Lecture_9_wo_answers

Lecture_9_wo_answers - EEMB120IntroductiontoEcology...

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EEMB 120 – Introduction to Ecology October 26, 2010
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Interactions Between Species Why study biotic interactions? Types of interactions Interspecific competition Limiting resources Mechanisms of competition Lotka-Volterra Theory Equations for the model Graphical solutions Assumptions Using the model framework in a real ecological system Last Lecture:  
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Modeling Interspecific Competition Can we use what we know about  intra specific competition to  develop a model for  inter specific competition ? Yes, start with two different logistic equations: One for each of the two interacting species dN 1   =  r 1 N 1  ( K 1  – N 1  ) dt                     K 1 dN 2   =  r 2 N 2  ( K 2  – N 2  ) dt                     K 2
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Modeling Interspecific Competition Lotka – Volterra Competition Model dN 1   =  r 1 N 1  ( K 1  – N 1  –  α 12  N 2  ) dt                            K 1 dN 2   =  r 2 N 2  ( K 2  – N 2  –  α 21  N 1  ) dt                              K 2 Competition  coefficients Competition coefficients convert individuals of Species 2 into an  equivalent number of Species 1 and vice versa Now, link these two equations together
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Modeling Interspecific Competition Solving for no growth: 0   =  r 1 N 1  ( K 1  – N 1  –  α 12  N 2  )                             K 1 0  =  r 2 N 2  ( K 2  – N 2  –  α 21  N 1  )                             K 2 So,    dN 1 /dt = 0 when N 1  = K 1  –  α 12 N 2       (or  0)         dN 2 /dt = 0 when N 2  = K 2  –  α 21 N 1      (or  0) dN 1 /dt = dN 2 /dt =
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Modeling Interspecific Competition dN 2 /dt = 0 – no growth N 2 N 1 K 2 K 2   α 21 dN 1 /dt = 0 – no growth N 2 N 1 K 1 K 1   α 12 Species 1 Species 2 For each species, there are regions of positive,  negative and zero growth
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Modeling Interspecific Competition dN 2 /dt = 0 K 2  = 50 K 2 / α 21  = 25 dN 1 /dt = 0 N 2 N 1 K 1  =100 K 1 / α 12  = 200 Now let’s place both zero growth isoclines  on the same graph K 1  = 100 K 2  = 50 α 12  = 0.5
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This note was uploaded on 11/11/2010 for the course EEMB 120 taught by Professor Nisbet during the Fall '08 term at UCSB.

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Lecture_9_wo_answers - EEMB120IntroductiontoEcology...

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