ecosystems emerging: 2. dissipation -...

Ecological Modelling 117 (1999) 3–39

Ecosystems emerging: 2. Dissipation�

Milan Stras' kraba a,*, Sven E. Jørgensen b, Bernard C. Patten c

a Biomathematical Laboratory, Entomological Institute,Academy of Sciences of the Czech Republic and Faculty of Biological Sciences, Uni6ersity of South Bohemia, Branis' o6ska 31,

37005 C& eske Bude' jo6ice, Czech Republicb DFH, Institut A, Miljøkemi, Uni6ersitetsparken 2, DK-2100 Copenhagen Ø, Denmark

c Institute of Ecology, Uni6ersity of Georgia, GA 30602, USA

Accepted 15 October 1998

Abstract

This third paper in the series on Ecosystems Emerging deals with properties resulting from the second law ofthermodynamics. Dissipation of energy and matter, which is degradation from more to less organized states, causescycling of matter and origination of networks. The second law is presented in two forms: the classical one and bymeans of exergy which measures useful energy. Energy and matter dissipation condition the formation of structures,growth, development and evolution. In contrast to the ecological cliche that energy does not cycle in ecosystems, itbecomes evident that energy must cycle like matter because the two are coupled. Matter cycling is necessary for thecontinued existence of ecosystems on earth because the closed planet has only a finite supply of material resources.Biological dissipation takes a variety of forms: respiration, excretion, egestion, natural and predatory mortality andothers. Relations of dissipation by organisms to size and temperature are causes of similar relations for a number oflife processes and also for certain ecological characteristics of organisms. This underlies the theory of ecosystem sizeand structure. Recognition of matter dissipation leads to substantial changes in ecological paradigms. For example,dissipation of nutrients can have positive effects on ecosystem production. Grazing mortality can speed primaryproduction. Therefore, ecological studies must focus more on fluxes than standing biomasses. Detrital and microbialfood paths play a significant role in ecosystems. The classical ideas of trophic pyramids and ecological efficiencies arechanged completely by studies of dissipation. Dissipation of information relates to decreasing biodiversity and thepresent crisis of environment can be explained as a dissipation-driven entropy crisis. © 1999 Elsevier Science B.V. Allrights reserved.

Keywords: Ecosystems; Dissipation; Second law of thermodynamics; Exergy; Environmental crisis

* Corresponding author. Tel.: +420-38-43765; fax: +420-38-45989.E-mail address: [email protected] (M. Stras' kraba)� This paper is part of the Ecosystems Emerging series [previously published papers, Jørgensen et al., 1992. Ecol. Model. 62, 1–28;

Patten et al., 1997. Ecol. Model. 96, 221–284; and following in this issue, Jørgensen et al., 1999. Ecol. Model. 117, 41–64].

0304-3800/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S 0304 -3800 (98 )00194 -X

M. Stras' kraba et al. / Ecological Modelling 117 (1999) 3–394

1. Introduction

In the preceding article of this series, about theconservation principle (Patten et al., 1997, re-ferred to hereinafter as EE1), we showed thatbasic interactions in systems with living compo-nents are deeply rooted in other systems at physi-cal and chemical levels of organization, thoughbiotic systems cannot be reduced totally to physi-cal principles. Recent developments in physics(Davies, 1988), evolutionary theory (Lima de-Faria, 1988) and complexity theory (Waldrup,1992) indicate that higher-level phenomena previ-ously ascribed to biology only, like self–organiza-tion and evolution, are characteristic of thephysical world as well.

However, in spite of the similarities, there is adifference in how physical principles are ex-pressed at different levels of organization. Agiven principle has different consequences for in-teractions between physical particles, betweenchemical species and between organisms. In thisseries we are dealing with a class of systems wecall ‘eco-systems’ (EE1, Fig. 2 and related text).These are not ‘ecosystems’ in the usual sense, butnonisolated (permeable to energy) or open (en-ergy–matter permeable) entities at any level oforganization which interact by exchange of en-ergy or matter with their abiotic and biotic sur-roundings. Through eco-systems as a canonicalconstruct we are endeavoring to identify not onlya minimal set of relevant principles behind‘ecosystems emerging’ (EE1, Fig. 1), but also tounderstand the specific forms in which these prin-ciples are realized in ecosystems and how thiscontributes to the prediction of ecosystem behav-ior. In this paper we extend ecosystem featureswhich were shown in EE1 to be based on theconservation principle. In EE1 energy was treatedas a conserved entity. Here we will show, byconnecting energy to information, that conserva-tion does not hold for measures characterizingenergy use or quality. The overall fate of energyand matter fluxing across the boundaries of eco-systems, thence ecosystems, will be detailed here,focusing on properties deriving from the secondlaw of thermodynamics. The most important con-

sequence of this law, dissipation, is treated indetail.

‘Dissipation’ is often taken to mean only en-ergy degradation, the loss of quality when energydoes work and is converted to waste heat. This istypified by frequent use of the grounding symbolin systems ecology diagrams. However, if matterdissipation is also considered, then more must betaken into account. The Judao-Christian Biblestates as a maxim, ‘Ashes to ashes, dust to dust’,but the losses are not fully in vain as they con-tribute to a larger circulation. Therefore, morebiological processes than just respiration are rele-vant from the dissipation point of view. We willalso show that information is dissipated inecosystems.

2. An improbable reality

As we did for conservation in EE1, it is in-structive to ask what a world would look likewithout dissipation? This is in fact not a newapproach; artists have produced many pictures ofreality without human mortality, death being oneof the consequences of dissipation.

In the absence of dissipation the earth’s atmo-sphere would be different because there would beno evaporation or transpiration to feed clouds.There would be no soil, as soil is formed byphysical weathering of geologic and biotic sub-strates. Detritus in its many forms as a typicaldissipation product would be lacking and organicchemicals would not be released by organisms.Probably there would be no evolution, as energydissipation is the driving force behind the antien-tropic formation of structures.

If there were not different qualities of energy,reflecting gradients, evolution would stop at somepoint because dissipation would not release mate-rials back from the organisms and there would benone left for further growth. Also, dissipationwould not break down organic macromoleculesto simple molecules again. There would be nocycling from excretion, mortality and decomposi-tion, no formation of detritus and no bacterialdecomposition. Matter would not cycle in theecosphere.

M. Stras' kraba et al. / Ecological Modelling 117 (1999) 3–39 5

3. The second law of thermodynamics: classicalformulations

In nature we can distinguish two kinds ofprocesses:1. Spontaneous processes which, without input of

high quality energy from outside, degrade highquality internal energy to energy of lowerquality. Such processes, if the degraded energyis not released to surroundings, are (fromEE1) isolated.

2. Nonspontaneous processes, which require anddegrade to lower quality energy inputs ofhigher quality from surroundings. Such pro-cess are (from EE1) nonisolated.

Although EE1 concluded that the conservationprinciple has primacy over all others, this was in abackground or accounting sense. Conservation ofenergy and matter is an underlying (necessary)but not fully determining (sufficient) conditionand the law usually expressed as actually govern-ing all processes in the universe is the second lawof thermodynamics. The second law states thatprocesses involving energy transformation will notoccur spontaneously unless there is a degradationof energy from a less random to a more randomform, or from a concentrated to a dispersed form.In other words all energy transformations willinvolve energy of high quality being degraded toenergy of lower quality. On earth, this degrada-tion is ultimately to heat energy (�300 K temper-ature) as the most degraded, most dispersed,waste form. In EE1 we explained that the sourceof virtually all terrestrial electromagnetic energywas the sun and the capacity of this energy to dowork was due to the difference between sun andearth surface temperatures—6000 K vs. 300 K,respectively. Heat from earth is dissipated to andcan still do work in deep space whose temperatureis just below 3 K. High energy ‘yellow’ photons ofthe solar electromagnetic spectrum are trans-formed to lower energy ‘infrared’ photons (heat);20 (6000/300) of the latter are produced for everyone of the former degraded. Dissipative radiationof this increased number of photons to space andaccompanying randomization, accounts for an in-crease in the overall entropy (see below) of theuniverse.

Measures expressing energy quality will be dealtwith shortly below and will also be further elabo-rated in the next two articles of this series. Asimple example of degradation of energy quality isprovided during electricity generation by fossilfuel combustion (see Fig. 5.2, Jørgensen, 1992).Ecological degradation based on the same princi-ples is far more complex. An example dealingwith nitrogen compounds is given below. Suchexamples of energy degradation through a trans-formation chain are examples of energy cascadeswhich were described at a general level in EE1.

Mathematically, the second law of thermody-namics is expressed on the basis of the variableentropy, S, as:

dS=dQ/T= (dU+dW)/T,

[M L2 T−2 Temp−1] (1)

where dS, change of entropy; dQ, change of en-ergy; T, temperature; dU, change of potentialenergy; and dW, change of mechanical energywith the property for any process that dS\0, i.e.that dissipation, meaning entropy production,must be positive. For irreversible processes dS\0and for reversible ones dS=0. For more explana-tion of thermodynamic terms and entropy seeJørgensen (1992).

Entropy corresponds to disorder and order ornegative entropy, represents information. Irre-versible dissipation of energy leads to randomiza-tion of increasing numbers of photons of lowerenergy. Such random distribution corresponds tothermodynamic equilibrium, which is the finalresting state for a system with no energy supplyfrom outside. Here, a distinction has to be madebetween a system in thermodynamic equilibriumand one in a dynamic steady state. The latter is anonresting state or sequence of states based on anidentical constant or mean rate of input andoutput. There is widespread confusion about theseterms in the literature and in the following textand articles of this series we will consistentlydistinguish between the two. The first situation,equilibrium, is a resting or unforced condition,while the second, steady state, is a nonrestingcondition forced by the difference between inputto output. When there is no energy input to a


system, it spontaneously drifts toward thermody-namic equilibrium where energy and matter aredistributed at random between a system and theenvironment such that the two become homoge-neous and identical. Organic molecules havespread everywhere and been degraded to an ‘inor-ganic soup’, the ultimate situation reached fromwherever the system was before. It means life isno more. On earth this would happen if therewere no solar energy reaching the globe, in eco-nomics if there were no production of food andgoods and in an ecological system if no substanceentered from the environment. On the other hand,all eco-systems accept energy and matter fromoutside and different steady states are reacheddepending on the balance between input and out-put. The distinction between equilibrial andsteady states may seem trivial and the two condi-tions are often confused. A nonequilibrial (forced)system at steady state will soon settle towardequilibrium (unforced) if its inputs are cut off.For example, Voinov and Svirezhev (1984) cameto the ‘surprising’ conclusion that a large lakeecosystem will cease to exist after some time ifthere is no input of nutrients.

As mentioned in EE1, a system proceedsthrough a sequence of states: from the initialstate, determined by initial conditions and systemparameters (and usually the terminal state of priordynamics), through a transient state, character-ized by continual changes of nonrepeating states,towards a steady state with no further, or at mostoscillatory, state changes. That the state of asystem is not changing does not mean there areno dynamics. Dynamics are indicated by rates ofenergy–matter gain, utilization and loss. Dynam-ics may be rapid if rates are high, or slow if ratesare low. In both cases when gains and losses areidentical, the enclosed mass will not change. Dy-namics cannot be derived from the state of asystem alone (see the state-space model for objectsand subjects in EE1). This system feature negatesthe classical ecological notion of a ‘biomass(trophic) pyramid’. There is no reason why thereshould be monotonically less biomass at succes-sive trophic levels. Inverted or nonmonotonicpyramids emerge in ‘unfolding’ transformationsof networks (generalized food webs) to

macrochains (aggregated food chains) (Patten,1992) due to variable turnover rates. For example,if lower trophic level organisms turn over materialrapidly and are simultaneously eaten in highamounts by slower-turnover consumers, thebiomass of prey can be low and that of predatorshigh. Fott (1975) observed in a fish pond a steadystate situation persisting for about 2 months withphytoplankton at a very low level correspondingto 3 mg l−1 reproducing at a rate of about 1–1.3doublings per day and Daphnia concentration of60–80 individuals per l. The situation with lowphytoplankton and high zooplankton is defined asa stage in the annual plankton development ofmany lakes called the ‘clear water stage’ (Sommeret al., 1986).

For dynamic systems generally, thermodynamicequilibrium may be considered a global attractorstate. In absence of further inputs, a system willcome to rest at this point irrespective of theenvironment and system parameters. On the otherhand, a dynamic steady state far from thermody-namic equilibrium, corresponds to a local attrac-tor. It is ‘local’ in the sense that it will changewhen the environment or system parameterschange. However, the term ‘attractor’ implies thatthe system is attracted or pulled by inside pro-cesses to the attractor state. Typically, however itis pushed towards this state by forces exerted byits input environment, particularly in the shorttime after the system is disturbed. The local ‘at-tractor’ is therefore really a forced state as itdepends on system inputs and such attractors innature are never fixed, but change as the systemchanges. Though considering the term ‘attractor’a misnomer in the context of forced systems, wewill continue to use it as qualified because itsusage is so widespread.

