturalists, forest and wildlife rangers, researchers...; LPO France, 2021). Despite the inherent value of a dataset of this scale for WVC research, it has never been cited in published work.

<figure><img src="image_14.png" /><figcaption>Fig. 8: The Faune-AuRA roadkill database for the year 2022. There are 7235 reports of roadkill, 20% of which are amphibians, 53% are mammals, 18% are birds and 9% are reptiles.</figcaption></figure>

Overall, the most reported species in Faune-AuRA is the European hedgehog *Erinaceus europaeus* (>5000 reports), following by the European badger *Meles meles* (~3000 reports) and the red fox *Vulpes vulpes* (~2000 reports). The most reported bird is the common blackbird *Turdus merula* (~800 reports), the most reported reptile is the green whip snake *Hierophis viridiflavus* (~700 reports) and the most reported amphibian is the common toad *Bufo bufo* (~1600 reports).

<figure><img src="image_15.png" /></figure>
In addition to producing roadkill maps and comparing the number of roadkill reports per species, we can detect temporal trends in Faune-AuRA. One striking example is the common toad road mortality, which is known to explode in spring during the annual breeding migration of the species (Hels & Buchwald, 2001). This pattern is present in the Faune-AuRA database (fig. 9). However, both the number of reports and the spatio-temporal patterns in this dataset may misrepresent the actual patterns of wildlife-vehicle collisions, as Faune-AuRA is an opportunistic reporting project which suffers from the numerous biases previously cited.

<figure><img src="image_16.png" /><figcaption>Fig. 9: Temporal trends in roadkill reporting of the common toad *Bufo bufo* to the Faune-AuRA citizen science project.</figcaption></figure>
# 5. Objectives and hypotheses

The main objective of this project is to work toward comprehensive predictive models for wildlife-vehicle collisions at large scales, both spatially and temporally. We will explore both mechanistic and statistical approaches (fig. 10). This thesis is composed of 4 manuscripts, either submitted or in preparation, plus 2 case studies. Case studies detail preliminary experiments, conducted during the thesis project to explore new methodological approaches.

## Objective 1:

The first chapter of this thesis will present a **mechanistic model of wildlife-vehicle collisions**. This model is an agent-based approach, **based on the individual trajectories of both animals and vehicles**, which aims at reuniting road encounter probabilities with vehicle collision probabilities in a unified framework. We aimed at providing a theoretical framework based on movement ecology that would encompass all aspects of road mortality risks.

We investigate the hypothesis that there is a **causal relationship** between predictors of WVC identified in empirical studies (such as road characteristics: traffic volume, speed, road sinuosity, and biological traits: animal speed, behaviour, and density) and wildlife-vehicle collisions. In addition, sensitivity analyses are used to identify the predictor(s) that have the biggest impact on collision numbers, a valuable insight for both the design of empirical studies and applied roadkill mitigation.

## Objective 2:

The subsequent chapters will focus on the **data collection process** in WVC studies. Robust roadkill datasets are valuable in both mechanistic and statistical approaches, and we focus particularly on an existing dataset from an **opportunistic citizen science project (Faune-Auvergne-Rhône-Alpes)** that collects data at the scale of the Auvergne-Rhône-Alpes region, France.
We aim at:

1. Improving the understanding of **carcass persistence** on roads. The main hypotheses we will explore are that:

- Roadkill persistence time in the Auvergne-Rhône-Alpes region is comparable to previously published work in other parts of the world,

- Roadkill persistence is influenced by factors such as traffic volume, weather, and roadkill species,

- Roadkill removal from roads is the result of several mechanisms, that will interact with the predictors cited above.

2. Providing estimates of the **detection probability** of roadkill carcasses and exploring the influence of external factors on the detectability of roadkill. In particular, we postulate that:

- Detectability is dependent on the roadkill carcass body size,

- Detectability differs between standardized roadkill surveys and opportunistic ones.

3. Demonstrating that **willingness to report** is another source of bias in citizen science roadkill monitoring, and providing estimates of the reporting probabilities of the contributors from the Faune-AuRA project.

**Objective 3:**

We plan to **integrate the estimates** of the 3 existing biases (persistence, detection, report) in the Faune-AuRA project to produce **corrected datasets**. This will improve the understanding of the impact of road mortality across the Auvergne-Rhône-Alpes region, and open perspectives for the use of this database for (1) mechanistic model validation and (2) statistical modelling. We anticipate significant disparities between the current number of reports in the dataset and the estimates of road mortality our corrections will produce.
<figure><img src="image_17.png" /><figcaption>Fig. 10: Conceptual framework of wildlife-vehicle collisions (WVC) prediction. This project will focus on working toward a large-scale predictive model of WVC through (1) mechanistic modelling approaches and (2) the roadkill data collection process, and in particular the citizen science monitoring scheme Faune-AuRA as a source of roadkill data in the Auvergne-Rhône-Alpes region of France.</figcaption></figure>
Chapter 1: Agent-based modelling of wildlife-vehicle
collisions

<figure><img src="image_18.png" /></figure>
# A biologically realistic model to predict wildlife-vehicle collision risks (under review)

Annaëlle Bénard, Thierry Lengagne and Christophe Bonenfant

under review in *Ecological Modelling*

## CONTEXT

In light of the ongoing biodiversity crisis, it is imperative to understand the mechanisms responsible for wildlife mortality on roads. However, there is currently no comprehensive theoretical framework addressing this issue. Numerous correlations have been identified between landscape characteristics, biological traits and collision risks, but it remains challenging to disentangle the relative effects of various risk factors in empirical studies.

## OBJECTIVES

- Construct an agent-based stochastic model of wildlife-vehicle collisions that incorporates recent insights from movement ecology.

- Evaluate the causal relationships between animal and vehicle movement parameters, such as speed, abundance and traffic, road sinuosity, animal space-use, and the risks of collision.

- Determine the relative impacts of these parameters on collision risks with sensitivity analyses.

## KEY RESULTS

- There are causal relationship between WVC risks and most parameters of animal and vehicle movements, which are contingent upon the space-use patterns of the individuals.

- Relationships between predictors and collision risks are often non-linear.

- Animal movement has a greater influence on collision risks than vehicle movement.

## CONCLUSIONS

- Mechanistic modelling in the field of wildlife-vehicle collisions has the potential to offer valuable insights and should be explored further, especially modelling focused on movement: animal patterns of movement and activity levels appear as the primary explanatory factors for collision risks.

- Variability in road mortality risk among individuals with different movement patterns may generate selection pressures.

- Effective mitigation of wildlife-vehicle collisions should be species-specific, but also behaviour-specific.
Abstract

Road networks have major ecological impacts on living organisms consequent to habitat loss and fragmentation, chemical and acoustic pollution, and direct mortality when wildlife-vehicle collisions are involved (WVC). The many past empirical studies revealed biological traits shared by species most vulnerable to roadkill (e.g., population density). Similarly, spatial locations of WVC hot-spots are associated to landscape features at large spatial scales, and to road characteristics at small spatial scale. We currently lack a comprehensive theoretical framework for WVC. Animal movement in relation to habitats is an essential driver of encounters with roads, but this remains largely ignored in studies, even when movement ecology provides the necessary tools to investigate the impact of animal movement on WVC. We built a general individual-based model incorporating recent knowledge in movement ecology (movement typology: roaming, migratory route crossing a road, active attraction and active repulsion of roads) to estimate WVC risks. We explored the relative effects of animal and vehicle movement parameters (speed, abundance, road sinuosity and animal movement pattern) on collision probability. We show that animal behaviour toward roads has major impacts on the number and risks of WVC, but also modulate the effects of other factors (animal traveling speed, species local abundance, road traffic volume) on WVC. Sensitivity analyses show that the movement and behaviour of the animal has more influence on WVC risks than any of the characteristics of roads and vehicles we tested. Our results suggest that (1) effective roadkill mitigation should be species-specific and could vary in efficiency depending on the target's movement pattern (mating and migratory seasons, foraging habits. . . ) and (2) empirical studies of WVC should incorporate knowledge about the behavioural habits of the focal species in relation to roads.
# 1. Introduction

The last century has witnessed a continuous and tremendous urbanization of almost all ecosystems, with profound influences on living organisms (Corlett, 2015). A particularly important anthropogenic factor generating major ecosystem modification and disturbance is the increasing densification and encroachment of the earth-bound transportation systems, and particularly of the road network (Davenport & Davenport, 2006). The presence of roads modify the local and large-scale environment of species as a consequence of chemical and noise pollution, changes in vegetation diversity, habitat loss and fragmentation (see Forman & Alexander, 1998; Coffin, 2007, for reviews). Roads can also have profound effects on ecosystem functioning and the biology of living organisms (Holderegger & Di Giulio, 2010). For instance, road mortality is a key driver of biodiversity loss in amphibians (Hels & Buchwald, 2001), birds and mammals (Grilo et al., 2020) and has been shown to affect animal behaviours (Andrews & Gibbons, 2005; Legagneux & Ducatez, 2013). In the context of the ongoing biodiversity crisis (Ceballos & Ehrlich, 2002), knowledge about the mechanisms that lead to road mortality in wildlife is therefore critical.

For decades, empirical studies have been accumulating, reporting on collision hot-spots (Teixeira et al., 2013; Silveira Miranda et al., 2020), animal foraging habits near roadsides (Carvalho-Roel et al., 2019), or the seasonal variation in the number of reported cases (Medinas et al., 2021). We now have a clearer picture of what factors mainly account for collision risks (Table 1). Species with life history traits such as extended home ranges or slow travel speeds, and species occurring at high abundances are more often subjected to roadkill. Road characteristics (such as high traffic volume) and landscape features (e.g. habitats promoting high levels of animal activity and mobility) account for WVC hot-spots locations at small spatial scales, but collisions distribution can also be predicted for large spatial scales with variables such as road density, hunting bags (Saint-Andrieux et al., 2020) or landscape connectivity (Girardet et al., 2015). However, the relative effects of risk factors are difficult to disentangle. For example, as traffic mortality depletes local populations, roadkill numbers will decrease and simply counting collisions in high-risk areas could lead to an underestimation of the importance of animal abundance as a key determining factor of roadkill hot-spots (Teixeira et al., 2017). So far few attempts at a theoretical model for wildlife-vehicle collisions (WVC) have been made, and our current knowledge on the quantitative effects of traffic on encounter and mortality risks for wildlife remains essentially descriptive, with little predictive abilities.

The very first model dealing with collision probabilities at a large spatial scale is the ideal gas model, first coined by physicist J. C. Maxwell in the context of molecule collisions in a gas (Maxwell, 1860). The ideal gas model posits that encounter rate within a defined volume or plane is a function of molecule
speed, density and collision zone (Hutchinson & Waser, 2007). Despite its heuristic value in ecology, to estimate encounter rates between males and females of a given species for example, it has seldom been used to study WVC as the general application in this context is not straightforward. For example, in most wildlife-vehicle encounters the animal is likely to die and will no longer be at risk of collision again, which is not reflected in colliding molecules. Others proposed WVC-specific mechanistic models: Hels & Buchwald (2001) modelled the probability of death for an amphibian crossing a road (see Gibbs & Shriver, 2002; van Langevelde & Jaarsma, 2005, for an application to other species), allowing the integration of road mortality into population persistence models (Gibbs & Shriver, 2002).

A shortcoming shared by all current WVC models is the lack of consideration for animal movement and habitat use behaviour, often limiting when one aims at describing the complexity of animal movement in a heterogeneous landscape (Siniff & Jessen, 1969). For example, not only do animals cross roads, but they can roam along roadsides to forage hence putting them at much higher risk of being hit by a car (scavenging: Schwartz et al. 2018; Ratton et al. 2014, hunting: Gomes et al. 2009; D'Amico et al. 2013, salt licking: Fraser & Thomas 1982). More importantly, collision probabilities in a landscape are intrinsically linked to the number of encounters an animal has with roads, and peaks in activity such as mate searching, breeding, and juvenile dispersal have repeatedly been cited to explain seasonal patterns in WVC numbers (Steiner et al., 2014; Ryu & Kim, 2021; Raymond et al., 2021). Despite this, the influence of patterns of space use by animals on WVC has yet to be adequately addressed in mechanistic models.

Patterns of space use are described within the frameworks of movement ecology. Species distributions are generally divided into broad strategies comprising several patterns of space use that depend both on the biological traits of the species and the environment: sedentary populations that occupy a restricted geographical area (often referred to as home range or territory), migratory individuals who exhibit long-distance and often periodic displacements, and nomadic populations whose movements are neither confined to specific geographic areas nor predictable (Mueller & Fagan, 2008). These large-scale patterns emerge from movement at the individual level: for example, oriented movement, based on environmental cues or memory, is the basis for migratory routes and sedentary ranges (Mueller & Fagan, 2008; Van Moorter et al., 2009). The advances of the last decades in bio-logging (e.g., animal-borne GPS collars, tags or transponders) have made it increasingly easy to acquire position data characterizing these individual trajectories for a growing number of species, therefore providing a solid empirical basis to develop mathematical models of animal movement. To our knowledge however, WVC studies seldom incorporate paradigms from movement ecology, although space use is the main driver of animal encounters with roads. Therefore, we argue that modelling wildlife-vehicle collisions from a movement
ecology perspective would improve our ability to understand the main factors driving WVC (Hels & Buchwald, 2001; van Langevelde & Jaarsma, 2005).

