Estuaries Vol 18, No. 4, p 547-555 December 1995

Nature's Pulsing Paradigm

WILLIAM E. O D U M 1

Department of Environmental Science Universit~ of Virginia Charlottesville, Virginia 22903

EUGENE P. O D U M 2

Institute ofEcolot, ~ University of Georgia Athens, Georgia 30601

H O W A R D Y. O D U M

Environmental Engineering Sciences University of Florida Gainesville, Florida 32601

ABSTRACT: While the s teady state is of ten seen as the final result o f deve lopmen t in nature, a more realistic concept may be that na ture pu lses regularly to make a puls ing s teady s t a t e - - a new parad igm gaining acceptance in ecology and many o ther fields. In this pape r we compare tidal salt marshes , tidal f reshwater marshes , and seasonal ly f looded fresh- water wetlands as examples o f pu lsed ecosystems. Despi te ma rked d i f fe rences in species composi t ion, biodiversity, and communi ty s t ructure , these wetland types are functionally similar because o f the c o m m o n denomina to r o f water flow pulses. Of t en a per iod o f high product ion al ternates with a per iod o f rapid consumpt ion in these f luctuating water-level s'ystenLs, a biotic puls ing to which many life histories, such as that o f the wood stork, are adapted. Puls ing o f m e d i u m f requency and ampl i tude o f ten provides an energy subsidy for the communi ty thus enhanc ing its productivity. The energy o f large-scale pulses such as s to rms are usually diss ipated in natural ecosys tems with little h a r m to the biotic network; however, when seawalls, dikes, or stabilized sand dunes are cons t ruc ted to conf ron t these s t rong pulses , the whole ecosys tem (and associated h u m a n s t ruc tures) nmy be severly damaged when the barr iers fail because too m u c h o f the s t o rm energy is concent ra ted on them. T he relat ionship between biologically med ia t ed iotern',d pulsing, such as plant- herbivore or predator-prey cycles, and physical ex te rna l puls ing is d iscussed not only in wetlands but in o ther ecosys tem types as well. An intr iguing hypothes is is that ecosys tem p e r f o r m a n c e and species survival are enhanced when external and internal pu lses are coupled. We suggest that if puls ing is general , then what is susta inable in ecosystems, is a repeat ing oscillation that is of ten po ised on the edge o f chaos.

In t roduct ion

The concepts by which we view nature are some- times called paradigms. One of our comfor tab le concepts of na ture visualizes growth followed by a leveling. In these days when society is beg inn ing to recognize the limits o f the b iosphere , people , sci- entists, and gove rnmen t s talk of sustainability, that is, manag ing growth so that the l ife-support car- rying capacity of the ear th is not exceeded. The steady state is seen as a goal for such efforts as well as the final result of self-o~-ganization in nature. However, there may be a more realistic concept , that na ture pulses even after carrying capacity or satuarat ion limits are reached (Fig. 1 ) - - a new par- adigm we define and present examples of in this paper.

2 Naturalists-ecologists are s addened by the unt imely dea th of William E. O d u m in April 1991.

2 Cor re spond ing author .

First, we review pulsing in wetlands ecosystems as a background for a discussion and model l ing of a general theory of the pulsing paradigm; special a t tent ion is given to the interact ion of external and internal pulses.

It is generally accepted that the key to wetland f imction and s t ructure is the pulsing water-flow re- gime, or the hydroper iod . Organisms not only adapt to the pulse but may also utilize tile water- flow energy to enhance productivity as shown in Figs. 2 and 3. Tidal wetlands, especially the con- trasting saline and freshwater marshes, provide ex- cellent sites for the study of the interact ion of phys- ical and biotic componen ts . Riverine swamp and f loodplain forests display o ther aspects of the puls- ing paradigm.

Compar i son o f Tidal Freshwater and Saltwater Wetlands

Ocean-dr iven lunar tides are not only a domi- nant physical factor in coastal estuaries but ex tend

�9 1995 Estuarme Research Federation 547 0160-8347/95/04547-09S01 50/0

5 4 8 W.E . Odum et al.

Pulsing Slgmold Growth

j Trne

Fig. 1. The sigmoid growth model with pulses superim- posed. Pulses arc no! trends, but very often are part of long- term trends.

T STAGNANT SEASONAL FLOODING I FLOWING ABRASIVE OR T,OAL FLOOO,NG

NO SUBSIDY ' SUBSIDY ~ * STRESS

Fig. 3. Graphic model of the relationship between produc- tivity and a flooding gradient in wetlands, shown as a subsidy- stress model.

1.6

1.2 OJ

= E O . 8

v

0 . 4

o

o/ OO o fo o

o o

go

O o O

I 1 I I 0 1 2

T IDE R A N G E - M E T E R S

806

t,,,l~ 700 =

500 Uplamd m

4OO

Moodlng Gradient

Fig. 2. Relalionship between hydroperiod and productivity. The upper graph illustrates tidal amplitude as it varies with bio- mass production in Spartina salt marshes (fi'om Steew~r et al. 1976). The lower graph illustrates the productivity of bottom- land forests along a flooding gradient (from Birch and Cooley 1983).

m a n y ki lometers ups t r eam in coastal plain rivers, c rea t ing tidal f reshwater wetlands. It is no t unusua l to have a g rea te r tidal r ange ups t r eam than in the estuary. For example , at the m o u t h o f the P o t o m a c River the tidal r ange is app rox ima te ly 70 cm while 100 km ups t r eam in tidal fi-eshwater marshes n e a r Wash ing lon the tidal ranges exceed 1 m. This can be a t t r ibu ted largely to the cons t r ic t ing o f the tidal water mass as it moves ups t r eam in a cont inua l ly na r rowing river channe l .

