1

Running head.-- 1

Survival bias and Markovian emigration 2

Title.-- 3

Reducing bias in survival under non-random temporary emigration 4

List of Authors.-- 5

Claudia L. Peñaloza1,4, William L. Kendall2 and Catherine A. Langtimm3 6

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1Colorado Cooperative Fish and Wildlife Research Unit, Department of Fish, Wildlife 8

and Conservation Biology, 1484 Campus Delivery - Colorado State University, Fort Collins, 9

Colorado, 80523, USA 10

2U.S. Geological Survey, Colorado Cooperative Fish and Wildlife Research Unit, Dept. 11

of Fish, Wildlife and Conservation Biology, 1484 Campus Delivery - Colorado State University, 12

Fort Collins, Colorado, 80523, USA 13

3U.S. Geological Survey, Sirenia Project, Southeast Ecological Science Center, 7920 NW 14

71st Street, Gainesville, Florida, 32653, USA 15

4 Present address: American Journal Experts, Calle Los Alpes, Quinta Pata-Pata, Prados del Este, Caracas,

Miranda, 1080-A, VENEZUELA. E-mail: claudiapenaloza@gmail.com

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Disclaimer. This draft manuscript is distributed solely for the purpose of scientific peer 16

review. Its content is deliberative and predecisional, so it must not be disclosed or released by 17

reviewers. Because the manuscript has not yet been approved for publication by the U. S. 18

Geological Survey (USGS), it does not represent any official USGS finding or policy. 19

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Abstract. Despite intensive monitoring, temporary emigration from the sampling 21

area can induce bias severe enough for managers to discard life-history parameter estimates 22

toward the terminus of the times series (terminal bias). Under random temporary emigration 23

unbiased parameters can be estimated with CJS models. However, unmodeled Markovian 24

temporary emigration causes bias in parameter estimates and an unobservable state is required to 25

model this type of emigration. The robust design is most flexible when modeling temporary 26

emigration, and partial solutions to mitigate bias have been identified, nonetheless there are 27

conditions were terminal bias prevails. Long-lived species with high adult survival and highly 28

variable non-random temporary emigration present terminal bias in survival estimates, despite 29

being modeled with the robust design and suggested constraints. Because this bias is due to 30

uncertainty about the fate of individuals that are undetected toward the end of the time series, 31

solutions should involve using additional information on survival status or location of these 32

individuals at that time. Using simulation, we evaluated the performance of models that jointly 33

analyze robust design data and an additional source of ancillary data (predictive covariate on 34

temporary emigration, telemetry, dead recovery, or auxiliary resightings) in reducing terminal 35

bias in survival estimates. The auxiliary resighting and predictive covariate models reduced 36

terminal bias the most. Additional telemetry data was effective at reducing terminal bias only 37

when individuals were tracked for a minimum of two years. High adult survival of long-lived 38

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species made the joint model with recovery data ineffective at reducing terminal bias because of 39

small-sample bias. The naïve constraint model (last and penultimate temporary emigration 40

parameters made equal), was the least efficient, though still able to reduce terminal bias when 41

compared to an unconstrained model. Joint analysis of several sources of data improved 42

parameter estimates and reduced terminal bias. Efforts to incorporate or acquire such data 43

should be considered by researchers and wildlife managers, especially in the years leading up to 44

status assessments of species of interest. Simulation modeling is a very cost effective method to 45

explore the potential impacts of using different sources of data to produce high quality 46

demographic data to inform management. 47

Key words: bias reduction; Florida manatees; incidental observations; Markovian 48

emigration; mark-recapture; non-random temporary emigration; program MARK simulations; 49

recoveries; Trichechus manatus latirostris; resightings; robust design; telemetry. 50

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INTRODUCTION 51

Informed decisions about conservation or management of a species or population are made in the 52

face of various sources of uncertainty. One of these sources is partial observability, where there 53

is uncertainty about the status of the population due to bias or imprecision in monitoring 54

programs, or because current information on population status at the time of the decision is 55

lacking. Due to this uncertainty, decision makers will often hedge their bets by averaging 56

monitoring data across several previous years to approximate current status. This approach 57

implicitly assumes that the population is fairly static over this time span. This approach, 58

although logical, is risky in cases where a population is either very small (e.g., for endangered 59

species) or very large (e.g., for pest species), or where it is subject to transient dynamics (stage 60

structured populations; e.g., Koons et al. 2005) that will take time to stabilize. 61

In some cases, timely estimates of population status are not available because little or no 62

effort is devoted to monitoring. With demographic monitoring based on tracking individually 63

tagged or identified animals, lack of timely status information can occur, even where 64

considerable sampling effort is expended right up to the time decisions are being made. 65

Specifically, two phenomena can induce bias severe enough for managers to discard estimates of 66

survival and other estimators near the terminus of the time series (we will call this terminal bias): 67

individual heterogeneity in detection probability or temporary emigration of marked individuals 68

from the area monitored. In this paper we focus on reducing bias due to temporary emigration as 69

the effect from heterogeneity in detection is smaller. See Appendix A for our evaluation 70

comparing individual heterogeneity and temporary emigration. 71

Temporary emigration occurs when a portion of the population of interest is unavailable 72

for monitoring. Temporary emigration can arise either because the population's range extends 73

