Modelling population dynamics in presence of hybridization

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Modelling population dynamics in presence of

hybridization

Nina Santostasi

To cite this version:

Nina Santostasi. Modelling population dynamics in presence of hybridization. Agricultural sci-ences. Université Montpellier; Università degli studi La Sapienza (Rome), 2020. English. �NNT : 2020MONTG017�. �tel-03144074�

SAPIENZA

Università di Roma

Facoltà di Scienze Matematiche Fisiche e Naturali

PH. D. IN ENVIRONMENTAL AND EVOLUTIONARY BIOLOGY

Cycle: XXII

(A.Y. 2019/2020)

Modelling population dynamics in presence of hybridization

Ph. D. Student

Nina Luisa Santostasi

Supervisors

Coordinator

Prof. Gabriella Pasqua

Prof. Paolo Ciucci

Dept. Biology and Biotechnologies,

THÈSE POUR OBTENIR LE GRADE DE DOCTEUR

DE L’UNIVERSITÉ DE MONTPELLIER

En Ecologie et Biodiversité

École doctorale GAIA

Unité de recherche UMR 5175- CEFE- Centre d’Ecologie Fonctionnelle et Evolutive

En partenariat international avec Sapienza Université de Rome, Italie

Présentée par Nina Luisa Santostasi

 Fèvrier 2020

Sous la direction de Olivier Gimenez et Paolo Ciucci

Modélisation de la dynamique des populations en présence

d'hybridation

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INDEX

1. GENERAL INTRODUCTION……… 2. CHAPTER 1: Development of a multievent capture–recapture model to estimateWKH

prevalence of admixed individuals in wildlife populationV...………...…………..2 3. APPENDIX CHAPTER 1……….………………3 4. CHAPTER 2: EstimatiQJ the prevalence of admixed wolf x dog individuals in a study area in the northern Apennines, Italy……….………..5 5. APPENDIX CHAPTER 2.……… 6. CHAPTER 3: Development of a population-based modelling approach to project hybridization dynamics………...……19 7. APPENDIX CHAPTER 3……….………..……1 8. CHAPTER 4: Development of an individual-based model to evaluate the effect of different hybridization management strategies for the wolf x dog case study………...….1 9. APPENDIX CHAPTER 4……….………….………..……2

1. GENERAL INTRODUCTION

1

1.1 Natural and anthropogenic hybridization

2

Hybridization, the interbreeding of individuals from genetically distinct populations, regardless of 3

their taxonomic status (Allendorf et al. 2001) is acknowledged to be a relatively common 4

evolutionary process both in the plant and animal kingdoms (Hewitt, 1988; Olden et al. 2004; 5

Grabenstein & Taylor 2018). Hybridization is mainly observed between otherwise allopatric taxa 6

that come into contact due to natural (natural hybridization) or anthropogenic causes (anthropogenic 7

hybridization, e.g., changes in the abundance and distribution of species, the removal of barriers 8

that cause isolated or restricted species to expand, and/or the uncontrolled diffusion of domestic 9

species). Todesco et al. (2016) performed a literature review of hybridization studies to identify the 10

ecological, evolutionary, and genetic factors that critically affect extinction risk through 11

hybridization. They found that 72% of studies regarding anthropogenic hybridization reported an 12

extinction threat and among those the most common anthropogenic causes of hybridization were 13

husbandry or agriculture (55% of the studies), invasive species (54%), and habitat disturbance 14

(36%). Most of the studies dealt with hybridization in plants, followed by fishes, birds, and 15

mammals. Extinction risk was more common in hybridizing vertebrates than plants and appeared to 16

be driven by fish (85% of the studies) and birds species (79% of the studies). 17

Anthropogenic hybridization is therefore considered as an increasing and significant threat to 18

biodiversity (Rhymer & Simberloff 1996; Crispo et al. 2011) that has the potential of driving rare 19

taxa to genomic extinction (the loss of combinations of genes and genotypes that have a unique 20

hybridization can cause extinction through genetic swamping (where the rare form is replaced by 27

hybrids; Allendorf et al. 2001). Following genomic extinction, the result is frequently a ‘hybrid 28

swarm’ in which all the individuals composing a population are hybrids. 29

30

1.2 When hybridization is a threat: importance of quantifying the prevalence of admixed individuals

31

in and its dynamics

32

As with any conservation threat, to evaluate potential management actions, it is fundamental to: 1) 33

understand if hybridization poses a threat to the viability of a population that requires human 34

intervention, 2) identify possible management actions and evaluate their effectiveness in an 35

adaptive management loop (Williams et al. 2011). For the first point, Allendorf et al. (2001) 36

proposed a classification framework to assess the severity of the hybridization threat. They divided 37

anthropogenic hybridization cases in different types based mainly on two criteria: the fitness and 38

relative abundance of admixed individuals (i.e., prevalence of admixed individuals). In the first 39

anthropogenic hybridization type ("hybridization without introgression"), first-generation hybrids 40

are sterile and the main threat for parental populations is the waste of reproductive effort 41

(demographic swamping). In the second type ("widespread introgression"), hybrids are fertile but 42

the parental populations are still prevalent and well distinguished. In the third type ("complete 43

admixture"), widespread introgression can evolve into a situation in which only the admixed 44

individuals remain (genetic swamping). Understanding the type of hybridization that is occuring is 45

therefore fundamental to assess the threat posed by anthropogenic hybridization on the viability of 46

the parental population and timely elaborate management strategies (Allendorf et al. 2001; Bohling 47

2016). To understand the hybridization type we need to quantify the proportion of admixed 48

individuals in a population at a given time (hereafter prevalence) and understand if such quantity is 49

predicted to increase toward complete admixture. 50

For the second point, depending on the hybridization type, a variety of management actions 51

hybrids to the management of the human disturbances that facilitatHG hybridization in the first 53

place (Allendorf et al. 2001; Bohling 2016). 54

55

1.2.1 Methodological challenges and solutions to estimate the prevalence of admixed

56

individuals

57

The relative abundance (prevalence) of different categories of individuals within a population is an 58

essential piece of information to understand processes in ecology, evolution, and conservation. For 59

example, the prevalence of infected individuals is critical to understand disease dynamics (Jennelle, 60

et al. 2007) and the prevalence of key demographic categories (e.g., mature females) is needed to 61

predict the viability of populations (Caswell 2000). Estimating the prevalence of different 62

population segments in wildlife populations is not trivial, therefore naive prevalence (the proportion 63

of individuals of a given class in the sample) is often used as a proxy (Jennelle et al. 2007). 64

However, this approach overlooks two main sources of bias: first, imperfect and/or heterogeneous 65

probability of detection leads to biased abundance and prevalence estimates when it is ignored 66

(Jennelle et al. 2007; Cubaynes et al. 2010), second, uncertainty in the classification of individuals 67

is common when individuals are assigned to a specific category based on clues (i.e., the assignment 68

of individuals to the category admixed and parental based on a limited number of genetic markers; 69

Vähä & Primmer 2006). 70

Reliable estimates of prevalence can be obtained by correcting field counts by the proportion 71

of undetected individuals (i.e., the ratio between the number of observed individuals and the 72

process in the model structure (Pradel 2005). Multievent models have been used to estimate a 79

variety of population parameters in the presence of uncertainty in classification (e.g., rates of entry 80

and exit from disease states: Conn & Cooch 2009; probability of skipping reproduction: Sanz-81

Aguilar et al. 2011, and the probability of survival of different age classes: Gervasi et al. 2017). 82

However, multievent models have never been used to estimate the abundance and prevalence of 83

different classes of individuals in a population. 84

85

1.2.2 Methods for projecting hybridization dynamics

86

Once hybridization has been estimated within a period of biological relevance (i.e., reproductive or 87

generational), it is important to understand if such quantity is predicted to increase towards 88

complete admixture. Moreover, if hybridization is recognized as a legitimate threat, the type and 89

intensity of management action need to be chosen and their outcome need to be evaluated 90

(Allendorf et al. 2001; Bohling 2016). 91

Population projection models are widely used in other contexts (e.g., harvest modelling 92

Sutherland 2001) to simulate population dynamics under different biological/evolutionary scenarios 93

and provide management recommendations (Cross & Beissinger 2001; Hradsky et al. 2019) but 94

their application to assess hybridization as a threat are few, though recently increasing (e.g., Nathan 95

et al. 2016). The first attempts to model hybridization-extinction dynamics had a genetic focus and 96

were based on changes in allelic frequencies at one or more loci (Huxel 1999; Ferdy & Austerlitz 97

2002). On the other hand, ecological models explicitly examine the effects of life-history traits (e.g., 98

survival and reproductive rates) on the hybridization outcome. Within this approach, two types of 99

models have been used to model hybridization dynamics (Hall & Ayres 2008): 1) individual-based 100

models that simulate the contribution of each individual to the hybridization dynamics of the entire 101

population (e.g., Thompson et al. 2003; Hooftman et al. 2007), and 2) population-based models that 102

can be used when only the mean fitness parameters of the main demographic stages are available 103

hybridization in plant species (Hall & Ayres 2008; Todesco et al. 2016). However, few studies used 105

individual-based models (Fredrickson & Hedrick 2006; Nathan et al. 2019) to simulate 106

hybridization dynamics in animal species. 107

108

1.3 General scope of the Ph.D. project

109

The general scope of my Ph.D. was to develop models for the assessment and management of 110

extinction risk due to anthropogenic hybridization. To provide a practical demonstration of the use 111

of the developed models we used them on an emblematic anthropogenic hybridization case study: 112

the hybridization between wolves (Canis lupus) and dogs (Canis lupus familiaris) in human 113

dominated landscapes. 114

115

1.3.1 Wolves x dog hybridization in Europe

116

Wolves and dogs are interfertile and the first-generation hybrids can backcross with both parental 117

sub-species, generating gene flow between the two gene pools (Vilà & Wayne 1999). Hybridization 118

between wolves and dogs occurred repeatedly since dog domestication (15-10.000 years BP; Larson 119

et al. 2012; Pilot et al. 2018), but more recent (i.e., up to 2 generations since admixture) 120

introgressive hybridization has been detected in various wolf populations in Eurasia (Galaverni et 121

al. 2017; Pacheco et al. 2017; Pilot et al. 2018; Dufresnes et al. 2019). In Europe, the expansion of 122

recovering wolf populations through human-dominated landscapes (Chapron et al. 2014), where 123

free-ranging dogs have since long become the most abundant carnivore (Ritchie et al. 2014) creates 124

genomic integrity of European wolf population is one the conservation priorities for wolves in 131

