So far, I've only known one: the MaxEnt theory. It uses the maximum information entropy developed by information theorist, which in turn inspired by the thermodynamics from physics, to predict the number of organism in an area. This theory is developed by John Harte. You can read about this theory in Quanta Magazine.

I also know the book Towards the Thermodynamics Theory for Ecological Systems, written by Jørgensen and Svirezhev.

I find it hard to find another theory similar with the two theories above. Do you know any theories using the thermodynamics or information principles to modelling in ecology?

I have opened a reddit discussion about this.

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    $\begingroup$ I'm still not quite sure what you are looking for. Do you want to know about additional theories in ecology that are similar to Harte's MaxEnt? Or are you more broadly interested in the application of thermodynamic principles in other fields? $\endgroup$
    – ChrKoenig
    Nov 12, 2015 at 13:22
  • $\begingroup$ First question should be prioritize, but the second one is interesting to know too $\endgroup$
    – Ooker
    Nov 12, 2015 at 15:30
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    $\begingroup$ You might wanna have a look at this paper: onlinelibrary.wiley.com/doi/10.1111/2041-210X.12152/abstract $\endgroup$
    – ChrKoenig
    Nov 12, 2015 at 15:41
  • $\begingroup$ @Hav0k thanks for the paper. I know what I'm looking for now: theories in ecology that use thermodynamic or information principles to modelling $\endgroup$
    – Ooker
    Nov 13, 2015 at 9:33

2 Answers 2


John Harte's work on applying the mathematical theory of maximum entropy to ecology is certainly one of the better known examples of the application of this area of mathematics to science, in part because he literally wrote the textbook: Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics (Oxford Series in Ecology and Evolution)

To be clear, maximum entropy (also known as MaxEnt in some of the literature, though most/all researchers use the longer form in publications) is a mathematical tool stemming from the fields of probability theory, statistics, and information theory. Its use is classically most often seen in thermodynamics, statistical thermodynamics, physics, and information theory, primarily because these were the areas in which E.T. Jaynes was working when he posited the idea. Wikipedia has links to his two seminal papers.But because of it's mathematical form, it can be applied in a multitude of areas, typically where one can utilize probabilistic methods.

If you're looking for additional areas of application, simply google the phrase "applied maximum entropy" and you'll find a wealth of areas including: econometrics, natural language processing, nuclear medicine, queuing systems, mass spectrometry, image processing, machine learning, and many others.

For ecology related work, a cross search on maximum entropy and "genetics", "evolution", "species", and similar words will provide a wealth of papers like "A maximum entropy approach to species distribution modeling".

Given the generic nature of your question, I might suggest that you'll find E.T. Jaynes' paper "On the Rationale of Maximum-Entropy Methods" (IEEE, 1982) useful.

Those generally interested in the broader applications of information theoretic methods to biology will likely appreciate some of the work that came out of last year's NIMBioS Workshop on Information and Entropy in Biological Systems (which Harte both attended and presented at), the BIRS Workshop Biological and Bio-Inspired Information Theory, and the 2014 CECAM Entropy in Biomolecular Systems. The NIMBios Workshop was organized by John Baez, a physicist, who has worked with MaxEnt methods and explored them on his blog "Azimuth".

Those with a more sophisticated mathematical background (including measure theory, functional analysis, etc.) may appreciate Henryk Gzyl's text The Method of Maximum Entropy (World Scientific: Series on Advances in Mathematics for Applied Sciences, Vol 29, 1995).

-- Additional thoughts after the question was edited --

First for those who don't have the background, I highly recommend reading the two seminal papers on information theory and statistical mechanics by ET Jaynes and the standard text on information theory Elements of Information Theory by Thomas M. Cover and Joy A. Thomas.

In addition to the information theoretic related areas, you might want to take a look at the discipline of complexity theory, which has primarily grown out of the Santa Fe Institute over the past several decades and which includes information theory as part of its disciplines. If you're unfamiliar with the broader topic, Melanie Mitchell has an excellent overview with her book Complexity: A Guided Tour. Also related to complexity is the area of cellular automata which one could view as a very base model of more complex ecological systems. Here, perhaps Stephen Wolfram's A New Kind of Science or Cellular Automata and Complexity will be enlightening. The broader theories coming out of these primarily mathematical areas may be useful to you.

In particular, given the types of models in ecosystems, I might suggest taking a look at some of the mathematical modeling going on at the intersection of complexity and economics. For a relatively simple introduction to this area, one could look at the relatively introductory text Complexity and the Economy by W. Brian Arthur which is very interesting. The economy is essentially a very specific type of ecology dealing with human beings, assets, and the monetary system.