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beyond the area that is effectively sampled or biology or behavior makes individuals temporarily 74

inaccessible or absent at sampling locations (e.g., salamanders in which most of the population is 75

subterranean, Bailey et al. 2004; small mammals that exhibit torpor, Kendall et al. 1997; pre-76

breeders or skipped breeders that do not attend a breeding aggregation site, Clobert et al. 1994, 77

Kendall and Bjorkland 2001, Stauffer et al. 2012). The effect of temporary emigration on 78

estimates of demographic parameters, especially toward the end of the time series of interest, 79

depends on the nature of the movement process. When temporary emigration from a sampling 80

area is random in nature (i.e., all individuals have the same probability of being absent at any 81

given time), survival estimates obtained through classic mark-recapture analysis (i.e., Cormack-82

Jolly-Seber, Cormack 1964, Jolly 1965, Seber 1965) remain unbiased (Kendall et al. 1997). 83

However, if temporary emigration is non-random (i.e., Markovian: the absence of an individual 84

at time + 1 depends on whether or not it was absent at time ) survival estimates may be biased 85

if temporary emigration is not modeled correctly (Kendall et al. 1997). That bias can grow as the 86

end of the time series nears (Langtimm 2009). 87

Temporary emigration can be modeled by incorporating an unobservable state (for which 88

detection probability is zero), which accounts for the individuals that are not present in the 89

sampling area at a given time. The robust design (RD, i.e., when multiple independent samples 90

are taken within one sampling season, see Pollock 1982, for an overview) permits the most 91

flexibility in this modeling (Kendall et al. 1997, Kendall and Bjorkland 2001, Converse et al. 92

2009), although without the RD, accounting for unobservable states can be achieved under more 93

restrictive assumptions (Fujiwara and Caswell 2002, Schaub et al. 2004, Hunter and Caswell 94

2009). However, even with the RD, unless survival is assumed constant over time, assumptions 95

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must still be made about movement at the final sampling period. Bias can be induced, especially 96

terminal bias, if these assumptions do not hold (Langtimm 2009). 97

Effects of temporary emigration on survival estimation and partial solutions to mitigate 98

bias have been well studied (see reviews by Kendall 2004, Hunter and Caswell 2009, Bailey et 99

al. 2010). Kendall et al. (1997) showed that with RD data, fully time-specific estimates of 100

survival and movement could be estimated without bias, if the last unmeasurable probabilities of 101

leaving and returning to the study area could be reasonably approximated by other estimable 102

parameters. They provided an example setting emigration rates for the last two time periods 103

equal. Schaub et al. (2004) clarified this further, demonstrating through symbolic algebra that 104

survival for the last time interval is confounded with the last probabilities of leaving and 105

returning to the study area. Through analysis of Florida manatee (Trichechus manatus 106

latirostris) photo-identification data and a simulation study, Langtimm (2009) demonstrated that 107

survival estimates, even under the RD, are biased at the end of a time series if the constraints 108

applied to the last unmeasurable emigration probabilities are inappropriate. Furthermore, bias 109

propagated back through time, affecting more than the last two survival estimates. The 110

magnitude of the bias and number of years affected, however, depended on the survival 111

probability and variability in the Markovian emigration. High survival and highly variable 112

temporary emigration probabilities produced more pronounced terminal bias. Bias decreased, or 113

was negligible, with lower survival probabilities or reduced Markovian temporary emigration. 114

These conditions for terminal bias are common not only to the Florida manatee 115

(Langtimm et al. 2004, Langtimm 2009) but also to other long-lived, mobile species such as 116

other mammals (Schwarz and Stobo 1997, Fujiwara and Caswell 2002, Schaub et al. 2004, 117

Goswami et al. 2007, Stauffer et al. 2012), sea turtles (Kendall and Bjorkland 2001), and birds 118

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(Manly et al. 1999, Converse et al. 2009). Although the life history of long-lived species tends 119

to include stable survival probabilities (Gaillard et al. 1998), many of these taxa are of 120

conservation concern, due to anthropogenic impacts that could affect survival. Therefore, 121

management requires regular status assessments. Non-random temporary emigration could bias 122

recent survival estimates, making them unusable in a management context. As terminal bias is 123

due to uncertainty about the fate (i.e., dead or alive, present or absent) of an individual that is not 124

detected toward the end of the time series, putative approaches to mitigate this bias would 125

logically involve additional information on either the survival status or location of individuals in 126

the terminal primary sampling period. Dead recoveries (Burnham 1993, Lindberg et al. 2001) 127

and auxiliary resightings outside of the main sampling period or area (sensu Barker 1997) can 128

provide direct information on survival status, assuming such data are universal (i.e., in each time 129

interval, even if they emigrate from the study area, there is a non-zero probability they are 130

resighted, or recovered if dead). These resightings can be collected opportunistically or as part 131

of a formal monitoring plan. Location specific information from telemetry can provide direct 132

information on temporary emigration (Powell et al. 2000), and perhaps survival. Finally, 133

emigration parameters can be modeled as a function of candidate environmental covariates (e.g., 134

seasons, rainfall, flood levels, etc.). 135

In this simulation study, we used readily available models to jointly analyze different 136

types of data (Burnham 1993, Barker 1997, Barker and White 2001, Lindberg et al. 2001, 137