By transforming energy from one form to an-other, waste heat, additional photons and thusentropy are produced in accordance with Eq. (1).Such processes occur spontaneously. The electri-cal energy accumulated in clouds, if exceeding acertain level, produces lightning that dissipates theaccumulated energy and creates a more balancedstate. Both energy and electric charge are con-served in this process (EE1). When the sun heatssome sections of land more than others, winds are


created that exchange sensible thermal energy be-tween the warmer and colder environments, mak-ing it more randomly distributed and closer tothermodynamic equilibrium. Winds created in thisway are examples of the spontaneous formationof highly organized structures during the dissipa-tion process. Organized winds have direction,speed, distribution of speed in spacetime andcomplicated behavior near the ground and obsta-cles, etc. and in all such complex behavior energy,matter, momentum and angular momentum areconserved (EE1).

The second law of thermodynamics states that inthe absence of external forcing (input of energy andmatter) systems spontaneously tend toward thestate of thermodynamic equilibrium. They do thisthrough energy and matter dissipation in whichenergy and matter are degraded from higher tolower quality. Thermodynamic equilibrium is theglobal attractor. In a dynamic steady state, inputand output are long-term balanced, so that themean state remains constant. The system is forcedto this state from an initial through a transientstate and we may call it a forced attractor. It is alocal attractor as it depends on inputs, outputs andsystem parameters. From the dynamic steady stateno estimate of the rates of input (and output) can bemade. The turno6er rates of biomass at different‘trophic’ le6els can 6ary significantly and hence lowbiomass of rapidly produced food can support highbiomass of slowly growing consumers. The ecologi-cal notion of ‘biomass pyramid’ with steady statebiomasses regularly decreasing at successi6e trophicle6els is negated.

4. Energy notions in ecology

We reviewed the various forms and sources (thefour fundamental forces) of energy in EE1. Inecosystem ecology energy has been consideredsince the seminal paper of Lindeman (1942) wasused as the measure for expressing masses andactivities within a system. During the worldwidestudies of the International Biological Program(IBP) much attention was devoted to energy andits flow. Energy inputs from the sun and in theform of chemical compounds have been found

useful for describing a number of ecosystem pro-cesses. E.P. Odum (1964) nominated ‘energetics’as the new ecology. However, the role of differentvariables critical to the occurrence of various or-ganisms was also investigated, as it was felt thatenergy is not a sufficient or unique measure(LeCren and Lowe-McConnel, 1980). Total en-ergy is not a good numeraire because it does nottake into consideration the qualitative differencesof different energy forms. Energy may be in formsincapable of producing any useful work in theecosystem. H.T. Odum (1983), and many otherpublications) stressed the use of another candi-date, embodied energy or ‘emergy’, to measurethe value or quality of different energy forms:useful energy. In a criticism of Odum’s approach,Mansson and McGlade (1993) showed that theconcept of useful energy is not adequate for ecol-ogy because it is not uniform: it differs for differ-ent users, like producers and consumers. Theydiscuss two other candidates for a more correctmeasure: Gibbs free energy and exergy. The freeenergy concept originating in chemistry enabledsome useful theoretical insights into ecosystemprocesses. However, the need to refer to a stan-dard state is often unsuitable for the calculationof energy changes in biochemical reactions,mainly because such states are too different fromthose occurring in nature. Also, there arequadrillions of states at the molecular level.

The most general energy measure to date, appli-cable to processes involving interactions withinand among systems, seems to be the concept ofexergy. This measures the difference in free energyagainst the surrounding environment which, ifthere is no change in pressure, corresponds to thedistance from thermodynamic equilibrium. Thisgives the maximum amount of work that can bedelivered to a reference or equilibrial state. Exergyis not conserved and cannot be negative.

The advantages of using exergy are obviousfrom the above definition and we will do soextensively in our ensuing articles on opennessand growth. However, there are alsodisadvantages:1. Quantitative determination of exergy is not

easy. If all energy transfers occur via matter,the determination of exergy is possible. Com-


plications occur during interactions of matterand radiation, as in photosynthesis. Also, thequalitative factors for recalculation of organ-ism biomass to exergy are not known and inone of the next papers of this series attemptswill be made to derive approximate qualitativemeasures.

2. The specific reference state is not known. Ahypothetical reference state has to be used.

3. Radiation (for photosynthesis) and radiativeheat transfer (for animals) are usually nottaken into account (but see Ulanowicz andHannon, 1987).

In spite of these disadvantages, exergy seems tobe the first candidate for use in ecology. We willextend its use and advantages in the next section,as well as in subsequent articles of this series.

Two thermodynamic concepts seem to be rele6antfor eco-systems as a measure of energy quality andapparent dri6ing force: the chemically based con-cept of Gibb’s free energy and the concept ofexergy. Both ha6e the disad6antage that a specificreference state is needed. This is generally notknown and a hypothetical reference state has to beused. Exergy gi6es the maximum amount of workthat can be deli6ered to the equilibrial state of theecosystem and is therefore the first candidate forecology.

5. The second law expressed by the concept ofexergy

Exergy is defined as the amount of work, whichis entropy-free energy, that a system can performas it is brought into thermodynamic equilibriumwith its environment. The system is an eco-systemin our established sense. It is characterized by aset of extensive variables (which depend on systemstate) S, Q, V, N1, N2, N3, where S is the entropy,Q the energy, V is volume and N1, N2, N3,…, aremoles of various chemical compounds and by aset of intensive variables (independent of state), T,p, mc1, mc2, mc3,…, where T is temperature, p ispressure and mc1, mc2, mc3 are chemical potentialsof the compounds N1, N2, N3,…. The system iscoupled to a reservoir, a reference state. The twotogether form a closed system. The reservoir (en-

vironment) is characterized by the intensive vari-ables TO, pO, m c1

O , m c2O , m c3

O ,… and as the system issmall compared with the reservoir, the intensivevariables of the reservoir are not significantlychanged by interactions between the system andthe reservoir. The system develops toward ther-modynamic equilibrium with the reservoir and issimultaneously able to release entropy-free energyto it. During this process, the volume of thesystem is constant. The entropy is also constant asthe process is an entropy-free energy transfer fromthe system to the reservoir. The intensive variablesof the system become equal to the values for thereservoir at equilibrium. The total transfer ofentropy-free energy in this case is the exergy ofthe system. It is seen from this definition thatexergy is dependent on the state of the totalsystem (=system+reservoir) and not entirely onthe state of the system only. Exergy is thereforenot a state variable.

In accordance with the first law of thermody-namics, the increase of energy in the reservoir,DQ, is:

DQ=Q–QO

where QO is the energy content of the system afterthe transfer of work in energy to the reservoir hastaken place. According to the definition of exergy,Ex, we have:

Ex=DQ=Q–QO

As:

Q=TS−pV+%c

mcNi

and

QO=TOS−pOV+%c

m cONi

we get the following expression for exergy:

Ex=S(T−TO)−V(p−pO)+%c

(mc−m cO) Ni

(2)

see any textbook on thermodynamics, e.g. Baehr,1978). As the reservoir, reference state, we canselect the same eco-system but at thermodynamicequilibrium, i.e. with all components inorganic


and at the highest oxidation state (nitrogen asnitrate, sulfur as sulfate and so on). The referencestate will in this case correspond to the eco-systemwithout life forms and with all chemical energyutilized or represented as an ‘inorganic soup’.Usually, T=TO and p=pO, which means thatthe exergy becomes equal to the Gibbs free en-ergy, or chemical energy content, of the system.Notice that Eq. (2) emphasizes that exergy isdependent on the state of the environment (thereservoir or reference state), since the exergy ofthe system depends on the intensive variables ofthe reservoir.

Exergy is not conserved. An exception is ifentropy-free energy is transferred; this impliesthat the transfer is irreversible. All processes inreality are, however, irreversible, which meansthat exergy is lost and entropy is produced. Lossof exergy and production of entropy are twodifferent descriptions of the same reality, namelythat all processes are irreversible and there isalways some loss of energy forms which can dowork to energy forms that cannot do work. En-ergy, per se, is conserved by all processes accord-ing to the first law of thermodynamics. It istherefore wrong to discuss an ‘energy’ efficiencyof an ‘energy’ transfer, because this will (by con-servation) always be 100%. But the exergy effi-ciency is not 100%, because this expresses theratio of useful energy to the total energy trans-ferred, which is always process dependent and lessthan 100% for real processes.

Exergy seems more useful than entropy to de-scribe the irreversibility of real processes, as it hasthe same units as energy and is an energy form.The definition of entropy is more difficult to relateto concepts associated with usual descriptions ofreality. In addition, entropy is not clearly definedfor far from equilibrium systems, particularly liv-ing systems (Kay, 1984). Finally, it should bementioned that the self-organizing abilities ofecosystems are strongly dependent on tempera-ture, as will be discussed in the next paper of thisseries on openness. Exergy takes temperature intoconsideration, as the definition shows, while en-tropy does not.

Notice also that information contains exergy.Boltzmann (1905) showed that the free energy of

the information actually possessed (in contrast tothe information needed to describe a system) is kTln I, where I is the pieces of information we haveabout the state of the system and k is Boltzmann’sconstant (=1.3803 � 10−23 J mol−1 deg−1). Thisimplies that one bit of information has exergyequal to kT ln (2). Transformation of informationfrom one system to another is often almost anentropy-free energy transfer. If the two systemshave different temperatures the entropy lost byone is not equal to the entropy gained by theother, while the exergy lost by one is equal to theenergy transferred and equal to the exergy gainedby the other system. In this case it is obviouslymore convenient to apply exergy than entropy.

The second law of thermodynamics can be ex-pressed in terms of exergy as follows:

DEx for any process 5 0,

which implies that exergy is always lost, i.e. workis lost in the form of heat which on earth (at 300K) cannot do work. The two formulations of thesecond law of thermodynamics by entropy andexergy are consistent, as

DEx= −T DS (3)

Also, exergy is related to information I as

Ex=T I.

In addition to being an efficient numeraire forenergy in ecological applications, exergy is also adriving force in ecosystem development(Jørgensen, 1992a; Jørgensen et al., 1995). This isexpressed by Schneider and Kay (1989), whopresent their ideas as an extended version of thesecond law. According to these authors, if a sys-tem is displaced from thermodynamic equilibriumthrough application of a flow of exergy, it willutilize all avenues available, that is build up asmuch dissipative structure as possible, to reducethe effects of the applied exergy gradient. Johnson(1981, 1995), however, holds that ecosystem de-velopment tends toward a state of least entropyproduction, whereas Mauersberger (1982) consid-ers the global attractor to be represented by thestate of lowest enthalpy and highest entropy (seelater section on dissipation at the chemical level).These two opposite viewpoints and how to unitethem will be discussed subsequently in this series.


Exergy, defined as the amount of work a systemcan perform when brought into thermodynamicequilibrium with the en6ironment, appears to be themost appropriate measure of energy quality forecological purposes. As a reference state we selectthe ecosystem at thermodynamic equilibrium (inor-ganic soup). Efficiencies of energy transfer arealways 100%. But exergy efficiency is B100% as itexpresses the ratio of useful to total energy.

6. Dissipation and its function in ecosystems

Dissipation is defined as the spontaneouschange from a more organized and ordered formto a more dispersed and random form. It involvesdegradation from a higher (further from equi-librium) to a lower (nearer equilibrium) thermo-dynamic state, corresponding to change from agreater to a lesser content of exergy and informa-tion. As with any physical system, all eco-systemsare energy and matter dissipative and informationis dissipated also along with its material carriers(the ‘avatars’ or ‘markers’ of EE1). Energy dissi-pation, because it accompanies performance ofwork, conditions the formation of structures, forwhich a steady supply of solar-derived exergy isrequired. Energy dissipation toward equilibriumdrives the dissipating system further from equi-librium into highly structured, information-con-taining states. This is an apparent paradox whereconstruction and deconstruction are opposed butgo hand in hand.

