Energy basis for hierarchies in urban and regional landscapes


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Energy basis for hierarchies in urban and regional landscapes
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x, 359 leaves : ill. ; 28 cm.
Brown, Mark Theodore, 1945-
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Environmental engineering   ( lcsh )
City planning   ( lcsh )
Regional planning   ( lcsh )
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Thesis--University of Florida.
Includes bibliographical references (leaves 347-357).
Statement of Responsibility:
by Mark T. Brown.
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The author was fortunate in having Dr. H. T. Odum as major

professor. His special way of perceiving life was an inspiration and

lent insight into understanding the complexities of many new areas of


My supervisory committee included J. F. Alexander, J. P. Heaney,

E. E. Pyatt and E. M. Starnes who contributed to this dissertation

through their time and energy in reviewing drafts and in discussions

of theoretical concepts. Much help was received from C. D. Kylstra

and I. Winarsky, who were of invaluable assistance through their

personal and intellectual support.

Special thanks are due to the graduate students of Systems

Ecology for sharing many new insights and concepts.

Initial drafts of this dissertation were typed by J. Breeze,

proofing and final typing by J. Cox, and drafting by C. Alfonso .

all of whom labored long and hard to bring the manuscript to


Mapping of the South Florida Region and Lee County was supported

under joint contract to the Division of State Planning, Department of

Administration, State of Florida, and the National Park Service, U.S.

Department of the Interior, H. T. Odum principal investigator.

Mapping of the St. Johns region was supported under joint contract to

the Jacksonville Area Planning Board and the St. Johns River Water

Management District, H. T. Odum principal investigator. Initial

studies of the Ft. Myers urban area were funded by Lee County Board of

County Commissioners, the author, and G. V. Genova principal investi-

gators. Preliminary studies of the Gainesville urban area were funded

by the Division of State Planning, Department of Administration, State

of Florida, J. F. Alexander principal investigator.

Support was also received from the Department of Energy on

contract EY-76-5-05-4398 entitled "Energy Models of the United States"

with the Department of Environmental Sciences, H. T. Odum principal



ACKNOWLEDGMENTS ............................................................ ii

ABSTRACT .................................................................viii

CHAPTER 1 INTRODUCTION.............................. ..................... 1

Theoretical Concepts ................................................ 6

An Energy Basis for Hierarchies.................................. .6

Energy Constraints.............................................. 7

Energy Quality and Embodied Energy............................... 9

Energy Quality and Transport Costs...............................10

Energy Quality and Frequency of Energy Sources...................11

Energy Quality and Power Density.................................12

Energy Spectral Distributions of Hierarchies.....................14

Previous Studies of Hierarchy.........................................15

Hierarchy as Concept............................................. 18

Hierarchical Construction and Rate of Evolution..................22

Hierarchical Systems and Connectivity............................23

Hierarchically Organized Systems and Stability...................24

Central Place Theory .............................................25

Settlement Location............................................ 29

Rank Size and Primacy of Cities..................................30

Landscape Evolution............................................ ..32

Social Process Model of Urban Growth.............................33

Hierarchical Distribution of Components in Systems...............35

Hierarchy in Social Systems.......................................37

Computer Simulations of Hierarchically Organized Systems.........42

Description of the Study Area........................................43

South Florida Study Area........................................ 43

St. Johns Study Area............................................ 46

Lee County Study Area...................... .......................47

Ft. Myers Urban Study Area...................................... 47

Gainesville Urban Study Area.....................................48

Plan of Study ......................................................... 48

CHAPTER 2 METHODS........................................................50

General Methods and Definitions.......................................50

Evaluation of Observed Hierarchies....................................55

Regional Analysis .................................................. 55

Land Use Maps ....................................................55

Gross Productivity of Land Uses..................................56

Classification of Cities by Average Power Density................65

Energy Budgets of Regions........................................65

Power Base for Cities............................................67

Investment Ratios....................................... .......68

Analysis of Energy Flow and Structure of Urban Systems ................68

Land Use Maps................................................. 69

Urban Land Use Power Densities...................................69

Average Urban Power Densities....................................75

Structure of Urban Land Uses.....................................75

Development Density and Imports/Exports...............................76

Analysis of Counties within Florida..............................76

Analysis of States within the United States......................77

Analysis of Countries............... .............................78

Embodied Energy Transformation Ratios (Quality Factors),
and the Range of Goods ............................................ 78

Embodied Energy .................................................. 79

Transformation Ratios (Quality Factors)..........................80

Calculation of Transformation Ratios.............................80

The Range of Goods............................................... 83

Simulation Models of Hierarchical Organization and
Energy Spectra.................................................. 83

CHAPTER 3 RESULTS....................................................... 89

Similarities of Differing Systems and Scales..........................89

Regional Hierarchies and Energy Spectra...............................99

Regional Land Use.............................................. 99

Energy Flow and Structure in Regional Systems...................114

The Landscape of Cities within Regions..........................120

The Flows of Energy in a Regional Hierarchy: Lee County........145

Development Density and Import/Exports...............................166

Development Density and Exports of Counties in Florida..........166

Development Density and Exports of States within
the United States.......................................... 187

Development Density and Exports of Countries....................187

Energy Flow and Structure in Urban Systems...........................192

Power Density and Volume of Structure...........................192

Chemical Potential Energy of Urban Land Uses....................198

Transformation Ratio (Quality Factor) of Urban Structure........203

Embodied Energy, Transformation Ratios (Quality Factors),
and the Range of Goods.......................... ..................208

Embodied Energy and Transformation Ratios .......................208

The Range of Transport of Goods.................................211

Simulation of Models of Hierarchical Organization and
Energy Spectra.................................................. 211

Theoretical Models.............................................. 213

Aquatic Food Chain............................................ 239

CHAPTER 4 DISCUSSION ................................................... 275

Rank Size Distribution of Components of Hierarchies..................276

Distribution of Increasing Quality Value in Hierarchies..............276

Evaluation of Embodied Energy and Transformation Ratios in
Hierarchically Organized Systems..................................277

Energy Quality in an Ecosystem Hierarchy.............................277

Energy Quality and Spatial Effect....................................283

Energy Convergence in Landscape Hierarchies..........................284

Energy Divergence (Dispersion) in Landscape Hierarchies..............284

Control Actions of High Quality Components...........................285

The Range of Transport of Goods as a Function of Quality.............286

Primary and Secondary Energy Sources and Their Effect on Hierarchies.287

Frequency of Energy Sources and Time Constants of Components.........288

Stability Through the "Filtering" Actions of Hierarchies.............291

High Quality Stress and Stability....................................293

A Theory of Regional Boundaries Derived from Place in the
Landscape Hierarchy...............................................293

Land Use Planning and Carrying Capacity..............................295

Parting Thoughts and Suggestions for Future Research.................299

APPENDIX 1-DESCRIPTION OF THE ENERGY LANGUAGE.............................301

LAND USE MAPS........................................................ 303



PRESENTED IN FIGURES 3.26 THROUGH 3.53.................................318

REFERENCES ................................................................347

BIOGRAPHICAL SKETCH ................................................ ...... 358

Abstract of Dissertation Presented to the Graduate Council of
the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



Mark T. Brown

August 1980

Chairman: Howard T. Odum
Major Department: Environmental Engineering Sciences

Flows of energy were related to the hierarchical organization

of urban and regional systems to test theories of energy control of

landscapes. Energy models and spectral graphs were used to represent

landscape systems as hierarchical organizations and show common

patterns. Data were assembled from landscapes of Florida and other

systems of the nation.

Regional networks of cities, land use, urban structure, energy

sources, and quality of goods were related to hierarchical

organization. The hypothesis of selection for maximum power was used

to explain the relevance of hierarchical organization of systems,

where spatial extent of components and frequency of energy sources

were related to energy quality and convergence of energy.

The embodied energy inflowing to cities was used as a means of

classifying hierarchical role of cities, and range of region as well

as area of region were calculated. The five classes of cities that

resulted had total embodied energy flow per year in Calories of coal

equivalents (CE) as follows: 182.4 x 1012 Cal CE/yr, 89.0 x 1012

Cal CE/yr, 16.7 x 1012 Cal CE/yr, 4.9 x 1012 Cal CE/yr, and 0.6

x 1012 Cal CE/yr. Range of region was derived by dividing

embodied energy flow of each city by the average embodied energy flow

for the region in which it was embedded, and varied from a high value

of 50.0 miles for the largest city to 2.9 miles for the smallest.

The propensity to import and export was related to the

development density of regions and then position in hierarchy. A

series of nomographs were drawn where exports increased in an apparent

linear relationship with development density. In general, the

nomograph derived suggested the following relationship between exports

and development density:

Exports/sq mi = C x Development Density (expressed as dollars of

Gross Domestic Product [GDP]/sq mi), where C varied from 0.13 to 0.285

depending on the size of region.

The power density and volume of structure associated with 11

different urban land uses were calculated using data from Ft. Myers

and Gainesville, Florida. Volume of structure and power density were

strongly related as both increased simultaneously with increasing

complexity of land uses.

Energy transformation ratios (quality factors) were calculated

for a number of goods and energies from dollar costs per pound and

were used to estimate the range of goods. Quality factors for goods

ranged from 1.3 Cal CE/Cal for finished wood to 2230 Cal CE/Cal for

computers. Ranges (or the distance traveled to obtain a good),

expressed in the number of miles traveled to obtain a pound of good

varied from 0.5 miles/lb for finished wood to 381 miles/lb for

computers. The energy quality of urban structure collectively was in

the range of 20 Cal CE/Cal.

The dynamic properties of 7 configurations of hierarchically

organized models were analyzed through computer simulation. The

models were organized in a five-compartment chain of autocatalytic

consumers with outside driving energy sources. The most stable form

had multiplicative feedback interaction from higher order components

to lower order components, and second order drain on each component.

Other configurations showed marked instability and oscillation when

perturbed away from the steady state solution.

A simulation of hierarchical organization was done using a model

of Lake Conway ecosystem previously evaluated. Simulations tested

were: stocking, harvesting, and pulsing energy source. The simulation

of perturbation responses suggested that stability is enhanced by

hierarchic organization.

The theory of energy control of hierarchically organized systems

provided suggestions for determining carrying capacity of human

activity in regions, and possible effects on the organization of the

landscape with decreasing availability of fossil fuels.

It is suggested that regional landscapes of man and nature form a

hierarchy with qualities measurable from their embodied energy, and

that spatial distribution of quality, value, and human activity may be

predicted from energy distributions.



Complex systems such as ecosystems, industrial processes, and

networks of cities in the landscape appear to be organized in webs of

energy flow with multiple levels of components (Fig. These may

be visualized in simplified form with diagrams as in Fig. 1.1b. The

patterns have spatial manifestations, with many small units converging

energy to a few larger ones (see Fig. Understanding these

hierarchical patterns is a major objective in the sciences of

environmental and human settlement. This dissertation is an

investigation of the relation of energy flows to hierarchies of the

regional and urban landscape.

