The Lotka-Volterra Equations for Competition between Two Species

first competition coefficient

0.6

second competition coefficient

0.6

intrinsic rate of increase of species 1

0.6

intrinsic rate of increase of species 2

0.2

carrying capacity of species 1

0.6

carrying capacity of species 2

0.5

The population dynamic of two competing species is governed by the following system of ODEs:

d

N

1

dt

=

r

1

N

1

(

K

1

-

N

1

-α

N

2

)

K

1

d

N

2

dt

=

r

2

N

2

(

K

2

-

N

2

-β

N

1

)

K

2

where

N

i

is the population density of species

i

(equal to 1 or 2),

r

i

the intrinsic rate of species

i

,

K

i

the carrying capacity of species

i

, and

α

and

β

the competition coefficients.

The competion may occur because (1) the two species share the same limited resources, or (2) individuals from different species have direct damaging behavior.

This Demonstration computes the population densities versus time (species 1 is shown in blue) and the snapshots show situations where one observes coexistence of both species or disappearance of one of the two species.