We here propose an individual-based model to simulate animal trajectories using biased and unbiased correlated random walks, as a mean of exploring the effects of road characteristics, species traits and patterns of space use on the number and probability of collisions between animals and vehicles. Our two main goals are i) to quantify the relative effects of several road characteristics (road sinuosity, vehicle speed and traffic volume) and species traits (animal speed, local abundance, movement patterns, foraging and dispersal behaviours) on WVC occurrences and ii) for a set of biologically realistic scenarios of animal movement, to identify what factors have the largest impact on wildlife-vehicle collision risks. Understanding which biological, human and environmental factors modulate the risks of wildlife-vehicle collisions is key to the selection and implementation of efficient mitigation policies such as fences, over or underpasses, and traffic signage that raises drivers' attention (Davenport & Davenport, 2006). Our model should help to build qualitative predictions either for inter-specific studies or WVC mitigation.
<table><caption>Table 1: An overview of the different factors correlated to the incidence of wildlife-vehicle collisions in the current literature.</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td rowspan="7">IOLOGICAL FACTORS</td><td>Animal Speed</td><td>While crossing a road, slower-moving animals such as herpetofauna will be more impacted by roadkill. Hels & Buchwald 2001, Eigenbrod et al. 2009, Grilo & Bissonette 2010, Van Langevelde & Jaarsma 2005</td></tr><tr><td>Habitat use</td><td>Highly mobile individuals cross roads more often. When mobility levels are season, age or sex-dependant, these biases are reflected in roadkill (more mobile individuals being killed more often). Steen & Smith 2006, Aresco 2005, Coelho et al. 2008, Newell 1999</td></tr><tr><td>Road-related behaviours</td><td>Some species can be attracted to roads, including but not limited to:<ul><li>Ungulates licking salt on or near roadsides (Rea et al. 2021)</li><li>Carrion feeders foraging on roadkill (Laurance et al. 2009, Mukherjee et al. 2013)</li><li>Birds using roadside perches (Grilo et al. 2011)</li><li>Reptiles using road surfaces to bask (Meek 2009)</li><li>Turtles laying eggs on road shoulders (Aresco 2005)</li><li>Amphibians breeding in road-adjacent water retention ponds (Smith & Dodd 2003, Hamer et al. 2012)</li></ul></td></tr><tr><td>Species local abundance</td><td>"To some extent, road-kill statistics actually give a crude but useful index of wildlife occurrences in a region" Seiler & Helldin 2006</td></tr><tr><td>Car avoidance behaviours</td><td>Species-specific or individual reactions to oncoming vehicles dictate whether the animal will have a chance of avoiding a collision. Documented behaviours that increase roadkill probabilities include:<ul><li>not detecting oncoming vehicles,</li><li>habituation and not perceiving moving vehicles as threats,</li><li>freezing in front of vehicles and following conspecifics on the road.</li></ul>Lima et al. 2015</td></tr><tr><td rowspan="4">ANTHROPOGENIC FACTORS</td><td>Traffic volume</td><td>Roadkill occurrences increase with traffic volume until a certain threshold where traffic-generated disturbances (movement, noise, chemical emissions) repel most of the wildlife Seiler 2005, van Langevelde et al. 2009</td></tr><tr><td>Traffic speed</td><td>High-speed roads generate more roadkill Hobday & Minstrell 2008, Farmer & Brooks 2012</td></tr><tr><td>Road characteristics</td><td>Roads on which WVC are more frequent include:<ul><li>wider roads with multiple lanes (Bright et al. 2015),</li><li>raised roads and embankments promoting low-altitude flight in birds (Canal et al. 2019)</li><li>sinuous roads (Grilo et al. 2011, Zuberogoitia et al. 2014)</li></ul></td></tr><tr><td>Mitigation measures</td><td><ul><li>Warning signage is often ineffective in preventing collisions (Huijser et al. 2015)</li><li>Road-crossing structures (bridges, underpasses) can counter-intuitively correspond to roadkill hotspots when looking at species they are not suitable for, e.g. by lacking proper fencing for smaller vertebrates (D'Amico et al. 2015)</li></ul></td></tr><tr><td rowspan="3">LANDSCAPE</td><td>Roadside features</td><td>"The concentration of forage or cover plants, accumulation of salt, or close proximity of wetland may cause some animals to concentrate their activities near roadsides" Livaitis & Tash 2008</td></tr><tr><td>Landscape connectivity</td><td>Landscape connectivity, by influencing animal movement, is a predictor of roadkill spatial patterns: roads in high-connectivity landscapes are more dangerous. Grilo et al. 2011, Fabrizio et al. 2019, Girardet et al. 2015</td></tr><tr><td>Adjacent habitats suitability</td><td>Roadkill occurrences in a species are higher in the presence of optimal habitats. At broad scales, habitat suitability models are used as predictors for spatial roadkill patterns. Balčiauskas et al. 2020, Wright et al. 2020</td></tr></tbody></table>
## 2. Material & Methods

Following previous work on simulations for the ideal gas model (Hutchinson & Waser, 2007), we constructed a discrete-time simulation of particles movement in which all trajectories were approximated by a series of straight-line steps of constant duration. Two classes of particles were considered: vehicles and animals, each with their own speed, movement patterns and density. We conducted preliminary testing of the model by replicating the conditions under which the ideal gas model applies, and subsequently ensured that simulation results matched the model's predictions. From there, we used biased and unbiased correlated random walk models to represent animal movement more realistically. Random walk parameter values were chosen to match real-life scenarios. The goal of the simulations was to keep track of the number of encounters between vehicles and animals per unit of time (fig. 1). We set a duration of 12 hours per simulation run, as a broad representation of the amount of time during which most diurnal and nocturnal terrestrial species are active (Refinetti, 1999). Two types of experiments were conducted: (1) to test the quantitative and qualitative effects of the different focal parameters (animal and vehicle speed, movement and densities) independently, we replicated the simulation for different values of the parameter under study, holding everything constant and (2) to evaluate the relative importance of each focal parameter on the number of WVC, we conducted one-at-a-time sensitivity analyses.

<figure><img src="image_19.png" /><figcaption>Fig. 1: **Conceptual diagram of the Wildlife-Vehicle Collision model** – We constructed a discrete time, agent based simulation of collisions between animals and vehicles. Using biased correlated random walks, we investigated the effects of individual and species-specific traits (behaviour, habitat use, animal speed, population densities) as well as road and vehicles characteristics (vehicle speed, volume of traffic, sinuosity of the road) on the number and probabilities of Wildlife-Vehicle Collisions during 12 hours simulation runs. A collision did not affect the vehicle, but the animal involved was killed and replaced by a new individual in order to keep animal density constant.</figcaption></figure>
## 2.1 Basic simulation layout

We first assumed two separate entities, thereafter designated 'vehicles' and 'animals', moving on a 30x30km2 plane mapped by x and y axes. We treated the plane like a torus, meaning that an animal or a vehicle crossing the edge reappeared at the same location, but on the opposite edge of the plane (see fig. 2). The vehicle movement followed a road defined as $0 \le x \le 30$ and $y = \cos(\alpha \cdot x)$, where $\alpha$ controlled road sinuosity. We computed an index of sinuosity for each simulated road as the ratio of the road's length to 30 (i.e. the x axis' length). A sinuosity index of 1 indicated a straight road, and the index increased as the road became more and more sinuous. The number of vehicles on the road at any given time followed a Poisson distribution (Breiman, 1963) and all vehicles moved at constant speed with no intra-class variability. For animal movement, we used biased correlated random walks (BCRW), a combination of correlated random walks where animals have a directional persistence and therefore avoid backtracking, and biased random walks where animals are attracted to one or several centers of attraction spatially defined on the simulation plane. BCRW are highly flexible models proven to fit animal trajectories at different spatial scales for a range of terrestrial species in heterogeneous landscapes (red deer (Cervus elaphus): Berthelot et al., 2020; caribou (Rangifer tarandus) and bears (Ursus arctos and U. maritimus): Auger-Methe et al., 2016; cactus bugs (Chelinidea vittiger): Schooley & Wiens, 2003).

Animals moved on the plane from time steps $t = 0$ to $T$ according to a BCRW:

$$x_a(t) = x_a(t - 1) + \cos(\theta_t) * d$$

$$y_a(t) = y_a(t - 1) + \sin(\theta_t) * d$$

$$x_a(0) \sim U(0,30)$$

$$y_a(0) \sim U(0,30)$$

with step length $d$ drawn from a zero-truncated normal distribution $N(\mu, .5)$, $\mu$ the mean animal speed and $U(0, 30)$ the uniform distribution between 0 and 30. We computed the direction of the walk $0 \le \theta_t \le 2\pi$ as the mean between the *correlated* direction $\theta_t \sim N(\theta_{t-1}, \sigma^2=5)$ with $\theta_0$ randomly drawn between 0 and $2\pi$, and the *biased* direction $\theta^b$, the direction of the nearest attraction center. It resulted that the direction of the walk was the outcome of two competing processes: the persistence, the animal's internal propensity to walk without backtracking in a given direction $\theta_0$, and the attraction toward the nearest attraction center. The relative importance of the attraction with respect to the persistence was defined by
the associated weight of attraction *w* (Duchesne et al., 2015). Accordingly, *w* controlled the strength with which animals are attracted to the attraction center: *w* = 0 produces unbiased correlated random walks (no attraction), and *w* → ∞ tends towards biased random walks. In practice, for high values of *w* the animal made a beeline towards the nearest center of attraction because the attraction to the nearest center takes over the persistence of the correlated walk in orienting the walk. Once the animal reached the attraction center, it orbited around it, as a result of the persistence pulling away in its own direction while the attraction component brought the animal back towards the center. In consequence, high values of *w* would imply less spread-out orbiting behaviours, mimicking animals staying in close proximity of the attraction center (see fig. S1 in supplementary material).

<figure><img src="image_20.png" /><figcaption>Fig. 2: Using biased correlated random walks, 5 scenarios of animal habitat use are implemented on the 30x30km² plane to study collisions between moving animals and vehicles. Animals and vehicles that reach one of the edges of the plane will continue their walk on the opposite edge. In other words, they move on a torus and can never leave the simulation plane.</figcaption></figure>
We defined an animal-vehicle collision as a time-step during which the distance between an animal and a vehicle was less than 5 meters (Euclidean distance). If that condition was satisfied, the animal died and stopped moving, while the car continued to move along the road. For each collision, a new animal would enter the plane in order to keep the animal density constant. We did not implement any sort of behavioural reactions from the animals to an incoming vehicle, or from the driver in the presence of an animal on the road or roadside. Given its stochastic nature, the model was run N = 1000 times to produce a mean collision number and estimate an individual probability of collision. The simulation used R package Rcpp (Eddelbuettel & Balamuta, 2018).

## 2.2 Behavioural scenarios of animal movement and space use

We considered 5 different scenarios designed to mimic real-life animal behaviours described in the literature (fig. 2).

### 2.2.1 Scenario 0: no influence of the road

In scenario 0, the weight of attraction *w* was set at 0 resulting in animals performing (unbiased) correlated random walks (CRW). In CRW, successive steps directions are correlated, resulting in a directional bias: the animal walked forward and rarely backtracked. CRW have been used to describe the movement of several species (Mouse (*Apodemus sylvaticus*): Benhamou 1991, Reindeer (*Rangifer tarandus*): Marell, Ball & Hofgaard 2002, Red fox (*Vulpes vulpes*), Snowshoe hare (*Lepus americanus*): Siniff & Jessen 1969). CRW imply that animals did not factor in the presence of a road or moving vehicles in their movement, which could be especially prevalent on smaller or unpaved roads (Brehme et al., 2013). This simple movement model also served as a null model, i.e. a scenario without attractive or repellent effects of road presence on animal movement.

### 2.2.2 Scenario 1: habitat fragmentation

All animals started the simulation run in the top-left corner of the simulation plane, always above the road, while the single attraction center ($w=1.5$) was randomly located below the road. The resulting BCRW simulated a migration of individuals between patches during which they had no choice but to cross the road. This scenario could match many migrating species such as amphibians converging towards open waters for reproduction (Hels & Buchwald, 2001; Sillero, 2008), large mammals migrating to their summer or winter ranges (Avgar et al., 2014) and crab species moving back to sea during breeding migrations (Ryu & Kim, 2020).
### 2.2.3 Scenarios 2 & 3: attraction to the road

Scenario 2 emerged from the frequently reported attraction to roads in many species: salt licking on roadsides by large mammalian herbivores (Fraser & Thomas, 1982), use of roads and roadsides for foraging or hunting (Diurnal raptors: Meunier et al., 2000; Passerines: D'Amico et al., 2013) or carnivores scavenging on carrions from animals hit by cars (Schwartz et al., 2018; Ratton et al., 2014). Arguably, this scenario could encompass the case of reptiles that bask on warm road surfaces (Meek, 2009). Attraction centers ($w = 3$) were placed every 300m on the road, such that animals converged towards the closest attraction center. Once an animal had reached an attraction center, it would orbit around until another attraction center in the vicinity became the new closest center, at which point the animal would leave its current attraction center to walk towards the new one. Little by little, an animal would visit several attraction centers during a simulation run, and would often walk on or in close proximity to the road while moving in-between attraction centers.