T h e p resence o r absence o f salt in a tidal marsh makes a d i f fe rence in the vegetative s t ruc ture and the tood web as well as in species compos i t ion , bu t pe rhaps n o t in overall productivi ty, which tends to be h igh ill bo th ecosystem types. Salt r educes the" net p r i m a r y product ivi ty o f vascular plants since they must invest m o r e ene rgy I o exc lude salt an d sultides, bu t at the c o m m u n i t y level this r e d u c t i o n may be c o m p e n s a t e d for by the con t r ibu t ion to product iv i ty by mar ine algae, g rea te r a rea t ion o f sed iments due to b u r r o w i n g o f t iddler crabs, and the p resence o f m o r e C~ plants.

Salt-marsh plants, largely pe renn ia l g r amino ids and ha lophyt ic shrubs, are f ibrous and r ema in s t and ing t h r o u g h o u t the year. In contras t , fresh- water lidal h e r b a c e o u s marsh plants are m o r e fleshy a nd m a n y d e c o m p o s e down to m u d level in the winter (W. E. O d u m a nd H o o v e r 1987). Col- on iza t ion a nd dispersal o f m a c r o p h y t e s in saline marshes is largely by w.'getative g rowth o f rh izomes; in f reshwater marshes by seeds. T h e a n a e r o b i c mi- crobial c o m p o n e n t is d o m i n a t e d by sulfate reduc- ers in the salt marsh and m e t h a n e p r o d u c e r s in tim f reshwater marsh. Sed imen t s in tidal f reshwater marshes on awwage are h ighe r in o rgan ic c o n t e n t

and are less sandy than those in the estuaries. Food chains in the salt marsh tend to end up in aquatic organisms-shr imp, crabs and tish in salt marshes, while semi-aquatic w; r tebra tes - - fo r example , filr- bearers, amphibians , reptiles, ducks and avian wad- ers, are more often at the end of food chains in the freshwater wetlands.

Species diversity of vascular plants ( including emergen t annual and perennia l aquatic macro- phytes, shrubs, and trees) is very much grcatcr up- stream, but diversity of fish and invertebrates can be very high in bo th tidal salt and freshwater eco- systems. Seasonal changes in species in salt marsh- es are mostly conf ined to the sediments where green mud-algae domina te in the s u m m e r and di- a toms donfinate in the winter. In contrast, there may be a p r o n o u c e d seasonal succession of vascu- lar plants in tidal freshwater marshes with peren- nials such as Peltrandra and Acorus domina t ing ear- ly and annuals such as Zizannia, Polygonum, and Ni- dens peaking later in the growing season. These and o ther contrasts between tidal salt and fresh- water marshes are detai led in W. E. O d u m ' s papers and m o n o g r a p h s (W. E. O d u m et al. 1984; W. E. O d u m and Hoover 1987; W. E. O d u m et al. 1987; W. E. O d u m 1988).

Despite the many differences in the physical na- ture of the env i ronmen t and in species composi- tion, the two marsh-types are more similar than dif- fe ren t in overall funct ion because of the forcing fimction of tidal pulsing. High productivity result- ing, in par t at least, f rom the energy subsidy of the tides (E. E O d u m 1980), is a c o m m o n denomi- na tor o f both marsh types. Ano the r c o m m o n de- n o m i n a t o r is that a large par t o f the food web is detri tus-based in these marshes and also in man- groves (W. E. O d u m et ai. 1972; W. E. O d u m and l lea ld 1975; W. E. O d u m and Heywood 1978; E. P. O d u m 1980; W. E. O d u m 1984).

The auxiliary energy of water tlow may not only alter the rate of p r imary a n d / o r secondary pro- ductivity but may also alter tim course of ecological succession. Where the input is regular in occur- rence, as in tidal systems, the ecosystem may be "pulse-stabil ized" at a youthfill stage character ized by high net communi ty product ion , some of which may nourish an adjacent less product ive system. The outwelling of organic mat te r and organisms f rom a product ive estuary to adjacent coastal wa- ters is an example of such a "source-s ink" process (E. P. O d u m 1980). Whe t he r an estuary exports or impor t s may d e p e n d on geomorphology , especially whether the connec t ion between estuary and the sea is narrow or b road (W. E. O d u m et al. 1979).