Patten et al. (1999) have recently shown in thecontext of network organizations that, at steadystate, this is exactly the case. First-passage flowsof energy from source to terminal nodes in net-works are equal to the dissipation from theseterminals and terminal node recycling is an addi-tional multiple of the first-passage flows. This istrue for flows both to node storages andthroughflows (total node flows). Thus, in steadystate networks, constructive processes are alwaysproportional, prior and driven by equilibrium di-rected dissipation. Thermodynamic equilibrium is,of course, the state of systems in which all elemen-tary particles (quarks and electrons) are randomlydistributed; there are no structures or ordered

arrangements (atoms, molecules, or higher), orgradients between these and exergy and informa-tion are totally lacking. When external energysources are applied, eco-systems generate, byvirtue of their inherent organization as networks,structure, order, organization and gradients inparallel with and proportional to the rates atwhich they become disordered when the sourcesare removed. With such removal, the systems willtend to settle back toward equilibrium as theirstructure, order and organization unravel at ratesproportional to their inherent dissipation. Ther-modynamic equilibrium, then, represents a single,global attractor state.

In EE1 the energy charge–discharge cycle ofecosystems was described. The charge phase rep-resents synthesis of higher energy states in pri-mary and secondary production. In the dischargephase this energy and the matter that carries it,are subsequently transformed, utilized for workand dissipated. The discharge phase correspondsto dissipation processes. In ecosystems it can takevery different forms. For energy we can start fromthe energy budget of an organism or population.For matter, in the rocks dissipation processes arecollectively called denudation which includes ef-fects of chemical transformations, water and ice,wind and organisms. For chemical components adistinction can be made between inorganic andorganic compounds. For inorganic compounds,dissipation is by chemical processes and the oxi-dation state is important. More complex is thedissipation of organic matter, particularly organiccomplexes. The activities of organisms play alarge role in this. Biogenic dissipation of matteroccurs by various processes (excretion, mortality,etc.), leading to ATP formation in aerobic respira-tion and anaerobic fermentation.

A typical feature in ecosystems is dissipativecascading, in which partial dissipation by oneprocess leads to further dissipation in a subse-quent process or processes. Also, dissipation isconnected to other ecosystem processes such aspredation, population density, chemical changes,etc. Ecosystem examples of such cascading will bediscussed later. An important consequence of dis-sipation in ecosystems is cycling of both energyand matter. Material cycling, it is widely agreed,


leads to the continuation of biological function inthe earth’s environments with limited matter sup-ply. In addition, departing from the persistentecological principle that energy, unlike matter,does not cycle in ecosystems, here it will be devel-oped, as held by Patten (1985) and others, thatenergy also cycles as the residual exergy in chemi-cal bonds of previously synthesized organicmatter.

In the sequel we will treat energy dissipation atthe following levels of hierarchical organization:chemical, physiological, community, ecosystemand whole globe.

Eco-systems and ecosystems are energy and mat-ter dissipati6e and information is dissipated with itsmatter carriers. Dissipation is the spontaneouschange from a more organized, higher quality forminto a lower quality, more random one. Dissipationis the engine for synthesis of chemical from radiantenergy in primary and secondary production. Inecosystems dissipation takes different forms fordifferent components, connected with conser6ati6ebudgets of energy and matter. Dissipation cascadeslead to process interconnection and to energy andmatter cycling. Cycling is basic for continuous exis-tence of ecosystems under the conditions of limitedresources on the earth. Energy cycles with matter,which differs from contemporary ecological dogma.

7. Energy dissipation at the chemical level

In chemistry, the energetic character of reac-tions is described most commonly by means of theGibbs function :

DG=H−T S [M L2 T−2] (4)

where H is the total heat content of the system(called enthalpy) and T and S are as before.

The direction of a particular reaction underconstant temperature and pressure is given byDG :

DG=Greactants−Gproducts [M L2 T−2] (5)

If DG is negative then the reaction has a tendencyto move spontaneously from reactants to prod-ucts. If DG is positive, the reaction will not pro-ceed spontaneously but the reverse reaction will

be the spontaneous one. In agreement with thesecond law of thermodynamics the reaction tendsto sink down the slope of the Gibbs function untilit attains thermodynamic equilibrium at the mini-mum. This, again, is the global attractor state.The apparent driving force in this case is a ten-dency to move toward the lowest enthalpy (H)and highest entropy (S).

For a particular reaction DG can be found, as Gfor various compounds is given in physical chem-istry handbooks. Then it is possible to determinethe respective equilibrium constant ke.

DG= −R T ln ke, or ln ke= −DG/(R T) (6)

where R is the gas constant. If the concentrationsof reactants are known, it is possible to determinethe concentrations at thermodynamic equilibrium.

As an example, we can give the estimates byKramer (1964) and Sutherland et al. (1966) for alarge lake, by Goldberg (1975) for the ocean andby White et al. (1993) for soil interstitial water.These authors found that thermodynamic equi-librium estimates are valid for minerals which donot participate very actively in biological pro-cesses. It has no meaning for nutrients that can beonly expected to be in a dynamic steady state.Details are to be found in recent handbooks ofaquatic chemistry, e.g. Stumm and Morgan(1970), Pankow (1991) and Baker (1994). Practicalpredictions can also be obtained by means ofprogram packages such as in Morel and Morgan(1972).

Mauersberger (1984, 1988) applied the princi-ples of chemical thermodynamics to derive theo-retically the shapes of dependence of basicprocesses in aquatic ecosystems on environmentalvariables. He based his development on massbalances of the components of chemical reactionsand biochemical processes of the form:

r dNj/dt=%j

VjrMjwr+Yj (7)

where r, the densities of reacting chemicals; Nj,the chemical components; Vjr, the stoichiometriccoefficient of the chemical reaction; Mj, the molarmass of the j-th chemical component; wr, thereaction rate for the r-th reaction; and Yj, thebiochemical reactions.


The resulting shapes shown in Figs. 1 and 2correspond fairly well to those empirically found(Figs. 1 and 3). The degree of agreement is notjust seen for the effect of individual variables forwhich we have a number of empirical descrip-tions, but also for the far less well understood anddescribed factor combinations.

Mauersberger demonstrated that the principlesof nonlinear systems far from thermodynamicequilibrium, able to use part of the energy ormatter exchanged with the outside world, areuseful for deriving the specific internal structurethat is characterized by dissipative processes. Theinteraction between the dissipative system and theexternal world influences the entropy producingand entropy reducing processes inside the ecosys-tem and across its boundaries.

Thermodynamic description of chemical reactionsin ecosystems is able to predict the amounts andforms of chemical elements in natural solutions,except those that, like plant nutrients, do partici-pate 6ery acti6ely in biological acti6ity. It alsopro6ides a theoretical basis for deri6ation of theshape of relations between the basic life processesof organisms and factors of the en6ironment.

8. Energy dissipation at the physiological level

The basic dissipation process at the physiologi-cal level is the decomposition of proteins in thepresence of oxygen into CO2, water and ammo-nium accompanied by the release of energy. Thespontaneous tendency of this process, calledcatabolism, is towards decomposition and pro-ceeds in steps.

The energy released by the catabolic processesof all organisms in ecosystems is used to maintainthe system in the organized state, to drive it farfrom thermodynamic equilibrium, far from thedecay to amorphous, nonliving mass. The organ-isms need energy to stay alive and homoiothermsalso to maintain a temperature different from theenvironment.

Catabolic processes involve decomposition offood components and organic matter produced byphotosynthesis into simpler molecules. In this re-spect, catabolism can be equated with combus-tion. The same amount of heat will be released incombustion and catabolism. The main differencefrom combustion is that decomposition proceedsat ordinary temperature without sudden liberation

Fig. 1. Confrontation of theoretically derived light dependence of algal photosynthesis for various light adaptation intensitites andtemperatures with observations. A: Light dependence of photosynthesis derived from thermodynamic theory by Mauersberger (1984)for low light and high light algae. B: Observations of this dependence on Chlorella 6ulgaris by Steeman-Nielsen et al. (1962) (crossesand circles) and the model by Kmet et al. (1993) (lines). C: Mauersberger’s curves for the light dependence of photosynthesis atdifferent temperatures. D: Observations on a natural population of Stephanodiscus hantzschii from Slapy Reservoir, Czech Republic,approximated by the model of Vollenweider (according to Stras' kraba and Gnauck, 1985).


Fig. 2. Confrontation of the shapes of relationships of the dependence of algal photosynthesis on temperature derived fromthermodynamic theory (Mauersberger 1984) with measurements. Top left: theoretical dependence of ecological process rates ontemperature. Bottom left: Observations of the dependence of algal photosynthesis on temperature (original observations byStras' kraba, Dvor' akova and Lukavsky) and the approximation equation by Shugart et al. (1974). Top right: Theoretical temperaturedependence of gross primary production (dot dash line), respiration (dashed line) and net primary production rate (full line) forconstant intensity of other variables (light, nutrients a.o.). For confrontation with observations see Table 2, data for Scenedesmusquadricauda. Bottom right: Shape of the temperature dependencies of photosynthesis upon temperature at different intensities oflight. The arrow indicates the influence of increasing light intensity. For confrontation with observations see Fig. 3.

of large amounts of heat. Catabolic processes areordered, catalyzed by enzymes and consist ofmany integrated stepwise reactions. Combustionis an uncontrolled, disorderly series of reactionsproceeding at high temperature. Elimination ofthe necessity for high temperature for decomposi-tion in organisms, removing the requirement forhigh energy of activation, is due to the function ofenzymes. The combination of an enzyme with itssubstrate, the chemical changes that occur in theenzyme-bound substrate and the liberation of theend product are all reactions that have a lowenergy of activation. The entire sequence of pro-cesses involved in catabolism can therefore pro-

ceed spontaneously at ordinary temperature andcatalysis is achieved.

Another essential function of enzymes is toprovide for an orderly stepwise decomposition oforganic nutrients. The third essential function isto make part of the energy available fromcatabolic processes useful for cells and organisms.The multiplicity of reactions and the energeticcoupling between them prevent the liberation ofvery large amounts of heat in any one step andpermit the accumulation of chemical bond energy,in the form of ATP within the cell. ATP is themost important single agent used by all livingsystems as carrier of energy.


8.1. Types of catabolism

It is customary to recognize three major classesof catabolism, which for all organisms aredevoted to the generation of ATP: aerobic respi-ration, anaerobic respiration and fermentation.

All these types use oxidation–reduction reactionsto provide the ultimate source of energy. Theefficiency of anaerobic respiration in energy gainis, according to McCarthy and Eppley (1972),about 15% when glucose is the energy source, butless when lactic acid or ethanol are the energysource.

Another process with a misleading name, pho-torespiration in algae, will be discussed in connec-tion with excretion. This represents the exclusionof excess low organic matter and not a catabolicenergy releasing process.

At the physiological le6el the intensity of energydissipation processes is expressed as respiration,anaerobic respiration and fermentation. The energydischarged by spontaneous decomposition processesis used for organic synthesis, representing thecharge phase of the life process. Respiration is themost efficient process, anaerobic respiration beingless and fermentation least efficient. Anaerobic bac-teria form characteristic stratification in water andsoil.

9. Size dependence of dissipation by organisms

Of the three classes of energy dissipation byorganisms respiration is the most important. Forindividual organisms, two basic trends occur: asize dependence and an evolutionary dependence.

The effect of organism size on respiration wasfirst brought to attention by animal physiologists:Brody (1945), Kleiber (1961), but particularlyHemmingsen (1960). Soon, ecologists recognizedthe usefulness of allometric relations (e.g.Humphreys, 1978; Ulanowicz and Platt, 1985).

Empirical studies demonstrated that not justrespiration, but many other physiological andecological characteristics are related to body sizeof organisms, extending from viruses through pro-tozoa and algae to the largest mammals. Sum-mary treatments of the question appeared injournals and later in monographs (Peters, 1983;Calder, 1984). For respiration, which is the vari-able of interest in the present context, therelationship

r=a W b (8)

Fig. 3. Observations of the dependence of photosyntheticactivity of Scenedesmus quadricauda on temperature for algaekept in different light intensities. Top: Original observation byStras' kraba, Dvor' akova and Lukavsky approximated by thecurves given in Fig. 1. Bottom: The same observations normal-ized. The following light intensities (in W m−2) were used:

– – – – I=7, – – – I=12, –.– I=32,...... I=43, – – – I=54,

– – – I=77. Note the similarity of the top figure with thetheoretical curve in Fig. 1 and the false impression of highdiversion of the curve’s origins after normalization.


Table 1Parameters of the allometric Eq. (8) for the dependence ofrespiration (=dissipation) (d−1 at 20°C) on body weight (pgcarbon) resulting from different studies. From Moloney andField (1989)

baOrganism

Rat to steer −0.25–−0.266–Mouse to elephant

Bacteria to mammals −0.25–−0.30933Marine plankton−0.1Unicellular algae 0.4−0.22512Marine amphipod−0.15Daphnia 10−0.31215Zooplankton−0.268Crustacea 16−0.2517Copepoda

changed over the course of evolution towardshigher values (see Jørgensen, 1992, Fig. 5.14from Schneider and Kay, 1989). Evolutionarilyold groups of organisms which take up dis-solved nutrients from solution (i.e. autotrophsand osmotrophs as represented by phytoplank-ton algae and bacteria) have low specific respira-tion rates, i.e. smaller a in Eq. (8). This isderived using the assumption that the slopes areidentical for different groups. Theoretical deriva-tions of the relationship were attempted byEconomos (1979), Heusner (1982) and Feldmanand McMahon (1983), among others.