Europe (Hindrickson et al. 2017). 132

Studies on wolf-dog hybridization in several European countries have been mostly based on 133

non-invasive genetic sampling (reviewed in Dufresnses et al. 2019) and found revealed relatively 134

low proportions RIDGPL[HGLQGLYLGXDOVLQWKHFROOHFWHGVDPSOHV”DQG”LQ:HVWHUQDQG 135

Eastern Europe, respectively). However, these results may be flawed due to two main reasons. First 136

many of these samples have been collected opportunistically and at a coarse spatial (i.e., national) 137

and temporal (i.e., decades) scales (Dufresnes et al. 2019), whereas hybridization occurs at the local 138

scale and within one generation time. In support to that we highlight that, although large scale 139

assessments failed to detect high prevalence of admixture (Randi & Lucchini, 2002; Verardi et al. 140

2006; Lorenzini et al. 2014) more recent studies, based on intensive sampling at the local scale 141

(Caniglia et al. 2013; Bassi et al. 2017; Salvatori et al. 2019; this study), revealed higher admixture 142

rates even if still based on naLve prevalence quantifications. 143

Second, naive prevalence quantifications may suffer from both the heterogeneous 144

detectability of parental and admixed individuals, and the uncertainty in their classification. The 145

systematic monitoring of prevalence in wild populations relies on non-invasive samples (e.g., hairs 146

or scats), therefore the relatively poor-quality DNA extracted from such samples only allows for the 147

amplification of a relatively low number of diagnostic loci (Randi et al. 2014), limiting the power to 148

discriminate between parental individuals and later (>2) generation backcrosses (Vähä & Primmer 149

2006). This generates uncertainty over the classification of some DOOHJHGO\DGPL[HGJHQRW\SHV• 150

3rd generation backcrosses; Vähä & Primmer 2006), that are generally arbitrarily assigned to wolves 151

(e.g., Pacheco et al. 2017; Dufrenses et al. 2019), a practice that avoids Type 1 error (i.e., 152

misclassifying wolves as admixed individuals) but not necessarily Type 2 error (i.e., misclassifying 153

admixed individuals as wolves). 154

Based on the low proportions of admixed individuals detected in Western European studies 155

dog hybridization is currently rare and where it occurs, it most likely takes place in the peripheral 157

portion of the wolf distribution (Lorenzini et al. 2014) and/or during phases of range expansion 158

(Galaverni et al. 2017; Kusak et al. 2018). The second is that introgression of dog genes into wolf 159

populations is expected to be buffered by behavioral and selective constraints (e.g., the unsuccessful 160

integration of pregnant females in the natal packs, the reduced survival of first generation hybrid 161

litters due to limited paternal care, the lower success of admixed individuals in territorial or 162

predatory interactions; Vilà & Wayne 1999), and/or by the dilution of dog genes through 163

backcrossing into the parental wolf populations (Verardi et al. 2006). Based on these assumptions 164

and possibly due to the inherent biological and social complexity characterizing control of wolf-dog 165

hybridization (Donfrancesco et al. 2019), active management has lagged behind in Europe, 166

notwithstanding formal guidelines and recommendations provided by the European Union 167

(Salvatori & Ciucci 2018; Salvatori et al. 2019). 168

169

1.3.2 Wolf x dog hybridization as a threat

170

Although there was consensus among a panel of 42 wolf x dog hybridization experts across the 171

world regarding the fact that anthropogenic hybridization should be mitigated (Donfrancesco et al. 172

2019), clear evidence has not yet been found that the introgression of dog genes is a real 173

conservation issue. 174

Dogs diverged from the grey wolf Canis lupus between 11,000 and 35,000 years ago (Freedman & 175

Wayne, 2017). However, Larson et al. (2012) suggested that the current gene pool of most dog 176

levels, changed concentrations of several neurotransmitters, prolongations in juvenile behavior, and 183

reductions in both total brain size and of particular brain regions (Wilkins et al. 2014). For dogs 184

several behavioural traits differentiated them from wild canids (Miklosi 2015) and the genetic basis 185

of these traits is being unveiled (vonHoldt et al. 2017). The consequence of the LQWURJUHVVLRQRI 186

such traits in a wild wolf population have not yet beHQ addressed. 187

The only case where some of the long term consequences of the introgression of dog alleles 188

in wild wolf population gene pool have been explored is the introgression (and following positive 189

selection) of the melanistic mutation at the K-locus in the wolf gene pool in North American wolves 190

(Anderson et al. 2009). This mutation determines the black color in dogs (Candille et al. 2007) 191

and was likely introduced into North American wolves by ancient hybridization with dogs (12-192

14,000 years ago; Anderson et al. 2009). Coulson et al. (2011) found that gray wolves had slightly 193

lower survival, recruitment, generation length, and lifetime reproductive success than black 194

heterozygotes for the melanistic mutation. Coulson et al. (2011) also observed that black 195

homozygotes had lower survival, recruitment, generation length, and lifetime reproductive success 196

than black heterozygotes and gray wolves. Stahler et al. (2013) carried a detailed analysis of the 197

life-history traits of the population for both different colors and sexes and found that gray females 198

had more surviving pups than black females, the latter of which were nearly all heterozygotes. It is 199

therefore possible that the beta-defensin gene that determines black color in wolves might have 200

pleiotropic effects on disease resistance or other immunologically related traits (Coulson et al. 201

2011) and result in fitness tradeoffs. 202

Although hybridization with dogs is not only a recent phenomenon and, in this particular case, it 203

seems to have led to potential adaptive variation (together with possible pleiotropic effects), it is 204

reasonable to hypothesize that the forces that shaped introgression of domesticated alleles in North 205

American wild wolf populations 12,000 years ago are much different than the forces that would act 206

on introgressed dog alleles in the Anthropocene. In addition to that, the relative abundance of 207

abundant carnivore in the world (Ritchie et al. 2014) while wolves faced almost eradication 209

(Chapron et al. 2014). As a result of conservation efforts, gray wolves are currently re-colonising 210

parts of their former range in Western Europe across human-dominated landscapes (Chapron et al. 211

2014). Although gray wolves are able to survive and reproduce in anthropogenic habitats, the 212

survival rates and the causes of mortality in these systems will likely differ from those in less 213

human-dominated settings. These habitats are characterized, among other things, by high densities 214

RIanthropogenic foods (e.g., livestock, human food waste) that has been OLQNHGWRFKDQJHVLQ dietary 215

habits of predators, which may OHDGWR JHQHWLFbehavioural DQGGHPRJUDSKLFchanges (Newsome et 216

al. 2015). In this context the interaction RIDQWKURSRJHQLFVHOHFWLRQDQG introgressed GRPHVWLFDWHG 217

DOOHOHVPD\FRQWULEXWHWRWKHchanges in ecological niche (and role) and evolutionary diversification. 218

7KHSRVVLEOHRXWFRPHVRIsuch process may lead to the evolution of a new dog-like wolf ecotype, or to the 219

JUDGXDOreplacement of wolves by admixed individuals in human-dominated landscapes (genetic 220

swamping). 221

Given these considerations and following a precautionary approach wolf x dog hybridization is 222

largely perceived as a threat by experts of the field (Donfrancesco et al. 2019), a vision that is 223

shared by the author of this manuscript. 224

225

1.3.3 Management of wolf x dog hybridization

226

The management of anthropogenic hybridization involves three types of actions (Donfrancesco et 227

al. 2019): preventive (e.g., community engagement and education to decrease the number of free-228

proactive measures are generally enforceable through the national and European legislation, agreed 235

upon and supported by experts and socially more acceptable. On the other hand reactive measures 236

are controversial due to the not-defined legal status of hybrids, the lack of consensus within both the 237

scientific community and the general public (Lorenzini et al. 2014; Donfrancesco et al. 2019). The 238

effectiveness of reactive management has also been questioned by several authors (Lorenzini et al. 239

2014, Pacheco et al. 2017). 240

It is difficult if not impossible to empirically assess the effectiveness of reactive 241

hybridization management strategies due to the general lack of long-term time data series and the 242

need to implement management timely. Demographic simulation models can help exploring 243

complex ecological and evolutionary processes that are not easily empirically measured (Nathan et 244

al. 2019) and can be instrumental to inform decision-making in a context of uncertainty (e.g., 245

Gervasi & Ciucci 2018). To our knowledge, while population projections have been used to test the 246

effectiveness of the sterilization of admixed breeders is in the intensively monitored red wolf (Canis 247

rufus) x coyote (Canis latrans) system in North Carolina (Fredrickson & Hedrick 2006), they have

248

never been used to compare management strategies in the context of wolf x dog hybridization and 249

in general rarely for animal species (but see Nathan et al. 2019). 250

251

1.4 Structure and specific objectives of the Ph.D manuscript

252

This manuscript consists in four chapters, three of which (Chapter 1, 3 and 4) aiming at developing 253

methodological frameworks to quantify the prevalence of admixed individuals and its dynamics. 254

