deletions | additions       diff --git a/Measuring Complexity in an Aquatic Ecosystem.tex b/Measuring Complexity in an Aquatic Ecosystem.tex  new file mode 100644  index 0000000..2b8f435  --- /dev/null  +++ b/Measuring Complexity in an Aquatic Ecosystem.tex 
...
%\documentclass[preprint,showpacs,showkeys,floatfix,preprintnumbers]{revtex4}  \documentclass[aps,prl,twocolumn,a4paper,showpacs]{revtex4}  \usepackage{amsfonts,amsmath,amssymb}  \usepackage{bm}\let\vec\bm  \usepackage{graphicx}  \usepackage{color}  \usepackage{hyperref}  \begin{document}  \newcommand{\truncateit}[1]{\truncate{0.8\textwidth}{#1}}  \newcommand{\scititle}[1]{\title[\truncateit{#1}]{#1}}  \title{Measuring Complexity in an Aquatic Ecosystem  }  \author{Nelson Fernández}  \author{Carlos Gershenson}  \maketitle  \textbf{Abstract}. We apply to aquatic ecosystem components, 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 in the Arctic Polar Circle. The results show that variables with a “homogeneous” distribution of its values in all states presented obtained higher values of emergence, while variables with a more “heterogeneous” value's distribution had a higher self-organization. It is confirmed that variables having high complexity values reflect a balance between change (emergence) and regularity/order (self-organization). 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. This approach showed how the ecological dynamics can be described in terms of information.   \section{Introduction}     Traditionally, science has been reductionistic. Reductionism—the most popular approach in science—is not appropriate for studying biological and ecological systems, as it attempts to simplify and separate in order to predict their future behavior and states. Due to prediction difficulty, biological and ecological systems have been considered as complex. This “complexity” is due to the relevant interactions between components [18]. It is important to highlight that, etymologically, the term complexity comes from the Latin plexus, which means interwoven. In other words, something complex is difficult to separate.     Including interactions in ecological studies, for complexity understanding is no easy. For example, it has been tried with global models that including the greatest number of variables, resulting also in serious deficiencies in predictability, especially for the limitation for the incorporation of all interactions ecosystem multi-elements and components (Moore et al. 2002). Alternative forms of explain de complex dynamics have been trying with the assessment of attributes like resilience and robustness (Ulanowicz et al. 2009). Also, ecological complexity has been related with stability. This way, complexity characterization has been supported in variables such as species richness (number of species), connectance (fraction of the possible interspecific interactions), interaction strength (effect of one species’ density on the growth rate of another specie) and evenness (abundance variance). Meanwhile, stability has been related with resilience (velocity to return to the equilibrium), resistance (variable’ grade of change) and variability (population density variance) (Pimm, 1984). However, these interpretations of interactions are conducts to find an explanation of functional complexity, than the evaluation of how complex is an ecosystem.     As complex systems, we need consider that biological and ecological systems have properties like emergence, self-organization, and life. It means, biological and ecological systems dynamics generate novel information from the relevant interactions among components. Interactions determine the future of systems 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. The balance between change (chaos) and stability (order) states has been proposed as a characteristic of complexity. Since more chaotic systems produce more information (emergence) and more stable systems are more organized, complexity can be defined as the balance between emergence and self-organization. In addition, there are two properties that support the above processes: homeostasis refers to regularity of states in the system and autopoiesis that reflects autonomy.     