Energy storage and flows throughout the landscape accompany

spatial hierarchies, as in Fig. 1.2a, and can be represented as

spectra, as in Fig. 1.2b. Theories developed to account for these

hierarchical patterns may be based, in part, on the theory that

systems compete for power, and survive by developing a structure of

energy flows that maximizes useful power. The maximum power principle

was enuciated by Lotka (1922) and additional corollaries were proposed

by Odum (1967, 1971, 1975, and Odum and Odum 1976). The type and form

of web adapting to different combinations of energy from the

environment produces different spectral distributions and spatial

patterns, which may be predicted from simple models.

Figure 1.1 The web of energy flow and components of complex systems.

(a) Showing many small components converging energy to a few large
ones; and

(b) a simplified diagram where like components are grouped, and
hypothetical flows of energy between components are indicated.



Control Action Feedback



Figure 1.2. Hierarchies that develop in a hypothetical landscape as a result of
energy storage and flows.

(a) Spatial hierarchy of hexagonal land areas, where smaller areas
converge energies to larger areas, and larger areas in turn
feed back energies to the smaller ones.

(b) Simplified energy circuit model organized as a chain of
autocatalytic units. Each unit represents all the land area at
each level of the landscape hierarchy.

(c) Hypothetical energy spectral distribution resulting from theory
of successive energy transformations. The general trend is for
landscape hierarchies to be composed of many small components
and fewer and fewer larger components.


Energy analysis diagrams help to relate energy flow and kinetics

of system performance, since they are a way of writing differential

equations that are easy to relate to data on energy flow. The energy

diagrams also help to provide overviews of organizational relation-

ships, and may help to combine concepts of economics, geography, and


In this dissertation data on regional and national patterns of

landscape organization are used to test theories of energy flow con-

trol of hierarchy. Simulation models are developed to quantitatively

relate ideas of mechanism and energetic to web structure, spatial

pattern, and spectral distributions observed in the hierarchies of

humanity and nature. Systems studied were two urban areas in Florida

(Ft. Myers and Gainesville), two large watersheds of Florida (the St.

Johns River Basin, and the Kissimmee Okeechobee Basin), a county in

southwest Florida (Lee County), the national patterns of energy flow,

and for comparison, various other types of hierarchies.

Theoretical Concepts

An Energy Basis for Hierarchies

Given in Figs. 1.1 and 1.2 are simplified energy circuit models

(Odum 1971) that depict energy flow and storage in hierarchically

organized systems. These diagrams show energy flow and control action

feedbacks in five compartment (level) hierarchies, and are the basic

configuration for the organization of data in this investigation of an

energy theory of hierarchically organized systems.

The following concepts and theories about the relationship of

energy, its spatial distribution and resulting hierarchies, are

postulates and are the basis for examining data on systems of Florida

and the nation.

Energy Constraints

Systems operate under the constraints of the First and Second

Laws of Thermodynamics, and Lotka's Maximum Power Principle (Lotka

1922) and corollaries as proposed by Odum (1975) and Odum and Odum

(1976) and are organized in a manner to remain competitive and stable

and increase inflowing energy when excess energy is available.

The organization of complex systems in a hierarchy of energy flow

and control action feedbacks may be a fundamental principle of all

systems of man and nature. As systems concentrate energy and build

storage, gradients of potential energy are created at each level of

concentration; but at the same time, much energy is degraded at each

level as a necessary by-product of production. Thus less and less

potential energy is available at each level to support successive

levels; and a hierarchy may emerge as a consequence of the "Law of

Degradation of Energy."

A basic question that is analyzed in this dissertation that

follows from the law of degradation of energy is "what relationship,

if any, exists between the total energy inflowing to a system and the

distribution of that energy amongst the levels within the system?" To

address this question, regional landscapes, urban landscapes, and a

natural ecosystem are organized as hierarchies and their energy

budgets and the distribution of energy within them are analyzed.

Complex systems not only concentrate energy in landscape

hierarchies, but disperse energy as well through divergence of

feedbacks and control actions. Inflowing energy is concentrated and

converged in successive levels of hierarchies as storage of high

quality energy, and is fed back in dispersing actions from higher

levels to lower ones. In general, as energies are stored and become

more concentrated through landscape convergence, they occupy less

area, but their spatial effect becomes greater. This spatial aspect

of hierarchically organized systems is addressed in this dissertation

by analyzing data from the regional landscapes of south Florida and

the St. Johns Rivers Basin, Lee County, Florida, and by analyzing the

quality and range of transport of various goods.

The principle of selection for maximum power suggests that those

systems that survive in competition with alternative choices are those

that develop the most power inflow and use it most effectively to meet

the needs of survival. Systems maintain competitive position, and

remain adapted and stable by building storage of high quality energy,

feeding back work and control actions from storage to increase

inflowing energy, generating diversity to increase energy inflowing

from other sources, and exporting energies to other systems to obtain

energies that are in short supply. Hierarchical organization of

systems may be a form of specialization that enables the development

of high quality storage that when fed back have higher amplifier

value than their cost. Thus hierarchical organization may enhance the

total systems ability to increase energy inflow, and remain adapted

and stable. The question of stability resulting from hierarchical

organization is addressed in this dissertation by simulating various

configurations of five level hierarchy models and simulating

perturbations of hierarchically organized systems to test recovery and

overall effect of stress.

Energy Quality and Embodied Energy

Odum (1976, 1977, 1978, 1978a) and Odum and Odum (1976) suggest

that there is a quality to energy which is a measure of its ability to

do work. Quality of energy is related to the degree to which it is

concentrated; with dilute energies like sunlight, winds, waves, and

other natural energies having lower quality than the more concentrated

energies of fossil fuels.

The quality of an energy is derived from the embodied energy of

flows and storage that are the result of the convergence property of

systems. Energy quality factors (transformation ratios) are defined

as the ratio of heat energy produced by a system to the total energy

utilized to power the system. As energies are converged in

hierarchies, less heat equivalent energy is produced in successive

levels as energy is dissipated at each level. The embodied energy at

each level is the total energy that powers the entire system; thus the

ratio of embodied energy to heat equivalent energy (quality factor)

increases with each successive level in the hierarchy.

Under the constraints of the Maximum Power Principle, a

theoretical relationship between the costs and the effect of an energy

is related to its quality. The Maximum Power Principle suggests that

systems that maximize their flows of energy survive in competition,

and that surviving systems are those that can generate inflows of

energy at least equal to the costs of doing so. Therefore, in the

long run, the costs of upgrading an energy must at least equal its

effect in causing to inflow more energy.

The quality of many energies and materials are calculated in this

dissertation from embodied energy. Energy quality is related to

position in a regional landscape system and in an aquatic ecosystem,

and is calculated from the total energy required to power each system

as suggested by Odum (1978).

Energy Quality and Transport Costs

In general, as the quality of energies increases, their

concentration increases as well. One theory held by Odum (see Odum et

al. 1976) suggests that transportation costs decrease with increasing

quality of energy as suggested by their increasing concentration.

Since the embodied energy in a good or energy is believed to be a

measure of the quality of that good or energy, it follows that as

embodied energy per unit of good or energy increases, the energy costs

of transportation per unit decreases. Theory suggests, then, that the

greater the embodied energy in a good or energy, the greater is the

range of the good or energy; where range is defined as the distance

over which the good or energy is transported to point of end-use.

Ranges of transport for many goods were related to the quality of

the goods, based on the theory of value of effect (utility) rather

than on a theory of minimizing costs. The embodied energy of goods is

strongly related to the concept of market area as enunciated by

Christaller (1966) for different order goods originating from

different order central places; is shown in this dissertation to be

related to spatial effect in graphs of the spatial distribution of

incoming energies and market areas of cities.

Energy Quality and Frequency of Energy Sources

Recently, Odum (1980) and Alexander (1978) in earlier studies of

the cycles of order and disorder, have suggested that the quality of

an energy is related to its frequency in the time domain. Others (see

Simons 1973) have suggested that frequency and place in hierarchy are

related to the extent that high frequency is associated with low place

in hierarchical order and low frequency with high hierarchical place.

Theory suggests that systems and components of systems may be

adapted to certain frequencies of energy inflow, and that the

magnitude and frequency of energies in the environment may be of

fundamental consequence in selecting which systems survive the test of

time. Examples of adaptation to differing frequencies are common.

Ecosystems and associated structure that live in areas of daily tidal

influence show many adaptations to the frequency of tidal exchange.

Seasonal frequencies in temperate climates control behavior of animal

population, select for certain plant species, and select against


One mechanism for adaptation to certain frequencies of energy

inflow may be the relative time constant of systems. Systems and

components of systems with very short time constants, in general are

associated with high frequency energy inflows, while the reverse is

true for systems with long time constants. Components of systems at

different levels in hierarchies may be adapted to certain frequencies

of energy inflow as a consequence of their time constants. The

general trend is for time constants to increase with increasingly

higher order in the hierarchy.

Adaptation to high frequency may be easier than adaptation to low

frequency; for high frequency energies are believed to be low in

quality, and magnitudes of energies tend to be lower. Thus systems

with long time constants "perceive" high frequency as relatively

constant inflow, but very low frequency inflow may be perceived as

less predictable and "pulsing" in character. Alexander (1978) has

suggested that energies that are considered catastrophic are those

with very low frequency such as earthquakes, volcano eruptions,

floods, and hurricanes; and suggests that adaptation to less

predictable pulses such as these are less common than adaptation to

higher frequency energy inflows.

The relationship of frequency to energy quality and the time

constants of components of hierarchically organized systems is

analyzed in this dissertation using data from the regional landscapes

of south Florida and the St. Johns study areas. Simulations of

different configurations of hierarchically organized models where time

constants are varied and where frequency of inflowing energy sources

are varied are also analyzed to test the relationship of frequency to

time constant of components.

Energy Quality and Power Density

One measure of the intensity of energy utilization in the

landscape is power density (Odum, Brown, and Costanza 1976), or the

rate of energy flow per unit area (Cal/acre year). In this

manner, the energy intensity of one area can be compared on a relative

scale with others. In urban systems, power density is considered to

be the rate of embodied energy consumption per unit area, and in

natural ecological systems of the landscape, power density is the rate

at which energy is fixed, as measured by gross primary production.

While it may seem that two different measures of power are being

applied here, it must be remembered that it is embodied energy that is

being considered, and that there is no difference between production

and consumption. That is to say, if one expressed the output of any

process in equivalent energies of the input, then production is equal

to the embodiment of all input energies.

Urban land-use power densities are expressed as two different

types: electrical and other primary fuels power density, and embodied

energy of goods and services power density.

Total power density of urban land uses is the addition of two

types of energy inflows: that inflowing from electricity and other

primary fuels, and that embodied in goods and services.

High power densities are only possible where there are sufficient

high quality energies inflowing to sustain them. Thus, the degree of

complexity and amount of structure per unit area is in direct

proportion to the amount of high quality energy available. Due to the

convergence of energies in hierarchies, less and less total structure

is associated with higher levels, but the structure in each level is

of a higher quality.

Power densities of urban land uses in the Ft. Myers and the

Gainesville study areas are analyzed in this dissertation and compared

to structural properties as well as place in hierarchy, and a quality

factor (transformation ratio) is calculated for urban structure as a

whole. A classification scheme that is based on power density is

developed for cities and is related to market area (as proposed by

Christaller 1966) and support area.

