Eel density analysis (EDA 2.2.1). Escapement of silver eels (Anguilla anguilla) from French rivers. 2018 report

Abstract

EDA (Eel Density Analysis) is a modelling tool which allows the prediction of yellow
eel densities and silver eel escapement from electrofishing survey networks. The
2018 version of EDA (2.2.1) is based on a dataset of 29183 electrofishing operations
compared to 24 541 for 2015 (version 2.2.0) and only 9 556 in the 2012 version (2.1).
The larger dataset is explained by the inclusion of deep water electrofishing operations
and the eel specific surveys. The model distinguishes from its 2012 (2.1) version by the
prediction of eel abundance per size class, separated with boundaries 150, 300, 450,
600 and 750 mm. The model estimates the eel biomass on the French territory at 1.724
+- (1.242, 2.27) millions of silver eels in 2015.
Anthropogenic impacts corresponding to the glass eel fisheries, amateur and commercial
yellow eel fisheries, silver eel fisheries and turbine mortalities, will be included
in the model to produce stock indicators Bcurrent, Bbest mandatory for the 2018 postevaluation of the eel management plan.

Full text

Eel density analysis (EDA 2.2.1)
Escapement of silver eels (Anguilla anguilla)
from French rivers
2018 report
Cédric Briand (1), Pierre-Marie Chapon (2), Laurent Beaulaton (2)
, Hilaire Drouineau (3), Patrick Lambert (3).
(1) EPTB-Vilaine (2) AFB-INRA (3) IRSTEA
version 2.2.1, 29th September 2018

Abstract
Résumé
EDA (Eel Density Analysis) est un outil de modélisation qui permet de prédire les
densités d’anguilles jaunes et l’échappement d’anguilles argentées à partir des données
des réseaux de pêches électriques. La version 2018 d’EDA (version 2.2.1) est basée sur
un jeu de données de 29183 opérations de pêches électriques contre 24 541 pour la ver-
sion de 2015 (version 2.2.0) et 9 556 pour la version EDA 2.1 de 2012. L’augmentation
du jeu de données s’explique par l’intégration des pêches en milieu profond et des
données des réseaux spécifiques anguilles. Le modèle se distingue également par la
prédiction des densités par classes de tailles séparées par les bornes 150, 300, 450, 600
et 750 mm. Il donne une estimation des biomasses produites sur le territoire Français
métropolitain à 1.724 ±(1.242, 2.27) millions d’anguilles argentées en 2015. Le mod-
èle qui prédit les départs d’argentées permettra d’intégrer les impacts anthropiques
liés aux turbines et à la pêche pour produire une estimation des indicateurs de stock
Bcurrent,Bbest demandés pour le rapportage de 2018.
Mots clés: anguille, densité, anguille argentée, modèle de production, stock, France,
UGA, modèle EDA, règlement CE 110/2007
Abstract
EDA (Eel Density Analysis) is a modelling tool which allows the prediction of yel-
low eel densities and silver eel escapement from electrofishing survey networks. The
2018 version of EDA (2.2.1) is based on a dataset of 29 183 electrofishing operations
compared to 24 541 for 2015 (version 2.2.0) and only 9 556 in the 2012 version (2.1).
The larger dataset is explained by the inclusion of deep water electrofishing operations
and the eel specific surveys. The model distinguishes from its 2012 (2.1) version by the
prediction of eel abundance per size class, separated with boundaries 150, 300, 450,
600 and 750 mm. The model estimates the eel biomass on the French territory at 1.724
±(1.242, 2.27) millions of silver eels in 2015.
Anthropogenic impacts corresponding to the glass eel fisheries, amateur and com-
mercial yellow eel fisheries, silver eel fisheries and turbine mortalities, will be included
in the model to produce stock indicators Bcurrent,Bbest mandatory for the 2018 poste-
valuation of the eel management plan.
Keywords: Eel, migration, Silver eel, production model, stock, France, EDA model, EU
regulation 110/2007

Contexte
Depuis les années 1980, les arrivées de civelles d’anguilles européennes (Anguilla
anguilla) ont diminué à un niveau entre 4 et 12 % de leur niveau de référence entre
1960-1979 (ICES,2017). Pour enrayer le déclin de l’anguille européenne observé
depuis la fin des années 70, le règlement européen 1100/2007, qui se décline dans des
plans de gestion nationaux, fixe comme objectif global ‘d’assurer un taux d’échappement
d’au moins 40 % de la biomasse d’anguilles argentées [...] d’un stock n’ayant subi
aucune influence anthropique’.
Le rapportage à la commission par les états membres de l’UE doit permettre d’évaluer
le niveau actuel d’échappement en anguilles argentées et de fournir une estimation de
la mortalité d’origine anthropique affectant le stock d’anguilles en France. Les dates de
rapportage prévues dans le règlement sont 2012, 2015 et 2018. Le modèle EDA 1.3 a
été utilisé pour produire une première estimation de la biomasse d’anguilles argentées
s’échappant du territoire lors de la mise en place du plan de gestion répondant au
règlement. En 2012, pour le premier rapportage, la version EDA 2.1 a été utilisée pour
fournir une nouvelle estimation des biomasses produites. La version du modèle (2.2.0)
a permis de mieux prendre en compte le calcul des impacts anthropiques et de limiter
l’incertitude quand aux productions d’anguilles argentées pour les milieux profonds.
Cette version du modèle 2.2.1 est simplement une mise à jour des données avec l’ajout
de trois années de 2012 à 2015. Il a été traduit en anglais pour faciliter l’échange et
l’évaluation du modèle dans le cadre du rapportage.
Les auteurs
• Cédric Briand, Responsable du pôle milieu naturel et animation bassin,
cedric.briand@eptb-vilaine.fr, EPTB-Vilaine
Calibration du modèle, construction des bases de données Postgres avec Pierre-Marie,
rapport & figures. Cartes avec Benjamin Magand (EPTB Vilaine).
• Laurent Beaulaton, chef du pôle AFB-INRA,
laurent.beaulaton@afbiodiversite.fr, AFB
Modèle d’argenture, supervision, coordination et relecture.
• Pierre -Marie Chapon, pôle ONEMA-INRA,
pierre-marie.chapon@onema.fr, ONEMA.
Compilation des données, validation des étapes de la construction des jeux de données
du modèle, construction des bases excel, centralisation et échanges avec les acteurs de
terrain.
• Hilaire Drouineau, Ingénieur de recherches, hilaire.drouineau@irstea.fr,
IRSTEA Bordeaux, pôle écohydraulique ONEMA-IMFT-IRSTEA.
Assistance technique et évaluation, relecture.
• Patrick Lambert, Ingénieur de recherches, patrick.lambert@irstea.fr,
IRSTEA Bordeaux, pôle écohydraulique ONEMA-IMFT-IRSTEA.
Assistance technique et évaluation, responsable du développment du modèle EDA pour
l’IRSTEA.
1

Contents
I Résumé opérationnel (en Français) 7
II Report 13
1 Introduction 14
2 Material and methods 16
2.1 A short historical overview of EDA ..................... 16
2.2 Modelling strategy ............................... 16
2.3 Dataset construction ............................. 17
2.3.1 Dam data ................................ 17
2.3.2 Electrofishing data .......................... 18
2.4 Other variables ................................. 23
2.5 Model calibration ............................... 23
2.6 Silvering .................................... 23
2.7 Predictions ................................... 25
2.8 Statistic and database tools used to calibrate the model .......... 25
3 Results 27
3.1 Topological variables ............................. 27
3.2 EDA adjustment ................................ 29
3.2.1 Delta model .............................. 29
3.2.2 Gamma model ............................. 35
3.3 Model diagnostic and prediction ....................... 40
3.3.1 Delta model .............................. 40
3.3.2 Delta-Gamma model ......................... 40
3.4 Temporal trends ................................ 48
3.4.1 Trend of yellow eel abundance per size class ............ 48
3.4.2 Trends in silver eel abundance .................... 49
3.4.3 Comparison to the recruitment series ................ 49
3.5 Analysis of model responses ......................... 50
3.5.1 Fishing type .............................. 50
3.5.2 Difficulty of access .......................... 52
3.5.3 EMU .................................. 54
3.6 Silvering rates ................................. 56
3.7 Silver eel numbers ............................... 59
3.8 Synthesis of results per EMU ......................... 61
3.9 Comparison with known productions .................... 63
2

