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Competition of Two Populations in Exponential Growth


Two populations that grow from the same unlimited source increase exponentially. But, even though there are no negative interactions, one of them will become increasingly dominant.


  • The early stages of growth of microorganisms in food
  • The growth of new plants when a field is abandoned
  • Diagram


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


    DQ1 = K1*E*Q - K3*Q
    DQ2 = K2*E*Q2 - K4*Q2


    The graph shows the growth of the populations Q (green) and Q2 (blue).
    Source code:

    "What if" Experiments:

  • If the two populations have the same initial number of individuals, but the efficiency of growth is greater in one than the other, the first outdistances the other very rapidly. Can you generate this result by making the production coefficient larger?
  • What´s the effect of quadratic feedback?