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Draft Technical Report Covariate Survival Analysis

DRAFT TECHNICAL REPORT

The effects of biotic and abiotic factors on juvenile steelhead survival: A retrospective analysis of data from the middle Columbia River during 2008-2015

Prepared For: Public Utility District No. 2 of Grant County

P.O. Box 878 30 C Street SW

Ephrata, Washington 98823

and

Blue Leaf Environmental, Inc. 2301 W Dolarway Rd, Suite 3

Ellensburg, WA 98926

Prepared By: Quinn Payton, Allen F. Evans, and Brad Cramer

Real Time Research, Inc. 1000 S.W. Emkay Drive

Bend, OR 97702

May 31, 2016

http://www.google.com/url?sa=i&rct=j&q=image+of+priest+rapids+dam+fish+bypass+project&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiYtcT54s3MAhUS52MKHfywBUcQjRwIBw&url=http://www.grantpud.org/blog/?p%3D1419&psig=AFQjCNEUc1klxGYWJ4gy8Tax257_PfaGfQ&ust=1462910025635584


TABLE OF CONTENTS

SUMMARY ..................................................................................................................................................... 3

INTRODUCTION ............................................................................................................................................. 4

METHODS ...................................................................................................................................................... 5

Study Area ................................................................................................................................................ 5

Fish Tagging, Recapture and Recovery .................................................................................................... 6

Survival of Double-tagged Fish ................................................................................................................ 7

Survival of Single-tagged Fish .................................................................................................................. 9

RESULTS ...................................................................................................................................................... 11

Fish Tagging, Recapture and Recovery .................................................................................................. 11

Survival of Double-tagged Fish .............................................................................................................. 11

Survival of Single-tagged Fish ................................................................................................................ 16

DISCUSSION ................................................................................................................................................. 18

ACKNOWLEDGEMENTS ............................................................................................................................... 20

LITERATURE CITED ...................................................................................................................................... 20

APPENDIX A: JOINT SURVIVAL AND PREDATION ESTIMATION ................................................................... 25


SUMMARY Identifying factors that influence the survival of Endangered Species Act (ESA) listed juvenile steelhead Oncorhynchus mykiss during outmigration through the middle Columbia River is integral to prioritizing recovery actions. To evaluate which factors best explain variation in steelhead survival during 2008-2015, we developed survival models that incorporated various biotic and abiotic factors experienced by smolts during outmigration as covariates. Biotic covariates investigated included predation by colonial waterbirds, the relative abundance of steelhead, fish travel times, and individual fish characteristics or traits. Abiotic covariates investigated included river temperature, river flows, water transit times, and dam operational strategies. Two independent release groups of fish were included in our analyses, with the suite of covariates investigated differing based on the data available for each release group. These groups were (1) fish tagged with acoustic telemetry (AT) and passive integrated transponder (PIT) tags (i.e., double-tagged fish) used to estimate survival between Rock Island and Priest Rapids dams (referred to as the Priest Rapids Project) and (2) fish tagged with PIT tags (i.e., single-tagged) used to estimate survival from Rock Island Dam to McNary Dam. In general, analyses of double-tagged fish focused on investigating the influence of abiotic factors on survival, while analysis of single-tagged fish focused on biotic factors. Analyses of data from double-tagged, which were based on a joint survival/mortality model, indicated that bird predation accounted for 11.9 to 62.2% (depending on the year and development) of all mortality experienced by steelhead migrating through the Priest Rapid Project. Logistic regression indicated that there was a strong inverse relationship between avian predation and steelhead survival. Furthermore, steelhead survival was (1) inversely related to water temperature and the proportion of steelhead migrating through the powerhouse at Wanapum Dam and (2) directly related to the relative abundance of steelhead within the Project. Analyses of data from double-tagged steelhead infer that the combination of water transit times and fish migration speed are also directly related to steelhead survival, with the odds of survival more than doubling (increasing by a factor of 2.42) for each km/hr increase in average migration speed through the Wanapum reservoir. Analyses of data from single-tagged steelhead, which did not include a measure of bird predation, provided strong support for survival models that included fish length, external condition (body injuries, descaling, fin damage and/or disease), and rearing-type (hatchery, wild). Survival was positively associated with fish length, with each additional cm in fork length being associated with 7% greater odds of surviving from Rock Island Dam to McNary Dam. Fish in compromised condition, which were disproportionately hatchery-reared, were 64% less likely to survive to McNary Dam compared with uncompromised (i.e., healthy) fish. Wild fish, which were generally in good external condition, were 117% more likely to survive to McNary Dam compared with hatchery fish. Collectively, results from this study indicated that a combination of population- and individual-level factors influence variation in steelhead survival during outmigration through the middle Columbia River. Results are consistent with and corroborate previously published studies that indicate predation from colonial waterbirds is one the greatest single factors influencing steelhead smolt survival in the Columbia River basin. Results also indicate that other factors, like dam operational strategies, fish condition, and travel times are important factors that affect differences in steelhead survival during outmigration.


