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 Can stock–recruitment points determine which spawning potential ratio is the best proxy for maximum sustainable yield reference points?

2013 ◽  
Vol 70 (6) ◽  
pp. 1075-1080 ◽  
Author(s):  
Christopher M. Legault ◽  
Elizabeth N. Brooks
Keyword(s):  
Life History ◽  
Mortality Rate ◽  
Maximum Sustainable Yield ◽  
Reference Points ◽  
Sustainable Yield ◽  
Marine Science ◽  
Fishing Mortality ◽  
Scatter Plots ◽  
Stock Recruitment ◽  
Spawning Potential Ratio

Abstract Legault, C. M., and Brooks, E. N. 2013. Can stock–recruitment points determine which spawning potential ratio is the best proxy for maximum sustainable yield reference points? – ICES Journal of Marine Science, 70: 1075–1080. The approach of examining scatter plots of stock–recruitment (S–R) estimates to determine appropriate spawning potential ratio (SPR)-based proxies for FMSY was investigated through simulation. As originally proposed, the approach assumed that points above a replacement line indicate year classes that produced a surplus of spawners, while points below that line failed to achieve replacement. In practice, this has been implemented by determining Fmed, the fishing mortality rate that produces a replacement line with 50% of the points above and 50% below the line. A new variation on this approach suggests FMSY proxies can be determined by examining the distribution of S–R points that are above or below replacement lines associated with specific SPRs. Through both analytical calculations and stochastic results, we demonstrate that this approach is fundamentally flawed and that in some cases the inference is diametrically opposed to the method's intended purpose. We reject this approach as a tool for determining FMSY proxies. We recommend that the current proxy of F40% be maintained as appropriate for a typical groundfish life history.

Eggs-per-recruit model for management of the California market squid (Loligo opalescens) fishery

2005 ◽  
Vol 62 (7) ◽  
pp. 1640-1650 ◽  
Author(s):  
Michael R Maxwell ◽  
Larry D Jacobson ◽  
Ramon J Conser
Keyword(s):  
Mortality Rate ◽  
Egg Laying ◽  
Reference Points ◽  
Model Parameters ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Loligo Opalescens ◽  
Maturation Rate ◽  
Sampling Procedures ◽  
Yield Per Recruit

We develop a per-recruit model for the management of the California market squid (Loligo opalescens) fishery. Based on recent confirmation of determinate fecundity in this species, we describe how catch fecundity (i.e., eggs remaining in the reproductive tracts of harvested females) can be used to simultaneously infer fishing mortality rate along with management reference points such as yield-per-recruit, spawned eggs-per-recruit, and proportional egg escapement. Rates of mortality and egg laying have important effects on these reference points. Somewhat surprisingly, increasing the rate of natural mortality decreased spawned eggs-per-recruit while increasing proportional egg escapement. Increasing the rate of egg laying increased both spawned eggs-per-recruit and egg escapement. Other parameters, such as the maturation rate and gear vulnerability of immature females, affected the reference points. In actual practice, the influence of these parameters for immature squid may go undetected if immature squid are excluded from analysis of the catch. Application of this model to routine management is feasible but requires refinement of sampling procedures, biological assumptions, and model parameters. This model is useful because it is grounded on empirical data collected relatively inexpensively from catch samples (catch fecundity) while allowing for the simultaneous calculation of instantaneous fishing mortality rate and egg escapement.

Incorporating Allee effects in fish stock–recruitment models and applications for determining reference points

2002 ◽  
Vol 59 (2) ◽  
pp. 242-249 ◽  
Author(s):  
D G Chen ◽  
J R Irvine ◽  
A J Cass
Keyword(s):  
Search Algorithm ◽  
Information Matrix ◽  
Natural Extension ◽  
Reference Points ◽  
Fish Stock ◽  
Model Parameters ◽  
Allee Effects ◽  
Probability Curve ◽  
New Model ◽  
Stock Recruitment

A new type of stock–recruitment model is examined that incorporates Allee effects, which may occur when fish populations are small. The model is a natural extension of traditional models, which only incorporate the negative effects of increasing density on fecundity and (or) survival. Because the new model is intrinsically nonlinear and because of convergence problems at local optima, we use a maximum likelihood approach with a global genetic search algorithm to estimate model parameters. Parameter uncertainty is obtained from the inverse of the Fisher information matrix. Based on this new model, an extinction probability curve is developed using the parameter defining the Allee effects. This curve can readily be used to calculate the theoretical probability of extinction for a single brood line in one generation for any particular spawner number or biomass. Alternatively, because managers may wish to assign reference points corresponding to particular extinction probabilities, spawner numbers can be determined for these reference points. Two Pacific salmon populations, North Thompson coho (Oncorhynchus kisutch) and Chilko sockeye (O. nerka), are used to demonstrate the approach. It is found that the Allee effect parameter is statistically significant for the Thompson coho, but not for Chilko sockeye.

