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.

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 An integrated tagging model to estimate mortality rates of Albemarle Sound – Roanoke River striped bass

2017 ◽  
Vol 74 (7) ◽  
pp. 1061-1076 ◽  
Author(s):  
Julianne E. Harris ◽  
Joseph E. Hightower
Keyword(s):  
Striped Bass ◽  
Stock Assessment ◽  
Mortality Rates ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Albemarle Sound ◽  
High Reward ◽  
Accuracy And Precision ◽  
Summer Mortality ◽  
Roanoke River

We developed an integrated tagging model to estimate mortality rates and run sizes of Albemarle Sound – Roanoke River striped bass (Morone saxatilis), including (i) a multistate component for telemetered fish with a high reward external tag; (ii) tag return components for fish with a low reward external or PIT tag; and (iii) catch-at-age data. Total annual instantaneous mortality was 1.08 for resident (458–899 mm total length, TL) and 0.45 for anadromous (≥900 mm TL) individuals. Annual instantaneous natural mortality was higher for resident (0.70) than for anadromous (0.21) fish due to high summer mortality in Albemarle Sound. Natural mortality for residents was substantially higher than currently assumed for stock assessment. Monthly fishing mortality from multiple sectors (including catch-and-release) corresponded to seasonal periods of legal harvest. Run size estimates were 499 000–715 000. Results and simulation suggest increasing sample size for the multistate component increases accuracy and precision of annual estimates and low reward tags are valuable for estimating monthly fishing mortality rates among sectors. Our results suggest that integrated tagging models can produce seasonal and annual mortality estimates needed for stock assessment and management.

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.

Relationship of Fishing Mortality to Natural Mortality and Growth at the Level of Maximum Sustainable Yield

1982 ◽  
Vol 39 (7) ◽  
pp. 1054-1058 ◽  
Author(s):  
R. B. Deriso
Keyword(s):  
Logistic Model ◽  
Mortality Rates ◽  
Maximum Sustainable Yield ◽  
Sustainable Yield ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Difference Model ◽  
Relationship Of ◽  
Yield Per Recruit ◽  
Delay Difference

Fishing mortality constraints are derived for fishes harvested at the maximum sustainable yield (MSY) determined by a delay-difference population model. Those constraints depend upon rates of natural mortality and growth as well as a simple constraint placed on abundance of the exploited population. The results are generalized for a wider class of population models where it is shown that MSY fishing mortality is constrained often to be less than the fishing mortality which maximizes yield per recruit. Fishing mortality rates are lower in the delay difference model in comparison to MSY fishing rates in the logistic model, when a quadratic spawner–recruit curve is applied.Key words: delay-difference model, logistic model, fishing mortality, maximum sustainable yield, yield per recruit

Estimation of Effective Effort from Catch-at-Age Data

1993 ◽  
Vol 50 (11) ◽  
pp. 2421-2428 ◽  
Author(s):  
J. E. Paloheimo ◽  
Yong Chen
Keyword(s):  
Age Groups ◽  
Simulated Data ◽  
Mortality Rates ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
A Value ◽  
Basic Equations ◽  
Highly Correlated ◽  
High Degree ◽  
Two Age Groups

We present a method for estimating effective efforts or fishing mortality rates based on a linearized version of the catch equation. Catch-at-age for at least two age groups over a series of years is required. The method presupposes a value for natural mortality rate (M). The method is validated using simulated data with an appropriate error structure. The algorithm always converges to a set of effective efforts that are compatible with the known catches. Nevertheless, the solution to the basic equations is not unique although the different solutions are typically highly correlated. If the M assumed by the algorithm is the same as the actual M the iterated effective efforts are typically very close to the true effective efforts or fishing mortality rates. If the assumed M is too high or too low the pattern of effective efforts is still recovered to a high degree of accuracy, typically 0.90 < r < 1.00, even though M may be off by as much as 60%. When data for three or more age groups are available the method is extended to at least squares procedure that takes into account the increasing uncertainty of catches with age.

scholarly journals Estimating natural and fishing mortality and tag reporting rate of southern rock lobster (Jasus edwardsii) from a multiyear tagging model

2001 ◽  
Vol 58 (12) ◽  
pp. 2490-2501 ◽  
Author(s):  
S D Frusher ◽  
J M Hoenig
Keyword(s):  
Mortality Rates ◽  
Fishing Effort ◽  
Reporting Rate ◽  
Standard Errors ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Rock Lobster ◽  
Relative Standard ◽  
Jasus Edwardsii ◽  
Mortality Estimates

Fishing and natural mortality rates and tag reporting rate for rock lobsters (Jasus edwardsii) in northwest Tasmania, Australia, were estimated using multiyear tagging models. These estimates are necessary for assessment of the resource. Several models were examined that had either two or three tagging events each year, and either combined sexes or kept sexes separate. The model that best described the dynamics of the fishery utilized three tagging events within a year. The year was divided into discrete periods and, within each year, fishing effort and duration of period were used to apportion fishing and natural mortalities, respectively, to the periods. The separation of fishing mortalities by sex was not found to improve the models. Although high (1.0–1.2·year–1), the instantaneous fishing mortality estimates were comparable to estimates obtained from other methods and the relative standard errors were low. Reporting rate estimates were also precise and indicated a lack of participation by the fishing industry. Estimates of natural mortality were low (0.00–0.02·year–1) but imprecise.

