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The above phase plane diagram depicts the interaction of two species: a pathogen (species 1, orange) and a probiotic (species 2, blue). Currently the carrying capacities are K1 = 700, K2 = 350; and the competition coefficients are a12 0.9, a21 = 0.4. Use this information

The above phase plane diagram depicts the interaction of two species: a pathogen (species 1, orange) and a probiotic (species 2, blue). Currently the carrying capacities are K1 = 700, K2 = 350; and the competition coefficients are a12 0.9, a21 = 0.4. Use this information

Biochemistry
Biochemistry
9th Edition
ISBN:9781319114671
Author:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Publisher:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Chapter1: Biochemistry: An Evolving Science
Section: Chapter Questions
Problem 1P
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1000 800- 600- 400 200- 200 400 600 800 1000 Pathogen (#) The above phase plane diagram depicts the interaction of two species: a pathogen (species 1, orange) and a probiotic (species 2, blue). Currently the carrying capacities are K1 = 700, K, = 350; and the competition coefficients are a12 = 0.9, a21 = 0.4. Use this information to answer parts (A)--(D). (A) If the probiotic population were to grow to its carrying capacity of 350, how many pathogenic individuals could the environment support? (B) The phase plane diagram predicts a steady state point---what is it? (I.e. at equilibrium, how many pathogenic and probiotic individuals do we expect?) (C) If the probiotic had a carrying capacity of 500 rather than 350, how many probiotic and pathogenic individuals should we expect at steady state? (D) An ideal probiotic would competitively exclude the pathogen. List two ways we might modify the current probiotic to achieve this. For full credit, be sure to explain which population parameters you might modify, and how any modifications would result in competitive exclusion of the pathogen. Probiotic (#)
Transcribed Image Text:1000 800- 600- 400 200- 200 400 600 800 1000 Pathogen (#) The above phase plane diagram depicts the interaction of two species: a pathogen (species 1, orange) and a probiotic (species 2, blue). Currently the carrying capacities are K1 = 700, K, = 350; and the competition coefficients are a12 = 0.9, a21 = 0.4. Use this information to answer parts (A)--(D). (A) If the probiotic population were to grow to its carrying capacity of 350, how many pathogenic individuals could the environment support? (B) The phase plane diagram predicts a steady state point---what is it? (I.e. at equilibrium, how many pathogenic and probiotic individuals do we expect?) (C) If the probiotic had a carrying capacity of 500 rather than 350, how many probiotic and pathogenic individuals should we expect at steady state? (D) An ideal probiotic would competitively exclude the pathogen. List two ways we might modify the current probiotic to achieve this. For full credit, be sure to explain which population parameters you might modify, and how any modifications would result in competitive exclusion of the pathogen. Probiotic (#)
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