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.