The second chapter is entirely dedicated to the application of the estimation model developed in 255

Chapter 1 to the case study on wolf x dog hybridization in the Northern Apennines, Italy. 256

257

1.4.1 Chapter 1. Development of a prevalence multievent capture–recapture model to

258

estimate prevalence of admixed individuals in wildlife populations

This chapter has been published: Santostasi, N.L., Ciucci, P., Caniglia, R., Fabbri, E., Molinari, L., 260

Reggioni, W., Gimenez, O. (2019). Use of hidden Markov capture–recapture models to estimate 261

abundance in the presence of uncertainty: Application to the estimation of prevalence of hybrids in 262

animal populations. Ecology and Evolution 9, 744-755. 263

In this chapter we: 1) developed a multievent capture–recapture model to estimate 264

prevalence in free-ranging populations accounting for imperfect detectability and uncertainty in 265

individual's classification, 2) carried out a simulation study to i) evaluate model performance, ii) 266

compare it to naive quantifications of prevalence and iii) assess the accuracy of model-based 267

estimates of prevalence under different sampling scenarios. The main results from this chapter were 268

that i) the prevalence of hybrids could be estimated while accounting for both detectability and 269

classification uncertainty ii) model-based prevalence consistently had better performance than 270

naive prevalence in the presence of differential detectability and assignment probability 271

and was unbiased for sampling scenarios with high detectability. Our results underline the 272

importance of a model-based approach to obtain unbiased estimates of prevalence of different 273

population segments. 274

275

1.4.2 Chapter 2. EstimatiQJ the prevalence of admixed wold x dog individuals in a study

276

area in the northern Apennines, Italy

277

This chapter is currently submitted: Santostasi, N.L., Gimenez, O., Caniglia, R., Fabbri, E., 278

illustrate the implications of the results for wolf conservation and for the management of wolf x dog 286

hybridization in human-dominated landscapes. In particular, by taking into account imperfect 287

detectability and the uncertainty associated with the assignment of backcrossed admixed 288

individuals, we estimated 64-78% recent hybrids occurring in 6 out of the 7 surveyed packs. 289

Ancestry analysis and genealogy reconstructions also confirmed multi-generational introgression 290

and indicated that some admixed packs had one or both breeders of recent admixture. Our findings 291

underline that in human-modified landscapes wolf-dog hybridization may raise to unexpected levels 292

if left unmanaged, and that reproductive barriers or dilution of dog genes through backcrossing 293

should not be expected, per se, to prevent occurrence and the spread of introgression. 294

295

1.4.3 Chapter 3. Development of a population-based modelling approach to project

296

hybridization dynamics

297

This chapter is currently accepted pending minor revisions: Santostasi, N.L., Ciucci, P., Bearzi, G., 298

Bonizzoni, S., Gimenez, O.(In press). Assessing the dynamics of hybridization through a matrix 299

modelling approach. Ecological Modelling. 300

In this chapter we present a new matrix population model to project population dynamics of 301

animal populations in presence of hybridization. We apply the model to two real-world case studies 302

of terrestrial (wolf x dog) and marine mammal species (common dolphin Delphinus delphis x 303

striped dolphin Stenella coeruleoalba). Specifically, we investigate 1) the possible outcomes of 304

wolf x dog hybridization events for an expanding wolf population in Italy, under different 305

reproductive isolation scenarios, 2) the genomic extinction probability of the two interbreeding 306

dolphin species within a semi-enclosed gulf in Greece, under different hybrids’ fitness scenarios, 3) 307

the sensitivity of the probability of genomic extinction to the main demographic parameters in the 308

two case studies. In particular our projections highlighted that i) hybridization leads to genomic 309

extinction in the absence of reproductive isolation, ii) rare or depleted species are particularly 310

parameters of parental species, iiii) maintaining healthy and abundant populations prevents genomic 312

extinction. 313

314

1.4.4 Chapter 4. Development of an individual-based model to evaluate the effect of

315

different management strategies for wolf x dog hybridization

316

In this chapter we built a detailed individual based model describing the life cycle of the 317

gray wolf by contemplating social dynamics traits linked to hybridization rates. We applied this 318

model to investigate the hybridization dynamics of wolves in a study population the Northern 319

Apennines, Italy, to evaluate the effectiveness of different management scenarios aimed to reduce 320

the abundance of admixed individuals during a ten-generation time. We showed that in presence of 321

frequent immigration of admixed individuals any management action proved ineffective. In 322

presence of immigration by pure wolves all management actions produced a decrease in prevalence, 323

although their relative effectiveness changed depending on the mating choice scenario. In all the 324

simulated scenarios, the impact of hybridization is predicted to extend at broad scales as large 325

numbers of admixed dispersers are produced. Moreover, we identified demographic and social 326

processes that need to be further investigated to more accurately project the outcomes of 327 management alternatives. 328 329 330 LITERATURE CITED 331

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Պ 11;r|;7ĹƔ";r|;l0;uƑƏƐѶ DOI: 10.1002/ece3.4819

O R I G I N A L R E S E A R C H

Use of hidden Markov capture–recapture models to estimate

abundance in the presence of uncertainty: Application to the

estimation of prevalence of hybrids in animal populations

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$_; u;Ѵ-|bˆ; -0†m7-m1; Őru;ˆ-Ѵ;m1;ő o= 7b==;u;m| ror†Ѵ-|bom v;]Ŋ ments is a fundamental piece of information to understand proŊ 1;vv;v bm ;1oѴo]‹ķ ;ˆoѴ†|bomķ -m7 1omv;uˆ-|bomĺ ou ;Š-lrѴ;ķ |_; prevalence of infected individuals is critical to understand the mechŊ -mbvlv7ubˆbm]7bv;-v;7‹m-lb1vŐ;mm;ѴѴ;ķoo1_ķomuo‹ķş";m-uķ ƑƏƏƕĸou;moŊ$ouu;vķ)oѴ=;ķ"-ˆbѴѴ;ķş-u-0;7ķƑƏƐѵőĸ|_;ru;ˆ-Ŋ Ѵ;m1;o=h;‹7;lo]u-r_b11-|;]oub;vŐ;ĺ]ĺķl-|†u;=;l-Ѵ;vőbvm;;7;7 |o -vv;vv |_; ˆb-0bѴb|‹ o= ;m7-m];u;7 ror†Ѵ-|bomv Ő-v‰;ѴѴķ ƑƏƏƏő -m7‰_;m_‹0ub7bŒ-|bomu;ru;v;m|v-|_u;-|ķ|_;ru;ˆ-Ѵ;m1;o=-7Ŋ lbŠ;7bm7bˆb7†-Ѵvbvm;;7;7|o;ˆ-Ѵ†-|;|_;-rruorub-|;l-m-];l;m| or|bomŐѴѴ;m7ou=ķ;-u‹ķ"ru†;ѴѴķş);m0†u]ķƑƏƏƐőĺ

