The Trophic-Dynamic Aspect of Ecology
Author(s): Raymond L. Lindeman
Reviewed work(s):
Source: Ecology, Vol. 23, No. 4 (Oct., 1942), pp. 399-417
Published by: Ecological Society of America
Stable URL: http://www.jstor.org/stable/1930126 .
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THE TROPHIC-DYNAMIC
RAYMOND
ASPECT OF ECOLOGY
L.
LINDEMAN
OsbornZoological Laboratory,Yale University
community. A more "bio-ecological"
species-distributionalapproach would
recognize both the plants and animals
as co-constituentsof restricted"biotic"
communities,such as "plankton communities,""benthic communities,"etc.,
in which membersof the living community "co-act" with each other and "react" with the non-livingenvironment
(Clementsand Shelford,'39; Carpenter,
CONCEPTS
"COMMUNITY"
'39, '40; T. Park, '41). Coactions and
by bio-ecologists
A chronologicalreview of the major reactionsare considered
of succession.
effectors
to
be
dynamic
the
viewpointsguidingsynecologicalthought
viewpoint, as
The
trophic-dynamic
indicates the followingstages: (1) the
paper, emphasizes the
static species-distributionalviewpoint; adopted in this
of
or "energy-availtrophic
relationship
(2) the dynamic species-distributional
thecommunitywithin
ing"
relationships
viewpoint,withemphasison successional
From
of
succession.
unit
to
the
process
phenomena;and (3) the trophic-dynamic
allied to
is
which
closely
this
viewpoint,
species-distrieither
viewpoint. From
approach
butional viewpoint,a lake, forexample, Vernadsky's"biogeochemical"
'40) and
and
Wollack,
Hutchinson
(cf.
might be considered by a botanist as
of
Friederichs
Sicht"
to
the
"oekologische
containingseveral distinct plant aggrea primfiary
gations, such as marginal emergent, ('30), a lake is consideredas
in
since all
its
own
right,
unit
ecological
floating-leafed,submerged,benthic, or
mentioned
"communities"
the
lesser
phytoplankton communities, some of
which might even be considered as above are dependent upon other comfood cycle (cf.
"climax" (cf. Tutin, '41). The associ- ponentsof the lacustrine
existence.
Upon
for
their
very
1)
figure
ated animals would be "biotic factors"
of
the
cycle,
trophic
consideration
further
to
tending
of the plant environment,
limit or modifythe developmentof the the discriminationbetweenlivingorgancommunity"
aquatic plant communities. To a strict isms as parts of the "biotic
nutriand
inorganic
and
dead
organisms
zoologist,on theotherhand,a lake would
"environment"
of
the
as
tives
parts
seem to contain animal communities
The
roughlycoincidentwith the plant com- seems arbitrary and unnatural.
lines
beclear-cut
of
drawing
difficulty
munities,althoughthe "associated vegenonand
the
tween
the
community
living
tation" would be consideredmerelyas a
is illustratedby the
part of the environment'of the animal living environment
of determiningthe status of a
difficulty
' The term habitatis used by certain ecologists slowly dying pondweed covered with
(Clements and Shelford, '39; Haskell, '40; T.
periphytes,some of which are also conPark, '41) as a synonym for environment
in the
dying. As indicatedin figure1,
tinually
usual sense and as here used, although Park
points out that most biologistsunderstand" hab- much of the non-livingnascent ooze is
itat" to mean "simply the place or niche that rapidly reincorporated through "disRecentprogressin thestudyofaquatic
food-cycle relationships invites a reappraisal of certain ecological tenets.
Quantitative productivitydata provide
a basis for enunciatingcertain trophic
principles, which, when applied to a
series of successional stages, shed new
light on the dynamics of ecological
succession.
an animal or plant occupies in nature" in a
species-distributionalsense. On the other hand,
Haskell, and apparently also Park, use " environment" as synonymouswith the cosmos. It is to
be hoped that ecologists will shortly be able to
reach some sort of agreement on the meanings
of these basic terms.
399
400
RAYMOND
L. LINDEMAN
Ecology,Vol. 23,No. 4
solved nutrients" back into the living magnitude, i.e., the biotic community
"biotic community." This constantor- plus its abiotic environment. The conganic-inorganiccycle of nutritivesub- cept of the ecosystemis believed by the
stance is so completelyintegratedthat writerto be of fundamentalimportance
to consider even such a unit as a lake in interpretingthe data of dynamic
primarilyas a biotic communityappears ecology.
to forcea "biological" emphasis upon a
morebasic functionalorganization.
TROPHIc DYNAMICS
This concept was perhaps first exrelationships
Qualitativefood-cycle
pressedby Thienemann('18), as a result
of his extensive limnologicalstudies on
Althoughcertainaspects of food relathelakes ofNorthGermany. Allee ('34)
tions
have been known for centuries,
expresseda similarview, stating: "The
many
processes within ecosystems are
picturethan finallyemerges . . . is of a
still
very
incompletelyunderstood. The
sort of superorganismicunity not alone
betweenthe plants and animals to form basic process in trophicdynamicsis the
bioticcommunities,but also betweenthe transferof energy from one part of
biota and the environment." Such a the ecosystemto another. All function,
conceptis inherentin the termecosystem, and indeed all life,withinan ecosystem
proposedby Tansley ('35) forthe funda- depends upon the utilizationof an extermental ecological unit.2 Rejecting the nal source of energy, solar radiation.
terms "complex organism" and "biotic A portionof thisincidentenergyis transcommunity,"Tansley writes, "But the formedby the processof photosynthesis
more fundamentalconception is, as it into the structureof living organisms.
seems to me, the whole system(in the In the language of communityeconomics
sense of physics),includingnot only the introducedby Thienemann ('26), autoorganism-complex,but also the whole trophic plants are producerorganisms,
what employingtheenergyobtainedby photocomplexof physicalfactorsforming
we call the environmentof the biome. synthesisto synthesizecomplex organic
. . .It is the systemsso formedwhich, substances from simple inorganic subfromthe point of view of the ecologist, stances. Although plants again release
are the basic units of nature on the face a portionof thispotentialenergyin cataof the earth.. . . These ecosystems,
as bolic processes,a greatsurplusoforganic
we may call them,are of the most vari- substanceis accumulated. Animalsand
ous kinds and sizes. They form one heterotrophicplants,as consumerorgancategory of the multitudinousphysical isms, feed upon this surplusof potential
systems of the universe, which range energy,oxidizinga considerableportion
fromthe universe as a whole down to of the consumed substance to release
the atom." Tansley goes on to discuss kineticenergyformetabolism,but transthe ecosystem as a category of rank formingthe remainderinto the complex
equal to the "biome" (Clements, '16), chemicalsubstancesof theirown bodies.
but points out that the term can also Following death, every organism is a
be used in a generalsense,as is the word potential source of energyfor saproph"community." The ecosystemmay be agous organisms (feeding directly on
formallydefinedas the systemcomposed dead tissues), which again may act as
of physical-chemical-biological
processes energysources for successive categories
active within a space-time unit of any of consumers. Heterotrophic bacteria
and fungi, representingthe most im2 The ecological system composed of the " bioportant saprophagous consumption of
coenosis + biotop " has been termedthe holocoen
by Friederichs('30) and the biosystemby Thiene- energy,may be convenientlydifferentiated fromanimal consumersas specialmann ('39).
October,1942
ASPECT
TROPHIC-DYNAMIC
OF ECOLOGY
j
SolarRadiation
SolarRadiation
A
External
N
Dissolved
Nutrients
Internal
A,
/
PhytoplanKters
Bacteria
2
tZooplantkters~z
\/'l
X
1
A3G
gQ
AIG.