4 Discussion 66
4.1 Temporal trend in escapement ........................ 66
4.2 Search for bias in the time series ....................... 66
4.3 Electrofishing type .............................. 67
4.4 Spatial repartition of eels. .......................... 68
4.5 Under estimation of eel production by EDA model ............ 69
4.6 Importance of large eel in the reproductive stock ............. 70
4.7 Perspectives .................................. 70
5 Glossary 76
III Annexes 79
Annexe 1: Equations 80
Annexe 2: : Comparison ERS-RHT 82
Annexe 3: Data source for eel specific surveys 86
Annexe 4: Données concernant les ouvrages 89
Annexe 5: Model response variables 90
Annexe 6: Predictions without dams 92
3

List of Figures
1.1 French management units .......................... 15
2.1 Percentage of missing data in the ROE ................... 17
2.2 Electrofishing types used in the model ................... 20
2.3 Eel densities observed in electrofishing from the BdMap and BD Agglo
(AFB data) ................................... 22
2.4 Eel densities observed in electrofishing from the RSA ........... 22
2.5 Histograms of silvering rates predicted by Beaulaton et al. (2015) model 24
3.1 Maps of Difficulty of access .......................... 28
3.2 Response curve for model ∆for four variables ............... 30
3.3 ∆model response for Difficulty of access Ai................ 31
3.4 Response curves per size class for the ∆model for year .......... 32
3.5 response curves for the ∆model for width ................. 33
3.6 Response curves for model Γfor four variables .............. 36
3.7 Response for the Γmodel for the Difficulty of access Ai.......... 37
3.8 Response curves for the Γmodel according to year for each class size . . 38
3.9 Response curves for the Γmodel for width ................. 39
3.10 Presence absence ∆model diagnostics ................... 41
3.11 Presence probability of eel .......................... 42
3.12 Map of the 50 % occurence for class <150mm, 150-300 et 300-450mm . 43
3.13 Map of residuals ................................ 44
3.14 Map of yellow eel densities predicted per size class ............ 46
3.15 Map of yellow eel densities .......................... 47
3.16 Trend in total yellow eel abundance for classes <150mm, 150-300, 300-
450mm and > 450mm ............................ 48
3.17 Historical trend of the number of Silver eel produced in French streams
(Bpotentiel) ................................... 49
3.18 Trend in recruitment and in size class series ................ 50
3.19 Eel capture probability for different electrofishing protocols (∆model) 51
3.20 Model variables and Silver eel production ................. 53
3.21 Distribution of the number of predicted silver eels ............ 54
3.22 Silver eel production and water surface ................... 55
3.23 Map of silvering rate of eel different size-class ............... 56
3.24 Map of silver eel sex-ratio produced in France ............... 57
3.25 Map of the proportion of small females <600 mm ............. 58
3.26 Map of the number of silver eel produced in France ............ 59
3.27 Map of the number of silver eels for the different size class ........ 60
3.28 Map the cumulated downstream migration ................ 61
4

3.29 Comparison of production estimated by EDA and in index rivers . . . . 65
5.1 Diagrams of comparison ERS-RHT ..................... 83
5.2 Hierarchichal clustering showing variable collinearity .......... 84
5.3 Répartion of electrofishing data ....................... 87
5.4 Eel specific survey database diagram .................... 88
5.5 Map of dam number as recored in ROE ................... 89
5.6 Map of elevations Hused in the model ................... 90
5.7 Map of July temperatures θused in the model ............... 91
5.8 Map of river width Wused in the model .................. 91
5.9 Cross correlations between the ICES wgeel recruitment time series and
series of yellow eel abundance per size class ................ 93
5

List of Tables
2.1 Number of operation and number of electrofishing stations used to cal-
ibrate the EDA2.2.1 in France. Nb ope = nb of electrofishing operations,
nb ope (d>0)= number of operation with eel. ............... 21
3.1 GLM-dam height ............................... 27
3.2 Table of model coefficients .......................... 34
3.3 Relative density coefficients for models Γand ∆, the model coefficients
corresponds to the ratio of density using full fishing ωf ul as a reference. 51
3.4 Average yellow eel density in eel/{100meter............... 61
3.5 Number of yellow eels (in million) predicted by EDA model ....... 62
3.6 Number of silver eel predicted by the EDA model. ............ 62
3.7 Biomass of silver eel (in ton) predicted by the EDA model. ........ 62
3.8 Table comparing predicted and observed numbers- part1 ........ 64
3.9 Table comparing predicted and observed numbers- part2 ........ 65
5.1 Table comparing ERS - RHT ......................... 85
5.2 Predicted dam height ............................. 89
5.3 Number of silver eels predicted by EDA on the RHT for a prediciton
without dams. ................................. 92
5.4 Biomass of silver eels ton predicted by EDA2.2.1 on the RHT river net-
work for a prediction without dams. .................... 92
5.5 Electrofishing station removed from the dataset. ............. 94
5.6 Water surface calculated on RHT km2.................... 95
6

Première partie
Résumé opérationnel (en Français)
7

Le modèle EDA 2.2.1 prédit les abondances d’anguilles jaunes, puis argentées à
partir des nombres d’anguilles mesurés lors des pêches électriques en France. Le ré-
seau hydrographique théorique est utilisé pour appliquer le modèle à l’ensemble des
segments hydrographiques et calculer la densité d’anguilles et les effectifs d’anguilles
jaunes. Un modèle d’argenture (Beaulaton et al.,2015) est ensuite utilisé pour calculer
la production d’anguilles argentées en effectif et en biomasse. Le modèle EDA ne s’ap-
plique qu’aux rivières, il ne donne pas d’estimation de production pour les lagunes, les
marais, les lacs et les zones côtières.
L’approche de modélisation est basée sur un modèle delta-gamma (Stefánsson,1996)
qui permet d’expliquer une large proportion de la variabilité de données d’abondance
principalement quand il y a une surreprésentation des valeurs nulles. Le modèle EDA
combine un modèle de présence-absence (modèle ∆ou binomial) pour déterminer la
probabilité d’une densité observée non nulle, et un modèle de densité (modèle Γ) pour
déterminer le niveau des densités non nulles. La multiplication de ces deux modèles
(modèle ∆Γ ) permet ensuite de calculer la densité d’anguilles prédite dans un tronçon.
Le modèle utilise les hauteurs d’ouvrage et la distance à la mer pour caractériser
l’accessibilité des bassins versants pour l’anguille. Le cumul des hauteurs d’ouvrages
est calculé depuis la mer, et les valeurs manquantes font l’objet d’une prédiction par
modélisation qui prend en compte les caractéristiques locales (pente et débit), la zone
géographique et le type d’ouvrage. D’autres variables décrivant les conditions au ni-
veau du tronçon hydrographique : pente, débit, température, largeur, UGA ont été uti-
lisées en plus de l’accessibilité pour caractériser les conditions au niveau des stations
de pêche. Les autres variables décrivant les pressions anthropiques : pêche civellière,
pêche d’anguille jaune, pollution n’ont pas été utilisées dans le modèle car les données
n’ont pas été jugées comme suffisantes. Les variables concernant l’utilisation du sol
(urbanisation, argriculture...) soit sur le bassin versant entourant le segment hydro-
graphique, soit sur le bassin en amont, n’ont pas non plus été utilisées dans le modèle,
car elles conduisent à des effets probablement factices.
La densité ou la présence d’anguille par opération ont été découpées par classes
de taille, <150, 150-300, 300-450, 450-600, 600-750 et >750 mm et utilisées comme
variable dépendante dans le modèle.
La meilleure calibration du modèle modèle ∆est obtenue en utilisant l’année (comme
facteur), l’unité de gestion anguille (UGA), la température de juillet, le protocole de
prospection (pêche complète, indice d’abondance anguille, pêche complète ciblée an-
guille, pêche grand milieu, pêche en berge), la largeur du cours d’eau, l’accessibilité,
la surface de la station de pêche et la classe de taille. Des réponses différentes en fonc-
tion de la classe de taille sont introduites dans le modèle pour l’accessibilité, la largeur
et l’évolution temporelle . Le modèle prédit correctement 87% des données du jeu de
calibration.
Le pourcentage de déviance expliqué par le modèle est de 40.93% pour un Kappa
de (K=0.580).
Le modèle Gamma explique 46% de la déviance. La meilleure calibration est obte-
nue en utilisant les mêmes variables que le modèle delta, avec l’altitude en plus et sans
8

