Stock Reduction Analysis, Another Solution to the Catch Equations

1982 ◽  
Vol 39 (11) ◽  
pp. 1467-1472 ◽  
Author(s):  
Daniel K. Kimura ◽  
Jack V. Tagart
Keyword(s):  
Mortality Rate ◽  
Stock Assessment ◽  
Clupea Harengus ◽  
New Method ◽  
Total Biomass ◽  
Natural Mortality ◽  
Catch Per Unit Effort ◽  
Available N ◽  
Stock Size ◽  
Virtual Population

In fishery stock assessments, catch equations provide the critical link between stock size, natural mortality rate, fishing rate, and catch size. Catch equations are most powerful when age data are available, allowing cohorts to be followed through time using Virtual Population and Cohort Analysis. In this paper we propose a simple new method of linking catch equations when age data are not available. Assuming catches are given in biomass, catch equations are written for each year with a constant recruitment (R), based on a single parameter, added to the total biomass at the beginning of each year. In addition to the catch equations, a final equation is added describing the change in biomass caused by the years of fishing. If n years of catch data are available, n + 1 equations can be written. By conditioning on instantaneous natural mortality rate (M), initial stock size (B1) and the decline in stock size (P) (note P = Bn+1/B1), the n + 1 simultaneous nonlinear equations can be solved iteratively for instantaneous fishing mortality rates (F1, …, Fn) and recruitment (R). When properly plotted, the solution set to this system of equations was found to be a helpful tool to aid in the evaluation of stock condition. In particular, the plots provide a method for incorporating ancillary information from diverse sources such as hydroacoustic surveys, analysis of catch per unit effort data, and Virtual Population Analysis. This new method of stock assessment, which we call Stock Reduction Analysis, is applied to Pacific ocean perch (Sebastes alutus), Pacific herring (Clupea harengus pallasi), and Pacific hake (Merluccius productus) stocks being actively managed by the State of Washington.Key words: Stock Reduction Analysis, stock assessment, catch equations, computer modeling

scholarly journals Total stock size and cannibalism regulate recruitment in cod (Gadus morhua) on the Faroe Plateau

2009 ◽  
Vol 67 (1) ◽  
pp. 111-124 ◽  
Author(s):  
Petur Steingrund ◽  
Rógvi Mouritsen ◽  
Jákup Reinert ◽  
Eilif Gaard ◽  
Hjálmar Hátún
Keyword(s):  
Larval Stage ◽  
Gadus Morhua ◽  
Stock Assessment ◽  
Total Biomass ◽  
Catch Per Unit Effort ◽  
Stock Size ◽  
Class Strength ◽  
Total Stock ◽  
Recruitment Event ◽  
Pelagic Larval Stage

Abstract Steingrund, P., Mouritsen, R., Reinert, J., Gaard, E., and Hátún, H. 2010. Total stock size and cannibalism regulate recruitment in cod (Gadus morhua) on the Faroe Plateau. – ICES Journal of Marine Science, 67: 111–124. Year-class strength of fish is often considered to be determined at the pelagic larval stage, but we show that year-class strength of cod on the Faroe Plateau seems to be determined later, at the 1- or 2-group stage. Adult cod (C), measured in terms of the catch per unit effort (cpue) of small longliners, move into nearshore nursery areas of juvenile cod when in poor condition and probably displace 1-year-old cod to deeper water, where they are cannibalized. In addition, the recruitment of 2-year-old cod, at least up to a certain level, is positively related to the total biomass (B) of older cod on the Faroe Plateau, which are present at about the same time as the recruitment event. This feature, which seems to be a new observation in terms of the recruitment dynamics of cod, is possibly related to enhanced foraging or a reduced predation risk. The recruitment of 2-year-old cod during the years 1984–2006 is described by aB/C + d (r2 = 0.87), where a and d are fitted constants. The implications for stock assessment and management are discussed.

