The document discusses using mathematical models to predict fish harvesting populations. It compares two growth models: the Malthusian and logistic growth models. The Malthusian model assumes exponential growth with unlimited resources. The logistic model assumes growth slows as the population approaches the environment's carrying capacity. The document aims to identify the preferable growth model to apply in fisheries management and ensure continuous and optimal fish supply.

1. NAME: ROHAYU BINTI
MOHAMED

2.  Mathematics offers a method for speculation about
biological principles that govern animal populations. Most
sensible rules for birth, growth, and death can be stated
mathematically.
 Ideally, these assumptions can be used to derive theorems
that characterize model behavior. Mathematical model
have been used widely to estimate the population dynamics
of animals for so many years as well as the human
population dynamics.
 In recent years, the use of mathematical models has been
extended to agriculture sector especially in fish harvesting
to ensure continuous and optimum supply (Faris et al.
2012). The method has been developed around the world
according to the mathematical modelling.

3.  Mathematical model not widely used in fisheries
management because the fisherman only care about
the fish but not about the method.
 Recently, consumers have become more conscious
does the fish will be distributed enough for them when
the number of people continuously increasing.

4. • To be able to make prediction of the fish harvesting by
using mathematical growth model.
• To compare the method between two growth model
which are logistic growth model and Malthusian
growth model on fish harvesting.
• To identify the preferable method between the two
growth model.

5.  Management of fisheries resources will be more
efficient based on the study of mathematics.
 Helps people to choose the best model that have been
identify to be applied in the fisheries management.

6.  The project focusing on fisheries department in
Terengganu and data was selected quarterly from 2008
to 2012 from Department Of Fisheries Malaysia official
website.

7.  Harvesting has been an area under discussion in
population as well as in community dynamics (Murray
1993).
 Thomas Robert Mathus (1766-1834) is the man behind
this exponential growth. He realized that species can
increase in number. The assumptions of exponential
growth rate are continuous reproduction. For example
there is no seasonality involve in their growth. When
resources are unlimited the environment is consider to
be constant in space and time. Several application of
exponential model are fishery, plant, insect quarantine
and microbiology. (Joseph, 2001).

8.  According to (Maidina and Krishna, n.d) Logistic growth
model curve is one of the best that describe a growth rate.
In many field such as fishery research, crop science and
biology, growth curves is very important.
 Logistic model was introduced by a Belgian mathematician
biologist P.F.Verhulst (1804-1849). There are varieties of
growth curves have been developed. Most predictive model
is shown based on logistic growth equation. They do
review and compare several such models and analyses
properties of interest for these. They also prove that the
new growth form incorporates additional growth models
which are markedly different from the logistic growth and
its variants. Lastly, they give a briefing about new curve
could be used for curve-fitting. (Tsoularis and Wallace,
2002).

9. Malthusian Growth Model
kP
dt
dP
 ------------------------------ (1)
By separation of variables of (1), we will get
tk
ePP 0 , where c
eP 0
• A model of population growth in which the growth rate is proportional
to the size of the population

10. Logistic Growth Model
A more accurate model postulates that the relative growth rate P0/P decreases when P
approaches the carrying capacity K of the environment. From equation (1), we add a
factor of
K
P
1 in the equation (1)
)( KPP
K
k
dt
dP
 --------------- (2)
By separation of variables of (2), we will get
tk
ePKP
KP
tP 


)(
)(
00
0

11.  Mohamed Faris Laham, Ishtrinayagy s. Krishnarajah & Jamilah Mohd
Shariff.(2012). Fish Harvesting Management Strategies Using Logistic Growth
Model. Malaysia 41(2)(2012): 171–177
 Maidina.T, Krishna.C, Implementation of methods to estimate the Growth
Curve of Yeast, Department of Mathematical Sciences Chalmers University of
Technology, Goteborg University, Goteborg, Sweden.
 Murray, J.D. (1993). Mathematical Biology 1: An Introduction.USA: Springer
Verlag.
 Steve, M., K. (1995). Malthusian Growth model. Saint Olaf Collage,
Northfield, Minnesota.
 Tsoularis, A., Wallace, J., (2002). Analysis of Logistic Models, Mathematical
Biosciences, Institute of Information and Mathematic Science, Massey
University.