Nontidal Wetlands In nont idal wetlands such as inland marshes,

f loodplain, and swamp torcsts, the pulse is seasonal

Nature's Pulsing Paradtgm 549

or per iodic ra ther than daily. Water levels rise and tall one or more times a year. O f course, tidaI wet- lands arc also subjected to seasonal f looding mad storms. The ampl i tude of f looding in inland wet- lands is often much grea ter and lasts longer, but they are less f requen t than the tidal pulses. The interaction between pulse height and periodicity is complex, bnt neverless many species of plants and animals are especially adapted to the longer te rm periodicity and uncertainty. C3~press, for example , tolerate extensive or i r regular f looding but must have a p ro longed drawdown exposing the surface of sediments before seeds will germina te . Conse- quently, many stands are even-aged.

The wood stork (Mycteria americana) is an ex- ample of a species especially adap ted to nont idal wetlands having a shallow, f luctuat ing water-level. As tirst worked out by Kahl (1964), this species breeds when small fishes arc be ing concen t ra ted in small pools as water levels are falling. Unlike many waders, this species is a " tact i le-feeder" that waits for fish to actually touch the h a l f ~ p e n e d beak before grasping them. in the past the wood stork bred abundant ly in south Florida dur ing the winter dry season when water levels in the Ever- glades and elsewhere were lowest. But, this natural seasonal pulse has been so disrupted by h u m a n water diversions and i m p o u n d m e n t s that the stork has now moved nor th to breed in small undis- turbed wetlands where the seasonal draw down in spring is more reliable.

Graphic Models of Productivity of Pulsed Wetlands

In general , increasing pulse ampl i tude increases net productivity in most types of wetlands up to an o p t i m u m point beyond which too much f looding reduces productivity. In coastal salt marshes, for ex- ample , productivity increases up to an average tidal range of 2 m or 3 m (Fig. 2, upper ) . This is why productivity of salt marshes in the Georgia-South Carol ina Bight, where tidal ampl i tude is high, is grea ter than to the no r th or south where the am- pl i tude is less. Tidal ampl i tude on the Gull" Coast is small, but f requen t s torms result in considerable water-level f luctuat ion to which the biota are adapt- ed. Regular tides above 3 m or so may cause such severe erosion that productivity is r educed (Bay of Fundy, tor example) . In this case, the energy may go into geologic ra ther than biologic work. A sim- ilar pat tern is seen in f loodplain and swamp forests (Table 1 and Fig. 2, lower). Productivity is highest where f looding is modera te , especially where high water occurs in the d o r m a n t season. Too much f looding is a stress that reduces productivity and diversity, but interest ing and valuable species may thrive in this env i ronment . Cypress and tupelo

550 W. E Odum et al.

TABI.E 1. Productivity estimates tidal and nontidal wetlands. All figures: g dry matter m -2 yr -~ in round numbers.

Tidal marshes Spamna alterniflora salt anarshes, Sapelo. (Gallagher et al. 1981; Pomeroy and Wiegert 1982)

Streamside marsh-strong daily tides Middle marsh--less strongly inundated daily High marsh--spring tide flooding only

Spartzna cynosormdes brackish tidal marsh (E.E Odum and Fanning 1973) I,ow elevation--daily tides tIigher elevation--periodic flooding

Zzzamops~s mdmcea fi'eshwater tidal marsh (E.I'. Odum, Birch and Cooley 1983) Tidal hnpounded (diked)

Swamp and floodplain forests (nontidal) Florida cypress (Mitch and Ewell 1979; Brown 1981)

Seasonal flooding (winter) Flowing water Stagnant (ponded)

Cypress-Gum-Louisiana (Conner et al. 1981) Seasonal flooding Flowing water Stagnant

Bottomland hardwood and Cypres,ML;um-GA (Birch and Cooley 1983) Seasonal flooding Occasional flooding Continuous flooding (stagnant) Upland--no flooding

3,700 2.400 1,200

2,100 900

1,530 1,172

3,000 2,000 1.000

1,200 700 200

800 600 550 450

gum, for example, may develop adventitous "water roots" (as well as "knees" and swollen buttresses) at the water-sediment interface that overcome the stress of an anaerobic root envi ronment resulting from cont inuous flooding.

Figure 3 is a general graph of the relation be- tween productivity and the pulsing gradient in wet- lands, shown as a subsidy-stress model (E. P. O d u m et al. 1979).

Bio log i ca l l y M e d i a t e d Interna l P u l s e s

Since wetlands are true ecotones in that they have properl ies and species not found in the ad- jacent land arid open water, it is important to note that internal structures and processes, such as tro- pic interactions, root masses, microbial and animal activity, play a role along with external forces in nlaintaining wetlands as pulsing ecotones (W. E. O d u m 1990).

By no means are all pulsings directly related to the external physical environment . All ecosystems exhibit internal pulses, mostly biologically mediat- ed, such as plant-herbivore, predator-prey, and par- asite-host oscillations. For example, extensive study and experimentat ion has so far failed to link any environmental physical factor with tile " b o o m and bust" cycles of tent caterpillars and budworms in nor the rn forests. The latest findings are that. spe- cial viruses are involved in the alternation of weak and strong generations. In a recent, review, Meyers (1993) states that, "these insects seem to have

been adapted by years of evolution to insure that outbreaks do not devastate the host trees." In fact, as a general rule, parasite-host and herbivore-plant interactions co-ew)lved for co-existence in a puls- ing state so that despite the oscillating evolutionary "arms race" the parasite or herbivore does not eliminate its food supply and thereby itself (Mex- ander 1981; Anderson and May 1982). Such co- evolution may inw)lve what we can term reward feedback, where the parasite or herbiw)re does something to promote the welfare of the host (or to put it in more general terms, where a down- stream c o m p o n e n t in a food web benefits an up- stream componen t ) . For example, it has been shown that the saliva of grasshoppers and mam- malian grazers contains growth hormones that stimulates the regrowth of the grass on which they feed (Dyer et al. 1986).

