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\subsection{Autopoiesis}
There are two ways for observing
autopoiesis. autopoiesis (\textit{A}). The first one is the
autopoiesis \textit{A} of the each variable. Variables with more complexity than other have a positive
autopoiesis \textit{A} reflecting more autonomy. Variables with low complexity than other have negative
autopoiesis, \textit{A}, reflecting less autonomy. Results of
autopoiesis \textit{A} by variable in each subsystem can be seen in annex **. In general, variables in categories of very high and high complexity, have more
autopoiesis \textit{A} and they resulting as more
autonomous; autonomous, as well; that means they have more capacity of adaptation in front the changes of their environment which is constituted by the other subsystem variables.
The second one form of determine autopoiesis
(\textit{A}) is among variables of different subsystems, according with the matter-energy flux in ecosystems. It is well-know that photosynthetic living beings depending of solar radiation and nutrients availability as the base for its metabolism process. Also, zooplankton depending of grazing phytoplankton populations.
Starting from complexity values of selected variables of
Physico-Chemical, Physico-chemical, Limiting Nutrients and Biomass showed in the table **, we
we compare
autopoiesis \textit{A} of
biomass Biomass related with the their Physico-chemical and
limiting nutrients Limiting Nutrients environment. Values of
biomass Biomass for planktonic and benthic zone are depicted in fig. **.
From the table **, we notice that
biomass Biomass in
T \textit{T} is near to zero in planktonic zone and zero in the benthic zone. It means that tropical biomass is almost static. We can verify this with their very-high category of self-organization obtained. This Implies that any pattern in complexity can be observed in biomass as the result of the influence of its environment which is represented by its Physico-chemical and
limiting nutrients Limiting Nutrients subsystem. This case gives a minimal
autopoiesis \textit{A} for all comparisons carried out with the trajectories of
biomass Biomass in tropical lake.
Values of
A>1 \textit{A>1} were reached by photosynthetic living beings located at the benthic zone of
Ar,NH \textit{Ar},\textit{NH} and
NL \textit{NL} in front of Physico-chemical and
limiting Limiting nutrients. Also,
A>1 \textit{A<1} was reached by
biomass/limiting nutrients Biomass/Limiting Nutrients of planktonic zone at
Ar \textit{Ar} and
NH \textit{NH} and by
biomass/Physico-Chemical Biomass/Physico-Chemical of planktonic zone of
NL. \textit{NL}. In terms of the Ashby's Law of Requisite Variety(Ashby, 1956), photosynthetic biomass in Polar and Template latitudes have more variety than its environment. More variety is related with a more number of states to face on environmental changes. Variety is the result of very high complexity and could be reflecting as more autonomy of the taxa therein. ***Verify species richness***
The remaining cases of biomass, obtain values less than one (A<1) and were related with their response in front of Physico-chemical in the planktonic zone of Ar and NH. Also NL biomass response in front of limiting nutrient at the same zone obtain A<1. This values between 0.72 and 0.98 shows that their environment changes more than the populations of photosynthetic living beings. As we can see, the weak or almost fair lake-specific response of the biomass, suggest that speciesinvolved in this subsystem could be affected in a high proportion in case of strong change events.
On the base of above findings, we thought that relationships evaluated in biomass of different lakes might be evaluated in the context of environmental variability.
\subsection{Homeostasis}
The homeostasis \textit{h} calculation by comparing the daily values of all variables is a useful indicator for periodic or seasonal dynamics characterization and determination. \textit{h} can represents the temporal variation of the state of each subsystem in each lake. This situation is more evident in the Physico-chemical subsystem of lakes which responds proportionally with the seasonal changes affecting variables like temperature, light and others relate with the hydrological cycle. Limiting Nutrient subsystems works in a larger scale than Physico-chemical subsystem; it seems that nutrients could vary more at week scales than day scales. For all three subsystems, biomass demonstrated has the largest scale variation; in special at the T which their biomass variation takes place in several months intervals. The above homeostasis results demonstrates the importance of the temporal timescale because \textit{h} can vary considerably if we compare states every minute or every month.
For
\textit{H} \textit{H}, the table ** relates the
mean values
and standard deviation for
an annual cycle all lakes and subsystems. Considering that the lakes studied maintains periods without changes, values of H are all in the category of very-high homeostasis. We observe that Biomass and Physico-chemical were more stable systems in a year than Limiting Nutrients subsystem. In detail by the lake at the Ar and NL Biomass is more regular than NL and T. Physico-chemical subsystem have a similar regularity for all lakes
being the lower NL. For Limiting Nutrients, the lower regularity is also NL and
subsystems... the high for Ar.
