A Generalization of the Murphy Catch Equation

1970 ◽  
Vol 27 (4) ◽  
pp. 821-825 ◽  
Author(s):  
Patrick K. Tomlinson
Keyword(s):  
Mortality Rate ◽  
Population Size ◽  
Generalized Equation ◽  
Time Interval ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Time Intervals

Given catches, by time intervals, from a known cohort of fish with known natural mortality rate and known fishing mortality rate for either the first or last time interval, the population size at the beginning of each interval and the fishing mortality rate during each interval may be estimated using a generalized Murphy catch equation. The generalized equation is constructed from the ratio of catches in successive intervals and depends on the assumption of simple exponential mortality within the intervals. The intervals may vary in length and have zero catches. The estimates may be badly biased depending on the nature of the catch sequence and the independent estimates of natural mortality and fishing mortality used to start the procedure.

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.

Movement, Growth and natural mortality rate of the Red Spot King Prawn, Penaeus longistylus Kubo, from the Great Barrier Reef Lagoon

1990 ◽  
Vol 41 (3) ◽  
pp. 399 ◽  
Author(s):  
MCL Dredge
Keyword(s):  
Growth Rate ◽  
Mortality Rate ◽  
Great Barrier Reef ◽  
Annual Variation ◽  
Growth Parameters ◽  
Natural Mortality ◽  
Barrier Reef ◽  
Fishing Mortality ◽  
Nursery Areas ◽  
Reef Lagoon

Movement, growth and natural mortality rate of the red spot king prawn, Penaeus longistylus, occurring in waters of the Great Barrier Reef off Townsville, Queensland, were investigated in a series of tagging experiments. Adult P. longistylus did not migrate after leaving nursery areas. Their growth rate was slower than that of the conspecific species P. plebejus, and significant inter-annual variation in growth parameters was observed. The natural mortality rate, assessed by sequential tagging experiments that eliminated the possibility of confounding with the rate of fishing mortality, was estimated to be 0.072 (week-1).

Influence of errors in natural mortality estimates in cohort analysis

1997 ◽  
Vol 54 (7) ◽  
pp. 1608-1612 ◽  
Author(s):  
G Mertz ◽  
R A Myers
Keyword(s):  
Mortality Rate ◽  
Similar Pattern ◽  
Cohort Analysis ◽  
Transient Behavior ◽  
Natural Mortality ◽  
Exact Formulation ◽  
Fishing Mortality ◽  
Bias Factor ◽  
Special Case ◽  
Mortality Estimates

The accuracy of the estimation of cohort strength from catch data may be greatly degraded if a poor estimate of the natural mortality rate is entered into the calculation. A straightforward, exact formulation for the error in cohort reconstruction due to a misspecified natural mortality rate is presented. The special case of constant fishing mortality is particularly transparent, allowing the error to be segmented into easily interpreted terms. A change in the fishing mortality may result in a distinct hump in the transient behavior of the bias factor, rather than a simple monotonic adjustment. This implies a similar pattern in estimated cohort strength.

scholarly journals POPULATION DYNAMICS OF MALAYAN LEAF FISH (Pristolepisgrooti Blkr.) IN RANAU LAKE, SOUTH SUMATRA

2018 ◽  
Vol 24 (2) ◽  
pp. 125
Author(s):  
Sevi Sawetri ◽  
Subagdja Subagdja ◽  
Dina Muthmainnah
Keyword(s):  
Mortality Rate ◽  
Growth Parameters ◽  
Total Mortality ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Frequency Data ◽  
Length Frequency ◽  
Lake Ecosystems ◽  
Exploitation Rate ◽  
Length Frequency Data

The Malayan leaf fish or locally named as kepor (Pristolepis grooti) is one of important biotic components in Ranau Lake ecosystems. This study aimed to estimate population dynamic and exploitation rate of kepor in Ranau Lake, South Sumatera. The population parameters are estimated based on length frequency data which were collected in March to October 2013. Growth parameters and fishing mortality rates were calculated using FiSAT software package. The results showed that kepor’s growth was negative allometric, which tended to gain length faster than weight. Kepor population was dominated (42%) by individual length of 10.0 to 11.0 cm. Predicted length infinity (L) was 17.28 cm with high value of growth rates (K) of 1.4 year-1. The natural mortality rate (M) is 2.57 year-1, the fishing mortality rate (F) is 5.36 year-1 and total mortality rate (Z) is 7.93 year-1. The exploitation rate of Malayan leaf fish in Ranau Lake (E = 0.68 year-1) has passed the optimum score.  

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.

The Effect of Reduction of Fishing Effort on Yield

1962 ◽  
Vol 19 (4) ◽  
pp. 521-529 ◽  
Author(s):  
Syoiti Tanaka
Keyword(s):  
Mortality Rate ◽  
Sudden Change ◽  
Japan Sea ◽  
Fish Population ◽  
Fishing Effort ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Yield Curves ◽  
Before And After ◽  
Steady Level

When a fish population has been depleted by heavy exploitation, with the yield from the population maintaining an unfavourable level, it is usual to expect that the situation will be improved by reduction of fishing effort. Following a sudden reduction of fishing mortality, p, from p1 to p2 at time τ = 0, the yield at once decreases and then increases gradually until it reaches another steady level higher than the former level.The present paper deals, using Baranov's model, with the transition stage of the population following a sudden change in p, as well as with the steady state before and after the change. Relations between equilibrium yield and fishing mortality rate (effort-yield curves) are calculated for various values of the parameters, λ0 (= l0/u, where l0 is the length of a recruit and u is the yearly increase in length), q (natural mortality rate), and b (remaining life span of a fish at the time of recruitment) (Fig. 2). It is noteworthy that for species that grow slowly after recruitment, i.e. when λ0 is large, reduction of fishing would have scarcely any effect on the yield (Fig. 4).Yield curves for the period of transition from the present to various lower levels of fishing are calculated for the case in which λ0 = 4, q = 0.15, b = 10 and p1 = 1.35. These represent parameters for the present state of the stock of sohachi flounders Cleisthenes herzensteini (Schmidt), in the southwestern area of the Japan Sea (Fig. 5).Possible density effects on growth rate and natural mortality rate, which are briefly discussed, appear to diminish considerably the effectiveness of any reduction in fishing effort (Fig. 6).