Brawsers--4-
3 Thienemann ('26) proposed the termreducers
forthe heterotrophicbacteria and fungi,but this
term suggests that decomposition is produced
solely by chemical reduction rather than oxidation, which is certainlynot the case. The term
decomposersis suggested as being more appropriate.
-*
-
-N
k
BenicPmaW
Betd
Geerlaized Predatorsn
redainhp
od-yl Predators
S~~~~~~wimfnii
of organic substance.
ized decomposers3
Waksman ('41) has suggested that certain of these bacteria be furtherdifferof organic and
entiated as transformers
inorganic compounds. The combined
action of animal consumersand bacterial
decomposerstends to dissipate the potential energy of organic substances,
themto the inorganic
again transforming
state. From this inorganic state the
autotrophicplants may utilize the dis-
Pandweids
>
OOZ
OmPmdoos
A3
401
na4
A3
aftors A3dman
A
solved nutrientsonce more in resynthesizing complex organic substance, thus
completingthe food cycle.
The careful study of food cycles reveals an intricate pattern of trophic
predilectionsand substitutionsunderlain
by certainbasic dependencies;food-cycle
diagrams, such as figure1, attempt to
portray these underlyingrelationships.
In general,predatorsare less specialized
in food habits than are theirprey. The
ecological importanceof this statement
seems to have been firstrecognizedby
Elton ('27), who discussed its effecton
the survival of preyspecies when predators are numerous and its effect in
enablingpredatorsto survivewhen their
402
RAYMOND
L. LINDEMAN
Ecology,Vol. 23,No. 4
usual prey are only periodicallyabun- figure 1) indicates that the terrestrial
dant. This abilityon the part of preda- food cycle is essentially "mono-cyclic"
tors, which tends to make the higher with macrophyticproducers,while the
trophiclevels ofa foodcycle less discrete lacustrine cycle, with two "life-forms"
than the lower, increasesthe difficulties of producers,may be consideredas "biof analyzing the energyrelationshipsin cyclic." The marine cycle, in which
this portionof the food cycle, and may planktersare the only producersof any
also tend to "shortenthe food-chain."
consequence, may be considered as
Fundamental food-cyclevariations in "mono-cyclic" with microphytic prodifferentecosystems may be observed ducers. The relativeabsence of massive
by comparinglacustrineand terrestrial supportingtissues in planktersand the
cycles. Althoughdissolved nutrientsin very rapid completionof theirlifecycle
the lake water and in the ooze corre- exerta great influenceon the differential
spond directlywith those in the soil, the productivitiesof terrestrialand aquatic
autotrophicproducersdiffer
considerably systems. The general convexityof terin form. Lacustrine producersinclude restrialsystems as contrastedwith the
macrophyticpondweeds, in which mas- concavityof aquatic substrataresultsin
sive supportingtissuesare at a minimum, strikingtrophicand successional differand microphyticphytoplankters,which ences, which will be discussed in a later
in larger lakes definitelydominate the section.
productionof organic substance. TerProductivity
restrial producers are predominantly
multicellular plants containing much
Definitions.-The quantitativeaspects
cellulose and lignin in various types of of trophicecology have been commonly
supporting tissues. Terrestrial herbi- expressed in terms of the productivity
vores, belongingto a great number of of the food groups concerned. Producspecialized food groups, act as primary tivity has been rather broadly defined
consumers(sensu Jacot, '40) of organic as the generalrate of production(Riley,
substance; these groups correspondto '40, and others), a term which may be
the "browsers" of aquatic ecosystems. applied to any or every food group in a
Terrestrial predators may be classified given ecosystem. The problem of proas more remote (secondary, tertiary, ductivityas related to biotic dynamics
quaternary, etc.) consumers,according has been critically analyzed by G. E.
to whethertheypreyupon herbivoresor Hutchinson ('42) in his recent book on
upon other predators; these correspond limnologicalprinciples. The two followroughly to the benthic predators and ingparagraphsare quoted fromHutchinswimmingpredators,respectively,of a son's chapter on "The Dynamics of
lake. Bacterial and fungaldecomposers Lake Biota":
in terrestrialsystems are concentrated The
dynamics of lake biota is here treated as
in the humus layer of the soil; in lakes, primarilya problem of energy transfer. . . the
where the "soil" is overlain by water, biotic utilization of solar energy entering the
decompositiontakes place both in the lake surface. Some of this energyis transformed
water,as organic particlesslowly settle, by photosynthesisinto the structure of phytoplankton organisms,representingan energyconand in thebenthic"soil." Nutrientsalts tent which may be expressed as Al (first
level).
are thus freed to be reutilized by the Some of the phytoplankters will be eaten by
autotrophicplants of both ecosystems.
plankton. This concept appears to have a numThe striking absence of terrestrial ber of adherents in this country. The author
"life-forms"analogous to plankters4(cf. feels that this analogy is misleading, as the
4France ('13) developed the concept of the
edaphon, in which the soil microbiota was represented as the terrestrialequivalent of aquatic
edaphon, which has almost no producers,represents only a dependent side-chain of the terrestrial cycle, and is much more comparable to the
lacustrine microbenthosthan to the plankton.
October,1942
TROPHIC-DYNAMIC
ASPECT
OF ECOLOGY
403
Numerous estimatesof average respirationforphotosyntheticproducersmay
be obtained from the literature. For
terrestrialplants, estimates range from
15 per cent (PUtter, re Spoehr, '26) to
43 per cent (LundegArdh, '24) under
varioustypesofnaturalconditions. For
aquatic producers,Hicks ('34) reported
a coefficientof about 15 per cent for
Lemna undercertainconditions. Wimpenny
('41) has indicated that the respiwhere XAis by definitionpositive and represents
of marineproducersin
the rate of contributionof energyfromA,,- (the ratorycoefficient
previous level) to A,, while Xn' is negative and
polar regions(diatoms) is probablymuch
represents the sum of the rate of energy dissi- less than that of the more "animal-like"
pated from An and the rate of energy content
producers (peridinians and coccolithohanded on to the followinglevel A,,+,. The more
phorids)
of warmerseas, and that teminterestingquantity is XAwhich is definedas the
true productivityof level An. In practice, it is peraturemay be an importantfactorin
necessary to use mean rates over finiteperiods determiningrespiratorycoefficientsin
of time as approximations to the mean rates general. Juday ('40), after conducting
XO, Xi, X2. . . .
numerous experiments with Manning
In the followingpages we shall con- and otherson the respirationof phytosiderthequantitativerelationshipsofthe plankters in Trout Lake, Wisconsin,
followingproductivities:Xo(rate of inci- concludedthat underaverage conditions
dent solar radiation), X, (rate of photo- these producersrespireabout 13 of the
syntheticproduction),X2 (rateofprimary organic matter which they synthesize.
or herbivorousconsumption),X3 (rate of This latter value, 33 per cent, is probsecondaryconsumptionor primarypre- ably the best available respiratorycodation), and X4 (rate of tertiarycon- efficientforlacustrineproducers.
sumption). The totalamountoforganic
Information on the respiration of
structureformedper year for any level aquatic primaryconsumersis obtained
A', which is commonlyexpressedas the from an illuminating study by Ivlev
annual "yield," actually represents a ('39a) on the energy relationships of
value uncorrected for dissipation of Tubifex. By means of ingenious techenergyby (1) respiration,(2) predation, niques, he determined calorific values
and (3) post-mortem decomposition. for assimilation and growth in eleven
Let us now consider the quantitative series of experiments. Using the averaspects of these losses.
ages of his calorificvalues, we can make
Respiratorycorrections.-The amount the followingsimplecalculations:assimiof energylost fromfood levels by cata- lation (16.77 cal.) - growth(10.33 cal.)
bolic processes (respiration)varies con- = respiration(6.44 cal.), so that respirasiderably for the differentstages in the
6.44
lifehistoriesof individuals,fordifferent tion in termsof growth= 1 33= 62.30
levels in the food cycle and for differ- per cent. As a check on the growth
ent seasonal temperatures. In termsof stage of these worms, we find that
annual production,however,individual
growth
deviates cancel out and respiratorydif- asmlti .=
61.7 per cent, a value in
assimilation
ferences between food groups may be
good agreementwith the classical conobserved.
clusions of Needham ('31, III, p. 1655)
I The term stage, in some respects
preferable
with
respect to embryos: the efficiency
to the term level,cannot be used in this trophic
of all developingembryosis numerically
sense because of its long-established usage as a
successional term (cf. p. 23).
similar,between60 and 70 per cent, and
zooplankters (energy content A2), which again
will be eaten by plankton predators (energy
content A3). The various successive levels (i.e.,
stages5) of the food cycle are thus seen to have
successively differentenergycontents (Al, A2, A3,
etc.).