Kendall et al. 2013), which may improve modeling of temporary emigration and survival, 138

thereby reducing the number of biased years. Specifically, we analyzed RD encounter data with 139

an additional source of data (predictive covariate of temporary emigration, telemetry, dead 140

recoveries, or auxiliary live resightings). We evaluated the performance of these models by 141

8

comparing bias and precision in the survival estimates obtained. To our knowledge, this is the 142

first attempt to quantify the reduction in bias obtained with different types of additional data, 143

while also assessing relative bias reduction under various conditions. 144

Although the RD approach has been shown to provide the most flexibility in modeling 145

temporary emigration, we realize that in many cases multiple sampling periods within a primary 146

period of interest are not available. Therefore, in Appendix B we assume no RD and consider 147

how well bias due to temporary emigration is mitigated by the use of covariates, telemetry, dead 148

recoveries, or auxiliary resightings. 149

METHODS 150

Overview of simulation approach 151

We used a classic RD structure (two secondary sampling sessions per primary sampling 152

period, Kendall et al. 1997), which directly models temporary emigration from live encounters 153

only, as our base model. We then constructed additional models for comparison by applying 154

parameter constraints to the RD model (including the use of time-specific categorical covariates) 155

or jointly modeling ancillary data from one of the following: telemetry, dead recoveries, or 156

auxiliary resightings. We generated 500 replicates of encounter history data under models with 157

time-invariant (constant) parameters and analyzed generated data as though it were true data 158

under time-dependent versions of the models. To simulate encounter histories we used survival, 159

emigration, and detection values similar to those used by Langtimm (2009), which were shown 160

to produce non-random temporary emigration and terminal bias. 161

Terminal bias was first identified for Florida manatees from the analysis of photo-162

identification mark-recapture data (Langtimm et al. 2004, Langtimm 2009), and it appeared as a 163

pronounced drop in survival estimates toward the end of the time series. The effect, however, 164

9

was found to be an artifact of temporary emigration. To avoid winter cold stress and mortality, 165

manatees seek warm-water refugia at natural springs and power-plant effluents when water 166

temperatures fall below 20 °C (Hartman 1979, Shane 1983). They form large winter 167

aggregations at these refugia, and populations in four regional management units are monitored 168

at these sites. During warmer winters some manatees may not use the major aggregation sites 169

but instead use less reliable warm water sites closer to foraging areas, effectively becoming 170

temporary emigrants from the primary sampling areas. Previous analyses determined that 171

manatees have high adult survival and highly variable non-random temporary emigration 172

probabilities (Langtimm et al. 1998, Langtimm et al. 2004, Langtimm 2009) causing more 173

pronounced terminal bias because a large proportion of the population survives and may be 174

outside of the study area at any given time. 175

We simulated ancillary data (telemetry, dead recoveries, auxiliary resightings) for the 176

joint analysis models using several different levels of detection, or predictive environmental 177

covariates, to explore the magnitude of improvements in bias and precision with increasing 178

information. 179

We evaluated model performance with several approaches. For each time interval ( ) the 180

difference between the survival probability ( ) used to generate the encounter histories and the 181

estimated survival probability for that time period ( ), averaged across the 500 replicates, 182

( ∑ , where indexes the replicate), provides a measure of absolute bias. Root mean 183

squared error (RMSE) provides a joint measure of bias and precision and was estimated with the 184

following formula: 185

∑ , 186

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where is a survival estimate from a single replicate, , and is the true survival used to 187

generate the data. Standardized bias of annual survival estimates evaluates confidence interval 188

coverage (Burnham et al. 1987, p. 215). We determined standardized bias (absolute bias divided 189

by standard error) with the following formula: 190

. ∑ . 191

For years in which standardized bias was > 0.50, the impact of bias on confidence interval 192

coverage is considered non-negligible, suggesting the survival estimate be eliminated for 193

consideration for management purposes. 194

Generation Models 195

Using the simulation feature in program MARK (White and Burnham 1999), we 196

simulated a 12-year study under various models, depending on the data sources of interest. The 197

Barker/RD model in program MARK (Kendall et al. 2013) utilizes closed RD live sighting data 198

combined with ancillary data from dead recoveries or auxiliary live encounters. This model 199

structure has the following parameters: 200

probability that an individual alive at primary period is alive at time + 1 ( = 1, … 201

, 11). 202

probability that an individual that is part of the study population in primary period , 203

is still part of the population in + 1, given that it survived from time to + 1 ( = 204

1, …, 11). 205

probability that an individual at risk of capture at primary period is at risk of 206

capture at time + 1 ( = 2, … , 12). 207

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probability that an individual not at risk of capture at primary period is at risk of 208

capture at time + 1 ( = 2, … , 12). 209

probability that an individual is captured in secondary sample of primary period 210

given that the individual is located in the sampling area and has not been captured 211

previously in period ( =1, 2; = 1, … , 12). 212

probability that an individual is captured in secondary sample of primary period 213

given that it was captured previously in period ( = 2; = 1, … , 12). 214

probability that an individual that dies between time and + 1 is found and reported 215

( = 1, …, 12). 216

probability that an individual that survives from to + 1 is resighted sometime 217

between and + 1 ( = 1, …, 12). 218

probability that an individual that dies during the interval, to + 1, without being 219

found dead, is resighted alive sometime between and + 1 before it died ( = 1, …, 220

12). 221

All other model structures used were special cases of this general structure, except those 222

involving telemetry. In all cases, we ignored the possibility of inherently permanent emigration 223