Energy Spectral Distributions of Hierarchies

The complex systems of multiple levels of components appear to be

organized in webs of energy flow. However, when visualized as chains

of energy flow, as in Fig., much of the complexity disappears and

a useful overview appears. Viewed, as in Fig. 1.1b, complex systems

may be simplified as energy chains where energy is transformed in

series. In each step some energy is used, some is dispersed, and some

energy is upgraded in quality and passed on to the next unit in the


In various recent publications, Odum (1977, 1979; and Odum and

Odum 1976) suggests that systems are organized in hierarchical fashion

to increase total power flow by cascading energy up the chain and

control actions back down. Low quality energies are concentrated,

increasing their quality, and passed on to the next step in the chain.

An energy spectrum results that has many downstream components and

fewer and fewer upstream components. When graphed, as in Fig. 1.2,

the organization exhibits a declining exponential function when energy

per unit is plotted against the number of units having that energy


If additional higher quality energy sources are available in the

environment, then systems develop whose energy sources are a mixture

of high and low quality, and the spectral distribution may not show a

simple exponential decay. High quality sources are utilized in the

system where their quality nearly matches that of the energy intensity

of the units in the spectrum (Odum 1979). A spectrum results that has

a "hump" where the second higher quality source is introduced, as

shown in Fig. 1.3.

When regional landscapes are organized as a hierarchy of

components, higher quality energy sources such as fossil fuels and the

goods derived from them, are seen to inflow and interact at levels in

the hierarchy where their quality nearly matches the quality of the

components at that level. Models of regional landscapes developed in

this dissertation incorporate this feature, and theoretical models are

developed to test the theory that energy spectral distributions are

altered significantly when secondary, high quality energies are

introduced into hierarchical organizations.

Previous Studies of Hierarchy

Many theories for hierarchical organization, and the resulting

distributions of components, dating from antiquity, are presented in

the following section. In all, the theories, observations, and

explanations presented in this review comprise a general overview of

hierarchy theory, spatial distribution in hierarchies, regional

economic theory as it relates to hierarchy, hierarchy in social

organization, geographic models for hierarchically organized

landscapes, and various other aspects of hierarchically organized

systems. Few previous studies have dealt with the energy control of

landscape hierarchies, but may with the economic aspects and some with

the physical constraints of hierarchical organization.

Figure 1.3. Energy spectrum that results from the introduction of a second
energy source of higher quality. Theory suggests that the second
higher quality source is introduced where its quality nearly
matches that of the units in the chain.


S\ 04

1000 2000 3000
1000 2000 3000





z 10 -




Z i -




Hierarchy as Concept

Hierarchy denotes a mode of thought that asserts order into a

conception of the universe in terms of precisely arranged levels of

organization. Usually the levels are vertical in dimension from

small to large; many to few; simple to complex. Plato provided a

basis for hierarchic levels of existence in what has been termed "the

principle of plentitude," which is to say that the levels of existence

are interlocked so as to yield a full universe. This principle sets

the stage for an infinite universe (The Dialogs of Plato, translated

by B. Jowett).

Aristotle, on the other hand, conceived of a finite universe

where "nature proceeds little by little from things lifeless to animal

life in such a way that it is impossible to determine the exact line

of demarcation, nor on which side thereof an intermediate should lie"

(Historia Animalium, Book VIII, Chapter I, p. 558a, translated by D.

W. Thompson).

The conception of a hierarchically organized universe was made

explicit by numerous writers during the Renaissance, and given a new

descriptive phrase the scale of nature" (Milton, Paradise

Lost, Book V, line 9, p. 113), yet still very much grounded in the

ideas of Plato and Aristotle.

During the Middle Ages hierarchy played an important role,

especially in the work of Saint Thomas Aquinas, where he suggests that

formal distinction always requires inequality. "Hence in natural

things, species seem to be arranged in degrees; as the mixed things

are more perfect than the elements, and plants more than minerals, and

animals than plants, and men than other animals; and in each of these

one species is more perfect than others (Summa Theologica, First

Part Question 47, Article 2, vol. 2, p. 260).

This concept of hierarchy entered the eighteenth century deprived

in most instances of its religious overtones, as Locke wrote of the

"Chain of Being" in An Essay Concerning Human Understanding (1690).

".. the species of creatures should also, by gentle degrees, ascend

upward from us as we see they gradually descend from us

downwards" (Book III, Chapter VI, Article 12, vol. 2, p. 217).

Gradually the concept of hierarchy was extracted from its narrow

confines as an explanation of the "Creator's Order" and scientific

thought prevailed. With the publication of The Origin of Species in

1859, Darwin converted the traditional "Scale of Nature" into a

hierarchical system which for all intents and purposes was a system of

classification only, not a reflection of reality. In his summary to

Chapter 14 Darwin states I have attempted to show that the

arrangement of all organic beings throughout all time in groups under

groups--that the nature of the relationships by which all living and

extinct organisms are united by complex, radiating, and circuitous

lines of affinities into a few grand classes, all naturally

follow if we admit the common parentage of allied forms ." (Darwin

1859, p. 456).

By the turn of the twentieth century the term hierarchy was in

frequent use; from taxonomy to models for a hierarchical universe. As

the amount of published scientific literature has grown exponentially

in the last 80 years so has the number of scientists using the term,

the idea, the concept, in the analysis of physical, biological and

social systems (Whyte 1969). Most notable in the latter years are:

Woodger, Whyte, Von Bertalanffy, Simon, Wilson, Weiss, and Laszlo.

Woodger (1937) defined the principles of hierarchical order using

mathematical logic, and previous to this (Woodger 1929) suggested an

"organismic theory" of biology where the organism is a hierarchical

system. Further, he says that ". the organism is a hierarchical

system with an organization above the chemical level that

requires investigation at all levels ." (Woodger 1929, p. 14).

Whyte (1949) calls for a "unitary principle" of nature that could

account for the development of regular spatial forms. The principle

states that asymmetry decreases in isolable (capable of being

isolated) processes. Whyte treats nature as processes rather than as

objects or products and concludes that nature is a disturbed system of

systems, and there is never anywhere a final end to process. He sees

systems as being parts of other more extensive systems that develop

their own inner symmetry always in relation to their next larger

system, and so to conform to the general state of the universe.

The hierarchical mode of organization is suggested by Von

Bertalanffy (1932) as a fundamental principle of biological law, and

becomes a major principle of his General System Theory. In later work

Von Bertalanffy (1933) identified four types of hierarchical order:

division hierarchy, spatial hierarchy, genetic hierarchy, and

hierarchical segregation. Most recently he suggests two possible

divisions of hierarchy: structural and functional hierarchies, but

hints that "In the last resort, structure and function may be the very

same thing ." (Von Bertalanffy 1968, p. 27).

Simon (1962) in his paper "The Architecture of Complexity"

suggests that complexity frequently takes the form of hierarchy, and

defines a hierarchical system as a system composed of interrelated

subsystems, each of the subsystems being in turn hierarchic in

structure until we reach some lowest level of elementary subsystem.

Laszlo (1972) suggests that all living things are phases in the

organization of the biosphere, and that they are wholes in one cut and

parts in another, and their own parts are systems on their own level,

and even their parts are that, until one scrapes the bottom of the

hierarchy with the atom and its elementary particles.

Whyte (1969) traces the idea of hierarchy from Plato's sequence

of higher and lower levels to the present, and suggests that the time

has arrived for the gradual development of a comprehensive physical

theory of the structural hierarchies of nature. He goes on to suggest

that structural hierarchies are more easily understood in terms of

discrete particles, rather than by using a field or continuum

representation. Here Whyte is using particle as Bunge uses level.

Bunge (1960, 1969) addresses the subject of hierarchy by enumerating

the use of the term level. He identifies nine different meanings for

the notion of level, but considers an appropriate definition of level

to be grades of being ordered, not in arbitrary ways, but in one or

more evolutionary series. He limits the use of the notion of level to

include both the idea of emergence in time without restricting the

direction, and the fact that level structure need not be restricted to

linear gradation but can be parallel or branched.

Mesarovic and Macko (1969) generate a mathematical theory of

coordination within hierarchical systems based on linear programming

models of minimizing overall costs by deriving values for local

control and input (at sublevels). They contend that the explanation

of the functioning of a hierarchical system should not be attempted in

terms of the overall goal, but rather in terms of the specific goals

valid for each particular level. Further, they suggest that a

frequently made mistake is to assume the highest level unit is in

charge of the overall goal. It has its own goal that of

coordination and the overall goal is achieved only by the

combined action of all units.

Hierarchical Construction and Rate of Evolution

Simon (1962, 1973) argues that the advantage of modularization as

outlined in the image of two watchmakers, one who makes watches in

modules, the other assembling watches element by element, suggests

that complex systems evolve far more quickly when hierarchically

organized. Simon (1973) states:

Specifically, on the simplest assumptions, the mathematical
model shows that if a system of K elementary components is
built up in a many-level hierarchy, and S components, on the
average, combine at any level into a component at the next
higher level, then the expected time of evolution for the
whole system will be proportional to the logarithm to base S
of K. In such a hierarchy, the time required for systems
containing, say, 1025 atoms to evolve from systems
containing 1023 atoms would be the same as the time
required for systems containing 103 atoms to evolve from
systems containing 10 atoms.

Another property of hierarchical systems is that they are nearly

decomposable. Decomposable systems (as outlined by Simon 1962, 1973)

are systems that can be broken up (in thought or analysis) into

subsystems such that the interactions within the subsystem are

relatively strong and numerous. Wilson (1969) calls the boundaries

along which systems can be decomposed natural interfaces, and suggests

that these interfaces can also be identified through the existence of

some form of closure. There are two forms of closure: tropological

closure the encompassing by closed surfaces of a spatial

neighborhood that coincides with or bounds the extension of a physical

object, and temporal closure a type of closure associated with

a neighborhood in time that coincides with or bounds the donation of

an entity. He suggests that a group may be defined not only by

interactions, but by operations and defines these as cyclical closure.

Levels may also be distinguished by a characteristic time or

frequency, which is to say that each level is temporally closed; thus

space and time are forms of closure.

Hierarchical Systems and Connectivity

A fundamental property of systems is their connectivity, or the

number of subsystems and the strength of their interaction. Levins

(1973) argues that any collection of interacting subsystems will

naturally evolve away from a homogeneous (uniform) totally connected

network (considered to be maximum complexity) to simple, persistent

relations, that are hierarchical in nature. These hierarchical

relations within a single network will overlap with like relations in

other networks causing dynamics that again will be too complex, and

which in turn will evolve into new hierarchical simplifications. This

complexity of connectivity is self-limiting, such that any small scale

connections that do not become hierarchically organized lose


Platt (1969) gives theorems of boundary conditions effecting

connectivity, and the relationship of boundary conditions to internal

structure of subsystems within networks. He suggests that when

comparing systems of different sizes (complexities) that connections

with the environment that are carried on over the whole boundary

surface at one level of sizes are carried on through specialized gates

at higher level sizes, and that the number of connections of any

system (subsystem) in general has a lower dimensionality than the

number of nodes within the subsystem itself.

Hierarchically Organized Systems and Stability

Levins (1973) suggests that low connectivity (and thus a high

degree of hierarchical organization) gives high repeatability,

allowing such systems to be selected. Thus, natural selection results

in a hierarchical structuring of clusters of components. At any level

components within the same cluster interact strongly, but different

clusters interact only loosely.

