NAME: ROHAYU BINTI

MOHAMED

Mathematics offers a method for speculation aboutbiological principles that govern animal populations. Mostsensible rules for birth, growth, and death can be statedmathematically.

Ideally, these assumptions can be used to derive theoremsthat characterize model behavior. Mathematical modelhave been used widely to estimate the population dynamicsof animals for so many years as well as the humanpopulation dynamics.

In recent years, the use of mathematical models has beenextended to agriculture sector especially in fish harvestingto ensure continuous and optimum supply (Faris et al.2012). The method has been developed around the worldaccording to the mathematical modelling.

Mathematical model not widely used in fisheriesmanagement because the fisherman only care aboutthe fish but not about the method.

Recently, consumers have become more consciousdoes the fish will be distributed enough for them whenthe number of people continuously increasing.

• To be able to make prediction of the fish harvesting byusing mathematical growth model.

• To compare the method between two growth modelwhich are logistic growth model and Malthusiangrowth model on fish harvesting.

• To identify the preferable method between the twogrowth model.

Management of fisheries resources will be moreefficient based on the study of mathematics.

Helps people to choose the best model that have beenidentify to be applied in the fisheries management.

The project focusing on fisheries department inTerengganu and data was selected quarterly from 2008to 2012 from Department Of Fisheries Malaysia officialwebsite.

Harvesting has been an area under discussion inpopulation as well as in community dynamics (Murray1993).

Thomas Robert Mathus (1766-1834) is the man behindthis exponential growth. He realized that species canincrease in number. The assumptions of exponentialgrowth rate are continuous reproduction. For examplethere is no seasonality involve in their growth. Whenresources are unlimited the environment is consider tobe constant in space and time. Several application ofexponential model are fishery, plant, insect quarantineand microbiology. (Joseph, 2001).

According to (Maidina and Krishna, n.d) Logistic growthmodel curve is one of the best that describe a growth rate.In many field such as fishery research, crop science andbiology, growth curves is very important.

Logistic model was introduced by a Belgian mathematicianbiologist P.F.Verhulst (1804-1849). There are varieties ofgrowth curves have been developed. Most predictive modelis shown based on logistic growth equation. They doreview and compare several such models and analysesproperties of interest for these. They also prove that thenew growth form incorporates additional growth modelswhich are markedly different from the logistic growth andits variants. Lastly, they give a briefing about new curvecould be used for curve-fitting. (Tsoularis and Wallace,2002).

Malthusian Growth Model

kPdt

dP ------------------------------ (1)

By separation of variables of (1), we will get

tkePP 0 , where ceP 0

• A model of population growth in which the growth rate is proportional to the size of the population

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

P1 in the equation (1)

)( KPPK

k

dt

dP --------------- (2)

By separation of variables of (2), we will get

tkePKP

KPtP

)()(

00

0

Mohamed Faris Laham, Ishtrinayagy s. Krishnarajah & Jamilah MohdShariff.(2012). Fish Harvesting Management Strategies Using Logistic GrowthModel.Malaysia 41(2)(2012): 171–177

Maidina.T, Krishna.C, Implementation of methods to estimate the GrowthCurve of Yeast, Department of Mathematical Sciences Chalmers University ofTechnology, Goteborg University, Goteborg, Sweden.

Murray, J.D. (1993). Mathematical Biology 1: An Introduction.USA: SpringerVerlag.

Steve, M., K. (1995). Malthusian Growth model. Saint Olaf Collage,Northfield, Minnesota.

Tsoularis, A., Wallace, J., (2002). Analysis of Logistic Models, MathematicalBiosciences, Institute of Information and Mathematic Science, MasseyUniversity.