(i.e., zero probability of return) and therefore set ≡ 1.0 throughout. To incorporate telemetry, 224

we used a fully multistate version of the RD model to permit detection in the otherwise 225

unobservable state. 226

We simulated two secondary sampling sessions per primary period for a total of 24 227

encounter occasions. We started out with a population of 500 animals in the first primary 228

sampling period, which we maintained thereafter while accounting for 96% survival rate ( = 229

500, = 20). Availability, or temporary emigration to and from the sampling area, alternated 230

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each year with sharply different values to represent highly variable migratory behavior ( ; 231

0.70, 0.50, 0.50, 0.25) respectively (Langtimm 2009). Capture 232

probabilities within secondary sessions were made equal ( , = , = , = 0.50). These 233

parameters values were the same for all generated models and were consistent with manatee 234

biology (Table 1, Langtimm 2009). 235

We generated data for our base model, the RD model (Kendall et al. 1997), by setting 236

recovery and auxiliary resighting probabilities to zero ( 0, and = = 0, respectively) in the 237

general Barker/RD model structure. 238

For the joint RD and telemetry model (RD_T), we chose a range of simulations to reflect 239

the high expense of using telemetry devices and possible technological limitations these may 240

have (i.e., limited battery life). We simulated the use of an increasing number of individuals 241

tagged with these devices over a decreasing number of years, which would represent using 242

resources budgeted for telemetry over a long period of time vs. using these resources in a short 243

period of time, e.g., in the last few years of a study leading up to a species status assessment. We 244

simulated using 10 transmitters for all years, 15 for the last 5 years, 20 for 3, 25 for 2, or 50 for 245

the last year of the study. Transmitters provided complete detectability ( = 1.0) of the tagged 246

individuals in or outside of the study area for an entire year, therefore giving perfect information 247

on detection and their temporary emigration probability. We chose a one-year battery life for 248

most scenarios to be conservative, based on our perception of the capabilities of current 249

technology, and to make it simple. We note that with just a one-year battery life, supplemental 250

information on is provided, but not on , i.e., telemetry would not provide information on the 251

probability of returning to the sampling area if an individual was not present the previous year. 252

Therefore we added one scenario where transmitters could have a two-year battery life. 253

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In the joint RD and dead recovery model (RD_RCV, Lindberg et al. 2001) auxiliary 254

resighting probabilities were fixed at zero ( = = 0), and we varied the recovery probability 255

( 0.1, 0.3, 0.5, 0.7, and 1.0) to simulate increasing data quantity with respect to dead recovery 256

and its effect on survival estimate bias. 257

In the joint RD with auxiliary resightings model (RD_AUX, Kendall et al. 2013) 258

recovery was fixed at zero ( = 0) and we varied resighting probabilities ( = 0.1, 0.3, 0.5, 0.7, 259

1.0 and = 0.05, 0.15, 0.25, 0.35, 0.5) to simulate increasing data quantity with respect to 260

auxiliary resightings and its effect on survival estimate bias. 261

We ran 500 replicates for each model using appropriate models available for simulation 262

in program MARK (see Appendix C and D for details). The RD with covariates model 263

(RD_CV) did not require generation of an additional data set as two levels of temporary 264

emigration were simulated in alternate years and could be assumed to vary with two categorical 265

environmental variables. 266

267

Estimation Models 268

The encounter histories generated with time-invariant parameter RD models alone, or 269

combined with telemetry, dead recoveries, or auxiliary resightings, were analyzed with time-270

dependent parameter models ( , , , , , and , , and where 271

applicable), where , indicates variation between and within primary periods. Where 272

conventional marks were combined with telemetry (RD_T), detection was assumed perfect for 273

telemetered individuals ( = 1.0). 274

The encounter histories generated for the base RD model were analyzed under three 275

different time-dependent RD models: an unconstrained temporary emigration model ( , 276

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) as a benchmark, a constrained model with the last and penultimate temporary emigration 277

parameters set equal (naïve constraint, , ), as suggested by Kendall 278

et al. (1997), and a constrained model with the last and antepenultimate temporary emigration 279

parameters set equal (correct constraint, , ), which matches the 280

true model under which the data were generated as implemented by Langtimm (2009). We 281

estimated parameters under these three constraint levels to illustrate the magnitude of terminal 282

bias if left uncorrected (unconstrained), the current available solution to correct this bias (naïve 283

constraint), and the best possible estimation of survival (correct constraint) without using 284

ancillary data. 285

We analyzed the same encounter histories using the predictive covariate model (RD_CV) 286

in which temporary emigration ( and ) is modeled as a two-parameter function of a covariate 287

related to temperature. This could involve a logit-linear relationship with a continuous measure 288

of temperature (e.g., 18.3, 19.0, 22.4°C). However, for simplicity of simulation, and without loss 289

of generality, we represent temperature by two categories (e.g., cold, warm). We set the 290

temporary emigration covariate (intercept + offset parameter) to alternate between two 291

categorical levels, where each level or parameter is estimable without needing direct information 292

on the last year because they reoccur throughout the time series. We ran different variations of 293

this theme: (1) alternating the two levels throughout the 11 encounter occasions; or (2) splitting 294

the 11 year relationship in two, two levels for the first six, seven, or eight years, and a second set 295

of two levels for the last five, four or three years, respectively. All cases of the covariate model 296

had the same two-level covariate alternating year after year, but the split relationship models had 297

fewer years of data to inform the estimation of the temporary emigration parameters in the last 298

year of the time series. These split relationship models were used to determine how many years 299

