Variables
H_{n} : Density of host at generation n
H_{n+1} : Density of host at generation n+1
P_{n} : Density of parasitoid at generation n
P_{n+1} : Density of parasitoid at generation n+1
Parameters
k : Reproductive rate of host
a : Searching efficiency constant of parasitoid
c : Average number of viable eggs deposited by parasitoid
on a single host
You can read more about this model at Phaser Web site .
In 1941, Debach and Smith in their laboratory experiment started with 36 housefly, Musca domestica, and 18 of its pupal parasite Nasonia vitripennis and followed the populations for seven generations. They arranged the fecundity rate of the host to be 2 (k = 2, c = 1), and determined the searching efficiency constant to be a = 0.045. Please read their original paper at the link below:
DE BACH, P. and SMITH, H.S. [1941]. "Are Population Oscillations Inherent in the Host-Parasite Relation?" Ecology, 22, 363-369. JSTOR URL
In particular examine their data on Table I on page 367 and Figure 1 on page 368 of their article. Their Figure 1 looks like the following Phaser view: Download the following phaser Project file debach_smith.ppf by just clicking on it ( or by right-click and save it to our computer. Now load this file into Phaser).
What is the experimental count of the host and parasitoid in the third and sixth generations in the paper
of DeBach and Smith?
What does the Phaser simulation of the Nicholson-Bailey model predict for these counts?
What are the relative errors in the
model predictions?
In 1989, fibres from the Shroud of Turin were found to contain about 92% of the level of C-14 in living matter. Determine the age of the shroud using PHASER. Suppose that there was 0.15% error in the determination of the percentage of C-14 in the sample of the shroud. What is the range of possible dates for the sample?
Some people do not agree with the results of the C-14 dating of the Shroud. Do some research on the Web (see the links above, for example) and identify an objection or raise one of your own. Argue for or against the objection.