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Due to a plethora of definitions, notions, and measures of these concepts have been proposed, the authors proposed abstract measures of emergence, selforganization, complexity, homeostasis an autopoiesis based on information theory, in focus to clarify their meaning with formal definitions (Gershenson and Fernández, 2012). Now we propose apply to aquatic ecosystem formal measures developed. From the application to the case of study, an Artic lake, we clarify the ecological meaning of these notions, and we showed how the ecological dynamics can be described in terms of information. This way the study of the complexity in biological and ecological cases, now is easier.  In the next section, we present a brief explanation of notions of self-organization, emergence, complexity, homeostasis, autopoiesis and  limnology, as the field that studies the lakes. In section 3, we present the synthetic measures of results of emergence, selforganization, complexity, and homeostasis. Section 4 describes our experiments and results with the Artic lake, which illustrate the useful of the proposed measures. This is followed by a discussion in Section 5. The article closes with proposals for future work and conclusions.