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of previous data are needed to correct terminal bias when using a predictive covariate (i.e., for 300

how many years does the temperature relationship need to hold for bias to be reduced or 301

eliminated). 302

Comparison of Modeling Approaches 303

To compare the relative performance of the different modeling approaches, we plotted 304

mean survival estimates and standard errors, by year, for each model type using results for 305

models representing moderate data quantity. The chosen ancillary data values are as follows: 306

RD_CV, 3-year relationship; RD_T, 25 devices for 2 years; RD_RCV, = 0.3, and RD_AUX, 307

= 0.3, = 0.15. We also compared RMSE and standardized bias in annual survival estimates 308

derived from these models. 309

RESULTS 310

Robust Design under Different Constraints 311

Bias and precision of survival estimates for the RD base model varied according to the 312

different constraints applied to the terminal temporary emigration probabilities (Fig. 1a). 313

Terminal survival estimates more closely approached 0.96 with greater precision under the naïve 314

constraint model (with the last and penultimate temporary emigration rates set equal, 315

, ) compared to the model with no constraints. An additional advantage of 316

the naïve constraint model is that the last survival and temporary emigration parameters are not 317

confounded and the last survival probability is estimable (Kendall et al. 1997). As expected and 318

demonstrated by Langtimm (2009), the correct RD model ( , ) 319

produced estimates with the least bias and greatest precision. 320

Robust Design with Predictive Covariates 321

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Bias was virtually eliminated for the entire time series if appropriate predictive covariates 322

were used. This was true for both single and split relationship models (Fig. 1b). Furthermore, if 323

a two-parameter relationship (e.g., two discrete values of the covariate or a linear relationship) 324

between an environmental predictor of temporary emigration was valid for at least the last three 325

years of sampling, terminal bias was reduced similar to models with up to 5 years of covariate 326

data. 327

Robust Design with Telemetry 328

Increasing the number of individuals monitored each year with telemetry devices, while 329

decreasing the span of years telemetry data were gathered, improved survival estimates overall 330

unless individuals were monitored for less than two years (Fig. 1c). Although bias was reduced 331

the most in year 11 (last year) when 50 devices were deployed only that year, survival estimate 332

bias for year 10 was not reduced compared to an unconstrained RD model despite the large 333

number of devices deployed in year 11 (Fig. 1d). Terminal bias was greatly reduced overall 334

when telemetry devices had an increased battery life, where animals can be monitored for two 335

consecutive years (Fig. 1d). With a one-year battery life, but not was estimable, i.e., 336

telemetry devices do not provide extra information on the probability of returning to the 337

sampling area if an individual was not present the previous year; becomes estimable through 338

telemetry with extra battery life. 339

Robust Design with Recovery 340

Precision and accuracy of survival estimates increased as dead recovery detection 341

improved (Fig. 1e). However, the last three to four survival estimates still presented substantial 342

bias regardless of the level of recovery. 343

Robust Design with Auxiliary Resightings 344

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Increasing the quantity of auxiliary resighting data (increased resighting probability, R 345

and R') reduced bias and improved precision in survival estimates throughout the entire time 346

series (Fig. 1f). 347

Comparison of Modeling Approaches 348

All of the modeling approaches showed accurate estimates of survival essentially at 0.96 349

for years 1-8 when moderate levels of ancillary data quality were modeled; precision based on 350

standard errors, however, varied among approaches (Fig. 2a). The differences in precision were 351

more apparent in the RMSE estimates (Fig. 2b). It was not until years 9-11 that estimates 352

deviated from the true value. The predictive covariate and auxiliary resightings models had the 353

most accurate average survival estimates (Fig. 2a); whereas the auxiliary resightings model had 354

the lowest RMSE among all the models we evaluated (Fig. 2b). 355

Comparison of standardized bias in survival estimates obtained for each model type 356

(Table 2) showed that the survival estimates for years 10 and 11 of the recovery model and year 357

10 of the naïve RD and telemetry models should be discarded due to reduced coverage of the 358

95% confidence interval (to less than 93%). The predictive covariates and auxiliary resightings 359

models were the only models in which standardized bias of survival estimates did not exceed 360

0.50 in any year. 361

DISCUSSION 362

Under the parameter values we specified for simulation, all models that jointly analyzed 363

additional information reduced terminal bias and increased precision in annual survival estimates 364

when compared to the basic RD model. Increasing the quantity of the ancillary data further 365

reduced bias and increased precision. However, some data sources were more effective than 366

others. 367

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The predictive covariate model corrected bias throughout the study with the single or 368

split covariate relationships, increasing precision the longer the covariate relationship held true 369

(Fig. 1b). Bias was virtually eliminated with this model (Fig. 2, Table 2). If data are available 370

and a relationship can be identified, the use of a predictive covariate can be a very cost effective 371

solution to mitigate terminal bias. However, in many cases temporary emigration could also be 372

influenced by additional unmeasured environmental covariates. Under such a weakened 373

relationship between the covariate and movement, we expect the ability of the covariate to 374

mitigate bias in survival to also be weakened. In addition, our use of a short time series on the 375

covariate was intended to account for the possibility of the relationship between the covariate 376

and movement to change over time (e.g., due to climate or some other type of system change). 377

