MIT 1 020 - Study Guide (4 pages)

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Study Guide



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Study Guide

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Pages:
4
School:
Massachusetts Institute of Technology
Course:
1 020 - Ecology II: Engineering for Sustainability

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MIT OpenCourseWare http ocw mit edu 1 020 Ecology II Engineering for Sustainability Spring 2008 For information about citing these materials or our Terms of Use visit http ocw mit edu terms MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Civil and Environmental Engineering 1 020 Ecology II Engineering for Sustainability Problem Set 2 Species Competition Due 5PM Monday March 3 2008 Problem Description This problem builds on the class lectures about predator prey ecosytems Rather than predation we consider two similar species competing for a common resource We use the Lotka Volterra competition model which embodies the competitive exclusion principle If two competing species coexist in the same niche in a stable environment then one species will eventually crowd out the other Or as a Chinese proverb succintly states One hill cannot shelter two tigers The model is based on the following versions of the logistic growth equation dX 1 X X2 r1 X 1 1 1 dt K 1 X X2 dX 2 r2 X 2 1 1 dt K2 h h 0 if X 2 2hnom h hnom if X 2 2hnom X 1 and X 2 are the population biomasses kg of the two competing species and h is a harveting rate kg day 1 that represents human removal of Species 2 Species 2 could represent a commercially attractive tree or fish species Species 1 could represent a niusance species that is excluded by the harvested species unless the harveting rate is too high Harvesting is not feasible if X 2 2hnom The Lotka Volterra competition model is based on an extension of the carrying capacity concept The sum of the two populations determines the pressure on a common resource that can sustain K1 carrying capacity of Species 1 or K 2 carrying capacity of Species 2 The remaining model inputs are the growth rate coefficients r1 and r2 days 1 and the initial populations 1 Model Specifications Construct a MATLAB model that simulates the two populations over the time period of 500 days You may adjust this period if you feel it would be useful You should adapt one of the MATLAB



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