INTRODUCTION Steelhead Oncorhynchus mykiss originating from the upper Columbia River are listed as threatened under the Endangered Species Act (ESA) and juveniles from this reach must navigate past up to eight hydroelectric dams during seaward migration. The National Oceanic and Atmospheric Administration (NOAA) has established survival standards for juvenile salmonids during their outmigration. Survival standards for smolt passing through the Priest Rapids Project (Wanapum and Priest Rapids dams and reservoirs) in the middle Columbia River require 93% fish survival through each development (one dam and reservoir) or 86% survival through the entire Project (NMFS 2004). To evaluate whether these survival standards were being met, Public Utility District No. 2 of Grant County (Grant PUD) conducted survival studies on juvenile steelhead during 2008-2010 and again during 2014-2015. Standards were evaluated using smolts tagged with acoustic telemetry (AT) tags and a network of hydrophones that resulted in precise measure of survival at various spatial and temporal scales within the Priest Rapids Project. Results indicated that steelhead survival varied significantly by year and that survival standards were not met in all years (Skalski et al. 2016). Multiple biotic and abiotic factors influence juvenile salmonid survival during outmigration through the Columbia River basin to the Pacific Ocean. For example, abiotic factors like river flows, river temperature, and hydroelectric dam operational strategies have been associated with intra- and inter-annually variation in steelhead survival (Petrosky and Schaller 2010; Haeseker et al. 2012). Biotic factors, like avian predation and the abundance or density of smolts during outmigration have also be linked to variation in steelhead survival (Hostetter et al. 2012; Evans et al. in press). In addition to these factors – factors that influence large groups or populations of fish (referred to as population-level factors; Juanes et al. 2000) – research has also demonstrated that individual fish characteristics or traits are related to variation in smolt survival during outmigration. For instance, the external condition (injuries, disease, descaling), size, and origin (hatchery, wild) of steelhead smolts have all been linked to survival during outmigration (Zabel 2008; Hostetter et al. 2011; Evans et al. 2014; Hostetter et al. 2015). Studies that investigate the influence of individual fish characteristics or traits on survival generally require large sample sizes of tagged fish and tagging that is representative of the run-timing and general composition of the population at-large (see Evans et al. 2014). Due to the costs and infrastructure associated with the use of AT tags (McMichael et al. 2010), passive integrated transponder (PIT) tags are typically used to investigate the relationship between individual fish characteristics and survival (Hostetter et al. 2011; Evans et al. 2014; Hostetter et al. 2015). As part of a study to investigate the influence of avian predation on smolt survival and to determine if individual fish characteristics were associated with smolt survival during outmigration, Grant PUD funded studies to PIT-tag, condition-score, release, and recapture/recover steelhead smolts from the middle Columbia River during 2008-2015. Efforts to compare and contrast which biotic and abiotic factors best explain variation in smolt survival using the same group of fish, over a long time series, are generally lacking but may be necessary to determine which factor(s) are the most important and how these factors may be inter-related. Furthermore, few studies have attempted to model survival probabilities using both population- and individual-level variables. The primary goal of this study was to evaluate if biotic and abiotic conditions experienced by steelhead smolts traveling through the middle Columbia River were associated with variation in survival at different spatial and temporal scales. More specifically, the objectives of this study were to evaluate the influence of biotic and abiotic factors on steelhead survival (1) based on AT-tagged smolts passing through the middle Columbia River during 2008-2010 and 2014-2015 and (2) based on PIT-tagged smolts passing through the middle and lower Columbia River during 2008-2015.


METHODS Study Area We investigated factors that best explain variation in juvenile steelhead survival in two river reaches: (1) a 90 kilometer (km) section of the middle Columbia River between the tailrace of Rock Island Dam and Priest Rapids Dam (hereafter referred to the Priest Rapids Project) and (2) a 259 km section of the middle and lower Columbia River between the tailrace of Rock Island Dam and McNary Dam. Survival estimates were based on releases and detections of AT fish within the Reach 1 and PIT-tagged fish within the Reach 2. The AT group were also PIT-tagged (i.e., double-tagged), while the PIT-tagged group were single-tagged (see Fish Tagging, Recapture, and Recovery below for details). Multiple acoustic arrays deployed within the Priest Rapids Project were used to estimate smolt survival in Reach 1 and PIT tag arrays located at McNary Dam were used to estimate smolt survival in Reach 2 (Figure 1).

Figure 1. Locations of juvenile steelhead release sites (red diamonds), acoustic or PIT tag arrays (yellow dots), hydroelectric dams (grey rectangles), and bird colonies (blue stars) used to estimate survival during 2008-2015.


Fish Tagging, Recapture and Recovery Detailed methods regarding the tagging and release of double-tagged (AT, PIT) steelhead used in this study are presented in Skalski et al. (2016). In brief, downstream migrating steelhead were collected at Wanapum and Priest Rapids dams by dip-netting smolts from the gatewell slots at each dam. Following established AT-tagging protocols for smolts in the region, steelhead were selected for tagging based on their weight (15–89 g) and external condition (no signs of disease; ≤20% descaling; no open wounds, hemorrhaging, or deformities; Weiland et al. 2015). Fish were anesthetized, implanted with an AT tag (Hydroacoustic Technology Model 795 during 2008-2010 or Lotek Model L-AMT during 2014-2015) and a PIT tag (Biomark Model SST12 during 2008-2010 or Biomark Model HPT12 during 2014-2015), and held in a recovery tank for 18 to 24 hrs. Following recovery, fish were transported by truck and released via helicopter at release sites in the tailraces of Rock Island Dam (Rkm 729), Wanapum Dam (Rkm 670), and Priest Rapids Dam (Rkm 639; Figure 1). Double-tagged steelhead were released daily between late April and late May during each study year. Detailed methods regarding the tagging and release of singled-tagged (PIT only) steelhead used in this study are presented in Evans et al. (2014). In brief, steelhead smolts were captured at the Rock Island Dam fish trap, PIT-tagged (Biomark Model SST12 during 2008-2013 or Biomark Model HPT12 during 2014-2015), and released into the tailrace of Rock Island dam to resume outmigration. Unlike steelhead smolts selected for AT tagging, smolts selected for PIT tagging were randomly selected for tagging (i.e., tagged regardless of their size and external condition and in-concert with, and in proportion to, the run-at-large). Data on the size (fork length) and external condition (disease, body injuries, descaling, and fin damage obtained via high-resolution digital photography) were collected from each PIT-tagged fish prior to release (see Evans et al. 2014 for details). PIT-tagged steelhead were released into the tailrace of Rock Island Dam daily between early April and mid-June each study year. Following release, double-tagged fish were detected alive (referred to as a “recapture” event) when passing telemetry arrays (a series of hydrophones placed in lines perpendicular to the shore; see Skalski et al. 2016) in the middle Columbia River (Figure 1). The actual number and spatial extent of the AT arrays used in the survival models varied by year (Timko et al. 2011, Skalski et al. 2016). Single-tagged fish were subsequently recaptured at PIT tag arrays located at hydroelectric dams and at an in-river array in the Columbia River estuary (see below). Tags from both release groups of fish (single- and double-tagged) were also recovered dead (referred to as a “recovery” event) on multiple fish-eating waterbird colonies which forage within the Priest Rapids Project (Figure 1). Such recoveries provide an additional source of information regarding the final fate of each study fish (see Simultaneous Survival and Predation Modelling below). The downstream boundary used in the survival models (using both single- and double-tagged fish) was the PIT tag array located at McNary Dam (Rkm 470; Figure 1). The final recapture event for both models was based on a set of one or more possible recaptures/recoveries including recaptures at the PIT tag arrays downstream of McNary Dam (i.e., John Day Dam [Rkm 347], Bonneville Dam [Rkm 235], and a pair-trawl detector located in estuary [Rkm 75]) and recoveries from bird colonies where birds are known to forage downstream of McNary Dam (i.e., Blalock Islands [Rkm 440], Three Mile Canyon Island [Rkm 413], Miller Rocks [Rkm 331], and East Sand Island [Rkm 8]). See Evans et al. (2012), Adkins et al. (2014), Evans et al. (in press) for additional information concerning these colonies and methods used to recover tags.


