Sensitivity analysis of coexistence in ecological communities: theory and application

Sensitivity analysis, the study of how ecological variables of interest respond to changes in external conditions, is a theoretically well‐developed and widely applied approach in population ecology. Though the application of sensitivity analysis to predicting the response of species‐rich communities to disturbances also has a long history, derivation of a mathematical framework for understanding the factors leading to robust coexistence has only been a recent undertaking. Here we suggest that this development opens up a new perspective, providing advances ranging from the applied to the theoretical. First, it yields a framework to be applied in specific cases for assessing the extinction risk of community modules in the face of environmental change. Second, it can be used to determine trait combinations allowing for coexistence that is robust to environmental variation, and limits to diversity in the presence of environmental variation, for specific community types. Third, it offers general insights into the nature of communities that are robust to environmental variation. We apply recent community‐level extensions of mathematical sensitivity analysis to example models for illustration. We discuss the advantages and limitations of the method, and some of the empirical questions the theoretical framework could help answer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109599/1/ele12350.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/109599/2/ele12350-sup-0001-AppendixS1.pd

Population regulation and adaptive dynamics of cross-feeding

The particular importance of evolutionary studies in microbial experimental systems is that starting from the level of the metabolism of individual cells, the adaptive dynamics can be followed step by step by biochemical, genetic, and population dynamical tools. Moreover, the coincidence of evolutionary and ecological time scales helps to clarify the mutual role of ecological and evolutionary principles in predicting adaptive dynamics in general. Ecological principles define the eco- logical conditions under which adaptive branching can occur. This paper overviews and interprets the results of empirical and modeling studies of the evolution of metabolic cross-feeding in glucose-limited E.coli chemostats and batch cultures in the context of theories of robust coexistence and adaptive dynamics. Empirical results consistently demonstrate that the interactions between cells are mediated by the changing metabolite concentrations in the cultures and modeling confirms that these changes may control the adaptive dynamics of the clones. In consequence, the potential results of evolution can be predicted at the functional level by evolutionary flux balance analysis (evoFBA), while the genetic changes are more contingent. evoFBA follows the scheme of adaptive dynamics theory by calculating the feedback environment that changes during the evolutionary process and provides a promising tool to further investigate adaptive divergence in small microbial communities. Three general conclusions close the paper