Kullback-Leibler divergence, which guides model evaluation in ecology, also underpins a measure of useful information that works on multiple levels of organization. We propose here to broaden our theoretical framework for exploring the evolution of subsystem correlations focused inward and outward with respect to a hierarchical set of physical subsystem boundaries. These will provide theoretical context for a broad range of "niche-network models", on the level of cells as well as individuals, which might for instance help us monitor the health of communities across levels of organization as well as across species. We're qualified to do this with: (i) help from critical connections across disciplines, (ii) background in the conceptual underpinnings, and (iii) experience with problems spanning multiple scales of space, time and organization.
The first task is to put the underpinning ideas into forms that will be useful across disciplines, and particularly in the biological and social sciences. This is a bottleneck given that important connections remain unknown, except to specialists, even though some were discovered in the late 1800's. Recent work explaining uses for KL-divergence to ecologists by Burnham and Anderson, and work on quantifying cultural evolution by Richerson and Boyd, as well as the widespread use of Bayesian informatics (esp. in molecular biology) will help pave the way.
The second task is to identify ways that this quantitative theory of order emergence and loss on multiple levels of organization can make contact with observation. The layered niche-network models mentioned above are one example. Reduced to a simplex model of layer multiplicity with six positive numbers per individual, they already show considerable potential for addressing current problems by measuring community health in single-species animal and human communities. While development of this proceeds apace "under separate cover", long term goals here are to: (i) strengthen the connection of such models to the overlying theory, (ii) examine sound ways to apply layered-network models to multi-type communities of cells as well as of metazoan individuals, and (iii) examine the utility of multi-layer awareness as an end in itself for expressing idea codes, something it would appear that eukaryotes (in their expression of molecule codes) have already discovered can have amazing results.
The strategy described will help to put biological evolution into a larger physical context, and portray cultural beliefs and scientific observation as complementary elements of sentient communities. The success that eukaryotes have at developing and sustaining individual metazoans, by informing molecular-code expression to multiple layers of organization, might thus be sought for human communities via attention to multi-level consistency in the expression of idea-codes. The need for (and impact of) awareness about media perspectives, and values informed to more than one scale, might be clarified or even quantified thereby.
The approach is deeply integrative. Beyond putting available work into information units, it provides new insight into a wide range of social patterns that have been independently discussed, like division of responsibility between large and small gamete metazoans, redirection of intra-species aggression, etc. In behavioral ecology, the approach may facilitate quantitative comparison of the extent and nature of community cultural-correlations, from one species to another or from one time to another for a given species. Particularly important questions arise when comparing the correlation networks operational in communities where humans evolved, to those networks that humans are being asked to participate in today.
Technical fields as diverse as thermodynamics, economics, anthropology, and the study of complex systems all suggest that a quantitative measure of community health may be important. Such a measure could serve as complement to gross domestic product if human communities make the transition to sustainability. Regardless, absent a concerted focus the rate at which niche layer-multiplicity erodes due to habitat modification and reduced free-energy per capita will likely increase in non-human and human communities. Thus tracking multiplicity may be a good idea.
In thermodynamics, the KL divergence between "ambient and actual" measures distance to equilibrium and (multiplied by ambient temperature) available work.
In ecology and related fields the KL divergence of "model from reality" is useful in ranking models against experimental data, according to the residuals they don't account for.
In communications theory, in clade analysis, and in quantum computing the KL divergence of "uncorrelated from correlated" measures the mutual information associated with fidelity, inheritance, and entanglement.
With this work, we show that the foregoing are special cases of KL divergence as a measure of "useful information". Each is, however, typically applied on only one level of organization at a time. In addition to offering some new and surprising applications, we also show how the most interesting future applications may be more explicit about their relationship to correlations on multiple levels.
A fun fact for physics students: All measurable values of "useful information" may have to be less than the mass of the observable universe times lightspeed squared over 2.715 Kelvin, or about 1092 bits.
