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  • Lake’s Complexity in a Latitudinal Gradient


    Abstract. ***


    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.

    (Tate 1995)


    Complexity Measures:

    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

    Complexity in ecology and measures of complexity in ecology

    McArthur (1955) were the first researcher to recognize the important role of Shannon’s entropy in ecological studies.


    Measures of complexity







    Case Studies

    The data of different lakes models used in this section was obtained using The Aquatic Ecosystem Simulator (Randerson and Bowker, 2008). The model used is deterministic, so there is no variation in different simulation runs. All variables and daily data we obtained from Artick, North1, North2 and Tropical lakes are shown in Anex 1.

    Arctic Lake (Ar)

    Arctic lakes are located at the Arctic Polar Circle. Their mean surface temperature is around 3ºC and their maximum is near to 9ºC and their minimum is cero celsius degrees. In general, Arctic lake systems are classified as oligotrophic due to their low primary production, represented in chlorophyll values of 0.8-2.1 mg/m3. The lake’s water column, or limnetic zone, is well-mixed; this means that there are no stratifications (layers with different temperatures). During winter (October to March), the surface of the lake is ice covered. During summer (April to September), ice melts and the water flow and evaporation increase, as shown in Figure **. Consequently, the two climatic periods (winter and summer) in the Arctic region cause a typical hydrologic behavior in lakes as the one shown in Figure **. This hydrologic behavior influences the physiochemical subsystem of the lake.

    Limiting Nutrients in the form of nitrates, silicates and carbon dioxide are between 90 and 100% available for phytoplankton in all year. Thus, phytoplankton and periphyton biomass is dominated by planktonic (38.6%) and Periphytic diatoms (45%). For zooplankton, the 91.7% is dominated by herbivorous. At the Benthos invertebrates detritivores with a 86.8% of total abundance and piscivorous fishes with the 85.8% are the two groups with high dominance in their respectively group.

    North Lowland Lake (NL)

    North lowland is an eutrophic lake, located in a warm North-Temperate climate (mean Tº of 14ºC). Their primary production expressed in mg/m3 of chlorophyll is around 6.3-19.2. Ther