The total number P of prey taken by a predator depends on the availability of prey. C. S. Holling proposed a function of the form P = cn/(1 + dn) to model the number of prey taken in certain situations. Here n is the density of prey available, and c and d are constants that depend on the organisms involved as well as on other environmental features. Holling took data gathered earlier by T. Burnett on the number of sawfly cocoons found by a small wasp parasite at given host density. In one such experiment conducted, Holling found the relationship P = 21.96n 1 + 2.41n, where P is the number of cocoons parasitized and n is the density of cocoons available (measured as number per square inch). (a) Draw a graph of P versus n. Include values of n up to 2 cocoons per square inch.
The total number P of prey taken by a predator depends on the availability of prey. C. S. Holling proposed a function of the form P = cn/(1 + dn) to model the number of prey taken in certain situations. Here n is the density of prey available, and c and d are constants that depend on the organisms involved as well as on other environmental features. Holling took data gathered earlier by T. Burnett on the number of sawfly cocoons found by a small wasp parasite at given host density. In one such experiment conducted, Holling found the relationship
| 21.96n |
| 1 + 2.41n |
where P is the number of cocoons parasitized and n is the density of cocoons available (measured as number per square inch).
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