Interspecific competition

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The model for interspecific competition is

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 (1)

and the equilibria for this model are

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 (2)

Well, this becomes a little confusing.

In the following we consider models with K1=2, K2=1, and r=0.5, u=0.5. The two remaining parameters, s and v, will be chosen so that in

Case 1: One species will dominate (independent of the initial population phase)

Case 2: Either one of the two species may dominate depending on the initial population phase

Case 3: The two species will coexist

Case 1. One species will dominate.

When s<K1/K2=2 and v>K2/K1=1/2, species 1 will dominate.

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 (3)

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 (4)

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When s>K1/K2=2 and v<K2/K1=1/2, species 2 will dominate.

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 (5)

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 (6)

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Case 2. Both species may dominate.

When s>K1/K2=2 and v>K2/K1=1/2, both species may dominate, the outcome of the competition depends on the initial population phase.

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 (7)

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 (8)

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Case 3. The two species will coexist.

When s<K1/K2=2 and v<K2/K1=1/2, the two species will coexist.

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 (9)

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 (10)

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