utiliser la surface en eau de la station (déjà comprise dans le calcul de la densité).
Les prédictions du modèle permettent d’observer une répartition des anguilles à
l’échelle du territoire conforme avec les connaissances disponibles sur l’anguille. Les
anguilles sont présentes sur une bonne partie du territoire, mais la présence en forte
densité (> 5 ind.100m−2toutes tailles cumulées) reste confinée aux zones côtières (Fi-
gure 1).
Figure 1 – Densités d’anguilles jaunes (en anguille.100 m−2) prédites en France Métropoli-
taine par le modèle EDA 2.2.1 en 2015.
La multiplication par un modèle de probabilité d’argenture (Beaulaton et al.,2015)
donne le nombre d’argentées des différentes classes de taille. Le nombre d’argentées est
prédit pour chaque année. Depuis le maximum observé au début des années 1990, la
tendance de production d’anguilles argentées du territoire est en baisse. Cette baisse
n’est toutefois pas continue, et la phase de baisse la plus importante a été observée
entre 1990 et 1995 (Figure 2).
9

Figure 2 – Estimation des effectifs d’anguilles argentées produites au niveau des cours
d’eaux de France métropolitaine. La ligne rouge correspond aux quatre périodes d’une ré-
gression segmentée calée sur la courbe de tendance.
10

Figure 3 – Production d’anguilles argentées, en biomasse, à l’échelle de la France, en 2015
et sa répartition par UGA. La taille des cercles pleins est relative à la biomasse, la taille des
cercles en pointillés noirs à la surface en eau estimée à partir du RHT. Les UGA dont le cercle
est à l’intérieur du cercle bleu ont une productivité plus faible que la moyenne.
Au niveau du territoire métropolitaine, un effectif de 1.724 ±(1.242,2.27) argen-
tées est prédit en 2015 pour une biomasse de 618 tonnes. La production d’anguilles
argentées du territoire français est regroupée à 60% sur les UGA Garonne (19.7%),
Loire (19.7%) et Seine Normandie (19.4%). La Bretagne (13%) et la Corse (3.5%), com-
pensent une surface en eau plus faible par les fortes densités résultant de la facilité
d’accès des cours d’eaux (Figure 3).
Un réseau de rivières index a été mis en place dans le cadre du plan de gestion
de l’anguille en France. Ces rivières renseignent en particulier sur la productivité en
anguilles argentées des bassins de différentes tailles réparties sur la façade Atlantique
et la Manche. La comparaison des effectifs produits sur ces bassins versants et des
résultats d’EDA montrent que les ordres de grandeur produits par le modèle sont glo-
balement sous-estimés d’un facteur 3 du fait de la sous estimation des surfaces en eau
dans le RHT (Figure 4).
11

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10
100
103
104
105
10 100 103104105
Obs NsBV t
Pred (EDA) NsBV t
Rivière
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Dronne Monfourat
Dronne Poltrot
Dronne Renamon
Frémur
Loire
Sèvre Niortaise
Somme
Soustons
Vilaine
estim.
●● corr.
estim.
Figure 4 – Comparaison des productions estimées par EDA (c
NsBV ,ta) et des productions
des bassins versants des rivières index et des pêcheries d’argentées NsBV ,t . Deux cas sont
considérés, (N) estimation de la production totale annuelle, dans le cas du Frémur et de
Soustons, les estimations d’EDA (•) sont augmentées pour prendre en compte les surfaces en
eau des lacs et des étangs, très importantes sur ces bassins et qui ne sont pas estimées dans
le RHT.
12

Part II
Report
13

Introduction
The european eel stock (Anguilla anguilla) range extends from the Baltic sea to the
Mediterranea Sea. Reproduction takes place in the Sargasso sea (Schmidt,1922;Miller
et al.,2014). European eel leptocephalus larvaes cross the Atlantlic and will later
transform into glass eel when they reach the continental slope (Tesch,1980;Schmidt,
1909). The glass eel phase will, using tide currents, colonize costal areas, estuaries and
possibly when conditions are favorable, progress inland during a short colonization of
fresh water. The elvers then turn into yellow eels, and this phase will gradually achieve
colonization of the continental freshwater habitats (Naismith and Knights,1988;Feun-
teun et al.,2003). This colonisation is hampered by dams (White and Knights,1997;
Briand et al.,2006). The distribution of eels is naturally concentrated in the down-
stream part of water basins (Ibbotson et al.,2002). Upon reaching a size of 30 cm, eel
will settle and most of them will remain confined in a reduced homerange territory for
the remainder of their continental life (Laffaille et al.,2005a;Tesch and Thorpe,2003;
Imbert et al.,2010). When they reach a certain size (Svedäng et al.,1996) yellow eels
will metamorphose into silver eels (Durif et al.,2006). The male silver eels mature at a
lower size and age than their female counterparts, the size limit between the two sexes
is about 45 cm (Tesch and Thorpe,2003).
From the end of the 1980’s, the arrival of european glass eel (Anguilla anguilla)
have diminished to a minimum level in 2009 of about 1 to 5 % of their level before
the decline. From 2010, a slight increase in recruitment has been observed, but the
level of glass eel arrival remains low, between 4 and 12 % of the reference level of the
1960’s-1970’s (ICES,2017). As a consequence in 2017, ICES in its advice indicates that
recruitment indices remain well below the 1960-1979 reference levels, and there is no
change in the perception of the status of the stock. The advice remains that all an-
thropogenic impacts (e.g. recreational and commercial fishing on all stages, hydro-
power, pumping stations, and pollution) that decrease production and escapement
of silver eels should be reduced to - or kept as close to - zero as possible.
The EU regulation 1100/2007 establishes a management framework whose object-
ive is to restore the eel stock. EU Member States have developed Eel Management Plans
(EMPs) for their river basin districts, designed to allow at least 40% of the biomass to
escape to the sea with high probability, relative to the best estimate of escapement that
would have existed if no anthropogenic influences had impacted the stock.
To test wether management objectives set by the EU regulation have been met,
the biomass of spawners produced by the different management units from member
states must be assessed, but also the mortality rates that eel experience from anthropic
source. France has to deliver a report to the commission, which contains an evaluation
of management measures applied to its share of the eel stock. The report must detail
14

results per eel management unit EMU (Figure 1.1).
In practise, it would be extremely hard to count the real number of silver eel pro-
duced at the scale of the French metropolitan territory. Indeed, the silver eel produc-
tions of 1200 basins in France are seldom estimated and those estimate are rarerly
exhaustive. The estimation of the silver eel production has been made using the EDA
(Eel Density Analysis) model. It uses yellow eel electrofishing data to predict densities,
and a silvering model to predict the number of silver eel produced per river stretch.
Figure 1.1 – Delimitation of the 10 french (EMUs) in metropolitan France, and localtion of
index rivers (map ONEMA/Eau France)
The objective of this work is to apply EDA on the french EMUs and provide an
estimation of French eel production. The modelled production will be compared to
actual numbers counted from different index rivers in France.
15