o‰;ˆ;uķ;v|bl-|bm]ru;ˆ-Ѵ;m1;=ou‰bѴ7Ѵb=;ror†Ѵ-|bomvbv1_-ѴŊ lenging and the raw percentage of individuals of a class in the sample Őm-bˆ; ru;ˆ-Ѵ;m1;ő bv o=|;m †v;7 -v - ruoŠ‹ Ő;mm;ѴѴ; ;|-Ѵĺķ ƑƏƏƕőĺ o‰;ˆ;uķ|_bv-rruo-1_oˆ;uѴoohv|‰ol-bmvo†u1;vo=0b-vĺ buv|ķ imperfect and/or heterogeneous detection leads to biased abunŊ 7-m1;;v|bl-|;v‰_;mb|bvb]mou;7Ő†0-‹m;v;|-ѴĺķƑƏƐƏĸ;mm;ѴѴ; ;|-ѴĺķƑƏƏƕőĺ";1om7ķ†m1;u|-bm|‹bm|_;1Ѵ-vvb=b1-|bomo=bm7bˆb7†-Ѵv Ő;ĺ]ĺķ 7bv;-v;7ņ_;-Ѵ|_‹ķ 0u;;7;uņmom0u;;7;uķ l-Ѵ;ņ=;l-Ѵ;ő bv 1olŊ mon in wildlife population studies where individuals are assigned to -vr;1b=b1v|-|†v0-v;7omblr;u=;1|1Ѵ†;vĺŠ-lrѴ;vbm1Ѵ†7;7;|;uŊ lbmbm]v;Šou0u;;7bm]v|-|†v0-v;7om|_;0;_-ˆbouo=bm7bˆb7†-Ѵv Ő;moˆ-u|ķu-7;ѴķşuoķƑƏƐƑőou;v|-0Ѵbv_bm]_;-Ѵ|_v|-|†v=uol |_; o0v;uˆ-|bom o= o†|;u v‹lr|olv omѴ‹ Őomm ş oo1_ķ ƑƏƏƖőĺ mo|_;uѴ;vv;ŠrѴou;70†|bm|ub]†bm]vb|†-|bombv-vvb]mbm]bm7bˆb7†-Ѵv |o];m;|b11Ѵ-vv;vŐv†0ror†Ѵ-|bomvő0-v;7om-Ѵblb|;7m†l0;uo=];Ŋ m;|b1l-uh;uvŐ(࢜_࢜şubll;uķƑƏƏѵőĺ !;Ѵb-0Ѵ; ;v|bl-|;v o= ‰bѴ7Ѵb=; -0†m7-m1; 1-m 0; o0|-bm;7 0‹ 1ouu;1|bm]=b;Ѵ71o†m|v0‹|_;ruorou|bomo=†m7;|;1|;7bm7bˆb7†-Ѵv Őbĺ;ĺķ|_;u-|bo0;|‰;;m|_;m†l0;uo=o0v;uˆ;7bm7bˆb7†-Ѵv-m7|_; ruo0-0bѴb|‹o=7;|;1|bomĸb1_oѴvķƐƖƖƑőĺ$_;ruo0-0bѴb|‹o=7;|;1|bom bv†v†-ѴѴ‹;v|bl-|;70‹†vbm]1-r|†u;ŋu;1-r|†u;lo7;ѴvŐ!ő=uol- v-lrѴ;o=bm7bˆb7†-Ѵ;m1o†m|;u_bv|oub;vŐ|bvķ†um_-lķ)_b|;ķş m7;uvomķ ƐƖƕѶőĺ m r-u|b1†Ѵ-uķ l†Ѵ|bv|-|; ! lo7;Ѵv ;v|bl-|; |_; ruo0-0bѴb|‹ o= 7;|;1|bom =ou 7b==;u;m| 1Ѵ-vv;v o= bm7bˆb7†-Ѵv 0‹ -vŊ vb]mbm]bm7bˆb7†-Ѵv|ov|-|b1ou7‹m-lb1v|-|;vĺo‰;ˆ;uķl†Ѵ|bv|-|; CR models assume the correct assignment of all individuals to their v|-|;Ő;0u;|omķ†um_-lķѴo0;u|ķşm7;uvomķƐƖƖƑőĺ†Ѵ|b;ˆ;m| lo7;Ѵvu;Ѵ-Š|_bv-vv†lr|bom0‹-1hmo‰Ѵ;7]bm]|_;†m1;u|-bm|‹o= |_; o0v;uˆ-|bom ruo1;vv bm |_; lo7;Ѵ v|u†1|†u; Őu-7;Ѵķ ƑƏƏƔőĺ m |_;v;lo7;Ѵvķ-_b77;m0boѴo]b1-Ѵruo1;vvŐ;ĺ]ĺķv†uˆbˆ-Ѵou7bvr;uv-Ѵő bvlo7;Ѵ;7-v--uhoˆ1_-bmo=v|-|;vŐu-7;ѴķƑƏƏƔőĺ$_;o0v;uˆ-Ŋ |bomruo1;vvŐ|_;7-|-ő-ubv;v=uol|_;†m7;uѴ‹bm]v|-|;v|_uo†]_|_; ruo0-0bѴb|‹o=7;|;1|bomĺ$obm1Ѵ†7;†m1;u|-bm|‹bmv|-|;-vvb]ml;m|ķ the observation process is further split into two steps: detection -m7v|-|;-vvb]ml;m|1om7b|bom-Ѵom7;|;1|bomŐbl;m;Œķ;0u;|omķ -bѴѴ-u7ķ_ot†;|ķşu-7;ѴķƑƏƐƑĸu-7;ѴķƑƏƏƔőĺ$_bv=oul†Ѵ-|bom bm1Ѵ†7;v-ruo0-0bѴb|‹o=-vvb]ml;m|Ő0;vb7;v|_;ruo0-0bѴb|‹o=7;Ŋ |;1|bom-m7|_;ruo0-0bѴb|b;v-vvo1b-|;7‰b|_|_;0boѴo]b1-Ѵruo1;vvőķ -ѴѴo‰bm]=ou|_;bm1Ѵ†vbomo=bm7bˆb7†-Ѵv1Ѵ-vvb=b;7‰b|_†m1;u|-bm|‹ †Ѵ|b;ˆ;m|lo7;Ѵv_-ˆ;0;;m†v;7|o;v|bl-|;-ˆ-ub;|‹o=ror†Ŋ Ѵ-|bomr-u-l;|;uvbm|_;ru;v;m1;o=†m1;u|-bm|‹bmv|-|;-vvb]ml;m|ĺ Š-lrѴ;vo=|_-|bm1Ѵ†7;|_;u-|;vo=;m|u‹-m7;Šb|=uol7bv;-v;v|-|;v Őommşoo1_ķƑƏƏƖőķ|_;ruo0-0bѴb|‹o=vhbrrbm]u;ruo7†1|bomŐ"-mŒŊ ]†bѴ-u ;|-Ѵĺķ ƑƏƐƐőķ -m7 |_; ruo0-0bѴb|‹ o= v†uˆbˆ-Ѵ o= 7b==;u;m| -]; 1Ѵ-vv;vŐ;uˆ-vb;|-ѴĺķƑƏƐƕőĺo‰;ˆ;uķl†Ѵ|b;ˆ;m|lo7;Ѵv_-ˆ;m;ˆ;u been used to estimate the abundance of individuals in different states 0;1-†v;|_;m†l;u-|ouo=|_;-0†m7-m1;;v|bl-|ouŐ|_;m†l0;uo= o0v;uˆ;7bm7bˆb7†-Ѵvőbv1om|-lbm-|;70‹†m1;u|-bmo0v;uˆ-|bomvĺ ;u;ķ‰;7;ˆ;Ѵor-1-r|†u;ŋu;1-r|†u;-rruo-1_|o;v|bl-|;|_; ru;ˆ-Ѵ;m1;o=-7lbŠ;7bm7bˆb7†-ѴvŐ_;u;-=|;uľ_‹0ub7vĿőbm-ror†Ѵ-|bom ‰_bѴ;vbl†Ѵ|-m;o†vѴ‹-11o†m|bm]=ou0o|_blr;u=;1|7;|;1|bom-m71Ѵ-vŊ vb=b1-|bom†m1;u|-bm|‹ĺ"r;1b=b1-ѴѴ‹ķ‰;v_o‰_o‰|o†v;|_;l†Ѵ|b;ˆ;m| CR framework to estimate abundance of individuals in different states Őbĺ;ĺķ ľ-u;m|-ѴķĿ ľ‹0ub7ķĿ ľ ;-7Ŀő bm |_; ru;v;m1; o= †m1;u|-bm|‹ bm v|-|;-vvb]ml;m|ĺ);=buv|†v;l†Ѵ|b;ˆ;m|lo7;Ѵv|o;v|bl-|;v†uˆbˆ-Ѵ -m77;|;1|bomr-u-l;|;uvĸv;1om7ķ‰;†v;|_;(b|;u0b-Ѵ]oub|_l|o-vŊ vb]m|_;†m1;u|-bmo0v;uˆ;7bm7bˆb7†-Ѵv|o|_;lov|Ѵbh;Ѵ‹v|-|;Ő!o†-mķ -bѴѴ-u7ķ†࣐7omķşu-7;ѴķƑƏƏƖĸ,†11_bmbķ-1 om-Ѵ7ķş-m]uo1hķ ƑƏƏƖőķ-m7Ѵ-v|Ѵ‹ķ‰;;v|bl-|;ru;ˆ-Ѵ;m1;ˆb--ouˆb|Œŋ$_olrvomŊѴbh; estimator combined with a bootstrapping procedure to produce stanŊ 7-u7;uuou-m71om=b7;m1;bm|;uˆ-ѴvŐ -ˆbvomşbmhѴ;‹ķƐƖƖƕőĺ

); -vv;vv |_; blrou|-m1; o= bm1ourou-|bm] 7;|;1|-0bѴb|‹ -m7 †m1;u|-bm|‹ bm v|-|; -vvb]ml;m| 0‹ 1olr-ubm] |_; r;u=oul-m1; o= lo7;ѴŊ0-v;7-m7m-bˆ;ru;ˆ-Ѵ;m1;†m7;u7b==;u;m|v1;m-ubovĺ$_;-1Ŋ 1†u-1‹o=!r-u-l;|;uvĽ;v|bl-|ouv7;r;m7vom|_;u;1-r|†u;u-|; -m7om|_;m†l0;uo=1-r|†u;o11-vbomvŐ|bv;|-ѴĺķƐƖƕѶőĺm1u;-vbm] |_;7;|;1|-0bѴb|‹-m7ņou|_;m†l0;uo=o11-vbomvu;t†bu;v7b==;u;m| sampling strategies and generates different costs in terms of financial -m7_†l-mu;vo†u1;vŐb;†u‹;|-ѴĺķƑƏƐƕőĺ$_;u;=ou;ķ‰;-Ѵvo;ŠrѴou; _o‰7b==;u;m|v-lrѴbm]v|u-|;]b;vl-‹-==;1||_;lo7;Ѵr;u=oul-m1;ĺ