Scenario 3 is a slightly modified version of scenario 2, intended for animals with flying ability (birds, bats...) and using roads as corridors for long-range displacements, or for hunting because roads "drive" preys in the landscape (Kerth & Melber, 2009; Schwartz et al., 2018). Flying animals often make low-altitude flight to catch a prey or land on the road to feed (Grilo et al., 2014; see also the "leap and strike" hunting behaviour of owls: Norberg & Norberg, 1970; Southern, 1954). To this end, we added a third dimension $z$ describing the altitude of the animals to their existing $(x,y)$ position on the plane. The altitude was a function of the distance to the nearest attraction center: $z(t) = \exp(0.3 * ||d||) - 1, ||d||$ the Euclidean distance between the animal and the closest attraction center. This distribution of altitudes entailed that animals got progressively closer to the ground as they approached the attraction center. In consequence, they were only susceptible to collision when within a radius of 5m around a center of attraction.

### 2.2.4 Scenario 4: road avoidance

The last scenario accommodated animal movement for road avoidance behaviours. Road avoidance has been reported in several species (Grizzly bear (*Ursus arctos*): Mace et al., 1996; Wild boar (*Sus scrofa*) and Red deer (*Cervus elaphus*): D'Amico et al., 2016), possibly resulting from chemical, noise pollution, or road surface avoidance (Andrews & Gibbons, 2005; Schaub et al., 2008; Jaeger et al., 2005). Building upon scenario 2, we only modified the attraction angle to be computed as $\theta + 180^{\circ}$, meaning that the animal moved away from the center instead of towards it.
## 2.3 Qualitative and quantitative predictions of the model

For each of the scenarios described above, we derived qualitative and quantitative predictions for 6 parameters of interest, by running the simulation at different values of this parameter while holding everything else constant. The parameters of interest were: animal mean speed, vehicle speed, animal density, traffic volume, weight of attraction centers $w$ (scenarios 1 through 4 only) and road sinuosity (Table 2).

Mean animal travel speed values covered the observed speed range of most terrestrial species (from slowest to fastest, migrating amphibians: Hels & Buchwald 2001, foraging badgers (*Meles meles*): San et al. 2007, migrating ungulates: Berger et al. 2006; Singh & Ericsson 2014). Considering that this range is wide, we extracted mean travel speed estimations for several species from the literature (Rowcliffe et al., 2016; Farley et al., 1993) and set our baseline at the mean value of $5 \text{ km.h}^{-1}$. Vehicle speed encompassed slow vehicles up to high-speed trains, and the baseline was set at the current speed limit on main roads in France ($80 \text{ km.h}^{-1}$). Local animal densities, traffic volume ranges and baselines were mostly dictated by computational limitations, although the baseline of $250 \text{ vehicles hour}^{-1}$ is representative of average sized roads in France (French Ministry of Ecological Transition, 2022).

The weight of attraction $w$ in BCRW scenarios was a dimensionless unit ranging from 1 (attraction to centers is equal to the correlated direction of the walk, spread-out orbiting behaviour around attraction center) to 20 (when attraction was 20 times more important in walk orientation, animals walked in nearly straight paths toward the attraction center and stayed mostly in place once it was reached). Baseline values for $w$ were scenario-dependent as $w = 5$ for scenario 1 ensured that over 90% of animals cross the road in less than 12 hours and $w = 3$ for scenarios 2 and 3 ensured that animals would effectively visit several attraction centers during the simulation run.

Finally, road sinuosity was investigated following observed sinuosities which are publicly available for the road network of Ireland (Transport Infrastructure Ireland, 2022). Two types of results were extracted from simulation runs: the mean number of collisions recorded over the course of a 12 hours run, and the individual probability of collision for animals. Considering that new individuals replaced dead animals, not all animals were present from the start of the simulation run and collision risk was not constant across all animals. Consequently, we estimated the individual probability of collision from a logistic regression (0: alive, 1: hit by a vehicle) as a function of the parameter under study, and where the time of arrival in the simulation was entered as an offset predictive variable (Agresti & Coull, 2002).
<table><caption>Table 2: The six parameters of interest, relating to animal and vehicle movement, and that appear to be pivotal factors driving collision numbers according to most studies (Table 1). While the effects of one parameter on collisions are being explored, all other parameters assume their baseline values. To produce quantitative and qualitative predictions, we explored for each parameter a range of values contained within biologically relevant intervals.</caption><thead><tr><th></th><th>Parameter of interest</th><th>Baseline value</th><th>Explored range</th></tr></thead><tbody><tr><td rowspan="3">ANIMAL</td><td>Mean speed (km.h<sup>-1</sup>)</td><td>5</td><td>0.1 – 30</td></tr><tr><td>Density (ind.km<sup>-2</sup>)</td><td>0.016</td><td>0.001 – 0.03</td></tr><tr><td>w</td><td>5 (scenario 1); 3 (scenarios 2-4)</td><td>1 – 20</td></tr><tr><td rowspan="3">VEHICLE</td><td>Speed (km.h<sup>-1</sup>)</td><td>80</td><td>30 – 300</td></tr><tr><td>Traffic volume (vehicle.h<sup>-1</sup>)</td><td>30</td><td>10 – 250</td></tr><tr><td>Road sinuosity index</td><td>1 (straight road)</td><td>1 – 3.5</td></tr></tbody></table>

## 2.4 Sensitivity analyses of collision number

Sensitivity analyses were conducted on each scenario, following a one-at-a-time approach, meaning that we measured the variation in collision numbers while keeping all input factors fixed except the one that is being perturbed (Saltelli et al., 2019). In practice, we computed the mean number of collisions y for factor of interest x at a reference value x₁, and after 10% increase in value (denoted x₂). To explore possible non-linearity, we repeated this for several reference values x₁ within the relevant range of x (see section 2.3 for parameter ranges). We then defined the sensitivity measure as ORₓ₁ = yₓ₂ / yₓ₁, i.e., the odd ratio of the collision probabilities that results from a 10% increase of parameter x at reference value x₁. For example, an ORₓ₁ of 1 indicated no change in the odds of collisions between parameter values x₁ and x₁+10%, while ORₓ₁ > 1 indicated greater odds of collision after a 10% increase in x₁. The overall strength of the influence of parameter x on the collision number in its relevant range was defined by how far the mean of the ratios (OR<sub>mean</sub>) for all tested values of x deviated from 1 (e.g., OR<sub>mean</sub> = 1 indicated no overall influence of factor x on collision numbers).
# 3. Results

## 3.1 Qualitative and quantitative model predictions

Applying baseline values to all parameters of interest, mean values ranged from 0.16 to 17.2 animal-vehicle collisions over 12 hours (individual probabilities of collision for animals: 0.4% - 45.6%). As expected, the movement of animals had major effects on the probability for an animal to get hit by a car (fig. 3). With baseline parameter values, animals attracted to the road (scenarios 2 and 3) were hit more often than in any other scenario, with an increase in odds of collision for terrestrial animals (scenario 2) compared to flying animals such as birds and bats (scenario 3). Compared to the null model (scenario 0, roaming with no attraction/avoidance of the road), migrating animals crossing the road exactly once (scenario 1) were hit more often, while the odds of collisions for active road avoidance (scenario 4) were reduced. This ranking between scenarios was not always maintained for other values of the tested parameters.

Overall, parameters response functions had similar shapes whether the outcome was measured as the mean number of collisions or as the individual probability of collision, with the exception of animal density. Vehicle speed had no effect on collision numbers and probabilities in any of the scenarios (fig. 3b and 4b). Animal density was positively and linearly associated with collision numbers, which translated into a constant individual probability of collision no matter the local abundance in animals (fig. 3d and 4d). The influence of the remaining parameters (animal speed, weight of attraction, traffic volume and road sinuosity) was non-linear and/or scenario-dependent.

Traveling faster reduced collision numbers and probabilities for migrating animals (scenario 1) but had the opposite effect on roaming and road-avoiding animals (scenarios 0 and 4). In scenarios with road-attracted animals, collision occurrences increased with mean animal speed up to moderate speed values, after which the relation was reversed (fig. 3a, 4a). Higher volumes of traffic on the road increased collision numbers and probabilities although scenarios 0, 2, 3 and 4 present inflexion points after which the increase in collision occurrences slowed down, which was not observed within the explored range of traffic volume for scenario 1 (fig. 3c, 4c). Similarly, increasingly sinuous roads had moderate to low positive effects on collision number and probabilities in all but one scenario: scenario 3 yielded no apparent effect of road sinuosity (fig. 3f, 4f). Finally, increasing weights of attraction (or repulsion for scenario 4) led to more collisions (and higher individual probabilities) in scenarios 2 and 3 with inflexion points around w=5, but increasing w values were associated to less collisions and lower probabilities of WVC in scenarios 1 and 4 (fig. 3e, 4e)
## 3.2 Sensitivity analyses

For roaming animals (scenario 0), the most influential parameter was the animal density (OR<sub>mean</sub>=1.091) followed by animal speed (OR<sub>mean</sub>=1.032). In all other scenarios (scenarios 1, 2, 3 and 4), the weight of attraction *w* had the largest influenced (respectively OR<sub>mean</sub>=0.888, 2.019, 1.155 and 0.843) followed by animal density (respect. OR<sub>mean</sub>= 1.098, 1.095, 1.101 and 1.108). The least influential parameters was traffic volume for scenario 0 (OR<sub>mean</sub>=0.996), vehicle speed for scenarios 1 and 3 (respect. OR<sub>mean</sub>=1.01, 1.006) and road sinuosity for scenarios 2 and 4 (respect. OR<sub>mean</sub>=0.998, 0.993). Using OR<sub>mean</sub> is, however, a simplified view of the non-linear effect of parameters, as it was sometimes pulled in one direction by one or a few extreme OR values. For example, some parameters such as the weight of attraction/repulsion generally had a substantial influence on collision numbers at lower values (*w* = 1) while higher values had OR values closer to 1 (fig. 5).
mean number of collisions over 12h

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /><figcaption>Fig. 3: **Mean number of collisions** - For each scenario, the total number of collisions occurring within a 12-hours simulation run (mean number over 1000 runs). The weight of attraction *w* has no meaning for (non biased) correlated random walks and is therefore not considered for scenario 0.</figcaption></figure>
individual probability of collision

<figure><img src="image_27.png" /><figcaption>(a) animal mean speed (km/h)</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>(c) traffic volume (vehicles/h)</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>(e) weight of attraction</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>(b) vehicle speed (km/h)</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>(d) animal density (ind/km²)</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>(f) road sinuosity index</figcaption></figure>

Fig. 4: **Individual probability of collision** - For each scenario, the individual probability of collision estimated from 6 separate logistic regressions in which the studied parameter was used as a response variable and the individual time of exposure to vehicles was used as an offset.
<figure><img src="image_33.png" /><figcaption>Fig. 5: **Sensitivity analyses** - We compute the odds ratios (OR) of the mean number of collisions for a 10% increase in a given parameter reference value. For example, the darkest circle (●) under "traffic volume" is the ratio of the mean number of collisions with 230 + 10% = 253 vehicles/hour over the mean number of collisions with 230 vehicles/hour. An OR > 1 shows that an increase in traffic volume has increased the number of collisions (and conversely for OR < 1). The further from 1 the mean is, the more influential the parameter is on collision numbers.</figcaption></figure>
# 4. Discussion

Road mortality of wildlife is a pervasive and widespread cause of biodiversity loss across the world that should be seriously considered in wildlife management and conservation programs. In spite of its ecological importance and relevance, we are still lacking a strong formalization of WVC to grasp what are its main biological, ecological and anthropogenic determinants. By combining earlier encounter models with the current knowledge about movement ecology, our work should help at formulating qualitative predictions for reducing the number of WVC or to predict what species should be at greater risks of being hit by a vehicle.

Our simulations show how collision numbers and probabilities differ markedly with the movement behaviour of animals, such as migration or ranging, or with its locomotion (terrestrial vs. flight). We suggest this contrast in mortality risk between individuals with different movement types could lead to selection forces on animal habitat use with regard to road avoidance or attraction. In practice, the knowledge about animal movement of species should be an essential part of WVC studies as it seems the most influential variable on WVC occurrence compared to any changes in vehicle speed or road sinuosity for instance.

## 4.1 Effects of animal movement on WVC risks

WVC broadly results from two competing mechanisms: the number of times an individual will cross or stay close to a road, and the time spent at risk of collision when on the road while crossing, foraging or basking. Both mechanisms are modulated by patterns of space use (in our simulation, the different scenarios of behaviour), and their modulations through the weight of attraction/repulsion *w* and the speed at which animals travel. Obviously, individuals actively avoiding roads (scenario 4) should be the least at risk of collision with a vehicle and, conversely, terrestrial individuals attracted to the road for foraging or basking (scenario 2) should be the most at risk. This is in line, for example, with Western green lizards (*Lacerta bilineata*) being road-killed in higher proportions than the other sympatric lizard species that do not bask on roads (Meek, 2009). Flying carrion feeders (mostly diurnal and nocturnal raptors) are less likely to be killed than their terrestrial counterparts, a difference that may be further widened by some species' cognition and ability to successfully evade oncoming vehicles, as is the case with corvids (Mukherjee et al., 2013; Lima et al., 2015). Nevertheless, we show here that other parameters of both animal and vehicle movement have the ability to modulate these conclusions. For example, slow moving
animals (less than 15km.h⁻¹) were more often hit when migrating (scenario 1) than roaming freely (scenario 0), but the reverse was true for faster animals (fig. 3a).