The colonies for which predation probabilities were calculated within the Project include Caspian tern colonies on Twinning Island in Banks Lake and Goose Island in Potholes Reservoir (Figure 1). Detailed methods regarding the recovery of PIT tags on these colonies, including a description of methods used to estimate detection and deposition probabilities, are provided in Evans et al. (in press). In brief, colonies were scanned for tags after the nesting season using hand-held PIT tag transceivers/antennas and the number of tags recovered adjusted/corrected for tag loss or non-detection due to the fraction of consumed tags deposited off-colony (at loafing, roosting, or off-colony areas) or deposited on-colony but not detected by researchers following each nesting season (see also Hostetter et al. 2015).

Survival of Double-tagged Fish We performed three analyses to estimate survival using double-tagged fish traveling through the Priest Rapids Project. First, we employed a novel adaptation of the Cormack-Jolly-Seber (Cormack 1964, Jolly 1965, Seber 1965) capture/recapture model to incorporate recoveries of tags on avian colonies to estimate both survival and mortality (i.e., predation and “other” mortality) rates simultaneously over consecutive AT arrays within the study area. Second, we conducted a covariate analysis that explored the associations between a suite of population-level variables and steelhead survival within the Project. Third, we used differences in detection times at adjacent arrays to evaluate the relationship between smolt migration speed (km/hr) and survival. Simultaneous survival and mortality modelling - A detailed description of our joint survival and avian predation model is provided in Appendix A. In brief, we developed a model that allows for the concurrent estimation of survival (1-mortality) and mortality due to colonial waterbird predation using a Bayesian analytical framework. The main impetus behind this approach was to provide a more holistic view of the fates encountered by steelhead during outmigration through the Priest Rapids Project. This method also results in estimates that are more precise and with reduced bias. While the recapture and recovery opportunities varied by year, the resulting estimates of survival and predation by Caspian terns used in the covariate analysis (see below) were calculated such that they would be comparable among years. Estimates were calculated specific to cohorts of fish grouped by release day and location. Covariate modelling - We compiled an a priori list of factors previously identified in the published literature as explaining differences in juvenile steelhead survival during outmigration. Variables or covariates were assembled into a framework of credible models to be investigated. The fitness of each set of variables in explaining variation in survival probabilities was accessed using the corrected Akaike Information Criterion (AICc) as calculated from weighted logistic regression models (Burnham and Anderson 2002). Population-level covariates used in the model include (1) relative fish abundance, (2) flow, (3) water temperature, (4) dam operational strategies, and (5) avian predation. We approximated relative fish abundance by using a running three-day average of the fish passage index at Rock Island Dam (FPC 2016). Flow conditions in the Priest Rapids Project were represented by measurements of discharge (kilo cubic feet per second [kcfs]), percentage spill, and an approximation of water transit times calculated as the ratio between reservoir elevation and discharge (hereafter water transit index [WTI]). Water temperature (C) was measured at each dam. Variables related to dam operations were measured at Wanapum and Priest Rapids dams and included percentage spill and the estimated percentage of fish traveling through the powerhouse from each cohort. Data relating to temperature, discharge, percentage spill, and elevation were all obtained from the Data Access in Real Time website (DART, www.cbr.washington.edu/dart). Similar to the Comparative Survival Study (McCann et al. 2015), we estimated percent passage through the powerhouse at Wanapum Dam using the AT-tagged fish. We

http://www.cbr.washington.edu/dart


attempted to define passage routes through Wanapum Dam for each AT-tagged steelhead using amplitude changes in the final two minutes of forebay detections during a fish’s approach to the dam. These measurements allowed us to identify which of the two closest loggers an individual fish was closest to at the time of passage. Powerhouse index (PH index) was then defined for each cohort as the proportion of fish assumed to have passed Wanapum Dam through the powerhouse rather than by other means (i.e., spillway, bypass, or ladder). The number of fish from each release group with accurate passage information was limited; therefore, a seven-day running average for PH index was calculated. Finally, avian predation in the Project was attributed to two nearby Caspian tern colonies at Twinning Island in Banks Lake and Goose Island in Potholes Reservoir. Point estimates of predation probabilities were calculated with the joint survival and avian predation model (see Appendix A). Only the Rock Island Dam release group of AT-tagged fish were used to make inferences about survival through the Priest Rapids Project (from Rock Island tailrace [Rkm 710] to the Priest Rapids tailrace [Rkm 624]) using uncorrected survival estimates. Past research has indicated that a delayed handling effect may be present in AT-tagged steelhead following release (Skalski et al. 2016). Analytical approaches used to account for this bias involve multiplicative corrections based on the paired-release model structure of AT survival studies. There are several concerns with applying a paired-release and handling mortality framework in the context of analyzing the effects of covariates on survival, however. Primarily, the handling effect is difficult to account for in cohorts of fish grouped by release day (fish assumed to experience the same population-level effects), handling effect varies greatly by year and spatial-scale (river reach), and any correction will create additional variation in survival estimates, perhaps confounding the effects of the covariates and/or creating unknown bias in the results. Furthermore, in some cases the adjustment for handling effect results in survival estimates > 1.0, which results in less than optimal modelling options (e.g., linear regression). Finally, any attempt to correct survival rates would suggest the need to correct predation probabilities as well; such corrections are much less tenable and would require strict, untestable assumptions. In order to provide greater justification for the narrow focus on Rock Island released fish, we ran additional covariate analyses on survival through the Priest Rapids Reservoir (from the array at [Rkm 657] to the Priest Rapids tailrace [Rkm 624]) separately for the fish released at Rock Island Dam and those released at Wanapum Dam. Comparing and contrasting results from these additional analyses provides a better understanding of any potential differences in survival between the release cohorts vulnerable to delayed handling effects and those presumably fully acclimated to the river. As noted above, a list of biologically justifiable models was constructed a priori with one variable from each of the above listed population-level covariate categories with at most one two-way interaction term. Possible interactions between covariates is known to be useful in explaining variation in survival (Zabel et al. 2002; Hostetter et al. 2012). In order to avoid overfitting models, we allowed the inclusion of at most one interaction term among those variables selected. We evaluated the relationship between estimated daily survival rates and the above variables using a weighted logistic regression models. Our model of survival, �̂�, can be expressed by the logistic regression equation,