Material and methods
2.1 A short historical overview of EDA
The EDA model was initially built EDA 1.x (EDA 1.1, EDA 1.2, EDA 1.3) in Britany
and Loire-Britany to predict the impact of dams on eel density, and try to provide the
best classification of obstacles (Leprevost,2007;Hoffmann,2008). From this work, in
a preliminary attempt, the EDA 1.3 version was applied to France for the eel manage-
ment plan. This version, which did not integrate the effect of obstacles, estimated a
production of 12 000 t of silver eels 1.
The EDA2.x (EDA2.0 et EDA2.1) versions have explored many explanatory vari-
ables such as landover (Corine Land Cover) or the impact of obstacles.
EDA 2.0 corresponds to the application of the model to 5 european EMUs and on a
virtual dataset (CREPE) in the POSE EU pilot project (Walker et al.,2011). It is based
on the CCM v2.1. This method has also been applied to Ireland (De Eyto et al.,2015).
EDA 2.1 (Jouanin et al.,2012) corresponds to the model used for the second French
reporting on 10 EMUs. It is based on the RHT (Pella et al.,2012). For river obstacles, it
was based on the cumulated number of obstacles from the sea. EDA2.1 results estimate
about 2200 t of silver eels in 2009 but the RHT water surface is only 2 114 km2, a third
of the watersurface reported in the BD Carthage database. Waterbodies, the lower part
of estuaries, and wetlands are not covered.
EDA 2.2.0 (Briand et al.,2015a) uses size structure for response with size classes of
150 mm. It also uses a wider of electrofishing types, including electrofishing on river
banks and point abundance sampling for deep rivers. The current version EDA 2.2.1
is just an update of the 2.2.0 model with data from 2012-2015.
2.2 Modelling strategy
The model is based on the delta-gamma approach (Stefánsson,1996) which allows to
explain a large part of the variance of abundance data especially when null values are
overrepresented. The EDA model combines :
• a presence - absence model (∆or binomial model) to determine the probability
of a non-zero observed density,
• and a density model (Γ) to assess the level of abundance in non null data.
1150 millions of Silver eel with an estimated weight of 0.8 kg. The total water surface was estimated
at 6 727 km2including 3 637 km2for the polygon layer (with 1 500 km2of estuaries and 110 km2of
lakes) and 3 090 km2for the vector layer of the BD Carthage
16

The multiplication of both models (∆Γ model) allows then to predict the density of eel
on a river segment. Each time, generalized additive models (Hastie and Tibshirani,
1990) have been used, with for the ∆model a binomial distribution and a logit link
and for the Γ, model, a gamma distribution and a log link.
2.3 Dataset construction
2.3.1 Dam data
The dataset has been built from the ROE. Missing values have been modelled as data
were quite heterogeneous between parts of France, and were sometimes systematically
missing in some areas (Figures 2.1,5.5) . The model uses flow, dam type and the River
segment slope to predict the height of the dam (see (Briand et al.,2015a) and Annex
III). The variable used in the model (h0) is either the reported height of the dam (h), or
Figure 2.1 – Percentage of missing data in the ROE for dam’s height.
the value predicted by Briand et al. (2015a) model (ˆ
h) when the height was missing in
the ROE database.
The cumulated dam height (Σh0
λi) has been calculated from the downstream part of
the streams (Equation 2.1). It is a very good descriptor of eel abundance variations in
all calibrations made with EDA models (Basque country, Loire, Brittany...) (Hoffmann,
2008;Walker et al.,2011;Jouanin et al.,2012).
Cumulated distance from the sea have been calculated in a similar way by adding
17

the sum of individual river segments ilength l:Σli(Equation 2.1).
Σh0
n(λ) =
n−1
X
i=1
(h0(λ,i))
Σli=
n−1
X
i=1
(li) + ln
2
i∈parcours mer {1...n}
(2.1)
The cumulative impact might not depend solely on the cumulated heights of the
dams but also their individual height: a 3m dam will have more impact than a succes-
sion of 3 dams of 1 meter. To test this assumption, a transformation has been applied
to dams higher than one meter (equation 2.2) :
h00 (λ) = 






h0λsi h0>1
h0si h061(2.2)
Distance to the sea and transformed dam height are two variable tested in the
model. But they are correlated. To combine them in one variable, the accessibility
Aiis defined as the sum of the distance to the sea and the cumulated dam height, that
an eel has to face before reaching a river segment i(Formule 2.3):
Ai(λ,β) = Σli+βΣh00
λi (2.3)
From the best model calibrated for EDA for other variables used in the model (see
next paragraph), the coefficient combination βand λ(λ∈[1,1.2,1.5,2]) providing the
lowest AIC (or best goodness of fit) have been selected. The optimisation has been a
step by step process, searching in turn for the best coefficient λ, then to the best β
coefficient.
2.3.2 Electrofishing data
Electrofishing data come from two sources : the large majority comes from the his-
torical BDMAP database from ONEMA and an addition temporary database BD Agglo
for most data after 2015 (N=26623). The remainder comes from a database built using
eel monitoring framework data (RSA) (N=2560).
2.3.2.1 BDMAP data
BdMap data correspond to electrofishing operations using different fishing protocols
(Belliard et al.,2008;Poulet et al.,2011), which are more or less suitable to describe
eel abundance. The previous version of the model (version 2.1) (Jouanin et al.,2012)
was only using two pass ectrofishing prospected on foot, i.e. complete electrofishing in
shallow area to build the prediction. This selection, while allowing the best quality for
calculation of the density at the scale of the station was proven biased when it came
to describe the abundance in the deep part of the river. This was demonstrated in
the POSE project by testing on known (but hidden to the modeller) theoretical river
networks(Walker et al.,2011).
For EDA 2.2.0, the choice was made to try to include other kind of electrofishing
in the model calibration. A sampling protocol variable (ω) describes the various type
18

of electrofishing protocols used : ωf u l full (two pass) electrofishing, ωbf bank fishing,
and ωdhf deep habitat fishing (partial point surveys) (Briand et al.,2015a).
The historical dataset contains too few data before 1984 so those have been re-
moved, but even before 1994 the number of electrofishing available remains low (Fig-
ure 2.3).
2.3.2.2 Eel specific electrofishing
Eel specfic survey data (RSA database) have been collected on index rivers (Somme,
Vilaine, Soustons, Parc Marais Poitevin) or during regional eel specific surveys (see An-
nex III). The method used is either eel specific point sampling (eel specific abundance
index ωeai ) (Germis,2009b,a;Laffaille et al.,2005b) or eel specific complete fishing
ωf ue (Feunteun,1994). These methods differ from the standard methods by keeping
the electrode for a longer duration, at least 30 seconds at a specific location (Figure
2.4).
2.3.2.3 Water surface
Densities are calculated as following:
Full fishing For either eel specific surveys ωf ue or standard electrofishing ωf ul , the
water surface corresponds to the water surface of the station. Stations where
water surface was reported as larger that 3000 m2have been removed from the
dataset, while stations where the surface was too small have been manually cor-
rected using the same station at other dates.
Bank fishing ωbf The water surface corresponds to 4 times the length of the station :
we consider that an anode placed in the water 0.5 m from the bank will reach an
additional distance of 1.5 m from the center of the anode, and that bank fishing
is done on the two banks.
Deep habitat fishing ωd hf Deep habitat fishing is done by point sampling, a surface
of 12.5 m2(1.5 m of action radius and 0.5 m of electrode move) is used as a
reference in the calculation (Belliard et al.,2008). This surface was correctly
reported in the database with 75 or 100 points for one station. The more standard
value of 100 points has been used as a replacement in the rare cases when both
the surface and the number of points were missing in the database.
Eel specific sampling ωeai For eel specific abundance index, a surface of 12.5 m2has
been used, as in the deep habitat sampling.
The surfaces are used to calculate the most accurate indice of eel density, though
we know it makes little sense in the case of point sampling. In the model, the predic-
tions are made on complete fishing and the other data serve as standardized estimates,
whose variations are used to provide information on eel abundance in the downstream
part of large rivers where complete fishing is not possible.
2.3.2.4 Estimation of total number in a station
The densities have been calculated using Carle and Strub (1978) (FSA package Ogle,
2017) for fishing with two pass or more. For fishing with only one pass, data have been
extrapolated using using the average fishing efficiency (ef ). Fishing efficiency, defined
as ef = 100∗N bp1/NCS is calculated as ef = 65.6 for complete fishing (N=15 856), ef =
19