By mimicking the presence of attractive or repulsive areas for animals in the landscape, the attraction/repulsion weight (w) ultimately controls the time spent in the vicinity of the road, which is positively correlated to collision numbers and probabilities. The relationship between w and the time spent on the road is easily interpreted for scenarios of road attraction (scenarios 2 and 3, w is positively correlated to time on road surface) and avoidance (scenario 4, w value is negatively correlated to time on road surface). When animals travel from a departure point to an attraction center (scenario 1), the time spent crossing is negatively correlated to w: high w values means straight trajectories between departure and attraction center, and thus less time on the road.

Collision risks in animals roaming freely in a landscape (scenario 0, no w variable) are dictated by their speed: the faster the animal, the more it explores its environment during a simulation run and thus encounter roads more often, even though each crossing becomes concurrently less dangerous as fast animals cross the road in less time (see fig. S2 in supplementary material). For the same reason, when animals cross the road only once (scenario 1), we would also expect the animal travel speed to be a key variable in decreasing collision numbers. However, this was not reflected by $Or_{mean}$ in the sensitivity analyses, the most likely explanation being that the mean sensitivity $OR_{mean}$ for travel speed in scenario 1 is pulled up by the odds ratio for very low travel speeds (odds ratio $OR_{0.5}$ comparing collisions at 0.5 and 0.55 km.h⁻¹) where more animals would cover the distance between their departure point and the road during the simulation when traveling at 0.55 km.h⁻¹ (fig. 5). Nevertheless, these results demonstrate that the cumulative time spent on or near roads by animals, through repeated road encounters and/or a long time spent on the road at each encounter (modulated here by patterns of space use, animal speed and biased random walk parameter w), is the most influential parameter driving collisions probabilities for an animal, and has more importance than road characteristics such as traffic volume or speed limits.

These findings are consistent with studies exploring the relationship between landscape features and roadkill hot-spots: factors such as the presence of attractive habitats on roadsides as well as a high connectivity landscapes conducive to wide ranges of movement are often linked to high road mortality (Table 1, see also de Freitas et al. 2013; de Freitas et al. 2015). Similarly, the temporal distribution of roadkill is dictated by the level of activity, and periods of high mobility such as rut, mating or migrating seasons are especially risky for animals (Table 1). Larger home ranges and spread-out exploratory behaviours contribute to higher fitness for individuals by increasing foraging opportunities (Andersson, 1978), but the presence of roads (also applicable to aircrafts, ships or trains) in a landscape lead to costs
in the form of road mortality and selection pressure may lead to road avoidance (Meisingset et al., 2013; Jaeger et al., 2005; Husby & Husby, 2014).

## 4.2 Effect of animal density on WVC risks

The impact of spatial and temporal variations in animals density has been repeatedly reported as a significant driver of WVC (Joyce & Mahoney, 2001; Taylor et al., 2010; Saint-Andrieux et al., 2020). Some authors suggested that the number of carcasses on roads could serve as an index of animal abundance (Seiler & Helldin, 2006; George et al., 2011). We show that this relationship is linear but strongly modulated by animal movement (fig. 3): compared to animals with no attraction or avoidance towards roads, the slope of the relation between local density and roadkill number is 8 times greater for terrestrial animals attracted to roads and about 70 times smaller when there is road avoidance. When dealing with different species, or with large temporal or spatial scales in which animal movement might be modified by biological seasons and/or landscape features, WVC counts are meaningless, unless the average movement of animals is precisely known. Furthermore, all slopes deviate from isometry ($\beta$ < 1), suggesting that the number of casualties on the roads underestimates high population abundances.

Animal density has an impact on collision numbers, but not on the probability of collision for the individual: WVC are coincidental and have no upper threshold for the number of roadkill, contrary to, for example, a predator looking to feed on a set number of prey. Because of this, there is no mechanism of dilution, or “safety in numbers”, in which we might expect a lower collision risk for the individual in a large group of conspecifics (Lehtonen & Jaatinen, 2016). We need to mention that changes in local density have documented effects on individual behaviour which were not explored in the model, and that will in turn affect movement (Kjellander et al., 2004; Dahle & Swenson, 2003; Sword, 2005).

## 4.3 Effects of traffic volume on WVC risks

A general consensus arises in the literature on the number of WVCs increases with road traffic (Fahrig et al., 1995; Rosen & Lowe, 1994; Inbar & Mayer, 1999; Joyce & Mahoney, 2001). This correlation is, however, much discussed with some authors proposing a linear relationship (Fahrig et al., 1995); and others a barrier effect (high-traffic roads having fewer WVCs than less frequented roads because animals avoid the noise and other disturbances they generate: Seiler & Helldin, 2006; Clevenger et al., 2002; van Langevelde et al., 2009). Others explained the lower-than-expected number of collisions reported on
some high-traffic roads by a depletion of local animal populations due to roadkill (Ascensao et al., 2019). Those arguments may be unnecessary given our results: the theoretical relationship between traffic and WVCs can be non-linear even in the absence of traffic-dependent road avoidance or source-sink dynamics, and roads with heavy traffic would not necessarily have higher collision rates than intermediate roads.

Whatever assumption we make on animal movement, the number and the individual probability of WVC grow asymptotically within the explored range of traffic (fig. 3 and 4). This observation agrees with the mechanistic model of WVCs by Hels & Buchwald (2001) that too predicts a logarithmic relationship between traffic volume and WVC occurrence. A noticeable difference between the two models is that while the probability of dying animals asymptotically approaches 1 for Hels & Buchwald's model, the asymptotic number and probability of WVC lie below a 100% in all our simulations. In one case no asymptote is visible (scenario 1), which possibly results from the limited range of traffic volume we considered due to computational limitations (major highways worldwide can see up to 15 000 vehicles per hour).

## 4.4 Effects of vehicle speed on WVC risks

In our model, the speed of the moving vehicles is unrelated to the number and individual risk of WVC over the simulated range of speed (0–300 km.h⁻¹, see fig. 3 and 4). At first sight, a lack of effect of vehicle speed may appear at odds with the previous theoretical models suitable for WVC, but it is not: in the ideal gas model (Hutchinson & Waser, 2007), the equations for encounters feature the length of the path of the molecule (speed × time spent moving) rather than the speed itself. In our model, the distance travelled by a vehicle is constant: they move from one end of the road to the other, and a higher speed does not equate with a longer distance, therefore speed does not increase WVC risks. In contrast, on the subject of the animal's speed, when higher speed means longer travel distances (for scenarios 0 and 4; and scenarios 1, 2 and 3 are more complex as the movement is also directed), it leads to higher WVC occurrences and risks. In addition, the travelled distance by vehicles was increased by simulating more tortuous roads (high sinuosity index), and the number and probabilities of collision for animals increased as well (fig. 3), as expected under the ideal gas framework.

For flying carrion feeders (scenario 3) only, sinuosity is not or slightly negatively correlated to WVC numbers and individual probabilities. We do not have a satisfactory answer to this, but suggest that the Euclidean distance between two attraction centers placed on the road changes with road sinuosity and could impact (with our method of simulating flight) the altitude and therefore the collision risk, which is
why terrestrial animals (scenario 2) are not impacted. Road sinuosity can also be treated as a measure of
the density of roads, i.e. the surface of road per unit of area, where sinuous roads equate to a higher
density than straight roads. In that sense, we show that the density of roads is positively correlated to
WVC number and risks.

Both vehicle speed and road sinuosity are among the least influential factors across all space use patterns: we would expect that fast-moving vehicles (e.g., high speed trains) to be no more dangerous to wildlife than slow vehicles. Empirically, speed is regarded as a significant component of WVCs: the faster the vehicles, the more likely is a collision with an animal (Table 1, see also Farmer & Brooks 2012; Hobday & Minstrell 2008). This discrepancy can be explained: fast-moving vehicles equates to reduced reaction time for both animals and drivers (Lima et al., 2015) and vehicles moving at high speeds are most of the time traveling on multi-lane highways with heavy traffic. The reported association between WVCs and vehicle speed may therefore be confounded with unsuccessful collision avoidance, traffic density (that we find to be a strong driver of WVC) or road width (in relation to the time spent crossing the road).

**4.5 Model limits**

We find that the time spent on the road is the critical factor driving WVC number and probabilities independently of space use patterns, and consequently behaviours we did not implement but that modify the time the animal spends on the road surface (road avoidance, pausing on the road, speeding away from vehicles, evading oncoming vehicles, see Jacobson et al. 2016; Lima et al. 2015) are likely to be key components of WVC occurrences. For example, the implementation of a barrier effect (avoidance of roads proportional to road traffic volume) would have predictable effects on WVC occurrences: we know that the strength of avoidance is negatively correlated to the number and probabilities of WVC (fig. 3 and fig. 4, scenario 4), which indicates that traffic-dependent road avoidance in animals roaming, migrating or foraging on the road (respectively scenarios 0, 1, 2 and 3) will decrease the number and probabilities of collisions proportionally to the volume of traffic. This would lead to the relation between traffic volume and WVC numbers to be an inverted U-shaped curve where roads of intermediate traffic volume are more dangerous than high-traffic and low-traffic roads, as conceptualized by Seiler (2006) and Jacobson et al. (2016). We can predict selection pressure on these behaviours will be strong for populations living in the proximity of roads, as documented in the example of road-adjacent cliff swallow populations being selected for longer wings, allowing for better chances of escaping oncoming vehicles (Brown & Bomberger Brown, 2013).
The main focus of this work was the movement of the animals, and we reduced "collisions" to the number of times an animal and a vehicle were located less than 5 meters away from each other. This will likely overestimate collision probabilities, especially for smaller-bodied species that can easily fit in-between car tires (Hels & Buchwald, 2001; van Langevelde & Jaarsma, 2005). This is a classical simplification from the ideal as model that we expect will not alter the general patterns we report but simply move all the curves down. Finally, we designed the simulation to have constant animal density, which does not allow for population depletion dynamics (justified by the limited temporal scale of 12 hours per simulation run). Based on our conclusions, the total number of roadkill would decrease linearly with population decline but have no impact on individual probabilities of collision (fig. 3 and fig. 4).

**4.6 Practical implications**

**4.6.1 Investigating roadkill patterns using movement data**

The theoretical framework developed here can direct future research on roadkill spatial and temporal patterns. We have shown that collision risks in a landscape for species are highly dependent on their movement characteristics: for example, WVC in species with a home range that are not attracted nor avoiding roads (described by scenario 0) should be best predicted by the speed of movement of the individuals (fig. 5, scenario 0). Faster travel speeds for the individuals should lead to increased collision risks with vehicles (fig. 3a). In section 3 of the supplementary material, we use the case of the European roe deer *Capreolus Capreolus*, whose movements fit the scenario 0 of our model (Saïd et al., 2009). Roe deer movement is season-dependant, with males having distinct peaks in activity during the mating season (March to August, Krop-Benesch et al. 2013). In figure S3a-b, we show the seasonal increases in male roe deer speed in adults and subadults from the GPS data of individuals tracked during the Bavarian forest, Germany. Temporal collision patterns for this species are also known to peak during spring (Steiner et al., 2021; Mayer et al., 2021). We show roadkill reports from the citizen science database (Faune-Auvergne-Rhône-Alpes) over a period of 12 years (2010 to 2022) in figure S3c. As predicted, seasonal increases in roe deer speed correlate to increases in roadkill reports. Efforts should be made at connecting more often movement ecology to roadkill research to understand the inter-specific and spatio-temporal variations in WVC.

**4.6.2 Roadkill mitigation**

In this study, we demonstrate that animal movement characteristics are far more important than road characteristics in managing roadkill. More precisely, the time spent on the road by the animal is the main
contributing factor to WVC occurrences, and total roadkill numbers depend on animal density rather than traffic volume or speed. In practice, mitigation measure should therefore focus on keeping animals away from the road by prioritizing fencing, or over-passes and other crossing structures for wildlife over driver-targeted measures such as signage and reduced traffic flow. Crossing structures can also restore connectivity in landscapes where roads represent a significant barrier to movement (Grilo et al., 2011). For species that forage on roads surfaces, we suggest that reducing the attractiveness of the road by removing carrion, salt pools and limiting the presence of preys (such as rodents) on roadsides is the most efficient solution. For example, decommissioning roadside salt pools has been shown to reduce the time moose spend on the road and could in theory reduce moose-vehicle collisions by up to 49% (Rea et al., 2021; Grosman et al., 2009). Mitigation policies should also be species-specific (Teixeira et al., 2013; Saint-Andrieux et al., 2020). Characteristics such as large home ranges, wide diet and habitat breadths will belong to species with a particularly high-risk of WVC, as the animals that explored more of the simulation plane (scenario 0, high animal speed) were more often killed than those that stayed in smaller areas (González-Suárez et al., 2018; Grilo et al., 2020; Ford & Fahrig, 2007).

## 4.7 Conclusion

Empirical studies focusing on animal behaviour and movement in addition to other biological traits, road-side habitat type and road characteristics can give valuable insights as to why some species are more often killed on roads than others. We show here that animal behaviour in the presence of roads is a key component of roadkill occurrences, and that understanding space use patterns can give insights on the vulnerability of a species to roadkill. Although this model is not intended to provide quantitative predictions of roadkill for particular species, we show that future predictive models should incorporate components of movement ecology to properly address road mortality. Animal behaviours in the proximity of transport infrastructures could also be of interest in evolutionary studies, an aspect of road ecology that is lacking so far in the literature (Brady & Richardson, 2017).

