## Mortality Information

There are two main data sources in which mortality information can be derived, age or size composition information and information from tagging programs. To demonstrate the utility of age composition information, consider following a single cohort of fish over time. The survival of this single cohort from one year to the next can be described using a simple equation:

where Na is the number of individuals at age a, and Z is the instantaneous total mortality rate. Solving eqn [2] for Z leads to the simple expression:

Thus, the total mortality rate can be obtained from information on the proportions at age in the population. It is not necessary to know the absolute abundance of each cohort, only the relative proportions of each cohort in the population. The method can also be extended to size composition data; however, information on fish growth must also be known. There are two main problems in using this simple approach to obtain independent information on total mortality rates: (1) it is often difficult to collect a representative sample that reflects the true population age structure due to sampling difficulties (e.g., sampling gears are almost always size-selective), and (2) the method assumes that annual recruitment to the population is nearly constant.

Estimates of mortality rates from tagging programs are based on the same general principle as that for age or size composition data; however, in this case total mortality rates are determined by following the fate ofa tagged population over time. There are two assumptions in tagging programs that must be met in order to use this information to estimate mortality: (1) assume no tagging-related mortality or the tagging mortality rate is known, and (2) assume no tag loss, or the loss rate is known. There is also a third assumption that must be met if the sampling program relies on commercial or recreational fisheries for the recovery of tags - that all recaptured tags are reported. Tagging programs have proved to be invaluable for the estimation of mortality as well as many other demographic parameters; however, violations of this last assumption have been problematic in fisheries stock assessment.

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