Weiss (1971), using variance to describe stability, suggests that

the total variance of a whole system is infinitely less than the sum

of the variances of its aggregate/components. The total system

preserves a high degree of invariability. He suggests that stability

results from hierarchically derived coordinating interactions, for

with incessant erratic fluctuations of components' local environments

total harmonious performance is impossible.

In general, overall increases in the level of organization tend

to increase cybernetic stability of systems and the diversification of

their properties, and structural instability and decreasing numbers

(Laszlo 1972). Thus, structural stability is proportional to

primativeness in level of organization, whereas cybernetic stability,

manifested as an increasing variety of self-stabilizing functions and

properties, is proportional to complexity. Laszlo (1973) gives the

example of complex organisms, such as mammals, as being more

vulnerable than protozoa, but are able to cope with environmental

changes that could be lethal to the latter.

Central Place Theory

Walter Christaller in 1933 (1966), suggested a basic theory to

answer the questions: Why do urban hierarchies exist, and what

determines the size and spacing of cities and the configuration of

their market areas in such hierarchies? To control extraneous

variables in answering these questions, Christaller made some

simplifying assumptions: First, he assumed identical consumers

distributed uniformly over an unbounded plane, and second, access

between all points of the plane was equally easy in any direction.

Therein lies much of the criticism of central place theory.

Christaller's conceptual framework may be summarized in six


1. The market town's main function is to provide goods and services

for the surrounding market area, and those market towns are

located centrally within their market areas.

2. The more goods and services provided, the higher is the order of

the central place.

3. Low order goods (convenience goods) that are purchased frequently

are provided by low-order places because the maximum distance

consumers will travel (range) is small.

4. Higher-order places are fewer in number and are more widely spaced

than lower-order places providing goods with greater ranges.

5. Consumers have a basic desire to travel as little as possible to

obtain the goods and services they need, and producers must have a

minimum sales level (depending on the range of the good) to make a

profit. Thus, a hierarchy of central places exists to facilitate

both consumer and producer.

6. Hierarchies have three spatial forms, organized according to:

1. A marketing principle

2. A transportation principle

3. An administrative principle

The marketing principle assumes that the location of a central

place of any order is at the midpoint of each set of three neighboring

places of the next higher order. Thus, a hexagonal market area was

derived where the corners of the hexagon are occupied by centers whose

order is one less than the order of the center at the centroid of the

hexagon. This first principle generated a rule of 3, or each center

of a higher order is surrounded by the equivalent of 3 market areas of

the next lower order.

A satisfactory transportation system is difficult to establish

under such a spatial organization. To accommodate transportation

networks, Christaller adjusts his original thesis somewhat so that the

distribution of central places is most favorable when as many

important places as possible lie on one traffic route between two

important towns. By shifting centers from the apex of the hexagon to

the midpoints of the sides of the hexagon, a nesting of hexagons

inside one another according to a rule of 4 is achieved (for every

center of a given order there will be 4 market areas of the next lower

order, and 3 places of the next lower order). But another problem

arose: the overlapping of smaller regions across the boundaries of

higher-order complementary regions is inconsistent with administrative

organization. To solve this dilemma, the central place of

higher-order administers to the total area of the six surrounding

low-order market areas, thus following a rule of sevens.

August Losch (1954) took Christaller's model one step further;

still assuming, however, a wide homogeneous plane containing only

self-sufficient farms that are regularly distributed in a hexagonal

pattern. He then showed how an economic landscape could be built from

the lowest order centers upwards.

Losch thought it desirable because of the complexities of the

real world, to devise a compound hierarchy incorporating all the

possible arrangements of hexagons. An economic landscape around a

single metropolitan center resulted. The landscape was divided into

six city-poor and six city-rich sectors surrounding each metropolitan


Both Christaller and Losch agree that the triangular/hexagonal

arrangement of production, or consumption sites represented the

optimal spatial organization for a single good. Their fundamental

difference is in the way spatial patterns of centers and market areas

are built. Their theories of spatial patterns among cities are based

on three concepts: range, threshold, and hierarchy.

These theories do not help to understand the interrelationships

between the size and spatial structure of the regional urban hierarchy

and regional growth. Richardson (1973) states that this difficulty

arises from the fact that there are no satisfactory theories for

explaining how hierarchies evolve, for Christaller's central place

theory, and Losch's market areas have no serious dynamic content and

thus have little value for exploring the regional growth process.

The critics of central place theory have identified at least four

specific weaknesses (see Beckmann 1955; Van Boventer 1969; Henderson

1972; and Timbergen 1968). First, central place theory assumes a

homogeneous plane. Second, it assumes a uniform geographical

population distribution, with no adjustment made for uneven population

distribution and greater local demand of large urban areas. Third,

interurban trade is unidirectional, i.e., large urban areas export to

smaller areas, but smaller areas do not export to larger ones. And

fourth, the rigid spacing is inconsistent with this uneven demand

generated by different sized urban areas.

Henderson (1972) developed a linear programming model which

eliminates uniform population distribution, and allows two-way trade.

Dokmeci (1973) presents a linear programming model that allows two-way

trade, and transport costs are minimized subject to cost constraints.

Purver (1975) developed a mixed integer linear programming model which

determines the optimal spatial allocation of productive and

residential activities in a central place framework. The model allows

two-way trade and eliminates uniform population densities.

While central place theory does not address adequately the

question of how hierarchies evolve, it does address why they evolve.

The cornerstone of central place theory is economies of scale; which

provide the only incentive for urban areas to arise in the central

place model.

Theorists have used gravity models and equations of diffusion for

allocating regional influence of centers and calculating the spread of

innovation from center to center; and more recently the use of

information theory to suggest the probability of spatial diffusion

(see Mansfield 1963; Beckmann 1970; Berry 1972; Hagerstrand 1966;

Isard and Peck 1954; and Beckmann 1956). However, while these models

do address the question of gradients, and flows of information from

center to center, there still remains the question of how hierarchies


Settlement Location

Since the first explicit statement of a regional urban hierarchy

by Christaller (1966) in 1933, much empirical evidence has been

gathered and analyzed to support the concept of a hierarchically

organized landscape of urban centers. Early models of spatial

interaction like those of Reilly (1929) and Tuominen (1949),

suggesting that the pull exerted by a place varies directly with its

size and decreases outwards with distance, were the beginning of

settlement location theory. Known as regular cluster models, they

suggest that smaller places are not likely to develop as close to

large places as they are to one another. Empirical evidence of

clustering is not conclusive; however Brush (1953) and later Dacey

(1962) analyzing hamlets in Wisconsin, found that clustering of

hamlets was apparent in areas furthest from larger towns.

Spacing of settlements is shown to be linked to the size of

settlement by Brush and Bracey (1955) in studies of settlement

patterns in Wisconsin and southern England. Later studies by Olsson

and Persson (1964) and Thomas (1961), using regression analysis, show

strong correlations between size of city and spacing for regions in

Sweden and Iowa.

The tendency of the landscape to have hierarchy is widely

observed. It is a common observation that there are very many small

cities and fewer larger cities in regions, and that the larger cities

provide a greater variety of goods and services than do smaller

cities. This is the fundamental organization principle of the central

place models of Christaller (1966) and Losch (1954). Using the notion

of threshold of a good, Berry and Garrison (1958a) have shown how

hierarchies arise in the landscape, and given satisfactory explanation

of a hierarchy of shopping centers within urban areas.

Rank Size and Primacy of Cities

Zipf (1941) and Stewart (1947) have suggested that there is a

mathematical relationship between rank of cities and population size.

Zipf's relationship takes the form of

Pr =

That is, the population of the rth ranking city, Pr, equals the

population of the largest city, P1, divided by rank r raised to an

exponent which generally has a value very close to unity. This

relationship was derived empirically, but Zipf argued that when it

held for an entire country, it indicated that national unity is

maintained through an integrated urban system.

At approximately the same time, Jefferson (1939) suggested the

concept of the primate city or where the largest city is several times

greater in population than the second ranked city. Other authors have

applied the term to whole distributions of cities (see Redfield and

Singer 1954).

MacArthur (1957) suggested an approach to the study of the

structure of animal communities by rank-abundance curves, by plotting

rank (commonest to rarest) on the abscissa and abundance on the

ordinate. A semi-log graph was used that resulted in straight line

graphs much like those observed by Zipf for cities. In later work by

Hutchinson and MacArthur (1959) a mathematical model was constructed

in which the properties of the niche of different species are defined

by numbers of kinds of different environmental elements. The model

implied few very small species with a rapid increase in number of

species up to a modal size and a slow decline in number to unity as

the size increased. When data for mammal fauna were graphed, a

relatively good fit with the model was approached, but many later

papers found poor fits.

Rank size irregularities have been associated with the existence

of integrated systems of cities in advanced countries by Berry and

Garrison (1958) and Beckmann (1958). Others have suggested that

primacy be associated with over urbanization, colonial economies, and

subsistence and peasant economies. In all, the regularities suggest

relationships between urban centers, and differences in regularity are

noticed with different economic and cultural structures, but the rank

size, and primacy relationships are not theoretical models and little

theoretical evidence is given as to why, or how these relationships

exist, except to suggest that there is a close correlation with rank

size regularities and the hierarchical landscape postulated by


Landscape Evolution

Leopold and Langbein (1962) suggested a theory of landscape

evolution based on entropy expressed in terms of probability of

various states. Essentially they introduce the concept that the

distribution of energy in river profiles tends toward the most

probable and that such profiles approach the condition in which the

downstream rate of production of entropy per unit mass is constant.

Drawing from the theory of Prigogine (1955), they introduce the

principle that stable stream systems must correspond to the stationary

state of any open system where the rate of production of entropy per

unit volume corresponds to a minimum compatible with the conditions

imposed on the system. Hence, a stable river system corresponds to

the principle of least work. They suggest the river channel has the

possibility of internal adjustment among hydraulic variables to meet

the requirement for maximum probability, and those adjustments tend

also to achieve minimization of work. While they were dealing

primarily with river profiles and the hydrologic character of

landscapes later theorists have suggested that the same concepts apply

to the landscapes of cities (see Woldenburg 1968, 1969, 1970;

Woldenberg and Berry 1967; Curry 1967; Semple and Golledge 1970;). In

general, current urban geographic theory suggests that urban systems

minimize entropy production by the "least work principle" (or least

effort as theorized by Zipf, 1949), and that spatial hierarchical

order is a function of the probability of all possible states.

Inherent in their theory is the assumption that urban system compo-

nents operate under constraints of competition, and that considerable

competitive advantage is gained with entropy minimization.

Berry (1972) suggests that central-place phenomena maintain

open-system equilibria as a result of allometric growth, and this

property is the result of continued energy inflows. Curry (1967)

suggests that frequency analysis and diffusion characteristics of

particles in space have relevance in understanding central place

phenomena, and processes of urban growth.

Social Process Model of Urban Growth

Park, Burgess, and McKenzie (1925) defined the processes of urban

growth (and in a general sense the evolution of landscape hierarchies)

as: concentration, centralization, segregation, invasion, and

succession, operating at all levels of aggregation. Their hypothesis

was that competition and the reciprocal benefits resulting from

exchange of goods and services are the basis for community.