scholarly journals A simple length-structured model based on life history ratios and incorporating size-dependent selectivity: application to spawning potential ratios for data-poor stocks

2016 ◽  
Vol 73 (12) ◽  
pp. 1787-1799 ◽  
Author(s):  
Adrian R. Hordyk ◽  
Kotaro Ono ◽  
Jeremy D. Prince ◽  
Carl J. Walters
Keyword(s):  
Life History ◽  
Growth Parameter ◽  
Mortality Rates ◽  
Life History Strategies ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Computationally Efficient ◽  
Size Dependent ◽  
Spawning Potential Ratio ◽  
Recursive Equations

Selectivity in fish is often size-dependent, which results in differential fishing mortality rates across fish of the same age, an effect known as “Lee’s Phenomenon”. We extend previous work on using length composition to estimate the spawning potential ratio (SPR) for data-limited stocks by developing a computationally efficient length-structured per-recruit model that splits the population into a number of subcohorts, or growth-type-groups, to account for size-dependent fishing mortality rates. Two simple recursive equations, using the life history ratio of the natural mortality rate to the von Bertalanffy growth parameter (M/K), were developed to generate length composition data, reducing the complexity of the previous approach. Using simulated and empirical data, we demonstrate that ignoring Lee’s Phenomenon results in overestimates of fishing mortality and negatively biased estimates of SPR. We also explored the behaviour of the model under various scenarios, including alternative life history strategies and the presence of size-dependent natural mortality. The model developed in this paper may be a useful tool to estimate the SPR for data-limited stock where it is not possible to apply more conventional methods.

Pre- and post-season tagging models: estimation of reporting rate and fishing and natural mortality rates

1998 ◽  
Vol 55 (1) ◽  
pp. 199-205 ◽  
Author(s):  
William S Hearn ◽  
Kenneth H Pollock ◽  
Elizabeth N Brooks
Keyword(s):  
Mortality Rates ◽  
Reporting Rate ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Special Cases ◽  
Simulation Results ◽  
Return Data

Brownie et al. (1985, U.S. Fish Wildl. Serv. Resour. Publ. 156, p. 159) presented models for tag returns from multiple taggings of animals when tagging is done twice per year. Here, we present a reformulation of their model suitable for pre- and post-season fishery tag return studies. Under this model, it is possible to estimate fishing mortality, natural mortality, and reporting rate from the tag return data alone. (Under once-a-year tagging models, the reporting rate usually has to be estimated externally.) We consider two special cases: (i) a pulse fishery and (ii) a continuous fishery over part of the year. An artificial example and simulation results are presented to illustrate the methodology and the properties of the various estimators. Unlike for catch-based methods, the correlation between estimates of fishing mortality and natural mortality is moderate. While pre- and post-season tagging studies are likely to be difficult to run in practice, other methods of estimating reporting rate are also difficult to implement, and therefore, this approach may prove quite useful, especially in fisheries that have heavy exploitation rates.

An Investigation of the Population Dynamics of Atlantic Menhaden (Brevoortia tyrannus)

1985 ◽  
Vol 42 (S1) ◽  
pp. s147-s157 ◽  
Author(s):  
R. L Reish ◽  
R. B. Deriso ◽  
D. Ruppert ◽  
R. J. Carroll
Keyword(s):  
Population Dynamics ◽  
Environmental Variables ◽  
Atlantic Menhaden ◽  
Ekman Transport ◽  
Natural Mortality ◽  
Fishing Mortality ◽  
Brevoortia Tyrannus ◽  
Ricker Model ◽  
Dependent Growth ◽  
Special Case

The following biological components concerning the population dynamics of Atlantic menhaden (Brevoortia tyrannus) were investigated: growth, natural mortality, migration, fishing mortality, and recruitment. We found that a hypothesis of density-dependent growth is strongly supported by the data and that the dependence of growth on abundance appears to occur prior to recruitment. Age-specific natural mortality estimates seem biologically reasonable, except the estimate for age 1 menhaden, which appears to be too low. Most of the estimated migration probabilities also seem to be biologically reasonable, especially during the summer season for age 2 fish. Estimated age-specific fishing mortality rates demonstrate the increased fishing pressure on age 3 and younger fish since the early 1960's. When the environmental variables (temperature and Ekman transport) are excluded from the spawner–recruit analysis, then the Beverton–Holt model fits as well as other models examined, and it is the only model that is significant at the 0.05 probability level. Of the environmental variables examined, only westward Ekman transport in the South Atlantic region shows a relationship with recruitment. The unnormalized gamma function, which includes the Ricker model as a special case, is more responsive to the inclusion of westward Ekman transport than the Beverton–Holt model.

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.

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