𝑙𝑜𝑔𝑖𝑡(�̂�𝑖) = 𝛼𝑦 + �⃗⃗� 𝒙𝑖⃗⃗ ⃗ + 𝜖𝑖

where 𝛼𝑦 represents the mean logit survival for year y, �⃗⃗� represents the vector of all covariate

coefficients as selected from the outlined categories above (i.e., 𝛽1 is the coefficient related to


steelhead abundance, etc.), and 𝜖𝑖 represents the random variation associated with the ith observation. The precision in the estimates of survival varied by year and release day. This difference in precision was accounted for by inverse variance weighting. That is, each estimate �̂�𝑖 was given weight 𝑤𝑖 = 1/𝑣𝑎𝑟(�̂�𝑖). All logistic regression models were run using R (R Core Team 2015). The resulting models were ranked using Akaike’s information criterion corrected for small sample size (AICc) and compared using the AICc difference (AICc; Burnham and Anderson 2002). Supplementary migration speed analysis - We investigated the interrelated effects of migration speed and water transit time on smolt survival. The use of AT tags provides precise information relating to the speed or travel times of each fish (an individual-level variable). Data on travel times, however, are only available for fish that survived migration through a particular river reach, potentially resulting in a bias by limiting data to the fastest individuals within that reach (Tuomikoski et al. 2013). Such a bias is presumably increased over longer river reaches. An alternative, but indirect, measure of fish travel times are water transit times (a population-level variable; proportional to reservoir elevation divided by outflow; Petrosky and Schaller 2010). Other studies have also implied that metrics of water transit time can be used as proxies for the average speed of fish through a river reach (Schaller et al. 2007). The AT-tagged fish used in this study provide a unique dataset to compare and contrast which metric (actual fish travel times or water transit times) best explains variation in steelhead survival in the Priest Rapids Project. We assessed the association between WTI and the observed average traveling speeds of AT smolts using descriptive statistics. We then assessed whether there was a significant association between traveling speed over a river segment and the subsequent detection of that fish at a downstream array. We performed this analysis using all steelhead interrogated at the final arrays in the forebay of Wanapum dam and the forebay of Priest Rapids dam. For each forebay, we model the

apparent survival, �̂�𝑖, of a fish i through the subsequent river segments using the logistic regression function,

𝑙𝑜𝑔𝑖𝑡(�̂�𝑖) = 𝛽𝑦𝑒𝑎𝑟 + 𝛽𝑚 ∗ 𝑚𝑠𝑖 + 𝛽𝑤 ∗ 𝑤𝑡𝑑 + 𝛽𝑥 ∗ (𝑚𝑠𝑖 ∗ 𝑤𝑡𝑑) + 𝑎𝑑|𝑦 + 𝜖𝑖

where 𝛽𝑚 accounts for the assumed differences among years, 𝛽𝑚 is the regression coefficient for migration speed, 𝛽𝑤 is the regression coefficient for water transit index, 𝛽𝑥 is the regression coefficient for interaction between migration speed and water transit index, 𝑎𝑑|𝑦

, and 𝜖𝑖 are the random effect

terms respectively for day within year and each individual fish arriving. Models including/excluding each of the fixed effects above were run, and compared and contrasted using 𝜒2 tests for fitness. The evaluation of each model was performed using the glmer function of the lme4 package (Douglas et. al. 2015) in R (R Core Team 2015). Covariance matrices were investigated for overdispersion (Hosmer and Lemeshow 2000) and none was detected.

Survival of Single-tagged Fish The estimates of survival associated with single-tagged fish were calculated between Rock Island Dam and McNary Dam, the first dam with adequate PIT tag interrogation capabilities downstream of Rock Island Dam (PSFMC 2016). Similar to analyses of double-tagged fish, mark-recapture-recovery data were used to model survival of single-tagged fish via a slightly modified CJS estimation technique. Survival estimates associated with single-tagged fish are less precise than those of double-tagged fish due to low detection probabilities of PIT-tagged fish passing McNary Dam. Despite this limitation, there are several major advantages of using single-tagged fish to estimate survival. First, the random tagging of PIT-tagged fish at Rock Island Dam creates a much more representative sample of the run-at-large. Second, detailed data regarding individual fish characteristic or traits are available for each fish


throughout the entire smolt outmigration period (April to May). Lastly, the survival estimates can be calculated at a much larger spatial scale and from all study years (2008-20015). Thus, our goal in analyzing single-tagged fish was to investigate the relationship between individual fish characteristics (size, condition, and rear-type) and survival from Rock Island Dam to McNary Dam. Covariate modelling - To model the relationships between steelhead survival and biotic factors we use a covariate CJS model with two recapture events. The first recapture event is the PIT tag array in the juvenile bypass at McNary dam. For the second recapture event we use the combination of all detections from PIT tag arrays located downstream of McNary Dam (i.e., at John Day Dam, at Bonneville Dam, and at the pair-trawl in the Columbia River estuary). We also incorporated recoveries of tags on bird colonies within foraging range of the river reach below McNary Dam based on foraging data provided in Evans et al. (in press)(see also Appendix A for list of individual bird colonies and locations). The evaluation of steelhead smolt condition was performed according to the non-invasive examination methods outlined by Hostetter et al. (2011). In brief, data on presence and severity of body injuries, descaling, fin damage, and disease were record on each fish. For the purposes of this modeling exercise, external condition factors were grouped or combined into a single categorical variable indicating fish in a “compromised” condition or “uncompromised” condition. Compromised fish were those that had (1) severe body injuries (defined as deformities, open wounds, or large surface area scarring on the head, trunk, operculum, or eyes), (2) significant descaling (defined as a loss of scales on more than 20% of the body); evidence of disease (defined by any external signs of bacterial, fungal, or viral infections), or (3) severe fin damage (defined as fin wear and damage greater than 50% on three or more fins). Fish size was measured as fork-length (cm) and each fish was classified by rear-type as hatchery or wild (see Hostetter et al. 2011 for additional details). We model �̂�1,𝑖, the estimated survival probability of steelhead i to McNary dam, using a logistic regression function,

𝑙𝑜𝑔𝑖𝑡(�̂�1,𝑖) = 𝛽𝑦 + 𝛽𝑦𝑤 + 𝛽𝐿1

𝐿𝑖 + 𝛽𝐿2

𝐿𝑖2 + 𝛽𝑅1[𝑟𝑒𝑎𝑟𝑖=wild] + 𝛽𝐶1[𝑐𝑜𝑛𝑑𝑖=good]

where 𝛽𝑦 + 𝛽𝑤 equal the average logit probability for all steelhead released in the same year and week,