Another area which I've seen a lot of literature over the last few years is applicable to the ideas of resiliency and complexity in cities, for assisting in designing more robust city planning. This really isn't that far from the naturally evolving systems being looked at in ecology settings.

For those looking for researchers in the area of complexity, I have a list of many who are on twitter in a variety of sub-areas. In addition to individuals, it also includes a number of institutes and related organizations as well.

I'd also suggest, that for the broadest theoretical setting, one could actually start with the topic known as "Big History" which takes the broadest approach of looking at history and the evolution of the cosmos over 13.7 billion years since the big bang. This conceptualization includes ideas like evolution, complexity, and emergence on the biggest scales, a set of theories that could be similarly applied to ecologies both large and small. For this viewpoint, I would suggest two works by David Christian including Maps of Time: An Introduction to Big History and Big History: The Big Bang, Life on Earth, and the Rise of Humanity.

In essence, with many of these topics and viewpoints, one is treating individual animals or even entire species as elementary particles and then using the mathematical models of statistical thermodynamics to tease out specific types of data or trends. As layers of overlapping "particles" interact with each other, they cause emergent types properties, and then these resultant emergent properties combine to create further layers of emergent properties, none of which might have been necessarily deduced from the initial conditions. Within Big History, these types of emergence go from the big bang and basic particles in the early universe to the ultimate evolution of humankind by way of a variety of stages.

  • $\begingroup$ Chapter 10 in Harte's book discuss about the connections between his theory and other theories. Thanks for the link $\endgroup$
    – Ooker
    Nov 13, 2015 at 8:02
  • $\begingroup$ I have rethought my question and slightly edited it. Glad if you come back and see. $\endgroup$
    – Ooker
    Nov 13, 2015 at 10:13
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    $\begingroup$ Many of the papers and texts mentioned above will have a wealth of additional references listed in their bibliographies sections. They're not necessarily ecology-specific, but I've been collecting literature at intersection of information theory & biology/molecular biology. Textbooks that may be applicable: goodreads.com/review/list/…. Similarly journal articles in a shared Mendeley group at: mendeley.com/groups/2545131/…. $\endgroup$ Nov 14, 2015 at 21:48
  • $\begingroup$ Thank you so much. I find the NIMBioS link is extremely useful $\endgroup$
    – Ooker
    Nov 21, 2015 at 9:15

An alternative way to understand this issue has been ultimately named (in its more recent publications) as Organic Biophysics of Ecosystems. Some of their publications (several of them are available either on ResearchGate or on https://interdisciplinaryscience.es/publications) are (If you are interested, I would advise reading the articles in the exact reverse order of time to that shown below).

This approach uses equations whose mathematical structure is simpler than other models in this field, and which are equivalent in structure to those equations used by conventional physics.

Rodríguez, R.A., Riera, R., Herrera, A.M., Duncan, J.M., Vanni, M.J., Delgado, J.D., González, M.J. 2019. Degrees of freedom: Definitions and their minimum and most meaningful combination for the modelling of ecosystem dynamics with the help of physical principles. Ecological Modelling 392: 226−235.

Rodríguez, R.A., Duncan. J.M., Delgado, J.D., Vanni, M.J., Riera, R., González, M.J. 2018. Additional empirical evidence on the intrinsic trend to stationarity in the long run and the nested relationship between abiotic, biotic and anthropogenic factors starting from the organic biophysics of ecosystems (OBEC). Ecological Modelling 383: 23-30.

Riera, R., Rodríguez, R.A. Herrera, A.M., Delgado, J.D., Fath, B.D. 2018. Endorheic currents in ecology: an example of the effects from scientific specialization and interdisciplinary isolation. Interdisciplinary Science Reviews 43(2): 175-191.

Rodríguez, R.A., Riera, R., Delgado, J.D. 2017d. Ecology: Science or philately? An interdisciplinary analysis of sustainability by exploring if it is possible to get more and more information by reducing collateral environmental damages. Science of the Total Environment 596/597: 43−52.

Rodríguez, R.A., Duncan, J.M., Vanni , M.J., Melkikh , A.V., Delgado, J.D., Riera, R., Herrera, A.M., Camarena Luhrs , T., Quirós , A., Fernández Palacios, J.M., Miranda, J.V., Perdomo , M.E., Fernández Rodríguez, M.J., Jiménez Rodríguez , A., Otto, R., Escudero, C.G., Navarro Cerrillo , R.M., González , M.J. 2017c. Exploring the analytical consequences of ecological subjects unwittingly neglected by the mainstream of evolutionary thought. Ecological Modelling 355: 70-83.

Rodríguez, R.A., Duncan, J.M., Delgado, J.D., Vanni, M.J., Riera, R., Herrera, A.M., González, M.J. 2017b Assessment of ecosystem trophodynamic power: A model based on the power equation for an oscillating string. Ecological Modelling 362: 80-86.