Despite the increasing attention that researchers are devoting to _‹0ub7bŒ-|bom1-v;vŐ"1_‰;mhķu;7;ķş"|u;b|ķƑƏƏѶĸ$o7;v1o;|-Ѵĺķ ƑƏƐѵőķ|_;u;_-ˆ;0;;momѴ‹ =;‰ -||;lr|v|o;v|bl-|;ru;ˆ-Ѵ;m1; o=_‹0ub7vbm‰bѴ7ror†Ѵ-|bomvŐ(-Œbm|oķ;f-ķ ;uu-m7ķşo7bm_oķ ƑƏƐƔőĺ);bѴѴ†v|u-|;o†ul;|_o7‰b|_-1-v;v|†7‹0‹;v|bl-|bm]|_; ru;ˆ-Ѵ;m1;o=‰oѴ=ŐCanis lupusőƵ7o]ŐCanis lupus familiariső_‹0ub7v bm-‰oѴ=ror†Ѵ-|bombmmou|_;um|-Ѵ‹ĺ$_bvbv-1-v;o=-m|_uoro];mb1 _‹0ub7bŒ-|bomŐbĺ;ĺķ|_;bm|;u0u;;7bm]o=bm7bˆb7†-Ѵv=uol];m;|b1-ѴѴ‹ 7bv|bm1| ror†Ѵ-|bomv 7†; |o _†l-m -1|bomĸ ѴѴ;m7ou= ;|-Ѵĺķ ƑƏƏƐő -m7bv1omvb7;u;7-l-fou|_u;-||o‰oѴ=];molb1bm|;]ub|‹Őob|-mbķ ƑƏƏƏőĺ $_;u;=ou;ķ -11†u-|;Ѵ‹ ;v|bl-|bm] |_; ru;ˆ-Ѵ;m1; o= _‹0ub7v bm ‰oѴ= ror†Ѵ-|bomv bv - ruboub|‹ |o ;Ѵ-0ou-|; 1omv;uˆ-|bom v|u-|;Ŋ ]b;vŐbm7ub1hvom;|-ѴĺķƑƏƐƕőĺ);v_o‰|_-|bm|_bv1-v;†vbm]m-bˆ; ru;ˆ-Ѵ;m1;-v-ruoŠ‹†m7;u;v|bl-|;v|_;ru;ˆ-Ѵ;m1;o=_‹0ub7vĺ ƑՊ|Պ$ " ƑĺƐՊ|Պb77;m-uhoˆlo7;Ѵ );-vv†l;7|_-|-mbl-Ѵv-u;bm7bˆb7†-ѴѴ‹u;1o]mbŒ;7-|7bv1u;|;;mŊ 1o†m|;uo11-vbomvķ|_;u;=ou;o0|-bmbm]-m;m1o†m|;u_bv|ou‹=ou;-1_

ƕƓѵՊ

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SANTOSTASI ETAL.

v|-|;vĹ-Ѵbˆ;-m7r-u;m|-ѴŐőķ-Ѵbˆ;-m7_‹0ub7Őőķou7;-7Ő őĺ); †m7;uѴbm;|_-|_;u;-=|;u|_;|;ulľ_‹0ub7Ŀu;=;uv|o-ѴѴ1-|;]oub;vo= -7lbŠ|†u;-m7mo|omѴ‹|o=buv|Ŋ];m;u-|bom_‹0ub7vĺ&romb|v=buv|;mŊ 1o†m|;uķ-mbm7bˆb7†-Ѵ_-v-ruo0-0bѴb|‹πp to be a parental and the

1olrѴ;l;m|-u‹ruo0-0bѴb|‹πhƷƐƴπp|o0;-_‹0ub7ĺ$_;bmb|b-Ѵv|-|;

ruo0-0bѴb|b;v7;v1ub0;|_;ruo0-0bѴb|‹|_-|-mbm7bˆb7†-Ѵbvbmom;ou -mo|_;uv|-|;‰_;m=buv|;m1o†m|;u;7ĺ$_;mķ|_;v|-|;v1_-m];oˆ;u |bl;-11ou7bm]|o-=buv|Ŋou7;u-uhoˆruo1;vvķ‰b|_|_;v|-|;ruoŊ 1;vv 0;bm] ]oˆ;um;7 0‹ -rr-u;m| v†uˆbˆ-Ѵ ruo0-0bѴb|b;v φp and φh.

ou;vr;1b=b1-ѴѴ‹ķ|_;v|-|;ruo1;vvķ‰_b1_v†ll-ubŒ;v|_;†m7;uѴ‹Ŋ bm]0boѴo]b1-Ѵruo1;vvķbvu;ru;v;m|;70‹-|u-mvb|bomruo0-0bѴb|‹l-Ŋ |ubŠ‰b|_v|-|;v-||bl;tbmuo‰vŐľ-u;m|-ѴķĿľ‹0ub7ķĿľ ;-7Ŀő-m7

t + Ɛbm1oѴ†lmvŐľ-u;m|-ѴķĿľ‹0ub7ķĿľ ;-7ĿőĹ

where parameter φp Őu;vrĺ φhő bv |_; ruo0-0bѴb|‹ |_-| -m bm7bˆb7†-Ѵ

-Ѵbˆ;-m7bmv|-|;ľ-u;m|-ѴĿŐu;vrĺľ‹0ub7Ŀő-||bl;t is still alive in |_;v|†7‹-u;--m7bmv|-|;ľ-u;m|-ѴĿŐu;vrĺľ‹0ub7Ŀő-||bl;t + 1 -m7 1ouu;vrom7v |o |_; -rr-u;m| v†uˆbˆ-Ѵ ruo0-0bѴb|‹ o= r-u;m|-Ѵ Őu;vrĺľ‹0ub7Ŀőbm7bˆb7†-Ѵvĺ

$_; v;1om7 |bl; v;ub;v Őou ;ˆ;m| ruo1;vvő bv ];m;u-|;7 =uol the states at each occasion and describes the observation proŊ cess. Individuals are detected at time t‰b|_ruo0-0bѴb|‹o=7;|;1Ŋ tion p_p for parental and p_h=ou_‹0ub7bm7bˆb7†-Ѵvĺ&rom7;|;1|bomķ -m-||;lr|bvl-7;o=-vvb]mbm]|_;bm7bˆb7†-Ѵv|o-_‹0ub7bŒ-|bom state based on genetic and/or morphologic diagnostic features -m7 |_;u; bv - ruo0-0bѴb|‹ δ that an individual is assigned to the v|-|; ľ-u;m|-ѴĿ ou ľ‹0ub7Ŀĺ = |_; 7b-]mov|b1 1Ѵ†;v -u; mo| v†=Ŋ =b1b;m||o-v1;u|-bm|_;_‹0ub7bŒ-|bomv|-|;ķ|_;bm7bˆb7†-Ѵbv1Ѵ-vŊ vb=b;7-v†m1;u|-bm‰b|_|_;1olrѴ;l;m|-u‹ruo0-0bѴb|‹Ɛƴδ. The o0v;uˆ-|bomruo1;vvbvv†ll-ubŒ;70‹-l-|ubŠ‰b|_v|-|;vbmuo‰v Őľ-u;m|-ѴķĿ ľ‹0ub7ķĿ ľ ;-7Ŀő -m7 ;ˆ;m|v bm 1oѴ†lmv ŐƏƷľo| 7;|;1|;7ķĿ ƐƷľ ;|;1|;7 -v r-u;m|-ѴķĿ ƑƷľ ;|;1|;7 -v _‹0ub7ķĿ ƒƷľ ;|;1|;7-v†m1;u|-bmĿőĹ

7;-7ĺt†bˆ-Ѵ;m|Ѵ‹ķ|_;;ˆ;m|ruo1;vv1-m0;7;1olrov;7-v|_; ruo7†1|o=-7;|;1|boml-|ubŠ0‹-m-vvb]ml;m|l-|ubŠ‰_b1_;ŠŊ ru;vv;v|_;ruo0-0bѴb|‹|_-|-mbm7bˆb7†-Ѵbv-vvb]m;7|o-v|-|; given that it has been detected:

‰_;m -m -mbl-Ѵ bv =buv| ;m1o†m|;u;7ķ |_; 1-r|†u; ruo1;vv bv mo| modeled because an animal must be encountered at least once to ;m|;u|_;7-|-v;|ķ0†||_;v|-|;-v1;u|-bml;m|u;l-bmvˆ-Ѵb7ĺ

$obѴѴ†v|u-|;|_;1-Ѵ1†Ѵ-|bomo=-m;m1o†m|;u_bv|ou‹ķѴ;|†v1omŊ vb7;u |_; 1-v; o= - ƒŊ‹;-u ! ;Šr;ubl;m|ĺ ou bmv|-m1;ķ |_; ;mŊ 1o†m|;u _bv|ou‹ ľƒƏƒĿ 7;mo|;v -m bm7bˆb7†-Ѵ ;m1o†m|;u;7 -| |_; first and third occasions but not at the second occasion. The state o=|_bvbm7bˆb7†-Ѵbvm;ˆ;u-vvb]m;7ĺvv†lbm]r-u-l;|;uv-u;1omŊ v|-m|ķ‰;_-ˆ;

m |_; ub]_| vb7; o= |_; ;t†-|bomķ |_; =buv| ;Ѵ;l;m| o= |_; v†lbv|_;ruo0-0bѴb|‹o=|_;o0v;uˆ;7_bv|ou‹b=|_;†m7;uѴ‹bm] v|-|;bvľ‹0ub7Ŀķ‰_bѴ;|_;v;1om7;Ѵ;l;m|bv|_;ruo0-0bѴb|‹o= |_;o0v;uˆ;7_bv|ou‹]bˆ;m|_-||_;†m7;uѴ‹bm]v|-|;bvľ-u;m|-ѴĿĺ The likelihood of the entire dataset is obtained as the product of the probabilities of all individual encounter histories assumŊ bm] bm7;r;m7;m1;ĺ m |_bv r-r;uķ ;v|bl-|;v o= bmb|b-Ѵ v|-|;v Őπp

and π_hőķ-rr-u;m|v†uˆbˆ-ѴŐφ_p and φ_hőķ7;|;1|bomŐp_p and p_hőķ-m7 -vvb]ml;m|ruo0-0bѴb|b;vŐδp and δhő-u;o0|-bm;70‹l-ŠblbŒbm]

|_;Ѵbh;Ѵb_oo7=†m1|bomĺ b==;u;m|lo7;Ѵv1-m0;0†bѴ|0‹-ѴѴo‰bm] |_;r-u-l;|;uv|oˆ-u‹-11ou7bm]|oķ=ou;Š-lrѴ;ķv|-|;ķ|bl;ķou ]uo†r o= bm7bˆb7†-Ѵv 1Ѵ-vvb=b;7 0-v;7 om 7bv1u;|; ˆ-ub-0Ѵ;v Ő;ĺ]ĺķ -];1Ѵ-vvouv;Šőĺ

