Analytical models for fishery reference points

1998 ◽  
Vol 55 (2) ◽  
pp. 515-528 ◽  
Author(s):  
Jon T Schnute ◽  
Laura J Richards
Keyword(s):  
Fishery Management ◽  
Reference Points ◽  
Analytical Models ◽  
Model Parameters ◽  
Harvest Management ◽  
Structured Population Models ◽  
General Utility ◽  
Special Cases ◽  
Age Structured ◽  
Mathematical Definitions

Fishery reference points are widely applied in formulating harvest management policies. We supply precise mathematical definitions for several reference points in common use. We then derive analytical expressions for these quantities from age-structured population models. In particular, we explain how the maximum sustainable harvest rate and catch (h*, C*), two quantities of management importance, can replace the classical recruitment parameters ( alpha , beta ) in the Beverton-Holt and Ricker recruitment curves. We also demonstrate dependencies of various reference points on subsets of model parameters. Although our analysis is restricted to special cases, our models still have general utility. For example, simple calculations from analytical formulas enable checks on the output from more complex models and guide the choice of reference points for fishery management.

A stochastic approach to stock reduction analysis

2006 ◽  
Vol 63 (1) ◽  
pp. 212-223 ◽  
Author(s):  
Carl J Walters ◽  
Steven J.D. Martell ◽  
Josh Korman
Keyword(s):  
Probability Distributions ◽  
Stochastic Approach ◽  
Reference Points ◽  
Stock Size ◽  
Structured Population Models ◽  
Alternative Hypotheses ◽  
Detailed Assessment ◽  
Importance Resampling ◽  
Age Structured ◽  
Fully Bayesian

Stock reduction analysis (SRA) can complement more detailed assessment methods by using long-term historical catches to estimate recruitment rates needed to have produced those catches, yet still end up with stock sizes near those estimated by the detailed methods. A longer historical perspective can also add information to the estimation of reference points such as unfished biomass (B0) or target biomass (BMSY). Deterministic SRA models provide a single stock size trajectory that is vanishingly unlikely to have actually occurred, while stochastic SRA attempts to provide probability distributions for stock size over time under alternative hypotheses about unfished recruitment rates and about variability around assumed stock–recruitment relationships. These distributions can be generated with age-structured population models by doing large numbers of Monte Carlo simulation trials and retaining those sample trials for which the stock would not have been driven to extinction by historical catches. By resampling from these trials using likelihood weights (sampling – importance resampling method), it is possible to move into fully Bayesian, state–space assessment modeling through a series of straightforward steps and to provide understandable visualization of how much the data help to reduce uncertainty about historical fishing impacts and stock status.

scholarly journals Interactions between ageing error and selectivity in statistical catch-at-age models: simulations and implications for assessment of the Chilean Patagonian toothfish fishery

2016 ◽  
Vol 73 (4) ◽  
pp. 1074-1090 ◽  
Author(s):  
Vania Henríquez ◽  
Roberto Licandeo ◽  
Luis A. Cubillos ◽  
Sean P. Cox
Keyword(s):  
Reference Points ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Time Varying ◽  
Age Composition ◽  
Composition Data ◽  
Spawning Stock ◽  
Patagonian Toothfish ◽  
Stock Depletion ◽  
Age Structured

Abstract In age-structured fisheries stock assessments, ageing errors within age composition data can lead to biased mortality rate and year-class strength estimates. These errors may be further compounded where fishery-dependent age composition data are influenced by temporal changes in fishery selectivity and selectivity misspecification. In this study, we investigated how ageing error within age composition data interacts with time-varying fishery selectivity and selectivity misspecification to affect estimates derived from a statistical catch-at-age (SCA) model that used fishery-dependent data. We tested three key model parameters: average unfished recruitment (R0), spawning stock depletion (Dfinal), and fishing mortality in the terminal year (Fterminal). The Patagonian toothfish (Dissostichus eleginoides) fishery in southern Chile was used as a case study. Age composition data used to assess this fishery were split into two sets based on scale (1989–2006) and otolith (2007–2012) readings, where the scale readings show clear age-truncation effects. We used a simulation-estimation approach to examine the bias and precision of parameter estimates under various combinations of ageing error, selectivity type (asymptotic or dome-shaped), selectivity misspecification, and variation in selectivity over time. Generally, ageing error led to overly optimistic perceptions of current fishery status relative to historical reference points. Ageing error generated imprecise and positively biased estimates of R0 (range 10 to >200%), Dfinal (range −20 to >100%), and Fterminal (range −15 to >150%). The bias in Dfinal and R0 was more severe when selectivity was dome-shaped. Time-varying selectivity (both asymptotic and dome-shaped) increased the bias in Dfinal and Fterminal, but decreased the bias in R0. The effect of ageing error was more severe, or was masked, with selectivity misspecification. Correcting the ageing error inside the SCA reduced bias and improved precision of estimated parameters .

scholarly journals Reference points based on dynamic optimization: a versatile algorithm for mixed-fishery management with bioeconomic age-structured models

2012 ◽  
Vol 69 (4) ◽  
pp. 660-669 ◽  
Author(s):  
José-María Da Rocha ◽  
María-José Gutiérrez ◽  
Santiago Cerviño
Keyword(s):  
Dynamic Optimization ◽  
Fishery Management ◽  
Single Species ◽  
Steady State Solution ◽  
Reference Points ◽  
Management Problem ◽  
Species Management ◽  
Intertemporal Discounting ◽  
Spawning Stock ◽  
Age Structured