Considering any food-cyclelevel A., energy is
enteringthe level and is leaving it. The rate of
change of the energy content A, thereforemay
be divided into a positive and a negative part:
dAn = n + n',
dt
404
RAYMOND
L. LINDEMAN
Ecology,Vol. 23,No. 4
independentof temperaturewithin the have a higher rate of respirationthan
range of biological tolerance. We may the more sluggish herbivorousspecies;
thereforeconclude that the wormswere the respiratory
rate ofEsox underresting
so conditionsat 20? C. was 3' times that
growingat nearlymaximal efficiency,
that the above respiratorycoefficientis of Cyprinus. The formofpisciangrowth
nearlyminimal. In the absence of fur- curves (cf. Hile, '41) suggests that the
ther data, we shall tentativelyaccept respiratorycoefficient
is much higherfor
62 per cent as the best available respira- fishestowards the end of their normal
foraquatic herbivores.
torycoefficient
life-span. Since thevalue obtainedfrom
foraquatic Ivlev (above) is based on moreextensive
The respiratorycoefficient
predators can be approximated from data than those of Moore, we shall tendata of another important study by tativelyaccept 140 per cent as an averIvlev ('39b), on the energytransforma- age respiratorycoefficientfor aquatic
tionsin predatoryyearlingcarp. Treat- predators.
ing his calorificvalues as in the preceding
Consideringthat predatorsare usually
paragraph,we findthat ingestion(1829 moreactive than theirherbivorousprey,
cal.) - defecation(454 cal.) = assimila- which are in turn more active than the
tion(1375 cal.), and assimilation- growth plants upon which they feed, it is not
(573 cal.) = respiration (802 cal.), so surprisingto find that respirationwith
that respiration in terms of growth respect to growthin producers (33 per
802
cent),in primaryconsumers(62 per cent)
= 140 per cent, a much higher and in secondaryconsumers(>100 per
coefficientthan that found for the pri- cent) increases progressively. These
maryconsumer,Tubifex. A roughcheck differencesprobably reflect a trophic
on this coefficient
was obtained by cal- principle of wide application: the perorificanalysis of data on the growthof centage loss of energydue to respiration
yearling green sunfishes (Lepomis cy- is progressivelygreaterforhigherlevels
anellus) publishedby W. G. Moore ('41), in the food cycle.
which indicate a respiratorycoefficient Predation corrections.-In considering
of 120 per cent with respect to growth, the predation losses fromeach level, it
suggestingthat thesefishesweregrowing is most. convenient to begin with the
more efficiently
than those studied by highest level, A,. In a mechanically
Ivlev. Since Moore's fisheswere fed on perfectfood cycle composed of organa highlyconcentratedfood (liver), this ically discretelevels, this loss by predagreater growth efficiencyis not sur- tion obviouslywould be zero. Since no
prising. If the maximum growth effi- natural food cycle is so mechanically
constituted,some "cannibalism" within
growth
ciency would occur when assimilation
such an arbitrarylevel can be expected,
asmlti
= 60-70 per cent (AEE of Needham, so that the actual value for predation
'31), the AEE of Moore's data (about loss fromAnprobablywill be somewhat
50 per cent) indicatesthat the minimum above zero. The predation loss from
respiratorycoefficientwith respect to level A,,- will representthe total amount
growthmightbe as low as 100 per cent of assimilable energypassed on into the
forcertainfishes. Food-conversiondata higherlevel (i.e., the true productivity,
from Thompson ('41) indicate a mini- X.), plus a quantity representingthe
of less than average,contentof substance killed but
mum respiratorycoefficient
150 per cent foryoungblack bass (Huro not assimilated by the predator,as will
salmoides) at 70? F., the exact percent- be discussed in the followingsection.
age depending upon how much of the The predation loss fromlevel An-2 will
ingestedfood(minnows)was assimilated. likewise representthe total amount of
Krogh ('41) showedthat predatoryfishes assimilableenergypassed on to the next
-
October,1942
level (i.e.,
X,-l)
TROPHIC-DYNAMIC
plus a similar factor for
ASPECT
unassimilatedmaterial,as illustratedby
the data of tables II and III. The
various categoriesof parasitesare somewhat comparable to those of predators,
but the details of theirenergyrelationships have not yet been clarified,and
cannot be included in this preliminary
account.
In conDecomposition corrections.
formitywith the principleof Le Chatelier, the energyof no food level can be
completelyextracted by the organisms
which feed upon it. In addition to the
energyrepresentedby organismswhich
survive to be included in the "annual
yield," much energy is contained in
"killed" tissues which the predatorsare
unable to digest and assimilate. Average coefficientsof indigestible tissues,
based largelyof the calorificequivalents
of the "crude fiber" fractions in the
chemical analyses of Birge and Juday
('22), are as follows:
Nannoplankters....................
Algal mesoplankters. .
Mature pondweeds.
Primaryconsumers..........
Secondary consumers....
Predatory fishes....
...
ca. 5 %
5-35%
ca. 20%
ca. 10%
ca. 8%
ca. 5%
Corrections for terrestrial producers
would certainly be much higher. Alto warthoughthe data are insufficient
thesevalues suggest
ranta generalization,
increasingdigestibilityof the higherfood
levels, particularlyfor the benthiccomponentsof aquatic cycles.
The loss of energydue to premature
causes usually
death fromnon-predatory
must be neglected,since such losses are
exceedingly difficultto evaluate and
undernormalconditionsprobablyrepresent relativelysmall componentsof the
annual production. However,considering that these losses may assume considerable proportionsat any time, the
must
above "decompositioncoefficients"
minimal.
be regardedas correspondingly
Following non-predateddeath, every
organismis a potentialsource of energy
for myriads of bacterial and fungal
405
OF ECOLOGY
saprophages, whose metabolic products
provide simple inorganic and organic
solutes reavailable to photosynthetic
producers. These saprophagesmay also
serve as energy sources for successive
levels of consumers,often considerably
supplementingthe normal diet of herbivores (ZoBell and Feltham, '38). Jacot
('40) considered saprophage-feedingor
coprophagousanimals as "low" primary
consumers,but the writerbelieves that
in the presentstate of our knowledgea
quantitativesubdivisionof primaryconsumersis unwarranted.
Application.-The value of these theoreticalenergyrelationshipscan be illustrated by analyzing data of the three
ecosystemsforwhich relativelycomprehensive productivityvalues have been
published (table I). The summaryacTABLE
I. Productivities of food-groups in
threeaquatic ecosystems,as g-callcm2Iyear,
uncorrectedfor losses due to respiration,predationand
decomposition. Data fromBrujewicz ('39), Juday
('40) and Lindeman ('41b).