ƑĺƑՊ|Պ0†m7-m1;-m7ru;ˆ-Ѵ;m1;;v|bl-|bom

-bˆ;ru;ˆ-Ѵ;m1;ŐPnaiveő-|-]bˆ;mo11-vbombv1-Ѵ1†Ѵ-|;7-v|_;ruoŊ

rou|bomo=o0v;uˆ;7_‹0ub7vbm|_;v-lrѴ;Ĺ ⎛ ⎜ ⎜ ⎜ ⎝ P H D P 𝜑_p 0 1_{− 𝜑p} H 0 𝜑_h 1_{− 𝜑h} D 0 0 1 ⎞ ⎟ ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ 0 1 2 3 P 1_{− pp} p_p𝛿 p 0 pp(1−𝛿p) H 1_{− ph} 0 ph𝛿h ph(1−𝛿h) ⎞ ⎟ ⎟ ⎛ ⎜ ⎜ ⎜ ⎝ 0 1 2 P 1 − pp pp 0 H 1_{− ph} 0 ph D 1 0 0 ⎞ ⎟ ⎟ ⎟ ⎠ ⎛ ⎜ ⎜ ⎜ ⎝ 0 1 2 3 0 1 0 0 0 1 0 𝛿_p 0 1₋𝛿_p 2 0 0 𝛿 h 1−𝛿h ⎞ ⎟ ⎟ ⎟ ⎠ Pr(303) = 𝜋h(1 − 𝛿h) 𝜑h(1 − ph) 𝜑hph(1 − 𝛿h ) +𝜋_p(1 − 𝛿_p) 𝜑_p(1 − p_p) 𝜑_pp_p(1 − 𝛿_p)

|

ՊƕƓƕ

SANTOSTASI ETAL.

where n_hbv|_;m†l0;uo=o0v;uˆ;7_‹0ub7vķ-m7n_p is the number o=o0v;uˆ;7r-u;m|-Ѵbm7bˆb7†-Ѵvķ ̂phbv|_;u;1-r|†u;ruo0-0bѴb|‹o=

_‹0ub7vķ-m7 ̂ppbv|_;u;1-r|†u;ruo0-0bѴb|‹o=r-u;m|-Ѵbm7bˆb7†-Ѵvĺ

o7;ѴŊ0-v;7ru;ˆ-Ѵ;m1;bv|_;m;v|bl-|;7-vĹ

$_; l-bm 7b==b1†Ѵ|‹ bv |_;u;=ou; bm 7;|;ulbmbm] |_; m†l0;u o= o0v;uˆ;7 r-u;m|-Ѵ bm7bˆb7†-Ѵv -m7 _‹0ub7vķ 0;1-†v; |_; †m1;u|-bm bm7bˆb7†-Ѵv_-ˆ;|o0;-vvb]m;7|oom;o=|_;|‰ov|-|;vŐľ‹0ub7Ŀ ouľ-u;m|-ѴĿőĺ$o7ovoķ‰;†v;|_;(b|;u0b-Ѵ]oub|_lŐ,†11_bmb;|-Ѵĺķ ƑƏƏƖő ‰_b1_ķ ]bˆ;m -m‹ o0v;uˆ-|bom v;t†;m1; Ő_;u;ķ |_; ;m1o†mŊ |;u_bv|oub;vő-m7|_;r-u-l;|;uv;v|bl-|;70‹|_;_b77;m-uhoˆ lo7;Ѵķ=bm7v|_;lov|ruo0-0Ѵ;†m7;uѴ‹bm]v;t†;m1;o=v|-|;v|_-| _-v ];m;u-|;7 |_; o0v;uˆ;7 7-|- Ő!o†-m ;|-Ѵĺķ ƑƏƏƖőĺ m1; |_; †m1;u|-bm o0v;uˆ-|bomv -u; -vvb]m;7 |o |_; lov| Ѵbh;Ѵ‹ v|-|;ķ |_; m†l0;uo=o0v;uˆ;7_‹0ub7-m7r-u;m|-Ѵbm7bˆb7†-Ѵv1-m0;u;1omŊ v|u†1|;7-m7|_;=oul†Ѵ-1-m0;†v;7|o;v|bl-|;ru;ˆ-Ѵ;m1;ĺ); o0|-bm 1om=b7;m1; bm|;uˆ-Ѵv =ou |_; _‹0ub7vĽ ru;ˆ-Ѵ;m1; 0‹ †vbm] - momr-u-l;|ub10oo|v|u-rruo1;7†u;Ő -ˆbvomşbmhѴ;‹ķƐƖƖƕőĺ ƑĺƒՊ|Պˆ-Ѵ†-|bomo=lo7;Ѵr;u=oul-m1;-m7 v-lrѴbm]v|u-|;]‹ $o|;v||_;lo7;Ѵr;u=oul-m1;ķ‰;];m;u-|;7;m1o†m|;u_bv|oŊ ub;v‰b|_hmo‰mru;ˆ-Ѵ;m1;lblb1hbm]o†u1-v;v|†7‹om‰oѴˆ;v -m77o]vbm|_;ou|_;umr;mmbm;vŐv;;m;Š|v;1|bomő-m71olŊ r-u;7lo7;ѴŊ0-v;7ru;ˆ-Ѵ;m1;-m7m-bˆ;ru;ˆ-Ѵ;m1;ĺ&vbm]|_; !Ő!ou;$;-lķƑƏƐƕőr-1h-];Őbll;Ѵl-mmķƑƏƐƏőķ‰; simulated a cohort of 100 individuals that we split into 2 states ľ‹0ub7Ŀ-m7ľ-u;m|-ѴĿĺ ou-ѴѴ|_;v1;m-ubovķ‰;v;||_;bmb|b-Ѵ proportion of wolves π_pƷƏĺƕ -m7 bmb|b-Ѵ ruorou|bom o= _‹0ub7v π_hƷƐƴπ_pƷƏĺƒ -v bm o†u 1-v; v|†7‹ v-lrѴ; Őv;; m;Š| v;1|bomőĺ &vbm]ˆ-Ѵ†;v;v|bl-|;70‹-mb]Ѵb-;|-ѴĺŐƑƏƐƑő=ou|_;v-l;‰oѴ= ror†Ѵ-|bomķ ‰; 1omvb7;u;7 v|-|;Ŋ7;r;m7;m| v†uˆbˆ-Ѵ Ő1omv|-m| oˆ;u|bl;ő‰b|_r-u;m|-Ѵv†uˆbˆ-ѴŐφpƷƏĺѶő_b]_;u|_-m_‹0ub7v†uŊ

ˆbˆ-ѴŐφhƷƏĺƕőĺ);|_;m1omvb7;u;7|_u;;_‹ro|_;|b1-Ѵv1;m-ubov

=ou7;|;1|-0bѴb|‹-m7-vvb]ml;m|ruo0-0bѴb|‹ĹŐv;;"†rrou|bm]bmŊ formation Table S1 for a complete list of parameters for the three v1;m-ubovőŐƐőv|-|;Ŋ7;r;m7;m|7;|;1|-0bѴb|‹Őpp > phő-m7_oloŊ

];m;o†v -vvb]ml;m| ruo0-0bѴb|‹ķ ŐƑő _olo];m;o†v 7;|;1|-0bѴŊ b|‹-m7v|-|;Ŋ7;r;m7;m|-vvb]ml;m|ruo0-0bѴb|‹Őδp > δhő-m7Őƒő

_olo];m;o†v 7;|;1|-0bѴb|‹ -m7 -vvb]ml;m| ruo0-0bѴb|‹ĺ )b|_bm |_;v; |_u;; l-bm v1;m-ubovķ ‰; ;ˆ-Ѵ†-|;7 |_; ;==;1| o= Ѵo‰;u -m7 _b]_;u v-lrѴbm] bm|;mvb|b;v 0‹ 1olr-ubm] v-lrѴbm] v|u-|;Ŋ ]b;v‰b|_Ѵo‰-m7_b]_7;|;1|-0bѴb|‹-m7‰b|_Ɣ-m7ƐƏ1-r|†u; o11-vbomvĺ ); vbl†Ѵ-|;7 ƐƏƏ 7-|-v;|v =ou ;-1_ 1ol0bm-|bom o= r-u-l;|;uv‰b|_bm|_;|_u;;l-bmv1;m-ubovĺ);=b||;71omv|-m| -m7v|-|;Ŋ7;r;m7;m|lo7;Ѵv|o|_;vbl†Ѵ-|;77-|-ķ-m7‰;1-ѴŊ 1†Ѵ-|;7|_;u;Ѵ-|bˆ;0b-v-m7|_;uoo|l;-mvt†-u;7;uuouŐ!"ő =ou |_; lo7;ѴŊ0-v;7 -m7 |_; m-bˆ; ru;ˆ-Ѵ;m1; ;v|bl-|ouvĺ );

-Ѵvo1-Ѵ1†Ѵ-|;7|_;1om=b7;m1;bm|;uˆ-Ѵ1oˆ;u-];=ou|_;lo7;ѴŊ based estimator of prevalence.

