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An Extension of the Stepwise Stochastic Simulation Approach for Estimating Distributions of Missing Life History Parameter Value

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An Extension of the Stepwise Stochastic Simulation Approach for Estimating Distributions of Missing Life History Parameter Value 77 National Marine Fisheries Service Fishery Bulletin First U.S. Commissioner established in 1881 of Fisheries and founder NOAA of Fishery Bulletin Abstract—The limited resources and An extension of the stepwise stochastic simulation high species diversity associated with coastal fisheries present challenges approach for estimating distributions of missing to their effective management. Data- limited approaches to assessment of life history parameter values for sharks, groupers, stocks are often used in these situa- and other taxa tions, but most assessments require basic life history information that is 1,3 often unavailable. We expanded a step- Kenneth A. Erickson (contact author) 2,3 wise meta- analytical approach in which Marc O. Nadon statistical relationships between key life history traits are used to estimate Email address for contact author: [email protected] parameters related to growth, maturity, and longevity. This approach was origi- 1 Department of Oceanography and Coastal Sciences nally devised for 6 fish families and has Louisiana State University been successfully implemented in the Energy Coast and Environment Building assessments of data- poor reef fish spe- 93 South Quad Drive, Room 2263 cies in Hawaii and Guam. We expanded Baton Rouge, Louisiana 70803 this approach to groupers, wrasses, grunts, and sharks and, here, present 2 Joint Institute for Marine and Atmospheric Research an R package that greatly simplifies its School of Ocean and Earth Science and Technology implementation. Further, we tested this University of Hawaii at Manoa expansion by selecting a species from 1000 Pope Road each of these taxa and compared results Honolulu, Hawaii 96822 from use of the stepwise approach to 3 Pacific Islands Fisheries Science Center results from life history studies. Our National Marine Fisheries Service, NOAA results indicate agreement between the 1845 Wasp Boulevard, Building 176 probability distributions from our step- Honolulu, Hawaii 96818 wise approach and those from previous studies. Distributions from the stepwise simulation had higher variability but reasonable accuracy in estimating miss- ing values of life history parameters. We also tested our approach against another meta- analytical life history Coastal fisheries provide sustenance length data (Ault et al., 1998, 2008; approach that was recently published and a source of income for millions of Gedamke and Hoenig, 2006; Nadon (and made available as the R pack- people across the globe (Kronen et al., et al., 2015; Hordyk et al., 2016; Rudd age FishLife) and found our stepwise 2010; Symes et al., 2015; FAO, 2016). and Thorson, 2018; Nadon, 2019). These approach to be generally more precise and accurate. These fisheries typically target hun- length- based methods require life his- dreds of species from different taxa, tory information related to growth: and this high species diversity makes parameters of the von Bertalanffy the management of these fisheries chal- growth function (von Bertalanffy, 1938), lenging (Ault et al., 2014). In addition, the asymptotic length (L∞) and growth resources for fisheries research and coefficient (K); natural mortality (M); management are often lacking, result- and length at maturity (Lmat, the length ing in a paucity of data that limits the at which 50% of individuals are mature). development of well- informed man- However, species- specific information agement plans (Fenner, 2012; Gilman on life history traits is missing for as Manuscript submitted 5 June 2020. et al., 2014; Hilborn and Ovando, 2014; many as 83% of exploited stocks glob- Manuscript accepted 30 April 2021. Berkson and Thorson, 2015). Assessing ally (Froese and Binohlan, 2000). To Fish. Bull. 119:77–92 (2021). Online publication date: 4 June 2021. these fisheries is further limited by a address this issue, Nadon and Ault doi: 10.7755/FB.119.1.9 lack of long- term catch and fishing (2016) developed a stepwise stochastic effort records needed to implement cer- simulation approach in which a local The views and opinions expressed or tain stock assessment models. estimate of maximum length (Lmax) and implied in this article are those of the To compensate for shortcomings, statistical relationships between life author (or authors) and do not necessarily reflect the position of the National recent stock assessment methods have history parameters are used to esti- Marine Fisheries Service, NOAA. been focused on the use of cost- efficient mate this missing information. 