Figure 2.2 – Electrofishing types used in the model, source BdMap,BD Agglo and RSA
database.
20

64.5 for eel specific fishing (N=445) and ef = 39.2 for bank fishing (N=2 805). Fishing
with only one event are the most frequent (94%) for bank fishing, and correspond to
75% to 3% of complete fishing operations and eel specific complete fishing. A lower
efficiency (40%) has been chosen for bank fishing and a common value rounded to 65%
for complete fishing and eel specific fishing methods.
Table 2.1 – Number of operation and number of electrofishing stations used to calibrate the
EDA2.2.1 in France. Nb ope = nb of electrofishing operations, nb ope (d>0)= number of
operation with eel.
EMU
nb ope.
nb ope. (d>0)
nb stations
month
year
Adour 971 677 392 2-12 1985-2015
Artois-Picardie 822 507 406 3-12 1987-2015
Bretagne 2556 2287 1097 1-11 1985-2015
Corse 379 305 130 2-12 1988-2015
Garonne 3912 1613 1403 1-12 1985-2015
Loire 5536 2085 2484 1-12 1985-2015
Meuse 767 132 365 1-12 1985-2015
Rhin 2495 661 1268 1-12 1985-2015
Rhône-Méditerranée 6430 1086 2855 1-12 1985-2015
Seine-Normandie 5315 2934 2107 1-12 1985-2015
France 29183 12287 12504 1-12 1985-2015
2.3.2.5 Operations removed from the dataset
Batches of illegally caught glass eel seized during enforcement operations (Adour) or
glass eel used for experiments (Loire) have been transported, quite often nearby elec-
trofising locations. Some fishing operations containing unexpectedly high small eel
densities, at several hundred kilometers from the sea have been discarded. They were
characterized by a sharp increase in small size class numbers followed by an ageing of
the eels. Those data force positive responses of delta and gamma models gam model
smoothers sometimes at quite large distance from the sea, and those results can be con-
sidered as biased and not representative of what is happening in most river courses.
The corresponding electrofishing stations are detailed in annex (Table 5.5).
21

Figure 2.3 – Eel densities observed in electrofishing for 100 m2, source BdMap and BD
Agglo. Data correspond to data selected in the model and collected from 2009 to 2015.
Figure 2.4 – Eel densities observed in electrofishing for 100 m2, eel specific surveys (RSA),
all years. Data correspond to data selected in the model and collected from 1998 to 2015.
22

2.4 Other variables
Most topological related variables like river width, flow, altitude and temperature
come from the RHT which computes these variables at the level of the segment. Other
variable like land cover have not been included after a carefull check of their possible
use in previous versions of EDA.
2.5 Model calibration
The 2.1 version of the EDA model used densities as dependent variable. In the 2.2
version the eel have been separated into size class τfor each electrofishing operation.
Size classes used in the model correspond to <150, 150-300, 300-450, 450-600, 600-
750 and >750 mm.
Variables have been tested for co-linerarity (Figures 5.2 et 5.1, Table 5.1 Annexe
III). Models have been selected according to the Akaike (AIC) criteria. The linearity of
model responses have been tested and variables for which a non linear response did
not bring an adjustment gain have been entered as linear responses (without spline) in
the final model. For GAM the degrees of freedom have been fixed before adjustment
to avoid overparametrization.
2.6 Silvering
EDA2.0 and 2.1 was considering a fixed silvering rate Πof 5% (Jouanin et al.,2012) or
2.5 % for Ireland (De Eyto et al.,2015). In the current version, the silvering probability
Πτ,i varies on each river segment. It is based on a model fitted on 1583 electrofishing
operations over 797 stations in France (Beaulaton et al.,2015). After a qualitative
assessment and data validation process, the silvering stage of eels has been predicted
according to Durif classification Durif et al. (2006,2009).
The mean silvering percentage per size class τhas been described using logistic
regressions with the average numbers of yellow eels c
Nyi,τ predicted by the EDA2.2.0 as
a predictor. The processes of model calibration and the result discussion are presented
in Beaulaton et al. (2015) report.
On average, the silvering rate used in EDA2.2.1 is larger than the silvering rate of 5
% used in the 2.2.0 and 2.2.1 models (Figure 2.5).
However, the 2.1 applied a silvering potential to the total density, that is, without
distinction of the size classes. In contrast, the EDA2.2 model has only used eels with
a size class larger than 300 mm, with a potential to become silver. These larger eels
represent only 46.5 % of the total number of yellow eels.
23

Figure 2.5 – Histograms of silvering rates predicted by Beaulaton et al. (2015) model. The
silvering rate of 0.05 of Jouanin et al. (2012) model was applied to the total number of eels
predicted by EDA2.0 EDA2.1 in the station.
24

2.7 Predictions
The number of yellow eels Ny is predicted from the model on each river segment i,
from the characteristics of each segment, and assuming that the electrofishing station
would cover a surface of 600 m2and would be prospected with a full two pass method.
Densities on the electrofishing station (c
dyi) correspond to the product of ∆and Γmod-
els. The number of yellow eels (d
Nyi) estimated per river segment correspond to the
product of density and water surface Si. (Formule 2.4) :
c
Nyτ,i =∆τ,iΓτ ,iSi=
dyi ,τ Si
c
dyi=
τ=750
X
τ=150 
dyi ,τ
(2.4)
with τsize class of eels, ithe river segment.
The number of silver eels is calculated as the product of numbers in each size class
with the silvering probability of this same class Πτ,i in each River segment of the RHT
(Beaulaton et al.,2015) (Formule 2.5):
c
Nsτ,i =c
dyτ,iSiΠτ ,i (2.5)
The biomass is calculated using the Silver eel mean weight ¯
pτ,i (Beaulaton et al.,2015)
(Formule 2.6): . b
Bsτ,i =c
Nsτ,i ∗¯
pτ,i (2.6)
Size-fecundity relationships are rare for european eel, however MacNamara and
McCarthy (2012) have recently proposed a relation for Irish silver eels (Formule III):
Fτ(τ > 450) = c
Nsτ,i ∗10−2.992+3.293∗log10 ¯
lτ(2.7)
A confidence interval on the prediction is obtained using the conf int.gam function
in package mgcv. This confidence interval is approximated as it does not account the
selection of smoothing components in the model. The 95 % confidence interval of
the number of yellow eels predicted by the ∆Γ model is calculated by multiplying the
confidence intervals in both models (Formule 2.8). This calculation overestimates the
true confidence interval in the model.
d
Nyi∈





