## Total Mortality Rate

Mortality includes all factors reducing abundance of a closed population. In fish models, mortality is typically modeled as an instantaneous rate Z. Thus, abundance decreases by a constant fraction in each instant of time:

The solution to eqn [15] at time t is

given initial abundance N0 at t = 0. The instantaneous mortality rate Z carries units inverse to those of t; for example, when t is expressed in years, Z has units yr—1 The annual proportion dying is 1 — exp(—Z).

If the population is structured by age, eqns [15] and [16] apply to each portion of the population, so that

where Na,t is abundance at age and time, and Zat is annual mortality rate at age.

The total mortality rate Z (age-specific or otherwise) is often partitioned into components, usually into natural mortality rate M and fishing mortality rate F, assumed noncompensatory. A property of instantaneous rates is that mortality from various sources is additive:

This allows the fishing mortality rate, a primary focus of fishery management, to be considered separately from other sources of mortality.

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