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Two Populations with Competitive Interactions


Two populations may compete by means of negative interactions. The competing populations are without food limitations and each population has a self crowding limitation. With sufficient negative effects, one population may drive out the other.


  • Two species of grain beetle in a jar, which is supplied some grain each day
  • Two species of weeds, where each secretes chemical substances that inhibit the root growth of the other.
  • Diagram


    E = Energy source
    Q, Q2 = two populations
    K1, K2 = growth rates
    K3, K4 = mortality rates
    K5, K6 = interaction coefficients


    DQ1 = K1*E*Q1 - K3*Q1*Q1 - K5*Q1*Q2
    DQ2 = K2*E*Q2 - K4*Q1*Q1 - K6*Q1*Q2


    The graph shows the changes of Q1 (blue) and Q2 (green) over a time period.
    Source code:

    "What if" Experiments:

  • Set the two interaction coefficients to equal zero. Is there competitive interaction?
  • With interactions still set at zero, decrease the available food supply. How does it change growth and steady state level?
  • Now vary the interaction coefficients and describe the competitive interactions.