The consequences of these basic relationshipsof dissipation for practical ecology and ecologi-cal modelling are extraordinary. It providesrough estimates of parameters needed in dy-namic ecosystem models and serves as a basisfor comparing the functioning of different or-ganisms in nature. In this sense it also repre-sents a bridge between theoretical and empiricalecology, being used for substituting taxonomicdifferentiation with much more easily deter-minable body-size spectra in studies of struc-tures and flows, particularly in marine andfreshwater environments (Sheldon et al., 1972;Sprules and Munawar, 1986; Sprules et al.,1991). Ulanowicz (1989) reviewed some of thestudies based on size-dependent structure ofoceanic food webs resulting from studies of flowand cycling. One example of the practical appli-cation of the allometric relation is the derivationof sustainable yield in fishery management(Charnov, 1993). This author has assumed theaverage allometric relations for growth rate andpopulation density (related to those for respira-tion) to derive the relationship for carrying ca-pacity and maximum sustainable yield of fish ontheir body size.

The dependence of respiration on the body sizeof organisms is now generally recognized, span-ning from 6iruses to elephants. E6olutionarily dif-ferences are manifested in the increasingdissipation intensity of e6olutionary higher organ-ism groups. The general trend represented by aslope of about − .33 is represented by lowerslopes of −0.25 within these groups.

was in most cases obtained by simple statisticaltreatment of log-transformed observation databy linear regression. As in many empirical stud-ies of this kind, the results were subject to largeerrors. These were due to the use of simple lin-ear regression instead of regression weighted forimpossibility to distinguish between ‘dependent’and ‘independent’ variables and to bias due tohigh scatter of data. In addition, data obtainedin different units had to be recalculated to thesame units and to standard temperature usingsome average recalculation factors, which was asource of additional errors and scatter. Exam-ples of the variability of the parameters of Eq.(8) in different investigations are given in Table1.

A general pattern started to crystallize, thatone source for the differences is in the slope ofthe relationships within each evolutionary groupof organisms and among the groups. Boudreauet al. (1991) demonstrated (for the specific pro-duction rate which is related to respiration) thatthe slope is much less, on the average close tothe value of −0.25, when we compare produc-tion rates of different sizes within the majorgroups of organisms, but range close to the ‘onethird rule’ (−0.33 to −0.38) for the majorgroups.

The differences stressed by Boudreau et al.(1991) are also in agreement with the findings ofZotin (1984) that the specific respiration


10. The Q10 law and the shape of the temperaturedependence of dissipation and other life processes

The temperature dependence of respiration ofany organism is determined by the reactions ofdifferent enzymes driving the process of respira-tion (Wieser, 1973; Precht et al., 1973; Huntleyand Lopez, 1992). The reason is that the activa-tion of molecules by enzymes increases with tem-perature. The consequence of the increasedactivation on respiration by some enzymes is pos-itive and of others negative. Therefore, the effectof temperature on respiration is positive up tosome temperature and then becomes negative. Inconsidering energy dissipation at the chemicallevel we showed above that Mauersberger ob-tained theoretically the shape of temperature de-pendence that is commonly observed. This shapeshows nonzero values of respiration at the lowesttemperatures encountered, an exponential rise ofdissipation going over to a peak at some tempera-tures, followed by a drop to zero values which ismuch steeper than the ascent (Fig. 2). In ecology,the temperature dependence of respiration andother dissipatory life processes has been approxi-mated by different relationships that proved ade-quate only within certain ranges of temperatures.The most simple relationship is linear. For arange of temperatures well above zero but not toohigh, the linear formulation expresses fairly wellthe nature of the relationship. However, it showsunrealistic values at low temperatures and is com-pletely out of range for very high temperatures.Recognition of the error of linear approximationat very low temperatures has led to use of anexponential dependence called the Arrheniuscurve. This is usually expressed in physiologicalliterature as a Q10 value. The Arrhenius curve isobtained by plotting the activity (respiration)against the reciprocal absolute temperature. As iswell known, the value of Q10 expresses the differ-ence between the activity for a 10°C span oftemperature. It is often forgotten that specifica-tion of a Q10 value includes the range of tempera-tures for which it is derived. In principle, if notspecified otherwise, this is the range between 15and 25°C. Belehradek (1935) has recognized thelimitations of the Arrhenius curve by not covering

the plateau when some optimum temperature forthe process is reached. He introduced an equationwhich represented a symmetric hat-shaped rela-tion with a maximum reached at a temperaturespecified by the value (parameter) Topt, then drop-ping to near-zero values afterwards. The disagree-ment of this shape with observations proved to bein the range of very high temperatures, whererespiration drops much faster than it rises andreaches zero instead of the positive values pre-dicted by Be' lehradek’s shape. As shown by Sol-hoy and Skartveit (1975) the selectedapproximation has considerable consequences onfield estimates of respiration.

To cover the full range of temperatures exactlyand simultaneously enabling relevant interspeciescomparisons, an equation with the following char-acteristics is needed: a rising leg starting withnonzero values and increasing exponentially to aplateau reached at a certain (optimal) tempera-ture, followed by a steep decline to zero at super-optimal temperatures. In addition, this equationhas to have parameters with some physical mean-ing, amenable to interpretations, comparisons andpossibly correlations with other ecosystem phe-nomena. Several equations will fulfill the condi-tion of the shape, however the condition ofinterpretable parameters is not realized. Both ba-sic requirements, adequate shape and well inter-pretable parameters, are fulfilled by:

R=r(Topt) f(T)

f(T)= (VT)XT exp(XT (1−VT))

VT= (Tmax−T)/(Tmax−Topt)

XT= (WT)2 (1+(1+40/WT))2/400 (9)

WT= ln Q10 (Tmax−Topt)

(see Fig. 2), introduced by O’Neil et al. (1972) andShugart et al. (1974). In spite of being quitecomplex, the equation has only four parameters,all of them with very clear physical meaning,being more or less easily seen on the graph of thefunction. These are Topt, the temperature at whichrespiration (R) is the highest; r(Topt), the maxi-mum rate of respiration reached at T=Topt; Tmax,the temperature at which respiration drops to zeroand Q10, called so due to its resemblance to


physiological Q10 and expressing the increase ofrespiration in the rising leg of the relationship.This parameter (Q10) can also be recalculated tothe value of respiration at the temperature T=0°C, which is easily abstracted from looking atthe graph of the function. Table 2 gives values ofthe parameters of Eq. (9) for different organismsin their corresponding environments.

Temperature dependence of respiration and otherdissipati6e and life processes is due to the tempera-ture dependence of acti6ation of molecules at ther-modynamic equilibrium. The shape of thedependence, which is both theoretically deri6ed andempirically 6erified, has a rising leg reaching amaximum and then dropping rapidly and is bestdescribed by a complex function with simple, mean-

Table 2Parameters of the temperature dependence (Eq. (9)) for respiration, growth and other processes of different organisms

Topt TmaxGroup, species, process Q10 r(Topt)

Bacteria14.8 19.8 3.9Vibrio marinus from depths of N. Atlantic, growth

Cytophaga johnsonae, psychrophil 1.332.927.02.0447.833.3Chlorobium, hot spring Yomuto in Japan, rel. growth

26.5 36.5Bacterial decomposition of sediments 1.71

AlgaeScenedesmus quadricauda

3.8452.731.7Cultivated at low light intensity37.1 45.1 2.12Cultivated at high light intensity

48.5 2.34Standard conditions, net production 35.51.6746.8Standard conditions, respiration 41.0

Cymbella24.0 1.76Epiphytic on Myriophyllum at 0°C 46.0

PhytoplanktonShiinjike pond

June 40.729.2 1.6452.6August 2.5230.3

Trientalis borealis, net photosynthesislowest of 16 parallels 31.211.0 1.17 2.45highest of 16 parallels 2.60 10.947.022.0

PlantsPinus needle growth

6.181.8223.1at 730 m a.s.l. –2.45 3.57at 1680 m a.s.l. 17.5 –

Polygonum distortoides13.3 – 4.06 4.13Photosynthesis, coastal, kept in low T

6.457.79–Photosynthesis, coastal, kept in 30°C 25.4–6.40Subalpine plant kept in 30°C 5.1122.4

Crustacea26.122.3 3.50Eudiaptomus gracilis, grazing rate 0.20

Daphnia hyalina20.0 28.0Filtration rate 3.00 7.50

Grazing rate 20.0 29.5 3.50 0.11

Insecta3.1019.0 2.70Isoperla nana, oxygen consumption –

–26.5Mollusca, Unionidae, fi6e species, oxygen consumption, relati6e to 20°C 2.26 137%


Fig. 4. Observations on the density dependence of energy dissipation by populations of bacteria and algae. Respiration by naturalpopulations of soil bacteria related to biomass. The different areas cover types of soils covered. From S& antruc' kova and Stras' kraba(1991).

ingful parameters, Q10 close to physiological Q10,Topt and Tmax.

11. Other variables determining dissipation byorganisms

For prediction of respiration other major vari-ables in addition to organism size, evolutionarystage and temperature play a role: (1) organismactivity and (2) concentration in the medium (3)oxygen concentration in the medium and (4) cy-cles of different magnitudes. This is not a com-plete list, as stress and other factors can changerespiration rates considerably.

11.1. Acti6ity

The distinction of passive (basal) and activemetabolism of animals is generally appreciated,but the same seems to be valid for other organismgroups. The size–dependent values above (Table2) are the sum of both, basal metabolism usuallyrepresenting just a small fraction of activemetabolism. Only one ecological measure of thedegree of organism activity is more widely ap-

plied: the population growth rate. Increasing res-piration with increasing growth rates of individualspecies is theoretically explained by a greater needfor ATP in rapidly growing organisms. Activitiesof animals are diversified: food gathering, preda-tor escape, the act of reproduction and rearing ofyoung. In fact each of these activities causes dif-ferent changes in respiration per unit activity, butfor global approximations no general rules havebeen recognized until recently. It is known thatactivity of organisms is conditioned by their nutri-tional status, level of activity, pregnancy, lactationand other factors. Plants with low supply of waterand nutrients as well as undernourished animalsdecrease their respiration.

11.2. Population density

This variable has the strongest effect quantita-tively, but has been largely neglected until re-cently. Estimates of its effects are now available.Density dependence of growth rates and othermeasures of organism activities are recognized forseveral organism classes (examples in Fig. 4). Thefigure indicates quantitative relations for use inholistic ecology and ecological modelling. Density


dependence covers the fact that diluted popula-tions of a species grow much faster and respiremuch more intensively if their populations arevery diluted than if population densities increase.For aquatic bacteria, Stras' krabova and S& imek(1984, 1988), S& imek (1986) and Stras' krabova(1993) observed in natural populations, labora-tory mesocosms and pure cultures that at lowdensities high specific respiration and specific up-take rates are found together with lower yields.With increasing densities, without altering specificgrowth rates, the specific respiration and specificuptake rates decrease and yields increase.S& antruc' kova and Stras' kraba (1991) demonstratedon the basis of their own measurements and ex-tensive literature data that soil bacteria from dif-ferent environments show extremely strongdensity dependence of specific respiration ratesmeasured as CO2 evolution per unit biomass andunit time. For algae, Javornicky (1980) has shownstrong dependence of the specific assimilation ratemeasured by the oxygen or C14 method on popu-lation density of whole phytoplankton associa-tions. Stras' kraba and Gnauck (1985) showed thesame effect experimentally for several algal andcyanobacterial species grown in saturated nutrientmedium. The effect is not explicable as a conse-quence of self-shading of algae in dense popula-tions, as the strongest decrease took place at verydiluted population densities. In nature such lowconcentrations are common situations. As shownin Fig. 4, density dependence is expressed soprofoundly that it exceeds the degree of the effectof other generally considered variables. In higherplants, the density dependence known under theterm of self-thinning is well known (Harper, 1977;Feldman and McMahon, 1983; Osawa and Allen,1993). Duarte and Kalff (1987) demonstrated thatboth marine macroalgae and freshwater helophytashow the same shape of density dependence asterrestrial plants. For invertebrates the phe-nomenon is mentioned in many ecology text-books. In contrast to bacteria, algae andmacrophytes, where the phenomenon seems gen-eral and also valid for mixed species populations,only some species from different invertebrategroups show it, while others closely related donot. It is not known what characteristics differen-

tiate species with and without density dependence.In fish, density dependence is assumed especiallyin larval and juvenile stages (Rotchild, 1986). Inmammals very high densities of some species areknown to produce stress factors with increased(rather than decreased) respiration rates (Selye,1956). Working hypotheses about the mechanismsleading to the observed density dependencies inmicroorganisms are discussed in Stras' kraba(1998).

