# Population dynamics of elusive species: The case of the common dolphin in the North-East Atlantic Ocean

Etienne Rouby

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## To cite this version:

Etienne Rouby. Population dynamics of elusive species: The case of the common dolphin in the North-East Atlantic Ocean. Life Sciences [q-bio]. La Rochelle Université, 2022. English. NNT: .tel-03878173

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https://theses.hal.science/tel-03878173

Submitted on 29 Nov 2022

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Distributed under a Creative Commons Attribution 4.0 International License
POPULATION DYNAMICS OF ELUSIVE SPECIES

The case of the Common dolphin
in the North-East Atlantic Ocean

ROUBY ETIENNE

Under the supervision of Vincent Ridoux and Matthieu Authier
La Rochelle Université 2022
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ÉCOLE DOCTORALE

618

Centre d'Etudes Biologiques de Chizé (UMR 7372)

Observatoire PELAGIS (UAR 3462)

THÈSE

présentée par :

Etienne ROUBY

soutenue le 25 Mars 2022

pour l'obtention du grade de Docteur de La Rochelle Université

Discipline : Biologie de l'environnement, des populations, écologie

**Population dynamics of elusive species:**
**The case of the common dolphin in the North-East Atlantic Ocean**

JURY :

Matthieu AUTHIER Ingénieur de Recherche, ADERA, Co-Encadrant

Emmanuelle CAM Professeure, Université de Bretagne Occidentale, Rapportrice

Anita GILLES Chargée de Recherche, University of Veterinary Medicine Hannover, Examinatrice

Christophe GUINET Directeur de recherche, La Rochelle Université, Président du Jury

Vincent RIDOUX Professeur, La Rochelle Université, Directeur et Encadrant

Liz SLOOTEN Professeure, University of Otago, Rapportrice
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# Remerciements

Ce travail de thèse est le fruit d'un effort collaboratif.

En premier lieu je tiens à remercier mes directeurs, Vincent Ridoux et Matthieu Authier, qui m'ont fait confiance. Vous avez été des mentors, chacun à votre manière. Travailler à vos côtés a été une expérience enrichissante à la fois sur le plan professionnel mais aussi humain. Pour vos contributions respectives à ce projet (qui ne sont pas des moindres), votre pédagogie et votre investissement, à vous deux, Messieurs, Merci.

Je remercie la direction et toute l'équipe de l'Observatoire Pelagis qui m'a accueilli avec bienveillance, considération et qui m'a permis de participer aux activités de l'Observatoire. Merci pour le partage d'expériences et de connaissances. Merci à celles et ceux qui ont été impliqués dans l'apport de données, l'aide avec la base, les sessions terrains et dissections. Merci à certains membres de l'équipe pour leurs conseils avisés quant à la manière de mener le projet ou bien de rédiger le manuscrit. Merci également aux stagiaires et contractuels de passage avec qui j'ai partagé des moments de vie. Je remercie également la direction, les équipes, doctorantes, doctorants et stagiaires du CEBC pour leur accueil au Centre.

Merci aux personnes qui ont contribué de prêt à ce projet. Audrey sans toi les lectures d'âge auraient été très difficiles. Pour ne pas dire impossibles. Merci pour ton implication dans ce projet et ta bonne humeur. Merci Paula pour le coup de main qui a apporté un second souffle salvateur. Merci Willy pour ton expérience en la matière et la passion pour la transmission dont tu fais preuve. Merci également à Cécile, Fabien et Eleonore pour m'avoir aidé à intégrer les échantillons quand cela était nécessaire.

Lola merci pour ton implication lors de ton stage. Tu as été un exemple d'investissement, de justesse scientifique et de persévérance. Tu as mené ce stage d'une main de Maître et cela a abouti de la plus belle des manières. Je te souhaite de la réussite pour ta thèse. Merci à Justine pour ton sérieux dans les lectures de lames histologiques de Gonades.

Mathieu, merci pour ta disponibilité, ta justesse analytique implacable et ton efficacité à toute épreuve. C'est un réel plaisir de collaborer activement avec toi.

Merci aux membres du Shom pour leur accueil et leur contribution à la partie la plus exploratoire de ce projet, Emilie, Marie et Victor. Merci à l'Equipe d'Ifremer, Laurent, Thomas et Sébastien pour leur collaboration active qui fût fructueuse. A Kelly aussi pour ton expertise dans chacun de nos travaux communs.

Pour leur accueil et leur professionnalisme je remercie les membres du département de biologie de La Rochelle Université, grâce à qui j'ai pu découvrir l'enseignement à l'Université.

Je tiens à remercier Emmanuelle Cam, Liz Slooten, Anita Gilles et Christophe Guinet pour leur intérêt vis à vis de ce travail ainsi que pour leur disponibilité à le parcourir.

Merci à Ken Arroyo Ohori et Federico Marotta pour la mise à disposition de leurs fichiers LaTeX avec lesquels j'ai pu concevoir ce manuscrit. Une mention spéciale aussi pour les équipes de Rstudio et de RStan dont les travaux permettent d'aller toujours plus loin pour faire parler les données.

D'un point de vue plus personnel maintenant je tiens à remercier ma Famille qui m'a toujours soutenu et encouragé dans la direction que j'ai pour l'instant choisie.
Merci aux personnes qui m'ont accompagné pour repousser bien des limites au cours de ces trois ans: PB, AK et SG. Merci spécialement à G pour ton exigence et tes transmissions.

Merci à mes amies et amis de La Rochelle avec qui c'est toujours un plaisir d'aller partager un verre ou quelques vagues. Merci à mes collègues de promotion à Nice et à Paris pour le parcours que nous avons accompli tous ensemble. Une considération éminente pour mes amis, le noyau du Sud-Est de la France. Nous sommes une équipe.

Je remercie le Ministère de la Transition Ecologique pour avoir accordé un intérêt tout particulier à la problématique du dauphin commun et avoir financé ce projet.

Enfin je tiens à remercier sincèrement les membres du Réseau National Echouage sur la côte Atlantique impliqués dans la collecte d'échantillons ayant servi au court de ce projet. Votre investissement bénévole est à la base de toute analyse scientifique. Grâce à votre dévouement, il est possible de produire des études permettant de nourrir des politiques de gestion de la mégafaune, ô combien importantes de nos jours. Sans vous rien ne peut se faire. Merci à chacune et à chacun d'entre vous:

Arthur ALT, Herve ANDRE, Christiane ANSELME, Alain AUDRY, Stéphane AUFFRET, Matthieu AU-
THIER, Denis BARDOT, Chrys BARTHE, Thierry BEAUVAIS, Matthieu BECOT, Vickie BEDUNEAU,
Rahmona BELGAID, Fabrice BERNARD, Bruno BERTRAND, Antoine BESNIER, Philippe BIBES,
Danielle BIHOES, Benoît BILHEUDE, Beverlie BILLEREY, Philippe BIRAC, Armel BONNERON, Cé-
dric BONZI, Guillaume BORRAGINI, Jean-Jacques BOUBERT, Colin BOUCHARD, Gilles BOURHIS,
David BOURLES, Vincent BOURNEL, Olivier BRIARD, Julen BRIDIER, Gaëtan BRINDEJONC, Mick-
aël BUANIC, Eric BUJARD, Matthieu CABAUSSEL, Jérôme CABELGUEN, Didier CADIOU, Philippe
CALES, Anna CAPIETTO, Marie CAPOULADE, Kristell CARRIC, Alexandre CAUCHY, Serge
CAULE, Antoine CHABROLLE, Romuald CHAIGNEAU, Laurent CHAILLOUX, Carine CHAR-
RONNEAU, Philippe CLAVIER, Jean Philippe COEFFET, Bernadette COTTALORDA, Monique
CROZE, Willy DABIN, Cécile DARS, Frédéric DECHAINE, Nathalie DELLIOU, Fabien DEMARET,
Ronan DEREDEC, Laurent DESBRUGERES, Alexandre DEWEZ, Philippe DIRAISON, Stéphane
DIXNEUF, Ghislain DOREMUS, Hugo DUBOIS, Pascal DUCASSE, Perrine DULAC, Christine
DUMAS, Benoit DUMEAU, Charles DUPE, Fabrice DUPONT, Jean-Bernard ETCHEBARNE, Jacques
FARRE, Justine FONTAINE, Matthieu FORTIN, Pascale FOSSECAVE, Loralie FRANCOIS, Hélène
GADENNE, Olivier GALLET, Susan GALLON, Gilles GARNIER, Marcel GAUDIN, Françoise
GAUDIN, Sébastien GAUTIER, Daniel GERARD, Cécile GICQUEL, Céline GIRARDEAU-GUEVARA,
Florent GOULO, Nolwenn GRANDJEAN-LEFEVRE, Matthias GRANDPIERRE, Joris GRENON,
Anaïde GRIT, Annick GROISARD, Myriam GUEGUEN, Benjamin GUICHARD, Stéphane GUYOT,
Gaëtan GUYOT, Sylvain HAIE, Sami HASSANI, Thomas HERAULT, Sylvain HUNAULT, Mathilde
HUON, Julien HUTEAU, Xabi INDABURU, Yann JACOB, Florence JEHENNE, Loïc JOMAT, Thierry
JOSSE, Emmanuel JOYEUX, Jean-Luc JUNG, Marie KERDAVID, Sylvie LABATUT, Sophie LABRUT,
Sébastien LABULLE, Camille LACROIX, Jean-Pierre LAFOND, Philippe LAMY, Alexandra LANG-
FORD, Patrick LAPOUYADE, Sophie LARAN, Evelyne LARGE, Claire LASPOUGEAS, Arnaud LE
CRAS, Anthony LE DOZE, Thomas LE GALL, Christophe LE PIMPEC, Claude LECOINTE, Cécile
LEFEUVRE, Marine LEICHER, Kévin LELEU, Marie LELONG, Audrey LEMOINE, Thierry LUCAS,
Hélène MAHEO, Jacques MARQUIS, Bernard MARTIN, Frank MATHE, Eléonore MEHEUST,
Mathieu MENDES, Paula MENDEZ-FERNANDEZ, Jeremie MENER, Jean-Roch MESLIN, Sylvain
MICHEL, Victor MILLOUR, Christian MIRTAIN, Gaël MOAL, Emilie MORAUXBULTEAU, Alizée
MORIN-REPINCAY, Annabelle MORISSET, Benoit NAUGUET, Marine NODJOUMI CHAD, Lu-
dovic NOISETTE, Sébastien PALIER, Eric PASSALAQUA, Yves PATUREL, Hélène PELTIER, Myriam
PERRIERE-RUMEBE, Enrique PETIT, Daniel PILVIN, Laurent PLANTIER, Yann PLANQUE, Alexandre PORTMANN, Jean-André PRAT, Sébastien PROUET, Erwan QUEMENEUR, Yann QUILLIVIC, Mélanie RACINE, Noriane RHOUY, Yamin RIDOUX, Catherine ROBERT, David ROBERT, Jean Guy ROBIN, Virginie ROG, Anne Sophie ROSIER, Mélina ROTH, Pierre ROUSSEAU, Jacques RUATTI, Yaouenn SABOT, Flore SAMARAN, Livier SCHWEYER, Laurent SOULIER, Jérôme SPITZ, Elodie STOLEAR, Antoine TALLEC, Isabel TARDIEU, Manon TISSIDRE, Hélène TOMOWIAK, Aurore TOULOT, Karin TOURNEMILLE, Jean-Charles TRAINAUD, Olivier TREVIDIC, Yann TURGIS, Yannis TURPIN, Olivier VAN CANNEYT, Samuel VEILLARD, Baptiste VERDOUX, Philippe VIGNAUD, Jean VIMPERE, Christophe VUILLEMOT, Frederic WALCH, Agnès WIGDOROWICZ-DUPONT, Gregory ZIEBACZ
# Scientific Productions

## Peer-Reviewed Publications

**Rouby, E.**, Ridoux, V. and Authier, M. Flexible parametric modeling of survival from age-at-death data: A mixed linear regression framework. 2020. Population Ecology. 63:108–122. Doi: https://doi.org/10.1002/1438-390X.12069108.

**Rouby, E.**, Dubroca, L., Cloâtre, T., Demaneche, S., Genu, M., Macleod, K., Peltier, H., Ridoux, V. and Authier, M. Estimating bycatch from non-representative samples (II): a case study of Pair trawlers and common dolphins in the Bay of Biscay. 2022. Frontiers in Marine Science. p:1946. Doi: https://doi.org/10.3389/fmars.2021.795942.

**Rouby, E.**, Authier, M., Mauchamp, A., Mendez-Fernandez, P., Dabin, W., Thobois, J. and Ridoux, V. North-East Atlantic common dolphin population viability and vital rates variations. In prep.

**Rouby, E.** and Genu, M. Setting Bycatch thresholds for common dolphin through Management Strategy Evaluation. In prep.

## Other

Gilbert, L., **Rouby, E.**, Tew-Kaï, E., Spitz, J., Peltier, H., Quilfen, V. and Authier, M. 2021. Spatiotemporal models highlight influence of oceanographic conditions on common dolphin bycatch risk in the Bay of Biscay. Marine Ecology Progress Series. 679:195-212. Doi: https://doi.org/10.3354/meps13894.

Authier, M., **Rouby, E.** and Macleod, K. 2021. Estimating cetacean bycatch from non-representative samples (I): a simulation study with regularized multilevel regression and post-stratification. Frontiers in Marine Science. 8:1459. Doi: https://doi.org/10.3389/fmars.2021.719956

## Conference Papers

### Poster presentations

**Rouby, E.**, Ridoux, V. and Authier, M. Marine mammals vital rate estimation through a new regression approach. World Marine Mammal conference 2019, Barcelona, Spain.

### Oral presentations

**Rouby, E.**, Authier, M., Mauchamp, A., Mendez-Fernandez, P., Dabin, W., Thobois, J. and Ridoux, V. Insight of North-East Atlantic Common Dolphin Population demographics and dynamics. Society for Marine Mammals 2022, Miami, Florida.
## ICES Working groups presentations

Working Group on Marine Mammal Ecology. ICES. January-February 2021. Common dolphin bycatch estimation.

Workshop on estimation of MOrtality of Marine MAmmals due to Bycatch. ICES. Modeling common dolphin bycatch risk at haul level: multilevel regression with post-stratification

## Teaching

Practical work on plant and animal physiology at the level of Licence 1 of Life and Health Sciences. Biology Department. La Rochelle Université

Tutorials in plant biology at Licence 1 level in Life and Health Sciences. Biology Department. La Rochelle Université

## Science popularisation

Ma thèse en 180 secondes. La Rochelle Université. Mars 2021. La Rochelle, France.

Conference Animation: Têtes chercheuses. Museum d'Histoire Naturelle February 2020. La Rochelle, France

Festival du film pas trop scientifique. La Rochelle Université. Novembre 2019. La Rochelle, France
# Abbreviations

**ASCOBANS** - Agreement on the Conservation of Small Cetaceans of the Baltic, North East Atlantic, Irish and North Seas

**CFP** - Common Fishery Policy

**CITES** - Convention on International Trade in Endangered Species of Wild Fauna and Flora

**CMR** - Capture-Mark-Recapture

**CO** - Conservation Objective

**DCF** - Data collection framework

**DPMA** - *Direction des pêches maritimes et de l'aquaculture*

**EC** - European Commission

**EU** - European Union

**GLG** - Growth Layer Group

**GNS** - Gillnetters

**GTR** - Gill trammel netters

**ICES** - International Council for the Exploration of the Sea

**Ifremer** - *Institut Français de Recherche pour l'Exploitation de la Mer*

**IUCN** - International Union for Conservation of Nature

**mPBR** - modified Potential Biological Removal

**MMPA** - Marine Mammal Protection Act

**MSFD** - Marine Strategy Framework Directive

**NAO** - North Atlantic Oscillation

**NEA** - North East Atlantic

**NGO** - Non Governmental Organisation

**ObsMer** - *Observation des captures en Mer*

**OMMEG** - OSPAR Marine Mammal Expert Group

**OSPAR** - Oslo-Paris Commission

**PBR** - Potential Biological Removal

**PTM** - Pair trawlers

**PTB** - Bottom pair trawlers

**RLA** - Removal Limit Algorithm
**RNE** - Réseau National Échouage

**Shom** - Service Hydrographique de la Marine Nationale

**UK** - United Kingdom

**USA** - United States of America

**VAST** - Vector-Autoregressive-Spatio-Temporal

**WGBYC** - ICES Working Group on Bycatch of Protected Species

**WGMME** - Working Group on Marine Mammal Ecology

**WKEMBYC** - ICES Workshop on fisheries Emergency Measures to minimize BYCatch of short-beaked common dolphins in the Bay of Biscay and harbor porpoise in the Baltic Sea

**WKMOMA** - Workshop on estimation of MOrtality of Marine MAmmals due to Bycatch
# Contents

<table><tr><td>Remerciements</td><td>v</td></tr><tr><td>Scientific Productions</td><td>vii</td></tr><tr><td>Abbreviations</td><td>viii</td></tr><tr><td>Contents</td><td>ix</td></tr><tr><td>BACKGROUND</td><td>1</td></tr><tr><td>1 General Introduction</td><td>2</td></tr><tr><td>1.1 Demography and management of marine megafauna</td><td>2</td></tr><tr><td>1.2 Describe, quantify and predict population dynamics</td><td>8</td></tr><tr><td>1.3 Estimation of life-history traits</td><td>15</td></tr><tr><td>1.4 The case of the common dolphin population in the North-East Atlantic ocean</td><td>21</td></tr><tr><td>1.5 Project outlines</td><td>22</td></tr><tr><td>THE PROJECT</td><td>25</td></tr><tr><td>2 The common dolphin in the North East Atlantic</td><td>26</td></tr><tr><td>2.1 Distribution and biology</td><td>28</td></tr><tr><td>2.2 Conservation and monitoring</td><td>33</td></tr><tr><td>3 Studying survival</td><td>43</td></tr><tr><td>3.1 Introduction: About survival analyses</td><td>45</td></tr><tr><td>3.2 Methodology: Designs and modelling</td><td>47</td></tr><tr><td>3.3 Results: Simulation study</td><td>58</td></tr><tr><td>3.4 Discussion: Implications of this new cross-sectional parametric approach</td><td>65</td></tr><tr><td>4 North-East Atlantic common dolphin population viability</td><td>70</td></tr><tr><td>4.1 Introduction: A need for demographic knowledge</td><td>72</td></tr><tr><td>4.2 Methodology: Stratified random sampling and Joint modelling</td><td>75</td></tr><tr><td>4.3 Results: Vital rates and population growth rate</td><td>89</td></tr><tr><td>4.4 Discussion: Important aspects and implication of the study</td><td>96</td></tr><tr><td>5 Quantifying the bycatch</td><td>102</td></tr><tr><td>5.1 Introduction: About the bycatch phenomenon</td><td>104</td></tr><tr><td>5.2 Methodology: Quantify the bycatch parameters</td><td>108</td></tr><tr><td>5.3 Results: Estimation of variables and number of dolphins bycaught</td><td>119</td></tr><tr><td>5.4 Discussion</td><td>123</td></tr></table>
<table><tr><td>6</td><td>Conservation Biology and Management Procedures</td><td>128</td></tr><tr><td>6.1</td><td>Introduction: Conservation biology and Management procedure</td><td>130</td></tr><tr><td>6.2</td><td>Methodology: Management Strategy Evaluation (MSE)</td><td>134</td></tr><tr><td>6.3</td><td>Results</td><td>142</td></tr><tr><td>6.4</td><td>Discussion</td><td>146</td></tr></table>

## DISCUSSION 152

<table><tr><td>7</td><td>General Discussion</td><td>153</td></tr><tr><td>7.1</td><td>Project approaches</td><td>153</td></tr><tr><td>7.2</td><td>Definition of the North-East Atlantic common dolphin population</td><td>158</td></tr><tr><td>7.3</td><td>Population dynamics of elusive species</td><td>167</td></tr><tr><td>7.4</td><td>Conclusion and perspectives</td><td>175</td></tr></table>

## Bibliography 177

## APPENDIX 200

Appendix 1: Abundance estimates and MSFD Marine regions 201

Appendix 2: Flexible regression approach simulation study 203

Appendix 3: Insights of the demographic approach 218

Appendix 4: Explain and quantify the incidental captures of common dolphins 222

Appendix 5: Tuna-Dolphin problem history 274
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BACKGROUND
<figure><img src="image_6.png" /></figure>
# General Introduction

1

## 1.1 Demography and management of marine megafauna

### Marine Megafauna: essential and impacted

The term megafauna comes from the combination of the Greek word "megalos", which means large, and the Latin word "fauna", which means the total number of animals living in a certain area at a certain time. The term megafauna is broad and ambiguous. It can refer to large animals, large vertebrates, large mammals or even giant mammals. In the scientific literature, the term can also lead to confusion. Moleón et al. (2020) recently proposed a critique of the use of the term megafauna through a literature review and proposed a goal-oriented framework for megafauna research. Megafauna can be defined in several ways. The most common definition is based on the size of organisms: mass for vertebrates and length for invertebrates. Another possibility is to define megafauna according to its functional role in the ecosystem and in particular in the food chain. The megafauna can be described as "apex megafauna" in the case of top predators or "keystone megafauna" in the case of keystone species.

