@article {165,
	title = {Complexity of lakes in a latitudinal gradient},
	journal = {Ecological Complexity},
	volume = {31},
	year = {2017},
	month = {9},
	pages = {1{\textendash}20},
	abstract = {Measuring complexity is fast becoming a key instrument to compare different ecosystems at various scales in ecology. To date there has been little agreement on how to properly describe complexity in terms of ecology. In this regard, this manuscript assesses the significance of using a set of proposed measures based on information theory. These measures are as follows: emergence, self-organization, complexity, homeostasis and autopoiesis. A combination of quantitative and qualitative approaches was used in the data analysis with the aim to apply these proposed measures. This study systematically reviews the data previously collected and generated by a model carried out on four aquatic ecosystems located between the Arctic region and the tropical zone. Thus, this research discusses the case of exploring a high level of self-organization in terms of movement, distribution, and quality of water between the northern temperate zone and the tropics. Moreover, it was assessed the significance of the presence of a complex variable (pH) in the middle of the latitudinal transect. Similarly, this study explores the relationship between self-organization and limiting nutrients (nitrogen, phosphorus and silicates). Furthermore, the importance of how a biomass subsystem is affected by seasonal variations is highlighted in this manuscript. This case study seeks to examine the changing nature of how seasonality affects the complexity dynamics of photosynthetic taxa (lakes located in northern temperate zone) at high latitudes, and it also investigates how a high level of self-organization at the tropical zone can lead to increase the amount of planktonic and benthic fish which determines the dynamics of complexity. This research also compares the emerging role of how a biomass subsystem has a highest temporal dynamics compared to he limiting nutrients{\textquoteright} subsystem. In the same way, the results associated to autopoiesis reflect a moderate degree of autonomy of photosynthetic biomass. It is also discussed the case of how complexity values change in the middle of the latitudinal gradient for all components. Finally, a comparison with Tsallis information was carried out in order to determine that these proposed measures are more suitable due to they are independent of any other parameter. Thus, this approach considers some elements closely related to information theory which determine and better describe ecological dynamics.},
	keywords = {Autopoiesis, Biocomplexity, Emergence, Homeostasis, Information theory, Self-organization},
	isbn = {1476-945X},
	doi = {10.1016/j.ecocom.2017.02.002},
	url = {http://dx.doi.org/10.1016/j.ecocom.2017.02.002},
	author = {Fern{\'a}ndez, Nelson and Aguilar, Jos{\'e} and Pi{\~n}a-Garc{\'\i}a, C. A. and Gershenson, Carlos}
}
@article {10.3389/frobt.2017.00010,
	title = {A Package for Measuring Emergence, Self-organization, and Complexity Based on Shannon Entropy},
	journal = {Frontiers in Robotics and AI},
	volume = {4},
	year = {2017},
	pages = {10},
	abstract = {We present Matlab/Octave functions to calculate measures of emergence, self-organization, and complexity of discrete and continuous data. The measures are based on Shannon{\textquoteright}s information and differential entropy, respectively. Examples from different datasets and probability distributions are used to illustrate the usage of the code.},
	issn = {2296-9144},
	doi = {10.3389/frobt.2017.00010},
	url = {http://journal.frontiersin.org/article/10.3389/frobt.2017.00010},
	author = {Santamar{\'\i}a-Bonfil, Guillermo and Gershenson, Carlos and Fern{\'a}ndez, Nelson}
}
@article {CxContinuous2016,
	title = {Measuring the Complexity of Continuous Distributions},
	journal = {Entropy},
	volume = {18},
	number = {3},
	year = {2016},
	pages = {72},
	abstract = {We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. Given that the measures were based on Shannon{\textquoteright}s information, the novel continuous complexity measures describe how a system{\textquoteright}s predictability changes in terms of the probability distribution parameters. This allows us to calculate the complexity of phenomena for which distributions are known. We find that a broad range of common parameters found in Gaussian and scale-free distributions present high complexity values. We also explore the relationship between our measure of complexity and information adaptation.},
	issn = {1099-4300},
	doi = {10.3390/e18030072},
	url = {http://www.mdpi.com/1099-4300/18/3/72},
	author = {Santamar{\'\i}a-Bonfil, Guillermo and Fern{\'a}ndez, Nelson and Gershenson, Carlos}
}
@inbook {Fernandez_Gershenson_2014,
	title = {Measuring Complexity in an Aquatic Ecosystem},
	booktitle = {Advances in Computational Biology},
	series = {Advances in Intelligent Systems and Computing},
	volume = {232},
	year = {2014},
	pages = {83-89},
	publisher = {Springer},
	organization = {Springer},
	abstract = {We apply formal measures of emergence, self-organization, homeostasis, autopoiesis and complexity to an aquatic ecosystem; in particular to the physiochemical component of an Arctic lake. These measures are based on information theory. Variables with an homogeneous distribution have higher values of emergence, while variables with a more heterogeneous distribution have a higher self-organization. Variables with a high complexity reflect a balance between change (emergence) and regularity/order (self-organization). In addition, homeostasis values coincide with the variation of the winter and summer seasons. Autopoiesis values show a higher degree of independence of biological components over their environment. Our approach shows how the ecological dynamics can be described in terms of information.},
	doi = {10.1007/978-3-319-01568-2_12},
	url = {http://arxiv.org/abs/1305.5413},
	author = {Fern{\'a}ndez, Nelson and Gershenson, Carlos},
	editor = {Castillo, Luis F. and Cristancho, Marco and Isaza, Gustavo and Pinz{\'o}n, Andr{\'e}s and Corchado Rodr{\'\i}guez, Juan Manuel}
}
