A Modified Nicholson Bodel w/ Density Dependence III
by Mike Martin

This page generates plots and data for a modification of the Nicholson-Bailey Model:

The Nicholson-Bailey model helps to descibe the dynamics between the population levels of two different insect species; one of the species, the host, can be paralyzed and used to host the eggs of the other insect species, the parasitoid.   This particular modification has the reproductive rate, r, from the original model replaced by a density-dependent expression (one involving rational expressions).   Nt is the density of the host species in generation t and Pt is the density of the parasitoid species in generation t.   The fraction of hosts not parasitized is e-aP where a is the searching efficiency (or the probability that a given parasitoid will encounter a host over the course of their lifetime) and P represents Pt.   r is the number of eggs laid by a host that survive through the larvaae, pupae, and adult stages.   Similarly, g represents the number of eggs laid by a parasitoid on a single host that survive through larvae, pupae, and adult stages.   b and c are curve-fitting parameters.   T is the last generation considered with the simulation.   N1 is the initial host density and P1 is the initial parasitoid density.   The sequence Nt is displayed in the graph in BLUE and the sequence Pt is given in BROWN.

Enter in the values of the non-negative parameters (descibed above), then press the "Evaluate" button.

a =  

g =  

r =  

b =  

c =  

T =  

N1 =  

P1 =  




References:

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Monod, J., J. Wyman, and J.P. Changeux (1965). On the nature of allosteric transitions: a plausible model. J. Mol. Biol., 12: 88-118.

S.J. Edelstein (1971). Extensions of the allosteric model for hemoglobin. Nature, 230:224-227.

Changeux JP, Edelstein SJ (1998). Allosteric receptors after 30 years. Neuron, 21: 959-980.

T.A. Duke, N. Le Novere, D. Bray (2001). Conformational spread in a ring of proteins: a stochastic approach to allostery. J. Mol Biol, 308:541-553.

Changeux J.P., S.J. Edelstein (2005). Allosteric mechanisms of signal transduction. Science, 2005 Jun 3;308(5727):1424-8.

Klipp, E, R Herwig, A Kowald, C Wierling, H Lehrach Systems Biology in Practice. Wiley, Berlin, Germany, 2005.