Parallelism, traveling waves and modular biodiversity interfaces in non-stationary ecosystems

<p class="MsoNormal" style="text-align: justify; text-justify: inter-ideograph; line-height: 120%; mso-pagination: none; layout-grid-mode: char; mso-layout-grid-align: none; punctuation-wrap: simple; text-autospace: none; margin: 12.0pt 0cm 6.0pt 0cm;"><span lang="EN-US" style="font-size: 10.0pt; mso-bidi-font-size: 11.0pt; line-height: 120%; font-family: 'Times New Roman',serif;">The present paper treats mainly two questions, namely the mathematical characterization of the notion of biodiversity of a border interface between two adjacent ecosystems, and the role of human interference in the physical reality of interacting multi-species systems. Mathematically, the techniques of reaction-diffusion modeling, Turing’s notion of flow matrices and Verhulst logistic growth dynamics are introduced, in order to model the complex interactions in a fractal, non-stationary ecosystem. A new key approach is the combined use of flow matrices and Verhulst growth dynamics with Laplace transforms. However, these findings so far remain theoretical, not in the least because of the widespread interference of human activities with ecological developments, both planned and unplanned.</span><span lang="EN-US" style="font-size: 10.0pt; mso-bidi-font-size: 11.0pt; line-height: 120%; font-family: 'Times New Roman',serif; mso-fareast-language: ZH-CN;"> </span><span lang="EN-US" style="font-size: 10.0pt; mso-bidi-font-size: 11.0pt; line-height: 120%; font-family: 'Times New Roman',serif;">When comparing mathematical models and the actual physical dynamics of ecosystems, parallel trends as well as species-specific, unique deviations are conspicuous. Especially the latter remain hard to predict, indicating the limited value of mathematical predictions for the actual biodiversity trends in the field. Moreover, in a specific case study from the Netherlands related to the ecology of game mammals and a top-predator (the Wolf), it appears that not only contemporary ecological management operations, but also the contingency of measures from a historical past (exceeding 200 years) play a significant role in understanding the human interference factor in nature (designated as the Anthropocene factor).</span></p>