## Acknowledgments

This work was performed using the computing facilities of the CC LBBE/PRABI. We thank Simon Benhamou, Jean-Michel Gaillard and Marion Valeix for comments on previous drafts of this work.
## Author Contributions

Annaëlle Bénard: coding work and analysis of the data generated, lead writing of the manuscript, equal contribution to the methodology. Thierry Lengagne and Christophe Bonenfant: equal contribution to the methodology, writing, reviewing and editing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication.

## Open research statement

Code is provided as private-for-peer review via the following link:

https://gitlab.in2p3.fr/annaëlle.benard/a-simulation-of-animal-vehicle-collisions.

Upon acceptance data will be publicly accessible. No data were collected for this study.
## References

Agresti, A. & Coull, B.A. (2002) The analysis of contingency tables under inequality constraints. *Journal of Statistical Planning and Inference*, 107, 45–73.

Andersson, M. (1978) Optimal foraging area: size and allocation of search effort. *Theoretical population biology*, 13, 397–409.

Andrews, K.M. & Gibbons, J.W. (2005) How do highways influence snake movement? *Behavioral responses to roads and vehicles*. *Copeia*, 2005, 772–782.

Ascensao, F., Kindel, A., Teixeira, F.Z., Barrientos, R., D'Amico, M., Borda-de Agua, L. & Pereira, H.M. (2019) Beware that the lack of wildlife mortality records can mask a serious impact of linear infrastructures. *Global Ecology and Conservation*, 19, e00661.

Auger-Methe, M., Derocher, A.E., DeMars, C.A., Plank, M.J., Codling, E.A. & Lewis, M.A. (2016) Evaluating random search strategies in three mammals from distinct feeding guilds. *Journal of Animal Ecology*, 85, 1411–1421.

Avgar, T., Street, G. & Fryxell, J. (2014) On the adaptive benefits of mammal migration. *Canadian Journal of Zoology*, 92, 481–490.

Benhamou, S. (1991) An analysis of movements of the wood mouse *Apodemus sylvaticus* in its home range. *Behavioural Processes*.

Berger, J., Cain, S.L. & Berger, K.M. (2006) Connecting the dots: an invariant migration corridor links the Holocene to the present. *Biology Letters*, 2, 528–531.

Berthelot, G., Saïd, S. & Bansaye, V. (2020) How to use random walks for modeling the movement of wild animals. preprint, bioRxiv.

Brady, S.P. & Richardson, J.L. (2017) Road ecology: shifting gears toward evolutionary perspectives. *Frontiers in Ecology and the Environment*, 15, 91–98.

Brehme, C.S., Tracey, J.A., Mcclenaghan, L.R. & Fisher, R.N. (2013) Permeability of Roads to Movement of Scrubland Lizards and Small Mammals: Animal Movement and Road Permeability. *Conservation Biology*, 27, 710–720.

Breiman, L. (1963) The poisson tendency in traffic distribution. *The Annals of Mathematical Statistics*, 34, 308–311.

Brown, C.R. & Bomberger Brown, M. (2013) Where has all the road kill gone? *Current Biology*, 23, R233–R234.

Carvalho-Roel, C.F., Iannini-Custodio, A.E. & Marcial Junior, O. (2019) Do roadkill aggregations of wild and domestic mammals overlap? *Revista de Biologia Tropical*, 67, 47–60.
Ceballos, G. & Ehrlich, P.R. (2002) Mammal population losses and the extinction crisis. *Science*, 296, 904–907.

Clevenger, A.P., Chruszcz, B. & Gunson, K.E. (2002) Spatial patterns and factors influencing small vertebrate fauna road-kill aggregations. *Biological Conservation*, 109, 285–287.

Coffin, A.W. (2007) From roadkill to road ecology: a review of the ecological effects of roads. *Journal of transport Geography*, 15, 396–406.

Corlett, R.T. (2015) The Anthropocene concept in ecology and conservation. *Trends in Ecology & Evolution*, 30, 36–41.

Dahle, B. & Swenson, J.E. (2003) Home ranges in adult scandinavian brown bears (*Ursus arctos*): effect of mass, sex, reproductive category, population density and habitat type. *Journal of Zoology*, 260, 329–335.

D'Amico, M., Periquet, S., Roman, J. & Revilla, E. (2016) Road avoidance responses determine the impact of heterogeneous road networks at a regional scale. *Journal of Applied Ecology*, 53, 181–190.

D'Amico, M., Rouco, C., Russell, J.C., Roman, J. & Revilla, E. (2013) Invaders on the Road: Synanthropic Bird Foraging Along Highways. *Oecologia Australis*, 17, 86–95.

Davenport, J. & Davenport, J. (2006) *The Ecology of Transportation: Managing Mobility for the Environment*, volume 10. ISSN: 1566-0745.

de Freitas, S.R., Sousa, C.O. & Bueno, C. (2013) Effects of landscape characteristics on roadkill of mammals, birds and reptiles in a highway crossing the atlantic forest in southeastern brazil. *International Conference on Ecology and Transportation (ICOET 2013)*. Arizona.

de Freitas, S.R., de Oliveira, A.N., Ciocheti, G., Vieira, M.V. & da Silva Matos, D.M. (2015) How landscape patterns influence road-kill of three species of mammals in the brazilian savanna. *Oecologia Australis*, 18.

Duchesne, T., Fortin, D. & Rivest, L.P. (2015) Equivalence between Step Selection Functions and Biased Correlated Random Walks for Statistical Inference on Animal Movement. *ONE*, 10, e0122947.

Eddelbuettel, D. & Balamuta, J.J. (2018) Extending extitR with extitC++: A Brief Introduction to extitRcpp. *The American Statistician*, 72, 28–36.

Fahrig, L., Pedlar, J.H., Pope, S.E., Taylor, P.D. & Wegner, J.F. (1995) Effect of road traffic on amphibian density. *Biological conservation*, 73, 177–182.

Farley, C.T., Glasheen, J. & McMahon, T.A. (1993) Running springs: speed and animal size. *Journal of experimental Biology*, 185, 71–86.

Farmer, R.G. & Brooks, R.J. (2012) Integrated risk factors for vertebrate roadkill in southern Ontario. *The Journal of Wildlife Management*, 76, 1215–1224.
Ford, A.T. & Fahrig, L. (2007) Diet and body size of North American mammal road mortalities. *Transportation Research Part D: Transport and Environment*, 12, 498–505.

Forman, R.T.T. & Alexander, L.E. (1998) Roads and their major ecological effects. *Annual Review of Ecology and Systematics*, 29, 207–231.

Fraser, D. & Thomas, E.R. (1982) Moose-Vehicle Accidents in Ontario : Relation to Highway Salt. *The Wildlife Society Bulletin*, 10, 261–265.

George, L., Macpherson, J.L., Balmforth, Z. & Bright, P.W. (2011) Using the dead to monitor the living: can road kill counts detect trends in mammal abundance? *Applied Ecology and Environmental Research*, 9, 27–41.

Gibbs, J.P. & Shriver, W.G. (2002) Estimating the Effects of Road Mortality on Turtle Populations. *Conservation Biology*, 16, 1647–1652.

Girardet, X., Conruyt-Rogeon, G. & Foltete, J.C. (2015) Does regional landscape connectivity influence the location of roe deer roadkill hotspots? *European Journal of Wildlife Research*, 61, 731–742.

Gomes, L., Grilo, C., Silva, C. & Mira, A. (2009) Identification methods and deterministic factors of owl roadkill hotspot locations in Mediterranean landscapes. *Ecological Research*, 24, 355–370.

Gonzalez-Suarez, M., Ferreira, F.Z. & Grilo, C. (2018) Spatial and species-level predictions of road mortality risk using trait data. *Global Ecology and Biogeography*, 27, 1093–1105.

Grilo, C., Reto, D., Filipe, J., Ascensao, F. & Revilla, E. (2014) Understanding the mechanisms behind road effects: linking occurrence with road mortality in owls. *Animal Conservation*, 17, 555–564.

Grilo, C., Bissonette, J. & Cramer, P. (2011) *Mitigation measures to reduce impacts on biodiversity*, pp. 73–114.

Grilo, C., Koroleva, E., Andrasik, R., B'il, M. & Gonzalez-Suarez, M. (2020) Roadkill risk and population vulnerability in European birds and mammals. *Frontiers in Ecology and the Environment*, 18, 323–328.

Grosman, P.D., Jaeger, J.A., Biron, P.M., Dussault, C. & Ouellet, J.P. (2009) Reducing moose-vehicle collisions through salt pool removal and displacement: An agent-based modeling approach. *Ecology and Society*, 14.

Hels, T. & Buchwald, E. (2001) The effect of road kills on amphibian populations. *Biological Conservation*, 99, 331–340.

Hobday, A.J. & Minstrell, M.L. (2008) Distribution and abundance of roadkill on Tasmanian highways: Human management options. *Wildlife Research*, 35, 712–726.

Holderegger, R. & Di Giulio, M. (2010) The genetic effects of roads: a review of empirical evidence. *Basic and Applied Ecology*, 11, 522–531.
Husby, A. & Husby, M. (2014) Interspecific analysis of vehicle avoidance behavior in birds. *Behavioural Ecology*, 25, 504–508.

Hutchinson, J.M. & Waser, P.M. (2007) Use, misuse and extensions of “ideal gas” models of animal encounter. *Biological Reviews*, 82, 335–359.

Inbar, M. & Mayer, R.T. (1999) Spatio-Temporal Trends in Armadillo Diurnal Activity and Road-Kills in Central Florida. *Wildlife Society Bulletin* (1973-2006), 27, 865–872.

Jacobson, S.L., Bliss-Ketchum, L.L., De Rivera, C.E. & Smith, W.P. (2016) A behavior-based framework for assessing barrier effects to wildlife from vehicle traffic volume. *Ecosphere*, 7, 1–15.

Jaeger, J.A., Bowman, J., Brennan, J., Fahrig, L., Bert, D., Bouchard, J., Charbonneau, N., Frank, K., Gruber, B. & Von Toschanowitz, K.T. (2005) Predicting when animal populations are at risk from roads: An interactive model of road avoidance behavior. *Ecological Modelling*, 185, 329–348.

Joyce, T.L. & Mahoney, S.P. (2001) Spatial and Temporal Distributions of Moose-Vehicle Collisions in Newfoundland. *Wildlife Society Bulletin* (1973-2006), 29, 281–291.

Kerth, G. & Melber, M. (2009) Species-specific barrier effects of a motorway on the habitat use of two threatened forest-living bat species. *Biological Conservation*, 142, 270–279.

Kjellander, P., Hewison, A., Liberg, O., Angibault, J.M., Bideau, E. & Cargnelutti, B. (2004) Experimental evidence for density-dependence of home-range size in roe deer (*Capreolus capreolus* L.): a comparison of two long-term studies. *Oecologia*, 139, 478–485.

Krop-Benesch, A., Berger, A., Hofer, H. & Heurich, M. (2013) Long-term measurement of roe deer (*Capreolus capreolus*) (Mammalia: Cervidae) activity using two-axis accelerometers in GPS-collars. *Italian Journal of Zoology*, 80, 69–81.

Legagneux, P. & Ducatez, S. (2013) European birds adjust their flight initiation distance to road speed limits. *Biology Letters*, 9, 20130417.

Lehtonen, J. & Jaatinen, K. (2016) Safety in numbers: the dilution effect and other drivers of group life in the face of danger. *Behavioral Ecology and Sociobiology*, 70, 449–458.

Lima, S.L., Blackwell, B.F., DeVault, T.L. & Fernández-Juricic, E. (2015) Animal reactions to oncoming vehicles: a conceptual review. *Biological reviews of the Cambridge Philosophical Society*, 90, 60–76.

Mace, R.D., Waller, J.S., Manley, T.L., Lyon, L.J. & Zuuring, H. (1996) Relationships Among Grizzly Bears, Roads and Habitat in the Swan Mountains Montana. *Journal of Applied Ecology*, 33, 1395–1404.
Publisher: [British Ecological Society, Wiley].

Maxwell, J.C. (1860) V. Illustrations of the dynamical theory of gases.—Part I. On the motions and collisions of perfectly elastic spheres. *The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science*, 19, 19–32.
Mayer, M., Coleman Nielsen, J., Elmeros, M. & Sunde, P. (2021) Understanding spatio-temporal patterns of deer-vehicle collisions to improve roadkill mitigation. *Journal of Environmental Management*, 295, 113148.

Medinas, D., Marques, J.T., Costa, P., Santos, S., Rebelo, H., Barbosa, A.M. & Mira, A. (2021) Spatiotemporal persistence of bat roadkill hotspots in response to dynamics of habitat suitability and activity patterns. *Journal of Environmental Management*, 277, 111412.

Meek, R. (2009) Patterns of reptile road-kills in the Vendée region of western France. *Herpetological Journal*, 19, 135–142.

Meisingset, E.L., Loe, L.E., Brekkum, Ø., Van Moorter, B. & Mysterud, A. (2013) Red deer habitat selection and movements in relation to roads. *Journal of Wildlife Management*, 77, 181–191.

Meunier, F.D., Verheyden, C. & Jouventin, P. (2000) Use of roadsides by diurnal raptors in agricultural landscapes. *Biological Conservation*, 92, 291–298.

Mueller, T. & Fagan, W.F. (2008) Search and navigation in dynamic environments–from individual behaviors to population distributions. *Oikos*, 117, 654–664.

Mukherjee, S., Ray-Mukherjee, J. & Sarabia, R. (2013) Behaviour of American Crows (*Corvus brachyrhynchos*) when encountering an oncoming vehicle. *The Canadian Field-Naturalist*, 127, 229–233.