The marine megafauna is a compartment of the ecosystem that includes long-lived marine species such as reptiles, birds, sharks, turtles and mammals. The species diversity of the marine megafauna is marked by the presence of top predators within it. These top predators are so called because they are at the top of the food web. They directly regulate the abundance and biomass of their prey, which may themselves be predators of other species. Within an ecosystem, each species is structured into populations. A population of marine megafauna can thus be defined as all the individuals of the same megafauna species living together in the same environment at the same time. The predatory action of top predators causes a trophic cascade of regulatory effects on the other populations that compose the ecosystems. This regulatory action of lower trophic levels in terms of abundance and biomass is theorised as top-down control (Hairston, F. E. Smith, and Slobodkin 1960; Paine 1969). The presence of top predator populations is therefore essential to maintain the balance of energy flows within the ecosystem. These populations therefore structure

1.1 Demography and management of marine megafauna . . 2

1.2 Describe, quantify and predict population dynamics . . . 8

1.3 Estimation of life-history traits . . . . . . . . . . . . . 15

1.4 The case of the common dolphin population in the North-East Atlantic ocean . . . . . . 21

1.5 Project outlines . . . . . . 22
the entire ecosystem despite their proportionally lower abundance than other populations. Their presence contributes to structuring the communities (set of populations) that make up the biotic part of the ecosystem (Odum and Barrett 1971). Populations of top predators can sometimes be considered as keystone species, a concept developed from the observation of the ecological importance of the purple starfish (*Pisaster ochraceus*, Brandt 1835; Paine 1969; L. S. Mills, Soulé, and Doak 1993; Paine 1995).

## Definition of the term "population" used in this project

I will use here the following definition of a population, provided by Berryman (Berryman 2002): "A group of individuals of the same species that live together in an area of sufficient size to permit normal dispersal and/or migration behaviour and which numerical changes are largely determined by birth and death processes."

The presence of certain species is essential for maintaining the diversity of ecosystems. Some species are considered keystone species, a concept that includes, but is not limited to, predatory species and species associated with megafauna (Figure 1.2). For example, elephant populations (genus *Loxodonta*, Anonymous 1827) control the tree population in the savannah and allow other herbivores access to the plains for grazing (Western 1989; Ishida et al. 2018). But top predator species are often key species for the ecosystem. For example, the grey wolf (*Canis lupus*, Linnaeus 1758) was an important top predator in Yellowstone National Park, preying mainly on the abundant elk (*Cervus canadensis*, Erxleben 1777) and bison (*Bison bison*, Linnaeus 1758) herds. The disappearance of the grey wolf from Yellowstone Park around 1920 led to a proliferation of elk that consumed primary producers in large numbers. Other populations dependent on primary producers were affected and the biodiversity of the ecosystem was greatly reduced (Ripple and Larsen 2000). The reintroduction of wolves in the 1990s helped to regulate the elk population and promote greater biological diversity (Ripple and Beschta 2012). The concept of keystone species should not be confused with the concept of umbrella species. Conusion is possible because both terms refer to a species on which other populations depend. One of the main differences is that umbrella species cover a wide geographical area and are linked to a wide variety of habitats and ecosystems. This difference is important from a conservation point of view. The umbrella species concept is linked to ecosystem conservation. It is recognised that the conservation of umbrella species is a means to preserve one or more ecosystems and their associated communities. An example of an top predator umbrella species is the Amur tiger (*Panthera tigris altaica*, Temminck 1844; Miquelle et al. 1999). Populations of

<figure><img src="image_7.png" /><figcaption>**Figure 1.1:** Schematic representation of the keystone role of predatory starfish *Pisaster ochraceus* in an intertidal ecosystem in Washington. (a) *Pisaster ochraceus* predation maintains a diverse community. (b) removal of *Pisaster ochraceus* allows mussels to dominate, and reduces species diversity. Based on (Paine 1969).</figcaption></figure>
this predator extend over a vast area covering part of Southeast Asia. They are at the top of the food chain in many ecosystems with different environments (Carroll and Miquelle 2006). The conservation of keystone and umbrella species is an interesting conservation approach, as it helps to maintain the diversity and balance of one or more ecosystems. From a marine ecosystem management (and conservation) perspective, it can be effective to focus on populations of top predatory marine species (Roberge and Angelstam 2004).

<figure><img src="image_8.png" /><figcaption>Figure 1.2: Conceptual definition of megafauna based on size and importance for the ecosystem.</figcaption></figure>

a. Large animals have an high impact on local ecosystems whereas the impact of smaller ones is more variable. There is a challenge to correctly define the size-effect relationship.

b. Two-dimensional qualitative disruption of animal species. The two-dimensional space is defined by body size and ecosystem effect. Keystone species have an high effect on ecosystems and only the largest keystone species are defined as megafauna.
Figure from Moleón et al. 2020.

Humans are currently impacting marine megafauna in a variety of ways. These impacts can be described as indirect if the human action affects an intermediate factor that has an impact on the population (e.g. human-induced climate variations). Conversely, they can be defined as direct if the human action directly affects the population (e.g. hunting or accidental capture in fishing gear). Recently, Authier et al. (2017) has proposed a new classification of impacts using the example of marine megafauna populations, these impacts are classified into three categories. Each is associated with a pressure that generates a different response within the population (Figure 1.3). The pressure is classified as tertiary if it generates a response in the behaviour of individuals in the population. Pressure is classified as secondary if it generates a response in the health of individuals in the population. Pressure is classified as primary if it generates a response in the demographic rates of the population or individuals within the population. In my opinion, this classification is relevant because it allows for more nuance. For example, it has been shown that pile driving during the construction of offshore wind farms can impact marine mammals such as the harbour porpoise (Phocoena phocoena, Linnaeus 1758) by causing displacement of individuals (Nabe-Nielsen et al. 2014; Pirotta et al. 2014; Graham et al. 2019). This displacement can generate an energy cost which is then passed on to other levels of response (Authier et al. 2017). These impacts constitute tertiary
pressures in the proposed new form of classification, which allows for better mapping of their effects on population status. Demography is considered to be the response level with the most direct effect on population status, although populations are rarely exposed to only one type of pressure, particularly marine megafauna (Authier et al. 2017). It is mainly this level of response that interests us here and in particular the primary pressure associated with it, especially for marine mammal species.

<figure><img src="image_9.png" /><figcaption>Figure 1.3: Typology of pressures based on their effects on marine megafauna. Figure from Authier et al. 2017.</figcaption></figure>

## Marine mammal demography

The life histories of marine mammal species are typical of long-lived species. The life history of an organism is its survival and reproductive pattern, as well as characteristics that directly affect survival and the timing or amount of reproduction. As long-lived species, marine mammals have low reproductive rates, high survival rates and a focus on caring for young individuals. They are iteroparous with several reproductive episodes during their lifetime (Cole 1954). They can also be described as *K* species, according to the definition of MacArthur and Wilson (2016), as they exhibit stable strategies with low growth rate values, high care for young survival and low fecundity in stable environments. If we take into account the continuous reference framework proposed by Pianka (1970) and Stearns (1976) which described the strategies as a continuum, they would tend towards the extreme of the slow strategy. The slow strategy is characterised by a long life expectancy with low reproductivity (i.e. high investment in survival and growth over reproduction). The life history of marine mammals is characterised by a trade-off between survival and reproductive vital rates that appears to favour survival over reproduction. Although life histories within a species, or even a population, may appear to be uniform, they may in fact differ between individuals.

### Vital rates definition

*Vital rates* are refereed as demographic parameters such as age-specific survival and fecundity distributions (Reilly and Barlow 1986).
Differences in life history between individuals in the same population can be explained by observable factors (e.g. age or sex) but some inter-individual variability is not accounted for by these factors (Camus and Lima 2002). This variability is defined as individual heterogeneity or frailty (Cam, Aubry, and Authier 2016). Heterogeneity can be defined as time-invariant if we consider the differences between individuals acquired at birth and inherent to the individual's phenotype (Van Noordwijk and de Jong 1986). Time-invariant differences between individuals are considered as the basis of the quality of individuals (Camus and Lima 2002; Vaupel, Manton, and Stallard 1979; Coulson and C. Thomas 1985). The quality of an individual can be seen as the latent probability of surviving and reproducing in a time interval. High quality individuals are therefore more likely to survive and reproduce than lower quality individuals who will tend to die younger. These differences between individuals due to time-invariant effects, acquired at birth, can lead to a selection process. The best phenotypes are thus selected by mortality selection within the birth cohorts (Curio 1983; Endler 1986). Lower quality individuals may not contribute to population renewal to the same extent as higher quality individuals, which would lead to an age-related decrease in the proportion of lower quality individuals in cohorts and this would lead to an increase in population-level survival (C. S. Thomas and Coulson 1988; Vaupel and Yashin 1985). The proportion of individuals with a low probability of survival, tends to decrease over time while the probability of survival of the remaining (i.e. better quality) individuals should increase (Camus and Lima 2002). Thus, the apparent probability of survival of the population would appear to increase while in reality the probability of survival of individuals would not change. This could be the source of surprising correlations between the probability of survival of an individual and its age, since this probability of survival would be linked to the population (Camus and Lima 2002). The probability of survival and viability of a population is also influenced by human activities. For marine mammals, one of the activities that has the greatest impact on them is fishing. This is particularly the case for odontocetes.

## Some concepts

**Fitness:** Ability of an individual of a given genotype to reproduce. Also called selective value or reproductive success.

**Cohort:** A group of individuals who have experienced the same event during the same period. The term cohort is usually used to refer to birth cohorts which refers to all individuals born in the same year.

**Phenotype:** The set of apparent characteristics of an individual conferred by its genotype, its development and its environment.
## The link between Frailty Hazard and Survival

In demography, frailty can be referred to as susceptibility to disease or death (Kannisto 1991). Individuals in a population do not have the same life histories, particularly with regard to hazard and survival. Differences between these components of the life history of individuals that are not explained by observable factors are called heterogeneity or frailty (Aalen 1994). Susceptibility to death or disease can vary from one individual to another but this variation cannot be explained directly (i.e. by observing the phenotype of individuals). It is impossible to take these variations into account as covariates in survival analyses because they are hidden. However, it is possible to statistically account for this inter-individual frailty in order to model its effect on the survival and hazard of a population. These models are called frailty models (R. Henderson and Oman 1999). Frailty models include the notion of individual frailty in demographic models (Kannisto 1991). Individual frailty is then taken into account statistically as a random effect having a multiplicative action on hazard (Hougaard 1995). This random effect can be individual or common to several individuals. In case of individual random effect, modelling is called univariate and frailty describes heterogeneity. In this thesis project, we have developed a new approach to survival analysis, based on taking into account the effect of individual frailty on hazard (Reed 2011).

## The case of odontocetes, especially delphinids

Among the marine megafauna, odontocetes are particularly threatened because they are often subject to bycatch pressure. Of the human activities that can have an impact on odontocete populations, fishing has the greatest impact on populations worldwide (A. J. Read, Drinker, and Northridge 2006). Odontocetes are cetaceans with teeth, as opposed to mysticetes, which are baleen whales. Because of their top predator position, odontocetes compete with humans for food resources (i.e. fish). These interactions can sometimes be positive for odontocete populations by favouring their survival. One example is the phenomenon of depredation, which is defined for marine mammals as the removal of fish caught on commercial fishing gear. Recently, it has been shown that among the orcas of the Crozet Island population (*Orcinus orca*, Linnaeus 1758), individuals with depredation behaviour have a better survival than those that do not engage in depredation (Margin-Figure 1.4). From a more general point of view, these interactions are deleterious to odontocetes as they can reduce the survival of pop-

<figure><img src="image_10.png" /><figcaption>**Figure 1.4: Survival probability of killer whales along time.** Non-depredating killer whales are represented with empty circles whereas depredating killer-whales are represented with black circles. Error bars are the 95% CI.

From Tixier et al. (2017).</figcaption></figure>
ulations (and by extension their growth and viability). One of
the most worrying phenomena associated with competition for
food resources is the phenomenon of bycatch. It is defined as the
accidental capture of a non-commercial or even protected species
(M. A. Hall 1996). Populations, even species, of odontocetes have
already disappeared or are on the brink of extinction because of
this additional mortality pressure, which they cannot withstand.
This is the case of a Chinese river dolphin named Baiji (Lipotes
vexillifer, Miller 1918). This species is now considered extinct. In-
tensive human activity in the Yangtze River, including shipping
traffic, water pollution and bycatch, is suspected to have caused its
extinction (Dudgeon 2005; D. Wang et al. 2006). Another example
is the vaquita (Phocoena sinus, Norris and McFarland 1958), whose
population is now almost extinct. The vaquita is in fact the most
critically endangered marine mammal, with very few individuals
remaining in the wild. This species is endemic to the shallow,
turbid and highly productive habitat of the upper Gulf of Califor-
nia, between Baja California and mainland Mexico (Rojas-Bracho,
Reeves, and Jaramillo-Legorreta 2006). The Vaquita population
has been subject to increasing bycatch pressures associated with
fisheries that target totoaba (Totoaba macdonaldi, Charles Henry
Gilbert 1980) and has been severely depleted. This fish, which is
about the same size as the vaquita, is targeted for the black market
trade in its swim bladders in China (Rojas-Bracho et al. 2019). The
implementation of management measures is one way to prevent
a population from becoming too depleted. It is based in part on
determining the viability of delphinid populations. This viability
can be determined from population dynamics models (Wade 1998;
Mannocci et al. 2012).

**1.2 Describe, quantify and predict population
dynamics**

**Contribution to the management**

Management of wildlife populations can be considered as
"management of wildlife populations in the context of the ecosystem" or could be considered in a broader sense by integrating
several socio-economic aspects (Fryxell, Sinclair, and Caughley
2014). Managing a population can be done in four ways: increasing
the population, decreasing the population, harvesting the population for a continuous yield, leaving the population alone and
monitoring it (Fryxell, Sinclair, and Caughley 2014). The management of each living resource therefore involves a trade-off between
promoting the continued existence of the resource (i.e. conservation
aspect) and obtaining an economic benefit from it (i.e. exploitation

<figure><img src="image_11.png" /><figcaption>**Figure 1.5: Vaquita (Phocoena sinus, Norris and McFarland 1958).** Picture from https://cseweb.ucsd.edu/~awilby/Brink-of-Extinction_NGS.html</figcaption></figure>
aspect; Harwood 2010). The concept behind managing exploited animal populations is intrinsically linked to growth rate. A population that is reduced from its maximum level of abundance given the environmental conditions (i.e. carrying capacity) will have a positive growth rate. It is on this positive growth rate that the removal of the population is carried out (Harwood 2010). More specifically, it is assumed that density-dependence influences population recruitment in a stock-recruitment relationship that is at the heart of population harvesting (Sale 1990). This foundation is inherited from fish stock management studies (Beverton and Holt 1957, 2012). The use of population growth models is therefore particularly interesting in the context of the management of exploited populations and in the event of accidental catches, the bycaught population can theoretically be considered as an exploited population (Barbraud et al. 2008; Lebreton 2005). Theoretical bases related to the science of fisheries management can therefore be applied to implement bycatch management measures. The basic premise changes. We no longer seek to exploit the population for a continuous yield, but we want to reduce bycatch to a sustainable level that is relative to the dynamics of the population concerned. To do this, we use models that take into account either abundance (Wade 1998) or abundance and vital rates by age (Hammond, Paradinas, and Smout 2019; Genu et al. 2021) within or outside of a Management Strategy Evaluation procedure (Punt et al. 2016). European waters are fishing grounds where many different gears are used at different times of the year, with complex and structured ecosystems, including marine megafauna (Peltier et al. 2021; Corrales et al. 2022). Among the 17 cetacean species frequently observed in these waters (and in particular in the Bay of Biscay), the common dolphin (*Delphinus delphis*, Linnaeus 1758) currently presents strong conservation challenges and is possibly a Keystone species (Peltier et al. 2021; Corrales et al. 2022; Murphy et al. 2021).

## Population growth models

Population dynamics is the scientific field of ecology concerned with the changes in abundance that populations experience over time and the factors that influence these changes (Gotelli 2008). The main objective of the study of the dynamics of a population is to carry out an evaluation of the population which can be considered as the evaluation of both the status of the population and its vitality (or viability, Skalski, Ryding, and Millspaugh 2010). The population status corresponds to the current state of the population with regard to certain characteristics such as age and sex structure or abundance in relation to a certain reference. Status using abundance can be assessed through time series of abundance estimates,

Here, the margin notes will include the mathematical expressions of what is said in the text. This is done so as not to interfere with the reading, but to provide a more mathematical background and insight.
but it is also possible to study the underlying mechanisms that shape these changes in abundance (J. D. Baker, A. Westgate, and Eguchi 2010). To do this, it is possible to assess the viability of the population through the evaluation of its demographic health and its capacity to maintain itself from one year to the next. Several models (i.e. representation of reality. In our case, representation of the dynamics of a population from a mathematical point of view) have been developed in order to represent the annual dynamics of populations.

## Geometric population growth models

Basic dynamic changes within a population are due to the losses of individuals through processes of death/emigration and additions through processes of births/immigration (J. D. Baker, A. Westgate, and Eguchi 2010). Considering a closed population (without immigration and emigration) it is possible to imagine its growth dynamic geometrically (i.e. in way that each abundance value is determined by the multiplication of its previous value by a constant factor) according to a continuous or a discrete time stamp (depending on population dynamic to be modelled). Considering a continuous time model (i.e. birth and deaths occurs continuously) associated with a continuous population growth, the rate of change in population size through a continuous time period could be explained as the difference between births and deaths. They depends on the total abundance, instantaneous births and death rates. In other words, the rate of change in population size through a continuous time period is equal to the intrinsic rate of increase *r* effect on population abundance (Gotelli 2008). The rate of increase value is determinant to understand the viability of the population and define if it is stationary (*r* = 0), decreasing (*r* < 0) or increasing (*r* > 0). It can also be used to model the abundance of the population at any time given the initial abundance estimate. Depending on the value of the rate of increase, the population can grow exponentially. One example of exponential growth on large mammal was demonstrated (Scheffer 1951) with the reindeer (Rangifer tarandus, Linné 1758). The intrinsic rate of increase of the population can also be expressed when no resource is limiting and can be referred as *r*<sub>max</sub> compared to the observed intrinsic rate of increase which can be defined as *r*<sub>real</sub> and the intrinsic rate of increase under a stable age distribution *r*<sub>stable</sub> (Skalski, Ryding, and Millspaugh 2010; Caughley and Birch 1971).

From the expression of the geometrical continuous time populations model, which admitted that birth and deaths occurs continuously, it is possible to represent the dynamic of populations for which births and deaths are not continuous. This is the case

The abundance at time *t* + 1 (*N*<sub>*t*+1</sub>) is obtained from the previous abundance at time *t* (*N*<sub>*t*</sub>), additions through births and immigrants (*B* + *I*) and losses through deaths and emigrants (*D* + *E*):

$$N_{t+1} = N_t + (B + I) - (D + E)$$

The rate of change in population size through time $\frac{dN_t}{dt}$ is expressed given instantaneous birth rate *b*, instantaneous death rate *d* and intrinsic rate of increase *r*:

$$\begin{aligned} \frac{dN_t}{dt} &= B - D \\ &= (b - d)N_t \\ &= rN_t \end{aligned}$$

The abundance at any time *t* (*N*<sub>*t*</sub>) is obtained from the initial abundance (*N*<sub>0</sub>), time *t*, the intrinsic rate of increase *r* and the exponential function *e*:

$$N_t = N_0 e^{rt}$$

*λ* is the finite rate of increase expressing the proportional changes in abundance from on year to the next ($\frac{N_{t+1}}{N_t}$). To project the population size at any time *t* the initial abundance *N*<sub>0</sub> is also used:

$$\begin{aligned} \lambda &= \frac{N_{t+1}}{N_t} \\ N_{t+1} &= N_t \lambda \\ N_t &= \lambda^t N_0 \end{aligned}$$
for numerous animal species which present a breeding season and unequal mortality levels through the year. Such models are refereed as geometrical discrete time populations models. The use of *r* as instantaneous rate of increase is replaced by the use of *λ* as finite rate of increase. This rate expresses the proportional changes in abundance as a multiplicative factor by which abundance changes from one year to the next (Skalski, Ryding, and Millspaugh 2010). As a proportional change, the rate *λ* expresses the viability of the population relatively to 1, reference value for a stationary population (*λ* = 1), growing population (*λ* > 1) and declining population (*λ* < 1). The way time is considered in the choice of representation of population dynamics regarding geometric growth determines the relationship between growth rates as *r* is the intrinsic per capita growth rate, *R* is the net discrete per capita growth rate and *λ* is the discrete per capita growth rate (J. D. Baker, A. Westgate, and Eguchi 2010).