𝛽𝐿1 and 𝛽𝐿2

are the linear and quadratic regression coefficients for fork length, 𝛽𝑅 is the average

multiplicative difference in the odds of survival between wild and hatchery fish, and 𝛽𝐶 is the expected factor difference in uncompromised versus compromised fish. We let �̂�1,𝑦 represent the year and week

specific detection at McNary dam. We let �̂�2,𝑦 ∗ �̂�2,𝑦 represent the joint survival-to/recapture-at

probability for the set of all downstream recapture events. Explicitly, these were modeled as

𝑙𝑜𝑔𝑖𝑡(�̂�1,𝑦) = 𝛾𝑦𝑒𝑎𝑟 + 𝛾𝑤𝑒𝑒𝑘

𝑙𝑜𝑔𝑖𝑡(�̂�2,𝑦 ∗ �̂�2,𝑦) = 𝛼𝑦𝑒𝑎𝑟 + 𝛼𝑤𝑒𝑒𝑘

Parameter estimates were calculated using a Hamiltonian Monte Carlo (HMC) process implemented via program STAN, accessed via the rstan package (Stan Development Team 2015) available for the statistical software R (R Core Team 2015). Three parallel chains were run for 5,000 iterations after a “warmup” of 1,000 iterations resulting in ~500 effective samples for each parameter. Chain convergence was tested using the Gelman-Rubin statistic (�̂�; Gelman et al. 2004). We report results as posterior modes along with the Highest Posterior Density (HPD) 95% credibility intervals. The resulting models were ranked by using Akaike’s information criterion corrected for small sample size (AICc) and compared using the AICc difference (AICc; Burnham and Anderson 2002).


RESULTS Fish Tagging, Recapture and Recovery Numbers of double-tagged fish release into the Priest Rapids Project varied by year and release site (tailrace of Rock Island, Wanapum, or Priest Rapids dams), ranging from 726 to 1,671 tagged fish annually (Table 1). Recapture probabilities of live fish passing telemetry arrays within the Project were very high (> 97%), resulting in precise measures of survival (Table 1). Survival of double-tagged fish through the Priest Rapids Project ranged from 69% to 80%. The precision of these estimates vary considerably depending on sample size and recapture probabilities. Predation probabilities of dead fish on bird colonies within foraging distance of the Project ranged annually from 5.8% to 11.7% (depending on the year), indicating predation from birds was appreciable in relation to total smolt mortality (1-survival).

Numbers of single-tagged fish released into tailrace of Rock Island dam also varied by year, ranging from 5,893 to 7,756 annually. Recapture probabilities of PIT-tagged fish at McNary Dam were generally low with a median of 6% and ranging weekly from <1% up to 19.0%, considerably lower than that of AT-tagged fish passing telemetry arrays in the Priest Rapids Project. Although a much lower fraction of single-tagged fish were recaptured following release compared with double-tagged fish, recoveries of PIT tags from single-tagged fish on bird colonies greatly improved estimates of survival for this group of fish, with an average of 27.8% of the downstream detections coming from recoveries of these tags on bird colonies. Table 1. Annually estimated survival (95% confidence interval) of double-tagged and single-tagged fish from Rock Island Dam to the Priest Rapids Dam tailrace and Rock Island to McNary dams, respectively. Sample sizes indicating the number of released fish (N) by day and week for double- and single-tagged fish, respectively. Survival rates are median estimated values using the best fitting models.

Year

Double-tagged fish Single-tagged fish

N

Days

RIS-PR Survival a

N

Weeks

RIS-McN Survival

2008 201 7 0.69 (0.62-0.74) 7271 10 0.61 (0.55-0.69)

2009 794 20 0.78 (0.76-0.83) 7114 11 0.56 (0.49-0.63)

2010 483 22 0.75 (0.71-0.78) 7365 10 0.59 (0.52-0.66)

2011 - - - 7756 11 0.68 (0.57-0.83)

2012 - - - 6712 10 0.55 (0.46-0.65)

2013 - - - 5893 10 0.59 (0.48-0.72)

2014 399 18 0.80 (0.75-0.83) 7663 9 0.63 (0.52-0.77)

2015 639 21 0.70 (0.67-0.74) 7069 9 0.69 (0.56-0.85) a Based on a single release group into the tailrace of Rock Island Dam, with no correction for handling effect made.

Survival of Double-tagged Fish Daily survival probabilities of steelhead released in the tailrace of Rock Island through the Wanapum and Priest Rapids projects ranged from 62.0% to 86.6% over the five-year study period (Figure 2). Annual average survival probability through the Priest Rapids Project varied from a low of 68.9% to a high of 79.8%. The simultaneous modelling of survival and mortality provides previously inaccessible levels of detail relating to the interrelated causes of mortality for steelhead. Daily predation probabilities by Caspian Terns ranged from 2.1% to 16.4%. Annual average tern predation probabilities ranged from 5.8% to 11.7%. Daily tern predation probabilities accounted for 11.9% to 62.2% of all mortality (1-


survival) experienced by steelhead migrating through the Priest Rapids during the study period (Figure 2). Covariate modelling. - The best fitting models for survival in the Priest Rapids reservoir were similar for both the fish released at Wanapum Dam and for those continuing their migration after previous release from Rock Island Dam (Table 2). Predation by Caspian terns and steelhead abundance as approximated by the Steelhead Index at Rock Island Dam were included in the most parsimonious models for both release groups. Increases in predation were found to be associated with decreases in the odds of survival whereas the opposite relationship was observed with fish abundance. WTI was also included in one of the models. Model selection using the releases at Rock Island Dam similarly resulted in these same factors being included in the list of most parsimonious models, however, the best fitting model additionally accounts for the percentage of fish passing through the powerhouse at Wanapum Dam.


Figure 2. Covariate values related to each release day of juvenile steelhead in the tailrace of Rock Island Dam. �̂� and

�̂� represent estimated survival and predation by Caspian terms between Rock Island Dam and Priest Rapids Dam. Additional graphs (top to bottom) illustrate release day specific values of steelhead passage index (a 3-day moving average); average outflow between Rock Island, Wanapum and Priest Rapids dams; average temperature between Wanapum and Priest Rapids dams; average spill percentage between Wanapum and Priest Rapids dams; sum of water transit index in Wanapum and Priest Rapids reservoirs; and powerhouse index at Wanapum Dam.


Table 2. A comparison of best fitting models for cohorts released in the tailrace at Wanapum Dam versus those continuing in-river from release in the tailrace at Rock Island Dam. Interactions are denoted by a colon. ∆AICc measures the difference in AICc for each model compared to the most parsimonious model.