Virtual Population Analysis (VPA) Equations for Nonhomogeneous Populations, and a Family of Approximations Including Improvements on Pope's Cohort Analysis

1986 ◽  
Vol 43 (12) ◽  
pp. 2406-2409 ◽  
Author(s):  
Alec D. MacCall
Keyword(s):  
Mortality Rate ◽  
Population Analysis ◽  
Seasonal Pattern ◽  
Cohort Analysis ◽  
Natural Mortality ◽  
Close Approximation ◽  
Virtual Population Analysis ◽  
Virtual Population ◽  
Special Case

A set of "backward" virtual population analysis (VPA) equations relates catch (Ct) from continuous fishing between times t and t + 1 to population n size (Nt, Nt+1) when a portion of the stock is unavailable to fishing. The usual VPA equations become a special case where the entire stock is available (i.e. the stock is homogeneous). A close approximation to the VPA equations is Nt = Nt+1 exp(M) + CtM/(1 − exp(−M)), which has properties similar to Pope's "cohort analysis" and is somewhat more accurate in the case of a continuous fishery, especially if the natural mortality rate (M) is large. Much closer simple approximations are possible if the seasonal pattern of catches is known.

Integrating catch-at-age and multiyear tagging data: a combined Brownie and Petersen estimation approach in a fishery context

2006 ◽  
Vol 63 (3) ◽  
pp. 534-548 ◽  
Author(s):  
Tom Polacheck ◽  
J Paige Eveson ◽  
Geoff M Laslett ◽  
Kenneth H Pollock ◽  
William S Hearn
Keyword(s):  
Mortality Rate ◽  
Population Size ◽  
Stock Assessment ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Catch Data ◽  
Coefficients Of Variation ◽  
Southern Bluefin Tuna ◽  
Catch Rates ◽  
Comprehensive Framework

A comprehensive framework for modelling data from multiyear tagging experiments in a fishery context is presented that incorporates catch data into the traditional Brownie tag–recapture model. Incorporation of catch data not only allows for improved estimation of natural and fishing mortality rates, but also for direct estimation of population size at the time of tagging. These are the primary quantities required to be estimated in stock assessments — having an approach for directly estimating them that does not require catch rates provides a potentially powerful alternative for augmenting traditional stock assessment methods. Simulations are used to demonstrate the value of directly incorporating catch data in the model. Results from the range of scenarios considered suggest that in addition to providing a precise estimate of population size (coefficients of variation ranging from ~15% to 30%), including catch data can decrease biases in the mortality rate estimates (natural mortality especially) and improve precision of fishing mortality rate estimates (by as much as 60% at age 1). The model is applied to southern bluefin tuna (Thunnus maccoyii) tag–recapture and catch data collected in the 1990s to provide estimates of natural mortality, fishing mortality, and abundance for five cohorts of fish.

scholarly journals A method for calculating a meta-analytical prior for the natural mortality rate using multiple life history correlates

2014 ◽  
Vol 72 (1) ◽  
pp. 62-69 ◽  
Author(s):  
Owen S. Hamel
Keyword(s):  
Life History ◽  
Mortality Rate ◽  
Stock Assessment ◽  
Meta Analysis ◽  
Assessment Model ◽  
Natural Mortality ◽  
Uncertainty Interval ◽  
Free Data ◽  
Stock Assessments ◽  
Measure Of Uncertainty

Abstract The natural mortality rate M is an important parameter for understanding population dynamics, and is extraordinarily difficult to estimate for many fish species. The uncertainty associated with M translates into increased uncertainty in fishery stock assessments. Estimation of M within a stock assessment model is complicated by its confounding with other life history and fishery parameters which are also uncertain, some of which are typically estimated within the model. Ageing error and variation in growth, which may not be fully modelled, can also affect estimation of M, as can various assumptions, including the form of the stock–recruitment function (e.g. Beverton–Holt, Ricker) and the level of compensation (or steepness), which may be fixed (or limited by a prior) in the model. To avoid these difficulties, stock assessors often assume point estimates for M derived from meta-analytical relationships between M and more easily measured life history characteristics, such as growth rate or longevity. However, these relationships depend on estimates of M for a great number of species, and those estimates are also subject to errors and biases (as are, to a lesser extent, the other life history parameters). Therefore, at the very least, some measure of uncertainty in M should be calculated and used for evaluating uncertainty in stock assessments and management strategy evaluations. Given error-free data on M and the covariate(s) for a meta-analysis, prediction intervals would provide the appropriate measure of uncertainty in M. In contrast, if the relationship between the covariate(s) and M is exact and the only error is in the estimates of M used for the meta-analysis, confidence intervals would appropriate. Using multiple published meta-analyses of M’s relationship with various life history correlates, and beginning with the uncertainty interval calculations, I develop a method for creating combined priors for M for use in stock assessment.

