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 The Kumaraswamy Pareto IV Distribution

2021 ◽  
Vol 50 (5) ◽  
pp. 1-22
Author(s):  
Muhammad Hussain Tahir ◽  
Gauss M. Cordeiro ◽  
Muhammad Mansoor ◽  
Muhammad Zubair ◽  
Ayman Alzaatreh
Keyword(s):  
Density Function ◽  
Residual Life ◽  
Information Matrix ◽  
Real Life ◽  
Quantile Function ◽  
Mean Residual Life ◽  
Model Parameters ◽  
New Model ◽  
Lorenz Curves ◽  
Mean Waiting Time

We introduce a new model named the Kumaraswamy Pareto IV distribution which extends the Pareto and Pareto IV distributions. The density function is very flexible and can be left-skewed, right-skewed and symmetrical shapes. It hasincreasing, decreasing, upside-down bathtub, bathtub, J and reversed-J shaped hazard rate shapes. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments,Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, probability weighted moments and generating function. We provide the density function of the order statistics and their moments. The Renyi and q entropies are also obtained. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of three real-life data sets. In fact, our proposed model provides a better fit to these data than the gamma-Pareto IV, gamma-Pareto, beta-Pareto,exponentiated Pareto and Pareto IV models.

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.

An age-structured model with leading management parameters, incorporating age-specific selectivity and maturity

2008 ◽  
Vol 65 (2) ◽  
pp. 286-296 ◽  
Author(s):  
Robyn E Forrest ◽  
Steven J.D. Martell ◽  
Michael C Melnychuk ◽  
Carl J Walters
Keyword(s):  
Life History Traits ◽  
Stock Assessment ◽  
Maximum Sustainable Yield ◽  
Reference Points ◽  
Fish Stock ◽  
Structured Model ◽  
Specific Selectivity ◽  
Stock Recruitment ◽  
Age Structured ◽  
Age Structured Model

Previous authors have shown analytically that the optimal equilibrium harvest rate (UMSY) for an iteroparous fish stock is a function of the slope of the stock-recruitment curve at low stock size (α) and that UMSY can therefore be considered a direct measure of stock productivity. As such, it can be used as a leading parameter in stock assessment models and directly estimated using Bayesian or similar techniques. Here we present an alternative method for deriving α from UMSY that incorporates age-specific selectivity and fecundity, avoiding assumptions of knife-edged recruitment and maturity. We present an age-structured model with two fisheries reference points (UMSY and maximum sustainable yield, MSY) as its leading parameters. We show equilibrium properties of the model, chiefly in terms of its ability to show relationships between life history traits, density dependence, and UMSY. We also demonstrate a simple Bayesian estimation routine to illustrate estimation of UMSY and MSY directly from data. We compare our results to those from a structurally identical model with leading biological parameters. Using models with leading management parameters can improve communicability of results to managers.

scholarly journals Subjective judgement in data subsetting: implications for CPUE standardisation and stock assessment of non-target chondrichthyans

2011 ◽  
Vol 62 (6) ◽  
pp. 734 ◽  
Author(s):  
J. M. Braccini ◽  
M.-P. Etienne ◽  
S. J. D. Martell
Keyword(s):  
Ad Hoc ◽  
Stock Assessment ◽  
Fishing Effort ◽  
Reference Points ◽  
Fish Stock ◽  
Model Parameters ◽  
Total Allowable Catch ◽  
Subjective Judgement ◽  
Definition Of ◽  
Catch Per Effort

Standardisation of catch-per-effort (CPUE) data is an essential component for nearly all stock assessments. The first step in CPUE standardisation is to separate the comparable from the non-comparable catch and effort records and this is normally done based on subjective rules. In the present study, we used catch-and-effort data from the elephant fish (Callorhinchus milii) to illustrate the differences in CPUE when using expert judgement to define different ad hoc selection criteria used to subset these data. The data subsets were then used in the standardisation of CPUE and the stock assessment of elephant fish. The catch-and-effort subsets produced different patterns of precision and trends, each of which led to different estimates (and related uncertainty) of model parameters and management reference points. For most CPUE series, there was a very high probability that the elephant fish stock is overexploited and that overfishing is occurring. The estimates of total allowable catch (TAC) and the uncertainty around these estimates also varied considerably depending on the CPUE series used. Our study shows how sensitive TAC estimation is when there is high uncertainty in the definition of the fishing effort targeted at the species analysed.