A Method of Estimating Mortality Rates from Change in Composition

1962 ◽  
Vol 19 (1) ◽  
pp. 159-168 ◽  
Author(s):  
Robert H. Lander
Keyword(s):  
Population Size ◽  
Mortality Rates ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Numerical Example ◽  
Final Population ◽  
Special Case

This paper examines the problem of estimating mortality rates from knowledge of catch and of the change in composition caused by selective fishing on one of two classes of a closed population.Estimators of fishing mortality in the presence and in the absence of natural mortality are given. An estimator of natural mortality is shown for the special case where final population size is known.A numerical example illustrates the method. Certain problems are discussed and two types of application are suggested.

scholarly journals Multiyear tagging studies incorporating fishing effort data

1998 ◽  
Vol 55 (6) ◽  
pp. 1466-1476 ◽  
Author(s):  
John M Hoenig ◽  
Nicholas J Barrowman ◽  
William S Hearn ◽  
Kenneth H Pollock
Keyword(s):  
Mortality Rate ◽  
Additional Data ◽  
Survival Rates ◽  
Fishing Effort ◽  
Reporting Rate ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Recovery Rates ◽  
Sampling Survey ◽  
Tag Shedding

The Brownie models for multiyear tagging studies can be used to estimate age- and year-specific annual survival rates and tag recovery rates. The latter are composites of the exploitation rates and rates of tag reporting, tag shedding, and tag-induced mortality. It is possible to estimate the exploitation rates if the other components of the tag recovery rates can be quantified. Instantaneous rates of fishing and natural mortality can be estimated if information is available on the seasonal distribution of fishing effort. The estimated rates are only moderately dependent on the timing of the fishing; consequently, the relative effort data can be crude. Information on the timing of the catch over the course of the year can be used as a substitute for the effort data. Fishing mortality can also be assumed to be proportional to fishing effort over years; consequently, if fishing effort is known then the tag reporting rate, natural mortality rate, and a single catchability coefficient can be estimated (instead of natural mortality and a series of fishing mortalities). Although it is possible in theory to estimate both the tag reporting rate and the natural mortality rate with all of these models, in practice it appears necessary to obtain some additional data relating to tag reporting rate to obtain acceptable results. The additional data can come from a variable reward tagging study, a creel or port sampling survey, or from tagged animals that are secretly added to the fishers' catches.

Minimum Size Regulations and the Implications for Yield and Value in the Canadian Atlantic Halibut (Hippoglossus hippoglossus) Fishery

1989 ◽  
Vol 46 (11) ◽  
pp. 1899-1903 ◽  
Author(s):  
John D. Neilson ◽  
W. R. Bowering
Keyword(s):  
Mortality Rate ◽  
Size Composition ◽  
Minimum Size ◽  
Atlantic Halibut ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Hippoglossus Hippoglossus ◽  
Size Regulation ◽  
Size Limit ◽  
Yield Per Recruit

The effect of a minimum size regulation on yield and value per recruit in the Canadian Atlantic halibut fishery was examined. The model indicated that under most scenarios, the size limit would not result in increased yield per recruit. In general, yield per recruit was more sensitive to fishing mortality than age of first entry to the fishery. While reduced yields were usually associated with the minimum size limit, the value per recruit increased with increasing age at entry to the fishery until age 7. The changes in value per recruit reflected the size composition of landings following the imposition of the size limit and the different values associated with various size categories. Both yield and value per recruit were sensitive to the choice of the natural mortality rate.

Population Dynamics and Management of the Northwest Atlantic Harp Seal (Phoca groenlandica)

1983 ◽  
Vol 40 (7) ◽  
pp. 919-932 ◽  
Author(s):  
Derek A. Roff ◽  
W. Don Bowen
Keyword(s):  
Population Dynamics ◽  
Mortality Rate ◽  
Population Size ◽  
Washington Dc ◽  
Natural Mortality ◽  
Total Catch ◽  
Vital Rates ◽  
Index Method ◽  
Phoca Groenlandica ◽  
Potential Sources

Previous methods of estimating population size and natural mortality rate in harp seals (Phoca groenlandica) are reviewed. Excepting the method of Beddington and Williams (Marine Mammal Comm., Washington, DC., Rep. MMC 79-03, 1980) all previous methods rely heavily upon the survival index method of estimating pup production. We describe the mathematical rationale underlying this method and indicate potential sources of bias. Beddington and Williams' analysis produces a combination of vital rates for 1952 that would not enable a population to persist in the absence of hunting. This suggests that the method may not be able to estimate these parameters accurately. This conclusion is supported by several unpublished analyses. We present an alternative method of analysis that is based on the concept of maximum likelihood. We estimate the rate of natural mortality and trend in 1 + population size from 1967 to 1980, using mark–recapture estimates of pup production in the late 1970s and the observed ratio of the survival of adjacent cohorts in the late 1960s and early 1970s to constrain population trajectories from a simulation model. From this analysis we conclude that the population is increasing and that the present total catch may be substantially smaller than the replacement yield.

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