## Logistic population growth models

The previously seen models admit that the population can grow forever which is not the case in natural population due to several factors such as predation, hunting, starvation or overcrowding (Leopold 1933). Natural populations can also be limited in growth due to a lack of resources and some environmental effects leading the growth in logistic population growth (Krebs 1994). The access to resources may be limited among organisms through population density. This factor can be defined as a density-dependent factor. Density-independent factors, on the other hand, have an effect on population growth rates independently of the population size or density. Density-dependent processes are important to take into account, as they directly influence the maximum sustainable yield value regarding fisheries and harvested species. The maximum sustainable yield (MSY) is the highest theoretical equilibrium yield that can be continuously taken from a stock under the average environmental conditions (Schaefer 1954). The highest catch value allows the population to sustain through somatic growth, spawning and recruitment (Tsikliras and Froese 2019). We will see that this concept may be adapted to set up management plans for accidentally harvested species. Density-dependence is an important factor shaping the growth of animal populations, in particular considering large mammals (Fowler 1981). The basis of the concept is the relationship between instantaneous birth rate, instantaneous death rate and abundance at a given time. When the population size tends to increase, the instantaneous death rate increases too. Assuming that resource are limited, the instantaneous birth rate tends to decrease as abundance increases. The equilibrium between both rates is obtained when the population attains the carrying

Relationships between growth rates:

$$ \lambda = R + 1 $$

$$ \lambda = e^r $$

Logistic models forms:

$$ \frac{dN_t}{dt} = r_{max} \times N_t \times \left(1 - \frac{N_t}{K}\right) $$

$$ N_{t+1} = N_t + N_t \times (\lambda_{max} - 1) \left(1 - \frac{N_t}{K}\right) $$

$$ N_{t+1} = N_t + N_t \times (\lambda_{max} - 1) \left(1 - \left(\frac{N_t}{K}\right)^{\theta}\right) $$
capacity (K) level which can be viewed as the maximum population size that a population can reach given its environment its resource limits and associated pressures.

<figure><img src="image_12.png" /><figcaption>**Figure 1.6:** Relation between per capita growth rate, abundance and carrying capacity. When abundance (N) is low, the per capita growth rate is high enough to allow the population to produce individuals and increase abundance to the carrying capacity which is the stable equilibrium point. In the case of a population subject to the Allee effect, a too low abundance below a critical threshold is associated with a decline in growth rate. It is no longer high enough to support mortality and the population disappears.</figcaption></figure>

From the link between those parameters, (Verhulst 1838) created the familiar logistic population growth model assuming a continuous time. From this model the discrete one was obtained and allows to represent the dynamic of a population given density-dependence with a discrete time stamp (Pearl 1925). Then, the generalized logistic model was introduced taking into account the rate ($\theta$) at which the population reaches its carrying capacity (J. D. Baker, A. Westgate, and Eguchi 2010). Depending on the value of this rate, the population can grow at a rate equal to that of a standard logistic growth ($\theta = 1$), can grow more rapidly in an exponential way close to the carrying capacity ($\theta > 1$), can fluctuates about the carrying capacity ($\theta \ge 10$) and can grow at a rate lower than that of the standard logistic due to an anticipated effect of density dependency on growth ($\theta < 1$) (Pella and Tomlinson 1969).

While density dependence is commonly seen as a limiting factor for population growth, Warder Clyde Allee proposed in 1931 another view, that can have strong consequences for modelling population dynamics, which he developed in his book: Allee et al. 1949. Its premise is that some populations are affected by a positive relationship between population growth rate and density when they reach low levels of abundance which can lead to their

Baseline Allee Effect model with K* as the Allee threshold (Courchamp, Clutton-Brock, and Grenfell 1999):

$$N_{t+1} = N_t \times \left( 1 + R_{max} \left( 1 - \frac{N_t}{K} \right) \times \left( \frac{N_t}{K^*} - 1 \right) \right)$$
extinction if the density of individuals is too low (Courchamp, Clutton-Brock, and Grenfell 1999). If abundance is not high enough, the reproduction or survival of the population may be impacted in a negative way which leads to a decrease in the per capita growth rate that can reaches negative values as it is depicted in Figure 1.6. The Allee effect can also be refereed as the depensation, positive density dependence (W. F. Morris et al. 2002) or Allee's principle (Odum and Barrett 1971). Factors that may lead to this inverse density dependence at low density can be classified into three types according to (Courchamp, Clutton-Brock, and Grenfell 1999) which has led to the recent emphasis on the importance of this idea in modelling population dynamics (Skalski, Ryding, and Millspaugh 2010). The first type of factor is genetic (i.e. genetic inbreeding). It is characterized by a loss of heterozygoty that lead to a decrease in fitness. The second type of factor is demographic (i.e. demographic stochasticity). It is characterized for example by sex-ratio fluctuations that lead to a low reproductive output (e.g. Kakapo *Strigops habroptilus*, Gray 1845). The third type of factor is interactive (i.e. facilitation or behavioural). It is characterized by less interactions that are important for the survival of the population ('(e.g. bluefin tunas *Thunnus thynnus*, Linné 1758) or the shortage of receptive mates (e.g. Kakapo) and cooperative breeders (e.g. African wild dogs *Lycaon pictus*, Temminck 1820) (Courchamp, Clutton-Brock, and Grenfell 1999). As it is illustrated in Figure 1.6 Allee effect produces unstable equilibrium at low densities and increases the probability of extinction. A strong Allee effect is characterized when there is population density below which the per capita growth rate. It is therefore dangerous to harvest a population that may be sensitive to the Allee effect. It is also possible that population growth models that do not consider Allee effects underestimate the risk of extinction (Skalski, Ryding, and Millspaugh 2010).

## Age-Structured population growth models

These population models are limited to study the influence of specific age-specific demographic rates on growth rates and it could be of interest to represent the dynamic of a population given particular age or stage classification (Leslie 1945; Lefkovitch 1965). The use of matrix population models allows to project the population state given initial abundance or in terms of percentages which is particularly useful for studying viability. Here only the Leslie matrix will be discussed as this concept is part of two aspects of the project. This matrix model reflects the dynamics of a unisex population (usually females) independently of the density dependency processes discussed earlier (Skalski, Ryding, and Millspaugh 2010;

Matrix notations and models for the Leslie 1945 matrix modelling approach:

$$ \underline{n}_{t+1} = L \underline{n}_t $$

$$ \begin{bmatrix} N_0 \\ N_1 \\ N_2 \\ N_3 \end{bmatrix}_{t+1} = \begin{bmatrix} N_0 \\ N_1 \\ N_2 \\ N_3 \end{bmatrix}_t \times \begin{bmatrix} F_0 & F_1 & F_2 & F_3 \\ S_0 & 0 & 0 & 0 \\ 0 & S_1 & 0 & 0 \\ 0 & 0 & S_2 & 0 \end{bmatrix} \quad (1.1) $$

$$ N_{0t+1} = N_{0t}F_0 + N_{1t}F_1 + N_{2t}F_2 + N_{3t}F_3 $$

$$ N_{1t+1} = N_{0t}S_0 $$

$$ N_{2t+1} = N_{1t}S_1 $$

$$ N_{3t+1} = N_{2t}S_2 $$
Leslie 1945). The conceptual model of this population dynamics
matrix model can be represented as follows:

<figure><img src="image_13.png" /><figcaption>**Figure 1.7: Conceptual model a age-based-matrix model.** Individuals can reach the maximum age of 3. Each age class contributes to the renewal of the population with its associated fecundity rate *F*. Each individual advances in age in the population with a probability equal to the age-specific survival rate.</figcaption></figure>

This population model involves two components to project
the number of females of a population through time that are the
number of females within each age-class and the probability for
female each age-class to both survive and produce a new female
in the population. These matrices are associated with eigenvectors
and eigenvalues which will not be discussed in detail as it is not
the purpose of this chapter but for more mathematical information
see Caswell 2000. They are key properties of populations that can
be represented by the matrix populations models. The asymptotic
population growth rate $\lambda$ corresponds to the dominant eigenvalue
and the stable age distribution is represented by the eigenvector.
Another interesting component of matrix population models are
obtained through perturbation analyses. Caswell 2000 explains
that the "results of perturbation analyses are sometimes more
interesting, more robust and more useful than the parameter
estimates themselves". The two common perturbation analyses
are the elasticity and the sensitivity analyses. They provide both
the proportional response of the growth rate to a proportional
perturbation in the vital rates and the magnitude of changes in the
growth rate with respect to each element of the matrix (J. D. Baker,
A. Westgate, and Eguchi 2010). These information are particularly
valuable in case of population management when it is necessary
to have information about the age-classes the most important to
manage in terms of the value of the growth rate.

Table 1.1 summarise important information about the mod-
els introduced here. Only those most relevant to the project are
presented. These models are of importance to assess the viabil-
ity of a population and have also been developed in the context
of exploitation of some populations (e.g. population of fishes or
whales). They therefore serve as a reference for the implementation
of management strategies. Both for populations that are exploited
voluntarily and for populations that are accidentally exploited.

Population matrix models that have an age-dependent struc-
ture need to be filled with vital rates. To obtain these age-dependent
vital rates (survival and fecundity), it is necessary to monitor mam-
mal populations. Two categories of monitoring exist and only one
is applicable to elusive populations.

<table><caption>Table 1.1: Examples of population dynamic models. Other exists but these are the main used in the project.</caption><thead><tr><th>Model</th><th>Equation</th><th>Reference</th><th>Chapter</th></tr></thead><tbody><tr><td>Exponential</td><td>N<sub>t+1</sub> = N<sub>t</sub>λ<sub>max</sub></td><td>Malthus, Winch, and P. James 1992</td><td>Chapter 4 in 4.9</td></tr><tr><td>Logistic</td><td>N<sub>t+1</sub> = N<sub>t</sub> + N<sub>t</sub> × (λ<sub>max</sub> - 1) (1 - (N<sub>t</sub>/K))</td><td>Hutchinson 1978</td><td>-</td></tr><tr><td>Generalized logistic</td><td>N<sub>t+1</sub> = N<sub>t</sub> + N<sub>t</sub> × (λ<sub>max</sub> - 1) (1 - (N<sub>t</sub>/K)<sup>θ</sup>)</td><td>Pella and Tomlinson 1969</td><td>Chapter 6 in 6.2</td></tr></tbody></table>

## Why "elusive" species ?

The term elusive comes from the Latin *elus*, and is an adjective meaning "difficult to find, define or achieve" (Oxford Dictionary). The term is used in this manuscript to refer to species that may have one or more of the following characteristics: difficult to track individually, sparsely distributed, for which it is difficult to estimate anthropogenic mortality and for which it is difficult to implement management policies.

## 1.3 Estimation of life-history traits

### Longitudinal monitoring to estimate vital rates

Quantifying the life history traits of a population is nowadays mainly carried out using longitudinal monitoring and capture-recapture protocols (CMR; B. K. Williams, Nichols, and Conroy 2002). The study of life history traits (which can be described as life history parameters) has become important since the end of the 20th century (Lebreton et al. 1992). This importance has materialised in the desire and need to detect differences in life history traits between populations in order to study their regulation, structure and viability (Stearns 1980; Noble and Slatyer 1980; Crawley and May 1987). These differences are thought to be the source of changes in life history, through a modification of fitness in relation to survival and fecundity (Manly 2013). While it is easier to estimate fecundity in wild populations, survival remains a major component of life history that is difficult to quantify (J. Clobert, Lebreton, and Allaine 1987). The importance of being able to follow each individual over the long term in order to deduce the value of vital rates in relation to survival seems to be an essential condition for achieving these objectives (Lebreton et al. 1992). The history of survival analysis modelling will not be detailed here. This will be done in the introduction to Chapter 3, which is a chapter specifically dedicated to survival analysis.
Long-term individual monitoring can use different forms of natural or artificial recognition methods. Longitudinal tracking protocols involve both the recognition of living individuals (Lebreton et al. 1992; Sandercock 2006) and dead individuals (Brownie 1985). For example, it is possible to follow individuals on the basis of physical marks that distinguish them from one another in the population (Castro and Rosa 2005; Wirsiig and Jefferson 1990). This is the case for giraffes, which can be recognised individually on the basis of their coat patterns (Berry and Bercovitch 2012). Where individuals cannot be observed directly, camera traps can be used to record the passage of individuals at points of interest (O'Connell, Nichols, and Karanth 2011). These camera traps are used to identify individuals of cryptic feline species such as the snow leopard, lynx or Siberian tiger (Jackson et al. 2006; Can and Togan 2009; T. M. Wang et al. 2014). Individual recognition can also be performed in marine mammals. The recognition of individuals is based on the shape of the tail fin and its patterns (e.g. humpback whale and sperm whale), the shape of the dorsal fin (e.g. bottlenose dolphin and killer whale) or by the recognition of specific callus patterns (Right whales; Pace, Corkeron, and Kraus 2017). These identifications of individuals in marine mammal populations are made possible by longitudinal tracking protocols called "photo identification". Sometimes it is not possible to identify a species on the basis of its natural markings, but it is possible to easily access individuals in a population and place artificial markings on them. These artificial markings can be rings, collars, ear tags, radio transmitters or bands. Ringing is widely used in population dynamics studies of birds that may sometimes be accessible in colonies (Busse and Meissner 2015). Tagging is also deployed in pinniped species that are accessible in breeding colonies (Costa et al. 2010; A. Henderson et al. 2020). Collars are preferred for small mammals or certain ungulates. For the latter, the use of earmarks is common (Swenson et al. 1999). Collars can also be designed as radio transmitters that are used to study both dispersal and survival (Millspaugh and Marzluff 2001; G. C. White and Garrott 2012). Finally, tags can also be used to collect demographic data when individuals are dead. This is particularly the case for rings used in monitoring programmes for hunted populations. These are known as ringing recovery protocols: (Brownie 1985).

This monitoring makes it possible to determine multiple demographic parameters of the population (i.e. vital rates or life-history traits) such as survival (Lebreton et al. 1992), dispersal rates (Brownie et al. 1993), recruitment rate of new breeders (Clobert 1995), breeding frequency and transitions between breeding states (Cam et al. 1998). The expansion of the use of CMR monitoring has made a considerable contribution to the quantification of many life history traits (Lebreton et al. 1992). However, it is not possible to use

## Longitudinal monitoring

Longitudinal monitoring involves repeated observations of individuals through a period of time. It can be performed using Capture-Mark-Recapture, band recovery and tagging protocols. For cetaceans, the most common longitudinal monitoring protocol is photo-identification (Wirsiig and Jefferson 1990). This monitoring allows the vital rates of the population to be obtained (Lebreton et al. 1992) along with variations in vital rates and individual-heterogeneity quantification (Camus and Lima 2002; Gimenez, Cam, and Gaillard 2018).
this monitoring on all species. For elusive species, it is necessary
to use the old approach, combined with difficult assumptions, less
sophisticated analysis methods and basic estimators of population
life-history traits.

<figure><img src="image_14.png" /><figcaption>Figure 1.8: Exemples of possible individual-based long term monitorings.</figcaption></figure>

A. Ear-tags.

B. Natural marks of rare animals observed thanks to camera traps.

C. Bird ringing.

D. Recovery of bands.

<figure><img src="image_15.png" /><figcaption>Figure 1.9: Exemples of possible individual-based long term monitorings for cetaceans.</figcaption></figure>

E. Callosities on Right-Whales.

F. Caudal fin markings on Humpback whales.

G. Dorsal fin shape on bottlenose dolphins.

H. Dorsal fin shape and natural markings on killer whales.

Cross-sectional monitoring to estimate vital rates

Basically, cross-sectional monitoring has been used to describe the age distribution from which life tables can be constructed to estimate age-specific survival and mortality rates (Skalski, Rydving, and Millspaugh 2010; Gompertz 1825). The use of this type
of monitoring is common in fisheries studies as it allows the age-
frequency distribution to be described. The age distribution of
a fish population is an essential piece of data that can provide
information on changes over time, how a stock responds to exploita-
tion and how it may recover from external disturbance (Jennings,
Reynolds, and S. C. Mills 1998; Greenstreet, Spence, and McMillan
1999). The age composition of a fish population can be determined
from otoliths, backbone and fin radii (Quist, Pegg, and DeVries
2012; Goldman et al. 2012; Carbonara and Follesa 2019), but also
from allometric age-length relationships (Westrheim and Ricker
1978; Ailloud and Hoenig 2019) using the age-length key which
may be subject to bias (Kimura 1977). The use of this cross-sectional
tracking scheme, especially from otolith ageing, is still common
in fisheries studies to obtain age composition and demographic
parameters (Durant et al. 2013).

In the case of tetrapod populations, age composition (or age distribution) is obtained by analysis of morphometric features or even samples of biological material (Caughley et al. 1977). The determination of the age of amphibians is generally done using osteological techniques (Peabody 1961) whereas sauropsids are generally aged according to their size (i.e. allometric relationship) (Caughley et al. 1977). For some bird species (Fulmar, Shag, Redshank and Great Skua), it is possible to count the endosteal layers of the tibia to determine the age of individuals (Klomp and Furness 1992). For turtles, age can be determined by the annuli method on the carapace (Sexton 1959; Gibbons and Semlitsch 1982). For mammals, the methods of age determination are varied. The eruption of the teeth can be an indicator, particularly for bovine species such as mouflons or equids (Garel et al. 2007), but also for sea otters (Nicholson et al. 2020). Body size and size frequency classes could also be an indicator of age (Klomp and Furness 1992). The most widely used and effective method for obtaining a population age distribution and creating the associated life table is the use of biological material taken from dead animals (Caughley et al. 1977). The biological material used consists of teeth (Laws 1953; Benjaminsen 1973), claws (R. B. Thomas et al. 1997) and horns (Geist 1966). The method (e.g. odontochronology) consists of counting the number of growth rings (or groups of growth layers) that make up the biological tissue. The age data obtained by this method is called age-at-death data and the age distribution can be called the age-at-death distribution. Classically, these data were obtained by harvesting and recovering dead carcasses (Caughley 1966).

The process of obtaining vital rates associated with survival and
mortality from these data therefore constitutes a cross-sectional
monitoring of wild animal populations (Caughley 1966). Since
Deevey Jr (1947), this type of monitoring has been used to estimate
vital rate parameters and construct associated life tables. From

Cross-sectional monitoring has his-
torically been widely used to moni-
tor fish stocks. It is still used today
to monitor fish populations and ex-
ploited stocks.

Cross-sectional monitoring

In contrast to long-term monitor-
ing of individuals, a population
can be monitored by means of
snapshots over a given period.
This type of monitoring is called
cross-sectional or transversal. For
example, the characteristics of a
few individuals in a population
will be collected at a given time.
From the data collected, an extrap-
olation will be made to the whole
population. It is from this type of
monitoring that the life tables are
constructed (Caughley 1966).
these life tables, it is possible to provide age-specific vital rates to inform population dynamics matrix models such as Leslie's matrix model (Leslie 1945). It is also possible to explore the covariation of age-specific life-history traits to test certain life history theories (Purvis and Harvey 1995).

<figure><img src="image_16.png" /><figcaption>**Figure 1.10:** Exemples of possible cross-sectional monitorings.

I. Length-age relation for reptiles from https://www.mcgeesswamptours.com/.
J. Otholits for fishes from Knopp et al. (2012).
K. Growth layer groups in tooth from Martin et al. (2011).
L. Endosteal layers in tibia for birds from Klomp and Furness (1992).
M. Claws growth layer groups from E. O. Ferreira, Loseto, and Ferguson (2011).</figcaption></figure>

However, the derivation of these rates is based on cross-sectional monitoring, which itself is based on basic assumptions that can be problematic (Caughley 1966). The most important assumption to take into account in this type of monitoring is that the age-at-death distribution obtained from the age-at-death data is representative of the stationary age distribution of the population (Caughley 1966). In other words, the sampled population must be in a stationary state (i.e. neither increasing nor decreasing) and there must be no selection bias of individuals at the time the data set is constructed (Caughley 1966). One problem is that mammal populations are rarely stationary in nature as they are in a con-

Preference for longitudinal monitoring

Longitudinal monitoring is preferred for species that offer adequate opportunities for longitudinal studies.
stant state of flux influenced by biotic and abiotic factors, which are themselves in a state of flux (Szuwalski and Hollowed 2016). Furthermore, when population dynamics studies are conducted, it is precisely to determine whether the population is viable because there is reason to believe that it is not (i.e. it is not stationary). The impetus for conducting a population dynamics study is often at odds with the basic assumption that must be made to conduct the study. Cross-sectional monitoring is associated with strong assumptions, unrepresentative data and the difficulty of trusting life history trait estimates. It is mainly for these reasons that cross-sectional monitoring has been abandoned in favour of longitudinal monitoring in species that offer adequate opportunities for longitudinal studies. Although cross-sectional monitoring is less expensive in terms of data collection (Seber 1965). In order to provide the best possible information on the demographic rates of these populations, it is necessary to carry out methodological developments associated with their monitoring. In particular, statistical developments through models integrating essential demographic parameters (e.g. frailty). This work would allow more accurate assessments of the viability of elusive mammal populations, taking into account various covariates and random effects.