Due to a plethora of definitions, notions, and measures of these concepts have been proposed, the authors proposed abstract measures of emergence, selforganization, complexity, homeostasis an autopoiesis based on information theory, in focus to clarify their meaning with formal definitions (Gershenson and Fernández, 2012). Now we propose apply to aquatic ecosystem formal measures developed. From the application to the case of study, an Artic lake, we clarify the ecological meaning of these notions, and we showed how the ecological dynamics can be described in terms of information. This way the study of the complexity in biological and ecological cases, now is easier.     In the next section, we present a brief explanation of notions of self-organization, emergence, complexity, homeostasis, autopoiesis and limnology (as the field that studies the lakes9. In section 3, we present the synthetic measures of results of emergence, selforganization, complexity, and homeostasis. Section 4 describes our experiments and results with the Artic lake, which illustrate the useful of the proposed measures. This is followed by a discussion in Section 5. The article closes with proposals for future work and conclusions.   \section{Background and Metrics}     \subsection{Emergence}     Emergence refers to properties of a phenomenon that are present now and were not before. If we suppose these properties as non-trivial, we could say it is harder now than before to reproduce the phenomenon       \subsection{Complextiy}     As we have mentioned, complexity comes fromLatin plexus, which means interwoven. Thus, something complex is difficult to separate. This means that its components are interdependent, i.e. their future is partly determined by their interactions. Thus, studying the components in isolation—as reductionistic approaches attempt—is not sufficient to describe the dynamics of complex systems.     As measure we can define complexity C as the balance between change (chaos) and stability (order). We have just defined such measures: emergence and self-organization. As function C:->..     Hence we propose:     C = 4 · E · S.     \subsection{Limnology}     Limnology is related with formal study of lakes. In particular treats with the distinctive properties of individual lakes and the nature of their interactions with their surrounding environment (Catchment basin). Aspects such as the influence of the geography, physiography and climate on the hydrology, hydrochemistry and dynamics of aquatic biota, are taken into account to search for underlying patterns and the underpinning processes (Reynolds, 2004).     Lakes has distinct zones of biological communities linked to the physical structure of the lake (Fig. 1). Classical zones studied are (i) Macrophyte or littoral zone, composed mainly by aquatic plants, which are rooted, floating or submerged. (ii) The planktonic zone corresponds to the open surface waters; away from the   shore in which organisms passively floating and drifting on the lakes' currents (phyto and zooplankton). Planktonic organism are incapable of swimming against a current, however some of them are somewhat motiles. (iii) Benthic zone is the lowest level of a body of water related with the substratum, including the sediment surface and subsurface layers. (iv) Mixing zone where the interchange of water from planktonic and benthic zone can be mixed.     At different zones, one or more components or subsystems can be an assessment for the ecosystem dynamics. Our case of study considered three components: physiochemical, limiting nutrients and photosynthetic biomass for the planktonic and benthic zones. The physiochemical component refers to the chemical composition of water. It is affected by various conditions and processes such as geological nature, the water cycle, dispersion, dilution, solute and solids generation (e.g. photosynthesis), and sedimentation. Related to the physiochemical component, limiting nutrients which are basic for photosynthesis are associated with the biogeochemical cycles of nitrogen, carbon, and phosphorous. These cycles permit the adsorption of gases into the water or the dilution of some limiting nutrients. In addition, among limnetic biota, photoautotrophic biomass is the basis for the trophic web establishment. The term autotrophs is used for organisms that increase their mass hrough the accumulation of proteins which they manufacture, mainly from inorganic radicals (Stumm, 2004). This type of organisms can be found at the planktonic and benthic zones.     \begin{figure}[tb]  \includegraphics[width=\columnwidth]{figures/Fig. 1. lago/Fig. 1. lago.png}  \caption{Replace this text with your caption}  \end{figure}  \section{Results}  We begin by considering a simple special case. Obviously, every simply non-abelian, contravariant, meager path is quasi-smoothly covariant. Clearly, if $\alpha \ge \aleph_0$ then ${\beta_{\lambda}} = e''$. Because $\bar{\mathfrak{{\ell}}} \ne {Q_{\mathscr{{K}},w}}$, if $\Delta$ is diffeomorphic to $F$ then $k'$ is contra-normal, intrinsic and pseudo-Volterra. Therefore if ${J_{j,\varphi}}$ is stable then Kronecker's criterion applies. On the other hand,   \begin{equation}  \eta = \frac{\pi^{1/2}m_e^{1/2}Ze^2 c^2}{\gamma_E 8 (2k_BT)^{3/2}}\ln\Lambda \approx 7\times10^{11}\ln\Lambda \;T^{-3/2} \,{\rm cm^2}\,{\rm s}^{-1}  \end{equation}  Since $\iota$ is stochastically $n$-dimensional and semi-naturally non-Lagrange, $\mathbf{{i}} ( \mathfrak{{h}}'' ) = \infty$. Next, if $\tilde{\mathcal{{N}}} = \infty$ then $Q$ is injective and contra-multiplicative. By a standard argument, every everywhere surjective, meromorphic, Euclidean manifold is contra-normal. This could shed important light on a conjecture of Einstein:  \begin{quote}  We dance for laughter, we dance for tears, we dance for madness, we dance for fears, we dance for hopes, we dance for screams, we are the dancers, we create the dreams. --- A. Einstein  \end{quote}  \subsection{Connections to Littlewood's Conjecture}  We show the energy radiated in the convective region to be proportional to the mass in the radiative layer between the stellar surface and the upper boundary of the convective zone, as shown in the following table and in Figure \ref{fig:fig1}.  \begin{table}  \begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|}  \textbf{Phase} & \textbf{Time} & \textbf{M$_1$} & \textbf{M$_2$} & \textbf{$\Delta M$} & \textbf{P} &   \textbf{$v_{\rm rot,1}$} & \textbf{$v_{\rm rot,2}$} & \textbf{Y$_{\rm c,2}$} & \textbf{Y$_{\rm s,2}$} & \textbf{$v_{\rm orbit,1}$} & \textbf{$v_{\rm orbit,2}$} \\   \T & Myr & M$_{\odot}$ & M$_{\odot}$ & M$_{\odot}$ & d &  km~s$^{-1}$ & km~s$^{-1}$ & & & km~s$^{-1}$ & km~s$^{-1}$ \\  1 ZAMS & 0 & 16 & 15 & -- & 5.0 & 230 & 230 & 0.248 & 0.248 & 188 & 201 \\   2 begin Case B & 9.89 & 15.92 & 14.94 & 0.14 & 5.1 & 96 & 85 & 0.879 & 0.248 & 186 & 198 \\  3 end Case B & 9.90 & 3.93 & 20.77 & 6.30 & 38.2 & 27 & 719 & 0.434 & 0.348 & 153 & 29 \\  4 ECCB primary & 11.30 & 3.71 & 20.86 & 6.44 & 42.7 & 40 & 767 & 0.457 & 0.441 & 149 & 27 \\  5 ECHB secondary & 18.10 & -- & 16.76 & -- & -- & --& 202 & 0.996 & 0.956 & -- & -- \\  6 ICB secondary & 18.56 & -- & 12.85 & -- & -- & --& 191 & 0.000 & 0.996 & -- & -- \\   7 ECCB secondary & 18.56 & -- & 12.83 & -- & -- & --& 258 & 0.000 & 0.996 & -- & -- \\  \hline  \end{tabular}  \caption{\textbf{Table 1. Some descriptive statistics about fruit and vegetable consumption among high school students in the U.S.}. While bananas and apples still top the list of most popular fresh fruits, the amount of bananas consumed grew from 7 pounds per person in 1970 to 10.4 pounds in 2010, whereas consumption of fresh apples decreased from 10.4 pounds to 9.5 pounds. Watermelons and grapes moved up in the rankings.}  \end{table}  \begin{figure}[tb]  \includegraphics[width=\columnwidth]{figures/figure_1/figure_1.jpg}  \caption{\textbf{\label{fig:fig1}. STM topography and crystal structure of top 100 fruits and vegetables consumed in the U.S.} The Bi atoms exposed after cleaving the sample are observed as bright spots. The in-plane unit cell vectors of the ideal crystal structure, $a$ and $b$, and of the superstructure, $a_{s}$, are indicated. Lines of constant phase are depicted. p-values were obtained using two-tailed unpaired t-test. Data are representative of five independent experiments with 2000 fruits and vegetables.}  \end{figure}  \bibliography{bibliography/biblio}  \end{document}