Abstract Da Rocha, J-M., Gutiérrez, M-J., and Cerviño, S. 2012. Reference points based on dynamic optimization: a versatile algorithm for mixed-fishery management with bioeconomic age-structured models. – ICES Journal of Marine Science, 69: 660–669. Single-species management objectives may not be consistent within mixed fisheries. They may lead species to unsafe situations, promote discarding of over-quota, and/or misreporting of catches. We provide an algorithm for characterizing bioeconomic reference points for a mixed fishery as the steady-state solution of a dynamic optimal management problem. The optimization problem takes into account that: (i) species are caught simultaneously in unselective fishing operations, and (ii) intertemporal discounting and fleet costs relate to reference points to discounted economic profits along optimal trajectories. We illustrate how the algorithm can be implemented by applying it to the European northern hake stock (Merluccius merluccius), where fleets also capture northern megrim (Lepidorhombus whiffiagonis) and northern anglerfish (Lophius piscatorius and Lophius budegassa). We find that optimal mixed management leads to a target reference point that is quite similar to two-thirds of the Fmsy single-species (hake) target. Mixed management is superior to single-species management because it leads the fishery to higher discounted profits, with higher long-term spawning-stock biomass for all species. We calculate that the losses due to the use of the Fmsy single-species (hake) target in this mixed fishery account for 11.4% of total discounted profits.

Implications of life-history invariants for biological reference points used in fishery management

2003 ◽  
Vol 60 (6) ◽  
pp. 710-720 ◽  
Author(s):  
Erik H Williams ◽  
Kyle W Shertzer
Keyword(s):  
Life History ◽  
Fishery Management ◽  
Deterministic Model ◽  
A Priori ◽  
Reference Points ◽  
Model Parameters ◽  
Natural Mortality ◽  
Wide Range ◽  
Stock Recruitment ◽  
Harvest Policies

Fish harvest policies typically rely on biological reference points for measures of a stock's status. We examine three common biological reference points based on fishing mortality rates corresponding to maximum sustainable yield with an age-structured deterministic model. We incorporate invariant life-history relationships into the model to maintain parsimony and focus model parameters on biologically plausible parameter space. A wide range of biological and fishery characteristics were used in the model so that our results pertain to the management of virtually any exploited population. Results indicate that two biological reference points based on spawning biomass are insensitive to life-history parameters, whereas one based on natural mortality is highly sensitive. All three depend largely on the choice of a stock–recruitment function and on steepness, a measure of the population growth rate. For each of the three, values have been previously proposed that were intended to safely apply to all fisheries; our results show that no such universal values exist. We recommend determining stock–recruitment functions a priori, establishing biological reference points on steepness explicitly and eliminating harvest policies based on the natural mortality rate altogether.

A perspective on steepness, reference points, and stock assessment

2013 ◽  
Vol 70 (6) ◽  
pp. 930-940 ◽  
Author(s):  
Marc Mangel ◽  
Alec D. MacCall ◽  
Jon Brodziak ◽  
E.J. Dick ◽  
Robyn E. Forrest ◽  
...  
Keyword(s):  
Life History ◽  
Fishery Management ◽  
Stock Assessment ◽  
Reference Points ◽  
Production Model ◽  
Published Data ◽  
Difficult Situation ◽  
Life History Parameters ◽  
Stock Recruitment ◽  
Age Structured

We provide a perspective on steepness, reference points for fishery management, and stock assessment. We first review published data and give new results showing that key reference points are fixed when steepness and other life history parameters are fixed in stock assessments using a Beverton–Holt stock–recruitment relationship. We use both production and age-structured models to explore these patterns. For the production model, we derive explicit relationships for steepness and life history parameters and then for steepness and major reference points. For the age-structured model, we are required to generally use numerical computation, and so we provide an example that complements the analytical results of the production model. We discuss what it means to set steepness equal to 1 and how to construct a prior for steepness. Ways out of the difficult situation raised by fixing steepness and life history parameters include not fixing them, using a more complicated stock–recruitment relationship, and being more explicit about the information content of the data and what that means for policy makers. We discuss the strengths and limitations of each approach.

scholarly journals Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity

2021 ◽  
Vol 11 (15) ◽  
pp. 6931
Author(s):  
Jie Liu ◽  
Martin Oberlack ◽  
Yongqi Wang
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Stagnation Point ◽  
Analytical Solutions ◽  
Wide Spectrum ◽  
Momentum Conservation ◽  
Stagnation Point Flow ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Special Cases

Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution.

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

Comparison of Analytical and Empirical Models to Capture Variations in Off-Road Vehicle Dynamics

2005 ◽  
Author(s):  
Paul J. Pearson ◽  
David M. Bevly
Keyword(s):  
Empirical Data ◽  
Vehicle Dynamics ◽  
Experimental Validation ◽  
Inertial Sensors ◽  
Analytical Models ◽  
Control Algorithms ◽  
Model Parameters ◽  
Steering Control ◽  
Steering Angle ◽  
Yaw Rate

This paper develops two analytical models that describe the yaw dynamics of a farm tractor and can be used to design or improve steering control algorithms for the tractor. These models are verified against empirical data. The particular dynamics described are the motions from steering angle to yaw rate. A John Deere 8420 tractor, outfitted with inertial sensors and controlled through a PC-104 form factor computer, was used for experimental validation. Conditions including different implements at varying depths, as would normally be found on a farm, were tested. This paper presents the development of the analytical models, validates them against empirical data, and gives trends on how the model parameters change for different configurations.

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