Fish Mortality&

Exploitation RatioBy

Asaar S. H. ElsherbenyAssistant Researcher

Fish Population Dynamics Lab.

Fisheries Division

Fish Mortality

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Fish Mortality

Estimation

Types & Definition

Importance

Definition

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Definition:

Fish Mortality refers to:The death of fish from a stock due to various causes

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Importance:Mortality estimates are important to managers. Determining mortality rates are critical for determining abundance of fish

populations. Using the model Z=M+F with M being Natural mortality and F being Fishing mortality (combined mortality from landings plus discard mortality) you can estimate the trend of a population.

The mortality rates give you the total deaths of a population when you compare these to the total births or recruits to the population, you can determine if a population is increasing or decreasing. Knowing these rates can help managers to set harvest limits to (MSY) maximum sustainable yield or (OSY) optimum sustainable yield to give the maximum benefit to the stakeholders of the resource

The determination of mortality is essential, as it considered one of the basic input parameters for population dynamics models used in fishery analyses and management.Estimates of fish mortality rates are often included in mathematical yield models to predict yield levels obtained under various exploitation scenarios. These are used as a resource management indices or in bioeconomic studies of fisheries

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Types & Definition:

A CB

C) Natural Mortality Coefficient (M)

B) Fishing Mortality Coefficient (F)

A) Total Mortality Coefficient (Z)

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Definitions:

Total mortality It refers to the total loss by death of individuals from a population during a certain time interval.In fisheries population dynamics, total mortality is denoted by (Z).(M) and (F) are additive instantaneous rates that sum up to (Z), the instantaneous total mortality coefficient; that is, Z=M+F. These rates are usually calculated on an annual basis

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Definitions:

Natural mortality The removal of fish from the stock due

to natural causes, not associated with fishing. Such causes can include disease, competition, cannibalism, old age, predation, pollution or any other natural factor that causes the death of fish.

In fisheries population dynamics, natural mortality is denoted by (M).

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Definitions:

Fishing mortality The removal of fish from the stock due

to fishing activities using any fishing gear. It is denoted by (F) in fisheries

models.

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Estimation of Total Mortality Coefficient (Z):

Several methods were developed to calculate the total mortality coefficient, some of them depend on age composition and the others depend on length frequency data.

The most common methods used are; Jones and Van Zalinge, 1981 (Analysis of the cumulative catch curve) and Pauly, 1983 (Analysis of the length converted catch curve) and both are depending on length frequency data.

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Estimation of Total Mortality Coefficient (Z):

Pauly method (1983):This method is based on the analysis of catch curve using length

frequency data. The catch curve is constructed through the conversion of length to age by using the growth parameters of the von Bertalanffy growth model. The total mortality coefficient was estimated through the following relationship:

ln (N/Dt) = a + b*t

Where:

N = frequency of each length class.

Dt = time needed to grow from t1 to t2 of a given length class.

t = relative age corresponding to the mid point of the length class.

a and b = constants.

This is a linear relationship, where: Y = ln (N/Dt) & X = (t1 + t2)/2

The constant ‘a’ and ‘b’ can be calculated by linear regression between ln (N/Dt) and X = (t1 + t2)/2. The slope (b) of this regression is equal to (-Z), then

Z = - slope

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Estimation of Total Mortality Coefficient (Z):

Jones and Van Zalinge method (1981):This method depends of the existence of linear relationship

between the natural logarithm of the cumulative frequency and the natural logarithm of (L∞ - L). This relationship is expressed as follows:

ln (CN) = a + (Z/K)*ln (L∞ - L)

Where:

CN = cumulative frequency.

Z = instantaneous rate of total mortality.

K = growth coefficient.

a and b = constants.

This is a linear relationship, where: Y = ln (CN) & X = ln (L∞ - L)

The constant ‘a’ and ‘b’ can be calculated by linear regression between ln (CN) and ln (L∞ - L). The slope of this regression is equal to (Z/k), then

Z = k* slope

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Estimation of Total Mortality Coefficient (Z):

Cumulative catch curve

Z = 2.12 / y Length converted catch curve

Z = 2.07 / y

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tyEstimation of Natural Mortality Coefficient (M):

Natural mortality is the most difficult parameter to estimate in fishery stock assessments.

There are several models that may be useful to approximate M. Some of these methods are:-

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tyEstimation of Natural Mortality Coefficient (M):

- Taylor’s method (1960):The Natural Mortality coefficient was estimated according the following equation:

M = 3/tmax

Where: tmax = maximum age attained.

 

- Ursin’s method (1967):M = W -1/3

Where: W = mean total body weight.

 

- Rikhter and Efanov’s Empirical Model (1976):M = ((1.52 / tmass) 0.72) - 0.16

Where: tmass = mean age at massive maturity.

 

- Pauly’s Empirical Equation (1980):log M = - 0.0066 - 0.279 log L∞+ 0.6543 Log K + 0.4634 log T

Where:

L∞ = asymptotic length.

K = growth coefficient.

T = average annual temperature of the stock’s habitat, in °C.

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Estimation of Fishing Mortality Coefficient (F):

The fishing mortality coefficient was estimated by subtracting the value of natural mortality coefficient from the value of total

mortality coefficient as follows:

F = Z - M

Exploitation Ratio

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Exploitaion Ratio (E):

Exploitation Ratio (E):

The proportion of a population that is caught during a certain period, usually a year.

The exploitation ratio allows one to roughly assess whether a stock is overexploited or not.

This is based on the assumption that a stock is optimally exploited at E = 0.5 when F equals M (Gulland, 1971).

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Exploitaion Ratio (E):

Exploitation Ratio (E):

The exploitation rate was estimated by the formula suggested by Gulland (1971)

through the following relation:

E = F / Z

Where:

E = exploitation ratio, i.e. the fraction of deaths caused by fishing.

F = fishing mortality coefficient.

Z = total mortality coefficient.

Species

Total

Mortality

Coefficients

Natural

Mortality

Coefficients

Fishing

Mortality

Coefficients

Exploitation

Ratio

S. savignyi

S. pharaonis

S. dollfusi

2.096

2.791

3.277

0.573

0.748

0.872

1.523

2.043

2.405

0.727

0.732

0.734

Mortality and Exploitation Rates

Fish Population Dynamics Lab.