scholarly journals Growth, maturation, and longevity of maturation cohorts of Norwegian spring-spawning herring

2004 ◽  
Vol 61 (2) ◽  
pp. 165-175 ◽  
Author(s):  
Raymond J.H. Beverton ◽  
Arvid Hylen ◽  
Ole-Johan Østvedt ◽  
John Alvsvaag ◽  
Terence C. Iles
Keyword(s):  
Mortality Rate ◽  
Small Proportion ◽  
Stock Assessment ◽  
Adult Life ◽  
Total Mortality ◽  
Mortality Rates ◽  
Natural Mortality ◽  
Marine Research ◽  
First Time ◽  
Age At Maturation

Abstract In 1907, the Bergen Institute of Marine Research started regular sampling of scales and lengths from landings of mature Norwegian spring-spawning herring. The actual age of each fish when caught was recorded, and from the early 1920s also the age at which it spawned for the first time. The present analyses concern biological samples secured during the fishing seasons 1940–1964. Herring in this stock do not all reach maturity at the same age. A small proportion of any one year class matures at 3 years. The majority matures from the age of 4–7 years, and a small proportion of some year classes at 8 and even 9 years of age. Subsequent age composition and growth of each maturation cohort were followed throughout mature life after spawning for the first time. The maximum age was found to increase with age at maturation, rising to an asymptote of about 22 years. The von Bertalanffy parameter L∞ shows an increasing trend with age at maturation, while K decreases. There is no strict length threshold at maturation and the curve joining the length at which each maturation cohort reaches maturity is less steep than the growth curve itself over the range of maturation ages. The data suggest that fish in this stock spawn, on average, eight times during a period of their life history in which the mortality rate is independent of age. After these eight spawnings, at an age referred to in this paper as the hinge age, the mortality rate increases sharply. Thus, the adult life is divided into two phases, called here pre-senescent and senescent. The total mortality rates in the pre-senescent phase are relatively stable for all maturation cohorts 3–9, but there is some evidence of a trend towards higher mortality rates during the senescent phase for the youngest maturing fish. This trend is caused mainly by a reduced natural mortality in the fish that mature when older. These findings have interesting demographic implications. Additional mortality due to fishing will change the relative contribution of young and old maturation cohorts in the senescent phase, thus making it appear that natural mortality is dependent on the intensity of fishing. Consequently, for stock assessment, analysis on a cohort basis seems advisable.

scholarly journals Length-weight relationship and population dynamics study of the giant catfish (Arius thalassinus) in the Bay of Bengal coast of Bangladesh

2020 ◽  
Vol 6 (3) ◽  
pp. 439-444
Author(s):  
Rokeya Sultana ◽  
Mohammed Shahidul Alam ◽  
KM Shahriar Nazrul ◽  
Al Mamun ◽  
Md Abdullah Al Mamun
Keyword(s):  
Mortality Rate ◽  
Bay Of Bengal ◽  
Stock Assessment ◽  
Correlation Coefficients ◽  
Assessment Tools ◽  
Model Parameters ◽  
Growth Equation ◽  
Natural Mortality ◽  
Weight Relationship ◽  
Bay Of Bengal Coast