Marell, A., Ball, J.P. & Hofgaard, A. (2002) Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Lévy flights. *Canadian Journal of Zoology*, 80, 854–865.

Norberg, R. & Norberg, R.A. (1970) Hunting Technique of Tengmalm's Owl *Aegolius funereus* (L.). *Ornis Scandinavica*, 1, 51.

Ratton, P., Secco, H. & da Rosa, C.A. (2014) Carcass permanency time and its implications to the roadkill data. *European Journal of Wildlife Research*, 60, 543–546.

Raymond, S., Schwartz, A.L.W., Thomas, R.J., Chadwick, E. & Perkins, S.E. (2021) Temporal patterns of wildlife roadkill in the UK. *PLoS One*, 16, e0258083.

Rea, R.V., Scheideman, M.C., Hesse, G. & Mumma, M.A. (2021) The effectiveness of decommissioning roadside mineral licks on reducing moose (*Alces alces*) activity near highways: implications for moose-vehicle collisions. *Canadian Journal of Zoology*, 99, 1009–1019.

Refinetti, R. (1999) Relationship between the daily rhythms of locomotor activity and body temperature in eight mammalian species. *American Journal of Physiology-Regulatory, Integrative and Comparative Physiology*, 277, R1493–R1500.

Rosen, P.C. & Lowe, C.H. (1994) Highway mortality of snakes in the sonoran desert of southern Arizona. *Biological Conservation*, 68, 143–148.
Rowcliffe, J.M., Jansen, P.A., Kays, R., Kranstauber, B. & Carbone, C. (2016) Wildlife speed cameras: measuring animal travel speed and day range using camera traps. *Remote Sensing in Ecology and Conservation*, 2, 84–94.

Ryu, M. & Kim, J.G. (2020) Influence of roadkill during breeding migration on the sex ratio of land crab (*Sesarma haematoche*). *Journal of Ecology and Environment*, 44, 23.

Ryu, M. & Kim, J.G. (2021) Coastal road mortality of land crab during spawning migration. *Scientific Reports*, 11, 6702.

Said, S., Gaillard, J.M., Widmer, O., Debias, F., Bourgoin, G., Delorme, D. & Roux, C. (2009) What shapes intra-specific variation in home range size? A case study of female roe deer. *Oikos*, 118, 1299–1306.

Saint-Andrieux, C., Calenge, C. & Bonenfant, C. (2020) Comparison of environmental, biological and anthropogenic causes of wildlife-vehicle collisions among three large herbivore species. *Population Ecology*, 62, 64–79.

Saltelli, A., Aleksankina, K., Becker, W., Fennell, P., Ferretti, F., Holst, N., Li, S. & Wu, Q. (2019) Why so many published sensitivity analyses are false: A systematic review of sensitivity analysis practices. *Environmental Modelling & Software*, 114, 29–39.

San, E.D.L., Ferrari, N. & Weber, J.M. (2007) Spatio-temporal ecology and density of badgers *Meles meles* in the swiss jura mountains. *European Journal of Wildlife Research*, 53, 265–275.

Schaub, A., Ostwald, J. & Siemens, B.M. (2008) Foraging bats avoid noise. *Journal of Experimental Biology*, 211, 3174–3180.

Schooley, R.L. & Wiens, J.A. (2003) Finding habitat patches and directional connectivity. *Oikos*, 102.

Schwartz, A.L., Williams, H.F., Chadwick, E., Thomas, R.J. & Perkins, S.E. (2018) Roadkill scavenging behaviour in an urban environment. *Journal of Urban Ecology*, 4, 1–7.

Seiler, A. & Helldin, J.O. (2006) Mortality in wildlife due to transportation. pp. 165–189.

Sillero, N. (2008) Amphibian mortality levels on Spanish country roads: Descriptive and spatial analysis. *Amphibia Reptilia*, 29, 337–347.

Silveira Miranda, J.E., de Melo, F.R. & Keichi Umetsu, R. (2020) Are Roadkill Hotspots in the Cerrado Equal Among Groups of Vertebrates? *Environmental management*, 65, 565–573.

Singh, N.J. & Ericsson, G. (2014) Changing motivations during migration: linking movement speed to reproductive status in a migratory large mammal. *Biology letters*, 10, 20140379.

Siniff, D.B. & Jessen, C.R. (1969) *A Simulation Model of Animal Movement Patterns. Advances in Ecological Research, volume 6*, pp. 185–219. Academic Press, Cambridge, MA, USA.

Southern, H.N. (1954) Tawny Owls and Their Prey. *Ibis*, 96.
Steiner, W., Leisch, F. & Hackl ¨ander, K. (2014) A review on the temporal pattern of deer-vehicle accidents: Impact of seasonal, diurnal and lunar effects in cervids. *Accident Analysis and Prevention*, 66, 168–181.

Steiner, W., Scholl, E.M., Leisch, F. & Hacklander, K. (2021) Temporal patterns of roe deer traffic accidents: Effects of season, daytime and lunar phase. *PLoS One*, 16, e0249082.

Sword, G.A. (2005) Local population density and the activation of movement in migratory band-forming mormon crickets. *Animal Behaviour*, 69, 437–444.

Taylor, B.D., Goldingay, R.L., Taylor, B.D. & Goldingay, R.L. (2010) Roads and wildlife: impacts, mitigation and implications for wildlife management in Australia. *Wildlife Research*, 37, 320–331.

Teixeira, F.Z., Coelho, I.P., Esperandio, I.B., Rosa Oliveira, N., Porto Peter, F., Dornelles, S.S., Rosa Delazeri, N., Tavares, M., Borges Martins, M. & Kindel, A. (2013) Are road-kill hotspots coincident among different vertebrate groups? *Oecologia Australis*, 17, 36–47.

Teixeira, F.Z., Kindel, A., Hartz, S.M., Mitchell, S. & Fahrig, L. (2017) When road-kill hotspots do not indicate the best sites for road-kill mitigation. *Journal of Applied Ecology*, 54, 1544–1551.

van Langevelde, F. & Jaarsma, C.F. (2005) Using traffic flow theory to model traffic mortality in mammals. *Landscape ecology*, 19, 895–907.

van Langevelde, F., van Dooremalen, C. & Jaarsma, C.F. (2009) Traffic mortality and the role of minor roads. *Journal of Environmental Management*, 90, 660–667.

Van Moorter, B., Visscher, D., Benhamou, S., B¨orger, L., Boyce, M.S. & Gaillard, J.M. (2009) Memory keeps you at home: A mechanistic model for home range emergence. *Oikos*, 118, 641–652.
<figure><img src="image_34.png" /><figcaption>Fig. S1: The animals' movements are simulated using biased correlated random walks. The orientation of the walks is computed for each time step as a weighted mean between the persistence (correlated random walk) and the directional bias towards a center of attraction (▲). (a): the weight of attraction is w=3. (b): the weight of the attraction is w=20. The higher the weight w of the directional bias, the quicker the animal reaches the center. Once the attraction center is reached, the animal will orbit around it indefinitely.</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>Fig. S2: For animals roaming freely (scenario 0), we retrieve from the WVC simulation both the mean number of animal-road encounters (black line) and the number of actual animal-vehicle collisions (grey line) per simulation run. The distance each animal travels during each run increases with animal speed, leading to more animals encountering the road more often. Simultaneously, faster animals decrease their probability of collision per road crossing as they cross the road in less time. As a result, the number of collisions does not increase with the same rate as the number of road encounters: increasing the mean animal speed produces more but less dangerous road encounters for animals.</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>Fig. S3: Seasonal patterns in male individuals' speed (deviation to the mean, a,b) and reported roadkill (c) for the European roe deer *Capreolus capreolus*. We obtained 672 roadkill data from the citizen science database Faune-Auvergne-Rhône-Alpes (fauneauvergnerhonealpes.org), between 2010 and 2022 in the Auvergne-Rhône-Alpes region of France. The speed for male roe deer (adults and sub-adults) was measured on GPS-tracked individuals during in the Bavarian forest (Germany). Male roe deer have distinct peaks in speed and activity during the mating season (March to August). Increases in individual speed correlate to increases in the number of roe deer-vehicles collisions reported, as predicted by the wildlife-vehicle model (fig. 2&4, scenario 0).</figcaption></figure>
Chapter 2: Roadkill persistence on the road

<figure><img src="image_37.png" /></figure>
# Influence of traffic and weather on small wildlife carcass persistence time on roads (under review)

Annaëlle Bénard, Thierry Lengagne and Christophe Bonenfant

*Transportation Research Part D: Transport and Environment*

DOI: 10.1016/j.trd.2023.104012

## CONTEXT

The expansion of road networks is posing a threat to the survival of many terrestrial species due to the increasing number of wildlife-vehicle collisions. However, the roadkill datasets underestimate collision numbers, as the persistence of roadkill carcasses is often shorter than the frequency at which roads are monitored.

At present, estimates of persistence only have a temporal resolution of 24 hours, while also concluding that most roadkill is removed within a day. Unfortunately, more detailed persistence estimates at finer temporal scales are not available for most species.

## OBJECTIVES

- Estimate the persistence of two types of small-bodied roadkill (amphibians and small passerines) with a temporal resolution of 2 hours.

- Evaluate the spatio-temporal structure of persistence times by testing roadkill persistence under varying conditions of traffic volume and in the presence and absence of rainfall.

- Integrate the persistence estimates into the Faune-AuRA roadkill dataset, allowing for more accurate estimates of the number of collisions in the Auvergne-Rhône-Alpes region.

## KEY RESULTS

- Amphibian persistence was strongly influenced by road traffic, with median persistence ranging from 1 to 18 hours. Passerine persistence was independent of road traffic, and they persisted on average less than 2 hours.

- Rainfall had no significant effect on persistence times.

- We estimated that up to 700,000 small passerines fatalities occurred in 2022 in the Auvergne-Rhône-Alpes.

## CONCLUSIONS

- Most amphibians and small passerines persist on roads for only a few hours, leading to a probable significant underestimation of their mortality in uncorrected roadkill datasets.

- Persistence of roadkill and its spatial structure are species-dependent. This structure suggests that uncorrected roadkill datasets also incorrectly estimate the influence of road traffic on collision rates.

- The magnitude of small passerine road mortality is much greater than previously suspected.
Abstract

The rapidly expanding road network threatens the persistence of many terrestrial species through mortality associated with wildlife-vehicle collisions. Roadkill monitoring under-estimate actual collision numbers, as the time during which roadkill carcasses remain visible on the road is often shorter than the frequency of road monitoring. By placing passerine and amphibian carcasses on stretches of roads we surveyed every 2 hours, we fine-tuned existing persistence estimates for these species. The time for half of the carcasses to disappear was less than 30 minutes for birds and 1-18 hours for amphibians depending on the volume of traffic, which is much shorter than previous estimates. We show the implications of these results by performing roadkill surveys on common toads 3 hours after the window of reproductive migration, showing roadkill is under-estimated by half, and by estimating from citizen science data that passerine collisions could be as high as 10 individuals/km²/year in France.
# 1. Introduction

Human activities and their role in the ongoing global biodiversity decline have been identified as the main cause of biodiversity loss over the past decades (Pollock et al., 2020). Of particular importance are linear transportation infrastructures such as roads (Forman et al., 2003) that threaten the viability of many wildlife populations (Moore et al., 2023), first and foremost of endangered species (Martin et al., 2018; Shepard et al., 2008; Taylor & Goldingay, 2009). The rapidly expanding road network concentrates all major threats of biodiversity at particular locations in space (Forman & Alexander, 1998; Rytwinski & Fahrig, 2015) jeopardizing the fitness of individuals. First, road surfaces hamper animal movement and gene flows through habitat fragmentation and destruction (Goosem, 2007; Lesbarrères & Fahrig, 2012; Prunier et al., 2014). Chemical pollutants accumulating on roads alter the composition of roadside vegetation communities, often favoring the expansion of invasive species (Lagerwerff & Specht, 2002; Nunes et al., 2020; Valladares et al., 2008). Traffic noise and light were shown to alter physiology and behaviour, lower the reproductive success, and deter the presence of multiple species up to several hundreds of meters away from the road (Lengagne, 2008; Parris & Schneider, 2009; Reijnen & Foppen, 1994; Troïanowski et al., 2017). Finally, of all these ecological effects, roadkill is perhaps the most critical driver of biodiversity loss in relation to roads: wildlife-vehicle collisions most likely affect all terrestrial species, but on a scale we have yet to fully understand (Grilo et al., 2020, 2021; Moore et al., 2023).

One reason for this lack of knowledge is the quantification of roadkill numbers that are likely heavily underestimated due to unknown persistence and imperfect detection of dead animals along roads. Past studies suggested that performing road surveys on foot or bike at low speed improves accuracy by increasing the detection rates of roadkill carcasses (Barrientos et al., 2018; Ogletree & Mead, 2020). Once killed, an animal can either be scavenged, mechanically disappear with the flow of vehicles, or be displaced by people. This persistence time of carcasses on the road dictates the amount of time carcasses are at risk of detection (Ratton et al., 2014). The direct consequence of a persistence time of carcasses shorter than the frequency of surveys is a severe underestimation of roadkill numbers. Surprisingly, few authors have focused on the importance of carcass persistence and its structuring factors in roadkill surveys (but see Ratton et al., 2014; Santos et al., 2011; Teixeira et al., 2013).

