Canadian Journal of Fisheries and Aquatic Sciences A stepwise stochastic simulation approach to estimate life history parameters for data-poor fisheries Journal: Canadian Journal of Fisheries and Aquatic Sciences Manuscript ID cjfas-2015-0303.R3 Manuscript Type: Article Date Submitted by the Author: 07-May-2016 Complete List of Authors: Nadon, Marc; Joint Institute for Marine and Atmospheric Research; NOAA, Pacific Islands Fisheries Science Center; University of Miami, Rosenstiel School of Marine and Atmospheric Science Ault, Jerald;Draft University of Miami, Rosenstiel School of Marine and Atmospheric Science FISHERY MANAGEMENT < General, MARINE FISHERIES < General, Keyword: MORTALITY < General, STOCK ASSESSMENT < General, LIFE HISTORY < General https://mc06.manuscriptcentral.com/cjfas-pubs Page 1 of 66 Canadian Journal of Fisheries and Aquatic Sciences 1 2 3 4 A stepwise stochastic simulation approach to estimate missing life 5 history parameters for data-poor fisheries 6 7 8 Running headline: Life history parameters for data-poor fisheries 9 10 Marc O. Nadon 1, 2, 3 and Jerald S. Ault 3 11 12 1 Joint Institute for Marine and AtmosphericDraft Research, 1000 Pope Road, Honolulu, HI 96822 13 U.S.A. 14 2 Pacific Island Fisheries Science Center, NOAA Fisheries, 1845 Wasp Boulevard, Honolulu, HI 15 96818 U.S.A. 16 3 University of Miami, Rosenstiel School of Marine and Atmospheric Science, 4600 17 Rickenbacker Causeway, Miami, FL 33149 U.S.A. 18 19 Corresponding author: 20 Marc Nadon – [email protected] 21 1845 Wasp Boulevard, Honolulu, HI 96816, USA 22 Phone: 808-725-5317 23 24 25 26 27 28 29 https://mc06.manuscriptcentral.com/cjfas-pubs Canadian Journal of Fisheries and Aquatic Sciences Page 2 of 66 2 30 1. Abstract 31 Coastal fisheries are typically characterized by species-rich catch compositions and limited 32 management resources which typically leads to notably data-poor situations for stock 33 assessment. Some parsimonious stock assessment approaches rely on cost-efficient size 34 composition data, but these also require estimates of life history parameters associated with 35 natural mortality, growth, and maturity. These parameters are unavailable for most exploited 36 stocks. Here, we present a novel approach that uses a local estimate of maximum length and 37 statistical relationships between key life history parameters to build multivariate probability 38 distributions that can be used to parameterize stock assessment models in the absence of species- 39 specific life history data. We tested this approach on three fish species for which empirical 40 length-at-age and maturity data were availableDraft (from Hawaii and Guam) and calculated 41 probability distributions of spawning potential ratios (SPR) at different exploitation rates. The 42 life history parameter and SPR probability distributions generated from our data-limited 43 analytical approach compared well with those obtained from bootstrap analyses of the empirical 44 life history data. This work provides a useful new tool that can greatly assist fishery stock 45 assessment scientists and managers in data-poor situations, typical of most of the world’s 46 fisheries. 47 48 49 Key words: coral reef fish, Beverton-Holt invariants, stock assessment, Bayesian priors, growth, 50 maturity, longevity, natural mortality, spawning potential ratio 51 https://mc06.manuscriptcentral.com/cjfas-pubs Page 3 of 66 Canadian Journal of Fisheries and Aquatic Sciences 3 52 1. Introduction 53 Coastal fisheries provide livelihoods and sustenance for hundreds of millions of people 54 worldwide, particularly in poorer tropical countries (Pauly et al. 2005). These fisheries are often 55 characterized by highly diverse catch compositions, sometimes reaching hundreds of species, 56 and are mostly managed with limited financial and human resources, if managed at all. For most 57 of these fisheries, limited information exists on historical catches, fishing effort, and baseline 58 population abundances (Fenner 2012). These issues make assessing these fisheries highly 59 problematic. Recently, methods have been proposed for data-poor situations that rely mainly on 60 cost-effective size composition data and some basic demographic knowledge of growth, 61 maturity, and longevity (Ault et al. 1998, 2008, 2014, Gedamke and Hoenig 2006, Hordyk et al. 62 2015). However, even these simple dataDraft requirements are often unmet due to a lack of life 63 history (LH) information for either a particular region or even globally. Specifically, Froese and 64 Binohlan (2000) have estimated that only 1200 out of 7000 (about 17%) of exploited species 65 worldwide have some life history data. Here, we propose a novel, standardized approach to 66 obtain probability distributions of LH parameters for under- and un-studied species by 67 employing a stepwise Monte Carlo simulation approach based on a meta-analysis of published 68 parameters and some relatively well-known relationships between individual parameters. 