78 Fishery Bulletin 119(1) Fundamental relationships between life history traits Additionally, we tested this approach against those of in fish species were first observed by Beverton and Holt life history studies and against the approach of Thorson (1959). They pointed out that M and K are typically et al. (2017) as applied in their R package FishLife. We related by a ratio close to 1.5, that the ratio of Lmat to L∞ also developed, and present here, a new R package, Step- is typically around 0.66, and that L∞ and K have a nega- wiseLH, that simplifies the implementation of the step- −h tive power relationship that has a general form of L∞~K , wise approach for all 10 included taxonomic groups. Our with a shape parameter (h), which is typically around results will improve the capability to conduct stock 0.5. These relationships are referred to as Beverton–Holt assessments for these taxonomic groups in data- limited invariants in the literature (Charnov, 1993) and are likely situations. conserved through natural selection because of their link with the maximization of offspring (Beverton and Holt, 1959; Jensen, 1996, 1997; Charnov, 2008). Results Materials and methods of recent meta- analytical studies indicate that ratios dif- fer significantly between taxa and are therefore better Details of the stepwise approach studied within taxa (Hordyk et al., 2015; Nadon and Ault, 2016; Thorson et al., 2017). The approach presented in Nadon and Ault (2016) involves Relationships of life history traits are useful for the a series of regression models in which relationships estimation of missing life history parameter values by between life history parameters are used to sequentially relating ones, such as M, for which information is elu- estimate missing values for life history parameters from sive to ones, such as L∞ and K, for which values are more the previously estimated parameters (Fig. 1, Table 1). Note easily obtained (Pauly, 1980), or by relating Lmax to other that the regression models that relate these parameters length parameters (e.g., Lmat) (Froese and Binohlan, 2000, 2003; Jaric´ and Gacˇic´, 2012). The aim of these studies was mainly to generate missing estimates for single param- eters, and these studies were not taxon- specific, limiting their utility by ignoring the complex multivariate distri- bution between key life history parameters. As a solu- tion, Nadon and Ault (2016) presented an approach that involves the use of Monte Carlo simulation draws and sev- eral regression model steps between life history parame- ters for 6 fish families. Their approach allows for complex relationships between parameters, while maintaining a multivariate error structure. This approach is analogous to the method in which a sequence of regressions is used for multiple imputation of missing data (Raghunathan et al., 2001; van Buuren, 2007; Ellington et al., 2015). Nadon and Ault (2016) determined family- specific rela- tionships between key life history traits after an exten- sive literature review for 6 families of coastal fish species: surgeonfishes, jacks, snappers, emperors, goatfishes, and parrotfishes. Peer- reviewed data- limited assessments of stocks in Hawaii (Nadon, 2017) and Guam (Nadon, 2019) have already been implemented by using this approach. The goal of our study was to extend the approach from Nadon and Ault (2016) to 3 additional families of trop- Figure 1 ical coastal fish species, groupers (Serranidae), wrasses Depiction of one iteration of the stepwise stochastic simula- (Labridae), and grunts (Haemulidae), as well as to sharks tion approach in which statistical relationships between key from the orders Carcharhiniformes and Lamniformes. We life history traits are used to estimate parameters related to acknowledge that taxonomy is an evolving field and with growth, maturity, and longevity. The simulation starts with new information can come new evidence for reclassifica- a local estimate of maximum length (Lmax), and regression tion. Recently, this evolution has touched groupers with models A–D (solid arrows) are used successively to estimate proposals to move the subfamily Epinephelinae, including a parameter from the one estimated in the previous model. The dashed arrows represent direct parameter calculations the genus Epinephelus, under the family Epinephelidae made by using deterministic equations (e.g., the oldest instead of under the family Serranidae (Craig and recorded age [Amax] is calculated by using natural mortality Hastings, 2007; Smith and Craig, 2007; Ma and Craig, [M]). The rest of the parameters in this depiction include 2018). Although some classifications put grouper taxa the asymptotic length (L∞), expected length at the oldest under Epinephelidae instead of Serranidae, for the pur- recorded age (LAmax), growth coefficient (K), and length at poses of this study, we used Serranidae as the family name which 50% of individuals are mature (Lmat). for species of Epinephelinae and other grouper species. Erickson and Nadon: Stepwise stochastic simulation for distributions
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