Estimating Walleye (Sander Vitreus) Movement and Fishing Mortality Using State-Space Models: Implications for Management of Spat
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330 ARTICLE Estimating walleye (Sander vitreus) movement and fishing mortality using state-space models: implications for management of spatially structured populations Seth J. Herbst, Bryan S. Stevens, Daniel B. Hayes, and Patrick A. Hanchin Abstract: Fish often exhibit complex movement patterns, and quantification of these patterns is critical for understanding many facets of fisheries ecology and management. In this study, we estimated movement and fishing mortality rates for exploited walleye (Sander vitreus) populations in a lake-chain system in northern Michigan. We developed a state-space model to estimate lake-specific movement and fishery parameters and fit models to observed angler tag return data using Bayesian estimation and inference procedures. Informative prior distributions for lake-specific spawning-site fidelity, fishing mortality, and system-wide tag reporting rates were developed using auxiliary data to aid model-fitting. Our results indicated that post- spawn movement among lakes was asymmetrical and ranged from approximately 1% to 42% per year, with the largest outmi- gration occurring from the Black River, which was primarily used by adult fish during the spawning season. Instantaneous fishing mortality rates differed among lakes and ranged from 0.16 to 0.27, with the highest rate coming from one of the smaller and uppermost lakes in the system. The approach developed provides a flexible framework that incorporates seasonal behav- ioral ecology (i.e., spawning-site fidelity) in estimation of movement for a mobile fish species that will ultimately provide information to aid research and management for spatially structured fish populations. Résumé : Les poissons présentent souvent des motifs de déplacement complexes, et la quantification de ces motifs est essentielle a` la compréhension de nombreuses facettes de l’écologie et de la gestion des ressources halieutiques. Nous avons estimé les déplacements et les taux de mortalité par pêche pour des populations exploitées de dorés jaunes (Sander vitreus) dans un réseau de chaînes de lacs dans le nord du Michigan. Nous avons élaboré un modèle d’espaces d’états pour estimer les déplace- ments et des paramètres touchant a` la pêche dans différents lacs et avons calé le modèle sur des données de retour d’étiquettes par des pêcheurs en utilisant des procédures d’estimation et d’inférence bayésiennes. Des distributions a priori informatives pour la fidélité aux lieux de frai selon le lac, la mortalité par pêche et la fréquence de signalements d’étiquettes a` l’échelle du réseau ont été produites en utilisant des données auxiliaires pour aider au calage du modèle. Nos résultats indiquent que les déplacements entre les lacs après le frai étaient asymétriques et allaient d’environ1%a` 42 % par année, la plus grande dévalaison For personal use only. s’étant produite a` partir de la rivière Black, qui était principalement utilisée par des poissons adultes durant la période de frai. Les taux de mortalité par pêche instantanée variaient selon le lac et allaient de 0,16 a` 0,27, le taux le plus élevé étant observé dans un des lacs les plus petits et les plus en amont du réseau. L’approche mise au point fournit un cadre souple qui intègre l’écologie des comportements saisonniers (c.-a`-d., la fidélité aux lieux de frai) dans l’estimation des déplacements pour une espèce de poissons mobiles qui fournira, a` terme, des renseignements qui aideront a` la recherche et a` la gestion pour des populations de poissons structurées dans l’espace. [Traduit par la Rédaction] Introduction estimate movement and demographic rates from tagging stud- ies. Common approaches assume probabilistic movement, de- Fish demonstrate variable movement patterns and complex mographic, and recapture processes (e.g., Brownie et al. 1993; spatial structures among open systems that can complicate deci- Schwarz et al. 1993) or deterministic movement and demographic sions related to harvest management and species conservation. processes with all stochasticity arising through the sampling Given these challenges, estimating movement rates within aquatic process (e.g., Hilborn 1990). A commonly used approach for tag- systems and understanding the spatial structure of fish stocks has recovery data developed by Hilborn (1990) embeds a biologically been an area of interest for ecologists and resource managers for meaningful but deterministic population model within a statisti- decades (Hilborn 1990; Schick et al. 2008; Li et al. 2015). cal estimation framework using a Poisson sampling model. Movement dynamics of fishes are frequently evaluated using More recently, extensions of the Hilborn tag-recovery model mark–recapture