A brief discussion of each of the five processes summarized from

McKenzie (1925), follows. Concentration: McKenzie (1925) defined

concentration as the tendency of an increasing number of persons to

settle in a given area or region to facilitate the most efficient

spatial distribution for the utilization of natural resources. Size

and stability are functions of food supply and role in the wider

environment through production and distribution of commodities, which

both are determined by the community's competitive status.

Centralization: centralization is described as a temporary form of

concentration, implying a congregation of people in a locality for a

definite purpose. It is the process of community formation. Thus,

civilization is a product of centralization. McKenzie (1925) states

that local points of centralization are in competition with other

points for the attention and patronage of the inhabitants of the

surrounding area and are in a temporary stage of unstable equilibrium

with other competing centers. The degree of centralization, then, is

a measure of its competitive status under prevailing cultural and

economic conditions. Segregation: Economic factors are the basic

attribute for selection and thus segregation of activities,

populations, and structure. Under competition, differentiation and

segregation result as a sorting and selecting process for the most

advantageous location and status. Invasion: Invasion is applied to

all factors-populations, structure, communities, or utilities; it is

the process of group displacment. It may involve population

displacement, or the encroachment of one area of segregation upon

another. Again, its main driving force is competitive status of

groups in relation to other groups of like kind. Succession:

Succession results from invasion. However, not all invasion results

in succession. There are generally considered to be four stages to

succession. The first is invasion, followed by reaction or

resistance. The third stage is the influx of the new group, and

fourth, climax or the achievement of a new equilibrium. In general,

invasion and the resulting successional stages can be brought about

with almost any type of change in the physical, economic, and to a

lesser extent, social factors. These changes result in competitive

advantage of one group over the existing group.

These theories generated the concentric-zone hypothesis of urban

form as outlined by Burgess (1930). It proposed that a city can be

divided into a series of five concentric circles. 1. central business

district; 2. zone of transition; 3. zone of workingmen's homes; 4.

middle class zone and 5. the commuters' zone.

Hierarchical Distributions of Components in Systems

In 1927, Pareto (1971) defined human society as a hierarchical

collectivity, and postulated what was termed Pareto's Law on the

distribution of income. Using the number of individuals receiving

incomes at or above a certain amount plotted against the amounts of

these incomes (in other words, a cumulative distribution), he derived

the following relationship:



log N = log A a log X

where N represents all the number of individuals at or above a

certain income limit, X, and A and a are constants. When log N was

plotted against log X, a straight line was obtained with slope (a)

equal to approximately -0.2.

Pareto asserted that the law was true for all countries and for

all times and deduced from it that, owing to the rigidity of the

distribution, there was only one way to increase economic welfare

(i.e., the share of the poorer classes in the national income), and

that was to increase total production of the economy.

Zipf (1965) in later work based on his original rank size

distribution of cities (Zipf 1941), found much the same relationship

as Pareto when he graphed empirical data of such things as: number of

businesses versus number of businesses of like kind, number of

employees versus number of specific occupations, and as mentioned

earlier, size of cities versus their rank. Zipf's number-frequency

relationships have the same form as do those of Pareto, and are

expressed by the equation:

log Y = C a log X

where Y is the number of individuals in any class X, and C and a are


Both Pareto and Zipf suggest that these relationships indicate a

measure of organization and that departures from straight line slopes

indicate disunity (Zipf 1941) or inequality (Pareto 1971).

Odum, Cantlon, and Kornicker (1960) postulated a hierarchical

organization of ecological communities using a cumulated logarithmic

species-diversity index, where the number of occupational niches are

related on a per capital support basis. They suggest that the

hierarchy postulate explains why the species-diversity index is a

measure of organization at the macroscopic level, since the equations

for each are similar.

Hierarchy in Social Systems

A classical theory of social organization is outlined by Weber

(1946, 1947) for formally organized causal systems such as

bureaucracies. Weber theorized that the size of administrative

structure is a direct function of increasing size of organization, and

that there is a very strong relationship between the size of an

organization and the division of labor; the larger organization, the

more subdivided are the responsibilities.

Later empirical studies by Blau and Schoenher (1971) and Blau,

Heydebrand, and Stauffer (1966) suggest two generalizations that

confirm Weber's theories on the organization of social systems: first,

that increasing size generates structural differentiation in

organizations along various dimensions at decelerating rates; and

second, that structural differentiation in organizations enlarges the

administrative component.

Weber's chief concern was of the administration of nation-states

and other large scale undertakings, such as armies and political

parties. A question that was at the center of his work was how to

design an efficient organizational structure for such large scale

systems. And, thus, the Bureaucratic Model evolved which he described

as a technically superior instrument for accomplishing complex tasks

(Weber 1947). Inherent in the model was the concept of hierarchy; in

that, a highly bureaucratic organization must have a firmly ordered

hierarchy of both structure and channels through which decisions and

information flow from lower to higher levels.

Weber's Bureaucratical model dominated social organization theory

until the open system (or natural system) model of organizations

suggested by Thompson (1967). His model does not take the environment

as a given, but assumes that an organization's environment is a major

force that shapes its goals, structure, and survival. Thompson's book

(1967) was a turning point in social organization theory with the

incorporation of such environmental concepts as natural selection,

resource utilization and scarcity, and efficiency; and treats the

various characteristics of organizational structure (hierarchy,

specialization, and so forth) as both internally generated, and as a

response to organizations' adaptations to their environments.

Monane (1967), in his book A Sociology of Human Systems, defines

social systems as open systems whose internal structure of components

are organized in a hierarchical fashion, where power increases and

number of individuals decreases as one moves up the social hierarchy.

In his model of social action Monane (1967) outlines the effects of

increasing populations. Social interaction increases at a much faster

rate, the number of parts and degree of specialization increases,

rules become more formalized, variation in norms increases, deviate

behavior increases, the ratio of formal norms to informal norms

increases, the number of levels in the influence and authority

hierarchies increase, the number of authority rank systems increase,

the problems of interactions vertically in the same hierarchy or

between hierarchies increases, the potential for conflict and friction

among the parts increases, the number of coordinative problems and the

need for coordination increases, and decentralization of authority

increases, but at the same time the most influential parts may

maintain or increase their influence.

The previous study offers little to further understanding of how

and why hierarchies exist, although Monane suggests that a significant

feature of component action is the tendency to cluster in particular

areas of a social system rather than to be evenly distributed

throughout. He suggests that clustering heightens action; and an

amplification spiral will emerge as components who want a great deal

of contact move closer to one another.

Aldrich (1979) proposes the following definition for social

organizations: goal directed, boundary-maintaining, activity systems,

and suggests what he terms a Population Ecology Model for

organizational development. Borrowing heavily from ecological theory,

the model represents an attempt to explain the process underlying

change. Aldrich refers to his model as a natural selection model, and

emphasizes that the primary objective of all organizations is to work

toward a better fit with their environment, by manipulating the nature

and distribution of environmental resources. Using the concepts of

Emery and Trist (1973) in categorizing environments, Aldrich presents

two types of environments and two types of resource distributions that

have direct effects on the complexity and survival of organizations.

Environments are either stable or unstable, and resources are

distributed either in a concentrated or dispersed manner. Thus, there

are four types of environment/resource patterns: stable environments

with concentrated resources, unstable environments with concentrated

resources, stable environments with dispersed resources, or unstable

environments with dispersed resources.

Recent theorists (see Aldrich 1979; Weick 1976; Glassman 1973;

Landau 1969; and Buckley 1967) portray organizations as

loosely coupled, hierarchic systems. Loose coupling is a central

characteristic of social organizations and such systems exhibit

relative independence of momentary environmental change (Glassman

1973). Due to hierarchic organization and weak connections between

some system components, loose coupling and hierarchic structure are

important system properties of social organizational structure because

they help us to understand the emergence and persistence of complex

forms and strategic adaptations made by individual organizations

(Aldrich 1979).

Weick (1976) listed seven advantages of loose coupling for


1. Loose coupling allows portions of the organization to persist

and evolve independently of other parts.

2. Loose coupling provides an organization with a selective

sensing mechanism.

3. Loose coupling is an excellent system for allowing local

adaptations of organizational subunits.

4. Loosely coupled systems permit the retention of a greater

number of mutations and novel solutions than do tightly

coupled systems.

5. Loose coupling permits the confinement of a breakdown in one

part so that it doesn't affect the rest of the organization.

6. Loose coupling may permit greater self-determination by

persons in organizational subunits.

7. A loosely coupled organization could be relatively

inexpensive to operate.

Blau (1972) showed that hierarchic structure of organizations

increased with increases in size and complexity, based on his analysis

of five types of work organizations: government employment security

offices, government finance offices, department stores, universities

and colleges, and hospitals. But Glassman (1973) suggests that

hierarchy is often a consequence of constraints imposed by

governments. Under these circumstances, hierarchy is not a result of

organizational adaptation to local environments, but rather a

consequence of constraint from above. Glassman states this is

particularly true of the social services sector, and gives as an

example the specification of the Comprehensive Employment and Training

Act of 1973, that federal, state, and local components were to be

arranged in a hierarchy of authority.

In all, the Population Ecology Model of Aldrich (1979) leads to

the expectation of finding highly similar forms of organizations in

similar environments. Similar social structural conditions, resource

distributions, and environmental exigencies should lead to convergence

of highly adaptive forms (Aldrich 1979), and that two central

characteristics of complex social organizations are hiererchic

ordering of subunits and loose coupling of components.


Computer Simulations of Hierarchically Organized Systems

Smith (1970) simulated models of three and four trophic levels

connected in series with and without internal recycling, to show the

effects of enrichment in mathematical models of aquatic systems.

Using digital simulation, he found, in general, that enrichment had

decreasing effect on trophic levels from plants to predators.

Comparison between the three trophic level model and that of the four

levels showed that the above trends were somewhat reversed in the four

trophic level model.

Overton (1975, 1977) has applied a hierarchical structure to

modeling of the Coniferous Biome. Ecosystems are decomposed into

sub-units in a hierarchical manner, and mathematical models are built

of the sub-units finally connected back again to achieve a whole

system model.

Using a digital simulation technique, Costanza (1979) modeled the

spatial growth of land use in south Florida, which resulted in

computer-generated maps of embodied energy intensity. The resulting

maps of land use embodied energy intensity had relatively good fit

with historical growth trends, and generated a spatial hierarchy of

land use.

In an earlier study, Costanza (1975) mapped incoming energies of

both natural and fossil fuel origin and overlayed these with land use

to show the distribution of land use within landscapes that results

from the spatial character of incoming energies.

Description of the Study Areas

Shown in Fig. 1.4 are the three regional areas of Florida and

two urban areas that were investigated in this dissertation. The

boundaries of the St. Johns study area correspond to the district

boundaries of the St. Johns River Water Management District, and those

of the south Florida study area correspond to the district boundaries

of the Central and South Florida Flood Control District as they were

in 1973. The boundaries of Lee County are the political boundaries,

and the study area limits for each of the urban areas of Ft. Myers and

Gainesville were drawn where the concentrations of urban land use

diminished into the natural landscape that surrounds (see methods

section for details of boundary conditions for urban study


South Florida Study Area

South Florida is an area of intense urban development along both

coasts with an extensive wetland system of marshes and swamps in

between. Its coastal areas are the basis for attracting seasonal

influxes of tourists that support a large segment of the economy.