Casp ian
Lake
Cedar
Bog
5eapa
Sa Mendota Lake
A.............59.5
Phytoplankters:
Phytobenthos:Al..............0.3
Zooplankters:A2...............20.0
Benthicbrowsers:A2...........1.8*
Benthicpredators:A3...........
20.6
Planktonpredators:A3.
.J.. . .0.8
"Forage" fishes:A3(+A2?) .... .
0.6
0.0
Carp: A3(+A2?).............
.
"Game" fishes:A4(+A3?) . 0.... .
06
Seals: As......................0.01
299
22
22
25.8
44.6
6.1
0.9*
0.8
0.2
?
0.2
0.3
0.0
0.0
0.0
0.1
0.0
* Roughly assuming that 2M of the bottom
fauna is herbivorous(cf. Juday, '22).
count of Brujewicz ('39) on "the dynamics of living matter in the Caspian
Sea" leaves much to be desired, as
bottom animals are not differentiated
into their relative food levels, and the
basis for determiningthe annual production of phytoplankters(which on
theoreticalgroundsappears to be much
too low) is not clearlyexplained. Furthermore,his values are stated in terms
of thousands of tons of dry weight for
the Caspian Sea as a whole, and must
be roughlytransformedto calories per
square centimeterof surfacearea. The
data forLake Mendota, Wisconsin,are
406
RAYMOND
taken directlyfroma general summary
(Juday, '40) of the many productivity
studies made on that eutrophic lake.
The data forCedar Bog Lake, Minnesota,
are taken from the author's four-year
analysis (Lindeman, '41b) of its foodcycle dynamics. The calorificvalues in
table I, representingannual production
of organic matter, are uncorrectedfor
energylosses.
TABLE
III. Productivityvalues for the Lake
Mendotafood cycle,in g-cal/cm2/year,
as corrected
by using coefficients
derivedin the precedingsections,and as givenby Juday ('40).
De
UncorCor- Juday's
cor. S
_rected
_-S Res. .s Prer.. D- rected
lcl*
rected
TrophicLevel pro- pira- da- comp~recte
proppi
duc- tion tion
protivity
Producers: Al. 321*
Primary consumers: A2. 24
Secondary
consumers:
A3........
TABLE II. Productivityvalues for the Cedar
conas corrected Tertiary
Bog Lake food cycle,in g-cal/cm2/year,
sumers:A4.
derivedin the preceding
by using the coefficients
sections.
Trophic level
Ecology,Vol. 23,No. 4
L. LINDEMAN
De- Cor1es- Pre- co -rected
Rnorctd pi
dacorn-proproductivity
prdciiytion
ductionPsl
tion tivity
Producers:yA 70.4?i 10.14 23.4 14.8 2.8 111.3
Primary
consumers:A2 7.0 ? 1.07
4.4 3.1 0.3 14.8
Secondary
3.1
1.8 0.0 0.0
consumers: A3 1.3?0.43*
* This value includes the productivityof the
small cyprinoidfishesfound in the lake.
tion~~~~tiit
107
42
10
480
428
15
2.3
it
1
0.3
0.0
2.3
6
0.12
0.2 0.0
0.0
0.3
0.7
0.3
41.6
144
* Hutchinson ('42) gives evidence that this
value is probably too high and may actually be
as low as 250.
t Apparentlysuch organismsas small " forage"
fishesare not included in any part of Juday's
balance sheet. The inclusion of these forms
might be expected to increase considerably the
productivityof secondary consumption.
ing-capacity"of lakes containingmostly
carp and other"coarse" fishes(primarily
A3), was about 500 per cent that of lakes
containing mostly "game" fishes (primarily A4), and concluded that "this
differencemust be about one complete
link in the food chain, since it usually
requires about five pounds of food to
produceone pound of fish." While such
high "metabolic losses" may hold for
tertiaryand quaternarypredatorsunder
certain field conditions,the physiological experimentspreviously cited indicate much lowerrespiratorycoefficients.
Even whenpredationand decomposition
correctionsare included, the resultant
productivityvalues are less than half
those obtained by using Juday's coefficient. Since we have shown that the
necessarycorrectionsvary progressively
with the differentfood levels, it seems
probable that Juday's "coefficientof
metabolism" is much too high for primary and secondaryconsumers.
Correctingfor the energy losses due
to respiration,predationand decomposition, as discussed in the precedingseclighton the
tions,casts a very different
relative productivitiesof food levels.
The calculation of correctionsfor the
Cedar Bog Lake values for producers,
primaryconsumersand secondaryconsumersare givenin table II. The applicationofsimilarcorrectionsto theenergy
values for the food levels of the Lake
Mendota food cycle given by Juday
('40), as shown in table III, indicates
that Lake Mendota is much more productive of producersand primaryconsumers than is Cedar Bog Lake, while
the productionof secondary consumers
is of the same orderof magnitudein the
two lakes.
In calculating total productivityfor
Lake Mendota, Juday ('40) used a
Biological efficiency
blanketcorrectionof 500 per cent of the
The quantitative relationshipsof any
annual productionof all consumerlevels
for"metabolism,"whichpresumablyin- food-cycle level may be expressed in
cludes both respirationand predation. terms of its efficiencywith respect to
Thompson ('41) found that the "carry- lowerlevels. QuotingHutchinson's('42)
October,1942
TROPHIC-DYNAMIC
ASPECT
OF ECOLOGY
407
of the produc- of the Lake Mendota productivities,no
definition,"the efficiency
tivity of any level (An) relative to the definiteconclusionscan be drawn from
productivityof any previous level (Am)
their relative efficiencies. The Cedar
Bog Lake ratios, however,indicate that
100. If the rate of solar the progressiveefficiencies
is definedas
increasefrom
Xm
energyenteringthe ecosystemis denoted about 0.10 per cent for production,to
of all levels may be 13.3 per cent for primaryconsumption,
as Xo,the efficiencies
referredback to this quantity Xo." In and to 22.3 per cent forsecondaryconof
general, however, the most interesting sumption. An uncorrectedefficiency
of
per
cent
37.5
consumption
tertiary
efficiencies
are those referredto the previous level's productivity(XA1) or those ?t 3.0 per cent (forthe weightratios of
"carnivorous"to "forage" fishesin Ala100. These lattermay bama ponds) is indicated in data pubexpressedas
X~n-1
of lished by Swingle and Smith ('40).
be termed the progressiveefficiencies
increasingefficiencies
the various food-cyclelevels, indicating These progressively
for each level the degree of utilization maywell representa fundamentaltrophic
of its potential food supply or energy principle,namely,that the consumersat
discussed in the progressivelyhigher levels in the food
source. All efficiencies
following pages are progressive effi- cycle are progressivelymore efficientin
ciencies, expressed in terms of relative the use of theirfood supply.
At firstsight, this generalization of
It is impor- increasingefficiency
in higherconsumer
100).
productivities
X~n-1
groups would appear to contradict the
tant to rememberthat efficiencyand
previous generalizationthat the loss of
productivityare not synonymous. Proenergydue to respirationis progressively
ductivityis a rate (i.e., in the units here
greater for higher levels in the food
bewhile efficiency,
used, cal/cm2/year),
cycle. These can be reconciledby reing a ratio, is a dimensionlessnumber.
memberingthat increased activity of
The pointsof referenceforany efficiency
predators considerably increases the
value should always be clearlystated.
chances of encounteringsuitable prey.