Interact ions B e t w e e n Externa l and Interna l P u l s e s

Suzane Painting describes, in a recent doctoral dissertation, an interesting case of "diet-switching" as a pulsing that results from the linking of differ- ent food chains with an external upwelling pnlse. As reported by Pomeroy (1992), upwellings off the west coasts of North and South America and Africa are rich in nitrates that support a dense phyto- plankton-zooplankton bloom. The phytoplankton quickly deplete the nitrogen and subside before tile zooplankton haw~ had lime to conlplete their

N a t u r e ' s Pulsing Paradigm 551

Pulsed Energy

Biomass Storage

X X ,j3,"~'~1 k2

Removal

R = S - kO*R*Q*W a \~.ll R = S/(1 + kO*Q*W)

dQ/dt = E I *R*Q*W - E2*Q- k3*Q*W

Push-pull Model of Physical Energy Pulses Fig. 4. Minimodel of the pulses of physical enerw and the production and lo~s of" biomass.

reproductive cycle. The zooplankton t h e n switch Io

feeding on protozoa that thrive on the smaller phy- toplankton and bacteria subsisting on the dissolved organic matter that has accumulated fl'om the hlooms. The oscillation of different fo?d chains as a response to external pulses in this manne r is probably of c o m m o n occurence.

What is little unders tood is how internal pulses, such as plant-herbivore cycles, are relaled to exter-

Pulse Energy

"~."7'"~7('.: ,..'\[:.J'~~f~~ ..".["v":~-7":')~..'-. -" ] / ' v ' . : '

Storage __- - - - - - - - -

Gross Production N, ' Yield N

r x r ~ e ~ . r e"~ r r ~ ' . r - .~ , '~ . ~ , a , . , , ~ .,-, r ~ . , , , , ' , , , . r ' , , . ~ . & , ' 3 . , : , ~ . ~ . ..~ . . . , . . . , . : . ~- : : , . , , ; ~ ; " . ~ _ i . ' - . ; - . L . , . . ~_ .~ -~ - - " 2 ~ ". .: : ' ~ -: : : ~ ." : : �9

-~ , . . , = . . ; . . , �9 : . . . . - . : , , : . . . . . . . : , . . - ' : ' i " . : . ! : ' - : : : ' . " : " ' "." " " ' - . . : . ' . " "

:- - ", ", ' t ; ' . : , ' , " " : : -[ . " .- ] -, " ' ' " - '

Net Production

Time

Fig. 5. Simulation of the model in Fig. 4 for an intermediate level of physical energy pulses.

nal pulses, such as tides. An intrigning hypolhcsis, to be discussed later in this paper, is thai synchro- nism of internal and external pillses enhances eco- system per formance as a wtmle.

Simulat ion Models

Minimodels are usefill to isolate effects that are part of more complex systems, ,nuch as one does with controlled experimenls. A push-pull model of physical energ 3, effects on biomass product ion is shown in Fig. 4. The work that comes from pulses of physical energy such as water-hwel flucuations are shown amplifying product ion on the left and removing biomass on the right, l'hysical energies improve the necessary circulation of inputs and waste products. Very strong physical energies may remove more biomass than is p roduced and also divert energies in other ways.

A typical simulation with opt imum levels of pulsed physical energy increases gross product ion arid causes net product ion greater than the con- current removal (Fig. 5). The average of several runs at different levels of physical energy are plot- ted in Fig. 6. At higher levels of energy, net pro- duction and biomass are diminished, even though

5 5 2 W E. Odum et al.

50

E .o nn

A

d / """~-~....... I I I

I

I i I

10 20 30 40

o" v t- .o

' o

~0-~ z

E-41~, l - .,.

/ \ / "" /

B

"x-IF.."

I ! I

10 20 30 40 0

0.2 C Gross Production (P)

E --" J ~ "

7 Removal (Y)~ ~ ~

0 10 20 30 40

Pulse Energy

Fig. 6. Resuhs of simulation of the model in Fig. 4 for dif- ti~rent levels of energy pulses: (A) stored biomass as a function of pulsed energy; (B) net product ion as a function of ptdsed energy; and (C) energy flow in gross product ion and removal processes as a fimction of pulsed energy.

the th roughput of product ion anti biomass does not diminish. Many kinds of stress p roduce this kind of effect, increasing turnover time and caus- ing small, high turnover organisms to replace the larger ones that maximize productivity at lower stress levels.

Whereas the model does help account for the opt ima observed in many produc t ion dau~ (Figs. 2 and 3), it is not sensitiwr enough to varying fre- quency nor to pulse alteration of p roduc t ion and consumption.

