Chapter 4.4, Problem 1SP

Student Project: Logistic Equation with a Threshold Population An improvement to the logistic model includes a threshold population. The threshold population is defined to be the minimum population that is necessary for the species to survive. We use the variable T to represent the threshold population. A differential equation that incoqoraes both the threshold population T and carrying capacity K is

   $\frac{dP}{dt}=-rP\left(1-\frac{P}{K}\right)\left(1-\frac{P}{T}\right)$  (4.12)

where r represents the growth rate. as before.

1. The threshold population is useful to biologists and can be utilized to determine whether a given species should be placed on the endangered list. A group of Australian researchers say they have determined the threshold population for any species to survive: 5000 adults. (Catherine Gabby. “A Magic Number,” Americon Scientist 98(1): 24. doi:l0.1511/2010.82.24. accessed April 9. 2015. http//www.anwricansoentist.org/iswes/pub/amagic-number). Therefore we use T = 5000 as the threshold population in this project. Suppose that the environmental carrying capacity In Montana for elk Is 25.000. Set up Equation 4.12 using the carrying capacity of 25,000 and threshold population of 5000. Assume an annual net growth rate of 18%.