Model (Rock Island release) ∆AICca

CATE predation, STHD index, WTI, PH index, and CATE predation:PH index

--

CATE predation, STHD index, PH index, and CATE predation:PH index

0.11

CATE predation, STHD index, PH index, temperature and CATE predation:temperature

0.29

CATE predation, STHD index, WTI, PH index, temperature and CATE predation:temperature

0.46

CATE predation, STHD index, PH index, and CATE predation:STHD index,

1.92

CATE predation, STHD index, temperature and CATE predation:temperature

1.96

Base Model 54.72

Model (Wanapum release) ∆AICcb

CATE predation, STHD index, and CATE predation:STHD index --

CATE predation, STHD index, WTI, and CATE predation:STHD index 1.671

Base Model 4.573 a The AICc of the top model was -115.38 b The AICc of the top model was -26.05

The most parsimonious survival model included covariates for steelhead index, powerhouse index, and temperature. Steelhead survival increased with decreasing Caspian tern predation and increasing steelhead index (Table 3). The top model also included water temperature and the percentage of fish detected in the Wanapum Dam powerhouse, which were both negatively associated with survival (Table 4). Support was also found for interactions between steelhead abundance and Caspian tern predation, as well as temperature and Caspian tern predation. In general, Caspian tern predation had the largest impact on survival, with the odds of survival decreasing by a factor 0.95 for every percentage increase in predation (95% CI: 0.94-0.96). Powerhouse passage also had notable impact on survival, with survival decreasing by a factor of 0.88 for every 10 percent increase in powerhouse passage (95% CI: 0.84-0.92).


Table 3. Best fitting models for cohorts released in the Priest Rapids Project (Rock Island and Wanapum releases). Interactions are denoted by a colon. ∆AICc measures the difference in AICc for each model compared to the most parsimonious model.

Model ∆AICca

CATE predation, STHD index, PH index, temperature and CATE predation:STHD index

--

CATE predation, STHD index, PH index, temperature and CATE predation:temperature

1.02

Base Model 153.25 a The AICc of the top model was -241.41

Table 4. Estimated multiplicative effects on the odds of survival (along with confidence bounds) for each variable included in the best fitting model with the associated F-test test of statistical significance.

Variable Effect 95% CI Df F value Pr(>F)

Year -- -- 4 154.5 < 0.001

CATE predation 0.95 0.94-0.96 1 112.3 < 0.001

STHD index 1.11 1.11-1.22 1 35.6 < 0.001

PH index 0.88 0.84-0.92 1 23.1 < 0.001

Temperature 1.06 0.92-0.96 1 24.0 < 0.001

CATE predation:STHD index 0.96 0.94-0.98 1 13.7 < 0.001

Supplementary migration speed analysis – We found water transit index to be an imperfect proxy of migration speed, however, both variables were found to be significantly associated with apparent survival on smaller spatial scales. We observed a correlation between the water transit index and average fish travel time in Wanapum Pool (r^2=-0.58). After accounting for variation among the year and day of a steelhead’s arrival at Wanapum Dam, we found a significant relationship between smolt migration speed in the Wanapum Pool and apparent survival through the Priest Rapids Pool (Figure 3; 𝜒1=10.78; p=0.001). The relationship between water transit time and apparent survival was not found to be significant by itself, however, a model including an interaction term between water transit time and migration speed was found to fit the data significantly better than the model accounting for migration speed by itself (𝜒2=20.55; p<0.001). We estimate every kph increase in average migration speed through the Wanapum Pool is associate with an increase in the probability of survival through the Priest Rapids pool by a factor 2.42 (95% CI: 1.56-3.23). The sign of the interaction coefficient in the full model indicates that the association between migration speed and survival diminishes as water transit time increases.


Figure 3. Fish speed and water transit index in the forebay of Wanapum Dam (left) and the forebay of Priest Rapids Dam (right).

We observed a similarly weak correlation between the water transit index and average fish travel time in Priest Rapids Pool (r^2=-0.57), as was observed in Wanapum Pool. After accounting for variation among the year and day of a steelhead’s arrival at Priest Rapids Dam, we found some evidence of a relationship between smolt migration speed in the latter portion of the Priest Rapids reservoir and apparent survival through the subsequent congruent study area (Figure 3; 𝜒1=3.00; p=0.083). The relationship between water transit time and apparent survival was found to be significant (𝜒1=8.52; p=0.004). A model including an interaction term between water transit time and migration speed was found to fit the data significantly better than this model accounting for water transit time only (𝜒2=5.49; p=0.004). The effect of migration speed through the Priest Rapids Pool was estimated to affect subsequent survival less than through the Wanapum Pool. We estimate every kph increase in average migration speed through the Priest Rapids Pool is associated with an increase in the probability of survival through the subsequent river reach by a factor of 1.20 (95% CI: 1.03-1.39). Again, the sign of the interaction coefficient in the full model indicates that the association between migration speed and survival diminishes as water transit time increases although to a lesser degree.

Survival of Single-tagged Fish Sample sizes of single-tagged fish were large in comparison to the sample sizes of double-tagged fish, generally around 7,000 single-tagged steelhead released over the 8-10 week study period each year. Between 72.2% and 76.9% of those fish were assumed to be hatchery reared (Table 5). The distribution of steelhead sizes (as measured by fork length) was relatively similar among years with median fork length being 19-20cm. Between 3.6% and 23.1% of each yearly cohort of steelhead were considered to be in a compromised condition. The most common condition anomaly was descaling, which was present in 23.7% of the study fish in compromised condition followed by body injuries.


Table 5. Individual fish characteristics investigated in survival models for steelhead travelling between Rock Island Dam to McNary Dam during 2008-2015. Data presented below are annual values, but were modelled using weekly values during the study year.

Year N Rear-type External Condition Average length (mm)

(min to max) Hatchery Wild Uncompromised Compromised

2008 7271 5373 1898 6497 774 193 (88-302)

2009 7114 5150 1964 6680 434 195 (96-291)

2010 7365 5387 1978 6750 615 197 (70-297)

2011 7756 5961 1795 5964 1792 204 (102-320)

2012 6712 5107 1605 6060 652 196 (92-320)

2013 5893 4284 1609 5471 422 193 (90-320)

2014 7663 5686 1977 7387 276 191 (77-308)

2015 7069 5105 1964 6106 963 193 (86-300)

Covariate modelling - The most parsimonious model, as determined by lowest AICc value, included variables for fork length, the indicator for compromised condition, and rearing type (Table 6). Of all the variables examined, only the quadratic term for fork length was excluded from the best model. Each factor had considerable effect on the odds of survival. We estimate that for each additional cm in fork length of a steelhead, as measured at Rock Island Dam, there is an increase in the odds of survival to McNary Dam by a factor of 1.07 (95% CI: 1.01-1.12; Table 7), after accounting for the other factors. We estimate that a steelhead arriving in a compromised condition at Rock Island Dam experiences a reduction in the odds of surviving to McNary Dam by a factor of 0.46 (95% CI: 0.38-0.54; Table 7), after accounting for the length and rear-type. We estimate the odds of a wild steelhead surviving from Rock Island Dam to McNary Dam to be 1.49 times greater than that of hatchery steelhead (95% CI:1.30-1.72; Table 7 and Figure 4), after accounting condition and length.