Mattet Tm Conserved Rer r162 ~ ] ~

dQldt=k;'E'M.k2~ k3"C*C~ ~ dC/dt=k3"Q*C*C+kS'Q-k4"C

T

"',,,,. ....'" .. .

�9 Consumer CIlm,~ 4~ { Growth ir ! / , prod=cer C:,max\ ~ ~ ~escent i

A

B

C

Ttme

Fig. 7. Pulsing alteration of product ion, consumpt ion and recycling in the internal oscillating Alexander model (II. T. O d u m 1983): (A) systems diagram and equations; (B) typical oscillations; and (C) modified use of the classical names "suc- cession" and "cl imax" suggested for regions of sustainable puls- ing.

General Pulsing Theory In all the scales of nature from tiny last systems

of bit)chemistry to file largest galaxies of the cos- ntos, we observe systems that pulse. Host-parasite and predator-prey cycles are examples. As Fig. 7 suggests, growth of one part of nature consumes and pulls down ano ther part of nature temporarily. Then a cycle is comple ted with retrogression and regrowth (Fig. 7). Since pulses occur at all scales, the larger scales impose their bursts on the smaller scales. Each part of nature is composed of pulsing componen t s and is occasionally impacted by a pulse fi'om the larger scale. An ecosystem is driven by pulses of its energy inputs and also by oscilla- tions from within its own network, as in the up- welling-diet switching case described earlier in this paper.

Pulsing in o n e place may be out of phase with that in ano ther so that growth and retrogression, as well as source-sink exchanges of materials and organisms, makes a patchy landscape with each area in a different stage of pulsing. The divcrsity that comes f rom patches is thus a part of the puls-

ing of patches; it may increase the gross perfor- mance of tire landscape as averaged over a longer scale.

The pulsing of nonliving systems of geology, me- teorology, and oceanography is par t o f the pulsing of the ecosystems. One of the main ways that the ear th part icipates in ecosystems and vice versa is t h rough the pulsing of rains, tides, floods, etc. Wet- lands are a good example of the way ecosystems organize to fit the pulses of resources arrd th rough their own cycles of growth impose pulses on the envi ronment . The kind of wetland depends on the f requency of impact ing oscillations.

The works of na ture are governed by energy laws. Energy is par t of all processes and is trans- fo rmed f rom one fo rm to ano the r in food chains. According to one theory, which was tirst offered a century ago, systems develop relat ionships that mutual ly re inforce the et t icient processing of en- ergy. For example , energy of sun and water flows ".are t r ans formed into the productivity of marsh veg- etation. The rate of flow of energy is power. As Lotka (1924, 1925) stated, systems that maximize useful power in p roduc t ion tend to prevail. How- ever, there is a t radeof f between efficiency and power (It. T. O d u m and Pinker ton 1955). A system that is a r r anged to be very efticient may go too slowly, delivering less productivity. A system that is a r ranged to go faster at lower efticiency may be too wastefifl o f energy. The question for us here is how are power and efficiency related in pulsing systems that a l ternate per iods of net p roduc t ion and times of net consumpt ion .

It may be that systems in level steady state do not have the o p t i m u m efficiency for max innun power, whereas the pulsing systems do more produc t ion in the long run. All this is still theory, but there has to be some basic reasons why all systems have the per iodic pulsing of their processes related to tire level o f their energy sources.

Pulsing, Energy, and Chaos May (1974) showed lhat the spurts of change in

iterative digital s imulat ion could cause the logistic equat ion mode l for growth to go into a fo rm of chaos. I f the inc rements of adding stock were large relative to the stock stored, the stock would j u m p to a high value. This high value would cause the next i teration to decrease massively so the stock j u m p e d to a lower level. The result was a j u m p i n g rap and down of the stock with time.

In our model ing, we have always been careful to identit~r an energy source with any mathemat ica l model , thus making tile system realistic to energy contraints. The " r " (intrinsic rate of natural in- crease) is really the specific growth rate based on an unl imited energy source (i.e., a source that pro-

Nature's Pulstng Paradtgm 553

rides a constant input concent ra t ion regardless of demand) . We write " r = k*E" so that the growth te rm is k*E*Q where Q is the stock, thus recogniz- ing that tile intrinsic rate is really p ropor t iona l to the extrinsic energy source concent ra t ion E (It. T. O d u m 1983, p. 144). If this energy source is in- creased, then the a m o u n t of flow involved for the same periods of growth and outflow is greater, the chaos becomes greater, involving more and more levels of j u m p i n g until the plot o f points with t ime appears without pa t te rn (hence the name chaos). Graphs of energy-driven logistic: chaos are shown in Beyers and O d u m (199.'3, p. 124). Since the it- erat ion in this logistic example is in tile digital compu t ing and not in the real world, we call this "artificial chaos."

However, tile principle that we draw fl 'om this illustration is that whenever an oscillation (puls- ing) is causing a system to fill and discharge, the more chaos is caused and tile larger and more complex are the oscillations.