/Xn
1001 The ultimateeffectof such antagonistic
The progressiveefficiencies
12
Xn-1 / principleswould presenta picture of a
forthe trophiclevels of Cedar Bog Lake predator completelywearing itself out
and Lake Mendota, as obtained from in the process of completely extermithe productivitiesderived in tables II natingits prey,a veryimprobablesituaand III, are presentedin table IV. In tion. However, Elton ('27) pointedout
viewoftheuncertaintiesconcerningsome that food-cyclesrarely have more than
TABLE IV. Productivitiesand progressiveeffi- five trophic levels. Among the several
factors involved, increasing respiration
cienciesin the Cedar Bog Lake and Lake
Mendotafood cycles,as g-cal/cm2/year
of successive levels of predators contrastedwiththeirsuccessivelyincreasing
Cedar Bog Lake
Lake Mendota
efficiencyof predation appears to be
importantin restrictingthe number of
EffiProducEffiProducciency
tivity
tivity
ciency
trophiclevels in a food cycle.
< 118,872
118,872
Radiation ..........
The effectof increasing temperature
480*
Producers: Al......
111.3
0.10%
0.40%
Primary consumers:
is alleged by Wimpenny('41) to cause a
41.6
A2 .14.8
13.3%
8.7%
ratio, predecreasingconsumer/producer
Secondary
consumers: A3....
3.1
5.5%
22.3%
2.3t
sumably because he believes that the
Tertiary
0.3
consumers: A4....
13.0%
"accelerationof vital velocities" of consumers at increasing temperatures is
* Probably too high; see footnoteof table III.
morerapid than that of producers. He
t Probably too low; see footnote of table III.
-
-
-
408
RAYMOND
L. LINDEMAN
cites as evidence Lohmann's ('12) data
for relative numbers (not biomass) of
Protophyta, Protozoa and Metazoa in
the centrifugeplankton of "cool" seas
(741:73:1) as contrasted with tropical
areas (458:24:1). Since Wimpennyhimself emphasizes that many metazoan
planktersare larger in size toward the
poles, these data do not furnishconvincing proof of the allegation. The
data given in table IV, since Cedar Bog
Lake has a much higher mean annual
water temperaturethan Lake Mendota,
appear to contradictWimpenny'sgeneralization that consumer/producer
ratios
fall as the temperatureincreases.
The Eltonian pyramid
The general relationships of higher
food-cyclelevels to one another and to
communitystructurewere greatlyclarified followingrecognition (Elton, '27)
of the importanceof size and of numbers
in the animals of an ecosystem. Beginningwith primaryconsumersof various
sizes, there are as a rule a number of
food-chainsradiatingoutwardsin which
the probabilityis that predatorswill become successivelylarger,while parasites
and hyper-parasites
will be progressively
smaller than their hosts. Since small
primaryconsumers can increase faster
than largersecondaryconsumersand are
so able to supportthe latter,the animals
Ecology,Vol. 23,No. 4
at the base of a food-chainare relatively
abundantwhilethose towardthe end are
progressivelyfewerin number. The resulting arrangementof sizes and numbers of animals, termedthe pyramidof
Numbers by Elton, is now commonly
known as the Eltonian Pyramid. Wil liams ('41), reporting on the "floor
fauna" of the Panama rain forest,has
recently published an interesting example of such a pyramid, which is
reproducedin figure2.
The Eltonian Pyramid may also be
expressed in terms of biomass. The
weight of all predatorsmust always be
muchlowerthanthat of all food animals,
and the total weight of the lattermuch
lowerthan the plant production(Bodenheimer, '38). To the human ecologist,
it is noteworthythat the populationdensityoftheessentiallyvegetarianChinese,
for example, is much greaterthan that
of the morecarnivorousEnglish.
The principle of the Eltonian Pyramid has been redefinedin termsof productivityby Hutchinson (unpublished)
in the followingformalizedterms: the
rate of production cannot be less and
will almost certainlybe greaterthan the
rate of primaryconsumption,which in
turncannot be less and will almost certainlybe greaterthan the rate of secondary consumption,which in turn . . .
etc. The energy-relationshipsof this
principlemay be epitomized by means
SIZE RANGE
IN Mm
1314
12-13.4
11-12'
810-1
7-4
5F7X
3-4
NUMBERorAmI ALs
FIG. 2.
Eltonian pyramid of numbers, for floor-faunainvertebratesof the Panama rain forest
(fromWilliams, '41).
October,1942
TROPHIC-DYNAMIC
ASPECT
OF ECOLOGY
409
of the productivitysymbolX,as follows: fluenceof some combinationof limiting
factors,which, until they are overcome
Xo > X1 > X2 . . . > Xn.
by species-substitution,etc., tend to
decrease
the accelerationof productivity
This rather obvious generalization is
confirmedby the data of all ecosystems and maintainit at a moreconstant rate.
This tendencytowardsstage-equilibrium
analyzed to date.
of productivitywill be discussed in the
followingpages.
IN SUCCESSION
TROPHIc-DYNAMICS
Dynamic processes withinan ecosyssuccession
in hydrarch
Productivity
tem, over a period of time, tend to
The descriptivedynamicsof hydrarch
produce certain obvious changes in its
is well known. Due to the
succession
species-composition,soil characteristics
and productivity. Change,accordingto essentially concave nature of the subCooper ('26), is the essentialcriterionof stratum, lake succession is internally
succession. From the trophic-dynamic complicated by a rather considerable
viewpoint,succession is the process of influxof nutritivesubstances fromthe
developmentin an ecosystem,brought drainage basin surrounding the lake.
about primarilyby the effectsof the The basins of lakes are gradually filled
organismson the environmentand upon withsediments,largelyorganogenic,upon
each other, towards a relativelystable which a series of vascular plant stages
successivelyreplace one another until a
conditionof equilibrium.
It is well known that in the initial more or less stable (climax) stage is
phases of hydrarch succession (oligo- attained. We are concernedhere,howtrophy-> eutrophy) productivity in- ever, primarilywith the productivity
creases rapidly; it is equally apparent aspects of the successionalprocess.
Thienemann ('26)
that the colonizationof a bare terrestrial Eutrophication.
area representsa similaraccelerationin presented a comprehensivetheoretical
productivity. In the later phases of discussion of the relation between lake
succession,productivityincreases much succession and productivity,as follows:
more slowly. As Hutchinsonand Wol- In oligotrophy,the pioneer phase, prolack ('40) pointedout, these generalized ductivity is rather low, limited by the
changes in the rate of productionmay amountof dissolvednutrientsin the lake
be expressedas a sigmoidcurve showing water. Oxygenis abundant at all times,
a roughresemblanceto the growthcurve almost all of the synthesized organic
of an organism or of a homogeneous matteris available foranimal food; bacteriareleasedissolvednutrientsfromthe
population.
remainder.
