The structure of optimal time- and age-dependent harvesting in the Lotka-McKendrik population model

Math Biosci. 2007 Jul;208(1):48-62. doi: 10.1016/j.mbs.2006.09.008. Epub 2006 Sep 23.

Abstract

The paper analyzes optimal harvesting of age-structured populations described by the Lotka-McKendrik model. It is shown that the optimal time- and age-dependent harvesting control involves only one age at natural conditions. This result leads to a new optimization problem with the time-dependent harvesting age as an unknown control. The integral Lotka model is employed to explicitly describe the time-varying age of harvesting. It is proven that in the case of the exponential discounting and infinite horizon the optimal strategy is a stationary solution with a constant harvesting age. A numeric example on optimal forest management illustrates the theoretical findings. Discussion and interpretation of the results are provided.

MeSH terms

  • Algorithms
  • Animals
  • Ecosystem*
  • Fertility
  • Forestry / economics
  • Forestry / methods
  • Models, Biological*
  • Population Density
  • Population Dynamics
  • Time Factors