Most attempts at estimating the persistence time of carcasses focus on scavenging rates using chicks and other small-bodied animals as bait for carrion feeders, and find that these carcasses seldom persist more than a few days after being placed on the road (Antworth et al., 2005; Ratton et al., 2014; Santos & Ascensão, 2019; Schwartz et al., 2018). Santos et al. (2011) recorded persistence times for a wide range of species and have highlighted the roles of road traffic, species and seasons on carcass removal rates.
They found that carcasses disappeared quicker from smaller roads, possibly because low traffic volumes allow carrion-feeders easier access to roadkill (see also Ratton et al., 2014). Rain and high humidity also accelerated carcass disappearance. Humid conditions promote faster soft tissue decay (Brand et al., 2003), and Santos et al. (2011) suggested that in the case of roadkill, humidity promotes carcass dismemberment by vehicles. To our knowledge, there is no other published data on the relation between rain and roadkill persistence. The position of the carcass on the road also has been shown to influence persistence, with rodent carcasses on the lane disappearing faster than carcasses on the road shoulder (Santos & Ascensão, 2019).

The median persistence time (i.e., the time at which 50% of the carcasses have disappeared) of small-bodied fauna including reptiles, amphibians, small birds (<200 g), bats and other small mammals (<300 g) is approximately 1 day (Santos & Ascensão, 2019; Santos et al., 2011). Considering that in these studies, the surveys were done every 24 hours, median persistence time for these species might in reality be even less than a day. Indeed, Stewart (1971) placed 50 house sparrow carcasses on the surface of a highway and found that none remained after 2 hours. Roadkill surveys, even when performed daily, may under-estimate the number of collisions for the smallest species. Given the distribution of body size among mobile and terrestrial vertebrates (Smith & Lyons, 2013), road mortality could likely be underappreciated for 60% of the extent species. Consequently, efficient mitigation and conservation measures for these species require accurate estimations of persistence time and its spatio-temporal variability (Teixeira et al., 2013).

Many small species of vertebrates are indeed of conservation concerns (Pereira et al., 2010). Roadkill data for small-bodied species such as rodents, small passerines or reptiles is scarce (but see Meek, 2009; Morelli et al., 2020; Ruiz-Capillas et al., 2015). Amphibian roadkill is better documented because massive roadkill occurs during the breeding season when amphibians leave their terrestrial habitat to gather in breeding ponds. It is the most endangered vertebrate group and has shown a significant decline in the last decades due to environmental disturbance (Wise, 2007). Mitigation measures were often used to reduce mortality during road crossings (Beebee, 2013; Helldin & Petrovan, 2019; Testud, 2020). Yet, for all small-bodied species including amphibians, we lack good quality data leading to robust estimations of persistence time, and consequently are left with unreliable estimates of roadkill occurrence.

To fill the gap in knowledge for small-bodied wildlife road mortality, we experimentally estimated the persistence time after a collision by placing carcasses on roads and monitoring their removal time and rate at a fine temporal resolution of 2 hours. We estimated persistence time on roads of different traffic volumes and under different weather conditions, predicting that persistence time would be shorter on
smaller roads and in high humidity conditions (Santos et al., 2011). As carcass position on the lane could
affect persistence (Antworth et al., 2005; Santos & Ascensão, 2019), we randomized the placement of the
animal. Santos et al. (2011) found significant differences in persistence between species of similar body
sizes but different taxa, so we used both small amphibians and birds (< 20g) in an effort to generalize our
results to other small-sized species. Lastly, using roadkill surveys we performed during the reproductive
migration of the common toad *Bufo bufo* and citizen science data on small passerine road mortality, we
estimated the proportion of missed carcasses, and therefore the number of amphibian roadkill during
surveys as well as the number of small passerine roadkill in the Auvergne-Rhône-Alpes region France.

**2. Material and Methods**

**2.1 Study location and sampling design**

We measured persistence time between March and July 2022 for dry days, October and December 2022 for rainy days. We bought amphibian carcasses (*Pelophylax kl. esculentus*) from a licensed supplier (SONODIS) and procured small passerine carcasses (< 20g) from a wildlife rehabilitation center (Le Tichodrome, Isère, France). We stored all carcasses at -20°C and thawed them for 24h before the day of the experiment.

We selected 4 roads for passerine trials, and 7 roads for amphibians (speed limit: 80 km.h⁻¹). We chose
experimental locations to cover a wide range of road traffic volumes (130 to 9 300 veh.day⁻¹). We
retrieved the average traffic volume estimation over the last 3 years from local authorities for all roads
but the smallest and less frequented ones (referred to as "*Petit Nice*" thereafter). We estimated missing
traffic volume values by placing a camera-trap overlooking the road, and recording 1-minute videos
every 5 minutes during 24 hours. We previously compared traffic estimations as provided by authorities
and our method using camera traps, and found camera traps yielded very satisfactory results (camera-trap
estimation: 11 220 veh.day⁻¹; official mean daily traffic estimation: 11 135 veh.day⁻¹).

On each road, we placed N=10 carcasses on the asphalt road surface. We chose the lane using a random
number generator so that carcasses could be on road shoulders, in the center of the lane so they would fit
in-between the tires of most vehicles, or directly in the path of the left or right vehicle tires (fig. 2). We
surveyed the carcasses on foot every two hours to determine whether they had disappeared. We
considered a complete removal of a carcass when the observer could no longer detect it when walking on
the road. Before running the experiment, we conducted training to ensure the different observers agreed
on what a 'removed' carcass was. For passerines, we replicated the experiment on a rain-free day when
the road surface was completely dry, and on a rainy day. For amphibians, we completed the experiments on the 8 locations during rain-free days, but replicates on rainy days were limited to 3 locations only corresponding to traffic volumes of 130, 4160 and 8 000 veh.day⁻¹.

## 2.2 Data analyses of persistence time

We obtained data in which the removal of the carcass from the road was only known to occur within an interval of two hours: for example, a carcass that was present on the first survey but had disappeared on the second had disappeared after a period of 2 to 4 hours on the road surface. The observations could be right-censored if the carcass was still present at the end of the experiment. As ignoring interval-censoring in survival data can lead to biases in survival estimates (Radke, 2003), we chose to model the persistence with interval-censored survival models, an extension of traditional survival models designed to analyze survival data in which the event of interest (here, disappearance from road) is only known to occur within a defined time interval (Anderson-Bergman, 2017). Interval censored models accommodate right-censored data points. We modeled the persistence of amphibians and small passerines in two separate models.

We used R package *icenReg* (Anderson-Bergman, 2017) for the R statistical software (R Core Team, 2021) which provides tools for implementing parametric interval-censored proportional hazards survival models. We selected the underlying parametric distributions of each model by visually comparing the available distributions to the corresponding Cox-PH model and selecting a distribution with no systematic deviation (Anderson-Bergman, 2017). Amphibian persistence was modeled using a gamma distribution, and passerine persistence using a log-normal distribution. We modeled the effects of road traffic volume (continuous variable), weather (2 modalities categorical variable: dry vs. rain) and position on the lane (2 modalities categorical variable: placed in the path of the tires or outside, see fig. 2) on the persistence of the carcasses. We included observer ID (A/B) to accommodate for systematic differences in measurement between the two observers when analyzing amphibian data, but not for passerines because it lined up with the weather variable (all dry days were conducted by observer A, and all rainy days by observer B). We entered road traffic volume on persistence as a linear covariable, and as a log-transformed variable to account for potential non-linear relationships with carcass persistence. We represented the predicted median persistence by each model (linear vs. log-transformed) and the median persistence times of each road using the Turnbull estimator. We selected the log-transformed model for amphibian persistence and the linear model for passerine persistence based on visual fit (fig. A1).
## 2.3 Estimation of roadkill numbers

Using our measurements of persistence times, we computed the number of road-killed amphibians and small passerines during road surveys. For amphibians, we performed two roadkill surveys on foot on separate evenings in March 2022, during the common toad reproductive migration at a known road-crossing location on road D1504. The time elapsed between the collision window and the survey was 3 hours, and the D1504 road a mean daily traffic volume estimated at 3379 veh.day⁻¹, which we adjusted to 1126 veh.day⁻¹ considering the rule of thumb that only 25% of the traffic occurs between 7p.m. and 7a.m, the time of the survey, while the persistence experiments were conducted during the day (Van Langevelde & Jaarsma, 2005). Using the traffic volume and the time elapsed between collision window and road survey, we estimated from the survival model the proportion of carcasses having already disappeared from the road surface.

For passerines, roadkill count data was extracted for birds species < 20g from Faune-Auvergne-Rhône-Alpes, a citizen science database that compiles species presence as well as roadkill data submitted in real time by volunteers from the region Auvergne-Rhône-Alpes (thereafter: AuRA), France. We extracted the daily roadkill reports during the year 2022. Following Teixeira et al. (2013), the roadkill rate $\lambda$ (collision.day⁻¹) can be estimated as $\lambda = \frac{N}{p.T_R}$ where N is the number of roadkill carcasses counted, p is the detection rate of the carcasses by the observer and the characteristic time $T_R$ is the time needed to reduce the number of remaining carcasses on the road by $1 - \frac{1}{e^1} \sim 63\%$. We estimated $T_R$ from the fitted survival model. We used it to estimate the daily number of collisions for 2022 in AuRA. We assumed detection rate p = 1 (all carcasses are detected) as we had no information about detection probabilities for small passerines. We explored the implications of imperfect carcass detection on passerine roadkill estimations in section 3 of the supplementary material.

To take into account the underlying distribution patterns of passerine species, we extracted the presence/absence data for each species in AuRA municipalities from Faune-AuRA, and for each municipality, computed the corresponding cumulative length of all roads accessible by car. We used this information to give estimates of the number of roadkill per kilometer of road in areas where the species was present.
# 3. Results

## 3.1 Carcasses persistence on the road

Half of the amphibians placed on the road disappeared within the first 5 hours on all roads except for the smallest ("Petit Nice" road, 130 veh.day⁻¹). We projected that at t=24h, 95% of the amphibians should disappear from all roads, except for Petit Nice (52% at t=24h). In the following, we report model estimates for all covariables by hazard ratio (standard error); z-value and p-value. In accordance with our predictions, roads with higher traffic led to shorter amphibian carcass persistence: an increase of 50% in daily traffic increases the probability of removal from the road by 1.23 (hazard ratio = 1.67 (0.09); z = 5.62; *p* < 0.001; fig. 1a). As predicted, we observed that probability of disappearance was 1.97 (0.23) times faster for amphibians placed in the path of car tires compared to road shoulder (z = 3.86; *p* < 0.001; fig. 2a). However, rain did not decrease or impact persistence (hazard ratio = 1.19 (0.3); z = 0.58; *p* = 0.56, fig. 1a). There were no differences in amphibian persistence between observers (hazard ratio = 0.94 (0.29); z = -0.19; *p* = 0.85).

Within the first 2 hours, 80% of the passerines were no longer visible on any of the roads. We modeled road traffic volume as a linear covariable of persistence (fig. A1). Our model predicted that virtually all passerine carcasses (97%) would disappear at time t = 24h. Contrary to all previous hypotheses, we found no differences in passerine persistence time depending on road traffic (hazard ratio = 1.0 (4.5e⁻⁵); z= 0.94 ; *p* = 0.347; fig. 1b), carcass position on the lane (hazard ratio = 0.99 (0.27); z = -0.003; *p* = 0.996; fig. 2b) or weather (hazard ratio = 1.23 (0.26); z = 0.81; *p* = 0.420; fig. 1b).
<figure><img src="image_38.png" /><figcaption>Fig. 1: **Carcass persistence on the road.** We performed roadkill persistence trials on 8 different roads for amphibians (a) and 4 roads for small passerines. At each location, 10 carcasses are placed on the road surface, and surveyed every two hours until complete disappearance. We represent the median persistence time (time for 50% of carcasses to disappear) of each road estimated during dry days without rainfall (▲) and rainy days (■). Predictions from the fitted parametric survival models are represented as black lines (grey lines as the 95% confidence interval).</figcaption></figure>
<figure><img src="image_39.png" /><figcaption>Fig. 2: **Kaplan-Meier curves of carcass persistence.** We randomly positioned carcasses of 90 frogs (a) and 80 carcasses from multiple species of small passerines (b) on the surface of different roads. We represent here the Kaplan-Meier survival curves of the first 12 hours of carcass persistence time across all roads. Carcasses were randomly positioned to be either in the path of the tires of most 4-wheeled vehicles (red), or outside of the path of the tires (blue). Parametric survival models showed that frog carcasses disappeared faster when placed in the path of vehicle tires while passerines had similar persistence on every position on the lane.</figcaption></figure>
## 3.2 Practical implications for roadkill estimations

On March 15th and March 20th 2022, we counted respectively 12 and 30 common toad carcasses on road D1504. Using the fitted survival model of amphibian persistence described above, we predicted the proportion of missing carcasses on the road according to traffic volume. After 3 hours, we estimated that 49.6% (95% confidence interval: 39.4, 60.5) of the carcasses had already been removed from the road at the time of survey meaning that, assuming perfect detection of carcasses on the road, they were 17.9 (16.7, 19.1) toad casualties on March 15th and 44.8 (41.8, 48.1) on March 20th.