Oligotrophythushas a very
of
course,
Such smoothlogisticgrowth,
is seldom found in natural succession, "thrifty"food cycle, with a relatively
except possibly in such cases as bare high "efficiency"of the consumerpopuareas developingdirectlyto the climax lations. With increasinginfluxof nutridrainagebasin
vegetationtype in the wake of a retreat- tivesfromthesurrounding
ingglacier. Most successionalserescon- and increasingprimaryproductivity(X1),
sist of a numberof stages("recognizable, oligotrophyis graduallychangedthrough
clearly-markedsubdivisions of a given mesotrophyto eutrophy,in which consere"-W. S. Cooper), so that their dition the productionof organic matter
will contain (X1)exceeds that which can be oxidized
productivitygrowth-curves
in distinctness (X1')by respiration,predationand bacteundulationscorresponding
to the distinctnessof the stages. The rial decomposition. The oxygensupply
presenceof stages in a successionalsere of the hypolimnionbecomes depleted,
apparentlyrepresentsthe persistentin- withdisastrouseffectson the oligotroph-
410
RAYMOND
L. LINDEMAN
Ecology,Vol. 23,No.4
conditioned bottom fauna. Organisms quantitative value for lakes with comespecially adapted to endure temporary parable edaphic nutrientsupplies being
anaerobiosisreplacethe oligotrophicspe- dependent on the morphometry(mean
cies, accompanied by anaerobic bacteria depth). Since deep lakes have a greater
whichduringthe stagnationperiodcause depth range for plankton photosynthereductionrather than oxidation of the sis, abundant oxygen and more chance
organic detritus. As a result of this fordecompositionof the planktondetriprocess, semi-reducedorganic ooze, or tus before reaching the bottom, such
gyttja,accumulates on the bottom. As deep lakes may be potentially as prooxygen supply thus becomes a limiting ductive as shallower lakes, in terms of
factorof productivity,relativeefficiency unit surface area. Factors tending to
of the consumergroups in utilizingthe lessen the comparative productivityof
synthesizedorganic substance becomes deep lakes are (1) lowertemperaturefor
the lake as a whole, and (2) greater
lower.
correspondingly
The validity of Thienemann's inter- dilutionof nutrientsin termsof volume
pretation, particularly regarding the of the illuminated"trophogeniczone" of
trophic mechanisms,has recentlybeen the lake. During eutrophicationin a
challengedby Hutchinson('41, '42), who deep lake, the phosphoruscontentof the
states that three distinct factors are sedimentfallsand nitrogenrises,untila
involved: (1) the edaphic factor,repre- N/P ratio of about 40/1 is established.
senting the potential nutrient supply "The decompositionof organic matter
(primarilyphosphorus)in the surround- presumablyis always liberatingsome of
ing drainage basin; (2) the age of the this phosphorusand nitrogen. Within
lake at any stage, indicatingthe degree limits,the more organic matter present
of utilizationof the nutrientsupply; and the easier will be such regeneration. It
(3) the morphometriccharacterat any is probable that benthic animals and
stage, dependent on both the original anion exchange play a part in such
morphometryof the lake basin and the processes" (Hutchinson,'42). The proage of the lake, and presumablyinflu- gressive fillingof the lake basin with
encing the oxygen concentrationin the sedimentsmakes the lake shallower,so
hypolimnion. He holds that true eu- that the oxygen supply of the hypotrophicationtakes place only in regions limnionis increasingly,and finallycomwell supplied with nutrients,lakes in pletely,exhausted duringsummerstagotherregionsdevelopinginto"ideotrophic nation. Oxidation of the sediments is
types." The influx of phosphorus is less complete,but sufficient
phosphorus
probablyverygreatin theearliestphases, is believed to be regeneratedfrom the
much greaterthan the supply of nitro- ooze surface so that productivity in
gen, as indicatedby verylow N/P ratios termsof surfacearea remainsrelatively
in the earliest sediments (Hutchinson constant. The nascent ooze acts as a
and Wollack, '40). A large portion of trophic buffer,in the chemical sense,
this phosphorus is believed to be in- tendingto maintainthe productivityof
soluble, as a componentof such mineral a lake in stage-equilibrium(typological
particles as apatite, etc., although cer- equilibriumof Hutchinson) during the
tainlysome of it is soluble. The supply eutrophicstage of its succession.
of available nitrogenincreasessomewhat
The concept of eutrophicstage-equimore slowly, being largely dependent librium seems to be partially confused
upon the fixationof nitrogenby micro- (cf..Thienemann, '26; Hutchinson and
organismseither in the lake or in the Wollack, '40) withthe theoreticallyideal
surroundingsoils. The photosynthetic conditionofcompletetrophicequilibrium,
productivity(X1)of lakes thus increases which may be roughly defined as the
rather rapidly in the early phases, its dynamic state of continuous,complete
October,1942
TROPHIC-DYNAMIC
ASPECT
OF ECOLOGY
411
utilizationand regenerationof chemical energywhichis lost fromthe food cycle,
nutrientsin an ecosystem,without loss is derivedlargelyfromlevel A1,as plant
or gain fromthe outside, under a peri- structures in general are decomposed
odicallyconstantenergysource-such as less easily than animal structures. The
mightbe found in a perfectlybalanced quantity of energypassed on into conaquarium or terrarium. Natural eco- sumer levels can only be surmisedfrom
systemsmay tend to approach a state of undecomposed fragmentsof organisms
trophic equilibrium under certain con- whichare believedto occupythoselevels.
ditions, but it is doubtful if any are Several types of animal "microfossils"
sufficiently
autochthonousto attain, or occur rather consistentlyin lake sedimaintain, true trophic equilibrium for ments,such as the carapaces and postany lengthof time. The biosphereas a abdomensof certaincladocerans,chironwhole, however,as Vernadsky('29, '39) omid head-capsules, fragmentsof the
so vigorouslyasserts,may exhibita high phantom-midgelarva Chaoborus,snail
degreeof true trophicequilibrium.
shells,polyzoan statoblasts,sponge spicThe existenceof prolongedeutrophic ules and rhizopodshells. Deevey ('42),
stage-equilibriumwas firstsuggestedas after making comprehensivemicrofossil
a resultof a study on the sedimentsof and chemicalanalysesofthesedimentsof
Grosser Pl6ner See in Germany (Gro- Linsley Pond, suggested that the abunschopf,'36). Its significancewas recog- dant half-carapaces of the planktonic
nized by Hutchinsonand Wollack ('40), browser Bosmina afford"a reasonable
who based their critical discussion on estimateof the quantity of zooplankton
chemical analyses (ibid.) and pollen produced" and that "the total organic
analyses (Deevey, '39) of the sediments matter of the sedimentis a reasonable
of Linsley Pond, Connecticut. They estimateof the organicmatterproduced
reporteda gradual transitionfromoligo- by phytoplanktonand littoral vegetatrophyto eutrophy(firstattained in the tion." He found a strikingsimilarity
oak-hemlock pollen period), in which in the shape of the curves representing
stage the lake has remainedfor a very Bosmina contentand total organic matlong time,perhapsmorethan4000 years. ter plotted against depth, which, when
They reportindicationsof a comparable plotted logarithmically against each
eutrophicstage-equilibriumin the sedi- other, showed a linear relationshipexments of nearby Upper Linsley Pond pressedby an empiricalpower equation.
(Hutchinsonand Wollack, unpublished). Citing Hutchinsonand Wollack ('40) to
Similar attainmentof stage-equilibrium the effectthat the developmentalcurve
is indicated in a preliminaryreporton fororganicmatterwas analogous to that
the sediments of Lake Windermerein forthe developmentof an organism,he
England (Jenkin, Mortimer and Pen- pressed the analogy furtherby suggestnington, '41). Every stage of a sere ing that the increase of zooplankton
is believed to possess a similar stage- (Bosmina) with referenceto the increase
equilibrium of variable duration, al- of organicmatter(Xi) fittedthe formula
though terrestrialstages have not yet y = bxkfor allometricgrowth (Huxley,
been definedin termsof productivity.
