Estimating cause- and size- specific mortality hazard rates using mark-recapture-recovery data

Estimating survival using data on marked individuals is a key component of population dynamics studies resulting management and conservation decisions. When human impacts on populations are considerable, such decisions require not only estimating survival but also quantifying how much mortality is due to anthropogenic versus natural causes. This is of particular importance when individuals vary in their vulnerability to different causes of mortality due to, for example, their body size, developmental stage, or reproductive state. In this study we used multistate mark-recapture models to estimate the effects of individual body size on harvest- and background mortality risks of large freshwater brown trout (Salmo trutta). In doing so, we accounted for additional individual differences in vulnerability to cause-specific mortality by distinguishing individuals passing a hydroelectric dam on their spawning migration from those that reproduced below the dam instead and further investigate temporal patterns of and correlations among mortality hazard rates over 50 years. We found that harvest mortality was highest for intermediate-sized trout, and outweighed background mortality for almost the entire observed size range of trout. For trout spawning above the dam, background mortality decreased for larger body sizes and at lower river discharge. Both mortality causes, as well as the probability of spawning above the dam, varied substantially over time but a trend was evident only for fishers’ reporting rate, which decreased from an average of 80% to only 10% over half a century. Our model demonstrates how continuous size effects can be integrated into analyses of cause-specific mortality by using a novel parameterisation with hazard rates. This allowed us to estimate effects of both size and environment on harvest- and background mortality with-out confounding, and provided an intuitive way to estimate temporal patterns within and correlation among the mortality sources. In combination with compu-tationally fast custom MCMC solutions this modelling framework provides unique opportunities for studying individual heterogeneity in cause-specific mortality using mark-recapture-recovery data.

Survival and deaths due to certain causes represent mutually exclusive events and 141 can thus be incorporated into multistate mark-recapture frameworks (Lebreton 142 et al. 1999). When explicitly including not only "alive" but also (observable) cause-143 specific "newly dead" states, the probability of transitioning from state "alive" to 144 state "newly dead from cause X" represents the probability of dying from cause 145 X Pradel 2004, Servanty et al. 2010). In the trout study population, 146 deaths due to harvest may be reported by fishers and are thus clearly distinguish-147 able from deaths due to other causes. Individuals in any alive state n can therefore 148 remain alive with survival probability S n or transition to states "newly dead from 149 harvest" (state 3) or "permanently dead" (state 4) with probabilities Ψ H n and Ψ O n 150 respectively ( Figure 2). The "permanently dead" state here represents all unob-151 servable dead individuals, which also include those that have recently died from 152 causes other than harvest. Furthermore, we make a distinction between individuals 153 that start the time interval by spawning above versus below the dam. Spawning 154 location may have a considerable effect on mortality, as individuals that spawn 155 above the dam need to pass this obstacle on both the upriver-and downriver 156 spawning migration. Consequently, we included two "alive" states in our model: states (t + 1) The elements of this matrix represent the probabilities of any individual i in a 164 given state (rows) transitioning to another state (columns) over the time interval 165 from t to t + 1. As such, all probabilities within a given row sum to 1.   195 Harvest in our study system has been done mostly using fishing rods or gillnets; 196 the former is often positively correlated with body size (Lewin et al. 2006) while 197 the latter has bell-shaped selectivity curves (Hamley 1975 ing migration in general, and passing of the dam in particular, may also depend 213 on body size. We thus modelled background mortality hazard rate as: Here the index n indicates the alive state (1 or 2), discF t is the average discharge 215 during the fall when post-spawned trout are expected to migrate downriver (Oct -216 Nov), β O 1,n and β H 4 are slope parameters for size-and discharge effects respectively, 217 and O t are random effect which are independent of state n.

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In a previous analysis of a subset of our data, Haugen et al. (2008) found that 219 the probability of using the fish ladder and thus spawning above the dam depended 220 on a complex interplay of individual body size and river discharge. We adopted 221 their basic model structure and extended it by allowing for random among-year 222 variation such that The discharge covariate used here, discS t , represents the average discharge over the 224 summer season when trout undertake their upriver spawning migration (Jul-Oct), 225 while size i,t is the individual length during the upriver spawning migration.

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The last main parameter in the model is reporting rate r and this can be puter algebra package Maple, we looked at intrinsic parameter redundancy in the 320 above described model including different covariate-and random effect structures.

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The analyses of parameter redundancy are described in more detail in Appendix 322 S3 and accompanying Maple code is also provided as supplementary material.

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Subsequently, we tested the ability of our models to correctly and accurately 324 estimate parameters given the available data. This we did by running the model on  year effects were included on at least harvest mortality hazard or reporting rates 341 (Table S3.1).

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When run on simulated data, the independent random effect model produced 343 posterior estimates closely resembling the true parameter values (Appendix S4.2).

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While there was considerable uncertainty in estimates of some parameters (e.g.  (Figures 5a & 5b).

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Model results did not support differences in harvest-or background mortal- harvest-and background mortality of large brown trout exposed to fishing as well 405 as a hydroelectric dam on their migration route. 406 We found harvest and background mortality of trout to strongly depend on harvest mortality and trout length was non-linear with a peak mortality at around 423 500 mm (Figure 4a). This peak is well below the average length in the spawning 424 population (670 mm), indicating that smaller mature fish are harvested dispro-mortality was also relatively high during this period (and survival consequently 502 quite reduced, Figure S1.12), highlighting the possibility for disease to not only 503 increase background mortality but also affect vulnerability to fishing.

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Despite harvest and background mortality increasing simultaneously during 505 the disease outbreak period, models predicted that the correlation between the 506 two mortality causes was more likely to be negative than positive (Figure 6). A

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While our analyses did include body size, spawning location, and origin, there 569 are other sources of individual heterogeneity that we did not account for here.

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These include -but are not limited to -disease state, birth/smolt cohort, and sex.

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Evidence for potential effects of disease state came from the model predictions  In this analysis, we refrained from including river and lake temperature as covari- tion that is easily applicable for any type of multistate mark-recapture model.

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Last, but not least, we have shown that identifiability issues that are common The following supporting information is available for this publication: Appendices 874 S1 -S5.  Figure 1: Illustration of the biennial spawning cycle and mark-recapture scheme of the studied trout population. All individuals are marked in the fish ladder while passing the dam on their upriver spawning migration. Two years later they may be recaptured on the next spawning migration, but only if they pass the fish ladder to spawn above the dam. Trout remain in the lake and are unobservable during non-spawning years.
(4) Permanently dead (1) Spawning upriver (3) Newly dead from harvest (2) Spawning downriver  Red and blue curves apply to individuals that have last spawned above and below the dam respectively. The black curve (harvest) applies to all individuals irrespective of their last spawning location. Solid lines represent the mean predictions while dashed lines indicate the 95% credibility intervals. The boxplot illustrates the informative data range: red = size distribution of individuals captured in the fish ladder (above-dam spawners), blue = simulated size distribution of below-dam spawners after surviving for two years following marking and subsequently not using the fish ladder.