Model 1

Model 1

Explicit Approximation (unstable)

Implicit Approximation (stable)

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Notes:

All mortality is represented by a single parameter Z (attrition) that includes natural mortality, fishing mortality and emigration.

The approximation method is important. The explicit method can produce negative values for the number of tags if the attrition rate is large. Normally one manipulates the size of the time step or the value of Z to ensure that N is always positive. On the other hand, the implicit method is always positive. Although this consideration seems trivial, it is ignored in some stock assessment textbooks. It is also important in situations where it is difficult to control the value of Z, such as in a numerical function minimization algorithm.