Previous studies (Odum and Brown 1976) indicate that the economy of

south Florida is largely a tourist economy with nearly 33% of the

total income coming from these sources. Agricultural sales amount to

6.2% of the income, and industrial sales 21.9%. The study area

encompasses approximately 16,670 square miles.

In the last 20 years south Florida has experienced very rapid

growth, with current populations estimated to be approximately 3.6

million people. Because of the attractiveness of coastal locations

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and the extensive areas of marsh and swamps in the center, urban

development has been confined to a narrow strip along the east coast

stretching from the Palm Beaches to Miami, where population density

averages 4500 people per square mile, and to the southwest coastal

areas of Naples and Ft. Myers (population density 1340 people/sq mi).

The central area of the Kissimmee River Basin is mostly agricultural

lands, with improved pasture the predominant use. South of Lake

Okeechobee and immediately adjacent to it are extensive areas of muck

agriculture where sugar cane is the main crop.

The ports of Miami and Port Everglades in Ft. Lauderdale are

international shipping ports. Miami receives and ships chiefly trade

goods many of which originated and are destined to South America,

while Port Everglades is the main port of entry in south Florida for

refined oil.

St. Johns Study Area

The St. Johns study area is an area of moderate urban development

with agriculture and forestry inland, and drained by one major river.

Jacksonville on the northeastern coast is the major city and has port

facilities for international trade. The coast has areas of intense

development around Jacksonville, Daytona, and Titusville where tourism

is a major industry. Inland, the landscape is a diverse mosaic of

agriculture, forestry, urban development, and natural lands.

The study area encompasses approximately 11,930 square miles and

has a population estimated at 2.7 million people, giving a gross

population density of 230 people per square mile. The largest

population densities are around Jacksonville (4280 people/sq mi),

Daytona (1950 people/sq mi), Gainesville (2950 people/sq mi), and

Orlando (1200 people/sq mi).

Lee County Study Area

Lee County is located on the southwest Florida Gulf Coast. The

Caloosahatchee River flowing from Lake Okeechobee to the Gulf bisects

the county and empties into and supports with contributions of

nutrient rich waters a very productive estuary. The coast is lined

with numerous islands all surrounded with mangrove and some high

energy beaches on the extreme Gulf side.

The county has two predominant locations of population density,

the city of Ft. Myers on the Caloosahatchee River and Ft. Myers Beach

on an island in the Gulf. The area is retirement oriented with

numerous developments throughout the county that attract retired

workers from the north.

The economy is predominantly a tourist economy, with large

contributions from transfer payments, and some agriculture sales.

Experiencing recent very rapid growth, the county population is now

approximately 215,000 people with a population density of 280 people

per square mile.

Ft. Myers Urban Study Area

Ft. Myers is located in Lee County, Florida, on the banks of the

Caloosahatchee River in southwest Florida. The county seat of

government, Ft. Myers, is also the major commercial center for the

surrounding counties of Hendry, Charlotte, and north Collier, as well

as a center of higher education, having southwest Florida's only

community college.

The city has a major regional airport and is serviced by rail

transport and planned interstate highway. With such transportation

links the city is the major center of tourist influx and agricultural

exports for southwest Florida.

Gainesville Urban Study Area

Gainesville is located in Alachua County in central Florida. The

county is an agricultural county with Gainesville the only major

metropolitan concentration of population. Gainesville is also a

county seat of government, and a center of higher education, having

the University of Florida.

The city is the major commercial center for surrounding counties

of Levy, Gilchrist, Marion, Putnam, Clay, Bradford, and Union.

Located adjacent to the city is a major regional airport and

interstate highway, affording easy transportation links to other

metropolitan areas to the north and south.

Plan of Study

In this study the hierarchical organization of the landscape

and resulting energy spectrum of energy storage and flow were

investigated at three levels: the regional level of ecosystems and

urban land uses, the organization of cities in the landscape, and the

organization of land uses within cities. In addition, the relation-

ship of intensity of development to the spatial area of influence was

investigated at different levels of organization in the nation, the

state, and within districts of the state. The specific plan for the

analysis of regions, districts and subdistricts is as follows.

First, maps were made of ecosystems and land uses at two levels

of study; the regions of Florida and cities within these regions;

Spectra of energy storage and energy flow were calculated from power

density data and land-use information.

Second, energy spectra for many different types and sizes of

systems were constructed to understand general trends of energy flow

and storage.

Third, generalized models of each urban land-use type were

evaluated, and a generalized hierarchical model of urban land uses was

drawn and energy flows between levels or sectors of the urban system

were evaluated.

Fourth, specific analysis of the external energy requirements of

areas of different sizes, and an energetic evaluation of the range of

goods and services (or threshold of goods and services) was


Fifth, a series of theoretical models of hierarchical

organization were simulated on analog and digital computers to explore

different energy flow and storage characteristics under different

organizations and pathway configurations. Then data from an aquatic

ecosystem of Florida were used to test theories of hierarchical

distribution and resulting energy spectra.



General Methods and Definitions

A graphic language is used throughout this dissertation to

describe energy flow and interaction in complex systems. The language

is a graphic means of depicting systems as Nth order differential

equations, since each symbol represents a mathematical relationship of

either energy flow, interaction, or storage relative to time. Given

in the appendix is a description of the language and accompanying

mathematical equations. For a complete description of the language

and its development see Odum (1960, 1967, 1971, 1973, and 1976).

Simple diagrams are drawn of many systems to help organize thinking

and show what energy flows and interactions are of most importance,

while in the section on simulation of theoretical models of

hierarchically organized systems, the diagrams are used as a means of

writing differential equations to be programmed on the computer.

The flows of energy through the landscape are measured in heat

Calories. However, Odum (1976, 1977, 1978) suggests that energy has a

quality associated with the degree to which it is concentrated. High

quality energies are those that are more concentrated and thus can do

more work per unit of heat energy, while low quality energies are more

dispersed and can do less work per unit of contained heat energy. In

this dissertation, energies are presented in both their heat

equivalents and in terms of their quality by expressing them in

Calories of Coal Equivalents (Cal CE). By converting energies to coal

equivalent Calories, all energies are expressed in the same form whose

ability to do work is familiar. Given in Table 2.1 are the energies

used in this study, and their equivalence factors, as well as their

quality expressed in Calories of coal equivalents.

The energy embodied in goods and services is one measure of their

quality, and is found by summing up all the energies that are used in

making a good or service. In most instances, because of the

complexities involved in tracing back through the production process,

it is not possible to directly account for all the energy that is

embodied in a good or service. Thus, Odum (1976) suggests that when a

purchase of goods and services represents a purchase of an average mix

of the goods and services in the national economy, a conversion factor

from dollars to energy may be used. The conversion factor is

calculated using equation (2.1).

7t= Zt (2.1)

where X = Total energy use in the U.S. including embodied energy of

the environment in Cal CE, Y = U.S. Gross National Product, and Zt =

Cal CE/$ in year t.

Since energy use and GNP are changing, and since inflation

affects the relationship between energy and money, a conversion factor

is needed for every year. Given in Table 2.2 are conversion factors

of representative years for converting the dollar costs of goods and

services to Calories of embodied energy.

Table 2.1. Energy transformation ratios (quality factors) used in this study.

Transformation ratio
Energy type Footnote Cal CE/Cal

Sunlight a 1/2000

Sugar of gross production
still distributed over
the landscape a 1/200

Wind a 1/27

Wood still distributed
over the landscape b 1/2.2

Coal a 1/1

Finished wood b 1.3

Ocean waves reaching shore a 1.35

Gasoline b 1.4

Elevated water a 1.5

Tide a 1.6

Water purity a 1.8

Natural gas b 2.0

Electricity a 4.0

Food (except meat) b 4.4

Steel b 4.4

Meat b 15.0

Misc. goods b 75.0

Phosphate a 293

aFrom Odum 1980.
bCalculated as part of this study. See Table 3.31.











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Evaluation of Observed Hierarchies

The trends of hierarchical organization and energy spectra were

graphed semi-logarithmically for systems of differing scales and

complexity. Data were gathered from various sources in the literature

and from various local, state, and federal agencies in published

reports and in some cases unpublished data.

Regional Analysis

Three regional areas of differing character and size were

analyzed for total energy budgets, land use, and resulting

hierarchical organization: the Kissimmee Everglades Basin in south

Florida, a subtropical region of relatively intense urban development;

the St. Johns River Basin, a region on the coast of central Florida

dominated by a major river, and agricultural lands with moderate urban

development; and Lee County, Florida, an area in southwest Florida

that is a coastal county with extensive tourism and an agricultural

base inland. This county has experienced recent, very rapid urban


Land Use Maps

Land use maps for the St. Johns Basin and Lee County were con-

structed from aerial photographs at a scale of 1:77, 117 or approxi-

mately 1 inch equals 1 mile. Photographs used were false color infra-

red and black and white infrared photographs taken in 1973. The land

use map for the south Florida region was prepared during previous

studies (Odum and Brown 1976). Land use categories for each of the

regional areas are given in Table 2.3 and descriptions are given in

Appendix 2. Land use areas were delineated directly from photo

graphs and transferred to controlled base maps, and then reduced to a

scale of 1:250,000 (for south Florida and the St. Johns basins) and

enlarged to a scale of 1:80,000 (Lee County, Florida). Presented in

Figs. 2.1, 2.2, and 2.3 are examples of specific areas of each map at

their original scales since the format of the original maps precludes

their inclusion, and reductions are so small as to make worthless any

information they contain. The regional map of south Florida, and the

Lee County map are published elsewhere (see Odum and Brown 1976) and

the regional map of the St. Johns study area may be obtained from

either the St. Johns River Water Management District office in

Palatka, Florida, or the Center for Wetlands at the University of

Florida, Gainesville.

Land use areas were measured in the following manner: south

Florida maps were cut up and weighed on analytical balance, where a

conversion factor of grams/acre was used to convert from weight to

area; St. Johns River Basin Maps were cut up and a leaf area index

machine that measures area using light sensitive photocells was used

to measure area directly. A conversion from square centimeters to

acres was necessary to convert machine measured area to acres of

land use. Lee County areas were cut up and measured in the same

manner as those for the south Florida study area.

Gross Productivity of Land Uses

Published estimates (see Odum and Brown 1976) of gross primary

production for natural ecosystems were used for natural and

Table 2.3. Land use classification system used in mapping regional areas.

