In recent years, the scientific study of complexity in ecological systems has increased understanding of a broad range of phenomena such as ecological richness, abundance, and hierarchical structure. As a result, different approximations have been explored to develop mathematical formalisms in order to represent the ecological complexity as ecological indicator (Parrot, 2005). The advantage of a complexity indicator in ecosystems is the possibility of relation with ecological integrity, diversity and/or resilience, for example. Relation with the spatial and temporal scales, with the structure and function as well are desired (Parro, 2010).
In spite of the valuable efforts in ecological modeling over the last decade to take into account the ecological interactions in much detail (Petrovskii and Petrovskay, 2012), more explorations are required to explain ecological dynamics in terms of complexity. A starting point for complexity studies is considering that ecological systems exhibit properties like emergence, self-organization, and life. In addition, there are two essential properties, homeostasis and autopoiesis, which supports the self-regulation and autonomy of the system. The above properties comes from the relevant interactions among system’s components and generates novel information. These interactions determine the future of ecosystems and its complex behavior. Novel information limits predictability as it is not included in initial or boundary conditions. It can be said that this novel information is emergent since it is not in the components, but produced by their interactions. Interactions can also be used by components to self-organize, i.e. produce a global pattern from local dynamics. Interactions are one the most important reason for complexity generation.
To support the formal description of complexity, self-organization and emergence, information theory (Shannon, 19499) has been used in different ways as it can see in Prokopenko et al (2009). Formals aspects for homeostasis and autopoiesis can be found in Fernández et al., 2014.
Considering there are multiple ways to describe the state of an ecosystem, the balance between change (chaos) and stability (order) states has been proposed as a characteristic of complexity (Langton,**; Kaufmann). This way, we can say that more chaotic systems produce more information (emergence), and more stable systems are more organized. Thus we propose, based on information theory, that complexity can be defined as the balance between emergence and self-organization (Gershenson & Fernández; Fernández et. al. 2015). This approach has been applied to some ecological systems (Fernández & Gershenson 2013; Fernández et al. 2013*eccs) with good results indicating that ecological dynamics can be described in terms of information.
This papers expand the useful of the application of complexity measuring applying formal expresions of complexity, self-organization, emergence, homeostasis and autopoiesis to the physiochemical, nutrients and biomass subsystems to four types of lakes located in a latitudinal gradiente (Arctic, North Lowland, North Hingland to Tropical), in focus to evaluate the usefulness and bennefits in ecological systems.
measures of statistical complexity Feldman and Crutchfield (1998) studied in the theoretical physics literature Lopez-Ruiz et al., 1995; Piasecki et al., 2002; Demetrius and Manke, 2005
McArthur (1955) were the first researcher to recognize the important role of Shannon’s entropy in ecological studies.
Ricotta:..."there have been few attempts to quantify the statistical complexity of a given species assemblage in ecology; Demetrius et al. (2004) examine the question from an evolutionary biology perspective; Demetrius and Manke (2005) present methods which can be applied to ecological networks (e.g., food webs); Juh´asz-Nagy (1976, 1984, 1993); Juh´ asz-Nagy and Podani (1983) was the first to develop a coherent information-theoretical framework for summarizing various aspects of spatial complexity in plant communities as a function of scale. (Ricotta and Anand, 2004): A measure of statistical complexity for plant communities based on Juh´ asz- Nagy’s model.