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. There are four seasons in a year, winter, spring, summer and autumn. In summer, the flow variations (Inflow and outflow fall to 3.5 from 25.2 and retention time increases to 100 days), the lack are lack or absence of seasonal wind and high temperatures (24ºC), causes the water column thermostratification. Stratification is expressed in generation of two layers. At the border of these layers, temperature changes dramatically (24ºC Surface to 20.6 in Planktonic layer, to 17.3 in Benthic layer). Water above and below of thermocline do not mix. The warmer water is near the surface and denser water is near the bottom. In winter, there is no ice covering in the surface. Opposite to the summer when the flow is minimum, in spring and autumn the water column overturns (Retention Time of 14 days and Zone Mixing of 100%), causing increases in conductivity. In summer, depletions of oxygen at the three layers are more drastic than Artic lakes (below 8.7 mg/lt). Oxygen is directly correlated with the zone mixing, inflow and outflow, and inverse correlated with the others parameters (fig. **), especially with pH and retention time.

All limiting nutrients are above of 90% available for phytoplankton in all seasons. According with this availability, phytoplankton and periphyton biomass composition is dominated by planktonic (47%) and benthic (34.3%) diatoms. This way, 100% of zooplankton composition is reached by herbivorous zooplankton and fish community is dominated by benthic fish (67.6%).

North Higland Lake (NH)

North highland lake corresponds with a mesotrophic ecosystem in a cool North-Temperate climate (Mean 5.3ºC). Levels of chlorophyll are between 2.2.-6.2 mg/m3. The surface is covered with ice in winter (end of November, December, January and early February). Ice covering forms a barrier to the wind which minimizes losses of water evaporation while the bottom of the lake remains unfrozen. The water column does not thermostratified and is permanently well mixed whit levels of 50 percent in summer and 90 percent in winter. The maximum flows are in spring and autumn (9.6) with minimum flow in summer(0.6). Evaporation is reduced because their water is more or less cold and vapour-pressure gradients are no large (mean of 9,262). Retention Time is maximum in summer with 100 days. Oxygen concentration is upper to 10 mg/lt in the three layers. pH mean values are around 7 to 7.3, but it moves in a range of 6.7 to 7.8 from the surface to bottom.

Variables correlations are more seasonal than the N1. It means the period of summer is related with high retention time, higher pH and winter season with the higher levels of oxygen, inflow and outflow and oxygen. However, there is a more strong correlation of benthic and sediment Oxygen.

Limiting Nutrients like nitrates and carbon dioxide are around of 95 percent available for phytoplankton. Phosphates and Silicates show variations and minor percentage of availability. The former around of 80% and the second one around 95% all year. Biomass composition is dominated by planktonic (46.7%) and benthic (41%) diatoms. Zooplankton composition is almost of herbivorous zooplankton (91.4%), but carnivorous zooplankton reaches a little percentage of 8.6. The group of benthic invertebrates appears with the dominance of the detritivores (87.5%). Fish community is dominated by benthic fish again but in a high proportion (88.9%).

Tropical Lake (T)

The Tropical Lake is a  Hyper-eutrophic ecosystem (Chlorophyll > 19.2 mg/lt) located in a moist Tropical climate, at north of the equator, near to the tropic of cancer with a mean temperature of 25ºC in surface layer. This has one wet season and one dry season. Higher irradiance conducts to higher temperatures (Mean) and smaller thermal differences between layers. For that reason,  the water column is permanently warm and stratified. Stratification is due to the heat exchange, but is less stable than at higher latitudes, the wind could have great incidence in the mixing of the water column. Thus, intraseasonal variations have an effect in thickness of the mixed layer than other morphometrically similar temperate lakes  (AES, Lewis). The maximum flow of water is in the wet season, and minimum flow is in the dry season. Episodes of heat and mixing, affects the nutrient cycling and plankton dynamics. It is highlighted that primary production in tropical lakes is about twice than higher latitudes. Also, it is known that Nitrogen is the more limiting nutrient.

In this case, there are more equilibrium among species inside phyto and periphyton communities (around 33% for diatoms, green algae and cyanobacteria). Zooplankton populations are dominated by herbivorous (90%), benthos by detritivores inverte