Fish Population Dynamic and Stock Assessment

8.1.2. Principles

This model is based on two major equations

a. Describes the production term

b. Energy balance of each group

The model is computed from the equation

P_i = Y_i + B_i . M_2i + E_i + BA_i + P_i . (1-E E_i)

P_i = Total production rate (i)

Y_i = Total fishery catch rate of (i)

M_2i = Total predation rate for group

B_i = Biomass of the group.

E_i = Net migration rate which includes emigration – immigration

BA_i is the biomass accumulation rate for (i) while MO_i = P_i (1-EE_i) is the other mortality rate for (i).

The above equation can be expressed as

B_i . (P/B)_i . EE_i $$\sum_ {J=1} ^ {n}$$B_j $$\cdot{Q \over B}$$;  DC_ji - YA - E_i -BA_i = 0

Where, P/B_i is the production / biomass ratio

Q/B_i is the Consumption / biomass ratio

DC_ji, the fraction of prey (i) in the average diet of predator (j).

The production rate, P_i could be calculated as the product of B_i. the biomass of (i), while the P_i/B_i is production / biomass ratios for group (i). The P_i/B_i rate mostly corresponds to total mortality Z.

The other mortality includes mortality due to decrease of old age and could be computed from

Mo_i = P_i . (1 – EE_i)

Where, EE_i is called ecotrophical efficiency of (i).

The ecotrophic efficiency is described as the production that is utilized in the system.

M₂ is the production term that links production and prey as

M_2i =$$\sum_{J=1}^n$$ . DC_ji

The summation includes all (n) predator groups (j) feeding on group (i),

Q_j is the total consumption rate for group (j)

DC_ji is the fraction of predator (j) diet contributed by prey (i).

Q_j is calculated as the product of B_j, the biomass of group (i) and Q_j / B_j the consumption / biomass ratio for group (j).

Ecopath model sets up a system with many linear equations for parameterization. This model usually solves the set of one of the following parameters for catch group in a system. The parameters are biomass, production / biomass ratio, consumption / biomass ratio or ecotrophic efficiency.