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Linear algebra presentation

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Zulqarnain haider
Zulqarnain haider

The document discusses using a Leslie matrix model to model the sustainable harvesting of animal populations. Sustainable harvesting means periodically removing animals from the population in a way that yields are the same each harvest and the age distribution of the remaining population is the same. The model applies a Leslie matrix to describe population growth over a period, then a harvesting matrix removes a fraction of each age class so that the unharvested population has the same age distribution as the original population.

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BARIZ KHUDA BAKHSH TAJAMMUL HUSSAIN JUNAID ISHAQ ASAD SHAIKH ZULQARNAIN HAIDER
HARVESTING OF ANIMAL POPULATION Leslie matrix model of population growth is used to model the sustainable harvesting of animal population. Harvesting means, the removal of animal from population.
SUSTAINABLE HARVESTING OF ANIMAL POPULATION A harvesting policy in which animal population is periodically harvested such that the yeild of each harvest is same and the age distribution of the population remaining after each harvest is same.
EXPLANATION: We begin with a population having a particular age distribution.It undergoes a growth period that is described by the Leslie matrix.At the end of growth period, a certain fraction of each age class is havested in such a way that the unharvested population has the same age distribution as the original population.
Linear algebra presentation
To describe this model mathematically, Let Be the age ditribution vector of the population at the beginning of growth period.
If L is the Leslie matrix describing the growth of the population, then the vector Lx is the age distribution vector of the population at the end of the growth period, immediately before the periodic harvest.
which is called harvesting matrix. So, is the number of animal harvested.
From the definition of sustainable harvesting policy we have, Or mathematically, Lx-HLx=x Thus we get the original population which is x.

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Linear algebra presentation

  • 1. BARIZ KHUDA BAKHSH TAJAMMUL HUSSAIN JUNAID ISHAQ ASAD SHAIKH ZULQARNAIN HAIDER
  • 2. HARVESTING OF ANIMAL POPULATION Leslie matrix model of population growth is used to model the sustainable harvesting of animal population. Harvesting means, the removal of animal from population.
  • 3. SUSTAINABLE HARVESTING OF ANIMAL POPULATION A harvesting policy in which animal population is periodically harvested such that the yeild of each harvest is same and the age distribution of the population remaining after each harvest is same.
  • 4. EXPLANATION: We begin with a population having a particular age distribution.It undergoes a growth period that is described by the Leslie matrix.At the end of growth period, a certain fraction of each age class is havested in such a way that the unharvested population has the same age distribution as the original population.
  • 6. To describe this model mathematically, Let Be the age ditribution vector of the population at the beginning of growth period.
  • 7. If L is the Leslie matrix describing the growth of the population, then the vector Lx is the age distribution vector of the population at the end of the growth period, immediately before the periodic harvest.
  • 8. which is called harvesting matrix. So, is the number of animal harvested.
  • 9. From the definition of sustainable harvesting policy we have, Or mathematically, Lx-HLx=x Thus we get the original population which is x.

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