However, the shorter the time series, the more difficult it would be to account for this change. 378

(Milly et al. 2008, Nichols et al. 2011). The use of predictive environmental covariates may only 379

be applicable in cases where the environmental phenomenon precedes the emigration behavior 380

enough that the latter can be predicted. For example, García Cruz et al. (2013) found that 381

hurricane incidence in one year was tightly correlated with survival and renesting intervals the 382

following year for adult female green turtles (Chelonia mydas) from Aves Island, Venezuela. 383

The use of telemetry may be very effective for obtaining highly detailed information on 384

the location of individual animals, and at present may well be the only way to accurately 385

determine temporary emigration rates for certain species. However, restrictions in battery life 386

limit its use for inferences on temporary emigration behavior operating on multi-annual cycles. 387

Similarly, the current high cost associated with this technique may preclude its use in sufficiently 388

large quantities for inference on large populations. The minimal improvement in survival 389

estimates for the scenario we simulated, 25 devices with a 1-year battery life for 2 years, would 390

19

not warrant the cost. However, bias reduction was much greater with an increased battery life, 391

which may be a more cost effective option as technology improves. 392

Data on dead recovery, irrespective of recovery rate, did not correct bias in the last two 393

years of the study (Fig. 1e); carcass data are subject to small sample bias when there is a low 394

probability of mortality. Because terminal bias is more prominent in species with high survival 395

(Langtimm 2009), small sample bias with recovery data may be common to most analyses of 396

large long-lived species using this approach. 397

Auxiliary resightings obtained outside of the study area or formal sampling period, at any 398

level, corrected bias in the penultimate year. At higher detection levels (30-100%), it corrected 399

bias and improved precision throughout the study (Fig. 1f). The use of auxiliary resightings was 400

the most effective way to reduce terminal bias (Fig. 2, Table 2) under our simulated survival and 401

temporary emigration values, followed closely by using predictive covariates to describe 402

temporary emigration. However, auxiliary resightings provide direct information on survival (to 403

the extent all individuals are subject to auxiliary resighting at some point in a time interval, 404

irrespective of presence in the study area), whereas a predictive covariate on temporary 405

emigration probabilities is an assumed index of temporary emigration that may or may not hold 406

true. Another advantage of the use of auxiliary resightings is that data can be collected 407

opportunistically or as part of a directed sampling design. The Barker model (Barker 1997) and 408

Barker/RD model (Kendall et al. 2013) can accommodate both and are efficient at analyzing data 409

collected at continuous, uneven, or irregular intervals (Ruiz-Gutiérrez et al. 2012, Kendall et al. 410

2013). This is particularly relevant for mobile species such as manatees (Deutsch et al. 2003), 411

bottlenose dolphins (Silva et al. 2009), and migratory birds (Ruiz-Gutiérrez et al. 2012) that 412

show seasonal changes in home range where monitoring can be targeted at several locations over 413

20

time. Furthermore, if it is feasible to allocate effort to auxiliary resightings, there is the potential 414

to adapt sampling to degraded monitoring conditions (new logistical constraints, changes in a 415

monitoring site from natural or human-induced factors) or an immediate management question 416

(e.g., an upcoming status review or evaluation of an unusual mortality event). Increasing effort, 417

as needed, to acquire resightings can ameliorate impacts from changing conditions and provide 418

managers with more reliable recent estimates. This will become more important with anticipated 419

climate and land use change. Additionally, certain organisms (e.g., cetaceans, Silva et al. 2009) 420

have very long monitoring periods and can violate the assumption of equal probability of 421

survival among individuals. The use of models that incorporate auxiliary resightings, like the 422

Barker/RD, would allow researchers to shorten the primary monitoring period for the analysis 423

while still incorporating sightings outside of the primary monitoring period or area, thus avoiding 424

this assumption violation (Ruiz-Gutiérrez et al. 2012). 425

For many species and systems the availability of ancillary data may be limited. When no 426

ancillary information is available, a constraint on the terminal availability probabilities is still the 427

best option. We have shown that even when the constraint is naïve, this approach performs 428

better than an unconstrained model (Fig. 2, Table 2). However, researchers and field biologists 429

with extensive understanding of the population and the system can often identify a constraint that 430

would be less naïve. That is, they might be able to identify a previous year that is similar to the 431

last year of the study with respect to temporary emigration. As with any surrogate for real data, 432

only subsequent monitoring and analysis will show how well the constraint assumptions held. 433

It should be noted that Langtimm (2009) found 4-5 years of significant bias using the 434

naïve constraint, based on standardized bias, whereas we found significant terminal bias only 435

extended 2 years before the end of time series in our simulations. We believe this difference 436

21

may be partly because of the larger standard error due to the smaller population size (and thus 437

sample size) used in our simulations. However, it also, reiterates that different initial conditions, 438

survival, and temporary emigration probabilities can lead to different results. 439

