the system undergoes a Hopf bifurcation. It comes as counterintuitive (hence the term 'paradox') because increasing the carrying capacity of the ecological system beyond a certain value leads to dynamic instability and extinction of the predator species. Arguments against paradox A credible, simple alternative to the Lotka–Volterra predator–prey model and its common prey dependent generalizations is the ratio dependent or Arditi–Ginzburg model. The two are the extremes of the spectrum of predator interference models. According to the authors of the alternative view, the data show that true interactions in nature are so far from the Lotka–Volterra extreme on the interference spectrum that the model can simply be discounted as wrong. They are much closer to the ratio dependent extreme so if a simple model is needed one can use the Arditi–Ginzburg model as the first approximation. The presence of the paradox is strongly dependent on the assumption of the prey dependence of the functional response; because of this the ratio dependent Arditi–Ginzburg model does not have the paradoxical behavior. The authors' claim that the paradox is absent in nature (simple laboratory systems may be the exception) is in fact a strong argument for their alternative view of the basic equations. See also Braess's paradox: Adding extra capacity to a network may reduce overall performance. Paradox of the pesticides: Applying pesticide may increase the pest population. References Other reading Mathematical and theoretical biology Predation