Stationary and Stable age distributions

The concepts of stationary and stable age distribution are both related and different. If the population growth rate is constant over time, as are its fertility and survival rates, its age distribution will eventually take a stable form. Age frequencies will remain constant over time. When a population is stationary, the population growth rate is equal to 1. Therefore, the stationary age distribution is the stable age distribution for which the population remains constant over time. A stationary population necessarily has a stationary and stable age distribution, but a population with a stable age distribution does not necessarily have a stationary age distribution. The stationary age distribution is a special case of the stable age distribution. (Caughley 1966).

<table><caption>Table 1.2: Pros and cons of both monitoring schemes.</caption><thead><tr><th>Monitoring</th><th>Strengths</th><th>Weaknesses</th><th>Key reference</th></tr></thead><tbody><tr><td>Longitudinal</td><td><ul><li>Underlying processes are highlighted</li><li>Individual differences to be highlighted</li><li>Population growth rate are estimated directly</li></ul></td><td><ul><li>Costly monitoring scheme</li><li>May involve small samples</li></ul></td><td><ul><li>Lebreton et al. 1992</li><li>Sandercock 2006</li></ul></td></tr><tr><td>Cross-Sectional</td><td><ul><li>Include large parts of the population</li><li>Allows to apply simple growth models</li><li>Not very costly compared to longitudinal</li></ul></td><td><ul><li>Does not highlight the changes an individual undergoes over the course of its life</li><li>Low representativeness of the data if the time series is short</li><li>Assumes the population to be at stationary age distribution</li></ul></td><td><ul><li>Caughley 1966</li><li>Deevey Jr 1947</li></ul></td></tr></tbody></table>
## 1.4 The case of the common dolphin
population in the North-East Atlantic ocean

The common dolphin is the most abundant and widespread odontocete cetacean species in the North-East Atlantic Ocean and is associated with significant management issues (Peltier et al. 2021; Perrin 2018). It is a top predatory species in the North-East Atlantic ecosystems, with a possible (i.e. no formal recognition) keystone role in the Bay of Biscay (Corrales et al. 2022; Lassalle et al. 2011). The Bay of Biscay (Margin-Figure 1.11) is a biologically productive area of the North-East Atlantic associated with high fishing activity, involving for example pair trawlers and larger scale driftnets (between the Azores and Ireland) since 1986 (Peltier et al. 2021). The history of fisheries management in this area is closely linked to the common dolphin. Several legislative initiatives related to common dolphin mortality events in the area took place between 1985 and 2020 (Figure 1.12). As with other odontocete populations worldwide, the main threat to the common dolphin population in the waters of the North-East Atlantic, and in particular in the Bay of Biscay, is bycatch (M. A. Hall 1996; Peltier et al. 2016; ICES 2019).

<figure><img src="image_17.png" /><figcaption>Figure 1.11: Diagram of Bay of Biscay location.</figcaption></figure>

Picture from https://es.m.wikipedia.org/wiki/Archivo:Bay_of_Biscay_map.png

<figure><img src="image_18.png" /><figcaption>**Figure 1.12: Main historical events in common dolphin bycatch management in the Bay of Biscay.** DCF, Data Collection Framework; EC, European Commission; UME, unusual mortality event. From Peltier et al. 2021.</figcaption></figure>
## Issues of the thesis project

It is necessary to assess the viability of the common dolphin population and to quantify the main human pressures (i.e. bycatch) on it in order to propose appropriate management objectives with regard to the conservation objectives of European waters. The common dolphin is defined here as an elusive species for which it is almost impossible to track individuals longitudinally through CMR or radiotagging protocols. Furthermore, despite the programmes for observing incidental catches at sea, it is difficult to quantify the actual number of common dolphins bycaught in the Bay of Biscay. It is therefore difficult to know whether the number of dolphins removed is sustainable for the population, given its demographic viability. A study should be designed to make the best use of the cross-sectional analysis protocol to obtain the population's vital rates. This study should also make it possible to use data from at-sea observers to quantify bycatch. Finally, it should also allow the proposal of sustainable removal thresholds that do not threaten the viability of the population.

## 1.5 Project outlines

<figure><img src="image_19.png" /><figcaption>Figure 1.13: Flowchart of the thesis project.</figcaption></figure>
The challenges of this thesis project are multiple and fall into two main categories. From an applied research point of view, it is now necessary to produce demographic indicators for small cetaceans in the North-East Atlantic and in particular for the common dolphin. These demographic rates are of interest from the point of view of the management of this population as they will provide information on its status in the context of the OSPAR Convention and the Marine Strategy Framework Directive. Some life history traits have been partially estimated and biological characteristics are already known but the need is still there. Secondly, given the apparent impact of fishing on the population in terms of additional mortality, it is essential to quantify this pressure. Finally, given the management issues related to the population, it is necessary to determine the maximum number of removal that the population can sustain in the current state of knowledge and by applying a precautionary principle. This limit constitutes a support point for public policies, in close collaboration with the European Commission. This work is therefore closely linked to the production of the ICES scientific expert groups' opinions and is sometimes cited in the reports of the working groups focused on the case of the North-East Atlantic common dolphin population. This thesis project therefore has a very applied basis.

In my opinion, it is important to place this applied basis in a more fundamental context. This recontextualisation is part of a desire to place the present work in the scientific history of the study of population dynamics. I believe that this work has its place as a reflection on the problem of studying the dynamics of elusive animal populations. It was therefore necessary to identify a methodological gap in terms of cross-sectional analyses and to partially fill it. A new approach to sample collection and vital rate modelling is proposed. A general discussion linking the work is also proposed.
The present manuscript summarises this three-year work in seven parts. The first part was the general introduction.

Chapter 2 is a description of the important aspects related to the common dolphin. This chapter is not intended for publication. It was written to provide an overview of the current state of knowledge on common dolphin demography and associated monitoring and conservation programmes.

Chapter 3 includes a description of survival analysis and a history of associated method-
ological developments. I then discuss the main problem identified and how we responded to it by
developing a new method for estimating survival that takes into account covariates and random
effects. This part was carried out during the first year of the project and was published: Rouby,
Ridoux, and Authier (2021). I presented this work at the poster session of the World Marine Mammal
Conference 2019*.

Chapter 4 is the central part of the manuscript, from the point of view of writing and organi-
sation of the project. It includes the acquisition of demographic data (age-at-death, reproductive-
status-at-death) after the definition of a sampling plan respecting carefully chosen criteria. It also
includes the analysis of these data using methods commonly accepted in the literature as well
as those developed in the framework of the project. The highlight of this work is the estimation
of the influence of several factors on the demographic rates of the North-East Atlantic common
dolphin population. I will present this work orally at the Society for Marine Mammal Conference
2021†. This part was carried out during the 3 years of the project and is currently being prepared for
publication.

<footnote>* https://www.wmmconference.org/</footnote>

<footnote>† https://www.smmconference.org/</footnote>
Chapter 5 corresponds to the quantification of the human impact on the dolphin population through bycatch and to the explanation of bycatch by studying oceanography. The first part required a methodological development but my greatest contribution was the use of this method with an applied case. The strength of this approach is that it allows an estimate from biased bycatch observation data. This work led to the publication of the development of the method: Authier2021a and my contribution was essentially related to part of the writing of this manuscript. Concerning the application, I was able to use this method on the dolphin case study. This work is published: Rouby et al. (n.d.). This work was carried out in close collaboration with Ifremer (Institut Français de Recherche pour l'Exploitation de la Mer), which provided the data and participated in the writing of the article. This work was carried out during the second and third years of the project. I presented it in the ICES working groups WGBYC and WGMME. I also presented it at the ICES workshop WKMOMA.

The second part of the development of this chapter, concerning the influence of oceanography on bycatch, is for me the most collaborative part. It was carried out as part of a Master 2 internship that I co-supervised with the support of Matthieu Authier and Emilie Tew-Kaí from the Shom (Service Hydrographique de la Marine Nationale) in Brest. The Shom provided us with oceanographic model outputs allowing us to link the occurrence of mesoscale oceanographic structures to dolphin mortality at sea. This work has been published as: Gilbert et al. (2021). I have chosen not to include this section in its entirety as I was not at the heart of the data analysis. This part will serve as a basis for introduction in Chapter 5. This work was carried out during the second year of the project.

Chapter 6, deals with the management and conservation aspects of the common dolphin population. It includes the practical and conceptual use of the preliminary draft (including demographic rates and numbers of dolphins caught) to produce tolerable bycatch thresholds on a European scale. This part still needs to be refined in the analysis but is in preparation to be proposed for publication. This work was carried out during the last 5 months of the thesis project. It is not currently planned to valorise this work in the form of a conference.
<figure><img src="image_20.png" /></figure>
THE PROJECT
<figure><img src="image_21.png" /></figure>
<figure><img src="image_22.png" /><figcaption>Figure 2.1: Common dolphin morphological recognition traits and morphological parameters.</figcaption></figure>

Figure from the International Whaling Commission handbook https://wwhandbook.iwc.int/en/species/common-dolphin
The common dolphin has undergone a recent change in phylogenetic classification. Within the odontocetes, it belongs to the family *Delphinidae* and the subfamily *Delphininae*. It belongs to the genus *Delphinus* which is closely related to the genera *Stenella*, *Lagenorhynchus*, *Sousa*, and *Tursiops* (Perrin 2018). Initially, two species of common dolphins were considered. The short-beaked common dolphin (*Delphinus delphis*) and the long-beaked common dolphin (*Delphinus capensis*). Recent genetic studies have modified the phylogeny of these species. Now, only one species of common dolphin is recognised (Committee on Taxonomy 2017). Within this species, there are 4 subspecies: the common dolphin (*Delphinus delphis delphis*), Eastern-North-Pacific long-beaked common dolphin (*Delphinus delphis bairdii*), Black Sea common dolphin (*Delphinus delphis ponticus*) and Indo-Pacific common dolphin (*Delphinus delphis tropicalis*) (Cunha et al. 2015; Margin-Figure 2.2).

## The subspecies studied here

Throughout the manuscript and subsequent chapters, when the term "common dolphin" is used, it will refer to the current subspecies of common dolphin *Delphinus delphis delphis* and to the former species considered in the classification as the short-beaked common dolphin *Delphinus delphis*. The name common dolphin (and its Latin name *Delphinus delphis* in figures) will be used to designate this subspecies only and it will be the only one studied in this project.

<figure><img src="image_23.png" /><figcaption>Figure 2.2: Common dolphin oceanic subspecies.</figcaption></figure>

Figure from Perrin (2018), illustration by Uko Gorter.

## 2.1 Distribution and biology

### On a global scale

The common dolphin is a widely distributed odontocete cetacean species with a known life cycle. Its distribution ranges from tropical to temperate waters across the globe (Perrin 2018; Figure 2.3). This species occupies both oceanic and continental shelf habitats. It appears to exhibit seasonal distributional movements, sometimes linked to changes in water temperature (Perrin 2018; E. E. Henderson et al. 2014). Individuals may form groups ranging in size from a few hundred to a thousand.

The common dolphin is a long-lived species, with a maximum recorded lifespan of 30 years (Perrin 2018). It is an iteroparous species with a calving interval of approximately 2-4 years. The gestation period is estimated to be 10-12 months. Maximum length is about 270cm for males, which are slightly longer than females. Calves at birth measure 80-90cm. The life history traits of the species
have common characteristics but are population dependent. In Table 2.1, characteristics (including age at sexual maturity) are presented for several common dolphin populations.

<figure><img src="image_24.png" /><figcaption>**Figure 2.3: Global distribution of the common dolphin.** The species is distributed in temperate and tropical waters. It is distributed in several populations.</figcaption></figure>

<table><caption>**Table 2.1: World common dolphin populations features.** This table summarises some important current knowledge about the global populations of common dolphins. Table from Murphy et al. (2021).</caption><thead><tr><th>Area</th><th>Climate</th><th>Sample period</th><th>Mating period</th><th>Age at sexual maturity</th><th>Dataset</th></tr></thead><tbody><tr><td>North-East Atlantic</td><td>Temperate</td><td>1990-2006</td><td>May-September (spring-summer)</td><td>8.22 years</td><td>Murphy et al. (2009)</td></tr><tr><td>North-West Atlantic</td><td>Temperate</td><td>1989-1998</td><td>July-August (summer)</td><td>8.33 years</td><td>A. J. Westgate and A. J. Read (2007)</td></tr><tr><td>Tropical-East Pacific</td><td>Tropical</td><td>1979-1993</td><td>Calve all year round</td><td>7.8 years</td><td>Danil and Chivers (2007)</td></tr><tr><td>North Pacific</td><td>Temperate</td><td>1990-1991</td><td>May-June (spring)</td><td>8 years</td><td>Ferrero and Walker (1995)</td></tr><tr><td>New Zealand</td><td>Temperate</td><td>1992-2012</td><td>Primarily austral summer</td><td>NA</td><td>Institute of Zoology (2015)</td></tr><tr><td>South Africa</td><td>Temperate</td><td>1969-1988</td><td>Austral summer</td><td>8-9 years</td><td>Mendolia (1990)</td></tr></tbody></table>
In the North East Atlantic and European waters

In European waters, the population appears to be abundant and absent from some areas. The common dolphin population appears to be distributed in both oceanic and continental shelf waters. However, common dolphins are rarely recorded in the Eastern Channel and North Sea. The highest densities and abundances of animals are found on the continental shelf (Hammond et al. 2017, 2013; Laran et al. 2017). The population in European waters is currently estimated at 634,286 individuals (352,227 - 1,142,213) while 493,591 (342,094 - 718,593) individuals are estimated in the Bay of Biscay (Hammond et al. 2017; high density area: Figure 2.4). The history of abundance estimates is provided in the Supplementary-Table 1.

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

**Figure 2.4: Common dolphin density within the North-East Atlantic.**
The density of common dolphins is expressed as animals/km². The highest densities are recorded for the continental shelf areas associated with the Bay of Biscay. The Celtic Seas and the oceanic part of the Bay of Biscay also have high densities, as well as the Spanish-Portuguese and Galician coasts. The English Channel and the North Sea, on the other hand, have low densities. These estimates are made in the framework of the SCANS III monitoring programme. Figure from Hammond et al. (2017).
Some life history traits and demographic parameters are known for this population. The studies highlight important demographic parameters such as the age distribution of the population, the proportion of mature females at each age and even the survival profile of females. It is only possible to monitor the population cross-sectionally. Published examples of biological data are provided in Figure 2.6 but there are unpublished datasets such as the one shown in the Margin-Figure 2.5. The maximum age recorded in the population is 29-30 years and longevity appears to be around 20-25 years. The age at sexual maturity of females varies slightly between studies but appears to average over 8 years (Mannocci et al. 2012; Murphy et al. 2009).

<figure><img src="image_26.png" /><figcaption>B</figcaption></figure>

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

**Figure 2.5: Common dolphin age-at-death data.** These age-at-death were obtained on stranded dolphins. Data are from Saavedra (2018). Data are not published and do not have associated survival estimates. However, it is possible to estimate the survival, mortality and viability of the population based on the protocol detailed in the study.

**Figure 2.6: Age at death and vital rates data available for the population.** Three types of biodemographic parameters are presented. The first line is age-at-death. The second is sexual maturity profiles of females. The third is the estimated survivorship of the population which is only available for study A.

Column A corresponds to the study Mannocci et al. (2012).

Column B corresponds to the study Murphy et al. (2009).

Figures are extracted from these studies.
Since the 1990s, an increasing number of common dolphins have been found stranded on European seashores. Among the European countries, France is the country with the highest number of stranded common dolphins on its beaches (Figure 2.8). In France, the number of individuals found is increasing almost constantly, with a stranding record of 1298 individuals for the year 2020 (Margin-Figure 2.7; data provided by *Observatoire Pelagis*). This phenomenon is notably characterised by Unusual Mortality Events (UME) that are seasonal (Peltier et al. 2021). The majority of dolphins stranded during the year are stranded in winter, from January to April (Dars et al. 2020). A significant proportion of stranded dolphins show evidence of capture in fishing gear. From 1990 to 2019, the number of stranded dolphins with evidence of incidental capture was approximately 205 ± 177 whereas from 2016 to 2019 this number increases to 520 ± 172 (Peltier et al. 2021; Dars et al. 2020). Examples of evidence of bycatch on stranded common dolphins are provided in Figure 2.19 at the end of this chapter.

<figure><img src="image_33.png" /></figure>

It is estimated that around 4,000 dolphins are incidentally caught in fishing gear each year in the Bay of Biscay (Peltier et al. 2016), which could pose a major threat to the viability of the population. Bycatch pressure appears to have increased since the late 1990s and is now a recurring pressure on the population (Peltier et al. 2021). From 2016 to 2018, the number of incidental captures of common dolphins has been estimated at between 5,000 and 10,000 (Peltier et al. 2020). This recurrent incidental capture pressure is a point of concern for the viability of the population. The mortality suffered by the population is in the order of 0.9% to 5.7% of its total abundance each year¹ (Peltier et al. 2016). Mannocci et al. (2012) projected its abundance over the next 100 years (after 2006) using the vital rates depicted in Figure 2.6 panel A. It appears that the population would not be viable. Data collected for population projections, and to quantify the number of incidental catches in absolute terms and relative to the total population abundance, are obtained from population monitoring programmes. The main types of monitoring associated with the common dolphin, as well as the main legislations and its current conservation status, are

<figure><img src="image_34.png" /><figcaption>**Figure 2.7:** Common dolphin strandings in France from 2016 to 2021. Data from Observatoire Pelagis.</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>**Figure 2.9:** Projected population trend. From the vital rates obtained in their study, Mannocci et al. (2012) projected the evolution of the population from the growth rate estimated by Leslie's matrix model. It appears that the population will become extinct within the next 100 years.
Figure from Mannocci et al. (2012).</figcaption></figure>

1: whole NE Atlantic population.
presented in the following section.

<figure><img src="image_36.png" /></figure>

**Figure 2.10: Common dolphin by-catch estimates from strandings.** Estimation was done using direct drift modelling (black points, associated with the confidence interval in grey bars), and using reverse drift modelling (grey polygon). These estimates use the dolphin's drift trajectory corrected by the probability of being buoyant (24%), stranded (depending on drift conditions) and discovered (95%). Drift conditions are weather dependent and are modelled by the meteo France drift model MOTHY. For more information on the method see Peltier et al. (2016) from which the figure is taken.

## 2.2 Conservation and monitoring

### In the North East Atlantic and European waters

The conservation status of the common dolphin differs according to the instrument or regulation used. At the international level and independently of populations, the species is currently classified as being of least concern on the IUCN² Red List of Threatened Species (Perrin 2018). Its international conservation status is that of a protected species under the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES), which has listed it in Appendix II (Perrin 2018; CITES 2021). On a global scale, the species is therefore not listed as threatened but as a protected species.

The conservation status of the population in European waters is less favourable and conservation objectives associated with monitoring programmes have been set up on a European scale. The Habitat Directive³ (European Directive on the conservation of natural habitats and of wild fauna and flora, 92/43/EEC) is an instrument of European environmental legislation. The objective of this instrument is to achieve a favourable conservation status for listed species and habitats, including the common dolphin (listed as a species in need of strict protection under Annex IV). In 2007, the conservation status of the common dolphin population was assessed as "Unknown". Since 2013, it is now assessed as "Unfavourable-Inadequate" in European Atlantic waters and "Unfavourable-Bad" within French waters (Murphy et al. 2021).

2: Common dolphin as a species is considered Least Concern on the IUCN list and is included in Appendix II of CITES.

3: The Habitat Directive classifies the North-East Atlantic population as Unfavourable-inadequate.
In order to promote the conservation status of the common dol-
phin in European waters, the European Commission adopted in
2004 the Bycatch regulation⁴ (Regulation no. 812/2004) which
encompasses requirements for bycatch monitoring schemes with
on-board observers schemes to be set up for vessels ≥15m (length),
and the implementation of pilot studies for vessels less than this
size. It also provides for the application of bycatch mitigation
measures using acoustic deterrent devices in areas and fisheries
that are either known or foreseen to have high levels of bycatch
(vessels ≥12m). This regulation is no longer in use and has been
replaced by the new bycatch regulation (Regulation no. 2019/1241).
It is within this framework of regulating catches and estimating
their value that the Observer programmes, such as "Obsmer"⁵,
have been set up. However, they are not dedicated to bycatch and
are carried out under the Direction Framework of the Common
Fishery Policy⁶. More details on this dataset and its use will be
provided in Chapter 5.

Data acquisition to achieve conservation objectives is also part of
the Marine Strategy Framework Directive(EU MSFD⁷ ; Directive
2008/56/EC). It establishes a framework within which Member
States shall take the necessary measures to achieve or maintain
"Good Environmental Status" (GES) of marine environment. This
European directive defines descriptors of good environmental
status of ecosystems. Within these descriptors, criteria are also
defined to enable the achievement of this good environmental
status. Among these criteria, we find, for example, the need for
biological indicators linked to the demography of the common
dolphin. All the descriptors and criteria important for the common
dolphin in terms of demography are detailed in Chapter 4.