When we repeated many of our simulations without the benefit of the RD (e.g., one 440

sampling occasion per period of interest), we found little bias in survival early in the time series 441

in all cases, and when supplemented with auxiliary resightings, virtually identical bias and 442

precision for the entire time series (Appendix B). However, bias and variance in capture 443

probability (and hence abundance) and movement probabilities was still substantially larger. The 444

mitigation of bias in the face of temporary emigration, without robust design data, should be 445

further investigated with different parameter values. Nevertheless, given the theoretical problems 446

with such a model, and especially given the persistent bias in other parameters of interest, we 447

encourage practitioners to employ a robust design whenever possible. 448

For many species and populations additional data may already exist or new monitoring 449

programs can be put in place. What solutions are employed will depend on the biology of the 450

population and resources available to researchers and managers. Gathering auxiliary resighting 451

data rather than trying to improve recovery, for example, may be an effective strategy for species 452

such as manatees, with naturally low adult mortality and relatively short-range migrations 453

between winter and summer habitats (Deutsch et al. 2003). However, for species that disperse 454

widely or migrate long distances from aggregation sites (e.g., sea turtles), increasing auxiliary 455

resightings outside of nesting beaches may not be feasible. In such cases, the use of telemetry 456

(e.g., satellite or possibly acoustic tags, K. Hart comm. pers., see Heupel et al. 2006) or 457

identifying a predictive environmental covariate (García Cruz et al. 2013) may prove to be 458

effective strategies to reduce terminal survival estimate bias. Hunted waterfowl have well 459

22

established programs for obtaining ancillary data opportunistically from the general public, for 460

example, band recoveries from hunters and auxiliary resightings from birdwatchers (Lindberg et 461

al. 2001, Conn et al. 2004). 462

In a broader context, the use of simulation as a tool to understand the behavior of 463

estimator bias under different scenarios, and the ability to compare the performance of available 464

methods in reducing said bias, should allow researches and managers to identify the most time 465

and cost effective solution for producing the best possible life-history parameter estimates to 466

inform management. Nonetheless, regardless of the type and quantity of data used, common 467

sense and the results of our simulations and Langtimm's (2009) show that point estimates and 468

standard errors from the analysis of real data should be expected to change as additional years of 469

observation are acquired. Whereas simulation assessments of bias and precision are based on the 470

mean estimate from many randomly generated sets of encounter histories, only one set of 471

encounter histories is available with real data, and the sample of individuals and their detection is 472

stochastic and subject to sampling error. Only with additional years of data and subsequent 473

observation of unobserved individuals will more accurate estimates be realized. 474

A final consideration for assessment of bias and whether or not to use terminal survival 475

estimates is how the estimates will be used for management decisions. How many years are 476

biased and how does that affect time trend models and the power to correctly identify increasing, 477

decreasing, or unchanging survival probabilities (Langtimm et al. 2004)? Population growth 478

rates of long-lived species are most sensitive to small changes in adult survival; what effect do 479

terminally biased estimates have on estimates of constant survival models used to estimate 480

asymptotic growth rates (Fletcher et al. 2011)? What is the effect on mean and temporal 481

variance of time-dependent estimates used in population viability analyses (Runge et al. 2007)? 482

23

When modeling hypotheses of factors affecting survival rates (e.g., management actions or 483

environmental events), is there power to detect an effect, and what are the consequences of 484

estimates that are biased low vs. biased high? The extent to which bias will influence 485

management decisions will depend on several issues and should be discussed between 486

researchers and managers when identifying management actions. 487

CONCLUSIONS 488

Timely information on demography is important to any population conservation decision, 489

and being forced to ignore the last several years of survival information because of bias is 490

undesirable. For organisms with high survival probability, modeling additional data from 491

auxiliary resightings of live individuals outside of the sampling area or period is the most 492

effective way of reducing survival estimate bias. Using additional data from dead recovery is the 493

least effective despite the intensive effort it might require. With enhanced battery life of 494

telemetry devices (≥ 2 years), the use of additional data from telemetered animals may be an 495

effective strategy to reduce bias, though care must be taken to ensure the sample adequately 496

represents the entire population. If a suitable relationship can be found, the use of a predictive 497

environmental covariate to describe temporary emigration can be cost effective, but in many 498

cases the validity of the relationship will be assumed and subject to question. Our results 499

indicate the relative benefits of additional sources of information individually, but we have not 500

evaluated the synergistic benefits of combining some or all of these additional sources. In 501

addition, we have used the particular case of manatee demography to illustrate these issues. We 502

encourage investigators to use simulation approaches such as what we have demonstrated to 503

evaluate potential bias and solutions using parameter values representative of their species or 504

system. 505

24

ACKNOWLEDGMENTS 506

Discussions with Evan Cooch were helpful in developing the simulations. Helpful 507

comments by Jim Nichols and an anonymous referee improved the manuscript. The use of trade 508

names or products does not constitute endorsement by the U. S. Government. 509

510

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632

APPENDIX A 633

Bias in survival estimators induced by individual heterogeneity in detection probability 634

(Ecological Archives XXXX-XXX-XX). 635

APPENDIX B 636

Mitigation of temporary emigration induced bias in survival estimates without the robust design, 637

by use of covariates, telemetry, dead recoveries, or auxiliary resightings (Ecological Archives 638

XXXX-XXX-XX). 639

30

APPENDIX C 640

Underlying structure of simulation models in program MARK (Ecological Archives XXXX-641

XXX-XX). 642

APPENDIX D 643

Parameter Index Matrices used in program MARK simulation to generate encounter histories and 644

estimate demographic parameters from models evaluated for survival estimate bias reduction 645

(Ecological Archives XXXX-XXX-XX). 646

647

31

Table 1. Structure of simulation models used to evaluate reduction in terminal bias of survival estimates. We modeled several 648

scenarios of available ancillary data to determine the effect on survival estimates. Fixed parameters are not shown. 649

Data Used Alias Generation Models Parameter Values Estimation Models

Live sightings RD . .