Rodríguez, R.A., Duncan, J.M., Riera, R., Delgado, J.D., Quirós, A., Vanni, M.J., Camarena, T., Miranda, J.V., Perdomo, M.A., Herrera, A.M., González, M.J. 2017a. Thermostatistical distribution of a trophic energy proxy: Extension for modelling energy pyramids at the inter taxocene scale and under non stationary conditions. Ecological Modelling 361: 113−121.

Rodríguez, R.A., Herrera, A.M., Duncan, J.M., Riera, R., Quirós, A., Perdomo, M.E., Jiménez-Rodríguez, A., Fernández-Palacios, J.M., Vanni, M.J., Otto, R., Escudero, C.G., Camarena, T., Navarro-Cerrillo, R.M., Delgado, J.D., González, M.J. 2016c. Response to comments on “Uncertainty principle in niche assessment: A solution to the dilemma redundancy vs. competitive exclusion, and some analytical consequences”. Ecological Modelling 341: 1‒4.

Rodríguez, R.A., Herrera, A.M., Quirós, A., Fernández-Rodríguez, M.J., Delgado, J.D., Jiménez-Rodríguez, A., Fernández-Palacios, J.M., Otto, R., Escudero, C.G., Camarena Luhrs, T., Miranda, J.V., Navarro-Cerrillo, R.M., Perdomo, M.E., Riera, R. 2016b. Exploring the spontaneous contribution of Claude E. Shannon to eco-evolutionary theory. Ecological Modelling 327: 57–64.

Rodríguez, R.A., Herrera, A.M., Santander, J., Miranda, J.V., Perdomo, M.E., Quirós, A., Riera, R., Fath, B.D. 2016a. From a stationary to a non-stationary ecological state equation: adding a tool for ecological monitoring. Ecological Modelling 320: 44–51.

Rodríguez, R.A., Herrera, A.M., Riera, R., Escudero C.G., Delgado, J.D. 2015b. Empirical clues about the fulfillment of quantum principles in ecology: potential meaning and theoretical challenges. Ecological Modelling 301: 90–97.

Rodríguez, R.A., Herrera, A.M., Riera, R., Delgado, J.D., Quirós, A., Perdomo, M.E. Santander, J., Miranda, J.V., Fernández-Rodríguez, M.J., Jiménez-Rodríguez, A., Fernández-Palacios, J.M., Otto, R., Escudero, C.G., Navarro-Cerrillo, R.M. 2015a. Thermostatistical distribution of a trophic energy proxy with analytical consequences for evolutionary ecology, species coexistence and the maximum entropy formalism. Ecological Modelling 296: 24–35.

Rodríguez, R.A., Delgado, J.D., Herrera, A.M., Riera, R., Navarro, R.M., Melián, C., Dieguez, L., Quirós, A. 2013b. Effects of two traits of the ecological state equation on our current understanding of species coexistence and ecosystem services. Ecological Modelling 265: 1–13.

Rodríguez, R.A., Herrera, A.M., Delgado, J.D., Otto, R., Quirós, A., Santander, J., Miranda, J.V., Fernández, M., Jiménez-Rodríguez, A., Riera, R., Navarro, R.M., Perdomo, M.E., Fernández-Palacios, J.M., Escudero, C.G., Arévalo, J.R., Diéguez, L. 2013a. Biomass-dispersal trade-off and the functional meaning of species diversity. Ecological Modelling 261/262: 8–18.

Rodríguez, R.A., Herrera, A.M., Otto, R., Delgado, J.D., Fernández-Palacios, J.M., Arévalo, J.R. 2012. Ecological state equation. Ecological Modelling 224: 18–24.

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    $\begingroup$ it's a little weird to respond with just a long list of your own papers. Not that I discourage people with specific expertise from participating, but using expertise to break down a complex topic into a simple and direct answer is preferred. $\endgroup$ Oct 29, 2020 at 21:59
  • $\begingroup$ "Some of their publications (...) are" -- Are what? $\endgroup$
    – Ooker
    Oct 30, 2020 at 3:58
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    $\begingroup$ Hey Ricardo, thanks for the answer and for bringing your expertise to Bio.SE! However, if you don't expand this answer to at least explicitly demonstrate/summarize how any of these papers answer or are are related to the OP's question, then this post will continue receiving negative votes and may even be marked as "spam" (only to promote your work). Please expand your answer so that the OP or future users actually receive an answer without having to leave this webpage. Your citations should remain as a source of additional details, but you need to expand your answer to avoid deletion. Thx! $\endgroup$ Nov 1, 2020 at 1:43

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