As par t of a review of Keith 's book on the 10-yr cycle of wildlife in Canada (H. T. O d u m 1964) it was suggested that the observed fact of shifting pe- riod of the wildlife oscillations might be accounted for by shifts in the rates without abandon ing the general idea that predator -prey oscillations were the main cause. IJater we s imulated one predator- prey cycle with low f requency being driven by a smaller per iod of high frequency. The simulation result (Beyers and O d u m 1993, p. 124-125) pro- duces oscillations with shifting periods. On a phase plane plot (graph of one species as a f imction of ano ther ) , the similation traces loops that change with each oscillation, but within an ou te r limiting loop, which in chaos te rminology is the attractor. Hanski et al. (1993) has also related the predator- driven 4-yr arctic roden t cycles to chaos theory.

S ince nea r ly all e cosys t ems are a p p a r e n t l y hierchical and pulsing, at least some ot" the time, the pulses of the smaller, faster species be ing cou- pled to the larger slow-turnover species, p roduce chaotic oscillations. There fore , we conclude that a corollary of the "puls ing pa rad igm" is that oscil- lations can be expec ted to b e c o m e chaotic: when energy levels are increased.

I_Jet us now turn the reasoning around. Chaotic models such as those we have just discussed can be stabilized without oscillations by relatively mino r adjustments in coefficients. Why then do systems self-organize with chaotic oscillations instead of de- veloping proper t ies and species that do not oscil- late? It may be that chaotic dynamic mechan isms provide a bet ter loading of ecosystem work to in- put energy, one that optimizes efficiency and max- imizes power in the long run.

Kauffman (1993) using examples and simula-

5,54 W E. Odum et al

lions of molecular, organismal and popula t ion bi- ology sought general systems principles about the evolution of life and its env i ronmenta l basis. I I e proposes that life in ecosystems is adap ted to, and more stable in the long run with, pulsing systems. On page 28(1 he writes: "Co-evolving systems whose m e m b e r s have tuned the s tructure of their fitness landscapes and couplings to o ther m e m b e r s such that the entire ecosystem is poised at the edge of chaos appc'ar to sustain the highest fitness. Thus we may adop t the hypothesis that selection attains systems which are poised both internally and col- lectivity."

Frequency Modulation, Niches, and Resonance

Somet imes we com pare wetlands to a H'equency modula ted radio. For different f requencies of puls- ing and hydroper iod , different species may he best adap ted to draw useful work. Different f requencies of input energ'y are different niches [or species op- portunity.

Campbel l (1984) studied with a long series o f c o m p u t e r simulations the transfer of enc'rgy f rom pulsing inpms Io systems with internal oscillations, such as predator-prey cycles. Max imum contr ibu- tion to the system's p roduc t ion was ob ta ined when the f requency of inputs were similar to the fre- quency of internal oscillation. Re in forcement of product ion comes ti 'om coupl ing of external and internal pulses is somet imes called resonance. Sys- tems with adap ted ha rmonics are re inforced by res- onance. Thus, dur ing self:<)rganization an ecosys- tem develops the c o m p o n e n t s that maximize en- ergy available f rom the pulsing. Campbel l ([984) tbund a mode l calibrated tbr sah-marsh dam had good proper t ies of energy capm,-e fi-om energy- pulsed inputs.

Zwick (1985) studied the coupl ing of pulsed in- puts to systelns with inertial impedance (ones gen- erated as a par t o f the process of storing input en- ergy surges). By using genera l systems models , be- havior long known for electrical and mechanica l systems was ex tended to biological and social sys- tems where pulses are aclively resisted while energy of the pulse is t r ans formed and stored.

Pulsing Enhancement of Ecosystem Performance

When ecosystems receiw~ pulsing on a small scale of space and t ime (high frequency pulsing), the pulses are general ly absorbed, their energy used adding small-scale variation and microdivers- ity. For example , microbial oscillations do not in- terfere with larger detri tus consumers .

When an ecosystem receives pulsing ot~ the same scale of space and time as its own oscillations (me-

dium fi 'equency pulsing), it can benefi t if it has species that can resist the pulses enough to catch and use the pulsing energy. As we have noted ear- lier in this pape r tidal pulses are used by many species to aid their feeding, behavior, life histories, and migration, therehy enhanc ing productivity of the whole system.

When ecosystems receive periodic pulsing of a much larger scale (low frequency pnlsing) the en- ergies may pass th rough without much absorpt ion if lhe c o m p o n e n t s don ' t resist the pe r tmba t ions . For example , W. E. ( ) d u m et al. (1987b) fomul that natural coaslal grassy dunes were able to sin-- rive infrequent s torms by main ta in ing a loose s tructure that allows the wave energies to he dissi- pated over the whole dune system; in o ther words, sands e rode and redeposi t without destroying the biotic network. On tile; outer banks of Nor th Car- olina, shifting dunes periodically blocked traffic on a highway that was built th rough the dune system. Hop ing to reduce this tendency, in t roduced grass- es were planted on the tore dunes to [0rm a more rigid and resistent tu r f that did indeed stabilize the dunes unde r condit ion of ordinary winds and waves. But, when the big s torm came, the efli~ct of the resistence was to catch too much of the energ 3' so that the whole system was destroyed and tile damage to the highway and o ther h u m a n struc- tures was much more severe than before. The same situation is evident where seawalls on beaches and dikes on rivers are constructed; small s torms and tloods are conta ined but big ones break throtugh the resisting st ,uctures, often doing m o r e damage than would occ tn jn the absence of such barr iers (Kautman and Pilkey 1983; W. E. O d u m el al. 1987). In general , it pays to design with nature ' s pulses ra ther than Io conf ront them[