In support of established conservation policies and conservation
objectives, international expert groups or agreements can operate.
The International Council for the Exploration of the Sea (ICES⁸) is
an Intergovernmental marine science organization which aims to
synthesise and coordinate scientific work to achieve the legislative
objectives set by the European Commission and provides science
advice to environmental ministries and international agencies
(such as OSPAR). ICES defines ecoregions (based on ecosystems)
and statistical areas (based on important fishing areas) (Figure 2.11).
With regard to the common dolphin population, ICES works on
its status mainly in two working groups. The first is the Working
Group on Marine Mammal Ecology (WGMME). The second is the
Working Group on Bycatch of Protected Species (WGBYC).

4: Bycatch regulation (Regulation no. 812/2004), now replaced by the bycatch regulation (Regulation no. 2019/1241) defined monitoring and bycatch mitigation schemes.

5: https://sih.ifremer.fr/
Ressources/ObsMer

6: https://www.instituteforgovernment.org.uk/explainers/common-fisheries-policy

7: The MSFD sets the goal of good environmental status for European waters. This status is described by descriptors whose state is informed by criteria. Criteria of relevance to the population will be detailed in Chapter 4

8: The ICES Scientific Expert Group advises governments on how to achieve the conservation objectives of the Habitats Directive and the MSFD.
<figure><img src="image_37.png" /></figure>

**Figure 2.11:** Ecoregions and statistical areas defined by ICES within the OSPAR area of the North-East Atlantic. The OSPAR area is divided by ICES into several ecoregions defined on the basis of biogeographic and oceanographic features and existing political, social, economic, and management divisions. Another division is made by taking into account statistical areas. These area are linked to ICES fishing areas are developed from historical links between an area and the collection of fisheries statistics.

Figure from https://www.ices.dk/Pages/default.aspx.

The Agreement on the Conservation of Small Cetaceans of the Baltic, North East Atlantic, Irish and North Seas (ASCOBANS⁹) aims to promote the achievement of European conservation objectives, in particular with regard to cetaceans, under the auspices of the United Nations. It focuses on the achievement of cetacean-related conservation objectives and provides Member States with recommendations for achieving these objectives. The agreement takes place within a defined area in European waters (Figure 2.12). It is within the framework of this agreement that the limit of 1.7% for total anthropogenic removal has been defined, using the harbour porpoise (*Phocoena phocoena*, Linnaeus 1758) as a case study¹⁰. On 30 August 2019, ASCOBANS proposed the Species Action Plan (SAP) for the North-East Atlantic population of common dolphins. This action plan sets targets to address the threats facing the population. It includes a series of research, mitigation and monitoring actions to improve the conservation status of the population. The SAP seeks to involve a variety of stakeholders, including national agencies,

<figure><img src="image_38.png" /></figure>

**Figure 2.12:** ASCOBANS Marine area. Originally, the area was restricted to English Channel, North Sea and Baltic Sea. From the 3 February of 2008, the area now takes into account Bay of Biscay, Celtic seas and offshore Portugal waters.

Figure from https://www.ascobans.org/en/legalinstrument/ascobans.
intergovernmental organisations, non-governmental organisations and regional bodies.

The Convention for the Protection of the Marine Environ-
ment of the North-East Atlantic¹¹ (OSPAR Convention) aims to
periodically assess the state of the marine environment, partly
in European waters. This convention originated in 1972 with the
Oslo convention. It has been ratified by 15 governments and the
European Union. The Convention entered into force on 25 March
1998. The OSPAR Commission provides a forum through which the
16 contracting parties coordinate international cooperation on the
protection of the marine environment of the North-East Atlantic.
It shares common regulation and management of human activities
(except fisheries). It facilitates the coordinated implementation of
the MSFD, with the aim of achieving "Good Environmental Status"
in European waters. It sets out recommendations for achieving
the objectives of the Habitats Directive and the MSFD. In 2017,
OSPAR implemented the "OSPAR Intermediate Assessment 2017"¹²
. This assessment aims at developing OSPAR's knowledg of the
marine environment of the North-East Atlantic and its current
status. It provides an update of the 2010 assessment and introduces
some new indicators and assessment methodology. Within this
framework, five regions have been defined within a maritime area
(Margin-Figure 2.13).

In order to inform on the conservation status of small
cetaceans and to assess their status in the light of the objectives of
the Habitat Directive and the MSFD, a series of abundance surveys
have been carried out. These abundance surveys are referred to as
"Small Cetaceans in European Atlantic waters and the North Sea",
(SCANS surveys and CODA which is a complement to SCANS II).
These programmes take into account both aerial and ship-based
monitoring. The first one was carried out in 1994 under the name
SCANS (Hammond et al. 2002). Sampling was carried out mainly
by ship from 26 June to 3 August (summer) and did not involve
the Bay of Biscay. The next one was SCANS II in 2005 (Hammond
et al. 2013). Sampling included the Bay of Biscay continental shelf
and more extensive aerial monitoring from 27 June to 4 August
(Summer). In addition to SCANS II, the CODA programme was
carried out in 2007 to cover the non-continental part of European
waters. The latest monitoring programme is SCANS III, conducted
in 2016 (Hammond et al. 2017). This time, the continental shelf
was sampled almost exclusively by aircraft, while the oceanic part
was sampled by boat. Sightings of common dolphins within the
framework of this programme are presented in Margin-Figure 2.14
and are the data allowing to estimate their abundance and density
as presented in Figure 2.4 above. Sampling took place between 27
June and 4 August 2016 (Figure 2.15).

9: ASCOBANS is an intergovernmen-
tal agreement focused on pressure
mitigation and monitoring of small
cetacean populations in European wa-
ters.

10: https://www.ascobans.org/en/species/threats/bycatch

<figure><img src="image_39.png" /><figcaption>**Figure 2.13: OSPAR Maritime Area.**
This area is divided into five Regions for assessment purposes: Arctic Waters (I), Greater North Sea (II), Celtic Seas (III), Bay of Biscay and Iberian Coast (IV) and Wider Atlantic (V).
Figure from www.ospar.org</figcaption></figure>

11: The OSPAR Convention has led to the creation of the OSPAR Commission, which is involved in monitoring, advising and setting legislative constraints on the actions of EU Member States to achieve the conservation objectives of the EU waters.

12: https://oap.ospar.org/en/ospar-assessments/intermediate-assessment-2017/

<figure><img src="image_40.png" /><figcaption>**Figure 2.14: Common dolphin sightings from SCANS III surveys.** Figure from Hammond et al. (2017).</figcaption></figure>
<figure><img src="image_41.png" /></figure>

**Figure 2.15: Sampling plans of the SCANS and CODA surveys.** Transect solid lines are the covered effort. Blue areas were surveyed by boat and pink areas were surveyed by planes. Campaigns made were conducted for SCANS in 1994 (topleft), SCANS-II in 2005 (topright), CODA in 2007 (bottom left) and SCANS-III in 2016 (bottom right).

Figure from Hammond et al. (2017).
<table><caption>Table 2.2: Summary of tools, legislative instruments and organisations relevant to the conservation status of the North-East Atlantic common dolphin population.</caption><thead><tr><th>Instrument/Tool/Organization</th><th>Type</th><th>Year</th><th>Application scale</th></tr></thead><tbody><tr><td>IUCN - International Union for Conservation of Nature Red List of Threatened Species</td><td>Non Governmental Organization</td><td>1964</td><td>Worldwide</td></tr><tr><td>ICES - The International Council for the Exploration of the Sea</td><td>Intergovernmental marine science organization</td><td>1964</td><td>North-Atlantic</td></tr><tr><td>CITES - Convention on International Trade in Endangered Species of Wild Fauna and Flora</td><td>International agreement</td><td>1979</td><td>Worldwide</td></tr><tr><td>ASCOBANS - Agreement on the Conservation of Small Cetaceans of the Baltic, North East Atlantic, Irish and North Seas</td><td>International agreement</td><td>1991</td><td>European waters</td></tr><tr><td>HD - Habitats Directive</td><td>European Directive</td><td>1992</td><td>European waters</td></tr><tr><td>OSPAR - Convention for the Protection of the Marine Environment of the North-East (Oslo-Paris)</td><td>International legislative instrument</td><td>1998</td><td>European waters</td></tr><tr><td>Bycatch Regulation no. 812/2004<sup>a</sup></td><td>European regulation</td><td>2004</td><td>European waters</td></tr><tr><td>MSFD - Marine Strategy Framework Directive</td><td>European Directive Fisheries policy of the European Union</td><td>2008</td><td>European waters</td></tr><tr><td>CFP - Common Fisheries Policy</td><td>European regulation</td><td>2014</td><td>European waters</td></tr><tr><td>Bycatch Regulation no. 2019/1241</td><td>European regulation</td><td>2019</td><td>European waters</td></tr></tbody></table>

<footnote><sup>a</sup> repealed in 2019</footnote>
**Current management unit for the common dolphin in the
North-East Atlantic**

To manage the common dolphin population, several management units have been proposed in the North-East Atlantic Ocean (ICES 2021a). On the basis of ecological tracers (stable isotopes, fatty acids, metal tracers, stomach contents), two management areas should be considered for the management of the common dolphin with oceanic and neritic ecological stocks (Caurant et al. 2009; Lahaye et al. 2005). Based on the low genetic differentiation throughout the North-East Atlantic, it is commonly admitted that common dolphins can be managed as a single management area (Murphy, Pinn, and Jepson 2013). In order to support the study and conservation of the common dolphin in the area covered, ICES WGBYC and OSPAR have defined the population as a single management unit based on genetic analyses (Murphy et al. 2021; ICES 2014, 2021a). The area of the proposed management unit for North-East Atlantic common dolphins covers OSPAR Regions II (Greater North Sea), III (Celtic Sea) and IV (Bay of Biscay and Iberian coast) (Margin-Figure 2.16 regions along with SCANS III and ObSERVE surveys blocks).

<figure><img src="image_42.png" /><figcaption>Figure 2.16: SCANS-III and ObSERVE surveys areas that approximate the North East Atlantic Assessment Unit. OSPAR Regions depict the AU proposed by ICES (2014). Figure from ICES (2021a).</figcaption></figure>

**In France**

The monitoring of the common dolphin population in French waters is mainly carried out in two ways. The first approach is a monitoring based on abundance surveys. In addition to the SCANS campaigns presented above, the seasonal SAMM abundance campaigns (Laran et al. 2017) were conducted (only in French waters) between November 2001 and February 2012 for the winter part and between May and August 2012 for the summer part (Figure 2.18). The objective of these campaigns is to explore seasonal changes in the abundance of small cetaceans in French waters to inform the Habitat Directive and the MSFD. These campaigns have highlighted a seasonal change in abundance of common dolphins in the Bay of Biscay. In winter, their abundance (estimated jointly with the stripped dolphins) was estimated at 285,000 (95% CI: 174,000-481,000) individuals compared to 494,000 in summer (95% CI: 342,000-719,000). These surveys provide information on biological indicators of abundance for common dolphins within the MSFD.
<figure><img src="image_43.png" /></figure>

**Figure 2.17: Sampling plans of the SAMM surveys.** Surveys were conducted between November 2001 and February 2012 (winter part) and between May and August 2012 (summer part).

Figure from Laran et al. (2017).

The other type of monitoring carried out in France is the monitoring of marine mammals strandings. This monitoring is carried out by the french national stranding network ("Réseau National Echouage") which covers the entire French coastline (metropolitan France + DOM-TOM). This network was created in 1970 by Dr. Duguy Raymond¹³ and today consists of around 500 trained volunteers. The French National Stranding Network is coordinated by the Observatoire Pelagis (CNRS/La Rochelle University), mandated by the French Ministry in charge of the environment. The observatory trains volunteers to collect samples according to a strict and standardised protocol (Van Canneyt et al. 2015). When a dolphin washes up on the beach, it is reported to the Pelagis observatory (often by citizens). The observatory sends a volunteer to the site to establish an initial diagnosis on the cause of death and to take biological samples, which vary according to the animal's state of decomposition (Figure 2.20 and Figure 2.19). Stranding reporting rates handled by the RNE are considered stable since the 1990s. The observed increases in strandings are therefore not due to a difference in reporting over this period but to other factors such as increased bycatch (Authier et al. 2014). The biological samples collected in this project were collected by the RNE.

We have seen that the common dolphin population is subject to major conservation issues in European waters. In particular, there is a need for demographic data within the framework of the MSFD, which must complement the abundance surveys carried out. Demographic data on this population are already available, including vital rates such as survivorship. However, survivorship is obtained using survival analysis methods that are not very flexible. In the next chapter, we will see a recent methodological development, which allows us to obtain survivorship curves by taking into account the effects of covariates and inter-individual frailty.

<figure><img src="image_44.png" /><figcaption>**Figure 2.18: Dr. Duguy Raymond.**
Photo from https://www.observatoire-pelagis.cnrs.fr/dr-raymond-duguy/.</figcaption></figure>

13: Link to a historical video on the stranding of pilot whales at "Ile d'Yeu" in 1963 https://dai.ly/xp3zp7. More informations on Dr. Duguy Raymond in https://www.observatoire-pelagis.cnrs.fr/dr-raymond-duguy/
<figure><img src="image_45.png" /></figure>

**Figure 2.19:** External examinations of the common dolphin. The pictures show different cases of mortality assumed by external examinations (which sometimes have to be confirmed on the basis of internal examinations or even biological analyses in the case of pathologies).

1. Amputated tail (Bycatch evidence).

2. Cut pectoral fin (Bycatch evidence).

3. Rope hanging from the tail (Bycatch evidence).

4. Trace of fishing nets (Bycatch evidence).

5. Fractured rostrum (Possible bycatch evidence).

6. Pathological necrosis (Pathology).

7. Possible bacterial infection (Pathology).

8. Unknown cause with scoliosis on calf (Unknown).

For information purposes, in 2020 80% of stranded dolphins are due to bycatch (according to external reviews). 14% are stranded without the cause being known. 3% from pathological reasons and 3% for unknown reasons. These percentages vary slightly after internal review. To see more detailed data: **rapportecouhage2020**.

©Observatoire Pelagis.
<figure><img src="image_46.png" /><figcaption>**Figure 2.20:** Influence of decomposition states on the demographic data collection and on bycatch estimates. The collection of teeth and gonads is carried out to obtain biological data on the population and to estimate its vital rates in the context of the MSFD (Mannocci et al. 2012). It is also possible to estimate the drift time of individuals based on their state. This drift time is then corrected by the probability of floating, the probability of running aground and finally the probability of being discovered. This correction makes it possible to estimate the number of dolphins captured by fishing gear each year (Peltier et al. 2016).</figcaption></figure>

©Observatoire Pelagis.
<figure><img src="image_47.png" /></figure>
Studying survival

3

Survival analyses are essential for estimating life-history parameters and producing life tables which are then used in the implementation of management strategies if required by the population status. Where longitudinal studies (e.g. capture-mark-recapture monitoring) are not feasible, the only data available may be cross-sectional, for example in the case of marine mammal strandings. Survival analysis deals with data on age-at-death (i.e. time-to-event) and allows for the estimation of survival and hazard rates assuming that the cross-sectional sample is representative. Accounting for a bathtub-shaped hazard, as expected in wild populations, has historically been difficult and has required specific models. We identified a simple linear regression model with individual frailty that can fit bathtub-shaped hazard, account for covariates, allow for goodness-of-fit assessments, and give accurate survival estimates in realistic settings. We first performed a Monte Carlo study and simulated age-at-death data to assess the precision of the estimates in relation to the sample size. We then applied the framework to a handful of case studies drawn from published studies of marine mammals, a group with many threatened and data-deficient species. We found that our framework is flexible and accurate in estimating survival with a sample size of 300. This approach holds promise for obtaining important demographic information on data-poor species.

3.1 Introduction: About survival analyses . . . . . . . . . . . . . . 45

3.2 Methodology: Designs and modelling . . . . . . . . . . . . . 47

3.3 Results: Simulation study 58

3.4 Discussion: Implications of this new cross-sectional para-metric approach . . . . . . . . . 65
<figure><img src="image_48.png" /><figcaption>**Survival analyses decision tree diagram.** The decision tree focuses on cross-sectional survival analyses.</figcaption></figure>

**Published work**

This chapter is associated with one publication:

Rouby, E., Ridoux, V. and Authier, M. Flexible parametric modeling of survival from age-at-death data: A mixed linear regression framework. Population Ecology. 63:108-122. Doi:10.1002/1438-390X.12069108.
**3.1 Introduction: About survival analyses**

Minimising human impacts on wildlife is a major challenge in the Anthropocene, where human-induced pressures are both geographically and temporally far-reaching, and have an acute impact on biodiversity (Bongaarts 2019). Long-lived species are particularly sensitive to these pressures, especially from a demographic point of view. Their demographic trajectory (e.g. extinction) can also affect the functioning of ecosystems, especially in the case of top predators (Beschta and Ripple 2009; Ritchie et al. 2012) since they can act as keystone species for entire ecosystem (Heithaus et al. 2008). Assessing the demographic viability of long-lived species in the face of current and future pressures is necessary for their proactive conservation and is sometimes used to complement indicators of abundance status; but such an undertaking can be hampered in practice by the logistical challenges of monitoring and collecting relevant data at appropriate spatio-temporal scales.

The classical method of assessing the viability of a pop-
ulation consists firstly of constructing a life table in which the
mortality and fertility rates of a cohort of individuals are given
at each (st)age of their life cycle (Caughley 1966). Knowledge of
mortality at each (st)age allows the study of associated hazards,
the estimation of vital rates, such as (cumulative) survival, and
the projection of the population trajectory over time using age or
stage matrix models (Leslie 1945; Lefkovitch 1965; Caswell 2000).
Historically, the data on age-at-death used to construct life tables
were obtained by cross-sectional monitoring (e.g. Gompertz 1825):
a sample of the population is taken at a specific time and the
observed age structure is assumed to be similar to that of a cohort
of individuals if we had been able to monitor them individually
from birth to death. This cross-sectional monitoring allows for a
quick demographic assessment (Margules and Austin 1990; Boyd,
Bowen, and Iverson 2010, pp. 126–127) whose accuracy, however,
relies on the assumption that the cross-sectional monitoring does
approximate a longitudinal monitoring.

An essential process to observe when studying demography,
regardless of the type of monitoring design, is survival. Survival is
an essential component of population demography as it contributes
strongly to the growth of a population and its life history, particu-
larly for large mammals such as cetaceans (Heppell, Caswell, and
Crowder 2000). Annual survival has been identified as more im-
portant than annual fecundity in shaping the fitness of species with
life spans greater than one year (Crone 2001). The study of survival
in a given population can be called "survival analysis". Historically,
survival analysis ranged from the collection of demographic data

Conservation needs demography
which is logistically challenging.

Cross-sectional monitoring may be
logistically easier than longitudi-
nal monitoring, depending on the
species.

Some definitions

**Survivorship:** Fraction of the population that is still alive at a given age.

**Age-specific Survival:** Fraction of the population of a given age that is still alive at the next age.

**Fecundity:** Physiological maximum potential reproductive output of an individual (usually female) over its lifetime.

**Fertility:** Current (actual) reproductive performance of an individual.

**Hazard rate:** age-specific mortality rate, or instantaneous probability of dying at time $t + dt$ given that an individual has survived until time $t$.
to statistical methodologies applied to characterise the time-to-event process (e.g. time to death) and has been transposed into ecology from epidemiology and industry (Kleinbaum and Klein 2010). The time to events can also be considered as sequential while characterising the time between several events (Skalski, Ryding, and Millspaugh 2010). The two main frameworks for measuring survival are annual survival (i.e. year-to-year frame) and survivorship (i.e. birth-to-death frame). The latter is the most informative and can be applied as a survivorship curve, or function, to an entire cohort (Ferguson 2002). To measure survival, several modelling or estimation methodologies have been developed, depending on the monitoring design. In this chapter, I briefly review each modelling and estimation approach that has been developed to measure the survival of wildlife populations. In the case of longitudinal monitoring, developments allow the effect of various variables on vital rates to be quantified at the population and individual level. Developments associated with cross-sectional monitoring do not currently allow such flexibility. The review begins with the approaches associated with longitudinal monitoring models, as these are the preferred approaches for obtaining population vital rates because of the less stringent underlying assumptions and greater flexibility. Next, I review the estimation and modelling of survival inherent in cross-sectional monitoring, approaches that require more restrictive and sometimes unrealistic assumptions (e.g. a stationary age distribution of the sampled population; Caughley 1966). However, they are of interest for rapid demographic assessment, for studies of populations in crisis (i.e. which paradoxically may not satisfy the stationary age assumption) and are often the only applicable methodologies for studying the demography of mammalian populations.