and (or) tag-recovery studies in which individuals have been developed incorporating size selectivity (Anganuzzi Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by MICHIGAN STATE UNIV on 05/17/18 are uniquely marked, released, and then later recaptured live or et al. 1994), natural (M) and fishing (F) mortality, and tag shed- recovered via harvest (Hilborn 1990; Brownie et al. 1993; Schwarz ding (⍀)(Aires-da-Silva et al. 2009). As such, these applications of et al. 1993; Pine et al. 2003). Multiple models have been used to fishery tag-recovery models contain parameters relevant to both Received 14 January 2015. Accepted 31 August 2015. Paper handled by Associate Editor John Post. S.J. Herbst,* B.S. Stevens, and D.B. Hayes. Department of Fisheries and Wildlife, Michigan State University, 480 Wilson Road, Room 13 Natural Resources Bldg., East Lansing, MI 48824, USA. P.A. Hanchin. Michigan Department of Natural Resources – Fisheries Research Station, 96 Grant Street, Charlevoix, MI 49720, USA. Corresponding author: Seth J. Herbst (e-mail: [email protected]). *Present address: Michigan Department of Natural Resources – Fisheries Division, 525 W. Allegan Street, Lansing, MI 48933, USA. Can. J. Fish. Aquat. Sci. 73: 330–348 (2016) dx.doi.org/10.1139/cjfas-2015-0021 Published at www.nrcresearchpress.com/cjfas on 3 September 2015. Herbst et al. 331 the biology and management of fishes (e.g., M, F, ⍀). These ap- their population dynamics, trophic ecology, conservation, and proaches, however, typically assume all variation in tag-recovery management (Landsman et al. 2011; Berger et al. 2012). As such, the data arises as a result of sampling processes, which is likely unre- goal of this study was to understand and quantify the movement alistic given that vital rates for both individual animals and pop- dynamics of walleye in a set of large interconnected lakes and ulations can exhibit considerable variation through space and river systems in northern Michigan. Specific objectives of this time (Ogle 2009; Hansen et al. 2011; Bjorkvoll et al. 2012). There- study were to (i) develop a tag-recovery model that accounts for fore, it is important to incorporate stochasticity in the underlying the biology of our study system and integrates prior sources of population model, and inclusion of both process and observation data to estimate movement and demographic parameters and uncertainty can increase the realism of tag-recovery applications (ii) quantify movement rates for walleye in a lake-chain system in in fisheries. northern Michigan during 2011–2013. To accomplish these objec- A state-space model is a special class of a hierarchical statis- tives, we developed a state-space tag-recovery model that adapts tical model for time series data that provides a rigorous the general framework of Hilborn (1990), described further by approach for modeling stochastic biological and observation pro- Quinn and Deriso (1999), to account for important movement cesses (Schnute 1994; King 2014). State-space frameworks also pro- dynamics and spawning-site fidelity observed in this system, vide a flexible approach for tailoring biological process models to while integrating prior data sources that allowed us to estimate life history of a study organism (Thomas et al. 2005; Newman et al. important demographic and fishery parameters (e.g., fishing mor- 2014). State-space approaches have been used to estimate demo- tality rate) in each lake. This model was implemented in a Bayes- graphic and movement parameters in mark–recapture studies ian estimation and inferential framework, which provided a (e.g., Gimenez et al. 2007; Kéry and Schaub 2011; Holbrook et al. flexible approach for understanding dynamics and permitted sto- 2014), but have seen less application for estimating movement chasticity in both biological and observation processes generating parameters of spatially structured fish populations using tag- recovery data (e.g., extensions of the Hilborn model). Moreover, the tag-recovery data (Gimenez et al. 2007). Bayesian applications of state-space models in fisheries provide Materials and methods additional flexibility by allowing one to easily constrain parame- ter values over realistic ranges or incorporate information from Study area data recorded from other time periods, populations, or species Michigan’s Inland Waterway is an interconnected chain of lakes through the use of informative prior distributions (Whitlock and located in the northern Lower Peninsula that consists of four large McAllister 2009; Kéry and Schaub 2011). When data to estimate lakes (Burt, Crooked, Mullett, and Pickerel) interconnected by a specific parameters are lacking for the population or site of inter- series of rivers and smaller tributaries (Fig. 1). The Cheboygan Lock est, constraining parameters through use of informative priors and Dam on the Cheboygan