ƑĺƓՊ|Պ-v;v|†7‹

); 1oѴѴ;1|;7 =u;v_ ‰oѴ= v1-|v bm |_; rr;mmbmo $ov1oŊ;lbѴb-mo -|bom-Ѵ -uh =uol †]†v| ƑƏƐѵ |o -‹ ƑƏƐƕĺ ); ;Š|u-1|;7ķ -lrѴb=b;7-m7v;t†;m1;7 =uol|_;v1-|v=oѴѴo‰bm]|_;ruoŊ 1;7†u;v 7;v1ub0;7 bm -mb]Ѵb-ķ -00ubķ -Ѵ-ˆ;umbķ bѴ-m;vbķ -m7 !-m7b ŐƑƏƐƓőĺ ); b7;m|b=b;7 ‰oѴˆ;vķ 7o]v -m7 r†|-|bˆ; _‹0ub7v 0-v;7om|_;-m-Ѵ‹vbvo=loѴ;1†Ѵ-ul-uh;uvѴbv|;7bm!-m7b;|-Ѵĺ ŐƑƏƐƓő -m7 †vbm] -‹;vb-m ];m;|b1 1Ѵ†v|;ubm] ruo1;7†u;v blrѴ;Ŋ l;m|;7 bm "$!&$&! ƑĺƒĺƓ Ő -Ѵ†v_ķ "|;r_;mvķ ş ub|1_-u7ķ ƑƏƏƒĸub|1_-u7ķ"|;r_;mvķş omm;ѴѴ‹ķƑƏƏƏőĺ);7bv|bm]†bv_;7 ‰oѴˆ;vķ _‹0ub7vķ -m7 †m1;u|-bm bm7bˆb7†-Ѵv 0-v;7 om |_;bu l;lŊ 0;uv_brruorou|bomv|o|_;‰oѴ=1Ѵ†v|;uŐqwolfő-m7ƖƏѷ-‹;vb-m

1u;7b0Ѵ;bm|;uˆ-ѴvŐőĺ);v;||_;|_u;v_oѴ7v=ou|_;|_u;;1-|Ŋ ;]oub;v 0-v;7 om |_; ];m;|b1 1Ѵ†v|;ubm] -m-Ѵ‹v;v r;u=oul;7 om vbl†Ѵ-|;7];mo|‹r;v0‹-1_;1o;|-ѴĺŐƑƏƐƕőķv;; b]ĺ"Ɛbm|_; "†rrѴ;l;m|-u‹-|;ub-Ѵvo=-1_;1o;|-ѴĺŐƑƏƐƕőĺ);1omvb7;u;7 as pure wolves those individuals whose q_wolf was included in the range of q_wolfˆ-Ѵ†;vo=vbl†Ѵ-|;7r†u;‰oѴˆ;v];mo|‹r;v-m77b7 mo| oˆ;uѴ-r ‰b|_ |_-| o= vbl†Ѵ-|;7 0-1h1uovv;v Ő_‹0ub7Ƶr-u;mŊ |-Ѵőĺ);1Ѵ-vvb=b;7-v†m1;u|-bm|_ov;bm7bˆb7†-Ѵv‰_ov;qwolf was

included in the range in which the q_wolf values of simulated pure ‰oѴˆ;v -m7 0-1h1uovv;v |o ‰oѴˆ;v Ő=buv| -m7 v;1om7 ];m;u-|bomő oˆ;uѴ-rr;7ĺ bm-ѴѴ‹ķ ‰; 1omvb7;u;7 -v _‹0ub7v |_ov; bm7bˆb7†-Ѵv whose q_wolf overlapped with the range of q_wolf values of simulated 0-1h1uovv;vŐ=buv|-m7v;1om7];m;u-|bomő-m7ņou_‹0ub7vŐ=buv|-m7 v;1om7];m;u-|bomőĺ);-77b|bom-ѴѴ‹1omvb7;u;7-v_‹0ub7v|_ov; bm7bˆb7†-Ѵv‰_b1_ru;v;m|;7-+_-rѴo|‹r;o=1-mbm;oub]bmou|_; 7;Ѵ;|bom -| |_; ŊѴo1†v Ő-mb]Ѵb- ;|-Ѵĺķ ƑƏƐƒĸ !-m7b ;|-Ѵĺķ ƑƏƐƓő regardless of their q_wolf values.

$_;!7-|-‰;u;rooѴ;7bmƑŊlom|_1-r|†u;o11-vbomvķ‰b|_ - |o|-Ѵ o= =bˆ; 1-r|†u; o11-vbomvĺ $_bu|‹Ŋmbm; bm7bˆb7†-Ѵv ‰;u; v-lrѴ;7ŐƐƖ‰oѴˆ;vķƐƑ_‹0ub7vķѶ†m1;u|-bmv0-v;7om|_;buqwolf

ˆ-Ѵ†;őĺ ); -rrѴb;7 |_; l†Ѵ|b;ˆ;m| ! lo7;Ѵ 7;v1ub0;7 -0oˆ; |o |;v| =ou 7b==;u;m1;v bm 7;|;1|-0bѴb|‹ -m7 -vvb]ml;m| ruo0-0bѴb|‹ 0;|‰;;m _‹0ub7 -m7 r-u;m|-Ѵ bm7bˆb7†-Ѵv -m7 |o ;v|bl-|; ru;ˆ-Ŋ Ѵ;m1; o= ‰oѴ=Ƶ7o] _‹0ub7v bm |_; ror†Ѵ-|bomĺ "bm1; |_; _‹0ub7Ŋ bŒ-|bom -vv;vvl;m| bv r;u=oul;7 omѴ‹ om1; =ou ;-1_ ];mo|‹r;ķ ‰; 1omv|u-bm;7 |_; -vvb]ml;m| ruo0-0bѴb|‹ |o 0; ;v|bl-|;7 omѴ‹ †rom =buv| 1-r|†u; Őv;; |_; lo7;Ѵv 7;|-bѴv bm |_; "†rrou|bm] bmŊ =oul-|bomőĺ);=b||;7lo7;Ѵv‰b|_v|-|;Ŋ7;r;m7;m|-m71omv|-m| parameters and a combination of the two. The models were fitted bm |_; Ŋ"&! vo=|‰-u; Ő_ot†;|ķ !o†-mķ ş u-7;Ѵķ ƑƏƏƖő -m7 |_;(b|;u0b-Ѵ]oub|_l‰-vblrѴ;l;m|;7†vbm]|_;!Ő!ou;$;-lķ ƑƏƐƕő r-1h-];  Őbll;Ѵl-mmķ ƑƏƐƏőĺ ); †v;7 |_; h-bh; m=oul-|bomub|;ubomŐő=oulo7;Ѵv;Ѵ;1|bomķ1omvb7;ubm]lo7Ŋ els within Δ1ƽƑ-v|_;lov|v†rrou|;7-m7†v;7lo7;Ѵ-ˆ;uŊ -]bm]|o-11o†m|=ou†m1;u|-bm|‹bmlo7;Ѵv;Ѵ;1|bomŐ†um_-lş m7;uvomķƑƏƏƑőĺ

Pmodel=

̂N_h ̂N_p+ ̂Nh

ƕƓѶՊ

_|

ՊՊՍ SANTOSTASI ETAL. ƒՊ|Պ!"&$" ƒĺƐՊ|Պˆ-Ѵ†-|bomo=lo7;Ѵr;u=oul-m1; -bˆ;ru;ˆ-Ѵ;m1;_-7_b]_;u!"-m7r;u1;m|u;Ѵ-|bˆ;0b-v|_-m lo7;ѴŊ0-v;7ru;ˆ-Ѵ;m1;bmv1;m-uboƐŐv|-|;Ŋ7;r;m7;m|7;|;1|-0bѴŊ b|‹-m7_olo];m;o†v-vvb]ml;m|ruo0-0bѴb|‹ĸ b]†u;Ɛķ$-0Ѵ;vƐķƑőĺ $_; v-l; o11†uu;7 bm v1;m-ubo Ƒ Ő_olo];m;o†v 7;|;1|-0bѴb|‹ -m7 v|-|;Ŋ7;r;m7;m| -vvb]ml;m| ruo0-0bѴb|‹ĸ "†rrou|bm] bm=oul-|bom b]†u; "Ɛ -m7 $-0Ѵ;v "Ƒķ "ƒőĺ -bˆ; -m7 lo7;ѴŊ0-v;7 ru;ˆ-Ѵ;m1; _-7vblbѴ-u!"-m7u;Ѵ-|bˆ;0b-vomѴ‹bmv1;m-uboƒŐ_olo];m;o†v 7;|;1|-0bѴb|‹ -m7 -vvb]ml;m| ruo0-0bѴb|‹ĸ "†rrou|bm] bm=oul-|bom b]†u;"Ɛ-m7$-0Ѵ;v"Ɠķ"Ɣőĺ $_;0b-v-vvo1b-|;7‰b|_lo7;ѴŊ0-v;7ru;ˆ-Ѵ;m1;|;m7;7|oƏbm   & !   Ɛ Պ "1;m-uboƐo=vbl†Ѵ-|bomŐv|-|;Ŋ7;r;m7;m|7;|;1|-0bѴb|‹-m7_olo];m;o†v-vvb]ml;m|ruo0-0bѴb|‹őĺ"-lrѴbm]v|u-|;]b;v‰b|_ ƔՆrr;ur-m;Ѵvőˆ;uv†vƐƏŐѴo‰;ur-m;Ѵvő1-r|†u;o11-vbomv-m7Ѵo‰ŐѴ;=|Ŋ1oѴ†lmr-m;Ѵvőˆ;uv†v_b]_Őub]_|Ŋ1oѴ†lmr-m;Ѵő7;|;1|-0bѴb|‹ĺ$u†; ru;ˆ-Ѵ;m1;bvu;ru;v;m|;7-v-7-v_;7Ѵbm;‰_bѴ;|_;ƐƏƏˆ-Ѵ†;vo=m-bˆ;-m7lo7;ѴŊ0-v;7ru;ˆ-Ѵ;m1;-u;7bvrѴ-‹;7bm|_;‰_b|;-m7]u-‹ 0oŠrѴo|vķu;vr;1|bˆ;Ѵ‹ $     Ɛ Պ "1;m-uboƐo=vbl†Ѵ-|bomŐv|-|;Ŋ7;r;m7;m| 7;|;1|-0bѴb|‹-m7_olo];m;o†v-vvb]ml;m|ruo0-0bѴb|‹ő 11ĺƐ 11ĺƑ 11ĺƒ 11ĺƓ 11ĺƔ !oo|l;-mvt†-u;7;uuou o‰7;|;1|-0bѴb|‹ -bˆ; 0.07 0.14 0.23 0.23 0.30 o7;ѴŊ0-v;7 0.30 0.15 ƏĺƏѵ 0.07 0.02 b]_7;|;1|-0bѴb|‹ -bˆ; ƏĺƑѵ Əĺƒѵ 0.48 0.41 0.48 o7;ѴŊ0-v;7 0.04 0.02 0.00 0.01 0.00 ;u1;m|u;Ѵ-|bˆ;0b-v