The methodological developments associated with estimat-
ing mammalian population survival from age-at-death data are
limited. They do not allow for easy estimation of covariates or
random effects and do not allow for easy comparison of the re-
sulting vital rate values. It would be interesting to develop a new
approach to survival estimation that overcomes these limitations.
There are two ways of estimating survival from age-at-death data
(for the sake of clarity, I do not discuss the Cox proportional hazard
model which allows the use of truncated data). The first estimation
method is called non-parametric. This method is mainly limited
in the case where the number of data is small. The second esti-
mation method is called parametric and is mainly limited by its
implementation and the impossibility of testing the factors and
comparing the quality of the estimates. It is in this context that
we have developed a new parametric flexible linear regression
approach to facilitate the estimation of survival in cross-sectionally
monitored populations. Our work is based on Reed's model (Reed

Survival is the essential component
that determines the value of the
growth rate of a population. The anal-
ysis and modelling of survival is very
important in demography.

Several methods of survival analy-
sis exist. They depend mainly on the
type of monitoring (longitudinal or
cross-sectional). In the case of cross-
sectional monitoring, they depend on
the inclusion of modelling parame-
ters (non-parametric and parametric).

We have developed a parametric
approach based on the Reed (2011)
model which has the following ad-
vantages: inclusion of covariates, in-
clusion of random effects, evaluation
of goodness of fit and individual het-
erogeneity parameter.
2011) which admits a bathtub-shaped hazard rate curve (i.e. representative of the long-lived mammalian mortality pattern). We believe that this approach is an important and innovative contribution to the literature of cross-sectional survival analyses, and thus to the study of associated population dynamics. Its strengths are the consideration of the effect of covariates, the facilitation of goodness-of-fit measurement, and the consideration of the effect of random variables that can highlight key temporal processes in relation to cohorts, as I will show in the Chapter 4.

## 3.2 Methodology: Designs and modelling

<figure><img src="image_49.png" /></figure>

**Figure 3.1: Lexis diagrams for each monitoring.** With the longitudinal monitoring, an individual born in 2001 is monitored through each year as it ages. With the cross-sectional monitoring, an individual is sampled in 2004 and its age (here 6 years) is determined at the time of its death.

### Survival models based on longitudinal monitoring

Longitudinal studies, in which individuals and cohorts are monitored from birth to death (Figure 3.1 for the associated lexical diagram) are, in wildlife ecology, a by-product of capture-recapture studies. The initial motivation for the latter was the accurate estimation of abundance in open populations when detectability is less than perfect (Seber 1965; Cormack 1964; Jolly 1965). Models (e.g. the Cormack-Jolly-Seber model) fitted to these life history data can provide accurate estimates of survival that can be fed into population matrix models (e.g. Fujiwara and Caswell 2001). Since the 1980s, the focus of capture-recapture studies in wildlife ecology shifted from abundance to survival estimation (Lebreton et al. 1992) and the inclusion of individual-level covariates, which has paved the way for a better understanding of life history evolution and natural selection in nature (Cam 2009). Models for estimating survival (initially abundance) use either the recovery of live animals ("live recapture") or dead animals ("band recovery"). Some models may also combine the two data sources (J. D. Baker, A. Westgate, and Eguchi 2010).

The objective of capture-recapture modelling is to develop probability-based models characterising the biological processes

Longitudinal monitoring was essentially a means of estimating abundance. They were then used to estimate vital rates.
that shape the capture history data (B. K. Williams, Nichols, and Conroy 2002). The common approach to each modelling mode is to model the subsequent entries of an individual, after the initial capture, as a function of parameters associated with both sampling and actual population change (B. K. Williams, Nichols, and Conroy 2002). Survival probabilities are then estimated by focusing on the loss of individuals within the population (Lebreton et al. 1992). There are several types of models, more or less complex. Here is a brief review of them. The first type of survival model is the single-age model. It considers a population in which individuals are considered to have a single age. The model traditionally used to estimate survival in this case is the Cormack-Jolly-Seber (CJS) model (Seber 1965; Cormack 1964; Jolly 1965). With this model, the only component of survival that can be estimated is apparent survival. The multiple-age model is an extension of the single-age model that allows capture and survival probabilities to vary with time and age. The model that generalises the single-age model to multiple-age modelling was developed by Pollock (Pollock 1981). The multi-state modelling approach allows some stochasticity to be incorporated between transition states. The states can be considered for example as different locations or phenotypes. This modelling approach was developed to study transition states. It was first introduced by Arnason (Arnason 1972). The inverse time modelling approach developed by (Pollock, Hines, and Nichols 1984) allows the recruitment process to be deduced by considering the recaptures in an inverse temporal order. All these approaches use capture-recapture data from live animals. Approaches have also been developed to use capture-recapture monitoring data incorporating the recapture of dead individuals. This is the case, for example, with survival modelling based on band recoveries, which is of interest for species that are harvested (Burnham 1993). A common feature of all these modelling approaches is that they are based on the use of data obtained through longitudinal monitoring. They require individuals and cohorts to be followed throughout their lives. For species where this may be difficult, other approaches have been developed. Approaches using the same data but taking into account only certain life stages or even using only abundance data have been developed to avoid the cost of long-term monitoring.

**Survival models with longitudinal monitoring and abundance data**

From an applied conservation perspective, the obvious drawback of capture-recapture studies is the time and man-power required to collect the data, especially for long-lived species. E. R. White, Nagy, and Gruber (2014) recently proposed a new development that allows to avoid birth-to-death monitoring at the

Longitudinal survival analysis models can be distinguished in this way: single-age model, multiple-age model, multi-state model and inverse-time model.
individual level. This is a physiologically structured model with age class as the structuring variable. Although the model is age-structured, only the juvenile population is observed. From juvenile mortality and adult fecundity, it is possible to infer adult mortality. However, this requires monitoring the juvenile part of the whole population in order to model the overall population dynamics. An alternative to long-term individual monitoring for estimating vital rates is the use of count data. This approach may involve building an N-mixed model based on knowledge of individual states. Zipkin et al. (2014) has proposed a development that allows the data to be taken into account even if the individual stage is unknown. Another way to obtain vital rates with count data, in the form of time series, is to conduct an inverse modelling approach: this method also has the advantage of considering state data at the individual level (E. J. González, Martorell, and B. 2016). Although these approaches are promising for elusive species, they remain difficult to apply to highly mobile ones. The time lag between data acquisition and the urgency of mitigation on conservation decisions can be acute, suggesting an interest in cross-sectional data which have the added advantage of being applicable to species where individual identification is difficult (B. K. Williams, Nichols, and Conroy 2002).

Survival models have been developed to relay partly on longitudinal data or to get rid of it and use abundance data.

## Survival models with cross-sectional monitoring

Long-lived, mobile and elusive (weakly marked) species are difficult to monitor longitudinally. This is particularly true for species that live in a large and sometimes three-dimensional space in the case of the marine environment. Instead, data on these species can be collected through cross-sectional monitoring. One or more samples are taken during a time series (snapshots; Figure 3.1). Sampling of the study population is carried out as described in 1.3. Once age-at-death data have been collected, they can be used to calculate the survival of the population. This calculation relies heavily on modelling choices. Assuming that cross-sectional age-at-death data are available and representative, ecologists are now faced with other choices, such as non-parametric or parametric modelling.

Elusive species are impossible to monitor on an individual basis and abundance data can be very scarce. It is therefore necessary to use age-at-death data. In the case of marine mammals, these are collected from stranded individuals.

## Non parametric modelling

The non-parametric modelling approach does not assume any functional form of the survival curve. This approach allows the raw observations (i.e. data) to dictate the shape of the survival curve. Two non-parametric approaches are commonly used in wildlife demography. The first was developed by E. L. Kaplan

Non-parametric survival modelling requires a large amount of data. It does not allow to obtain survivorship in the case of elusive species.
and Meier (1958) and is referred to as the Kaplan-Meier estimator, or product limit estimator. It consists of monitoring a cohort of individuals, whether or not they entered the study at the same time, and reporting the remaining number of individuals at each age. A fictitious cohort can be reconstructed from the ages-at-death. The first study to transpose this approach from epidemiology to wildlife demography was conducted by Pollock et al. (1989). They conclude that this estimator is flexible and useful in wildlife studies and have optimised it to allow successive entries of individuals in the survival estimate. This approach considers the maximum survival $l(t)$ at time 0 (discrete time approach): $l(0) = 1.00$. At each age-at-death interval, the survivorship decreases to 0 until the last animal of age $x$ die: $l(x) = 0.00$. The survivorship at each time $t$ can be estimated as follows with $nlt$ = number of animals alive (at risk) at time $t$ and $ndt$ = number of animals that died in the interval between time $t$ and $t + 1$:

$$l(t) = \frac{nlt - ndt}{nlt} \qquad (3.1)$$

A limitation of this approach is that it performs poorly with small amounts of data because the number of points on the survival curve depends directly on the amount of data. If the number of data points is small, the curve is not smooth and has an unreliable stepwise appearance.

An alternative was developed by Nelson (1972) and Aalen (1978). This approach is known as the Nelson-Aalen estimator. The survivorship is modified based on the cumulative hazard function. The approach has better properties regarding small sample size. The cumulative hazard function is constructed as detailed here with $nlx$ = number of animals alive (at risk) at age $x$ and $ndx$ = number of animals that died in the interval between age $x$ and $x + 1$:

$$h(t) = \sum_{x=0}^{t} \frac{ndx}{nlx} \qquad (3.2)$$

The corresponding survivorship function at time $t$ is:

$$l(t) = e^{-h(t)} \qquad (3.3)$$

Despite its ability to accommodate smaller datasets, it is also limited for the types of datasets we are interested in studying the survival of animal populations. The use of these methods, in particular the Kaplan-Meier method, appears to be more suitable for describing "observed" survival and not estimated by modelling. The use of a parametric modelling approach is more suitable with

<figure><img src="image_50.png" /><figcaption>Figure 3.2: Example of Kaplan-Meier survivorship curve.</figcaption></figure>
small samples to estimate survival and characterise the mortality
process of a fictitious cohort in a population over time (Skalski,
Ryding, and Millspaugh 2010). It has the advantage of providing
smoothing and summarising the data into a small number of
parameters. Even with a small sample size, parametric modelling
allows smooth survival to be estimated and parameters to be
compared (Kleinbaum and Klein 2010).

Parametric modelling

The parametric modelling approach requires the choice of
a shape for the mortality curve or hazard rate. The accuracy of the
approach depends primarily on the suitability of the shape of the
mortality curve for the species whose survival and mortality are to
be modelled. The challenge is to find a parsimonious model that
takes into account the available data without fitting the analysis
into a convenient but not necessarily realistic curve shape. Each
parametric model is associated with a probability density function
(i.e. pdf), a cumulative distribution function (i.e. cdf) and a sur-
vivorship function (i.e. l(x)) associated with a hazard rate function
as follows : h(x) = pdf(x) / l(x). Examples of survival models commonly
used with associated distribution is provided in Figure 3.3.

For long-lived animal species, a realistic model should pro-
vide the so-called "bathtub curve", which is characterised by high
juvenile mortality, followed by lower and rather constant adult
mortality and finally a late increase due to senescence (Siler 1979;
Choquet et al. 2011a). The hazard should decrease as the animal
adapts to its environment and becomes stronger, remain constant
in mid-life when the animal is in its prime, and increase with senes-
cence (Emlen 1970). Although there are models to accommodate
this bathtub pattern (Siler 1979; Heligman and Pollard 1980), they
can be difficult to fit (Saavedra 2018). Moreover, their goodness of
fit is hard to measure and compare. Finally, they do not allow for
testing the effect of various factors on survival and mortality.

Parametric survival modelling allows
the use of small data sets. But it re-
quires the definition of a type of mor-
tality curve.

Realistic parametric model for long-
lived mammals = bathtub shape mor-
tality or hazard rate curve.
<figure><img src="image_51.png" /><figcaption>**Figure 3.3: Survival parametric models commonly used.** For each survival model and distribution, the cumulative survival (survivorship $l(x)$, the hazard rate curve and the age-specific survival ($S(x)$) are depicted.</figcaption></figure>

a. Uniform distribution. Hazard mortality curve grows slowly and a little more at the end.

b. Exponential distribution. Hazard mortality curve remains constant over lifetime.

c. Weibull distribution. Hazard mortality curve increases after a short plateau at 0.

d. Gompertz distribution. Hazard mortality curve increases after a long plateau near 0.

e. Siler distribution. Hazard mortality curve is in U-shape or so called-Bathtub shape with a decrease, plateau and increase.
Figure from Skalski, Ryding, and Millspaugh 2010.
## Our parametric modelling approach

Our aim is to develop a parametric approach for the construction of life tables in a data-poor context, with long-lived vertebrate species in mind. We will first present a simple regression modelling framework for the analysis of age-at-death data (with or without right censoring) that can accommodate mortality patterns such as constant, increasing/decreasing, unimodal or bathtub-shaped. Importantly, this framework allows for the transparent inclusion of individual-level covariates and random effects. We then perform a Monte Carlo simulation study with five biological scenarios to evaluate our framework, focusing on the accurate estimation of survivorship and mortality. Finally, we illustrate our methodology on a handful of real-life case studies, focusing on marine mammals. This group includes many elusive and long-lived species that are threatened (Avila, Kaschner, and Dormann 2018), data-deficient (Parsons 2016) and difficult to study with a longitudinal approach. The most common age-at-death data for marine mammals are obtained from strandings (i.e. cross-sectional monitoring). Teeth are collected from individuals found dead on the shore and are then processed to allow the reading of growth layer groups that are indicative of the age of the stranded animal (Mannocci et al. 2012). The stranding filter may introduce a selection bias of individuals between the natural population and the age-at-death dataset (Barlow and Hohn 1984). However, stranding samples are a source of age data from which vital rates can be obtained (J. D. Baker, A. Westgate, and Eguchi 2010). In this framework, several underlying assumptions are associated with the developed approach:

Reed's model can fit this hazard curve. It can do so by including a parameter for individual heterogeneity. We believe that this model can be integrated into a parametric approach.

### Baseline assumptions (use of this parametric approach)

* 1. Each age-at-death is known and correctly recorded

* 2. The cohort is representative of the overall population

* 3. The fate of each individual is independent

* 4. The shape of the survivorship and mortality distribution are known and well chosen to represent the life history of the species

## Definitions

Survival analysis deals with the analysis of the timing of death (E. L. Kaplan and Meier 1958; Tanner and Wong 1984; T. G. Clark et al. 2003; Lesaffre and Lawson 2012). We assume data $y \ge 0$ to be time-to-event data, for example longevity, survival time or age-at-death data. Such data can be collected from strandings of
animals (that is marine animals that are washed ashore), or any
recovery of dead specimens (e.g. *Lepus europaeus*, Pallas 1778; *Ovis
dalli*, Nelson 1884) when aging is possible (e.g. from growth layer
groups). Let the index *i* denotes the *i*th individual, and *N* the
sample size. The equation *y*ᵢ ~ D(θ) reads as datum *y*ᵢ follows
statistical distribution D of parameters θ and with probability
density function *f*(*y*; θ) and cumulative density function *F*(*y*; θ) =
Pr(*y* ≤ *t*) = ∫₀^*t* *f*(*y*; θ)dy.

The survival function S(t; θ) gives the probability of being alive at time t, that is Pr(y > t) = 1 - Pr(y ≤ t) = 1 - F(y; θ). At the population level, this quantity correspond to the fraction of the population that is still alive at age x, that is cumulative survival or simply survivorship. The hazard rate, or age-specific mortality rate, is the instantaneous probability of dying at time t + dt given that and individual i has survived until time t.

$$
h(t) = \lim_{dt \to 0} \frac{\Pr(t \le y_i < t + dt; y_i > t)}{dt} \quad (3.4)
$$

With parametric models, the hazard rate can be expressed
in terms of the probability density and survivorship functions:

$$
h(t; \theta) = \frac{f(t; \theta)}{S(t; \theta)}, \text{ with } S(t; \theta) > 0 \quad (3.5)
$$

Data simulation scenarios

We considered five biological scenarios (i.e. five different
life histories) corresponding to different patterns in survivorship
and the underlying hazard (Margin-Figure 3.4):

1. a unimodal distribution of age-at-death corresponding to a unimodal hazard, whereby mortality risk increases in early ages, peaks and decreases in late life;

2. a mixture of two hazards corresponding to either a unimodal (a) or bimodal (b) distribution of age-at-death;

3. a bathtub-shaped hazard due to individual frailty, that is individual-specific risk of mortality; and

4. a bathtub-shaped hazard with an additional bump in early life due, for example, to an additional source of mortality.

Each scenario is associated to survivorship and hazard
functions (Figure 3.4).
<figure><img src="image_52.png" /><figcaption>Figure 3.4: Biological scenarios considered in the Monte Carlo simulation study.</figcaption></figure>

1: low juvenile mortality, a high adult mortality and no senescence.

2a: low juvenile mortality and a higher adult mortality plateau.

2b: high juvenile mortality and a lower adult mortality that decreases in a linear fashion.

3: high juvenile mortality, a lower adult mortality and senescence (bathtub shaped hazard).

4: high juvenile mortality and a high adult mortality, with a transient dip in mortality risk between these two life-stages.

## Statistical Analysis of age-at-death data

We used parametric models $M^θ$ of age-at-death data $y$ to estimate hazard and survivorship rates. We assumed that the exact timing of death is available, but our framework can easily accommodate censoring (that is cases when death is known to have occurred before or after measurement). Our framework consists in modelling the logarithmic transform of $y_i$ in a regression framework (location-scale model)

$$ \log y_i = \mu + \sigma \times \epsilon_i - \frac{Z_i}{\beta} \quad (3.6) $$

The choice of the statistical distribution for the residuals $\epsilon_i$ determines the shape of the underlying hazard rate. We considered three different choices, each corresponding to a model¹.

* $M_1$: $\epsilon_i \sim N(0, 1)$ and $\frac{1}{\beta} = 0$ ($\beta = +\infty$)

This model assumes a log-normal distribution for $y_i$, which corresponds to a unimodal hazard curve.

* $M_2$: $\epsilon_i \sim G(0, 1)$ and $\frac{1}{\beta} = 0$ ($\beta = +\infty$)

This model assumes a Gumbel distribution for the residuals $\epsilon_i$, which corresponds to a Weibull distribution for $y_i$. It is known as the Accelerated Failure Model. The hazard rate is monotonic: it can be constant, increasing or decreasing depending on the value of $\sigma$.

* $M_3$: $\epsilon_i \sim N(0, 1)$ and $\frac{1}{\beta} > 0$

This choice leads to assume a normal-Laplace distribution for $\log y_i$, which induces a flexible hazard curve depending on the value of $\beta$ (Reed 2011). In particular, the hazard can be a bathtub-shaped, as expected for example for long-lived species of vertebrates in the wild (Choquet et al. 2011a).

Parameters specification of Model 3.6:

* $\mu$: location parameter.

* $\sigma$: positive scale parameter.

* $Z_i$: individual independent standard exponential deviates.

* $\frac{1}{\beta}$: positive scale parameter and individual frailty (Kannisto 1991; Reed 2011) or persistent demographic heterogeneity *sensu* Cam, Aubry, and Authier 2016.

1: See SI Text 2 of https://esj-journals.onlinelibrary.wiley.com/doi/10.1002/1438-390X.12069. The next supplementary material that will be referred in margin notes will always be available at this URL. To find the supplementary material mentioned, see this URL
Our framework transcribed by the equation 3.6 3 a flexible
location-scale model and boils down to a generalized linear mixed
model (GLMM; Bolker et al. 2009) with a handful of parameters
$\theta = (\mu, \sigma, \beta)$ to accommodate a large diversity of survivorship
and hazard curves². One attractive feature of this framework is
the seamless incorporation of *p* individual-level covariates $x_{ip}$ in
equation 3.6 (Reed 2011):

2: See SI Text 2.

$$
\log y_i = \mu + \sum_{j=1}^{p} \gamma_p x_{ip} + \sigma \times \epsilon_i - \frac{Z_i}{\beta} \quad (3.7)
$$

An important restriction of our approach is that only time-
invariant individual-level covariates can be included. It is also
impossible to take into account changes in states within the life
history trajectory at the individual level. However this approach
covers interesting cases such as sex-differences in survival, differ-
ences due to geography or cause of mortality (that is comparing
different populations of the same species).

Monte Carlo study

Our aim is to carry a Monte Carlo study (e.g. T. P. Morris, I. R. White, and Crowther 2019) to investigate whether our modelling framework can provide accurate survivorship and hazard rate estimates from age-at-death data. We considered 5 biological scenarios to cover a diversity of realistic mortality patterns. For each scenario, we simulated 100 datasets of sample size 100, 200, 300, 400, 500 and 1000 to provide recommendations on the minimum sample size required for accurate estimation. Data simulation was carried out in R version 3.6.0 (R Core Team 2019) using base functions such as rnorm and rexp. Each simulated dataset was then analyzed with our framework that considered 3 parametric models. Crucially, we considered scenarios for which the true model was not among the set (Table 3.1). In other words, we assessed the performance of our framework under the possibility that none of the candidate models is correctly specified with respect to the data at hand. For example M2 is a Weibull model, which is widely used in survival analysis (Kleinbaum and Klein 2010) it is biologically unreasonable for marine megafauna and top predators as a model over their entire lifetime because it cannot accommodate the expected bathtub-shape hazard.

