PCWA-L 480.pdf - PCWA Middle Fork American River Project ...

Scaling Individual Bioenergetics to Populations
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.... 300
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z 100
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Figure 1. Population mortality by mortality type in one year.
A SON D
Within Fish Bioenergetics 3.0, mortality is modeled for each cohort using a simple exponential
decay model
m't
Nt = No e'
where No and N, represent the number of fish at time zero and time t, respectively, and m is the
total daily instantaneous rate of mortality that occurred within the population. When multiple
sources of mortality act together on a cohort, each type of mortality,is applied to the cohort each
day, and the. number surviving tlie combined mortality Is projected forward to the following day.
Remember that While the daily instantaneous rates of mortality are l;ldditive (mna'"a' + m"hlng + ...),
the actual probabilities of mortality are not. For instance, If the natural rate of mortality (n) is 30%
per year, and the rate of fishing mortality (m) is 20% per year, the combined total mortality Is 45%
per year (n+m-nm). This expression simply st;>tes that a ffsh can die from natural mortality or
fishing mortality, but the same fish can not die from both types of mortality.
Within Fish Bioenergetics 3.0, the order of dl;lily events for a fish is: eat, grow, spawn and die.
Spawning and m0l1ality only occur if required by tha user input. The importance of this chronology
will be triVial for most bioenergetic runs, however, the user shouid realize that dally consumption
values will be calculated before the fish dies. The reduction in consumption associated with the
Inclusion of mOl1ality in the Lake Perca yellow perch cohort is shown in
Figure 2.·
It Is important to realize that Fish Bioenergetics 3.0 is not a population·modei because we do not
explicitiy consider recruitment. However, by accounting for mortality rates, the net predatory
Impact effect of a group of fish Can be estimated. .