GRADUAL CHANGES AND SUDDEN SHIFTS IN ECOSYSTEMS WITH HUMAN INTERACTIONS: A NONLINEAR DYNAMICAL APPROACH

The interplay of both natural causes and human activities/interventions drives both gradual changes and sudden shifts on entire ecosystems with many times catastrophic consequences. Thus, the systematic modeling, analysis and forecasting of the complex behavior of ecosystems in response to their ongoing changes constitutes one of the major challenges of nowadays. Over the last few years, simple mathematical models in the form of ordinary and/or partial differential equations have been proposed to approximate in a qualitatively manner the observed complex phenomena. While, the vast majority of the studies dictate the importanceofthenotionofbifurcationforthebetterunderstandingofthemechanisms that pertain to regime shifts, most of them use simple temporal simulations to analyse and thus identify criticalities that mark the onset of phase transitions. Inthispaper,westresstheimportanceofusingthefullarsenalofnumericalbifurcation theory to systematically identify and characterize criticalities in ecological models in the two dimensional parameter space. Towards this aim we revisit the analysis of a simple model of a forest-grassland mosaic ecosystem. We construct thebifurcationdiagramsinthetwodimensional(2D)parameterspacewithrespect 118 to the weight of human inuence and natural causes. Based on the 2D bifurcation analysis we show that simple simulations and even simple 1D bifurcation analysis could be inadequate and even drive to misleading conclusions for the overall system behavior.