Table 6. Top two best fitting models for predicting juvenile steelhead survival from Rock Island Dam to McNary Dam based individual level characteristics. Interactions are denoted by colons. ∆AICc measures the difference in AICc for each model compared to the most parsimonious model.

Model ∆AICca

Length, condition, and rearing --

Length, condition, rearing and length:condition 5.10

Base model 38.29 a The AICc of the top model was -39,490.19


Table 7. Estimated multiplicative effects on the odds of survival, confidence intervals for the variables included in the best fitting model, and p-values of tests for statistical significance.

Variable Effect 95% CI Df p-value

Length 1.07 1.01-1.12 1 < 0.001

Condition 0.46 0.38-0.54 1 < 0.001

Rearing 1.49 1.30-1.72 1 < 0.001

Figure 4. Example effects of length on median survival from Rock Island Dam to McNary Dam for hatchery (left) and wild (right) steelhead smolts with 95% confidence intervals. Solid lines are the associated estimate for those fish in an uncompromised condition, dotted lines are associated with those fish in compromised condition.

In general, hatchery fish observed at Rock Island Dam were more likely to be in a compromised condition as compared to wild fish, but were greater in length. Hatchery steelhead were 2.88 times more likely to arrive at Rock Island Dam in compromised condition as compared to their wild counterparts (95% CI: 2.76-3.01). However, hatchery steelhead arrived at Rock Island Dam with fork length 23mm greater, on average, than wild fish (95%CI: 22.8-23.2). Even after accounting for the differences in condition and size of hatchery and wild fish, hatchery fish had lower survival as compared to wild fish (see above).

DISCUSSION This study is among the first to compare and contrast the effects of different biotic and abiotic factors on survival of outmigrating juvenile steelhead over the course of several consecutive years; providing a comprehensive evaluation of smolt survival in the middle Columbia River. Results indicate that multiple


factors, at both population- and individual-levels, explain variation in steelhead survival. Analyses of double-tagged fish passing through the Priest Rapids Project provided consistent support for survival models that included the covariates of Caspian tern predation, steelhead abundance, temperature, and powerhouse passage indices. Interaction terms were also significant in many top models, demonstrating the complexity and inter-related nature of factors that regulate fish survival during outmigration through the Priest Rapids Project. Analyses of single-tagged fish provided over-whelming evidence that fish size, condition, and rearing type are all important factors regulating steelhead survival. All top candidate survival models of population-level effects included Caspian tern predation as a key factor explaining differences in steelhead survival. Estimates indicated that tern predation alone accounted for 12 to 62% (depending on the year and development) of all mortality experienced by steelhead migrating through the Priest Rapid Project. These results are not unexpected and corroborate previously published studies which identified Caspian tern predation as one the greatest factors influencing steelhead smolt survival during outmigration in the Columbia River basin (Collis et al. 2001; Ryan et al. 2003; Antolos et al. 2004; Evans et al. 2012; Evans et al. in press). The observed importance of steelhead abundance along with the interaction between abundance and Caspian tern predation in middle Columbia River is also well documented in the literature (Hostetter et al. 2012; Evans et al. 2013; Evans et al. 2016). The interaction between annual water temperature and predation by Caspian terns is more difficult to explain but is perhaps not directly related to the water temperatures per se but to fish condition as it is affected by water temperature. For example, previous research has demonstrated that increased water temperatures are associated with a greater incidence of fish disease, stress, and other maladies that make fish more susceptible to bird predation (Hostetter et al. 2012). Analysis of single-tagged steelhead found evidence of a direct relationship between steelhead survival and increased water transit times and fish migration speed in both the Wanapum and Priest Rapids developments. Petrosky and Schaller (2010) found that juvenile-to-adult steelhead survival was associated with water velocities, whereby return rates were highest for groups of fish migrating during high flow events, which often occurs during the peak outmigration periods, the period when double-tagged fish used in this study were released. Haeseker et al. (2012) also found that survival rates were associated with water transit times and spill patterns experienced by juvenile Snake River steelhead. Our study results suggests that both fish migration speed and water transit times are important independent factors in explaining differences in fish survival; however as water transit times decrease (i.e., faster water movement), fish migration speed becomes less important in explaining differences in fish survival. We also observed direct relationship between smolt abundance and survival. Such an association suggests that any actions taken to mitigate the impacts of a factor found detrimental to fish survival may have compounding effects. For example, if decreases in water transit times or avian predation results in increased survival, this also increases smolt abundance which would further increase survival. Increased smolt abundance may lead to higher abundance of adult returns (Tuomikoski 2013) which can lead to future increases in smolt abundance, and so on. A full life cycle model, facilitated by the simultaneous modelling of survival and the various causes of mortality, may prove useful in analyzing broader compounding effects of various management options over greater temporal scales. Analyses of single-tagged fish provided strong support for survival models with variables for fish condition, size, and rearing type. External maladies identified in this study (i.e., body injuries, descaling, fin damage, and/or disease) have been linked to multiple health and survival performance metrics in


salmonids. Results from this study indicated that after accounting for differences in fish length and external condition, hatchery fish were less likely to survive from Rock Island Dam to McNary Dam than wild fish. Newman (1997) found that hatchery juvenile steelhead from the Columbia River basin were significantly less likely to survive out-migration than were wild fish. Evans et al. (2014) found that after accounting for size, fish condition, and year, wild Snake River and Upper Columbia River steelhead were significant more likely to survive to adulthood than their hatchery counterparts. Incorporation of fish in compromised condition into large-scale survival studies is still lacking in the region, but may be necessary to understand complex interactions that influence survival. For example, in the present study, fish in compromised condition were not tagged with AT tags, so data to refute or support hypotheses regarding interactions between survival, condition, and water temperature are lacking for the double-tagged fish used in this study. Finally, it should be noted that significant uncertainty remains with respect to the relationship between long-term survival and each of the factors explored here, most notably localized avian predation. The simultaneous modeling of survival and avian predation potentially offers a unique analytical approach to estimating the extent to which foraging by avian predators is additive in its effects on mortality. Burnham et al. (1984) describe a general methodology to assess the degree of compensatory versus additive mortality. Incorporating the framework of Burnham et al. (1984) in future predation studies in concert with our simultaneous modelling of survival and various causes of mortality could significantly increase the statistical power of such an analysis. This type of investigation may prove useful in measuring the true net benefits of avian predation management and other management actions in increasing juvenile steelhead survival in the region (USACE 2014).

