index Drain Logistic Compete Coop Exclus Interact Oscillat Preypred Netprod Openaq Pulse Saltmrsh Prairie Fire Lagoon Climax Species Specarea

## Competition for Limited Sources

#### Description:

If two species are using a common source of food which is in short supply, the growth of one may deprive the other of its source of food. Under some conditions the species which grows faster causes the other to die out.

#### Examples:

• Two species of grain beetle in a jar, which is supplied some grain each day
• Competition between two timber companies developing on a limited area of growing trees
• #### Variables:

I = Energy source
Q, Q2 = two populations
K1, K2 = growth rates
K3, K4 = mortality rates

#### Equations:

R = I/(1 + K1*Q + K2*Q2)
D1 = K5*R*Q - K3*Q
D2 = K6*R*Q2 - K4*Q2

#### Simulation:

left: The graph shows the growth of Q and Q2 over a time period.

right: Graph of one population as a function of another.
Source code: Exclus.java

#### "What if" Experiments:

Think about two populations of competitive species.

• Determine what happens if the two populations start with the same initial numbers, but one has a slightly higher growth rate.
• By varying the growth rate and decay rate coefficients, can you find a set of values which allows for coexistence?