X
i
(b
∆i−2SE(∆i))(b
Γi−2SE(Γi))Si,X
i
(b
∆i+ 2SE(∆i))(b
Γi+ 2SE(Γi))Si





(2.8)
with Siwater surface of the river segment. Here, we ignore uncertainties related to the
prediction of water surfaces.
This report uses a threshold of 450 mm as the limit between males and females,
this means that silver eels shorter than 450mm will be considered as males.
2.8 Statistic and database tools used to calibrate the model
All calculations have been made using postgreSQL and R 3.4.3 software, with in par-
ticular the use of the following packages : PresenceAbsence (Freeman and Moisen,
25

2008), mgcv (Wood,2006), visreg (Breheny and Burchett,2014), stargazer (Hlavac,
2013), sweave (R Core Team,2013), knitr (Xie,2014), ggplot2 (Wickham,2009), sqldf
(Grothendieck,2017). Historical trends have been calculated using the segmented
package fixing a priori the number and areas of breakpoints in the regression line
(Muggeo,2008).
26

Results
3.1 Topological variables
The heights of dams was not homogeneously recorded accross France (Figure 2.1). The
amount of information seems nevertheless sufficient to characterize migratory trans-
parency from obstacle height data (Figure 3.1 gives an overview of cumulated impact
which is consistent with our expertise).Thereby, this information is better than in the
previous model (2.1), which could only take into account the count of dams from the
sea (Jouanin et al.,2012), as too many data concerning height was missing.
It is however necessary to model missing values to homogeneize data at the scale
of the French territory The GLM model retains slope ϕ, flow Qand dam category
(κ=dam, spillway, gates, rockfilled splillway . . . ). The most important variable is the
type of dam (Table 3.1). A separate prediction of height is done in each EMU U(For-
mule 5.1).
log(h)∼log(Q+ 1) + log(ϕ+ 1) + κ:U(3.1)
A routing algorithm based on hierarchical tree-like structure of the network allows to
calculate distance to the sea (Figure 3.1c) and the cumulated height of dams using the
various transformed height variables (Figure 3.1b). In areas were multiple obstacles
are reported, there might be cumulated heights larger than field altitude when pre-
dicted height of dams are used (Figure 3.1b in grey). However, this type of informa-
tion also exists when using raw data from the national database ROE in areas of low
altitude (Figure 3.1a in grey).
Df Deviance Resid. Df Resid. Dev F Pr(>F)
NULL 24649 18236.83
log(Q+ 1) 1 455.8 24648 17780 768.11 0.0000
log(ϕ+ 1) 1 233.7 24647 17547 393.83 0.0000
U8 123.7 24639 17423 26.06 0.0000
κ6 2566.8 24633 14856 720.84 0.0000
U:κ48 266.6 24585 14590 9.36 0.0000
Table 3.1 – GLM model of height according to the dam’s type κ, slope ϕ, flow Qand EMU
U.
27

(a) Σh(b) Σh0
(c) Σl(d) Σh01.5
(e) A
Figure 3.1 – Maps of variables used to build Difficulty of access. Cumulated height from
the sea. (a) Σh0= cumulated values including predicted height of dams for missing values,
(b) Σh= Cumulated values uncorrected. Gray shaded polygons indicate areas where the
cumulated height is higher than altitude. (c) Σl= distance to the sea, (d) Σh01.5Sum of
transformed height using a 1.5 power (see paragraph 3.5.2), (e) A(λ= 1.5,β = 1.7) (formule
2.3)Difficulty of access, sum from the sea of transformed dam height and distance to the sea.
28

3.2 EDA adjustment
A first selection of response variables was done in EDA 2.2.0 by testing all combina-
tions of uncorrelated variables for the ∆model (2340 combinations) and the Γmodel
(1260).
From this selection of candidate variables, model selection has been performed by
analysing possible interactions with size class. The number of degrees of freedom in
the model was not large enougth to integrate interactions between response variable
and year or EMU, even if those predictions might have been interesting for the analysis.
The calibration of the variables building the Difficulty of access λ(the power) and β
(factor providing the relative importance of dams and distance to the sea) have been
done once the model structure has been set for other variables. For time reasons, no
new calibration has been done with updated data in model 2.2.1.
Models are analysed using their response curves, this means that the response is
predicted by varying one parameter of the model (e.g. river width Wi) while other
are fixed at pre-determined values, either their average, or a value making sense for
model interpretation (e.g. Difficulty of access A=1, log(A)=0). We have chosen to
illustrate the response for eels of small size, near the sea, and on small streams. Figures
3.2,3.3,3.4,3.5,3.6,3.7,3.8 et 3.9 take as a reference : τ(size class)=150-300 mm,
θ(temperature)=18 C, Ai(Difficulty of access)=1, t(year)=2015, ω(electrofishing
type)=full fishing ωf ul ,Wi(width)=3m, Ui(EMU)=Britany, H(altitude)=0.
3.2.1 Delta model (∆)
The best model is (formula 3.2, Table 3.2) :
di,j >0≈α1ti ∗τ+α2Ui+α3θi+α4ω+s(Sp) + s(Wi∗τ)+
s(log(Ai(λ= 1.5, β = 1.7)) ∗τ) + (link =log)(3.2)
tYear, discrete (factor),
UiEMU,
θJuly temperature,
ωFishing protocol,
WiRiver width,
AiDifficulty of access (see formula 2.3),
Sp Electrofishing station surface,
τSize class, the model uses interactions with year,
sPolynomial smoothing function,
α1...α4Model coefficients,
Model residuals.
The presence probablity is first analysed for the response to the surface of the elec-
trofishing station Sp, july temperature θ, electrofishing method ωand EMU U(Figure
3.2). Probabilites of capture increase logically with the water surface, but stop doing
so beyond 1000 m2. Capture probabilities increase with July temperature. For fishing
protocols, regression coefficient come in this order : maximum for full fishing eel ωf ue,
then eel abundance index ωeai , deep habitat fishing ωdhf , full fishing ωf ul and finally
bank fishing ωbf .
29

EMUs in the Biscay area have a large probability of presence but suprisingly, the
maximum coefficient is found in the Seine basin (in the Channel). The coefficients
diminish from North (Britanny) to South (Adour (taken as a reference in Table 3.2)).
They are much lower in the Rhône and Corsica basins flowing in the Mediterranean
sea.
0 500 1000 1500 2000 2500 3000
0.75
0.80
0.85
0.90
0.95
Fished water surface (Sp m2)
prob. mod.(∆)
16 18 20 22 24
0.70
0.75
0.80
0.85
0.90
0.95
1.00
July temperature (θ°C)
prob. mod.(∆)
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
Prospection metho (ω)
prob. mod. ∆)
com coa iaa ber gm
0.3
0.4
0.5
0.6
0.7
0.8
0.9
UGA (U)
prob. mod. (∆)
Rhi
Art
Sei
Bre
Loi
Gar
Ado
Rho
Cor
Figure 3.2 – Response curves for model ∆for the water surface of electrofishing station Sp,
july temperature θ, prospection method ω, and emu U. Predictions are done in reference
conditions indicated at paragraph 3.2.
The Difficulty of access A(Formula 2.3) causes a clear effect on eel presence prob-
ability for size <150mm, 150-300 mm, and 300-450 mm. The sigmoid inflexion point
is located near log (A) = 5, which would correspond to a distance of 150 km from the
sea without dams (Figure 3.3). The probabilities of presence are also lower for eels of
large size (>450 mmm) and not significant for eels larger that 750 mm.
The temporal trend of presence probability per size class is constrasted (Figure 3.4.)
The probability to find small eels (<150 mmm Figure 3.11a) in electrofishing increases
from 1998 to 2003 then decreases. A similar breakpoint is found in 2003 in almost all
series (Figure 3.11b,3.11c). Probabilities to catch eels of 450-600 mm increase from
1985 to 1991 then diminish regularly (Figure 3.11d). A similar trend is found for the
600-750 mm size class (Figure 3.11e) but with much lower probabilities.
The presence probability shows an interaction between width and size classes.
Large eels (600-750 mm and >750 mm) have a greater presence probability in wider
streams. The largest increase is observed for the 450-600 mm size class (Figure 3.5).
30

log(Dist. sea + 1.7sumH1.5)
prob. mod. (∆)
0.0
0.2
0.4
0.6
0.8
0 5 10
150
150_300
0 5 10
300_450
450_600
0 5 10
600_750
0.0
0.2
0.4
0.6
0.8
750
Figure 3.3 – Response curve for ∆model for Difficulty of access A(formula 2.3). The pre-
dictions correspond to other variables set to reference conditions as indicated in paragraph
3.2.
Near linear responses are obtained for size classes 150 mm, 150-300 mm and 300 mm.
For the smallest size class of eel the probability is less significant (< 0.05) (Table 3.2).
31