11.3. Oxygen

The difference in energy dissipation during aer-obic and anaerobic respiration was stressedabove. Oxygen conditions are particularly impor-tant for aquatic organisms, but possibly also forsoil organisms. Soil seems to be generally anaerobic environment (White et al., 1993). Someaquatic species are capable of switching betweenaerobic and anaerobic respiration. As an example,we can give the life conditions for the fish Caras-sius carassius in small ponds supplied withamounts of organic matter from the surroundingtrees studied by Blaz' ka (1958). In winter under icecover the whole pond becomes anoxic and themetabolism of some organisms changes com-pletely. In algae, photosynthesis depends on theoxygen concentration, with oxygen supersatura-tion inhibiting photosynthesis.

11.4. Cycles

Basic natural cycles are circadian and seasonal,but other time-related cycles like the feeding cycleor lactation cycle can also be distinguished. Circa-dian cycles cause regular changes in the activitiesof organisms and related respiration intensities.The much lower respiration rates of dormantanimals are well known, in particular for humans.Respiration of algae during the night or in deeperdark strata of waterbodies when no photosynthe-sis is occurring is also much lower, approachingbasal metabolism. This feature, which we presenthere from a mixture of theory and empiricalobservations on cultures, is not yet incorporatedinto recent ecological thinking or models ofaquatic ecosystems. Still much less appreciated is


the observation by Cohen and Parnas (1976) thatalgae have adapted their cycle as if anticipatingthe daily light cycle.

Seasonal (annual) cycles of organism activitiesare well recognized. Hibernation and formation ofoverwintering resting stages are known in Crus-tacea (Watson and Smallman, 1971), insects(Danks, 1987) and mammals (Davis and Golley,1963). Exact clues for mechanisms releasing dif-ferent groups and species from the hibernatingstate are insufficiently known and some kind ofinternal clock is assumed to work in a number ofcases.

In addition to organism size, e6olutionary statusand temperature, dissipation by organisms is code-termined by their degree of acti6ity, by populationdensity, oxygen concentrations and circadian, sea-sonal and other cycles, as well as other 6ariables.Density dependence is a feature neglected in con-temporary ecology, that shows a 6ery strong effecton dissipation and other life processes inmicroorganisms.

12. Energy dissipation at the community level

On the community level the complicated inter-relations during an energy dissipation process canbe demonstrated by the energy budget of a pelagicphytoplankton community (Fig. 5). Wind energyis transferred to the kinetic energy of water mix-ing. The amount of energy dissipated depends inpart on the depth of mixing, which is dependentupon wind drag and the internal structure of thewater mass. The internal structure due to differen-tiation of layers of different density depends oncounteracting forces of the wind producing mix-ing and of density stratification acting againstthis. In deep water bodies the wind-mixed zonereaches to depths determined by wind speed, lakeor sea surface area and absorption of short-waveradiation by water and its contents. Phytoplank-ton development in this upper layer depends onlight availability. Several expressions of phyto-plankton biomass, P in a mixed water column atsteady state have been proposed (e.g. Bannister,1979; Steel, 1980; Baumert and Uhlmann, 1983).

On the community le6el a close relationship ex-ists between energy dissipation and formation ofstructure, as well as feedback between the nonli6ingand li6ing world. The example of positi6e feedbackbetween lake stratification and phytoplankton pro-duction demonstrates the intensification of gradi-ents by life. This shows that heat dissipation notonly interacts with chemical and biological pro-cesses but is also the source of physical structureformation.

13. Size dependence of community biomass andpopulation density

Whatever the complexities of interrelations dur-ing the dissipation process, the biomass and popu-lation density structure of different communitiesseems to be driven by relatively simple rules.

Fig. 5. An example of the complex positive and negativefeedback relations between physical and biological processesduring energy dissipation on the community level in a waterbody (top) and the consequences for the depth distribution oflight, temperature, rate of phytoplankton photosynthetic pro-duction and phytoplankton biomass. For derivation, seeStras' kraba (1998).


Moreover, they are derived from the size depen-dence of dissipation by organisms.

The size distribution of both biomass and pop-ulation density of different communities is eitherflat (e.g. Sheldon et al., 1972) or dome-shaped(e.g. Sprules et al., 1983). Han and Stras' kraba(1998) investigated the underlying theory. It ap-peared that the shapes of the spectra are highlydependent on the breadth of size categories intowhich organisms are lumped, whether a linear orlogarithmic scale is used and whatever measure ofsize is used (length, equivalent sphere diameter—ESD, body mass). The authors found that distri-butions of biomass and population densities bothdepend mainly on the size dependence of somaticgrowth and rate of mortality (both predatory andnonpredatory). They assumed, on the basis ofobservations, that for the coefficients b in Eq. (8)b1+b2:1, for b1 is growth and b2 mortality. Theshapes of the spectra depend on the ratios ofcoefficients a in Eq. (8) for growth (a1) and mor-tality (a2). When a1/a2 equals 1.25, the theoreticalbiomass spectral density fits the flat spectrum asobserved by Sheldon et al. (1972) for tropical andsubtropical plankton in the Atlantic and Pacificoceans when the logarithmic intervals of EDSwere used. When a1/a2 equals 1.48, the theoreticalspectrum corresponding to the nearly flat spec-trum of Beers et al. (1975) for microplankton inthe North Pacific with logarithmic intervals ofbody mass was obtained. For terrestrial organ-isms with the ratio a1/a2 significantly lower thanthe exponent b1, the theoretical spectrum is inagreement with the theoretical conclusions byDamuth (1987) for terrestrial organisms, assum-ing balanced production and mortality rate.When, for reasons of ecological imbalance, thesum of b1+b2"1, the theoretical biomass spec-trum shows a peak with position strongly depen-dent on the ratio a1/a2. The structural (biomass)spectra have consequences for two functionalspectra, those for production and respiration.Both these functional spectra show shapes similarto that of the biomass spectrum expressed inlogarithmic size intervals. However, for the dome-like spectra within each trophic group (see deriva-tion of Boudreau et al. (1991) discussed in theprevious section on size dependence of dissipation

Fig. 6. Confrontation of the theoretical population density-sizespectrum obtained by the model by Han and Stras' kraba(1998) and the spectrum for fish from the Red Deer Lake inOntario grouped in linear intervals of 4 g as observed byChadwick (1976).

by organisms), peaks for the biomass spectrumand functional spectra are located at differentbody sizes. It appears that within a trophic groupthe mid-sized organisms play a more significantrole in energetic processes than other size classes.In the whole community small organisms appearto be more important to the total energy budget.An example of the agreement between a theoreti-cal and observed spectrum is given in Fig. 6.

Biomass and population density of different sizeswithin communities are dri6en by simple rules whichare deri6ed from the allometric dependencies ofgrowth and respiration (dissipation) rates of differ-ent organisms. The coefficients of the allometricequations and their ratios are determining the spec-tra. Two dominant shapes of biomass and popula-tion density size spectra are an o6erall flatexponential spectrum and a spectrum with dome-like shapes within each functional group. The theo-retical size distribution of production anddestruction rates in the community is similar to thatfor biomass, but for dome-like spectra the peaksare shifted to different sizes. The result is thatwithin functional groups the mid-size organismsplay a more significant role in the total energybudget, while for the whole community small sizeorganisms are more important.


14. Energy dissipation at the global level

On a global scale, the development of gradientsbetween the warm earth and a cooler overlyingatmosphere, as well as the uneven horizontal dis-tribution of solar heating, result in highly orga-nized cloud and wind patterns. This hasconsiderable consequences for other processes.

Fig. 7 demonstrates some aspects of these processand the high feedback coupling between them.Solar radiation incident on the upper layers of theearth’s atmosphere gives a very smooth regularpicture, with maxima at the equator and a smoothtransition to nearly even incidence in the polarregions. However, the percentage of this radiationreaching the ground on the average is far less

Fig. 7. Dissipation at the global scale. The development of gradients and complex structures in the atmosphere and the highfeedback coupling with other physical and biological processes. The diagram is circular, there is no beginning and no end, no clear‘cause’ and ‘consequence’. The only highly independent force is the solar radiation at the top of the atmosphere, the rest beinginterrelated. A: Radiation at the top of the atmosphere and at the ground. Schematically from Stras' kraba (1980). B: Average airtemperature at different geographical latitudes. From Stras' kraba (1993). C: Distribution of terrestrial plant biomass as effected byprecipitation and low latitudes and by temperature at higher ones. Based on the distribution of temperature and precipitation inparts B and D, respectively and on the dependencies derived by Lieth (1976). D: Annual average precipitation and evaporation overthe globe. From Sellers and Mintz (1986). E: Major pathways of global air circulation. F: Soil weathering. From Strakhov (1967),a Figure reproduced in Hamblin (1985) and other handbooks with errors). For more explanation see the text.


smooth, with maxima (one in the Southern andthe other in the Northern Hemisphere) at lati-tudes around 20° (Fig. 7A). This is the conse-quence of processes of both heat and massdissipation during formation of clouds andwinds representing the formation of global cir-culation structures. The resulting distribution ofthe annual average air temperature (Fig. 7B)and associated humidity gives rise to zonal dis-tribution of vegetation (Fig. 7C) and soil (Fig.7F). There is an obvious tight coupling betweengrowth of vegetation and soil formation, drivenby temperature and humidity. Less obvious butvery strong is their feedback effect on the globalpattern of atmospheric circulation (Fig. 7E) andthe distribution of the radiation budget of theearth’s surface and the global water budgetshown in Fig. 7D. The effect of temperatureand precipitation as well as the role of evapo-transpiration in the energy budget of the atmo-sphere has been quantified by Lieth (1976). Thisauthor stressed that these interrelations lead tostabilization of the temperature regime andBudyko (1974) introduced them into global bud-get considerations. The cycle of effects is hereclosed, giving the distribution of humidity andcloud cover which are the reason for the dis-crepancy between the radiation incident at thetop of the atmosphere and that at the earthsurface (see EE1 for the related energy budgets).The global patterns of the distribution of hu-midity and radiation have major consequencesfor some aspects of the world distribution ofhuman activities. For example, reservoirs con-structed at certain latitudes are doomed to haveenormous water losses due to high evaporationrates at these latitudes.

Results of the surface energy budget for fourlarge ecosystems for 50 days in summer aregiven in Schneider and Kay (1989). From satel-lite measurements, insolation, albedo, net long-and short-wave energy absorbed at the earthsurface and net radiation of available energywere derived and used to calculate significantheat fluxes from a model of physiological andbiological processes which influence radiation,momentum and mass and heat transfer due tovegetation-surface-atmosphere interactions. Re-

Fig. 8. Surface energy budget of four regions according to datain Schneider and Kay (1989). 1, Energy absorbed at thesurface, W m−2 d−1, right scale; 2, reradiation, long-wave, %;3, evapotranspiration, %; 4, sensible heat flux, %. The positionalong the x-axis is on a qualitative basis only.

sults for the Amazon basin, uniformly coveredby rainforest; for central and eastern UnitedStates, covered mainly by cultivated land, grass-land and mixed forests; for Asia, with a hetero-geneous mix of tropical rainforest, cultivatedland and desert; and for the Sahara Desert aregiven in Fig. 8. The regions are arranged frommost to least overgrown. Evapotranspiration,representing dissipated energy, strongly decreasesfrom the densest to sparsest vegetation coverwhile nondegraded energy represented by long-wave reradiation and conduction increase. Mostenergy is absorbed from regions with mixedplant cover.

On a global scale the dissipation of gradientsbetween the sun (6000 K), the temperature of theearth (300 K) and outer space (3 K) creates com-plicated structures of clouds, winds and otherflows in the en6ironment. These produce globalair circulation affecting, in a feedback cycle, theglobal pattern of the distribution of humidity andradiation at the earth surface, which is related totemperature distribution on the globe. Humidity(with precipitation) and temperature are the majordeterminants of soil formation associated alsowith plant biomass distribution. Plant e6apotran-spiration is the major force for the shift in thedistribution of radiation at the top of the atmo-sphere, with maxima at the equator and in thedistribution of radiation at the ground, with max-ima at about 20° of latitude.