'32), "where y = Bosmina, x = total
The trophicaspects of eutrophication organic matter, b = a constant giving
cannot be determinedeasily from the the value of y when x = 1, and k = the
sediments. In general, however, the 'allometryconstant,'or the slope of the
ratiooforganicmatterto the silt washed line when a double log plot is made."
into the lake fromthe marginsaffords If we representthe organic matterproan approximationof the photosynthetic duced as Xi and furtherassume that
productivity. This undecomposed or- Bosmina represents the primary conganic matter,representing
benthicbrowsers,
the amountof sumers(X2), neglecting
412
RAYMOND
L. LINDEMAN
theformulabecomesX2 = bXlk. Whether
this formulawould expressthe relationship found in other levels of the food
cycle, the developmentof other stages,
or otherecosystems,remainsto be demonstrated.6 Stratigraphic analyses in
Cedar Bog Lake (Lindeman and Lindeman, unpublished) suggest a roughly
similar increase of both organic matter
and Bosmina carapaces in the earliest
sediments. In the modern senescent
lake, however,double logarithmicplottingsof the calorificvalues forXiagainst
Ecology,Vol. 23,No. 4
continuing,at a rate correspondingto
the rate of sedimentaccumulation. In
the words of Hutchinson and Wollack
('40), "this means that duringthe equilibrium period the lake, through the
internal activities of its biocoenosis, is
continuallyapproachinga conditionwhen
it ceases to be a lake."
Senescence.-As a result of long-continued sedimentation, eutrophic lakes
attain senescence, first manifested in
bays and wind-protectedareas. Senescence is usually characterizedby such
X2, and X2 againstX3, forthe fouryears pond-likeconditionsas (1) tremendous
studied, show no semblance of linear increase in shallow littoral area popurelationship,i.e., do not fit any power lated with pondweedsand (2) increased
equation. If Deevey is correct in his marginal invasion of terrestrialstages.
ofthe LinsleyPond micro- Cedar Bog Lake, which the author has
interpretation
fossils,allometricgrowthwould appear studiedforseveral years,is in late senesto characterizethe phases of pre-equilib- cence,rapidlychangingto the terrestrial
rium succession as the term "growth" stages of its succession. On casual
indeed implies.
inspection,the massed verdureof pondThe relative duration of eutrophic weeds and epiphytes,togetherwith spostage-equilibriumis not yet completely radic algal blooms, appears to indicate
understood. As exemplifiedby Linsley great photosyntheticproductivity. As
Pond, the relation of stage-equilibrium pointed out by Wesenberg-Lund('12),
to succession is intimately concerned littoral areas of lakes are virtual hotwiththe trophicprocessesof (1) external houses, absorbing more radiant energy
influxand efflux(partly controlledby per unit volume than deeper areas. At
climate), (2) photosyntheticproductiv- the presenttime the entireaquatic area
ity, (3) sedimentation(partlyby physio- of Cedar Bog Lake is essentiallylittoral
graphic silting) and (4) regenerationof in nature,and its productivityper cubic
nutritivesfrom the sediments. These meterof water is probablygreaterthan
processes apparently maintain a rela- at any time in its history. However,
tivelyconstantratioto each otherduring since radiant energy (Xo) enters a lake
the extended equilibrium period. Yet only fromthe surface,productivitymust
the foodcycleis not in truetrophicequi- be definedin termsof surfacearea. In
librium,and continues to fill the lake these terms,the presentphotosynthetic
with organic sediments. Succession is productivity pales into insignificance
whencomparedwith less advanced lakes
6 It should be mentioned in this connection
in similaredaphic regions; forinstance,
that Meschkat ('37) found that the relationship
X1
is less than 13 that of Lake Mendota,
of population density of tubificids to organic
Wisconsin (cf. table IV). These facts
matter in the bottom of a polluted "Buhnenfeld" could be expressed by the formulay = a-, attest the essential accuracy of Welch's
where y representsthe population density, x is
('35) generalization that productivity
the "determining environmentalfactor," and a
declines greatly duringsenescence. An
is a constant. He pointed out that for such an
expression to hold the population density must interesting principle demonstrated in
be maximal. Hentschel ('36), on less secure Cedar Bog Lake (Lindeman, '41b) is
grounds,suggested applying a similar expression
that duringlate lake senescencegeneral
to the relationship between populations of marine plankton and the "controlling factor" of productivity(X,) is increasinglyinfluenced by climaticfactors,actingthrough
theirenvironment.
October,1942
TROPHIC-DYNAMIC
ASPECT
OF ECOLOGY
413
water level changes, drainage, duration thussubject to a certainnutrientloss by
of winterice, snow cover, etc., to affect erosion,which may or may not be made
the presence and abundance of practi- up by increased availability of such
cally all foodgroupsin the lake.
nutrientsas can be extracted fromthe
Terrestrialstages.-As an aquatic eco- "C" soil horizon.
system passes into terrestrialphases,
Successional productivitycurves.-In
fluctuationsin atmospheric factors in- recapitulating the probable photosyncreasingly affect its productivity. As thetic productivityrelationshipsin hysuccession proceeds, both the species- drarch succession, we shall venture to
compositionand the productivityof an diagram (figure3) a hypotheticalhydroecosystemincreasinglyreflectthe effects sere,developingfroma moderatelydeep
of the regional climate. Qualitatively, lake in a fertilecold temperate region
these climaticeffectsare knownforsoil underrelativelyconstantclimaticcondimorphology
(Joffe,
'36), autotrophicvege- tions. The initial period of oligotrophy
tation (Clements,'16), fauna (Clements is believed to be relativelyshort(Hutchand Shelford,'39) and soil microbiota inson and Wollack, '40; Lindeman
(Braun-Blanquet, '32), in fact forevery '41a), with productivityrapidlyincreasimportantcomponentof the food cycle. ing until eutrophicstage-equilibriumis
Quantitatively,these effectshave been attained. The duration of high euso littlestudied that generalizationsare trophic productivitydepends upon the
most hazardous. It seems probable, mean depth of the basin and upon the
however, that productivity tends to rate of sedimentation,and productivity
increase until the system approaches fluctuatesabout a high eutrophicmean
maturity. Clements and Shelford('39, until the lake becomes too shallow for
p. 116) assertthat both plant and animal maximum growthof phytoplanktonor
productivityis generallygreatestin the regenerationof nutrientsfromthe ooze.
subclimax,except possiblyin the case of As the lake becomesshallowerand more
grasslands. Terrestrial ecosystems are senescent, productivityis increasingly
primarily convex topographically and influencedby climatic fluctuationsand
/
EUTROPHY AE
/
CLIMA
FOREST
~~~~~~~~~~~~BO
I-
0
MAT
0.
SENESCENCE
UOGOTROPHY
TIME
FIG. 3.
->
Hypothetical productivity growth-curveof a hydrosere,developing from a deep lake
to climax in a fertile,cold-temperateregion.
414
RAYMOND
L. LINDEMAN
graduallydeclines to a minimumas the
lake is completelyfilledwith sediments.
The terrestrialaspects of hydrarch
succession in cold temperate regions
usually follow sharply defined,distinctive stages. In lake basins which are
poorly drained, the firststage consists
of a mat, oftenpartlyfloating,made up
primarilyof sedges and grasses or (in
more coastal regions) such heaths as
Chamaedaphneand Kalmia with certain
species ofsphagnummoss (cf. Rigg, '40).
The mat stage is usually followedby a
bog foreststage, in whichthe dominant
species is Larix laricina, Picea mariana
or Thuja occidentalis. The bog forest
stage may be relatively permanent
("edaphic" climax) or succeeded to a
greateror lesser degree by the regional
climax vegetation. The stage-productivities indicated in figure3 represent
only crude relative estimates,as practically no quantitativedata are available.
Ecology,Vol. 23,No. 4
original observations,but are probably
of the correctorderof magnitude. The
mean photosyntheticefficiencyfor the
sea is given as 0.31 per cent (afterRiley,
'41). The mean photosynthetic efficiency for terrestrialareas of the earth
is given as 0.09 per cent ? 0.02 per cent
(afterNoddack, '37), forforestsas 0.16
per cent,forcultivatedlands as 0.13 per
cent, for steppes as 0.05 per cent, and
fordesertsas 0.004 per cent. The mean
photosyntheticefficiencyfor the earth
as a whole is given as 0.25 per cent.