ACKNOWLEDGEMENTS This project was funded by Public Utility District No. 2 of Grant County via a subcontract to Real Time Research from Blue Leaf Environmental. We especially want to thank Curt Dotson of Grant County PUD and Mark Timko of Blue Leaf Environmental for their assistance and support. We want to thank Kyle Hatch, Leah Sullivan, and Cindy Fitzgerald of Blue Leaf Environmental for preparation of acoustic data and general support regarding data preparation. Finally, this work would not have been possible without the hard work and dedication of numerous field researchers and data analyst, for which we are grateful. Any use of trade, firm, or product names is for descriptive purposes and does not imply endorsement.

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APPENDIX A: JOINT SURVIVAL AND PREDATION ESTIMATION We developed a model with which we can synthesize all the available data with respect to survival and avian predation of juvenile smolts into a single holistic framework. We model survival over sequential segments using non-physical recapture events along with recoveries from causes of mortality known to occur strictly downstream in order to estimate recapture probabilities and infer survival. For the purpose of this study, colonies outside the foraging range of fish traveling between Rock Island Dam and McNary Dam included California and ring-billed gulls nesting on the Blalock Island the John Day Reservoir, gulls nesting on Miller Rocks Island in The Dalles Reservoir, and Caspian terns and double-crested cormorants nesting on East Sand Island in the Columbia River estuary (see Evans et al. in-press). We model the specific causes of mortality within each segment using detections of PIT-tags recovered from bird colonies to infer survival and the impacts avian foraging on smolt migration success. Combining these two sources of information allows us higher precision with respect to all the parameters involved (i.e., survival and predation probabilities as well as recapture and recovery probabilities).

We let 𝑍𝑖𝑗 be an indicator variable representing the survival of fish i through segment j. We let ωwj be

the probability of survival by a tagged fish from through the jth segment in day w. We let 𝑫𝑖𝑗 = [𝐷𝑖𝑗1,

𝐷𝑖𝑗2, … , 𝐷𝑖𝑗𝑜𝑡ℎ𝑒𝑟] be a (C+1) x 1 indicator vector representing the cause of mortality for a fish which

does not survive through segment j. Each element 𝐷𝑖𝑗𝑐 indicates whether fish i was depredated by

piscivorous waterbirds colony c of the C known breeding colonies within segment j. 𝐷𝑖𝑗𝑜𝑡ℎ𝑒𝑟 represents

the mortality of a fish from any other cause in segment j. We further let 𝜽𝑤𝑗 = [𝜃𝑤𝑗1, 𝜃𝑤𝑗2, … 𝜃𝑤𝑗𝑜𝑡ℎ𝑒𝑟] where 𝜃𝑤𝑗𝑐 is the probability of predation by colony c in

the jth segment associated with the tagged smolts released on day w and 𝜃𝑤𝑗𝑜𝑡ℎ𝑒𝑟 represents the

probability of mortality by any other cause with respect to the same release day and segment. Therefore

[𝑍𝑖𝑗 , 𝑫𝑖𝑗] ~ Multinomial(𝑍𝑖(𝑗−1), [ωrwj, 𝜽𝑟𝑤𝑗]).

We let 𝑌𝑖𝑗 be the indicator variable of whether fish i is detected at the downstream interrogation array

associated with segment jth. We let 𝛿𝑟𝑤𝑗 be the probability a surviving fish, released in day w, is detected

at this array. Therefore

𝑌𝑖𝑗 ~ Bernoulli(𝛿𝑤𝑗 ∗ 𝑍𝑖(𝑗−1)).

We hold 𝛿𝑟𝑤𝑗 constant for across weeks for each acoustic array within each year. Downstream

recapture probabilities are assumed to vary over the course of the year.

Causes of mortality within each segment are informed with supplementary information. In this study,

information regarding mortality was derived using the number of PIT tags found on a given bird colony,

with a correction to account for the probabilistic process of consumed tags being deposited by birds on

their nesting colony (referred to as “deposition probability”) and the imperfect detected of these tags by

researchers following the nesting season (referred to as “detection probability”). Complete details

concerning these two processes can be found in Hostetter et al. (2015) and Evans et al (in-press). The

model then calculates not only the abundance of tags being removed but the probable location of their

removal as well.


We let 𝑅𝑖𝑐 be the vector indicating whether the tag associated with the fish i was recovered on colony c.

We let 𝜙𝑐represent the probability that a tag consumed by a bird from colony c is deposited on the

colony. We let 𝜓𝑐𝑤 represent the probability a tag deposited on colony c in week w is detected at the

end of the nesting season. Therefore

𝑅𝑖𝑐 ~ Bernoulli(𝜙𝑐 ∗ 𝜓𝑐𝑤 ∗ ∑ 𝐷𝑖𝑗𝑐𝑗 ).

To independently measure detection efficiency at each bird colony, PIT tags are intentionally sown on

multiple days over the course of the breeding season. We let 𝑓𝑐𝑤 represent the number of PIT tags

found of the 𝑛𝑐𝑤 intentionally sown on colony c on day w. We let 𝜓𝑐𝑤 represent the probability that a

tag deposited on colony c in day w is detected. Therefore

𝑓𝑖𝑐 ~ Binomial(𝑛𝑐𝑤, 𝜓𝑐𝑤).

Each 𝜓𝑐𝑤 is assumed to be a logistic function of day:

𝜓𝑐𝑤 = 𝛽0𝑐 + 𝛽1𝑐 ∗ (𝑤 – 𝑚𝑐),

where 𝑚𝑐 represents the median day of the breeding season at colony c.

Estimates were calculated using a Hamiltonian Monte Carlo (HMC) process implemented through the use of the program STAN (Sampling Through Adaptive Neighborhoods), accessed via the rstan package (Stan Development Team 2015a) available for the statistical software R (R Core Team 2015). This requires the above state-space model to be written as recursive formulas (Stan Development Team 2015b). Three parallel chains were run for 5,000 iterations after a “warmup” of 1,000 iterations resulting in ~500 effective samples for each parameter. Chain convergence was tested using the Gelman-Rubin statistic (�̂�; Gelman et al. 2004). We report survival and predation results as posterior modes along with the Highest Posterior Density (HPD) 95% credibility intervals (95% c.i.).

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