Geometric vs. Logistic Growth Model: An empirical approach
Modeling of Agricultural Systems [AGS721]
LAB 2
Geometric vs. Logistic Growth Model: An empirical
approach
Suppose that you are going to study the population dynamic of yeast in the laboratory. Your objective is to predict the population growth of yeast cells within 24 hours.
1. Given the assumption that there is unlimited amount of food and space where yeasts are grown. Using the population growth model (integral form) as shown below:
Construct population dynamic both tabular and graphical forms. Given that the initial yeast population is 10 cells and the instantaneous rate of increase (r) of yeast is 0.05.
2. Assume the same assumption as above (1),
calculate population growth of yeast using population growth model (differential
form) where rate of increase is
and population growth model is
Construct population dynamic both tabular and graphical forms. First set dt equals to 1 then increase and decrease dt (e.g. dt=1.5, dt=2.0, dt=0.5, dt=0.1 etc.).
Compare the results from (1) and (2). What happend when dt value is getting smaller or larger.
3. Assume that there is limited food source and space where yeasts are grown. Hence, the population of yeast could be expressed by logistic growth model given below;
where
Nt=population at time t
t=time
k = carrying capacity (maximum value of N)
a = a constant of integration defining the position of the curve relative to the origin
e=natural logarithms (2.71828)
r=rate of population growth per individual
unit
Given: K=1,000; a=4.19; r=0.05; N=10
Construct population dynamic both tabular and
graphical forms using the logistic function.
Describe the behavior of the dynamic of
yeast population.
Note: Use spread sheet software like MS-Excel or Lotus-123 to work with this exercise.
References:
Cullen, M.R. Mathematics for the Biosciences. PWS Publishers, Boston, Massachusetts.
Krebs, C.J. 1985. Ecology: The Experimental Analysis of Distribution and Abundance. Harper and Row, Publishers, New York.
Stiling, P.D. 1966. Ecology: Theories and Applications
(2nd Edition). Prentice Hall International Inc.