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ՊƕƓƖ SANTOSTASI ETAL. v_o‰;70‹|_;0oŠrѴo|Ѵ-u];uu-m];vŐ b]†u;vƑŋƓĸ"†rrou|bm]bm=ouŊ l-|bom b]†u;v"Ƒŋ"ƐƏőĺ om=b7;m1;bm|;uˆ-Ѵ1oˆ;u-];‰-v-Ѵ‰-‹vƾƏĺѶƖ=ou-ѴѴv1;m-ubov ‰b|_Ɣv-lrѴbm]o11-vbomvŐ$-0Ѵ;ƒĸ"†rrou|bm]bm=oul-|bom$-0Ѵ;v "ѵķ"ƕőĺ ouv1;m-ubov‰b|_ƐƏo11-vbomvŐ$-0Ѵ;Ɠĸ"†rrou|bm]bm=ouŊ l-|bom$-0Ѵ;v"Ѷķ"Ɩő1oˆ;u-];7;1u;-v;7-=|;u|_;ƕ|_ŋѶ|_o11-Ŋ ;m7o=|_;v|†7‹Ő7†;|o-Ѵo‰-rr-u;m|v†uˆbˆ-Ѵő-==;1|v|_;-11†u-1‹ o=|_;;v|bl-|;vŐ b]†u;Ɛĸ"†rrou|bm]bm=oul-|bom b]†u;v"Ɛķ"Ƒőĺ ƒĺƑՊ|Պˆ-Ѵ†-|bomo=v-lrѴbm]v|u-|;]b;v $_;r;u=oul-m1;o=lo7;ѴŊ0-v;7ru;ˆ-Ѵ;m1;blruoˆ;7lou;-| $     Ƒ Պ "1;m-uboƐo=vbl†Ѵ-|bomŐv|-|;Ŋ7;r;m7;m|7;|;1|-0bѴb|‹-m7_olo];m;o†v-vvb]ml;m|ruo0-0bѴb|‹ő 11ĺƐ 11ĺƑ 11ĺƒ 11ĺƓ 11ĺƔ 11ĺѵ 11ĺƕ 11ĺѶ 11ĺƖ 11ĺƐƏ !oo|l;-mvt†-u;7;uuou o‰7;|;1|-0bѴb|‹ -bˆ; 0.14 0.22 0.21 0.33 0.33 0.30 0.40 Əĺƒѵ ƏĺƑѵ 0.78 o7;ѴŊ0-v;7 0.1 0.04 0.05 0.01 0.01 0.00 0.00 0.00 0.02 0.02 b]_7;|;1|-0bѴb|‹ -bˆ; 0.23 0.51 0.37 0.45 0.49 0.50 0.39 Əĺƒѵ ƏĺƐѵ ƏĺƐѵ o7;ѴŊ0-v;7 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ;u1;m|u;Ѵ-|bˆ;0b-v o‰7;|;1|-0bѴb|‹ -bˆ; ƴƏĺƏƓ ƴƏĺƏƔ ƴƏĺƏƔ ƴƏĺƏѵ ƴƏĺƏѵ ƴƏĺƏƔ ƴƏĺƏѵ ƴƏĺƏѵ ƴƏĺƏƔ ƴƏĺƏƒ o7;ѴŊ0-v;7 ƴƏĺƏƒ ƴƏĺƏƑ ƴƏĺƏƑ ƴƏĺƏƐ ƴƏĺƏƐ ƴƏĺƏƏ ƴƏĺƏƏ ƴƏĺƏƐ ƴƏĺƏƐ ƴƏĺƏƐ b]_7;|;1|-0bѴb|‹ -bˆ; ƴƏĺƏƔ ƴƏĺƏƕ ƴƏĺƏѵ ƴƏĺƏƕ ƴƏĺƏƕ ƴƏĺƏƕ ƴƏĺƏѵ ƴƏĺƏѵ ƴƏĺƏƓ ƴƏĺƏƓ o7;ѴŊ0-v;7 0.01 0.00 0.01 0.00 0.01 0.01 0.00 0.01 0.01 0.00 Noteĺ!oo|l;-mvt†-u;7;uuou-m7u;Ѵ-|bˆ;0b-vo=m-bˆ;-m7lo7;ѴŊ0-v;7ru;ˆ-Ѵ;m1;=ouv-lrѴbm]v|u-|;]b;v‰b|_ƐƏ1-r|†u;o11-vbomvŐ11őĺ

  & !   Ƒ Պ Scenario 1 of simulation Őv|-|;Ŋ7;r;m7;m|7;|;1|-0bѴb|‹-m7 _olo];m;o†v-vvb]ml;m|ruo0-0bѴb|‹őĺ oŠrѴo|vo=ƐƏƏvbl†Ѵ-|;7v†uˆbˆ-Ѵ ;v|bl-|;v=our-u;m|-ѴvŐѴ;=||‰or-m;Ѵvő -m7_‹0ub7vŐub]_||‰or-m;Ѵvő=ou;-1_ v-lrѴbm]v|u-|;]‹ĺ"-lrѴbm]v|u-|;]b;v ‰b|_Ѵo‰7;|;1|-0bѴb|‹-u;bm|_;|or uo‰ķ-m7v-lrѴbm]v|u-|;]b;v‰b|__b]_ 7;|;1|-0bѴb|‹-u;bm|_;0o||oluo‰ĺ Estimates obtained with sampling strategies with 5 and 10 capture occasions are compared in each panel

ƕƔƏՊ

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SANTOSTASI ETAL.

=uol Ѵo‰ |o _b]_ĺ m 1om|u-v|ķ bm v-lrѴbm] v|u-|;]b;v ‰b|_ Ѵo‰ 7;|;1|-0bѴb|‹ķ |_; !" -m7 |_; u;Ѵ-|bˆ; 0b-v o= lo7;ѴŊ0-v;7 ru;ˆ-Ѵ;m1; 7;1u;-v;7 Ѵ;vv u-rb7Ѵ‹ =uol Ɣ |o ƐƏ 1-r|†u; o11-Ŋ vbomvŐ b]†u;Ɛķ$-0Ѵ;vƐķƑőĺ);o0v;uˆ;7|_;v-l;r-||;um0o|_ bmv1;m-uboƑŐ"†rrou|bm]bm=oul-|bom b]†u;v"Ɛķ"Ƒķ$-0Ѵ;v"Ƒķ "ƒő-m7bmv1;m-uboƒķ-Ѵ|_o†]_bm|_;Ѵ-||;u|_;0b-v‰-vvl-ѴѴu;Ŋ ]-u7Ѵ;vvo=|_;v-lrѴbm]v|u-|;]‹Ő"†rrou|bm]bm=oul-|bom$-0Ѵ;v "Ɠķ"Ɣőĺ ƒĺƒՊ|Պ-v;v|†7‹ $_;0;v|Ŋv†rrou|;7lo7;Ѵ_-71omv|-m|r-u-l;|;uvŐ$-0Ѵ;Ɣőĺ o7;Ѵv ‰b|_ v|-|;Ŋ7;r;m7;m| -rr-u;m| v†uˆbˆ-Ѵķ 7;|;1|-0bѴb|‹ķ -m7 ruo0-0bѴb|‹ o= -vvb]ml;m| ‰;u; -Ѵvo v†rrou|;7 ŐΔ1ƺƑőĺ $_;lo7;Ѵv‰b|_v|-|;Ŋ7;r;m7;m|ruo0-0bѴb|‹o=-vvb]ml;m|‰;u; mo|b7;m|b=b-0Ѵ;7†;|o|_;u;7†1;7v-lrѴ;vbŒ;ķ-m7‰;7bv1-u7;7

  & !   ƒ Պ Scenario 1 of simulation Őv|-|;Ŋ7;r;m7;m|7;|;1|-0bѴb|‹-m7 _olo];m;o†v-vvb]ml;m|ruo0-0bѴb|‹őĺ oŠrѴo|vo=ƐƏƏvbl†Ѵ-|;77;|;1|-0bѴb|‹ ;v|bl-|;v=our-u;m|-ѴvŐѴ;=||‰or-m;Ѵvő -m7_‹0ub7vŐub]_||‰or-m;Ѵvő=ou;-1_ v-lrѴbm]v|u-|;]‹ĺ"-lrѴbm]v|u-|;]b;v ‰b|_Ѵo‰7;|;1|-0bѴb|‹-u;bm|_;|or uo‰ķ-m7v-lrѴbm]v|u-|;]b;v‰b|__b]_ 7;|;1|-0bѴb|‹-u;bm|_;0o||oluo‰ĺ Estimates obtained with sampling strategies with 5 and 10 capture occasions are compared in each panel