An economy is a sociology is an ecology is an energy balance is a carbon balance.
Carrying capacity and Dunbar's number are useful and descriptive ecological constructs.
A related ecological construct that describes the growth, form, volume, and mortality of plant biomass is the -3/2 Power Rule of Self Thinning.
Carrying capacity, Dunbar's number, amount and quality of biomass, renewable energy, sociology, and human economy all ultimately depend on photosynthesis and carbon fixation into plants.
Some abstracts:
(1)
Self-thinning rule: a causal interpretation from ecological field theory"The self-thinning rule relates plant mass to plant density in crowded, even-aged stands by a power-law equation with an exponent −3/2.
The rule is widely accepted as an empirical generalization and quantitative rule that applies across the plant kingdom. It has been called the only law in plant ecology. But the evidence supporting it has recently come under critical scrutiny. The theoretical and empirical bases for the density–mass boundary have been questioned. Here we use ecological field theory and statistical mechanics to show how the stochastic nature of ecological interactions among individuals, due to spatial field effects such as the availability of neighborhood resources at the microscopic level, leads to self-thinning at the macroscopic level. The self-thinning rule emerges as a natural result of our theoretical approach. Puzzling experimental data that contradict the rule are also explained.
Keywords: Ecological field theory; Self-thinning rule; Emerging property; Spatial patterns; Statistical physics"
http://www.sciencedirect.com/science/ar ... 0000003136(2)
Analysis of the 3/2 Power Law of Self-Thinning "The 3/2 power law states that the relative rate of self-thinning with respect to biomass growth per unit area is a universal constant equal to two. The law could be true in two cases: (1) when all factors of stand dynamics unaccounted for by the law (in particular, change in plant form and change in crown closure) are nonexistent; and (2) when the effects of the unaccounted factors on the rate of self-thinning cancel each other. As the presented reasons and evidence show, the major neglected factors indeed oppositely affect the rate of self-thinning. In general, however, these factors rarely balance each other, and the rate predictably changes with age, species, site quality, and other factors. The limiting line of self-thinning does not have any constant slope (on the log-log scale); generally, this line is a curve. A realistic model of self-thinning should be more inclusive than the law and particularly reflect the change in crown closure, or gap dynamics. An analysis of the law suggests the use of tree size as a predictor of their number; the utilization of the fact that diameter is better correlated with crown width and tree number than tree mass; and the development of a more adequate form of expressing allometric relationships than the elementary power function. For. Sci. 33(2):517-537.
Keywords: Allometric regression; Reineke's equation; crown closure; gap dynamics; stand dynamics; tree morphology"
http://www.ingentaconnect.com/content/s ... 2/art00024(3)
A Reevaluation of the -3/2 Power Rule of Plant Self-Thinning "The self-thinning rule predicts that for a crowded even-aged plant population a log-log plot of average plant mass vs. plant density will reveal a straight @'self-thinning@' line of slope--@?. The rule is supported by examples from many individual populations, and by the existence of an interspecific relationship that yields a line of slope--@? in a log-log plot displaying average mass and density data from many populations of different species. I examined and reanalyzed the evidence to evaluate the strength of support for this widely accepted rule. Some problems in fitting thinning lines and testing agreement with the rule have no truly satisfactory solution, but three improvements on commonly used methods were made: the analysis related stand biomass density to plant density because the alternative of relating average plant mass to plant density is statistically invalid; principal components analysis was used rather than regression, because regression relies on unrealistic assumptions about errors in the data; and statistical tests of hypotheses were used to interpret the results. The results of this reanalysis were that 19 of 63 individual-population data sets previously cited in support of the thinning rule actually showed no significant correlation between stand biomass density and plant density, and 20 gave thinning slopes significantly different (P < .05) from the thinning rule prediction. Four other analyses provided additional evidence against a single quantitative thinning rule for all plants: slopes of the thinning lines were more variable than currently accepted, differed significantly among plant groups, were significantly correlated with shade tolerance in forest trees, and differed among stands of the same species. The same results held for the intercepts of self-thinning lines. Despite the failure of the thinning rule for individual populations, the combined data for all populations are still consistent with an interspecific relationship of slope--@?; therefore, the existence of the interspecific relationship does not necessarily support the within-population thinning rule. The within-population and interspecific relationships are apparently different phenomena that may arise from different constraints, so the two relationships should be tested and explained separately."
In my former field of forest ecology, one uses research and practical models including the Langsaeter Curve, Reineke's Stand Density Index, and net and gross Leaf Area Index to analyze and predict growth of individual trees in stands and stands of trees and to develop "rules of thumb" and silviculture prescriptions to translate theory to field. With computers and GIS and spatial mathematics forests can be plugged into the nuances of human environment, economic and social, like never before. Idealistically, forest management is tweaking or passively watching these intellectual constructs mold the forests to desired present and future conditions. While these models all developed separately, the approaches converge on the more general law of plant ecology, the -3/2 Power Rule of Self Thinning. Society can chose to exploit the forest for short turn needs or treat the forest with an agriculture model or adjust humanity with the unfolding patterns of nature. Without plants, we die. In my moral system, humans should be very conservative, even loving, in how we interact with the biosphere. See Nordic's signature line.
The
general case of the -3/2 Rule of Self Thinning applies to even-aged (shared time of initiation) plants ranging from algae to bacteria in petri to lawn to corn to Douglas-fir and relates size and number of individual plants relative to growing space and resources in a closed system. Of course, reality and practice are messy. The Langsaeter Curve (German forestry from early in the science) tells us that forest stands go through periods of stand initiation, free to grow, inter-tree competition, senescence, mortality, and stand renewal by catastrophic or gap dynamic. The -3/2 Rule of Self Thinning applies most to the period of inter-tree competition to mortality.
When one perceives reality as CAFR or other meta-valuations or human institutions in general from the perspective of humanity, we are looking at a system or rather enveloping systems of ecological economics. Messy. We spend our time looking for the right system or the right politic or new science or spirituality to adjust ourselves and attempt to understand or influence with the natural world.
The elephant in the room is that we have over shot "carrying capacity" for the number of people and what we consider reasonable lifestyles. We are in deep doodoo. Humans have caused an extinction event and environmental crisis. Our institutions and the huge masses of people are not responsive, function against one another, and are estranged from nature.. Corporations are not the answer as they fail the biosphere and humanity and free the predator. Like Luther Bissett recently, our best actions as individuals may be to seek a personal relationship and solace with nature.
I mean, I 