scholarly journals Linking the performance of a data-limited empirical catch rule to life-history traits

2020 ◽  
Vol 77 (5) ◽  
pp. 1914-1926
Author(s):  
Simon H Fischer ◽  
José A A De Oliveira ◽  
Laurence T Kell
Keyword(s):  
Time Series ◽  
Life History ◽  
Life Histories ◽  
Life History Traits ◽  
Growth Parameter ◽  
Reference Points ◽  
Total Allowable Catch ◽  
Fish Stocks ◽  
Wide Range ◽  
Spawning Stock

Abstract Worldwide, the majorities of fish stocks are data-limited and lack fully quantitative stock assessments. Within ICES, such data-limited stocks are currently managed by setting total allowable catch without the use of target reference points. To ensure that such advice is precautionary, we used management strategy evaluation to evaluate an empirical rule that bases catch advice on recent catches, information from a biomass survey index, catch length frequencies, and MSY reference point proxies. Twenty-nine fish stocks were simulated covering a wide range of life histories. The performance of the rule varied substantially between stocks, and the risk of breaching limit reference points was inversely correlated to the von Bertalanffy growth parameter k. Stocks with k>0.32 year−1 had a high probability of stock collapse. A time series cluster analysis revealed four types of dynamics, i.e. groups with similar terminal spawning stock biomass (collapsed, BMSY, 2BMSY, 3BMSY). It was shown that a single generic catch rule cannot be applied across all life histories, and management should instead be linked to life-history traits, and in particular, the nature of the time series of stock metrics. The lessons learnt can help future work to shape scientific research into data-limited fisheries management and to ensure that fisheries are MSY compliant and precautionary.

Modelling fishing-induced adaptations and consequences for natural mortality

2010 ◽  
Vol 67 (7) ◽  
pp. 1086-1097 ◽  
Author(s):  
Christian Jørgensen ◽  
Øyvind Fiksen
Keyword(s):  
Life History ◽  
Body Size ◽  
Life Histories ◽  
Life History Traits ◽  
Reproductive Behaviour ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Trade Offs ◽  
Wide Range ◽  
Investment In Reproduction

When trade-offs involving predation and mortality are perturbed by human activities, behaviour and life histories are expected to change, with consequences for natural mortality rates. We present a general life history model for fish in which three common relationships link natural mortality to life history traits and behaviour. First, survival increases with body size. Second, survival declines with growth rate due to risks involved with resource acquisition and allocation. Third, fish that invest heavily in reproduction suffer from decreased survival due to costly reproductive behaviour or morphology that makes escapes from predators less successful. The model predicts increased natural mortality rate as an adaptive response to harvesting. This extends previous models that have shown that harvesting may cause smaller body size, higher growth rates, and higher investment in reproduction. The predicted increase in natural mortality is roughly half the fishing mortality over a wide range of harvest levels and parameter combinations such that fishing two fish kills three after evolutionary adaptations have taken place.

Biological reference points for fish stocks in a multispecies context

2001 ◽  
Vol 58 (11) ◽  
pp. 2167-2176 ◽  
Author(s):  
Jeremy S Collie ◽  
Henrik Gislason
Keyword(s):  
Life History ◽  
Growth Rates ◽  
Prey Species ◽  
Prey Availability ◽  
Mortality Rates ◽  
Reference Points ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Predator Species ◽  
Life History Parameters

Biological reference points (BRPs) are widely used to define safe levels of harvesting for marine fish populations. Most BRPs are either minimum acceptable biomass levels or maximum fishing mortality rates. The values of BRPs are determined from historical abundance data and the life-history parameters of the fish species. However, when the life-history parameters change over time, the BRPs become moving targets. In particular, the natural mortality rate of prey species depends on predator levels; conversely, predator growth rates depend on prey availability. We tested a suite of BRPs for their robustness to observed changes in natural mortality and growth rates. We used the relatively simple Baltic Sea fish community for this sensitivity test, with cod as predator and sprat and herring as prey. In general, the BRPs were much more sensitive to the changes in natural mortality rates than to growth variation. For a prey species like sprat, fishing mortality reference levels should be conditioned on the level of predation mortality. For a predator species, a conservative level of fishing mortality can be identified that will prevent growth overfishing and ensure stock replacement. These first-order multispecies interactions should be considered when defining BRPs for medium-term (5–10 year) management decisions.

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.

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