# BIOC50H3 Lecture : lecture note 21 for BGYB50

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!!!

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