Dynamics of the discrete Seno population model: Combined effects of harvest timing and intensity on population stability

The paper contains new results on the impact of harvesting times and intensities on the stability properties of Seno population models. It is proved that sufficiently high harvest intensities are stabilizing for any harvesting time in the sense that they create a positive equilibrium that attracts all positive solutions. Moreover, in the special case that the nonlinearity in the Seno model is a Ricker function, we derive a global stability result independent of timing and valid for low to medium harvesting efforts. The proof is based on a characterization of those harvesting intensities which guarantee a negative Schwarzian derivative for all harvesting times. Finally, we rigorously show that timing can be stabilizing as well as destabilizing by itself. In particular, a recent conjecture formulated by Cid et al. (2014) [1] is shown to be false.