Summary Tile prevalence of pulsing in all scales of the

earth and beyond and the widespread energy transfer th rough coupl ing of oscillators seems to be the general rule. Very steady steady-states are the except ion, a l though they can be induced m microcosms by cutt ing off tile outside pulses (Be- yers and H. T. O d u m 1993). The interact ion o f external and inlernal pulses often enhances , but somet ime seeins to detract f rom, the overall per- t b rmance of the ecosystem. An attractive hypoth- esis is that by pulsing and appropr ia te coupl ing of external and internal pulsing, a h igher perfor- mance is obtained, which genera tes more uork, thus re infbrcing the system's characteristics. I f pulsing is general , then what is sustainable in eco- systems is a repeat ing oscillation.

I JTERATURE CrI'ED

ALE~XI~ER, M. 1981. W] W mrcrobial parasites and predators do not eliminate their prey and hosts. Annual bb~fiew of Mzcro- &olo~. 35:113-133.

ANDERSON, R. M. AND R. M. MAY 1982. Coevolution of hosts and parasites. Parasttolo~ 85:411-426.

BIRCn, J. B. ANDJ. L. COOLEY. 1983. The effect of hydroperiod on floodplain forest production. ERC 08-83 Environmental Research Center, Georgia Institute of Technology, Atlanta, Georgia.

BROW, N, S. 1981. A comparison of structure, primary produc- tivity and transpiration of cypress ecosystems in Florida. Eco- logical Monographs 51:403~-~27.

BEYI';RS, R.J. AND It. 32 ODUM. 1983. Ecological Microcosms. Springer-Verlag, New York.

CAMPBELt., D. E. 1984. Energy tilter properties of ecosystems. Ph.D. Dissertation, Environmental Engineering Sciences, Uni- versity of Florida, (;zinesville, Florida.

CONNFR, W. I-1., J. B. (~,OSSEI.INK, AND R. Y. PARRONDO. 1981. Comparison of vegetation of three I,ouisiana swamp site ~ith different flooding regimes. American Journal of Botany 68:320- 331.

DYER, M. I,., D. I.. l)LAx(;Ei,ls, :'d'~t~ W. M. POST. 1986. A model for herbivore feedback in plant productivity. Mathemattcal Bz- osciences 79:171-184.

GAI.I~XGHER, .J. I,., R. J. RE1MOLD, R. A. LINTIILRST, AND W. J. PFEIH"ER. 1981. Aerial production, mortality, and mineral ac- cumulation-export dynamics in Spartina altermflora and Juncus 7aemerianus plant stands. Ecob~ 61:303-312.

IIANSKI, I., P. TURCttIN, E. KORPI.MAKI, AND 11. HENTI'ONEN. 1993. Population oscillations of boreal rodents: Regulation by mnstelid predators leads to chaos. Nature 361:232-233.

KMIL, M. P. 1964. The food ecology of the wood stork. Ecolo~cal Monographs 34:97-117.

K.kUFMAN, W. AND 0.11. PII.KEi: 1983. The Beaches Are Moving. l)nke Uni-versity Press, I)urham, North Carolina.

K~,t:FFMAN, S. A. 1993. The Origin of Order. Oxford University Press, UK

I.OrKA A.J. 1922, A contribution to the energetics of evolution. Proceedzngs of the National Academy of Seiences 8:140-155.

LOTWL A.J. 1925. Elelnenrs of Physical Biology. William & Wil- kins, Baltimore, Maryland.

MA'~. R. M. 1974. Biological populations with non-overlaping generations stable points, stable cycles, and chaos. Saev~ce 186: 645~547

MrIcH, W.J. ANI) K. C. E~.T.Lt,. 1979. Comparative biomass and growth of cypress in Flolhda. Amo~can Midland Naturalist 101: 417-~26

ME~I.:~S,J. II. 1993. Population outbreaks in toresl lepidoptera. American Sctentzst 81:240-251.

ODUM, E. R 1980. The status of three ecosystem-level hypotll- eses regarding salt marsh estuaries. Tidal subsidy, outwelling and detritus based food chains, p. 485-495. In V. S. Kennedy ted.), Estuarine Perspectives. Academic Press, New York.

OI)t!M, E. P., J. B. BIRCrl, AND.]. L. COOI,FY. 1983. Comparison of giant cuttgrass productivity in tidal and ilnponnded marsh- es with special leference to tidal subsidy and waste assimila- tion. Estuarws 6:88--94

OI)UM, E. P. AND M. E. FANNING. 1973. Comparison of the pro- ductivity of Spartina altermfloca and Spartma ~nosuroides in Georgia coastal marshes. Geo~gm Jout hal of Saence 31:1-12.