0.65
0.70
0.75
0.80
0.85
0.90
0.95
year (t)
prob. mod. (∆)
1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015
(a) <150 mm
0.90
0.92
0.94
0.96
0.98
year (t)
prob. mod. (∆)
1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015
(b) 150-300 mm
0.90
0.92
0.94
0.96
0.98
year (t)
prob. mod. (∆)
1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015
(c) 300-450mm
0.4
0.5
0.6
0.7
year (t)
prob. mod. (∆)
1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015
(d) 450-600mm
0.05
0.10
0.15
0.20
year (t)
prob. mod. (∆)
1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015
(e) 600-750mm
0.005
0.010
0.015
0.020
0.025
0.030
0.035
year (t)
prob. mod. (∆)
1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015
(f) 750mm
Figure 3.4 – Response curves per size class for the ∆model for year. Attention, the probabil-
ity values on the y axis differ from one plot to the next. The predictions are done in reference
conditions indicated in paragraph 3.2.
32

0 50 100 150 200 250 300
0.0
0.2
0.4
0.6
0.8
1.0
width (W) m
prob. mod. (∆)
150
150_300 300_450
450_600 600_750
750
Figure 3.5 – Response curves for the ∆model for width. Predictions are made using reference
for other variables as indicated in paragraph3.2.
33

Table 3.2 – Coefficients for models ∆and Γand 95% confidence intervals, UEMU (reference
Adour), ωfishing method, ωf ue full eel fishing, ωeai eel abundance index, ωbf bank fishing,
ωdhf deep habitat fishing (reference ωf ul full fishing), θtemperature, Haltitude, tyear, τ
size class, Wwidth, ADifficulty of access. Terms using s() indicate a smoothing function,
the number of degrees of freedom for the smoothing function (edf) are indicated, when edf=1
the response is linear, interaction terms (one per combination year - size), are not reported.
Dependent variable:
Presence absence (∆) density (positive values) (Γ)
GAM GAM: Gamma
(logistic) (log link)
U Art 4.044∗∗∗ (0.059) 0.492∗∗∗ (0.067)
U Bre 4.788∗∗∗ (0.050) 0.348∗∗∗ (0.053)
U Cor 0.283∗∗∗ (0.073) 0.344∗(0.077)
U Gar 2.058∗∗∗ (0.043) 0.312∗∗∗ (0.041)
U Loi 3.232∗∗∗ (0.043) 0.304∗∗∗ (0.045)
U Rhi 4.008∗∗∗ (0.055) 0.565∗∗∗ (0.063)
U Rho 0.243∗∗∗ (0.048) 0.223∗∗ (0.054)
U Sei 7.178∗∗∗ (0.047) 0.383∗∗∗ (0.013)
ωf ue 1.713∗∗∗ (0.048) 1.289∗∗∗ (0.037)
ωeai 1.069∗∗∗ (0.037) 0.031∗∗ (0.035)
ωbf 0.980∗∗∗ (0.033) −0.269∗∗∗ (0.027)
ωdhf 1.261∗∗∗ (0.029) −0.536∗∗∗ (0.027)
θ1.496∗∗∗ (0.010) 0.017NS (0.013)
H− −0.001∗∗∗ (0.0001)
t:τ .. ..
τ(150 −300) −0.79∗∗ (0.307)
τ(300 −450) −0.639∗∗ (0.299)
τ(450 −600) −1.019∗∗∗ (0.304)
τ(600 −750) −1.907∗∗∗ (0.323)
τ(>750) −2.976∗∗∗ (0.408)
s(W)|W:τ(150) .∗∗ (edf = 1.97) −0.008∗∗∗ (0.0009)
s(W)|W:τ(150 −300) .∗∗∗ (edf = 1.98) 0.0003 (0.0005)
s(W)|W:τ(300 −450) .∗∗∗ (edf = 1.98) 0.003∗∗∗ (0.0004)
s(W)|W:τ(450 −600) .∗∗∗ (edf = 1.98) 0.002∗∗∗ (0.0004)
s(W)|W:τ(600 −750) .∗∗∗ (edf = 1.87) 0.0009∗(0.0004)
s(W)|W:τ(>750) .∗∗∗ (edf = 1.98) −0.0002 (0.0006)
s(Sp).∗∗∗ (edf = 2.94)
s(A) : τ(150) .∗∗∗ (edf = 1.97) .∗∗∗ (edf = 1.98)
s(A) : τ(150 −300) .∗∗∗ (edf = 1.98) .∗∗∗ (edf = 1.98)
s(A) : τ(300 −450) .∗∗∗ (edf = 1.98) .∗∗∗ (edf = 1.97)
s(A) : τ(450 −600) .∗∗∗ (edf = 1.98) .∗∗∗ (edf = 1.98)
s(A) : τ(600 −750) .∗∗∗ (edf = 1.97) .∗∗∗ (edf = 1.86)
s(A) : τ(>750) .NS (edf = 1.98) .N S (edf = 1.00)
Constant 0.0∗∗∗ (0.415) 0.787∗∗ (0.371)
Observations 175 068 33 906
Ajusted R20.423 0.221
% Explained deviance 40.9 54.2
Note: N S p>=0.1; ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01; edf=Estimated degrees of freedom
34

3.2.2 Gamma model (Γ)
The best moded writes (formule 3.3) :
di,j [di,j >0] ≈β1ti ∗τ+β2Ui+β3θi+β4ω+β5Wi∗τ+s(log(Ai ,λ=1.5)∗τ) + β6H+(3.3)
tYear (as a factor),
UiEMU,
θJuly temperature,
ωProspection protocol,
WiRiver width,
AiDifficulty of access (see formula 2.3),
τSize class, the model calculates interactions,
sPolynomial smoothing function,
HAltitude,
β1...β6Model coefficients,
Model residuals.
The surface of the station which was one of the response variables used to describe
the presence-absence of eels on a fishing station is not integrated into the Γmodel.
Indeed, it is already taken into account in the calculation of the density.
The effect of the temperature is positive as in the ∆model. Larger altitude result,
as one might expect, in lower density (Table 3.2). The responses for the fishing types
do not follow the order found for the ∆model :
•ωf ue (full fishing for eel) remains the first.
•ωdhf has the lowest coefficient while it ranked second for the ∆model. So there
is a high probability to find an eel during a deep habitat partial electrofishing,
but densities will be low.
•ωeai The eel abundance index ranks second for the Γmodel.
The temperature effect it not significant in the ∆model.
Densities diminish with the Difficulty of access A. Similarly to the ∆model, the
diminution is larger for smaller sizes. Interestingly, response curves for size class 450-
600 mm and 600-750 mm do not have the same modal aspect as they did for the ∆
model: the largest desnities are always found downstream, whatever the size of eels.
Eels >750 mm are not significantly distributed according to Difficulty of access as was
the case of the delta model, and the coefficient adjusted is linear (Tableau 3.2, Figure
3.7).
Annual responses for the Γmodel are very different according to the size class. Sizes
<150 mm, 150-300 mm show a maximum during the 2000th (Figures 3.8a,3.8b and
3.8c). Densities of smaller eels (<150 mm) increase since 2008 (Figure 3.8a). Densities
of class 450-600 and 600-750 mm diminish again from a maximum at the end of the
1980’s (Figures 3.8d and 3.8e).
The size class <150 mm shows the most acute response according to width with
a clear decrease when streams width increase (Figure 3.9 in red). This response is
different to that of the ∆model for wich probability of presence didn’t depend on river
width (Figure 3.5 in red). This result indicates that the small sized eels are found in
large streams but that they will not correspond to high densities, probably because the
propection method is not adapted to small eels. Densities of eel larger than 300mm
tend to increase with stream size.
35