= 0.96

0.50

Unconstrained ( , )

Naïve ( , , )

Correct ( , , )

+ Covariates

on RD_CV . .

Two level covariate (all years)

Split two level covariate (last 5, 4, 3 yrs)

+ Telemetry RD_T . . 10, 15, 20, 25 and 50 devices

for all, 5, 3, 2 and 1 years 1 /

+ Recovery RD_RCV . . . r = 0.1, 0.3, 0.5, 0.7, 1.0

+ Auxiliary

resightings RD_AUX . . . .

R = 0.1, 0.3, 0.5, 0.7, 1.0

R' = 0.05, 0.15, 0.25, 0.35, 0.5

Notes: Simulated data were generated under constant models (".", dot models) for all parameters except temporary emigration ( , ), which was modeled with

two alternating levels to represent stark differences in migratory behavior to produce terminal bias ( ; 0.70, 0.50, 0.50, 0.25).

Estimation models were time-dependent ("t" models) for all parameters. In the telemetry model, telemetered individuals (T) had perfect detection ( = 1) at all

32

times (observable or unobservable), whereas detection for recaptured individuals (Recap) was time-dependent ( ).

650

33

Table 2. Comparison of standardized bias for survival estimates obtained from simulation 651

models used to evaluate reduction in terminal bias. Values in bold highlight standardized bias 652

greater than 0.50 where expected coverage of the 95% confidence interval would be reduced to 653

less than 93%. Values used for ancillary data models are as follows: predictive covariates, linear 654

relationship between survival and temporary emigration valid for the last 3 years; telemetry, 25 655

devices for last 2 years (one-year battery life); recovery, = 0.2, and auxiliary resightings, = 656

0.3, = 0.15. 657

Standardized Bias

Year Unconstrained Naïve Predictive

Covariates Telemetry Recovery

Auxiliary

resightings

1 0.11 0.11 0.07 -0.04 -0.02 0.03

2 -0.05 -0.05 0.03 -0.05 -0.01 -0.02

3 -0.06 -0.06 -0.03 0.02 0.05 -0.04

4 0.02 0.02 -0.06 0.03 0.00 0.04

5 0.11 0.11 0.10 -0.01 -0.01 -0.02

6 -0.08 -0.05 -0.05 -0.01 -0.02 0.02

7 0.02 0.07 0.07 -0.02 0.02 -0.05

8 -0.32 -0.10 -0.10 -0.24 0.16 -0.06

9 -0.72 -0.22 -0.11 -0.21 0.29 -0.04

10 -2.15 -0.50 -0.08 -0.55 0.58 -0.17

11 NA* NA** -0.21 -0.36 0.60 -0.32

* Survival is unestimable due to confounding with temporary emigration probabilities in year 11 of the

unconstrained RD model.

34

**Survival was estimated at 1.0 for every replicate in year 11 of the naïve constraint RD model, yielding a

standard error = 0.0, which precludes determining standardized bias for this estimate.

658

35

FIGURE LEGENDS 659

Figure 1. Survival estimates obtained from simulations of the robust design with constraints and 660

different types of ancillary data, averaged across 500 replicates. a) Robust design with correct, 661

naïve and unconstrained temporary emigration probabilities (the survival estimate in year 11 for 662

the unconstrained model is unestimable due to confounding with temporary emigration 663

probabilities). b) Use of predictive covariates to model temporary emigration as a single 664

relationship for the entire simulation period (All Years) and three models with a split relationship 665

(a two level relationship for the first few years and a second two level relationship for remaining 666

years) for the last five (5 yrs), four (4 yrs) and three (3 yrs) years of the simulation. c) Data from 667

telemetered individuals with variable number of telemetry devices and deployment time (10 668

devices all years, 15 devices 5 years, 20 devices 3 years, 25 devices 2 years, and 50 devices 1 669

year). d) Unconstrained and naïve robust design and data from 50 individuals with telemetry 670

devices with a 1-year battery life deployed in year 11 or a 2-year battery life deployed in year 10. 671

e) Dead recovery data with different recovery probabilities ( = 0.1, 0.3, 0.5, 0.7, 1.0). f) 672

Auxiliary resightings of live animals outside of primary sampling periods or areas using different 673

resighting probabilities ( and ; only is shown, for corresponding see Table 1). Bars 674

represent standard errors for parameter estimates. 675

Figure 2. Model performance comparison with respect to bias in survival estimates obtained 676

from simulations (n = 500 replicates). a) Absolute bias and standard error (bars) of survival 677

estimates relative to generation models. b) Root mean squared error of survival estimates 678

relative to generation models. Values used for ancillary data models; predictive covariates, 3-679

year relationship, telemetry, 25 devices for each of 2 years, recovery, = 0.3, and auxiliary 680

resightings, = 0.3, = 0.15. We did not graph the RMSE for year 11 of the naïve constraint 681

36

robust design model because survival was estimated at 1.0 for every replicate, yielding a 682

standard error = 0.0, which produces an artificially small and misleading RMSE. 683

37

FIGURES 684

685

Figure 1 686

38

687

688

Figure 2 689