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Lecture

lecture note 21 for BGYB50

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Department
Biological Sciences
Course Code
BIOC50H3
Professor
Herbert Kronzucker

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LECTURE 21:
- The Lotka-Volterra competition equations yield four possible outcomes (see your
textbook for the four graphs that result):
(a) K1 > K2/!21 and K2 < K1/!12 (species 2 is eliminated),
(b) K1 < K2/!21 and K2 > K1/!12 (species 1 is eliminated),
(c) K1 > K2/!21 and K2 > K1/!12 (either species could win; outcome depends on
starting population mixture),
(d) K1 < K2/!21 and K2 < K1/!12 (both species coexist)
- The isoclines for the two species plotted indicate precise demarcation lines
(“coastlines) between areas of positive growth (the areas below the isoclines) and
negative growth (the areas above the isoclines) for the competing populations; points
directly on the isoclines denote zero growth
- Random points can be drawn into these graphs (each point simply denotes a certain
mixture of individuals of species 1 and 2), and we can then evaluate what the trajectory
of any such starting point (any two-species population mixture) will be typically these
mixtures change, i.e. the points willmove with time (see the vectors in the textbook),
toward to end point of the competition (which is either K1, K2, or the stable equilibrium
point at the intersection of the two isoclines in one scenario)
- STUDY THE LOTKA-VOLTERRA EQUATIONS AND GRAPHS DO NOT JUST
MEMORIZE THEM, BUT PRACTICE THEM ON PIECES OF PAPER!!!
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Description
LECTURE 21: - The Lotka-Volterra competition equations yield four possible outcomes (see your textbook for the four graphs that result): (a) K1 > K2/!21 and K2 < K1/!12 (species 2 is eliminated), (b) K1 < K2/!21 and K2 > K1/!12 (species 1 is eliminated), (c) K1 > K2/!21 and K2 > K1/!12 (either species could win; outcome depends on starting population mixture), (d) K1 < K2/!21 and K2 < K1/!12 (both species coexist) - The isoclines for the two species plotted indicate precise demarcation lines (“coastlines”) between areas of positive growth (the areas below the isoclines) and negative growth (the areas above the isoclines) for the competing populations; points directly on the isoclines denote zero growth - Random points can be drawn into these graphs (each point simply denotes a certain mixture of individuals of species 1 and 2), and we can then evaluate what the trajectory of any such starting point (any two-species population mixture) will be – typically these mixtures change, i.e. the points will “move” with time (see the vectors in the textbook), toward to end point of the competition (which is either K1, K2, or the stable equilibrium point at the intersection of the two isoclines in one scenario) - STUDY THE LOTKA-VOLTERRA EQUATIONS AND GRAPHS – DO NOT JUST MEMORIZE THEM, BUT PRACTICE THEM ON PIECES OF PAPER!!! www.notesolution.comLECTURE 21: - The Lotka-Volterra competition equations yield four possible outcomes (see your textbook for the four graphs that result): (a) K1> K 2 21 and K2< K 1 12 (species 2 is eliminated), (b) K1< K 2 21 and K2> K 1 12 (species 1 is eliminated), (c) K1> K 2 21 and K2> K 1 12 (either species could win; outcome depends on starting population mixture), (d) K1< K 2 21 and K2< K 1 12 (both species coexist) - The isoclines for the two species plotted indicate precise demarcation lines (coastlines) between areas of positive growth (the areas below the isoclines) and negative growth (the areas above the isoclines) for the competing populations; points directly on the isocline
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