South Lee
System St. Johns Florida County

Urban Open land x x x
Recreation x x x
Residential (low density) x x x
Residential (medium density) x x x
Residential (high density) x x
Industrial x x x
Mining x
Commercial and services x x x
Institutional x
Transportation x x x
Utility and communicative x x

Agricultural Improved pasture x x x
Cropland x x x
Citrus groves x x x
Nursery and speciality crop x
Confined feeding operation x
Planted pine x
Clear-cut areas x
Sugar cane x x

Natural Grassy scrub x x x
Sand pine scrub x x
Sandhill community x
Pine flatwood x x x
Xeric hammock x
Mesic hammock x x x
Swamp hammock x
Hardwood swamp riverinee) x
Riverine cypress x
Cypress dome x x x
Bayheads and bogs x x x
Wet prairie x x x
Freshwater marsh x x x
Rivers and streams x x x
Lakes and ponds x x x
Reservoir x x x
Borrow pit x
Tidal flat x x x
Beach and dune x x x
Coastal hammock x
Salt marsh x x x
Mangroves x x x
Spoil bank x

Table 2.3. (continued)

South Lee
System St. Johns Florida County

Medium-salinity plankton estuary x x x
Oligohaline system x x x
Neutral embayment x x x
Marine meadow x x x
Coastal plankton x x x
High velocity channel x x x
Oyster reefs x x
Coral reefs x x
Emerging new systems associated
man x x

Figure 2.1. Detail of land use map of the south Florida study area, showing the
land uses of the coastal region around the Palm Beach area.
Numbered land use classification systems and descriptions of land
use categories are given in Appendix 2. Approximate scale: 1 inch
equals 4 miles.

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Figure 2.2. Detail of land use map of the St. Johns study area, showing the
land uses of the coastal region around Daytona and New Smyrna Beach
and inland. Numbered land use classification systems and
descriptions of land use categories are given in Appendix 2.
Approximate scale: 1 inch equals 4 miles.


04O I 2 3 MILES




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Figure 2.3. Detail of land use map of Lee County, Florida, showing the land
uses in the vicinity of Ft. Myers and the Caloosahatchee River.
Numbered land use classification systems and descriptions of land
use categories are given in Appendix 2. Approximate scale: 1 inch
equals 1 mile.

agricultural land uses (see Table 2.4). Urban land use power

densities were calculated from studies in Ft. Myers and Gainesville,

Florida (see Analysis of Energy Flow and Structure of Urban


Classification of Cities by Average Power Density

An average city power density was determined for all cities

within each region by using averages derived in detailed studies of

the two urban areas, Gainesville and Ft. Myers, Florida (see overall

power density of urban study areas). The area of each city is not

necessarily the actual area within legal city limits, rather it is the

area that when viewed from aerial photographs that is contiguous with

all urban land uses. In some cases this area may be smaller than

actual city limits, and in other cases where suburban sprawl is

evident, the area may be considerably larger.

Energy Budgets for Regions

The energy budget of a region is made up of renewable energies of

sunlight, winds, tides, waves, and rain; and nonrenewable sources of

fuels, goods, and services. Renewable energies are calculated using

methods developed in previous studies of regions (see Odum and Brown

1976) and the calculations are given as notes to tables. Nonrenewable

energies are calculated from land use power densities and fuel

consumption data for each region.

Energy flow and the energy in structure may be expressed in two

ways. First, it may be in actual heat Calories that are associated

with the flow or storage. And the second is to express the flow or

storage in embodied energy (sometimes referred to as sequestered

Table 2.4. Estimates of gross primary production (GPP) and total structure
associated with ecosystems of south Florida landscape (from Odum and
Brown 1976).

Subsystem Subsystem
gross productivity structure
Subsystem x 106 CE/acre yr x 106 CE/acre

Improved pasture 5.1 24.7

Vegetable crops 21.3 294.8

Tree crops 9.6 74.9

Sugar cane 22.2 313.1

Grassy scrub systems 4.0 16.5

Pineland systems 6.4 80.1

Hardwood systems 7.7 235.9

Lakes and ponds 1.4 7.4

Cypress domes and
strands 7.3 214.5

Wet prairie 5.4 51.6

Scrub cypress 5.8 61.3

Freshwater marsh 7.4 228.7

Sawgrass marsh 8.1 273.7

Beach and dune
systems 0.3 4.0

Salt flats 0.3 4.0

Scrub mangroves 1.0 7.2

Saltwater marsh 5.0 29.5

Mangroves 7.3 218.4

energy) and reduce the energies to equivalents of one type such as

coal equivalents. Energy transformation ratios (quality factors)

given in Table 2.1 are multiplied by the heat Calories of the

particular flow or storage, thus converting heat Calories to coal

equivalent Calories (CE Cal). Energy transformation ratios are

expressed as Cal CE/Cal heat for the particular energy or


Power Base for Cities

The land area surrounding a city that is necessary to average the

power density of the particular city to that of the region is

considered to be the range of the city and is the area that is

required as a power base for the processing and upgrading of dilute

natural energies. Once the average power density of the overall

region is known, city ranges or their power base areas were determined

by dividing total inflowing embodied energy for each type of city by

the regional average power density as follows:

Rt = (2.2)

where E = Total inflowing embodied energy (Cal CE/yr), P = regional

average power density (Cal CE/acre yr), and Rt = area of range

of city in year t.

Spatially, the areas are mapped using circles of the proper

dimension to encircle each city by calculating diameter from area of

range. The resulting map of each of the regions graphically describes

the interaction of high quality fossil fuels and natural resident

energies, or the concept of investment ratio.

Investment Ratios

The investment ratio is a measure of the matching of high quality

energies with lower quality resident energies, under the theory that

when ratios are high, high quality energy is being used in excess, and

may be doing lower quality tasks where lower quality energy may be

better utilized. The ratio is expressed as Calories of high quality

energy per Calorie of low quality energy; both expressed in embodied

energy of one type.

It = -E (2.3)

where E = calories of high quality energy, S = calories of sunlight

energy, and It = Investment ratio in year t.

A regional energy budget expressed in this manner becomes a

measure of the fossil fuel based energy intensiveness of the region.

Investment ratios for regions were calculated using equation (2.3)


Analysis of Energy Flow and Structure of Urban Systems

Two urban areas were analyzed in detail for total energy

budgets and power densities, energy budgets and power densities of

land uses within the urban areas, and resulting hierarchic

organization of the urban landscape: Ft. Myers, Florida, an urban

area on the southwest coast of Florida whose main economic inputs are

from tourism, and is a government center and Gainesville, Florida, an

urban area in central Florida that is a governmental center, and

center of university education.

Land Use Maps

Land use maps were drawn from aerial photographs at a scale of 1"

= 2000'. Table 2.5 lists the land use classification used.

Photographs used were black and white infrared aerial photographs

taken in the following years: 1973 for the Ft. Myers urban area, and

1974 for the Gainesville urban area. The study areas were delineated

from the photographs where contiguous areas of development were

considered to be part of the urban areas whether or not they fell

inside of city limits. All area measurements were based on this area

rather than on published data of the area within official city limits.

Ground truthing of land use maps was done by windshield survey.

Measurements of areas from land use maps was done by cutting the

individual land uses from the map and weighing on an analytical

balance. A conversion factor was used to derive area in acres from

weight of paper.

Urban Land Use Power Densities

Power density is a measure of energy flow per unit of time per

unit of area. In this study power density is expressed in units of

Cals CE/acre year. Power density is expressed as the addition of

energy consumption of fuels and electricity per unit area (referred to

as direct power density), and consumption of the energy embodied in

goods and services per unit area (referred to as indirect power

density). Total power density results from the addition of both of

these types of input energies. The generalized land use model in Fig.

2.4 was used to evaluate energy consumption by land use.

Table 2.5. Land use classification system used in mapping the urban study areas
of Gainesville and Ft. Myers, Florida.

Map code System name

1 Cleared land
2 Recreation and open space
3 Low density single-family residential
4 Medium density single-family residential
5 High density single-family residential
6 Low density mobile home
7 Medium density mobile home
8 High density mobile home
9 Low density multiple-family residential
10 Medium density multiple-family residential
11 Commercial strip
12 Commercial mall/shopping center
13 Central business district (CBD)
14 Industrial
15 Transportation terminals
16 Power plants and utility
17 Schools
18 Universities and community colleges


19 Improved pasture
20 Cropland
21 Citrus groves
22 Planted pine


23 Grassy scrub
24 Melaleuca
25 Sand pine scrub
26 Sandhill community
27 Pine flatwood
28 Xeric hammock
29 Mesic hammock
30 Swamp hammock
31 Hardwood swamp riverinee)
32 Riverine cypress
33 Cypress dome
34 Wet prairie
35 Freshwater marsh
36 Rivers and streams
37 Lakes and ponds
38 Reservoir and borrow pits

Figure 2.4.

Generalized land use diagram used to evaluate power densities of
urban land uses. Flows A through G are expressed in embodied
energy of the same type (Cal CE).

Direct power density = D + E

Indirect power density = F

Total high quality power density = D + E + F

Total heat calories used = H
D + E + F
Investment ratio = A

Ratio of high quality to low quality energy = A + B + C

Total embodied energy of product = G


The average direct power density for each of the land use

classifications were calculated by first selecting a representative

sample of structures in each of the land use types, and then obtaining

yearly energy consumption data from local utility records for each of

the selected structures. A mean yearly energy consumption for typical

structures in each of the land uses was calculated, and when

multiplied by the number of structures in a land use area gave the

total direct energy consumption of that land use. The total direct

energy consumption of a land use was then divided by the area (in

acres) of the land use area to obtain the direct power density.

Energy consumption data were taken from Regional Utility Board of

Gainesville-Alachua County and Gainesville Gas Corporation billing

records in the Gainesville, Florida, study area. Billing records of

Florida Power and Light Corporation were used for the Ft. Myers,

Florida, study area. There were no central natural gas distribution

companies in the Ft. Myers area, and very little gas is consumed in

southern Florida (Division of State Planning 1976). Thus, natural gas

consumption was not considered to make up a large portion of the total

energy consumption of the land uses in the Ft. Myers study area.

The consumption of gasoline by vehicular traffic within each land

use was not used to calculate power densities of land uses, but was

used to calculate overall power densities of urban areas (see average

urban power density).

In general, the sample size of structures within each of the land

use categories was ten percent (10%). However, the large number of

residential consumers necessitated a different sampling technique.

Ten examples of each residential land use type were selected and ten

(10) structures within each of these types were used to calculate

average consumption of direct energy. A 10% sample size of commercial

structures in the commercial strip category was used to calculate

average direct energy consumption. Commercial malls and shopping

centers were considered separate land uses from that of the commercial

strip, and since there were only three such land uses in each of the

study areas, a 100% sample size was used. A 10% sample size was used

for the central business district (CBD) and that of industrial land

uses, of each of the study areas. A 10% sample size of schools was

used, but since there was only one university in each study area (they

were considered to have different functions and thus power densities

than that calculated for the land use category of schools) and energy

consumption data for each was readily available, power density was

calculated directly.

Indirect power density was calculated for the land use categories

in the Ft. Myers study area only. A detailed model of energy flow

between the main sectors of the local economy for the year 1973 was

evaluated to obtain the energy embodied in goods and services that

were consumed in the residential, commercial, industrial, and

construction sectors of the economy. Evaluation of the flows of

dollars between sectors of the economy were used and converted to

embodied energies using a conversion factor of 21,000 Cal CE/$.

Embodied energy in goods and services that were consumed in each

of the subcategories of residential and commercial land uses were

derived by assuming that goods and services consumed were proportional

to that portion of the total direct energy that was consumed by each

subland use category.