For passerines, 201 small passerines from 21 species were reported by contributors in 2022 (see Table 1 for a complete list). We estimate the characteristic time $T_R$ at 0.0283 days (95% confidence interval: 0.009, 0.088). Accounting for carcass removal rates amounts to 7093 (2270, 22120) passerines road-killed in 2022 in the AuRA region (Table 1). The most commonly killed species on roads is the house sparrow *Passer domesticus* with 0.87 individuals killed per year every 100km, and the least common is the long-tailed tit *Aegithalos caudatus* with 0.019 individuals. These estimates assume that carcasses are always detected and reported by Faune-AuRA contributors. Straightforward estimates of roadkill numbers accounting for imperfect detection and report can be derived from these results: assuming that 1% of passerine carcasses present on the road are seen and reported, 0.87/0.01 = 87 house sparrows and 0.019/0.01 = 19 long-tailed tits are killed annually per 100km of road, and 709 300 (227 000, 2 212 000) passerines could have been killed on roads in the AuRA region in 2022 (fig. A2).
<table><caption>Table 1: We used roadkill reports for small passerine (< 20g) in the Auvergne-Rhône-Alpes (AuRA) region of France from the citizen science database Faune-AuRA in 2022. We corrected the reports for carcass removal rate from road (Teixeira et al., 2013) and then, using the presence data from Faune-AuRA to infer species distribution patterns, we give estimations of roadkill per 100 km of road in areas where the species is present. These estimations of roadkill rates account for the speed of carcass disappearance from the road, but not for the number of carcasses missed or not reported by the observers.</caption><thead><tr><th></th><th>Reported in<br>Faune-AuRA<br>(2022)</th><th>Number of collisions after<br>correcting for persistence<br>(95% confidence interval)</th><th>Number of roadkill<br>per 100km of road<br>(95% confidence interval)</th></tr></thead><tbody><tr><td>Long-tailed tit<br><i>Aegithalos caudatus</i></td><td>1</td><td>35.3 (11.3, 110.1)</td><td>0.019 (0.006, 0.06)</td></tr><tr><td>European goldfinch<br><i>Carduelis carduelis</i></td><td>5</td><td>176.5 (56.5, 550.3)</td><td>0.081 (0.03, 0.25)</td></tr><tr><td>Eurasian blue tit<br><i>Cyanistes caeruleus</i></td><td>2</td><td>70.6 (22.6, 220.1)</td><td>0.030 (0.01, 0.09)</td></tr><tr><td>Cirl bunting<br><i>Emberiza cirlus</i></td><td>1</td><td>35.3 (11.3, 110.1)</td><td>0.025 (0.008, 0.08)</td></tr><tr><td>Yellowhammer<br><i>Emberiza citrinella</i></td><td>2</td><td>70.6 (22.6, 220.1)</td><td>0.069 (0.022, 0.21)</td></tr><tr><td>European robin<br><i>Erithacus rubecula</i></td><td>58</td><td>2046.9 (655.2, 6382.9)</td><td>0.84 (0.28, 2.63)</td></tr><tr><td>Common chaffinch<br><i>Fringilla coelebs</i></td><td>16</td><td>564.6 (180.7, 1760.8)</td><td>0.23 (0.07, 0.7)</td></tr><tr><td>White wagtail<br><i>Motacilla alba</i></td><td>6</td><td>211.8 (67.8, 660.3)</td><td>0.12 (0.03, 0.33)</td></tr><tr><td>Great tit<br><i>Parus major</i></td><td>10</td><td>352.9 (112.9, 1100.5)</td><td>0.14 (0.05, 0.44)</td></tr><tr><td>House sparrow<br><i>Passer domesticus</i></td><td>56</td><td>1976.3 (632.6, 6162.8)</td><td>0.87 (0.28, 2.7)</td></tr><tr><td>Black redstart<br><i>Phoenicurus ochruros</i></td><td>11</td><td>388.2 (124.3, 1210.6)</td><td>0.18 (0.06, 0.56)</td></tr><tr><td>Common redstart<br><i>Phoenicurus phoenicurus</i></td><td>3</td><td>105.9 (33.9, 330.2)</td><td>0.081 (0.03, 0.25)</td></tr><tr><td>Willow warbler<br><i>Phylloscopus trochilus</i></td><td>1</td><td>35.3 (11.3, 110.1)</td><td>0.05 (0.02,0.15)</td></tr><tr><td>Whinchat<br><i>Saxicola rubetra</i></td><td>1</td><td>35.3 (11.3, 110.1)</td><td>0.052 (0.02, 0.16)</td></tr><tr><td>European stonechat<br><i>Saxicola rubicola</i></td><td>6</td><td>211.8 (67.8, 660.3)</td><td>0.13 (0.04, 0.42)</td></tr><tr><td>European serin<br><i>Serinus serinus</i></td><td>1</td><td>35.3 (11.3, 110.1)</td><td>0.022 (0.007, 0.07)</td></tr><tr><td>Eurasian blackcap<br><i>Sylvia atricapilla</i></td><td>12</td><td>423.5 (135.6, 1320.6)</td><td>0.18 (0.06, 0.56)</td></tr><tr><td>Garden warbler<br><i>Sylvia borin</i></td><td>1</td><td>35.3 (11.3, 110.1)</td><td>0.057 (0.02, 0.18)</td></tr><tr><td>Common whitethroat<br><i>Sylvia communis</i></td><td>1</td><td>35.3 (11.3, 110.1)</td><td>0.034 (0.01, 0.11)</td></tr><tr><td>Sardinian warbler<br><i>Sylvia melanocephala</i></td><td>1</td><td>35.3 (11.3, 110.1)</td><td>0.14 (0.04, 0.44)</td></tr><tr><td>Eurasian wren<br><i>Troglodytes troglodytes</i></td><td>3</td><td>105.9 (33.9, 330.2)</td><td>0.05 (0.02, 0.16)</td></tr></tbody><tfoot><tr><td><strong>TOTAL</strong></td><td><strong>201</strong></td><td><strong>7093 (2270.6, 22120.2)</strong></td><td><strong>3.39 (1.08, 10.57)</strong></td></tr></tfoot></table>
# 4. Discussion

## 4.1 Persistence on road and implications for road monitoring

Most small carcasses of amphibians and birds in this experiment were removed from the road surface in less than a day. We estimated the median persistence time (i.e., the time needed for half of the carcasses to be removed from the road) of small passerines (< 20g) at t = 22 minutes using a parametric survival model, and this persistence was not affected by road traffic volume, position of the carcass on the road or rain. Common toad carcass persistence was similarly unaffected by rain but was largely dependent on the traffic volume of the road within the explored range (130 - 9000 veh.day⁻¹): the more vehicles, the less time the carcasses remained visible. On roads with 1000 vehicles per day or more, amphibian median persistence time is 5 hours or less. Amphibians placed directly in the path of the tires disappeared nearly twice as fast as the amphibians positioned elsewhere on the road surface.

Santos et al. (2011) found that 50% of small carcasses disappeared in one day for small-sized species (amphibians, reptiles and small birds). Our results agree with these previous observations, and the fine-tuning of previous estimations shows that the median persistence time is actually less than 24h for both amphibians and small birds. For passerines, 80% of carcasses had disappeared within 2 hours across all locations, and 94% after 12h. For amphibians, after 12h we found that over half of the carcasses had disappeared across all locations: 60% had disappeared from *Petit Nice*, a road with little vehicular traffic, and none remained on the major road *Caluire Saône*. Daily roadkill surveys have been previously recommended for accurate roadkill data for small-bodied species (Henry et al., 2021; Santos et al., 2015). Our results suggest instead that even daily road monitoring will largely underestimate the actual number of collisions of amphibians and small passerines with road vehicles. In fact, the short persistence of these species on the road indicates that roadkill surveys will always underestimate casualties unless we monitor roads continuously. Because this is an impossible task, authors should focus instead on implementing persistence corrections (see Teixeira et al., 2013) to their survey methodology. Body size is often cited as the biggest predictor of carcass persistence time on the road (Barrientos et al., 2018; Guinard et al., 2012; Henry et al., 2021). Nevertheless, we found substantial differences in the persistence time between amphibians and small passerines of similar sizes. Hence, the generalization of persistence times between small-bodied species is not possible, and our results are not suitable to assess the persistence of lizards, snakes, bats and other small mammals. We suggest instead that other experiments of persistence with fine-tuning should be conducted on these species to assess the proportion of missed carcasses by daily road surveys.
Scavenger activity is often cited as the main cause of carcasses disappearance in roadkill persistence studies (Antworth et al., 2005; Erritzoe et al., 2003; Slater, 2002). For instance, Schwartz et al. (2018) determined that fresh roadkill attracts corvids and foxes that could remove up to 62% of the carcasses within 2 hours. Smaller roads might be easier to access for carrion-feeders than highly-frequented ones, and roadkill persistence studies report that roadkill generally disappeared faster on smaller roads compared to more frequented ones (Santos et al., 2011; Slater, 2002). We found instead that amphibian persistence decreased with the volume of traffic, suggesting that this is not true for all taxa, or that scavenging is not the main mechanism of carcass removal in this case. It has been suggested that common toads are not attractive to carrion-feeders due to their though skin (Hels & Buchwald, 2001). Instead, mechanical fragmentation of tissues by cars appears to play a major role in amphibian carcass disappearance: the accumulation of repeated crushing of biological tissues by tires flattened most of the carcasses we placed on the road surface that became less and less visible at each observation. This mechanism is consistent with findings that traffic volume significantly decreases persistence time in amphibians (fig. 1a) and that carcasses directly in the path of the tires of most vehicles were removed 2 times faster compared to carcasses placed outside of it (fig. 2a).

Passerine carcasses disappeared at higher rates than amphibians (80% within the first 2 hours) and at the same speed across all tested locations and all positions on the lane. Ratton et al. (2014) and Antworth et al. (2005) found longer carcass persistence when using *Gallus domesticus* chick carcasses (resp. 66% removed within 12h and 40% within 2h). However, the chick carcasses weighted slightly more than the wild passerine species used here: reportedly around 30 grams in both studies, against 20g or less in this experiment. Domestic species are also known to have higher removal rates than wild species in open fields (Prosser et al., 2008). To our knowledge, the only other roadkill persistence experiment at a fine temporal resolution using passerines was conducted by Stewart (1971) with house sparrows *Passer domesticus*. Interestingly, he reported persistence estimates similar to our results (100% removal within the first two hours) on a highway but found very contrasted results on a smaller country road: all carcasses were still visible after 12 hours. On the contrary, and similarly to our findings, chick persistence did not vary between a frequented highway and a low traffic dirt road in Ratton et al. (2014). Small birds persistence on roads appear to be highly variable between species and locations.

Contrary to common toads, passerine persistence on roads showed no correlation to road traffic volume. It could be that the temporal resolution of 2-hours intervals is not fine enough to capture the variability in passerine removal rates from roads. During the experiments, and contrary to amphibians, bird carcasses often disappeared without a trace in-between surveys, which could instead suggest that the high removal rate is the result of scavenging activity (Antworth et al., 2005). We conducted a complementary
experiment with continuous observation of the carcasses during 2 hours (Supp. Mat. Section 3). We placed 12 passerine carcasses randomly on a highly-frequented portion of road (8000 veh.day⁻¹) in an urban setting with no unpaved shoulder where the speed limit was 50 km.h⁻¹. We found a higher persistence than previous estimates : 5 out of 12 (41%) were invisible by the end of the 2 hours, against an average across all roads of 80% in the main experiments. Carcasses disappeared at variable rates, with some becoming undetectable after the passage of 10 vehicles and other being still visible after 800 vehicles (median = 178 vehicles, fig. A3). All carcasses were crushed by vehicle's tires, including carcasses originally placed out of the path of the tires (center of the road, center of the lane in-between tires, roadside) that were either crushed by vehicles swerving on the lane to avoid obstacles such as parked cars or displaced by the turbulence following passing vehicles. Contrary to the common toad, we observed that passerine body shape and feathers could promote carcass mobility on the road surface. Passerines carcasses that are displaced by passing vehicles can also potentially end up in the vegetation of the road shoulder, masking them from view during surveys (AB personal observations).

Season and weather influence the speed of carcass disappearance in open fields where removal is usually the result of decomposition or scavenging, and the highest rates of removal are found during the summer months when temperatures are high (Costantini et al., 2017; Prosser et al., 2008; Sharanowski et al., 2008). Carcass persistence on roads was instead found to be lower during spring in France (Guinard et al., 2012), and high temperatures and humid conditions accelerated the disappearance of carcasses from roads in Portugal (Santos et al., 2011). We tested here the effect of rainfall on persistence time, and expected carcasses to disappear faster under the rain. We found instead similar persistence between dry and rainy days for both amphibians and passerines (fig. 1). Rain and humidity might not make a difference when a small-bodied fresh carcass is confronted to a tire, as opposed to bigger animals. Instead of weather, persistence on the road for small species could vary between seasons following scavenger activity (Guinard et al., 2012; Schwartz et al., 2018).

## 4.2 Impact of vehicular collisions in biodiversity loss

Collisions of wildlife with vehicles have long-been suspected of being a significant threat to the persistence of many amphibian populations (Glista et al., 2008; Puky, 2005) but estimating the biodiversity loss in terms of abundance remains a major challenge. In the case of common toads, because amphibian roadkill during the reproductive migration happens during a short time window, we were able to estimate the time since collision. When the speed of carcass removal from the road is also known, estimates of the proportion of carcasses that have disappeared and were subsequently missed during the survey are straightforward, assuming that all toads present on the road during the survey were detected. In the roadkill survey we conducted, ignoring carcass persistence leads to underestimations of the