View source for Total Allowable Harvest

[[Category: Examples]]
=== Example model ===

'''Description:''' The problem applies to any population of fish or animal whose dynamics are poorly known but can be summarized in a simple model:

:<code>N_t + 1 = N_t*Lambda - landed catch*(1 + loss rate)</code>

where «N_t» is the population size (number of individuals) at time ''t'', «N_t+1» is the population size at time ''t + 1'', «Lambda» is the intrinsic rate of increase and the «loss rate» is the percentage of fish or animals killed but not retrieved relative to the «landed catch», or catch secured.

The question here is to determine how many fish or animals can be caught (landed) annually so that the probability of the population declining X%  in Y years (decline threshold) is less than Z% (risk tolerance).  

Two models are available for download.  One uses the Optimizer ([[NlpDefine]]) to find the maximum landed catch at the risk tolerance level for the given decline threshold. The other (for those using a version of Analytica without Optimizer) uses [[StepInterp]] in an iterative way to get that maximum landed catch.    

'''Keywords:''' Population analysis, dynamic models, optimization analysis

'''Author:''' Models contributed by Pierre Richard

'''Download:'''
* [[media:Total Allowable Removal model with Optimizer.ana | Total Allowable w Optimizer.ana]]
* [[media:Total Allowable Removal model w StepInterp.ana|Total Allowable w StepInterp.ana]]