Hutchinsonhas suggested(cf. Hutchinson and Lindeman, '41) that numerical
efficiency
values may provide "the most
fundamental possible classification of
biologicalformationsand of theirdevelopmentalstages."
Almost nothingis known concerning
the efficienciesof consumer groups in
succession. The general chronological
increase in numbers of Bosmina carapaces withrespectto organicmatterand
Efficiency
of Chaoborusfragmentswith respect to
relationships
in succession
Bosmina carapaces in the sedimentsof
The successionalchangesof photosyn- Linsley Pond (Deevey, '42) suggests
thetic efficiencyin natural areas (with progressivelyincreasing efficienciesof
zooplankters and plankton predators.
respect to solar radiation, i.e., Xi 100
On the other hand, Hutchinson ('42)
have not been intensivelystudied. In concludesfroma comparisonof the P: Z
lake succession,photosynthetic
efficiency (phytoplankton:zooplankton) biomass
would be expected to follow the same ratiosofseveraloligotrophicalpine lakes,
course deduced for productivity,rising ca 1: 2 (Ruttner,'37), as comparedwith
to a more or less constantvalue during the ratios for Linsley Pond, 1: 0.22
eutrophicstage-equilibrium,and declin- (Riley, '40) and three eutrophic Bavaing duringsenescence,as suggestedby a rian lakes, 1: 0.25 (Heinrich, '34), that
photosynthetic
efficiency
of at least 0.27 "as the phytoplanktoncrop is increased
per cent for eutrophic Lake Mendota the zooplanktonby no means keeps pace
(Juday, '40) and of 0.10 per cent for with the increase." Data compiled by
senescent Cedar Bog Lake. For the Deevey ('41) for lakes in both mesoterrestrialhydrosere, efficiencywould trophic (Connecticut) and eutrophic
likewise follow a curve similar to that regions (southern Wisconsin), indicate
postulated forproductivity.
that the deeper or morphometrically
Rough estimates of photosynthetic "younger" lakes have a lower ratio of
forvarious climatic regionsof bottom fauna to the standing crop of
efficiency
the earth have been summarized from plankton (10-15 per cent) than the
the literature by Hutchinson (unpub- shallower lakes which have attained
lished). These estimates,correctedfor eutrophicequilibrium (22-27 per cent).
respiration,do not appear to be very The ratiosforsenescentCedar Bog Lake,
reliable because of imperfectionsin the while not directly comparable because
October,1942
TROPHIC-DYNAMIC
of its essentiallylittoralnature,are even
higher. These meagerdata suggestthat
the efficiencies
of consumergroups may
increase throughoutthe aquatic phases
of succession.
For terrestrialstages, no consumer
efficiencydata are available. A suggestive series of species-frequenciesin
mesarch succession was published by
Vera Smith-Davidson ('32), which indicated greatly increasing numbers of
arthropodsin successivestagesapproaching the regionalclimax. Since the photosyntheticproductivityof the stages
probablyalso increased,it is impossible
to determineprogressiveefficiency
relationships. The problems of biological
efficienciespresent a practically virgin
field,which appears to offerabundant
rewardsforstudiesguided by a trophicdynamicviewpoint.
ASPECT
415
OF ECOLOGY
sumers,secondaryconsumers,etc., each
successivelydependentupon the preceding level as a source of energy,with the
producers(A1) directlydependent upon
the rate of incidentsolar radiation (productivityX0)as a source of energy.
3. The more remote an organism is
fromthe initial source of energy (solar
radiation), the less probable that it will
be dependentsolely upon the preceding
trophiclevel as a source of energy.
4. The progressive energy relationships of the food levels of an "Eltonian
Pyramid" may be epitomizedin termsof
the productivitysymbolX, as follows:
XO > Xl > X2.
. . > Xn.
5. The percentageloss of energydue
to respirationis progressively
greaterfor
higherlevels in the foodcycle. Respiration with respectto growthis about 33
per
cent for producers,62 per cent for
In conclusion,it should be emphasized
primary
consumers,and more than 100
that the trophic-dynamic
principlesindiper
cent
forsecondaryconsumers.
cated in the followingsummarycannot
6.
The
consumers at progressively
be expectedto hold foreverysinglecase,
higher
in the food cycle appear to
levels
in accord with the known facts of biobe
progressively
moreefficient
in the use
logical variability. a priori, however,
of their food supply. This generalizathese principlesappear to be valid for
the vast majorityof cases, and may be tioncan be reconciledwiththe preceding
one by rememberingthat increased acexpectedto possess a statisticallysignificant probabilityof validityforany case tivityof predatorsconsiderablyincreases
selectedat random. Since the available the chances of encountering suitable
data summarizedin this paper are far prey.
7. Productivityand efficiency
increase
too meager to establish such generalizaduring
the
early
of
phases
successional
tions on a statistical basis, it is highly
In lake succession, proimportantthat furtherstudies be initi- development.
ductivity
and
photosynthetic
efficiency
ated to test the validity of these and
increase
from
to
a
oligotrophy
prolonged
othertrophic-dynamic
principles.
eutrophicstage-equilibriumand decline
with lake senescence,risingagain in the
SUMMARY
terrestrialstages of hydrarchsuccession.
1. Analysesof food-cyclerelationships
8. The progressiveefficiencies
of conindicatethat a biotic communitycannot sumerlevels,on the basis of verymeager
be clearly differentiated
fromits abiotic data, apparentlytendto increasethroughenvironment;the ecosystemis hence re- out the aquatic phases of succession.
garded as the more fundamentalecological unit.
ACKNOWLEDGMENTS
2. The organismswithinan ecosystem
The author is deeply indebted to Professor
may be grouped into a seriesof moreor
G. E. Hutchinson of Yale University,who has
less discrete trophic levels (Al, A2, A3, stimulated
many of the trophic concepts develAn) as producers, primary con- oped here, generously placed at the author's
416
RAYMOND
L. LINDEMAN
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valuable counsel, and aided the finaldevelopment
of this paper in every way possible. Many of
the concepts embodied in the successional sections of this paper were developed independently
by Professor Hutchinson at Yale and by the
author as a graduate student at the University
of Minnesota. Subsequent to an exchange of
notes, a joint preliminaryabstract was published
(Hutchinson and Lindeman, '41). The author
wishes to express gratitude to the mentors and
friends at the University of Minnesota who
encouraged and helpfully criticized the initial
development of these concepts, particularlyDrs.
W. S. Cooper, Samuel Eddy, A. C. Hodson,
D. B. Lawrence and J. B. Moyle, as well as
other membersof the local Ecological Discussion
Group. The author is also indebted to Drs.
J. R. Carpenter, E. S. Deevey, H. J. Lutz,
A. E. Parr, G. A. Riley and V. E. Shelford,as
well as the persons mentionedabove, forcritical
reading of preliminary manuscripts. Grateful
acknowledgmentis made to the Graduate School,
Yale University, for the award of a Sterling
Fellowship in Biology during 1941-1942.
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ADDENDUM
While this, his sixth completed paper, was in
the press, Raymond Lindeman died after a long
illness on 29 June, 1942, in his twenty-seventh
year. While his loss is grievous to all who knew
him, it is more fitting here to dwell on the
achievements of his brief working life. The
present paper represents a synthesis of Lindeman's work on the modern ecology and past
history of a small senescent lake in Minnesota.
In studying this locality he came to realize, as
othersbeforehim had done, that the most profitable method of analysis lay in reduction of all
the interrelated biological events to energetic
terms. The attempt to do this led him far