Average Urban Power Densities

The overall power density of each of the study areas was obtained

by adding transportation energy consumption to direct energy

consumption and embodied energy of goods and services consumed by land

uses. The total area of each land use was multiplied by its

appropriate power density, thus giving the energy consumption by land

uses within the urban area. The energy consumed in transportation was

added to this figure to obtain total energy consumption, and divided

by the area within the study area to obtain average urban power


A ratio of land use energy consumption to energy consumed in

transportation was derived to facilitate the calculation of power

densities of all urban areas in each of the regions in the regional

analysis section.

Structure of Urban Land Uses

The structure associated with each land use was calculated for

the Gainesville urban study area in the following manner. Property

tax records of the City of Gainesville were used to evaluate the

assessed value and total square feet of structure for different land

uses. The same structures for each land use type that were used in

the calculation of power densities were used to evaluate the average

structure (expressed in both cu ft and in Cal CE per acre of different

land uses). The energy embodied in structure was calculated by

multiplying the assessed value (assessment is 100% in the City of

Gainesville) by a conversion factor of 20,000 Cal CE/$ for 1973. The

conversion factor is an estimate of the total energy in the U.S.

economy divided by the U.S. Gross National Product for 1973. The

actual conversion factor is 19,600 Cal CE/$ (see Table 2.2), but

rounded to 20,000 Cal CE/$ for this study.

The volume of structure associated with each of the land use

categories in the Ft. Myers study area was derived by measuring the

square feet of structure from aerial photographs at a scale of 1" =

2000' for approximately a 10% sample of all structures in all land use

categories. Using heights of structure that were derived from

windshield survey, volume of structure was calculated by multiplying

area of structure by average height.

Development Density and Imports/Exports

One measure of production and consumption in regional systems

is gross domestic product (GDP) as determined from the total flow of

dollars within a regional economy. While domestic product is not

always available for regions, it may be determined from employment

data and averages for productivity per employee in each economic


Analysis of Counties within Florida

Gross domestic products for 15 counties in Florida were

determined from employment data, and "development density" was

calculated by dividing GDP by land area of each county.

Location quotients (or what might be called export multipliers)

for each county were determined in the following manner: employment

data for eight broad economic sectors (agriculture, manufacturing,

wholesale and retail trade, government, services, transportation and

public utilities, banking and finance, and construction) were obtained

from Bureau of Economics and Business Research (1978) for each county.

Percent employment by economic sector was determined and compared to

the same data for the U.S. economy. Departures from the U.S. percent

employment were considered to indicate that portion of each economic

sector that was export employment (for a detailed discussion of

location quotients and methods, see Heilbrun 1974).

Exports were determined by multiplying number of export employees

in each economic sector by the productivity per employee for that

sector. Productivity per employee was determined from Florida State

data obtained from the Bureau of Economics and Business Research

(1978) by dividing domestic product in each economic sector by the

number of employees in that sector. It was assumed that local

differences in employee productivity were negligible.

Analysis of States within the United States

Gross domestic product was determined as in the county analysis

except that U.S. data were used for employee productivity.

Development density was determined by dividing GDP by the area of each

of the selected states. Export multipliers, and total exports were

determined using state employment data obtained from the U.S. Dept. of

Commerce, Bureau of Census (1977) and using the method outlined for

the above counties.

Analysis of Countries

Gross domestic product and exports were obtained from United

Nations (1977) for 21 selected countries. No calculations are

necessary since published data are available directly.

Embodied Energy, Transformation Ratios (Quality
Factors), and the Range of Goods

One basic principle of central place theory that explains how

the locational patterns of cities lead to the broad dispersion of

market towns or central places of differing sizes throughout the

landscape in hierarchies is the principle of interdependence of

urbanization and trade. It is believed that cities are the

instruments by which the specialized regions of a national economy are

tied together, and that the main function of cities is to provide

goods and services for surrounding market areas.

Other essential features of central place theory concern the

range and thresholds of goods and services provided by market places.

The range of a good is the distance a consumer is willing to travel to

obtain the good, and therefore, they can be thought of as having some

inherent "quality" or ordering. Convenience goods and other goods

that are purchased frequently are considered to be low-order goods,

while goods purchased less often, or goods of a specialized nature are

considered higher-order goods.

The threshold of a good or service is the minimum sales level

necessary for the seller to make a profit. Generally, the greater

range of a good, the greater is the threshold.

Another way of ordering goods is to order according to the energy

that is embodied in the good. As mentioned earlier, the maximum power

principle as enuciated by Lotka (1922) and amplified by Odum (1967,

1971, 1975) and Odum and Odum (1976) suggests that energy is utilized

in the functions and productive processes of systems only if outputs

from these processes, when fed back, cause to inflow to the system at

least as much energy as their cost. This suggests then, that the

energy that is embodied in goods and services is, in some manner,

proportional to the energy realized when the good or service is fed

back in the economy.

Embodied Energy

Previous work by Odum and others (see Odum 1980, and Odum and

Brown 1976) has developed the embodied energy in energy sources and

some goods that appear in Table 2.1. Where embodied energies for

goods and energies did not exist, they were calculated from the dollar

costs using the appropriate conversion factor from Table 2.2. Current

retail dollar costs per pound of material were obtained from various

sources under the assumption that retail costs reflect all energies

that are embodied in a good, including those of human labor, up to the

point of final demand. When dollar costs per pound are multiplied by

the dollar to energy conversion factor listed in Table 2.2, the result

is energy in Calories CE per pound of material.

Tranformation Ratios (Quality Factors)

The transformation ratio has the dimensions of Cal CE/Cal heat

and is one measure of the quality of a good or energy. Transformation

ratios were calculated for a number of goods and energy by first

calculating embodied energies, second evaluating actual energies (or

heat energy), and third dividing embodied energies by actual energies.

The resulting ratio has the dimensions of Calories of embodied energy

per Calorie of heat energy as in equation 2.4 below:

T = (2.4)

where EE = Calories of embodied energy in coal equivalents, EH =

Calories of heat (as measured by free energy), and T = transformation

ratio in Cal CE/Cal.

Calculation of Transformation Ratios

Transformation ratios were calculated as shown in Fig. 2.5, using

the general equation above 2.4. When the ratios are determined for

large aggregates of systems, slight variation in the general method

described above is necessary to avoid double counting. In Fig. 2.5

the feedback (B) is partially fossil fuel energy, and partially

environmental energies that are upgraded through environmental

systems. To avoid double counting, the environmental energies are

subtracted from the total feedback energy, if they are significant.

In Fig. 2.5, that portion of the feedback energy (Af) that is

the result of the upgrading of the lower quality energy from the left

(A) is subtracted from the feedback pathway (B).

Figure 2.5.

Diagram showing the general method for calculating transformation
ratios. The portion of the feedback energy (Af) that is directly
from the low quality energy inflow at the left (A) is subtracted
from the feedback pathway (B).





A +(B-Af)



The Range of Goods

The range of selected goods was calculated from embodied energy

per pound and the energy costs per pound to ship by most common

carrier from retail distribution point to end use point. Most

consumer goods were assumed to be transported by private automobile,

and most building products, industrial tools, and electronic equipment

by truck. Odum (1976), using the data of Hurst, estimated that the

average energy costs per mile for private automobile, including the

high energy value of the driver to be 5.4 x 103 Cal CE/mile. A

similar value for truck transport was used. By dividing embodied

energy/lb by energy cost/lb mile, range is determined.

Simulation Models of Hierarchical Organization and Energy Spectra

A series of theoretical models were simulated on both digital

and analog computers to test hypotheses and evaluate structure and

characteristic properties of systems organized in hierarchical

fashion. As the models grew in complexity and insight was gained, a

final model that was a synthesis of previous models was simulated

using data from the literature for an aquatic ecosystem.

Models were drawn using the energy circuit language and computer

programs were written directly from the graphic model. The facilities

of the Northeast Regional Data Center on the campus of the University

of Florida were used for digital computer simulation, and Dynamo

Simulation language (Pugh 1970) was used. Some models were simulated

on an EAI Miniac analog computer. Digital programs for each model are

given in Appendix 5.

Since the energy circuit language is a way of writing

differential equations in graphic form, the differential equations for

each model may be taken directly from each diagram. They are written

separately for convenience as well. The simulation models had one

thing common to all. Each is a chain of five (5) autocatalytic

components, connected in series. Differences in the successive models

are in the kinetics of the connections between components; with the

first models having simple linear flows between components, and later

models being more complex.

Figures 2.6 and 2.7 show autocatalytic components that have

constant flow energy sources as examples of computer programming. In

Fig. 2.6 the differential equation, Forrester Diagram (Forrester

1963), and Dynamo equations are given for the energy diagram. In Fig.

2.7 the differential equation and analog diagram are given.

Figure 2.6.

Example of Forrester diagram (Forrester 1963) and Dynamo equations
for digital simulation of a simple autocatalytic module, expressed
first as an energy language diagram.



JR -= Jo
I + (CQ)

Q = k|JRQ k2JRQ k3Q -k4Q



L Q.k = Q.J + DT(J,.Jk J2.Jk J3.Jk J4.Jk)
R Ji.kL = k *JR.k *Q.k
R J2.kL = k2*JR.k*Q.k C k = Coef
R J3.kL = k3*Q.k C k2 = Coe
R J4.kL = k4*Q.k C k3 = Coe

A JR I= +(Co0Q.k)

N Q = Initial Condition


C k4 = Coefficient
C Co = Coefficient

Figure 2.7. Example of differential equation and analog diagram for analog
simulation of simple autocatalytic module.



I + (CoQ)
Q = kIJRQ k2JRQ k3Q k4Q




Similarities of Differing Systems and Scales

Empirical evidence of hierarchical trends in large scale,

complex systems of the landscape are presented as energy spectra in

graphical form, where the number of units in each level of the

hierarchy are graphed on the vertical axis, and the power per unit (or

power density per unit) is graphed on the horizontal axis. The

systems depicted are complete networks of components, where it is

clear that there is some directional flow of energy that is

concentrated from dilute sources to more concentrated uses at

differing scales of the landscape.

Figure 3.1 is an energy spectrum of cities in Florida. Zipf

(1941), using population and rank of cities, described a frequency

distribuiton that existed for cities in the United States and other

countries. He empirically reasoned that all countries that exhibited

internal unity would have a distribution with slope -1; and that

departures from this standard slope suggested disunity. Wherever

there were departures from the standard slope, i.e., where the slope

was not smooth, but tended to vary either positively or negatively

from the ideal, he suggested that forces were in operation that would

Figure 3.1.(a) Energy spectrum of cities in Florida graphed semi-logarith-
mically, showing the trend of frequent occurrence of low power
cities and less frequent occurrence of the very high power
cities in the landscape.
(b) Log-log plot of the energy spectrum of cities in Florida, after
Zipf (1941), showing a negative slope of approximately 1.

Notes to Fig. 3.1.

Data on population of incorporated cities of the State of Florida are from
the Bureau of Economic and Business Research, University of Florida (1977).
Power density is calculated from population data by multiplying city population
by 2.5 x 105 Cal CE per capital per year, which is the average energy
consumption per capital in the U.S. in 1973.
The distribution of city power density was done graphically, where cities
with similar power densities were grouped together and assigned a weighted
average power density.