# Competition for Territory: The Levins Model for Two Species

Competition for Territory: The Levins Model for Two Species

This population dynamics model (being the extension of the well-known Levins metapopulation model) describes the competition for territory of two species having different colonization strategies. The model equations are:

p'(t)=cp(t)1-p(t)-p(t)-ep(t)+op(t)p(t)

1

1

1

1

2

1

1

1

2

p'(t)=cp(t)1-p(t)-p(t)-ep(t)-op(t)p(t)

2

2

2

1

2

2

2

1

2

where and are the portion of the territory at time occupied by species 1 and 2, respectively. The occupation is exclusive. Hence, the assumptions and hold.

p(t)

1

p(t)

2

t

0≤p(t),0≤p(t)

1

2

p(t)+p(t)≤1

1

2

The meaning of the parameters is as follows:

c

1

c≥0

2

e

1

e≥0

2

o