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$C_{E}PT$ Symmetry of the Simple Ecological Dynamical Equations

Vladan Pankovic·Rade Glavatovic·Milan Predojevic
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Abstract

It is shown that all simple ecological, i.e. population dynamical equations (unlimited exponential population growth (or decrease) dynamics, logistic or Verhulst equation, usual and generalized Lotka-Volterra equations) hold a symmetry, called $C_{E}PT$ symmetry. Namely, all simple ecological dynamical equations are invariant (symmetric) in respect to successive application of the time reversal transformation - $T$, space coordinates reversal or parity transformation - $P$, and predator-prey reversal transformation - $C_{E}$ that changes preys in the predators or pure (healthy) in the impure (fatal) environment, and vice versa. It is deeply conceptually analogous to remarkable $CPT$ symmetry of the fundamental physical dynamical equations. Further, it is shown that by more accurate, "microscopic" analysis, given $C_{E}PT$ symmetry becomes explicitly broken.

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Vladan Pankovic, Rade Glavatovic, Milan Predojevic. 2005-10-10. $C_{E}PT$ Symmetry of the Simple Ecological Dynamical Equations. https://arxiv.org/abs/q-bio/0510020

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