The present study investigated the length-weight relationship, population parameters and the instantaneous natural mortality rate of Arius thalassinus from two major landing center of Bangladesh using the FAO-ICLARM Stock Assessment Tools (FiSAT II). A total of 1789 specimens were collected between January 2016 and December 2017. The estimated values of the exponent “b” was ranged from 3.019 (pre-monsoon) to 3.293 (monsoon), indicating an isometric growth pattern of the species with high correlation coefficients (0.904 to 0.927). The equation of length–weight relationship was: W=0.005L3.181. Model parameters of the von Bertalanffy growth equation were: L∞ = 97.60 cm and K = 0.33-1 year. The estimated growth performance index (Ø) was 3.497. The instantaneous natural mortality rate (M) was 0.62-1 year and a high exploitation rate (E) 0.62 (>0.50) showed that this fish is over-exploited in the Bay of Bengal coast of Bangladesh. Res. Agric., Livest. Fish.6(3): 439-444, December 2019

Variable Natural Mortality Rates Inflate Variance of Recruitments Estimated from Virtual Population Analysis (VPA)

1992 ◽  
Vol 49 (10) ◽  
pp. 2020-2027 ◽  
Author(s):  
Michael F. Lapointe ◽  
Randall M. Peterman ◽  
Brian J. Rothschild
Keyword(s):  
Mortality Rate ◽  
Environmental Factor ◽  
Statistical Power ◽  
Population Analysis ◽  
Sensitivity Analyses ◽  
Natural Mortality ◽  
Environmental Correlates ◽  
Virtual Population Analysis ◽  
Virtual Population ◽  
Over Time

We used a simulation model to determine whether estimates offish recruitment obtained from virtual population analysis (VPA) (1) have the correct interannual variability and (2) yield high statistical power (>0.8) when correlated with an environmental factor, given that the "true" instantaneous adult natural mortality rate (M) likely varies over time but a constant M is used in VPA (MVPA). Under such circumstances, VPA exaggerates variability in recruitment, which reduces the probability of correctly detecting environmental correlates with recruitment. The magnitude of these effects increases with increases in (1) the absolute value of the true mean M, (2) the variation in M over time, (3) the relative error in MVPA, and (4) the magnitude of MVPA relative to FL (instantaneous terminal fishing mortality rate) and decreases with increases in magnitude of the true variation of recruitment or the true correlation with the environmental factor (all else being equal). This bias is not large under most conditions, but it is likely to be more important in short-lived, high-M species than the similar but counteracting bias caused by aging errors. Sensitivity analyses can demonstrate how various MVPA values affect conclusions about environmental correlates with recruitment.

Catch and Release in Marine Recreational Fisheries

2002 ◽  
Keyword(s):  
Mortality Rate ◽  
Potential Benefit ◽  
Stock Assessment ◽  
The United States ◽  
Natural Mortality ◽  
Release Process ◽  
Catch And Release ◽  
Simulation Techniques ◽  
Longline Fisheries ◽  
Tag Shedding

<em>Abstract.</em>—Most billfish caught by recreational and U.S. longline fishermen are returned to the sea and, because of their overfished status, the United States has urged that all live billfish taken in Atlantic longline fisheries be released. Knowledge of the proportion of these fish that die due to the catch-and-release process, is important both for stock assessment, and to know the potential benefit of releasing fish taken as bycatch in commercial fisheries. Existing information indicates that the magnitude of this mortality is low, but comes from a limited number of studies using small numbers of ultrasonic tags. Recent technology that uses tags that release from the fish after a preprogrammed time, and then transmit data to satellites, offers the potential for developing better estimates of release mortality. This paper uses simulation techniques to examine factors leading to robust estimates of release mortality. Most sources of error in tagging experiments will lead to upward bias in the estimates. These include tag failure, tagging induced mortality, natural mortality, and tag shedding. Given the importance of the estimate to future billfish management, initial studies should focus on proving the technology. Tag failures produce ambiguous results and should be minimized, to the extent possible, or eliminated from the analysis where appropriate. Under perfect conditions (no tag failure, no tag induced mortality, and no tag shedding), individual experiments should apply a minimum of about 100 tags. The length of time from tagging until the tag releases from the fish should only be long enough for the catch-and-release mortality to be fully expressed. Because each fishing mode is likely to have a different release mortality rate, each experiment only estimates the release mortality rate for the species, gear, and fishing method employed in the fishery studied. The number of tags required to estimate the total number of deaths of released fish, of all species, could be in the tens of thousands. However, a well-researched experimental design might reduce the required number of tags significantly.

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