Detecting environmental regimes in fish stock-recruitment relationships by fuzzy logic

2001 ◽  
Vol 58 (11) ◽  
pp. 2139-2148 ◽  
Author(s):  
D G Chen
Keyword(s):  
Fuzzy Logic ◽  
Environmental Variable ◽  
Clupea Harengus ◽  
Fish Stock ◽  
Environmental Regimes ◽  
Fuzzy Logic Approach ◽  
Stock Recruitment ◽  
Logic Approach ◽  
Traditional Approaches ◽  
The Impact

A fuzzy logic approach is developed to model and test the impact of environmental regimes on fish stock–recruitment relationships. Traditional methods use environmental variables to classify stock–recruitment data into different membership percentiles followed by fitting the stock–recruitment models for each subset. In contrast, the fuzzy logic approach uses a continuous membership function to provide a rational basis for the classification. Thus, parameter estimation is based on a more logically consistent foundation without resorting to subjective partitions. This new approach is applied to herring stock from the west coast of Vancouver Island (Clupea harengus pallasi) using sea surface temperature as the environmental variable and to Pacific halibut stock (Hippoglossus stenolepis) using the Pacific Decadal Oscillation as the environmental variable. From these applications, the herring stock–recruitment relationships were found to vary significantly during different regimes, whereas this was not the case for halibut. However, in both instances, the fuzzy logic approach demonstrated that density-dependent effects differed between regimes. The fuzzy logic model consistently outperformed traditional approaches as measured by several diagnostic criteria. Because fuzzy logic models address uncertainty better than traditional approaches, they have the potential to improve our ability to understand factors influencing stock–recruitment relationships and thereby manage fisheries more effectively.

scholarly journals Quirky patterns in time-series of estimates of recruitment could be artefacts

2014 ◽  
Vol 72 (1) ◽  
pp. 111-116 ◽  
Author(s):  
M. Dickey-Collas ◽  
N. T. Hintzen ◽  
R. D. M. Nash ◽  
P-J. Schön ◽  
M. R. Payne
Keyword(s):  
Time Series ◽  
Stock Assessment ◽  
Meta Analysis ◽  
Reference Points ◽  
Fish Stocks ◽  
Stock Recruitment ◽  
Modelling Assumptions ◽  
Meta Analyses ◽  
Recruitment Model ◽  
Recruitment Time

Abstract The accessibility of databases of global or regional stock assessment outputs is leading to an increase in meta-analysis of the dynamics of fish stocks. In most of these analyses, each of the time-series is generally assumed to be directly comparable. However, the approach to stock assessment employed, and the associated modelling assumptions, can have an important influence on the characteristics of each time-series. We explore this idea by investigating recruitment time-series with three different recruitment parameterizations: a stock–recruitment model, a random-walk time-series model, and non-parametric “free” estimation of recruitment. We show that the recruitment time-series is sensitive to model assumptions and this can impact reference points in management, the perception of variability in recruitment and thus undermine meta-analyses. The assumption of the direct comparability of recruitment time-series in databases is therefore not consistent across or within species and stocks. Caution is therefore required as perhaps the characteristics of the time-series of stock dynamics may be determined by the model used to generate them, rather than underlying ecological phenomena. This is especially true when information about cohort abundance is noisy or lacking.

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.

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

scholarly journals Thermal conductivity of unsaturated clay-rocks

2010 ◽  
Vol 14 (1) ◽  
pp. 91-98 ◽  
Author(s):  
D. Jougnot ◽  
A. Revil
Keyword(s):  
Thermal Conductivity ◽  
Porous Material ◽  
Solid Phase ◽  
Model Parameters ◽  
Electrical Parameters ◽  
New Model ◽  
Unsaturated Clay ◽  
Unsaturated Porous Material ◽  
Clay Rocks ◽  
Good Agreement

Abstract. The parameters used to describe the electrical conductivity of a porous material can be used to describe also its thermal conductivity. A new relationship is developed to connect the thermal conductivity of an unsaturated porous material to the thermal conductivity of the different phases of the composite, and two electrical parameters called the first and second Archie's exponents. A good agreement is obtained between the new model and thermal conductivity measurements performed using packs of glass beads and core samples of the Callovo-Oxfordian clay-rocks at different saturations of the water phase. We showed that the three model parameters optimised to fit the new model against experimental data (namely the thermal conductivity of the solid phase and the two Archie's exponents) are consistent with independent estimates. We also observed that the anisotropy of the effective thermal conductivity of the Callovo-Oxfordian clay-rock was mainly due to the anisotropy of the thermal conductivity of the solid phase.

The Totalitarian Model Revisited

1998 ◽  
Vol 31 (3) ◽  
pp. 271-285 ◽  
Author(s):  
Sujian Guo
Keyword(s):  
Regime Change ◽  
Reference Points ◽  
Political Regime ◽  
Formal Modeling ◽  
Theoretical Problem ◽  
Refined Model ◽  
New Model ◽  
Macro Model ◽  
Communist Countries

A theoretical problem in defining “regime identity” of a political regime in conceptual and comparative terms is that there are no generally accepted theoretical criteria that could be used to demarcate the beginning and ending of a political regime and to assess the nature of a regime change in communist and post-communist countries. This article attempts to address the significance of this problem, revisit the utility of the totalitarian model, and develop a refined macro-model that can serve as the means to solve the problem and as reference points to define regime identity, assess and measure the regime change in theoretical and comparative terms. The refined model can serve both to observe, explain, and predict the regime change in general and to enrich our understanding of specific cases in particular. Based on the insights yielded by the new model, other researchers could modify this model by using techniques of formal modeling or by dropping some features while retaining others of the model.

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