15. Dissipation in ecosystems with a focus onphysical and chemical matter

Matter dissipation occurs at all stages of mate-rial organization in ecosystems: physical, chemicaland biological. Dissipation of matter is associatedwith the dissipation of energy and both are cou-pled with biological processes. It is therefore mat-ter that is the focus when dealing withpredominantly physical or chemical processes.

15.1. Denudation

Global processes responsible for greatest mate-rial dissipation on the terrestrial surface seem tobe those associated with denudation. We placethis before other dissipative processes as physicalprocesses on a landscape scale play a leading role.White et al. (1993) give a thorough presentationof the scope and extent of denudation processes.Their estimate of world denudation losses of sus-pended sediment based on data from the late1970’s reach about 13 500 � 109 kg y−1 of sedi-ment and 3900 � 109 kg y−1 of solute. Majorenergy sources behind denudation are precipita-tion and the potential energy of topographic re-lief. As both of these vary widely across the landsurface, there are large spatial variations in de-nudation. Participating processes include fluvial,aeolian and biotic and major controlling variablesare climate, relief, lithology and vegetation typeand cover. The estimated rates above have to berelated to the year of study, as relief and vegeta-tion cover may change rapidly and have done soin recent years. Quantitative relations between thedegree of denudation and slope enable theamounts of matter transported to be estimated,provided that land use and corresponding vegeta-tive cover are known. This is the background formodels of nutrient inputs to waterbodies (e.g.Vollenweider, 1968 and many recent papers).

15.2. Dissipation of nitrogen

Nitrogen is dissipated to an extent that itsspreading to the atmosphere and oceans via riverflow exceeds nitrogen structuring. One of themain dissipation courses in the global nitrogen

cycle is associated with agricultural activities (fer-tilization) and creation of sewers. The originalshort cycle of nitrogen from nature (crops) tomankind and back to nature (as manure) wasinterrupted and is flowing instead via rivers to thesea.

15.3. Phosphorus dissipation in waterbodies

Phosphorus has been recognized as the domi-nant critical nutrient for most freshwater. Thecycle of phosphorus in a standing water body isillustrated in Fig. 9. The figure shows results of asimulation model indicating the budget of phos-phorus in terms of masses in compartments andflows between them (Stras' kraba and Gnauck,1985). The processes of degradation of particulatematter, sedimentation of resulting detritus anddischarge of all forms of phosphorus instreamflow are coupled with the uptake and re-lease of phosphorus by phytoplankton and itstransformation into zooplankton and otheraquatic organisms. The cyclic character of tem-perature and related stratification conditions pro-duces large differences in the fate of phosphorusduring different periods.

The Fig. 9 data depict only one particular lakein a specific situation. A more holistic look isgiven in Fig. 10, which compares the global in-put–output budget of a number of lakes andreservoirs (Stras' kraba et al., 1995). Only a re-stricted set of water bodies is included, namelythose deep enough to stratify. Phosphorus reten-tion capacity strongly increases in these waterswith retention time.

Dissipation due to physical and chemical pro-cesses is always coupled with biological processes inecosystems. The physical process of greatest mag-nitude is denudation by rock weathering and ero-sion, accompanied by soil formation. The study offlu6ial processes points to a need to extend modelsof nutrient loads to water bodies. Erosion leads tosoil degradation, a process important for the nitro-gen dissipation. The interruption of nitrogen cyclingbetween soil [crops [man [ soil causes a needfor artificial supply of nitrogen to soil. This causeslater its mass appearance in waters. Washout ofnitrogen to the sea is the consequence. Phosphorus


dissipation in standing waters shows how an ecosys-tem is able to retain some elements. Such ecosystemstudies pro6ide knowledge for reasonable en6iron-mental management.

16. Dissipation of matter by organisms

Matter dissipation by organisms is associatedwith respiration, excretion, exudation and death.An example of matter dissipation by the popula-tion of phytoplankton in a lake is shown in Fig.11. The matter dissipated during the year approx-imately equals the amount of matter produced,some matter being buried in the sediments inwaters and in the soil in terrestrial environments.Proportions of different participating processeschange markedly during the year.

The dependence of nutrient excretion on bodysize and external variables like temperature arenearly identical with those mentioned above forrespiration (Peters and Rigler, 1973). Phosphorusexcretion in Crustacea (Daphnia magna), as anexample, is observed to depend on the differentstages of an individual’s parthenogenetic repro-ductive cycle. Excretion is lower in animals carry-ing more mature embryos, while after ecdysis Prelease is about seven times higher than usual(Scavia and McFarland, 1982). Nutrient excretionleads to nutrient cycling, a process whose recogni-tion has contributed heavily to recent changes inecological paradigms. Whipple and Patten (1993)labeled the dissipative flows ‘egestive flows’ andestimated for a marsh ecosystem model in Oke-fenokee Swamp that this represents about 50% ofthe total flow.

Fig. 9. Major pathways of phosphorus dissipation in a waterbody as represented in a dynamic model of a three-layer aquaticecosystem AQUAMOD3 by Kozerski and Dvor' akova (1982) and Stras' kraba and Gnauck (1985). Situation in a temperate reservoirin spring (Julian day 120). Left, the compartments and processes covered. Right, The storages and flows between compartments,corresponding to the processes in the left part. Values in boxes in kg P per compartment, rates in kg P d−1. Both chemical andbiological processes are involved, both being driven by the physical processes of stratification and mixing. Heavy lines indicate themost important processes causing rapid cycling of phosphorus in the environment, but also major accumulation of phosphorus inthe bottom sediments.


Fig. 10. Global dissipation of phosphorus in waterbodiesbased on the annual input–output budget of a number oflakes and reservoirs. Note the effect of a hydrodynamic vari-able (average theoretical retention time of water in the givenlake or reservoir) and the difference between lakes and reser-voirs due to different physical variables in the two water bodytypes and their effect on processes of phytoplankton growthand its uptake of phosphorus as well as abiotic phosphorusparticles and phytoplankton sedimentation.

16.2. Mortality

Mortality is basically of two kinds, natural andpredatory. In the first case the cadavers are par-tially devoured and the remainder contributes toformation of detritus. This is then utilized by anumber of small organisms with sizes down tobacteria. In both terrestrial (particularly soil) andaquatic ecosystems this is a source of the organicpool reutilized by various organism, modifying

Fig. 11. Matter dissipation by a population of organisms. Toppart, annual course of processes of a phytoplankton popula-tion in the epilimnion of a stratified lake with low transparentwater according to the model AQUAMOD2 by Stras' krabaand Gnauck (1985). All values in mg CHA. mg CHA−1 d−1

(approximately equivalent to mg P mg P−1 d−1). 1, grossproduction; 2, grazing by filtratory zooplankton; 3, sedimenta-tion; 4, exchange with the hypolimnion; 5, respiration; and 6,net population change. Note the high degree of matter dissi-pated in the water body and transferred to other biotic com-partments (zooplankton) for further dissipation. Bottom partshows the changing ratio between the importance of differentprocesses during the annual cycle.

16.1. Exudation

Exudation is a form of organic matter releaseby phytoplankton, generally in the form ofpolysaccharides (Goldsworthy, 1970; Shelp andCanvin, 1980). It is due to the inability of phyto-plankton to stop the production process: excessorganics are released into the surroundings inthis way. Exudation by the dominant aquaticprimary producers is the cause for microbial foodwebs and microbial loops, again a source forrecent changes in ecological paradigms (see be-low).


their surroundings. A special case of mortality isknown in plankton; in particular in several phyto-plankton groups with very low motility. Sedimen-tation of phytoplankton cells causes their sinkingto layers with light intensity so low that theirmortality is increased. This causes loss of particu-late nutrients from the water ultimately into sedi-ments (see above—phosphorus dissipation inwater bodies). Mortality rates due to sedimenta-tion vary with groups and species, algal cell orcolony sizes, turbulence and stratification of themedium. Bossard and Uehlinger (1993) demon-strated in limnocoral experiments that zooplank-ton grazing increased sedimentation losses.

Biological dissipation processes are representedby excretion, exudation and mortality due to preda-tion and natural causes. Excretion is go6erned bysimilar quantitati6e rules as respiration. Nutrientsare usually released in organic forms, reutilized byprimary producers either directly or after break-down by bacteria. The biological role of excretionand exudation is rapid regeneration of nutrients forfurther growth. This increases matter cycling. Mor-tality creates detritus and soil organic matter,sources of food and energy for large groups oforganisms.

17. Positive effects of matter dissipation inecosystems

Experimental and in-situ observations indicatethat dissipation of nutrients, both by predatorymortality and excretion, has a positive effect onthe production capabilities of ecosystems.

As for excretion, the phytoplankton–zooplank-ton model by Carpenter and Kitchell (1984)demonstrated that phytoplankton primary pro-duction per unit volume of water increases withincreasing zooplankton biomass up to some level,but then rapidly decreases due to overgrazing. Inthis model the increased production was due tothe combined effect of excretion of the criticalnutrient by zooplankton as well as to selection ofalgae of different sizes. At low grazing pressure,larger phytoplankters with relatively low growthrates outcompete smaller, more rapidly growingphytoplankton. DeAngelis (1992) showed that

simple models can realistically predict relationsbetween nutrient[phytoplankton[zooplanktonmasses. Recirculation by herbivores of nutrientsthat would otherwise be lost from the systemresults in highest specific primary production andrelatively high levels of total primary production.Experiments of Sterner (1989) which establishedan herbivore gradient and monitored phytoplank-ton growth rates, demonstrated highest netgrowth at some nonzero grazing intensity. In-crease in algal reproduction rate with increasingzooplankton concentrations, which simulta-neously cause a linear increase in phytoplanktonmortality, was also observed. Boavida and Heath(1984) posed the question whether phosphatasesreleased by Daphnia magna originated from itsalgal food. Their experiments indicated this wasnot the case and that production contributes di-rectly to phosphorus regeneration mechanismsthat aid the growth of food resources.

17.1. Mortality

Mortality is the source of detritus, or undecom-posed soil and aquatic organic matter. A numberof organisms can live on the contained energy andnutrients and play a role in mineralization. DeAn-gelis (1992) summarized the roles of detritus inecosystems. Detritus is important in nutrient dy-namics, with implications for ecosystem stability.Detrital pools increase resilience, which is theability of organisms to recover more rapidly thanthey would if only external nutrient sources hadto be relied upon. In streams which dependlargely on detritus, a flood flushing most of thisfood source out causes lowered resilience.

In terrestrial systems, Dyer et al. (1986) havesummarized a number of observations on grasses,cultivated crops, flowers and juvenile trees sup-porting the hypothesis of an herbivore optimiza-tion curve: maximum productivity is reachedunder light grazing by herbivores and then de-creases and eventually becomes negative as graz-ing becomes severe. The effect is greatest ingrasses because these have lateral meristems.However, there is insufficient experimental evi-dence to determine if this is due to recirculation ofnutrients or other effects. Seastedt et al. (1988)


presented empirical evidence and simple modelsindicating that moderate grazing mortality of treefoliage often increases densities and biomass ofbelow-ground herbivores and detritivores. Rootgrowth reacts neutrally or is reduced. The positiveresponse is hypothesized to result from increasednitrogen concentrations in the roots, increasedconsumer assimilation efficiencies and acquisitionof soil inorganic nitrogen by microbes colonizingsenescent roots.

Matter dissipation has positi6e effects on ecosys-tem producti6ity, as shown both by obser6ationsand models. The hypothesis of the ‘herbi6ore opti-mization cur6e’ is well supported by obser6ations,but exact mechanisms can only be speculated.

18. Dissipation of matter and changes inecological focus and paradigms

The notion of cycling in ecosystems is changingecological thinking significantly. The conse-quences are 3-fold: (1) focus on flows (fluxes)rather than on masses and reevaluation of theclassical notion of dominant direct effects; (2)reevaluation of the importance of herbivorousfood chains and recognition of the importance ofdetrital food chains and bacterial loops in ecosys-tems; (3) recognition of the importance of lossesfor population dynamics and competition; and (4)reevaluation of paradigms about ecological effi-ciencies, trophic pyramids and associated basicecosystem features.

