Page 164 - ASBIRES-2017_Preceedings

Gunasekara & Dharmawardane

2 LITERATURE If H(t) is a periodic function, the fish
population will not be able to extinct in
Laham et.al. (2012) studied about the
harvesting strategies for tilapia fish farming. fishing time and it varies according to the
Since the research describes about the season by season. The equilibrium point of
harvesting tilapia fish in a farm that implies the logistic growth model, without fishing is
the harvesting is done under restrictions. In given by 780500 when r=0.8. This means
this research two logistic growth models i.e. that if the initial population starts with
constant harvesting and periodic harvesting 780500, it remains as it is in the equilibrium
have been used in order to estimate the point. If it starts with zero, it will remain at
highest continuing yield from fish zero. As indicated in the research the period
harvesting strategies implemented. This of maturity for the tilapia fish is 6 months
research indicated that the optimum quantity and 80% of them will survive to maturity.
for harvesting that can ensure the continuous This implicitly implies 20% will die during
tilapia fish supply and the best harvesting the maturity period.
strategy is periodic harvesting and it helps
fish farmers to increase the supply to meet Even though fishing is harvested as an
the demand for tilapia fish. industry it is obvious that it cannot be
maintained 100% survival rate but 80%,
The number of tilapia fish that fish ponds which is not an acceptable level. The
2
can sustain is 5 for every 1m surface area. logistic growth model with harvesting shows
2
The selected pond has an area of 156100 m . that the value of harvesting is found to be
Sustainable or carrying capacity is 780500 equal to 156100. It is obvious that when the
fish.
value of harvesting is greater than 156100,
The logistic growth model is given by the fish population will go to extinction
regardless the initial population size.

= [1 − /] (1) In the logistic growth model with

periodic fishing when ponds have initial
Where p indicates the size of the population as full carrying capacity of
population, r is called the rate of survived 780500,156100 numbers of fish is assumed
fish at maturity stage and k is carrying for harvesting during first 6 months while
capacity. In this research two models have 515584 do not involve harvesting. This
been constructed namely the logistic growth
model with constant harvesting pattern repeats several years. The tilapia fish
will increase until it approaches the carrying

= (1 − ) − () (2) capacity. This research concluded that
logistic periodic seasonal harvesting strategy

Where H is the harvesting function can be used to improve productivity. The
and the value of harvesting is a constant. fish farming does not have enough time to
Moreover, p(t) depends on its initial value recover the fish population under constant
p(0),r and k. harvesting. Idels & Wang (2008) mainly
concerned about the inverse effect of fish
The logistic growth model with periodic abundance on the fishing effort. New fishing
harvesting is given by effort was developed using the density effect

= (1 − ) − () (3) of fish population.

Six fishery strategies were analyzed i.e.
156100 ≤ 6, constant harvesting, proportional harvesting,
Where H (t) ={
0 > 6, restricted proportional harvesting,
proportional threshold harvesting, seasonal
H (t+12) =H (t). Here H(t) is a periodic harvesting and rotational harvesting.
function of time with the period of one year.

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