October23Lecture

# October23Lecture - EEMB 120 Introduction to Ecology...

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EEMB 120 – Introduction to Ecology October 23, 2008

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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:
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
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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## This note was uploaded on 02/26/2009 for the course EEMB 122 taught by Professor Levine during the Spring '09 term at UCSB.

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October23Lecture - EEMB 120 Introduction to Ecology...

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