0 200 400 600 800 1000
0.0
0.5
1.0
1.5
Altitude (H) (in m)
Density eel.100m−2 ( Γ )
16 18 20 22 24
July temperature (θ)
Density eel.100m−2 ( Γ )
1.0
1.5
2.0
2.5
3.0
Prospection method (ω)
Density eel.100m−2 ( Γ )
com coa iaa ber gm
EMU (U)
Density eel.100m−2 ( Γ )
Rhi
Art
Sei
Bre
Loi
Gar
Ado
Rho
Cor
Figure 3.6 – Response curves for model Γfor altitude, July temperature, prospection method
and EMU. Predictions are made using reference for other variables as indicated in para-
graph3.2.
36

Dist. sea + 1.7∑H1.5
Density eel.100m−2 ( Γ )
0
5
10
15
0 5 10
150
150_300
0 5 10
300_450
450_600
0 5 10
600_750
0
5
10
15
750
Figure 3.7 – Response curve for the Γmodel for the Difficulty of access A(formule 2.3).
37

10
20
30
40
year (t)
Density eel.100m−2 ( Γ )
1985 1989 1993 1997 2001 2005 2009 2013
(a) <150 mm
5
10
15
20
25
year (t)
Density eel.100m−2 ( Γ )
1985 1989 1993 1997 2001 2005 2009 2013
(b) 150-300 mm
5
10
15
year (t)
Density eel.100m−2 ( Γ )
1985 1989 1993 1997 2001 2005 2009 2013
(c) 300-450mm
1
2
3
4
year (t)
Density eel.100m−2 ( Γ )
1985 1989 1993 1997 2001 2005 2009 2013
(d) 450-600mm
0.4
0.6
0.8
1.0
1.2
1.4
year (t)
Density eel.100m−2 ( Γ )
1985 1989 1993 1997 2001 2005 2009 2013
(e) 600-750mm
0.2
0.4
0.6
0.8
1.0
1.2
year (t)
Density eel.100m−2 ( Γ )
1985 1989 1993 1997 2001 2005 2009 2013
(f) 750mm
Figure 3.8 – Response curves for the Γmodel according to year for each class size . Attention,
the y axis displays different scales.
38

0 50 100 150 200 250 300
0
5
10
15
with(m)
Density eel.100m−2 ( Γ )
150
150_300 300_450
450_600 600_750
750
Figure 3.9 – Response curves for the Γmodel for width.
39

3.3 Model diagnostic and prediction
3.3.1 Delta model (∆)
The ∆model predictions are shown in Figure 3.11 and in Figure 3.12. When they
reach a larger size, eels are found more upstream and the spatial variation in the col-
onization is mostly the consequence of dams reported in the ROE (Figure 3.12). In the
calibration plot for presence/ absence, the Kappa is maximum (K=0.580) for a pres-
ence probability of about 40% (Figure 3.10). This means that at the 40% threshold,
there will be a large number of (65%) stations where the actual presence is correctly
predicted, without diminishing too much the number of stations where eel are absent
and the absence is indeed predicted by the model (92%). Finally, at a 40 % presence
probability, the model correcly predicts 87% of the stations in the calibration set.
The percentage of deviance explained by the model is 40.93%. In comparison, the
2.1 model of Jouanin et al. (2012) had a better Kappa (0.71) and a larger percentage
of explained deviance 54 %. But this model was only calibrated on 9 556 operations
against 175 068 lines (operation x size class) for the 2.2.1 version of the model.
The model tends to under-estimate null data in places where eel are absent (Fig-
ure 3.10, see two upper graphs, for probabilities close to zero). This means that far
from the sea, or in areas affected by a large number of obstacles where the presence
probability is low, the ∆Γ model runs the risk to overestimate the eel production. How-
ever, looking at the residual map there is no systematic bias either positive (observed
> predicted) or negative (observed < predicted) at the exception of the Rhône basin
for which predictions are probably too optimistic (All dots are black, eel are predicted
as present in areas where they are actually absent 3.13a). Accounting for the migrat-
ory transparency is possibly not sufficient to account for migration difficulties on this
stream in the downstream part. Presence probabilities also seem under-estimated in
the Rhine.
As a whole, presence probability maps shows a progression of the distribution area
as eels grow (Figures 3.11a,3.11b and 3.11c). From 300 mm, the size at which male
eels start to silver, the presence probability of eels in streams tends to diminish, but
the extension of the area where eel are present at low density continues to progress
from class 300-450 to 450-600mm (Figure 3.11d).
The area were eels are present will in practise 1extend to the same level as the 450-
600 mm but given the small proportion of large eels in the population, areas where the
occurence probability is larger than 0.2 tend to shrink for size class 600-750 mm and
750 mm (in green Figures 3.11e et 3.11f).
3.3.2 Delta-Gamma model (∆Γ )
The percentage of deviance explained by the Gamma model is 46%. This value is better
than that obtained during the calibration of EDA2.1 (Jouanin et al.,2012). The log link
of the Γdistributions allows to normalize residuals of the density model (Γ) for which
only positive values have been selected. There does not seem to be any obvious flaw
1The scale is common to all maps and does not display probability of presence lower than 0.2, the
distribution area of 750 mm size eels is thus not visible, to its largest extent, the distribution area of this
size class corresponds to the distribution in Figure 3.11, as the size class 750 mm is the one depending
the less on the distance to the sea in models ∆and Γ.
40

predicted probability
number of plots
0 5000 15000 250000 5000 15000 25000
98245
0.0 0.2 0.4 0.6 0.8 1.0
present
absent
●●
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Observed vs. Predicted
Predicted Probability of Occurrence
observed as proportion of bin
●
●
●
●
●
120076
22300
12884
10831
8977
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
ROC Plot
1−Specificity (false positives)
Sensitivity (true positives)
●
●
0.50
0.22
0.36
●
●
0.50 Default
0.22 Sens=Spec
0.36 MaxKappa
AUC:
0.91 predict.mpa..type....response..
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
Error Rate verses Threshold
Threshold
Accuracy Measures
●
●
sensitivity
specificity
Kappa
Accuracy plot for presence absence
Figure 3.10 – Presence absence ∆model diagnostics. From left to right and top to bottom, (1)
predicted probabilities histogram, bars ordered according to observed values (2) Calibration
graph allowing to evaluate the adjustment quality, (3) Receiver Operating Curve (ROC),
provides a method of evaluation of the model independent of the threshold, a good model
must have a large number of true positive values while the number of false positive remains
low (4) Diagram of error rate versus threshold provides specificity, sensitivity and Kappa
curves according to the threshold.
41

(a) <150 mm (b) 150-300 mm
(c) 300-450mm (d) 450-600mm
(e) 600-750mm (f) 750mm
Figure 3.11 – Presence probability of eel for the ∆model in 2015.
42

Figure 3.12 – Line delimitating areas where the probability falls below one chance on two
for size class <150mm, 150-300 et 300-450mm, this corresponds to the colonisation front
(Feunteun et al.,2008). Predictions are made for year 2015.
43

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