69 Beverton and Holt (1959) and Beverton (1963) were the first to identify fundamental 70 linkages between LH parameters in fishes. They observed that: (1) natural mortality rate M is 71 positively correlated to von Bertalanffy’s Brody growth coefficient K, such that the ratio of M/K 72 is typically close to 1.5 (i.e., whereas longer lived fishes tend to grow more slowly); (2) length at 73 50% maturity ( Lmat ) is positively correlated to asymptotic length Linf where the ratio Lmat /Linf is 74 generally around 0.66 (i.e., species tend to mature at a specific fraction of their maximum size); https://mc06.manuscriptcentral.com/cjfas-pubs Canadian Journal of Fisheries and Aquatic Sciences Page 4 of 66 4 75 and, (3) von Bertalanffy growth model coefficients Linf and K are negatively correlated following -h 76 a general power function of the form Linf ~ K ; where h is typically about 0.5. These ratios, 77 generally referred to as Beverton-Holt (BH) invariants (Charnov 1993), have been shown to be 78 related to the maximization of reproductive output (Jensen 1996, 1997, Charnov 2008). As a 79 consequence, these relationships have likely been conserved through natural selection, as 80 originally theorized by Beverton and Holt (1959). Some recent studies (e.g., Prince et al. 2015) 81 noted that these “invariants” may actually differ significantly between taxonomic groups, and 82 thus are better retained within taxa. 83 One important interest in studying these relationships is their potential use in the 84 estimation of elusive LH parameters such as M by relating these to more tractable ones, such as 85 Linf , K, and perhaps water temperature (seeDraft Kenchington 2014 for a review of other empirical M 86 relationships). Recent studies have proposed other relationships related to maximum length and 87 optimum length (Froese and Binohlan 2000, 2003, Jarić and Gačić 2012). These studies were 88 mainly concerned with imputing estimates for individual unavailable parameters. However, it is 89 not clear how these relationships might be used to generate complete multivariate distributions 90 for all key LH parameters (e.g., Linf , K, Lmat , M) given that these are all typically correlated to 91 some degree. Standard multivariate distributions (e.g., multivariate normal) can describe the 92 variance-covariance structure of multiple parameters, but preclude the use of more complex 93 relationships between parameters (e.g., power, exponential, polynomial) and non-normal error 94 distributions (e.g., log-normal, gamma). 95 As a solution, we propose using a stepwise stochastic simulation approach that seeks to 96 preserve the inherent correlation structure between these parameters, an approach analogous to 97 the “sequence of regressions” (or fully conditional specification - FCS) method used for multiple https://mc06.manuscriptcentral.com/cjfas-pubs Page 5 of 66 Canadian Journal of Fisheries and Aquatic Sciences 5 98 imputation of missing data (Raghunathan et al. 2001, van Buuren 2007, Ellington et al. 2015). 99 To accomplish this, we first reviewed the literature on the life history of six commonly targeted 100 families of coral reef fishes to generate family-specific models linking the four main LH 101 parameters: Linf ~ Lmax , K ~ Linf , M ~ K, and Lmat ~ Lλ where Lmax is a local estimate of maximum 102 length and Lλ is the expected length at oldest recorded age (i.e., the length predicted by a specific 103 growth curve for the oldest age; see Table 1 for definitions). With these models, it is theoretically 104 possible to generate the underlying complex multivariate probability distributions for these 105 parameters by taking successive random samples from the estimated regression models, starting 106 with a local estimate of Lmax . Here, we tested this approach for three well-studied species for 107 which empirical data on lengths, ages, and maturity were available. We used bootstrap analyses 108 to generate probability distributions of LHDraft parameters from biological studies and compared 109 these distributions to those obtained through our stepwise approach. Finally, we derived 110 spawning potential ratios (SPRs) at various fixed exploitation rates using these imputed life 111 history distributions and compared the two resulting datasets. 112 1. Methods 113 The approach presented here only requires a local estimate of Lmax to generate probability 114 distributions of missing LH parameters. To do so, it is first necessary to model the family-level 115 relationships between these parameters using published