18.1. Focusing on matter fluxes in ecosystems

Differential equations introduced with dynamicsimulation modelling express the rate of change ofstate variables due to fluxes between compart-ments. However, ecosystem studies as exemplifiedby the IBP dominantly studied nutrient concen-trations and biomasses rather than individual pro-cesses leading to intercompartmental flows. Therewas a lack of knowledge of the ways external andinternal variables determine rates of change. Asan example of the situation at the end of the1970s, Platt et al. (1981) mentioned the need inbiological oceanography to encourage measure-

ment of fluxes in respect to the exploration ofholistic ecosystem properties. They also indicatethe importance of network analysis. It is true thatOdum (1960) called his modelling approach an‘energy circuit language’, stressing intercompart-mental energy flows, but because he concentratedon energy and did not subscribe to energy cyclingin his models, cycling within the circuits was notfully appreciated. The grounding symbol repre-senting waste heat losses plays an important rolein all Odum-type models. A milestone in processidentification was the detailed analysis of individ-ual feeding processes in predatory insects(Holling, 1966). This led to a number of studies ofenergy time budgets in feeding cycles and to thenotion of optimal foraging (Charnov, 1976). To-day, this aspect of animal ecology is one of thebest understood (Stephens and Krebs, 1987;Krebs and Davies, 1991).

Recycled nutrients and regenerated productionare the new terms appearing in ecology. DeAnge-lis (1992) used a steady-state solution of a simplemodel consisting of nutrients[phytoplankton[detritus[zooplankton to demonstrate that if thenutrient loading is large and nutrient excretionand exudation low, there is high nutrient recyclingthrough the detritus pool. The amount of nutri-ents accumulated in biomass can considerablyexceed the amount of nutrients is solution.

A method suggested for the quantitative studyof ecological fluxes is economic steady-state in-put–output analysis. This was first introducedinto ecology by Hannon (1973) and developedfurther by Patten et al. (1976), Ulanowicz andKemp (1979), Patten (1982), Patten and Higashi(1994) and others. The ‘environ’ and ‘ascendency’theories of Patten and Ulanowicz, respectively,are outgrowths from these analyses. Levins (1974)introduced loop analysis which seeks only qualita-tive conclusions. This method was successfullyapplied by Briand and McCauley (1978) for a lakeecosystem. Their predictions concerning the direc-tion of changes in state variables following pertur-bations were corroborated by the author’s lakemanipulation experiments and by studies of otherauthors on different lakes.

Network analysis is now central to ecosystemstudies (Wulff et al., 1989 for the sea; Patten and


Matis, 1982 for a wetland; Schulze and Zwolfer,1994 for terrestrial ecosystems) and the resultsshow that both energy and matter cycling aremuch greater than previously thought, which im-plies the importance of indirect effects (Patten,1983). In streams the nutrient spiraling hypothesis(Webster et al., 1975; Webster and Patten, 1979;Newbold, 1992) became accepted.

18.2. Detritus and microbial food chains

The ecological literature of the early 1980’sstressed grazing food chains as dominant inecosystems (LeCren and Lowe-McConnel, 1980,for freshwater; Platt et al., 1981 for the sea;Clarholm, 1981, for soil). However, simulta-neously revolutionary ideas changing this axiomstarted to appear, especially in connection withmarine studies. Williams (1981), Azam et al.(1983) and others demonstrated that in the seabacteria and detritus play a major role in nutrientcycles. Pomeroy (1974) used the term ‘microbialweb’ and Cushing (1989) specified conditions un-der which the microbial web dominates (stratifiedwaters) over herbivorous pathways (verticallymixed environments). Early recognition of theimportance of bacteria in aquatic environments isconnected with algal photorespiration. Recently,Legendre and Rassoulzadegan (1995) distin-guished that herbivorous food webs and microbialloops are only extreme cases, but intermediatesare represented by what is called the microbialweb and ‘multivorous web’. The situation infreshwater is similar to that in the sea. The impor-tance of micro- and ultra-plankton, polysaccha-ride exudates by algae and bacteria and theirconsumption by flagellates (Bird and Kalff, 1986)and ciliates in lakes and reservoirs are now beingstudied intensively (Stras' krabova et al., 1990,1994; S& imek et al., 1990).

In terrestrial environments the importance ofroot exudates and their utilization by soil bacteria(and to a great extent also by higher fungi) wasknown earlier than similar phenomena from thesea (Pomeroy, 1974). However, the bulk of or-ganic inputs consists of structural and secondaryplant products (Clarholm, 1985). Detritus is cen-tral in soil processes. Pedogenesis and the charac-

teristics of different soils depend highly onorganic matter of detritus. Detritus is the poolbuffering soil against disturbances, increasing itsstability. However, in the part of terrestrial ecol-ogy that focuses on plant–animal (particularlyinsect) interactions, the role of detritus is nottaken into consideration, though its importancefor plant development through the soil and rootsystem is without question.

18.3. Importance of losses

Early ecological investigations of variables af-fecting ecological processes were focused domi-nantly on variables affecting population gains:photosynthesis in primary producers, grazing andgrowth for higher trophic levels. This approachstill dominates in much of terrestrial ecology andwe still have more information about gains thanabout losses. However, studies of aquatic systems,dominated by small-sized species at the primaryproduction level, have shown that it is impossibleto predict population changes and species compe-tition without studying dissipative losses due torespiration, excretion and mortality by grazingand natural causes. In terrestrial environments, asimilar but perhaps less apparent situation exists(see the ‘herbivore optimization curve’ above).

19. Dissipation of information in ecosystems

Information is not dissipated per se, but isbased ultimately upon dissipation of the energy–matter markers or avatars by which informationalways is carried.

In the ecosystem information is contained inthe structures created in the course of energydissipation. These structures can be of differentextent: individual organisms, their populations,organization of interrelations between individualsof a population (e.g. social structures) and organi-zation of food-web networks. Different size struc-tures (like patches of organisms), large organismalformations (like coral reefs or Amazon forests),but also abiotic structures (like river meanders,landform elements in landscapes) all contain in-formation about the processes which created


them. In individual organisms the source carrierof information is the genetic code, contained inthe structure of DNA. DNA contains informationaccumulated during evolution, including duringthe relatively recent history of the speciespopulation.

Various information measures are used in ecol-ogy and the need for expressing the informationcontent of ecosystems increases. The index ofinformation of Shannon and Weaver (1963),based on entropy, is widely used as a special caseof a more general class of diversity indices. Theindex quantifies the structural information, butnot the semantic content, of a code. In ecologicaluses it is interpreted as the information content ofa sample community based on the richness andabundance of taxonomic units present. Shannon’sand other diversity indices are inadequate forvaluing biodiversity because in it species are con-sidered equivalent. In fact, local loss of a widelydistributed species may have less significance thanthat of an endemic species. Recently, Pahl-Wostl(1995) stressed that the indices do not give guid-ance for protection and conservation of ecosys-tems. There seems no direct relationship betweenproperties at the community or ecosystem level(Schulze and Mooney, 1993) and the number ofcomponent species. Therefore, Pahl-Wostl tries todevelop functional and dynamic diversity mea-sures to assess the potential components ofecosystem diversity that maintain species coexis-tence and ecosystem function and organization.This is the line of development started byUlanowicz (1980, 1986) and Hirata (Hirata andUlanowicz, 1984; Hirata, 1995), based on theearlier ideas of Ruthledge et al. (1976). The infor-mation measures are based on network analysis,on the mutual information of the channel. Hi-rata’s recent development covers simple nets withno provision for feedbacks and multiple cycling,which is the obvious next step to be made.

However, beyond just estimating the informa-tion value of an ecosystem network or the speciespresent, there is also information dissipation to beconsidered. Some information is dissipated witheach material structure degraded. This informa-tion dissipation is equivalent to the informationcontent of the matter involved. However, it is

highly questionable whether following this linewill be useful for ecology. Organisms, in degrad-ing energy (exergy) in respiration or excretion, donot lose net information but in the larger view ofall the processes involved actually gain exergy forthe development of new structures and with thisexperience an implied growth of informationcontent.

There is some loss of information in connectionwith individual mortality, as far as we accept thatdue to natural genetic variability every individualresulting from sexual reproduction is an original.It will not be difficult to express dissipation asrelated to mortality. But again, will such calcula-tion contribute to our understanding? We will atleast need a measure of the very specific informa-tion that the individual carries. How much infor-mation is dissipated when a prey is eaten by apredator?

A true loss of information occurs when a geno-type or species is gone. However, we need todevelop a measure of the information content ofthe corresponding genotype, the value of a traitbeing less than the value of the species. Forpractical purposes we can start with species ratherthan genotypes because information about speciesis more available. Also, here we encounterdifficulties: higher organisms have higher informa-tion content per unit biomass and endemic, spe-cialized organisms have different informationcontent than widely distributed ruderal species.This became evident to Spitzer et al. (1993) duringa study of plant and insect communities in amontane rainforest in Vietnam. Highest diversitywas found in the ruderal communities aroundvillages and lowest in the pristine mountains witha number of endemic species. The conclusion tobe drawn from this diversity evaluation is toprotect first the ruderal communities!

When considering the practical aspects of na-ture protection and conservation, we might thinkalong two lines: (1) loss of information due todisappearance of an individual, genetic trait, orspecies; and (2) loss of information due to de-creasing the ability of the ecosystem to maintainspecies coexistence and systemic function and or-ganization. These two lines are not independent:each species has its function in particular ecosys-


tems (though replaceable by other species havingor gaining similar function) and the ecosystemvalue of a species depends on the specific condi-tions of existence of the particular ecosystem.From the human point of view each species has itsown intrinsic value (see the next section).

We can imagine four ways to value the infor-mation content of different organisms: (1) basedon their evolutionary status, as expressed, e.g. bytheir specific dissipation; (2) valuing the species(or, possibly, the genotype) by weighting with thereciprocal of the area occupied; (3) calculating ina particular ecosystem network how much energyor matter was used for building a unit of biomass,extending the approach by Hirata (1995) for mul-tiple cycles; and (4) information dissipation basedon the ecosystem network approach as proposedby Pahl-Wostl (1995).

Information is dissipated indirectly with dissipa-tion of its matter markers. In ecosystems infor-mation is contained in structures created by theenergy dissipation process: abiotic structures,chemical components, organisms, organized interre-lations between organisms. Measures of informa-tion useful for ecosystems are based on mattercycling. Most important information dissipation isconnected with disappearance of genotypes and spe-cies. Ways to 6alue different organisms are sug-gested.

20. Dissipation and the present environmentalcrisis

The current environmental crisis is an entropycrisis, as demonstrated by the examples below.

20.1. Dissipation of energy

Dissipation of energy and energetic materialslike fossil fuels results in an increase in carbondioxide in the atmosphere. Greenhouse warmingis now at the center of scientific and politicaldebate. The more a system attempts to maintainand extend order, the more energy is required andthe faster it must go just to remain in place. Thisincreases the stress on the environment, as well ason the system itself. Human technology-based

systems in the civilized world are now experienc-ing such symptomatic speed-up.

20.2. Dissipation of carbon

Dissipation of carbon into the atmosphere is abroadly debated process because of its potentialeffect as a greenhouse gas on global warming ofthe atmosphere. According to measurements con-centrations of carbon dioxide have risen within 30years (1958–1988) from 315 to 355 mg l−1 of airand continue to rise in an exponential manner.There is little dispute about the origin of thisincrease in human activities. The uncertainty iswhether this increase, together with similar dissi-pation of other greenhouse gases, is the reason forglobal warming, or if temperature rise is the con-sequence of natural climatic variability.

20.3. Dissipation of matter

Dissipation of matter induced by humankind isassociated with the chemical industry and othertechnological activities of society. Pollution cre-ates disorder in the form of matter dissipationfrom more organized and concentrated states tomore randomized and diluted ones which areunable to be brought back to order again. Mostof the waste material is dissipated: it was firststructured by use of energy and then uselesslydissipated.

A warning example of large scale dissipation isgiven by the dispersion of lead from automobileexhausts and other processes all over the globe, asdocumented by the recent accumulation of Pb inthe Greenland ice pack. Although nearly no pol-lution is created in the Arctic and Antarctic andthe territories of highest concentrations of pollut-ing activities are remote by a thousand kilometers,the concentration rise in recent periods is dra-matic. To bring dissipated quantities of lead backinto concentrated, useful form is virtuallyimpossible.

On a less global scale a similar fate is observedfor other heavy metals. Increasing concentrationsappear in soil and water without their exactsources being known. The appearance creates hy-gienic difficulties in drinking water supplies. In


purification plants a part of the heavy metals isconcentrated into sludge, which cannot then beused for agricultural purposes as their depositioncreates toxicity problems.

20.4. Phosphorus dissipation

Phosphorus dissipation in water bodies showsthat much phosphorus not incorporated into ter-restrial production enters water. Over time it be-comes incorporated into aquatic sediments. Suchlosses can be recovered back for terrestrial pro-duction by using the sediments as field fertilizers.Recently this is often not feasible because of highconcentrations of heavy metals also accumulatedin the sediments. The difficulty for waterbodies isthat sediment phosphorus can be released back towater layers under certain conditions. As a conse-quence, a mere stopping of further phosphorusinput appears insufficient for decreasing waterbody eutrophication. Phosphorus released fromsediments back to water can supply the free waterof lakes for many years with sufficient amounts ofphosphorus to continue production of large unde-sirable crops of algae.

