October23Lecture

October23Lecture - EEMB 120 Introduction to Ecology October...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
EEMB 120 – Introduction to Ecology October 23, 2008
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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:
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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 =
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

October23Lecture - EEMB 120 Introduction to Ecology October...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online