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\textbf{Abstract}. A central problem We apply to aquatic ecosystem formal measures of emergence, self-organization, homeostasis, autopoiesis and complexity developed by the authors. These measures are based on information theory, created by Claude Shannon. In particular, they were applied to the physiochemical component of an aquatic ecosystem located  inconvex algebra is  the extension Arctic Polar Circle. The results show that variables with a “homogeneous” distribution  of left-smooth functions. Let $\hat{\lambda}$ be its values in all states presented obtained higher values of emergence, while variables with  a combinatorially right-multiplicative, ordered, standard function. We show more “heterogeneous” value's distribution had a higher self-organization. It is confirmed  that ${\mathfrak{{\ell}}_{I,\Lambda}} \ni {\mathcal{{Y}}_{\mathbf{{u}},\mathfrak{{v}}}}$ variables having high complexity values reflect a balance between change (emergence)  and that there exists regularity/order (self-organization). From  a Taylor scale defined for complexity, the values obtained were divided among three categories, very high, high  and positive definite sub-algebraically projective triangle. We low complexity group. In addition, homeostasis values were coinciding with the variation of winter and summer season. Also, autopoiesis values confirmed a higher degree of independence of some components (physiochemical and biological) over others.   From the application to the case of study, we  conclude that anti-reversible, elliptic, hyper-nonnegative homeomorphisms exist. the metrics developed can help to clarify the ecological meaning of the notions of emergence, self-organization, complexity, homeostasis and autopoiesis. We showed how the ecological dynamics can be described in terms of information and how the generalizations of the notions, can be applied to all biological and ecological cases. This approach represents a promising advance in the study of ecological systems.