Concerning nitrogen dissipation, concentrationsof ammonia and urea from centralized feedlots isstarting to become a global-scale problem withimplications for global warming as nitrogen ox-ides are greenhouse gases. Slow dissipative disper-sion of organic nitrogen, on the other hand,functions in regeneration of nutrients.

Ripl (1992) and Ripl and Feibicke (1992) criti-cized the dominant water quality managementapproach based on the nutrient limitation con-cept. These authors stressed the need for a moreglobal view based on highly structured energypulses acting upon the water cycle and the result-ing system self-organization by energy dissipation.Their Energy[Transport[Reaction (ERT)model is theoretically based on the idea of threeproperties of water acting recursively as a dissipa-tive energy processor: (1) the physical processorproperty (evaporation and condensation), (2) thechemical processor property (dissolution and pre-cipitation and (3) the biological processor property(photosynthesis and respiration). They demon-strate that randomization of energy, water and

matter flow is characteristic of human interferencein ecosystems. Accelerated water and materialefflux from land to sea due to natural weatheringand human agency reduces the degrees of freedomof energy dissipation and destabilizes the system.Increased temperature amplitudes cause air turbu-lence by reduced evapotranspiration in damagedvegetation cover. Increased material and energyflow is induced by an increase in agricultural cropnet production due to increased matter efflux withthe water. In some cases this amounts to chargelosses of more than 0.1 kg m−2 y−1, hardly to bereplaced by fertilization. Losses of matter fromthe landscape have risen 50–150 times in com-parison to unaffected soil systems. Concentrationsof phosphorus and nitrogen in North Germanrivers now amount on the average to 200–500 mgl−1 P and 2–4 mg l−1 N. The use of externalenergy from fossil fuels and increase of mattertransport by the loss of binding organics andwater-soluble material like carbonates in soilmade it necessary to compensate in part for thecontinuous loss of nutrients by intensified fertil-ization. One consequence has been concentrationof immobile components almost insoluble in wa-ter, like quartz, heavy metals and toxic organicresidues from industrial and agricultural produc-tion processes. The relation of useful to harmfulsubstances in land and water ecosystems is shift-ing. One possible approach to the sanitation of acatchment is the minimization of matter losses,mainly by restoring wetland and other naturalvegetation cover. This provides necessary nitrogensinks for runoff from farmlands, which can beused for production of raw materials and energy.The recycling of biologically well-treated effluentsfree from noxious substances into wetland areasand sites for intensive food production (verticalgreenhouses with a high degree of recycling andbuilt-in catchments with highly reduced groundwater flow) seem to be possibilities for stoppinglosses. Vegetation recovery is important as theselective biological membranes of roots and rhi-zomes are probably the only low-energy means ofdetoxifying soil by dilution with living biomassand by fixing toxic substances by means of areduced transport possibility with the water ingley and podsol structures. On a global scale,


transition to organic farming seems to be the wayto be followed.

The most important form of information dissi-pation associated with human activities is the lossof biodiversity. This has been expressed, becauseit is a necessary consequence of success of onespecies over another in a zero-sum resourceworld, as Ecology’s AWFUL Theorem (Patten,1998). It is well recognized that high genetic diver-sity is needed for a number of utilitarian reasons:(1) many microorganism, plants and animals areyet undiscovered sources for medicaments; (2) anumber of plants in the tropics are continuouslybeing discovered as sources of food for localpopulations, some with high potential for broadutilization; (3) the genetic qualities and specializa-tion of existing crops and stocks need to berejuvenated and cultivated for newly appearingconditions, including new pests and globalchanges, which is impossible without sufficientnatural diversity of wild relatives; (4) structuraladaptations of organisms inspire engineers to newtechnical innovations; (5) the processes and meth-ods of organism adaptation serve as models foradaptation of humans to different conditions; (6)natural complexity is for humankind a source ofways to solve complex problems (e.g. new ap-proaches like adaptive technical systems, cyber-netics, viability theory, principles ofself-organization); and (7) sustainability of natu-ral ecosystems is a teaching ground for society inits need to achieve sustainability. In addition toinstrumental values of species, there are also in-trinsic values often cited as reasons to maintainhigh biodiversity. Foremost among these are theaesthetic appeal of diverse floras and faunas andthe inherent right of other species to coexist onthe planet with our own

Human activities substantially increase the dis-sipation of energy, matter and information. Dissi-pation is inevitable. Its positive role is in renewaland aggradation: the recharge of energy and mat-ter in new configurations for improving naturaland human welfare and enhancing evolution. Theproblem is in the degree to which anthropogenicactivities increase dissipation, how much of this isthis necessary for ‘progress’ and how can thecreation of disorder be managed so as not to

exceed the positive effects of the parallel orderingprocess. At present, most of the dissipation seemsnot to be so inevitable. It is apparently just wan-ton wastage of energy and materials. It is possiblethere may be some optimum intermediate relationor efficiency between ordering and disordering,aggradation and degradation, even though thetwo have been shown to be directly proportionalin steady state networks (Patten et al., 1999). Wemight anticipate, not having resolved yet whethernatural self-organization is toward greatest(Schneider and Kay, 1989) or least (Johnson,1981, 1995) dissipation, that nature evolves to-ward an optimum which is intermediate betweenthe maximum and minimum. Further study ofthis should become a goal of ecology and anthro-pology. Humanity suffers from excessive dissipa-tion at the present time and must look for waysnot to be overwhelmed by it. Conditions free ofexcessive dissipation products seem necessary forhealthy life.

The en6ironmental crisis is an entropy crisis, aspollution creates disorder. Technical acti6ities dissi-pate energy, matter and information. An extremeexample of the extent of matter dissipation is massdissipation of lead from automobile exhausts intothe atmosphere. This leads to spreading across thewhole earth, as demonstrated by increasing leadconcentrations in polar ice. Carbon, nitrogen andphosphorus are dissipated wastefully and createdifficulties in the scales from local to global. Dissi-pation of information is e6ident in rapidly decreas-ing biodi6ersity. Some solutions based on theprinciples of energy and matter dissipation aredemonstrated. An optimum degree of dissipation isneeded, where negati6e aspects do not exceed posi-ti6e ones, as the source for organization ande6olution.

21. Predictive power and ecological consequencesof the second law of thermodynamics, or how tolive with dissipation

Prediction is one of the major goals of scientifictheory. Some theoretical principles, like conserva-tion and dissipation, are so basic and of generalvalidity that they are deeply rooted in our minds


and daily activities. Prediction is possible onlywhen basic principles and their restrictions areunderstood and followed. However, the contem-porary human neglect of the extensive negativeconsequences of excessive dissipation of energy,matter and information demonstrates that this isnot completely so. It is becoming evident thatbasic theoretical principles retain validity forecosystems, in spite of the fact that laws likeconservation and dissipation were originallyderived for much simpler, purely physical, sys-tems. The claim that such principles are not validfor ecosystems because of many ‘exceptions’ isbased on neglecting the restrictions and othercircumstances of their validity and also on failureto appreciate how complex ecosystems really are,obscuring their simple expression.

An example is the theory of state-space dynam-ical systems which underlies this series (Patten etal., 1997) and of the universal sequence frominitial through transient to dynamic steady statesthrough which all such systems pass in behavioraldevelopment. This sequence is reflected in ecologi-cal succession in movement from a barren (pri-mary succession) or disturbed (secondarysuccession) initial state through a successionalsere (transient states) toward a mono- or poly-cli-max (steady states). The climax states representlocal ‘attractors’ to which the ecosystems, under acombination of internal conditions (current states)and external forcing (inputs), trend in develop-ment (see EE1). The pattern is fixed by deeptheory even though in reality the final dynamicsteady states (climax communities) may never bereached or held for very long due to slow, quasi-periodic changes in the ambient environment orintermittent, aperiodic disturbances. It is muchpreferred to understand ecosystems as manifesta-tions of underlying theory rather than (as ecolo-gists tend to do) endlessly debate the significanceof climaxes and whether they really exist or not.In the long term, motion and change are perpet-ual in the ecosphere and shorter term trends tosteady-state attractors are only waypoints alongthe way to broader continuing change.

Ecosystems and eco-systems generally, are sub-ject to principles of thermodynamics and otherphysical constraints. However, organisms develop

structural and physiological adaptations and byso doing avoid the negative consequences of theseconstraints and evolve alternative solutions thatlead to increased freedom. The new solutions cannever negate the operation of the basic laws. Tothe contrary, they are based on them.

Thermodynamic laws are constraints on ecosys-tem development and determine among otherconstraints the changes of the system. Patten et al.(1999) have attempted to reveal the relationshipbetween energy dissipation, cycling of matter andenergy and exergy storage as a consequence of thethermodynamic constraints on a network insteady state. The development of these interactiveprocesses is based on simultaneous effect of con-straints originating from all thermodynamic lawsand will therefore be touched on in two laterpapers of this series dealing with growth (dis-cussing the tentative fourth law of thermodynam-ics) and with constraints.

Many ecological models, in particular thosemore mathematically oriented, neglect (explicitlyor implicitly) dissipation as one of the importantprocesses of ecosystem functioning. Conclusionsfrom such models are bound to be erroneous. Thestate space model asserts that it is in generalimpossible to derive system dynamics from mea-surement of states alone. The dominant attentionto states in presentday ecology, in the form ofbiomasses of organisms and concentrations ofchemicals, is only slowly changing towards thestudy of processes and network flows. The worldof nature is much more than just the aggregates ofenergy and matter the senses encounter as tangi-ble objects and subjects (see EE1). It also is madeup of less obvious transactive flows between theseentities and often also virtual relations, like com-petition and mutualism, set up by these. There-fore, the significance of flows in ecosystems will beincreasingly accented in later contributions of thisseries.

The dissipation of matter is a necessary but notsufficient condition for cycling in ecosystems as thesequential uptake of degraded matter depends bothon the forms of degraded matter and organsimsuptake ability. In situations of limited resourcea6ailability cycling is 6ery important for ecosys-tems. Presently accepted ideas about ecological


efficiencies will be changed e6entually principally bythe consideration of cycling. The widely repeatedecological cliche that matter circulates but energyflows unidirectionally is untenable because energyflows conser6ati6ely with its matter carriers. Thereis no difference in kind between the two, only indegree: energy is degraded more rapidly than mat-ter. Once degraded to heat (on earth) it cannot berecycled (like matter) for further useful work.

22. Conclusion: ecologys AWFUL Theorem andthe coming environmental crisis

This paper has explored the wide range ofapplicability in ecology of the dissipation princi-ple derived from the second law of thermodynam-ics. ‘Whatever goes up must come down’ is theessence of the dissipation principle, meaning thatmovement of ontic states away from thermody-namic equilibrium must always be accompaniedby equivalent and opposite restoration of equi-librium elsewhere. Aggradation, meaning the de-velopment of antientropic order, organization,heterogeneity, gradients and the like is alwaysaccompanied by an equivalent amount ofdegradation.

Life and living are concerned with the aggrada-tive movement of biotic states further and furtherfrom equilibrium, but this can only be achievedby an equivalent dissipative return of environmen-tal states to equilibrium. Thus, living processesproceed under the paradoxical condition that ev-ery local gain must be accompanied by an equiva-lent loss, an ‘externality’ as it were. Translated toopen eco-systems, entity–environment pairs (EE1,Fig. 2), it means that evolution of systems tomore highly ordered states requires degradationof the surrounding environment to an equivalentdegree. This can be seen as an extension of ecolo-gy’s AWFUL Theorem (Patten et al., 1997) to thegeneral entity–environment (‘eco-systemic’) rela-tionship. Any progress of an entity, say humanity,up the adaptational or evolutionary ladder lead-ing away from thermodynamic equilibrium mustcarry with it an equivalent degradation of thesurrounding environment. Thus, an enigma existsfor the human community: how to perpetuate and

increase continued success as a species in the faceof commensurate environmental degradation,mandated by the dissipation principle, degrada-tion that must eventually curtail further advance-ment because it will outstrip the ability to adapt(by technological or other means). The problemof the future for humanity, it seems, will be toachieve a proper balance between the propensityfor growth and the corresponding deterioration ofthe planet that this requires. On the other hand,to discontinue progress away from equilibriumwill be to halt human evolution. That is thedilemma of the coming environmental age.

Acknowledgements

Support of this project by grants from theMinistry of Education, Youth and Sports of theCzech Republic, No. VS96086 and the GrantAgency of the Academy of Sciences of the CzechRepublic, No. A6007610, are appreciated.

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