Model fitting was done with software Stan version 2.18 (Carpenter et al. 2017a) called from R via the library rstan (Stan Development Team 2018). Three chains were run with a warm-up of 500 iterations, followed by an additional 1000 iterations. No thinning

<table><caption>**Table 3.1: Design of the Monte Carlo study.** Model *M*₂ acts as a negative control as it was never used to simulate data. Scenarios 2a, 2b and 4 corresponds to data generated from mixture models not included in the set. They serve as tests of the performance of our framework. Scenarios 1 and 3 act as positive control as they correspond to data simulated under models *M*₁ and *M*₃ respectively.</caption>
  <thead>
    <tr>
      <th>Model/Scenario</th>
      <th>1</th>
      <th>2a</th>
      <th>2b</th>
      <th>3</th>
      <th>4</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>M<sub>1</sub></td>
      <td>+</td>
      <td>-</td>
      <td>-</td>
      <td>-</td>
      <td>-</td>
    </tr>
    <tr>
      <td>M<sub>2</sub></td>
      <td>-</td>
      <td>-</td>
      <td>-</td>
      <td>-</td>
      <td>-</td>
    </tr>
    <tr>
      <td>M<sub>3</sub></td>
      <td>-</td>
      <td>-</td>
      <td>-</td>
      <td>+</td>
      <td>-</td>
    </tr>
  </tbody>
</table>
was performed but the delta parameter of the NUTS algorithm was increased from 0.80 to 0.95 to avoid divergent transitions and the maximum tree depth increased to 15. Parameter convergence was assumed when its $\hat{R}$ statistics was lower than 1.10. Upon convergence, the 3 chains were pooled to obtain a sample of ≈ 1000 values from the posterior distribution.

Model fit was assessed with the Widely Applicable Information Criterion (WAIC, (2014)), computed with R package loo (Vehtari, Gelman, and Gabry 2017). Survivorship estimates from each model were computed from the posterior distribution of parameters, and visually compared to the true survivorship curve and a non-parametric (Kaplan-Meier) estimate. Because we carried out a simulation study, the true survivorship curve was known and could have been used to compute the Root Mean Squared Error (RMSE). However, in practice, this is not the case and we chose instead to compute RMSE with respect to the non-parametric Kaplan-Meier survivorship estimates. The latter were thus assumed to represent the best estimates available to researchers, and the aim was to assess whether a parametric model could provide a fit as good as that from a non-parametric approach.

$$ \text{RMSE}_{\mathcal{M}} = \sqrt{\mathbb{E} \left[ (\hat{S}_{\text{KS}}(t) - \hat{S}_{\mathcal{M}}(t))^2 \right]} \quad (3.8) $$

In order to assess model selection and model check, it is necessary to determine if the models represents well the data. (Conn et al. 2018) recently reviewed some ways to proceed. We choose to do a prior predictive check to test for adequacy between models and time to event data³. We also did a posterior predictive check⁴ to see whereas data simulated through the fitted models are similar to that observed from the (Barlow and Hohn 1984) dataset. The comparison is done with both the true Kaplan-Meier survivorship curve and the ones from posterior simulated datasets.⁵

Our focus was on accurate estimation of survivorship, and thus we assessed goodness-of-fit by comparing the expected mean survivorship under each model to the observed Kaplan-Meier estimates. This focus was in line with downstream use of such estimates in matrix population models: here the salient statistics we want our model to reproduce (Gelman 2003) is the survivorship function.

Our study design is summarized in Table 1 and Figure 2. It consisted in a comprehensive factorial design crossing (a) sample size (100, 200, 300, 400, 500 and 1000), (b) mortality patterns (5 scenarios), (c) parametric models (3 models) and (d) individual covariate inclusion. Two covariates ($x_1, x_2$) were generated by sampling from a Bernoulli distribution with probability 0.5. These

Parameters specification of equation 3.8:

$\hat{S}_{\text{KS}}(t)$: Kaplan-Meier estimate of survivorship at age $t$.

$\hat{S}_{\mathcal{M}}(t)$: parametric model $\mathcal{M}$ over a sequence of values of $t$.

3: SI text 3 and Figure S1.

4: SI text 3 and Figure S2.

5: SI text 3.
covariates could represent for example sex or two sub-populations
in different geographic areas.

Applications

We analyzed real datasets from published case studies (Table 2) within our framework, and compared the estimated parametric survivorship curves with the non-parametric Kaplan-Meier one. All species are marine mammals except the spur-thighed tortoise (Testudo graeca, Mertens 1946) which was included to compare our approach with that of (Rodriguez-Caro et al. 2019) in a data-poor context for conservation. It is important to precise that data from (Rodriguez-Caro et al. 2019) were obtained from live animals, still alive at the time of measurement (Sanz-Aguilar et al. 2011; Rodriguez-Caro et al. 2013). However, we used these data as if they were age-at-death data and ignored right-censoring.

<figure><img src="image_53.png" /><figcaption>**Figure 3.5: Monte Carlo study flowchart.** We considered five biological scenarios, six different sample sizes for data, and three models for analysis. For each combination, we assessed model fit and the accuracy of parameter estimates. Model selection is done with Watanabe-Akaike information criterion (WAIC) and root-mean-square error (RMSE).</figcaption></figure>

**3.3 Results: Simulation study**

Across all scenarios and sample size, parameter convergence
(assessed with $\hat{R}$) was not equivalently reached depending on the
model and scenario⁶. $M_1$ always converged very easily. In contrast,
$M_2$ and $M_3$ were not as good as $M_1$ to converge with 1000 iterations
(500 as warm up). More precisely, convergence for $M_3$ was difficult

6: Figure S3 and Figure S4 a.
for $\beta$ given this configuration⁷. An increased in the number of iterations per chains (here from 1000 to 2000) solved the problem.

7: Figure S5 to S10.

## Hazard rate estimation

Estimated hazard curves are shown in Figure 3.6 for each combination of scenario, model and sample size. Models $M_1$ and $M_3$ were the best fitting ones in the first and third scenarios respectively (i.e. positive control, Table 3.1): estimates were accurate and precision increased with sample size. For scenarios 2a, 2b and 4, all estimates were biased, and precision increased with sample size. In contrast, model $M_2$ never provided accurate hazard estimates (i.e negative control). The same results were obtained when covariates were included.

<figure><img src="image_54.png" /><figcaption>**Figure 3.6:** Estimated hazard curves confidence intervals for each combination of scenarios (rows), models (columns), and sample size (facets). Estimated confidence intervals are depicted in each panel and compared to the true hazard curves (in black). Even-numbered scenarios (2a, 2b and 4) are on the left, and odd-numbered ones (1 and 3) on the right.</figcaption></figure>
Survivorship estimation

Estimated cumulative survival curves are shown in Figure 3.7 for each combination of scenario, model and sample size. Across all scenarios and sample sizes, estimates from model $M_3$ were the most accurate⁸. Precision increased with sample size. In particular, survivorship rates estimated with $M_3$ were very close to Kaplan-Meier estimates for sample size ≥ 300. This sampling size also provided a good confidence interval precision with a maximum width of 0.04 % while estimating survivorship⁹. Predictive ability, as measured with WAIC, was the greatest for model $M_3$: it was consistently ranked first across each combination of scenario and sample size, even for scenario 1 where model $M_1$ was the true data-generating mechanism¹⁰.

8: Figure S5, SI Text 4 and Figure S11.

9: Figure S12.

10: SI Text 4 and Figure S13.

<figure><img src="image_55.png" /><figcaption>**Figure 3.7:** Estimated survivorship confidence intervals for each combination of scenarios (rows), models (columns) and sample size (facets). Estimated confidence intervals are depicted in each panel and compared to the truth (in black). Even-numbered scenarios (2a, 2b and 4) are on the left, and odd-numbered ones (1 and 3) on the right.</figcaption></figure>
Covariate Effects

Covariate effect estimation is summarised on Figure 3.8 as a difference between survivorship rates. Model $\mathcal{M}_2$ could not estimate difference in survivorship. Model $\mathcal{M}_1$ is only effective for both scenario 1 and 2a. $\mathcal{M}_3$ could estimate accurately covariate effects when the difference is expressed as an unimodal pattern (i.e. scenario 1, 2a and 3). The precision of the estimated effect increased with sample size for models $\mathcal{M}_1$ and $\mathcal{M}_3$. With small sample size, sign errors on the effect of covariate was possible but disappeared with sample size $\ge 300$.

<figure><img src="image_56.png" /><figcaption>**Figure 3.8:** Estimated survivorship difference under each scenario. The covariate effect could correspond to that of sex (e.g., x = 1 for females and x = 0 for males). Ten estimated difference curves are depicted in each panel and compared with the truth.</figcaption></figure>
Case studies

Estimated survivorship curves from published dataset are
plotted against the Kaplan-Meier curves in Figure 3.9 for each
model. Model M3 was the most flexible: it provided the most accu-
rate estimates for each dataset. Uncertainty, as measured with 80%
credible intervals were narrower with model M3, and overlapped
most with Kaplan-Meier estimates. Model M3 consistently had the
lowest WAIC.

In the handful of case studies where covariates were available,
a similar pattern arose. Including covariate can be expected to
account for more variation in the data, and a lower WAIC. For
both M1 and M2, this was indeed the case. For M3 it was only
true with the (Murphy et al. 2012) dataset¹¹. The estimated co-
variate effect for both (Barlow and Hohn 1984) and (Kesselring
et al. 2017) case studies is summarised on Figure 3.10.¹² Models
M1 and M3 both estimated a survivorship difference between each
covariate. As it is the case without covariates (Figure 3.9), the M3
curve fits the Kaplan-Meier estimate better. However, there is a
discrepancy between both, for each covariate. M3 is able to spot a
difference depending on covariate, but is not able to perfectly fit
the Kaplan-Meier estimate.

<footnote>11: SI Text 4 and Table S1.</footnote>

<footnote>12: SI Text 5.</footnote>
<figure><img src="image_57.png" /><figcaption>**Figure 3.9: Survivorship curves estimated from published data sets.** Each subpanel corresponds to a case studies in Table 2. Data set size is represented horizontally. Panels are associated to the following data sets:</figcaption></figure>

a. Murphy et al. 2012

b. Slooten 1991

c. Rodriguez-Caro et al. 2019

d. Murphy et al. 2009

e. Kesselring et al. 2017

f. Saavedra 2018

g. Barlow and Hohn 1984.
<figure><img src="image_58.png" /><figcaption>Figure 3.10: Estimated survivorship difference for both case studies.</figcaption></figure>
## 3.4 Discussion: Implications of this new cross-sectional parametric approach

We assessed the ability of a simple linear mixed model to estimate hazard and survivorship rates with cross-sectional age-at-death data. We used Monte Carlo simulations to investigate the accuracy and precision of estimates across a variety of mortality patterns and several sample sizes. We compared the performance of three different models and found one model, the model $M_3$, to be consistently better at predicting survival, even when misspecified.

### Age-at-death data and sampling bias

A crucial but implicit assumption of the cross-sectional approach to survival analysis is that the sample is representative of the population as a whole, particularly with regard to age structure (Caughley 1966). This assumption relates to the dataset, not to the modelling. The way in which the age-at-death data are collected is therefore crucial in supporting this assumption. Approximate protocols involving, for example, the recording of dead carcasses, hunting bags or population censuses must meet the representativity premise. However, it is possible that an implicit process (e.g. bycatch) shapes the observed age frequency (e.g. from stranded animals). In this case, it is necessary to explore some potential age-dependent selection bias in the population (Barlow and Hohn 1984). With stranding data, the assumption of a stationary age distribution needs to be supported by ancillary data, but ultimately it is likely to remain a working hypothesis on which any cross-sectional methods will be based. In the case of cetaceans, many species are not amenable to study with a longitudinal design, and strandings remain an important source of information (e.g. Murphy et al. 2009), particularly demographic information (Saavedra 2018; Ferguson, Stirling, and McLoughlin 2006). When longitudinal studies are not possible, there are very limited options to obtain demographic information. In some cases, a comparative approach may be possible where information on species with similar life histories can be leveraged (Caswell et al. 1998; Hashimoto et al. 2013). This choice is essentially based on the assumption of similarity between species. Even if comparative data are available, the ecological context may be too different to justify this approach in some instances. Strandings may be the only available source of data, and even if they are suspected to suffer from some selection bias, a pragmatic approach to conservation requires to use them (Boyd, Bowen, and Iverson 2010), keeping in

To use age-at-death data, we assume that the population is under a stationary age distribution which is rarely the case in nature...

... so we should use auxiliary data to interpret results. But if age-at-death data is the only source of data available, so it should be used whenever possible.
mind the inherent limitations of these data.

Many conservation instruments specifically require the use of the "best available science" (according to the Marine Strategy Framework Directive EC 2008/56 in Europe). The operative expression "the best available science" can be broadly understood as what lies at the intersection of state-of-the-art methods, good data and accurate knowledge. In practice, there may be a hiatus between the canonical approach that should be, and the pragmatic one that can be pursued at the time conservation actions need to be decided. A conclusion of a species being data-deficient often leads to the doldrums with respect to conservation decisions (Parsons 2016). Likewise, the many uncertainties that can affect any scientific studies can easily lead to inaction regarding the implementation of conservation measures (Ascher 2004). It is because we are starkly aware of these limitations that we carried out this study to identify a pragmatic approach to estimate survivorship rates from age-at-death data. Crucially, all the models we used are conditional of the underlying sample being representative of the population it is taken from. Granting this assumption, we identified a simple model from (Reed 2011) to obtain accurate estimates.

We can inform conservation policies and management strategies with demographic parameters obtained from age-at-death data.

## Prediction Accuracy and Models’ Goodness of fit

Traditionally, estimating survivorship rates with cross-sectional data was done with parametric models such as the Siler or Heligman-Pollard models, and this is still the case for some marine mammals (Mannocci et al. 2012; Siler 1979; Heligman and Pollard 1980; Huang et al. 2012). These models aim at reproducing a bathtub-shaped hazard curve, but need several parameters to do so. Furthermore, they can be difficult to fit although new tools have been developed to use these models (Saavedra 2018). A remaining challenge with these models is to assess goodness of fit, to incorporate individual-level covariates and perform model selection. The simple parametric form of (Reed 2011) for analyzing the logarithm of age-at-death data provides a bathtub-shaped hazard with a linear mixed model, the current workhorse of ecologists (Bolker et al. 2009). This linear mixed modelling framework allows for a seamless incorporation of covariates, and to use standard tools for model selection and goodness-of-fit assessments. In other words, model *M*<sub>3</sub> brings back survival analysis within the comfort zone of ecologists. We harnessed the simplicity of (Reed 2011) to conduct our Monte Carlo study, and found that the model suggested by (Reed 2011), our model *M*<sub>3</sub>, was very accurate in predicting survivorship (i.e. it consistently had the lowest RMSE), even in cases when it was not the true model behind the data<sup>13</sup>.

This result The most commonly used models for obtaining marine mammal survival from age-at-death data are the Siler and Heligman Pollard models.

These models can be used to obtain vital rates but their use is limited. Their construction is not simple and they do not allow for the estimation of vital rates as a function of various factors.
is important as it suggests to start building model of increasing
complexity from M₃ (as it is done after Chapter 4) and use tools
such as WAIC (Gelman, Hwang, and Vehtari 2014) to balance
model complexity with prediction accuracy.

From our simulations, we can recommend a sample size of at
least 300 individuals to obtain accurate and precise estimates of
survivorship, from which age-specific survival estimates can be
derived<sup>14</sup> This sample size recommendation is practical and real-
istic (e.g. Mannocci et al. 2012; Murphy et al. 2009; Kesselring et al.
2017). This recommendation is mostly to obtain precise estimates,
but may be relaxed in some cases where only sparse data may be
available (data-poor context hereafter). Estimates from a simple
linear model with an individual frailty term, were accurate, if
imprecise, with a sample size as small as 100. The possibility to
use sparse data is critical as it can help conservation of elusive
species, such as marine mammals, many of which being classified
as data-deficient (Parsons 2016; Schipper et al. 2008). Some of
the case studies presented in this paper support this statement,
although, with so few data, including covariates in the model will
be difficult or will require great care (see for example Cox et al.
2019). Rodriguez-Caro et al. (2019) recently provided an approach
to estimate survival in data-poor settings using inverse modelling,
also to obtain accurate estimates of demographic rates. With the
latter, population matrix models can then be used to assess pop-
ulation dynamics and the fate of populations over time (Caswell
2000).

Hazard and Frailty

A linear mixed model can fit age-at-death data very well: this ability comes for the individual frailty term, which corresponds to an individual random effect in the mixed modelling framework. Individual frailty in statistical models translate the empirical observation that two similar individuals (with respect to observable features of their phenotypes) can nevertheless differ markedly in their longevity (Cam, Aubry, and Authier 2016; Kannisto 1991). The parametric form (i.e. exponential) for individual frailty gives extra flexibility to the model, and can accommodate a bathtub-shaped hazard curve (Reed 2011). However, in our simulations, we found that estimating hazard rates was more difficult than estimating survivorship rates (Figures 3.6 & 3.7). Thus, even though we identified a model ($M_3$) for reliable and accurate estimation of survivorship, the same model was less reliable with respect to hazard. In other words, the individual frailty term in our model $M_3$ should not be over-interpreted, and is probably best seen as a statistical device for robust estimation. Hazard estimation is a difficult statistical problem (Watson and Leadbetter 1964), for which there are better

14: SI Figure 14.

Our approach correctly estimates survivorship with 300 age-at-death data and correctly approximates hazard with 500 age-at-death data.

The inter-individual frailty parame-
ter that allows the mortality curve
to have a bathtub shape should not
be interpreted alone. It is not yet a
biological indication in its own right.
tools available, especially non-parametric ones (see for example
Hanson and Jara 2013), than the simple parametric approach we
considered in this study. Non-parametric approaches to infer the
shape of the hazard curve are data-hungry: Hanson and Jara (2013)
use Bayesian non parametrics, which is better described as a model
with a massive number of parameters (Hoff 2013). The traditional
Kaplan-Meier approach is truly a non parametric approach but
it does not give access to the underlying hazard, and give rough
(that is, non-smooth; Figure 3.7) survivorship rates with small
sample size. In data-poor settings, parametric modelling remains
attractive because it has interpretable parameters (e.g. individual
frailty) and because these parameters can smooth out noise in data,
yielding more precise estimates if the model is at least approxi-
mately correct, or more pragmatically, if it is grounded in theory
(e.g. bathtub-shaped hazard for natural populations) and cannot be
rejected from a goodness-of-fit test. It is precisely in this data-poor
setting that we envision our parametric modelling approach to
be most useful. Because the approach boils down to linear mixed
effects modelling, great flexibility in model specification of ad-
ditional random effects (e.g. year effects, sex-specific frailties) is
possible provided there are enough data to offset the increase in
complexity.

Benefits and limits

We believe our approach is very valuable to estimate sur-
vivorship from sparse data but may be inadequate for bimodal
age-at-death data distribution. A bimodal distribution of age-at-
death data may be a sign of selection in data collection (Barlow
and Hohn 1984). Rather than consider the sampling as biased, our
approach can accommodate the selection phenomenon through
two ways. Firstly, it is possible to consider the selection bias as a
covariate in the study if one such covariate is available (e.g. By-
catch index). If no such covariate is available, it may be possible
to build a mixture of two models (e.g. M₁ and M₃) in order to
take into account an additional mortality on some age classes.
However, such a development requires to conduct its own sim-
ulation study which is beyond the scope of this study. Since our
approach is based on linear regression, it is straightforward to
expand the model (e.g. random year effects, mixtures) while us-
ing familiar and well established methods for model selection
(e.g. WAIC) and assessment of model fit (e.g. posterior predictive
checks, R² statistics). These features are assets, and suggest that our
approach is complementary to existing ones (e.g. Saavedra 2018;
Siler 1979; Heligman and Pollard 1980) to estimate vital rates in
some data-poor species. On the basis of the size and morphology
of the animals, the largest can be defined as "megafauna" (Estes

Our model performs well in case of
unimodal age-at-death distribution...
et al. 2016). Large animals, usually long-lived vertebrates, refereed as "megafauna" are generally elusive. When associated with the marine environment (referred as "marine megafauna") it may be more difficult to obtain data and study these animals given their living environment. This is particularly true for demographic data and studies. Given their functional importance (Pimiento et al. 2020), there is a need to inform the biology and the demography of these species. The approach presented here may be of interest to study the demography of marine megafauna, in particularly marine mamals such as the common dolphin in the North-East Atlantic. And this is what we will see in the next Chapter.

... and can allow joint estimation of fertility in a joint modelling approach.
<figure><img src="image_59.png" /></figure>
<figure><img src="image_60.png" /><figcaption>Flowchart of the study presented in this chapter.</figcaption></figure>

Publication in prep.