OI~UM, E. R,.l. "E FINN, AND E. H. FRANZ. 1979. Perturbation theory and the subsidy-srre~s gradient. BioSctence 29:349-352

ODUM, tl. T. 1964. Review of Keith's Wildlife's Ten Year Cycles. A meru'an Scientist 52:2.

ODb'm, H. T. 1983 Systems Ecology, Jolm Wiley & Sons, New York.

ODUM, H. T. AND R. C. PlNI~.I'RTON. 1955. Times speed regula-

Nature's Pulsing Paradigm 555

tor; tile optimum efficiency for maxinmm power output in physical and biological systems. American Sctentist 43:321-343.

ODUM, W. E. 1988. Comparatiw~ ecology of tidal freshwater and salt marshes Annual Ib~fiew of Ecology and Svstematics 19:147- 176.

ODUM, W. E. 1990. lnternal processes influencing the mainte- nance of ecotones. Chapter 6 In R. J. Naiman and tl. De- camps (eds.), The Ecology and Management of Aquatic-Te1~ restrial Ecosystems. Parthenon Publishing Group. Park Ridge, New Jersey.

ODUM, W. E. AND E. J. HEALD. 1975. The detritus hased food web of an estuarine mangrove community, p. 265-286. In L. E. Cronin ted.), Estuarine Research, Vol. 1. Academic Press, New York.

ODUM, W. E. AND M. A. Ih.:~WOOD, 1978. Decomposition of intertidal freshwater plants, p. 89 97. [n R. E. Good, F. Wbigh- am, and R. I,. Simpson (eds.), Freshwater Wetlands, Ecologi- cal Processes and Management Potential. Academic Press, New ~brk.

ODUM, W. E., J. s. FISHER, AND J. c. PICKF~M.. 1979. Factors controlling the flux of particulate carl)on from estuarine wet- lands, p. 69-80. h~ R.J. Livingston (ed.), Ecological Processes in Co:tstal and Marine Systems. Marine Science Series No.10. Plenum Publishing Corporation, New York.

ODUM, W. E. ANDJ. K. HOOVER. 1987. A comparison of vascular plant communities ira tidal freshwater and sahwater marshes, p. 526--534. In D. D. Hook, W. H. McKec, Jr., H. K. Smith, J. C;regory, v. G. BurrelI,Jr., M. R. I)eVoe, R. E. Sojka, S. Gilbert, R. Banks, L. II. Stolzy, C. Brooks, T. D. Matthews, and T. tI. Shear (eds.), The Ecology and Management of Wetlands. Vol- ume 1 : Ecology of Wetlands. Timber Press, Portland, Oregon.

ODUM, "VV. E., I,. P. ROZAS, AND ("~. C. M(:IvoR 1987a. A com- parison of fish and invertebrate community composition in tidal ti'eshwater and oligohaline marsh systems, p. 561-5(59. h~ D. D. Itook, W. II. McKee, Jr., II. K. Smith, J. Gregory, V. G. Burrell,.Jr., M. R. DeVoe, R. E. Sojka, S. Gilbert, R. Banks, L. II. Stolz b C. Brooks, "12 D. Matthews, and T. H. Shear (cds.), The Ecolog 3, and Management of Wetlands. Vohnne 1: Ecolog T of Wetlands. Timber Press, Portland, Oregon.

OI)UM, W. E., T. J. SMIIH, AND R. DOI.AN. 1987b. Suppression of natural disturbance: l,ong-term ecological change on the Outer Banks of North Carolina, p. 123-135. In M. G. Turner ted.), Landscape Heterogeniety and Disturbance. Ecological Studies 65, Springer-Verlag, New York.

()I)UM, W. E., "E J. SMITH, J. K. IIoow:R, AND C. C. MCI.VOR. 1984. The Ecology of Tidal Freshwmer Marshes of the United States East Coast: A Community Profile. United States Fish and Wildlife Service. FWS/OB&83/17.

ODI:M, W. E., J. C. ZIEMAN, AND E.J. I IEALD. 1972. The impor- tance of vascular" plant detritus to estuaries, p. 91-11,t. In R. H. ('habreck ted.), Proceedings of the ('oastal Marsh and Es- tuary Management Symposimn. Louisiana State University Di- vision of Continuing Education, Baton Rouge, I.ouisiana.

PAINTING, S.J. 1989. Bacterioplankton dynamics in the south- ern Benguela upwelling region. Pb.D. Dissertation. University of Cape Town, South Afi-ica.

POMEROV, I,. R. 1992. The microbial food web. Oceanus 35:28- 35.

POMEROY, L. R...xgr) R. G. WIFGFRT. 1982. Ecology of a Salt Marsh. Ecological Studies 38. Springer-Verlag, New York.

SrEEW:R, E. Z., R. S. WARREN. A'<D W. A. NIERING. 1976. Tidal energy subsidy and standing crop production of Spartina al- ternifloria. Estumine, Coastal and MaNne Science 4:473--478.

ZWmK, P. D. 1985. Energ'y systems and inertial oscillation. Ph.D. Dissertation, Universit), of Florida, Gainesville, Florida.

Recemed for consideratmn, December 16, 1993 Accepted for p~tbticatmn, May 7, 1995