Title: Modeling robust stability measures in ecology via pseudospectra and its localizations
Abstract: One of the contemporary paradigms developed to understand interplay between stability and complexity of the soil ecosystems is a mechanistic model of an energetic food web which consists of living organic matter (plants, animals, bacteria, fungi, etc.) and nonliving organic matter (detritus with allochthonous and autochthonous source). While typical analysis of stability is usually done via eigenvalues, in the setting of food webs such approach suffers from important drawbacks and can be misleading. Therefore, using the concept of a matrix pseudospectra, we present an approach to derive and compute indicators for the (robust) stability, which allows one to incorporate the level of uncertainty (errors in measurements, stochastic fluctuactions, etc.) in empirical data, as well as the timescale for possible transitional instabilities and the maximal amplification of initial perturbations. In addition, in cases when precise pseudospectral computations are not needed or not practical, we will discuss use of recently developed pseudospectra localization techniques that allow effects of robust stability to be linked with specific relationships between matrix entries that typically reflect modeling parameters. Finally, derived techniques will be applied to soil food webs in researched in Netherlands and empirical data measured in the field.