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ps8q - MIT Department of Biology 7.014 Introductory Biology...

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MIT Department of Biology 7.014 Introductory Biology, Spring 2004 7.014 Spring 2004 PS 8 1 of 6 7.014 Problem Set 8 Please print out this problem set and record your answers on the printed copy. Problem sets will not be accepted late. Question 1 You are studying how the growth of a population of your favorite species of frog, Xenopus tropicalis . You construct a massive pond for the frogs and provide them with an unlimited food supply. a) You begin your experiment with 50 frogs and after 10 months you find 61 frogs in your pond. Assume a continuous growth model for the population. i) What is the intrinsic rate of increase in units of months -1 for the frogs (to the nearest hundredth)? ii) How long will it take for your initial population of frogs to double (in months)? b) You allow the population of frogs to increase to double the initial population, but then you realize that you don’t really have the space or resources to allow the population to continue to grow unchecked. You consider two possible ways to naturally cut the rate of growth of the population. i) You decide to simply cut the supply of food to the frogs (harsh though this may sound you reason that it will cause a decrease in new breeding and eventually you will reach a steady state population). After another 10 months you find that you have population of 106 frogs. Assuming the value for r max is the same as it was in part a, and that population growth is following the logistic equation, estimate what the carrying capacity (in number of frogs) is for your environment. 1
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7.014 Spring 2004 PS 8 2 of 6 Question 1, continued b) ii) Your second option is to introduce frog-eating snakes into your pond environment.
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