This chapter is associated with one publication which is under preparation:
Rouby, E., Authier, M., Mauchamp, A., Mendez-Fernandez, P., Dabin, W., Thobois, J. and Ridoux,
V. North-East Atlantic common dolphin population viability and vital rates variations. In prep.
## 4.1 Introduction: A need for demographic knowledge

The common dolphin is one of the marine mammal species assessed under the MSFD, in particular under descriptors 1 and 4 which include marine mammals (Table 4.1 for details of the descriptors and their relevance to marine mammals; M. B. Santos and Pierce 2015). This marine mammal species is found in all temperate and tropical parts of the oceans (Perrin 2018). Individuals are organised into distinct populations, or stocks, which may be associated with different management issues (Natoli et al. 2006; Amaral et al. 2012). The North-East Atlantic population is a population with high conservation stakes today, particularly with regard to the MSFD (European Parliament 2008), since it is the most abundant cetacean species in European waters (Hammond et al. 2017). It is important to conserve this population for the purposes of the MSFD, but it is currently subject to high levels of extrinsic mortality through bycatch (Murphy et al. 2021; Peltier et al. 2016) which can impact on its viability (Mannocci et al. 2012).

<table><caption>**Table 4.1: Summary of the MSFD descriptors and how they relate to the project.** Each descriptor is summarised. For each, its relevance to marine mammals is addressed. As well as the associated demographic need. For a more precise description of the descriptors see M. B. Santos and Pierce (2015) or European Parliament (2008).</caption><thead><tr><th>Descriptor</th><th>Relevance for marine mammals</th><th>Need for marine mammals demographic information</th></tr></thead><tbody><tr><td>1. Maintain biological diversity</td><td>Marine mammals is an important functional group as marine megafauna and sometimes keystone species</td><td>Yes</td></tr><tr><td>2. Non-indigenous species</td><td>Not addressed</td><td>No</td></tr><tr><td>3. Populations of commercial fish/shellfish biologically safe</td><td>Not addressed</td><td>No</td></tr><tr><td>4. Elements of marine food webs occur at normal abundance</td><td>All marine mammals in european waters are top predators</td><td>Yes</td></tr><tr><td>5. Human-induced eutrophication is minimised</td><td>Not addressed</td><td>No</td></tr><tr><td>6. Sea-floor integrity maintained</td><td>Not addressed</td><td>No</td></tr><tr><td>7. Hydrographical conditions not unfavourable</td><td>Not addressed</td><td>No</td></tr><tr><td>8. Concentrations of contaminants</td><td>Due to their trophic position, marine mammals bioaccumulate pollutants</td><td>No</td></tr><tr><td>9. Contaminants in fish and other seafood</td><td>Not addressed</td><td>No</td></tr><tr><td>10. Properties and quantities of marine litter do not cause harm</td><td>Ingestion of plastics and entanglement in debris</td><td>No</td></tr><tr><td>11. Introduction of energy, including underwater noise, non-disruptive</td><td>Underwater noise can have a range of effects on marine mammals</td><td>No</td></tr></tbody></table>

The MSFD descriptors are used to assess the status of the population and are based on sets of criteria. Under the MSFD, descriptor 1 requires the production of indicators of demographic status to assess the viability of the common dolphin population in the face of bycatch pressure (Benjamins et al. 2014). The aevaluation of the achievement of the objectives set by the descriptors is carried out on the basis of a set of criteria which constitute a
descriptor¹. Within descriptor 1 in particular, the demography of marine mammals (and therefore the common dolphin) occupies an important place (European Parliament 2008). The only biological indicators recognised to define the status of the population in the North-East Atlantic (i.e. increasing, stabilising or decreasing) are the abundance estimates obtained from aerial and boat surveys² (Hammond et al. 2017, 2013). Seasonal abundance estimates have been collected on a smaller scale (Laran et al. 2017; Authier et al. 2018) but their purpose is rather to provide information on the abundance of the common dolphin population on a seasonal basis. Such abundance estimates are not sufficient to provide information on the status and viability of the population, and the impact of bycatch on its viability (Murphy et al. 2021; M. B. Santos and Pierce 2015). There is a need to produce demographic indicators (vital rates) to better inform the management policy of the MSFD and describe the status of the population (Murphy et al. 2021).

Demography is a more refined indicator than abundance for determining the status of a population and an essential complement in terms of management. The use of abundance data to indicate the viability of a population is mainly based on observed trends and the determination of depletion levels (B. L. Taylor et al. 2007). In the context of bycatch pressures, demography can be a supplementary indicator to abundance surveys to study the anthropogenic demographic impact on the common dolphin population (see A. J. Read, Drinker, and Northridge (2006) for a broader discussion regarding marine mammals). Before detecting a change in abundance, it is possible that the values of the life history traits will change because their evolution depends on the extrinsic pressures (e.g. bycatch) that the population is undergoing (Stearns 2000). In the case of the common dolphin, the primary pressure on the population seems to be strong, given the number of individuals found stranded on the French seashore (Dars et al. 2020). Obtaining demographic data on this population appears both essential from an applied point of view and interesting from a more fundamental point of view in order to highlight possible variations in the values of important vital rates associated with survival and reproduction. The vital rates of the common dolphin population have already been estimated, as well as the life tables, and the population has been considered non-viable under current bycatch pressures (Mannocci et al. 2012) but it is necessary to complete these analyses.

Obtaining vital rates can be improved by using a more representative sampling method and more flexible statistical methods. Previous demographic work has provided age-at-death data using all available biological material, as is usually done to study the demography of odontocetes (Barlow and Hohn 1984). From these

<footnote>1: See Table 4.2 for a schematic presentation of each criteria within the descriptors relevant to marine mammals and their need for demography</footnote>

<footnote>2: See Appendix Table 1 to find out about surveys by campaign and by season.</footnote>
<table><caption>**Table 4.2: Summary of descriptor criteria within which the production of demographic state indicators is required.** See European Parliament (2008) for a less schematic description and the detailed elements. The primary and secondary aspects are not shown here for the sake of clarity. But the demographic issues appear as secondary.</caption><thead><tr><th>Descriptor</th><th>Criteria</th><th>Need for demography</th></tr></thead><tbody><tr><td rowspan="4">1. Maintain biological diversity</td><td>D1C1 The mortality rate per species due to bycatch is below the level that would pose a threat to the species, so the long-term viability of the species is assured</td><td>Yes through the use of population growth models taking into account removals and quantification of the bycatch effect on vital rates</td></tr><tr><td>D1C2 Anthropogenic pressures do not adversely affect the abundance of populations of the species concerned, so that the long-term viability of these populations is guaranteed</td><td>No</td></tr><tr><td>D1C3 The demographic characteristics (e.g. size or age structure, sex distribution, fertility rates, survival rates) of the species' populations indicate a healthy population, unaffected by anthropogenic pressures</td><td>Yes through the production of life-tables and vital rates using new cross-sectional methodologies</td></tr><tr><td>D1C4 The range of the species and, where appropriate, their pattern of distribution within that range, is consistent with prevailing physiographic, geographic and climatic conditions</td><td>No</td></tr><tr><td rowspan="5">4. Elements of marine food webs occur at normal abundance</td><td>D1C5 The habitat for the species has the necessary extent and condition to support the different stages in the life history of the species</td><td>No</td></tr><tr><td>D4C1 – Primary Diversity (species composition and relative abundance) of the trophic guild is not affected by anthropogenic pressures</td><td>No</td></tr><tr><td>D4C2 – Primary: The balance of total abundance between trophic guilds is not affected by anthropogenic pressures</td><td>No</td></tr><tr><td>D4C3 – Secondary The size distribution of individuals within a trophic guild is not affected by anthropogenic pressures</td><td>No</td></tr><tr><td>D4C4 – Secondary The productivity of the trophic guild is not affected by anthropogenic pressures</td><td>Yes through the use of population growth models taking into account anthropogenic pressures</td></tr></tbody></table>

data, vital rates were estimated using standard survival models from the literature (Siler 1979). Sampling bias is poorly controlled and it is difficult to identify variations in the estimated vital rates and the effect of variables (e.g. cause of death, area or sex). We provide here a complementary and updated demographic estimates which helps to fuel the debate on how to consider and study an elusive marine mammal population such as the common dolphin in the North-East Atlantic. In order to better control the bias in the representativeness of the strandings, we performed a stratified random sampling to select individuals (females and males). For each individual, where possible, we obtained age-at-death data using odontochronological methods on dental tissue. We then constructed another dataset of reproductive status from the analysis of all available gonad samples for both males and females. The data
on age and reproductive-status-at-death range from 1997 to 2019. From these data, we obtained vital rates associated with survival and reproduction using a joint model (including survival and reproduction). The survival part is based on the model construction presented in Chapter 3. The reproduction part is based on an Accelerated Failure Time model construction. Vital rates were estimated in three ways: without effect, with covariates (sex and cause of death) and with random effect (years of death). Finally, we filled a Leslie matrix model with the obtained vital rates to obtain the population growth rate and to geometrically project its evolution.

## 4.2 Methodology: Stratified random sampling and Joint modelling

The methodology developed in this study implies five major actions (or steps):

* 1. Define the sampling plan

* 2. Acquire data from biological samples

* 3. Estimate vital rates (with covariates and random effects)

* 4. Build life-tables

* 5. Project the fate of the population

### Sampling of a stranded population

A major problem with randomly selecting individuals for analysis from a stranded population is that representativeness bias is not controlled. Random selection can add representativeness bias to the already existing bias associated with the stranding filter. Ideally, age and reproductive-status-at-death distributions should be exactly the same between the stranded population and our sample. This would allow us to avoid adding bias and to be sure that the only bias associated with our results is due to the stranding filter. One way to control for this selection bias is to implement a stratified random sampling design. This is based on the choice of important criteria defining strata within which random sampling is carried out (Figure 4.2).

<figure><img src="image_61.png" /><figcaption>Figure 4.1: Strandings records on the Atlantic French seashore recorded by the "Observatoire Pelagis" between 1997 and 2021. The number of stranded dolphins has been increasing since 1997 with a record number of strandings in 2020. In the project presented, the time series extends to part of 2019. The whole of 2019 as well as 2020 and 2021 are presented to show the latest stranding estimates.</figcaption></figure>

Data from Observatoire Pelagis website: https://www.observatoire-pelagis.cnrs.fr/?lang=en
<figure><img src="image_62.png" /></figure>

**Figure 4.2: Diagram of the stratified random sampling.** In this figure, the stratified random sampling method is illustrated. From the stranded population, each individual is assigned a value for the criteria of interest. These values are used to stratify the individuals. Within each stratum, random sampling is then carried out. The sample is obtained. The strata presented here and their associated criteria values are schematic. The number of strata is determined by the number of criteria values.

In order to maximise representativeness, a sampling design must be defined that takes into account several criteria that can influence the representativeness of demographic data. We used a statistical sampling method used in various scientific fields (e.g forestry ecology, polls surveys or psychology) that has never been applied to study marine mammal demography from stranded individuals. The objective is to define a sampling plan that will allow the selection of the most representative individuals of the stranded population, from which biological samples will be obtained to provide data on age and reproductive-status-at-death. The 3 main steps (Figure 4.4) are as follows:

► **1.** The first step is to define the need for representativeness. On what basis to select individuals. To select the individuals, we chose 5 criteria that can influence the distributions of the demographic parameters. This selection is made in a non-hierarchical way:

The first is **length** since length is an indicator of age and reproductive status.

The second is **year**, since year can provide information on a possible cohort effect or even a change in the value of vital rates over time.

The third is **sex** since it can be an element influencing age-at-death and it is essential to respect the proportions observed in the stranded population.

The fourth is the **cause of death** because it seems necessary to transcribe the mortality signal as observed in the field.

<figure><img src="image_63.png" /></figure>

**Figure 4.3: Map of all the stranded common dolphins records from 1997 to 2021.** It can be seen that all strandings are recorded on the Bay of Biscay but none are recorded in the English-Channel.

Data from Observatoire Pelagis website: https://www.observatoire-pelagis.cnrs.fr/?lang=en
Examples of external examinations of stranded individuals to determine the cause of death of the animal are described Figure 2.19.

The fifth is the **location** that is not very important and can be removed, but it is intended to select individuals stranded all along the coast.

Having defined the criteria to be considered, it is necessary to calculate their proportion within the stranded population. The proportion of each criterion for the age-at-death dataset can be seen in Figure 4.8.

2. Next comes the stratification step. For each stranded individual recorded in the stranding database, a value for each of the 5 criteria was assigned. Using the example in diagram 4.2, some individuals will have the following criteria values: 180-199cm, 2002, Male, Natural death, Department 17 while others will have: 180-200cm, 2014, Female, Bycatch death, French Department 17. These individuals share common criteria but do not belong to the same stratum because they differ by at least one criterion value. The stratification stage consists of classifying all the individuals in the stranded population database into different strata to ensure inter-stratum representativeness.

3. Finally, random selection within each stratum is used to ensure intra-stratum representativeness. Individuals from the stranding database are selected on the basis of their criteria values but also on the availability of samples. Indeed, it is not possible to obtain teeth and gonads from all stranded individuals despite the existence of the National Stranding Network ("Réseau National Echouage" in French). Sample collection is dependent on the state of degradation of the animal (Figure 2.20).

In summary, the list of individuals in the age-at-death dataset is obtained by stratified random sampling. The list of individuals in the reproductive-status-at-death dataset is obtained by considering all available gonad samples.

## Data acquisition through histology

### Teeth: age-at-death dataset

The number of individuals with an age in the age at death dataset is 642. The methodology used to determine the age of an individual from its dental tissue involves a technique called

<figure><img src="image_64.png" /><figcaption>**Figure 4.4: Main steps in stratified random sampling.** This figure complements the diagram. It describes the important conceptual steps to recreate the sampling protocol.</figcaption></figure>
odontochronology. This technique involves counting the annual layers in the teeth resulting from the incrementation of cementum and dentin in the dental tissue (Perrin and Myrick 1980). The deposition of these layers is mainly due to seasonal phenomena but other phenomena linked to the organism (stress) can cause the appearance of accessory growth layers (Hohn 2009). One year of life corresponds to 1 Growth layer Group (GLG) which consists of an alternating light and dark layer. This technique is considered valid for determining the age of common dolphins (Mannocci et al. 2012; Murphy et al. 2009).

The objective is to observe these growth layers. To do this, it is necessary to treat the teeth. The first step was to decalcify the teeth. Here the teeth were placed in a bath of concentrated DC3 acid. The decalcification time ranged from 3 to 48 hours depending on the size of the tooth. Then teeth have been cut using a freezing microtome in a longitudinal section plan, a cut known as "dolphin cut" (Bowen and Northridge 2010). For each individual, three teeth were removed, all from the mid-left jaw. Six sections were produced from each tooth for a total of 18 sections. These sections were then stained. The staining was carried out with toluidine blue (a frequently used stain) which allows the growth curves to be highlighted (Bowen and Northridge 2010). The stained sections were finally placed on slides for microscopic observation. Three slides per individual were produced, each with 6 sections. An example of the final product is available in Figure 4.5, which shows the growth curves at the apex, middle and base of the tooth for three individuals of different ages and without the same proportion of accessory striae.

<figure><img src="image_65.png" /></figure>

Two age determinations were made to construct the age-at-death dataset. In each case, three readers were required. One

<figure><img src="image_66.png" /><figcaption>**Figure 4.6:** Growth layer groups (GLGs) in a common dolphin teeth. Years are depicted with numbers and neonatal line with "n". Photo from Murphy and Rogan (2006).</figcaption></figure>

<caption>**Figure 4.5:** Tooth sections from three individuals in the age-at-death dataset. For each individual (a, b and c), Growth Layer Groups and accessory striae can be seen. The reading is done from the left or right side of the tooth. The age can be read on three areas for confirmation: the apex (1), the middle (2) and the base (3).</caption>
of the readers was common to both periods, the trainer with the
most experience in age determination. For age determination that
occurred during the project, if the difference between readers
was less than 2 years, estimates were averaged. If the difference
was more or equal to 2 years, readers were discussing to reach a
consensus. If it was not possible, only age reading of the trainer
was taken into account. All readings were made without prior
knowledge of body length or sex.

**Gonads: reproductive-status-at-death dataset**

The number of individuals with age and reproductive status
in the reproductive status dataset is 240. For all the individuals,
age was also available. When the state of decomposition of the
animal allowed collection of the gonads, the left and right gonads
were sampled and preserved in 10% formalin with 10 volumes
of ethanol. Reproductive status was assessed for both males and
females. We also chose to consider males because the analytical
framework allows allows for the inclusion of covariates (Rouby,
Ridoux, and Authier 2021).

the size of the male testicles depends on the season with an increased
size during the mating periods (May to September) (Evans and
Teilmann 2009). It is hypothesised that this size adaptation is
associated with spermatic competition (Murphy, Collet, and Rogan
2005). For this reason, macroscopic examination alone does not
allow the reproductive status of the male to be determined. We
sent the testicular samples to an independent histology laboratory
which provided us with testicular histological slides. From these
cross-sections, we determined the reproductive status based on the
signs of spermatogenesis, including spermatozoa in the tubules
and/or mature spermatozoa present in the epididymes (A. J.
Westgate and A. J. Read 2007; Figure 4.7).

<figure><img src="image_67.png" /></figure>

**Figure 4.7:** Histological sections of common dolphin gonads. The female gonads (ovaries) are indicated by the letter f. De Graaf follicles can be seen in the sections. The male gonads (testicles) are indicated by the letter m. **m.1:** immature individual with small underdeveloped seminiferous tubules and a relatively high degree of interstitial tissue. **m.2:** Mature but regressed testis. Small tubules and high amount of interstitial tissue. **m.3:** mature in production with increased tubule size and few interstitial tissues. **m.4:** higher enlargement of the mature tubule showing signs of spermatogenesis.
Black scale bar = 100 µm
For females, maturity was determined from the ovarian structures which are referred as *corpus*. Only the left ovary was observed as it is usually larger than the right one and contains twice as many *corpus*. The primary follicle, which contains an oocyte embryo, develops into a secondary and then a tertiary follicle before maturing into a "de Graaf" follicle. The oocyte is expelled into the fallopian tube when the follicle reaches the "de Graaf" stage. The follicle then deteriorates as a *corpus luteum* and finally into a scar on the ovary (R. J. Harrison and Ridgwa 1971) which are refereed to as *corpus albicans* (Figure 1 in Appendix 7.4). The concept of persistent *corpus albicans* have been questioned for the common dolphin and it is now assumed that it is not possible to estimate the number of gestation based on the presence of *corpus albicans* (Dabin et al. 2008). Table 4.3 summarises the determination of the reproductive status of females based on histological observation.

<table><caption>Table 4.3: Characteristics of the different reproductive stages.</caption><thead><tr><td>Ovarian features</td><td>Reproductive state</td></tr></thead><tbody><tr><td>No mature follicle</td><td>Immature</td></tr><tr><td>De Graaf follicle and no <i>corpus albicans</i></td><td>Pubsent</td></tr><tr><td>De Graaf follicle and one or some <i>corpus albicans</i></td><td>Resting mature</td></tr><tr><td><i>corpus luteum</i> with or without a fetus</td><td>Pregnant</td></tr><tr><td><i>corpus luteum</i> and productive mammary glands</td><td>Mature pregnant lactating</td></tr></tbody></table>

The definition of pubescent status is possible for both sexes and for several species of delphinids (Murphy, Collet, and Ro-gan 2005; Goodall et al. 1997; Rosas and Monteiro-Filho 2002; M. B. Santos et al. 2008). For females the age-at-first-reproduction is commonly assumed when there is a *corpus albicans* (Slooten 1991). Females are assumed to be pregnant as soon as they reach maturity (Mannocci et al. 2012) despite of the non-persistence of ovarian scares (*corpus albicans*) for the common dolphin (Dabin et al. 2008). Using pubescent status, we did not explore the age-at-first-reproduction (AFR) and age-at-sexual-maturity (ASM) as it is commonly done in the literature. We explored the access to puberty. I think that this parameter is more sensitive to life history changes. However, we still compute the proportion of sexually mature females as it is commonly done in the literature in order to better compare our observations with previous works on this population.
<figure><img src="image_68.png" /><figcaption>**Figure 4.8: Comparisons of proportions of each criterion value for the stranding database and the two study datasets.**
The stranding database is shown in yellow. The age-at-death dataset in dark blue. The reproductive-status-at-death dataset in blue-green. Stratified random sampling allows for similar proportions between the age-at-death dataset and the stranding database, including cause of death, years, size and sex. Within the reproductive-status-at-death dataset, there is a large proportion of samples from the Biocetª program conducted in 2002. There is also a greater proportion of females than males, contrary to what is seen in strandings. Individuals of 180-199cm also seem to be over-represented. The causes of death are globally balanced but not representative of the stranding signal.</figcaption></figure>

<footnote>ª EU-funded BIOCET project (Bioaccumulation of persistent organic pollutants in small cetaceans in European waters: transport pathways and impact on reproduction, EVK3-2000-00027). See Pierce et al. (2008) for a study within this program.</footnote>