The Trophic-Dynamic Aspect of Ecology Raymond L. Lindeman

The Trophic-Dynamic Aspect of Ecology

Raymond L. Lindeman

Ecology, Vol. 23, No. 4. (Oct., 1942), pp. 399-417.

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http://www.jstor.org Mon Sep 24 13:51:25 2007 THE TROPHIC-DYNAMIC ASPECT OF ECOLOGY

RAYMONDL. LINDEMAN Osborn Zoological Laboratory, Yale University

Recent progress in the study of aquatic community. A more "bio-ecological" food-cycle relationships invites a re- species-distributional approach would appraisal of certain ecological tenets. recognize both the plants and animals Quantitative productivity data provide as co-constituents of restricted "biotic" a basis for enunciating certain trophic communities, such as "plankton com- principles, which, when applied to a munities," "benthic communities," etc., series of successional stages, shed new in which members of the living commu- light on the dynamics of ecological nity "co-act" with each other and "re- succession. act" with the non-living environment (Clements and Shelford, '39 ;Carpenter, '39, '40; T. Park, '41). Coactions and reactions are considered bv bio-ecoloaists A chronoloaical- review of the maior u viewpoints guiding synecological thought to be the dynamic effectors of succession. indicates the following stages: (1) the The trophic-dynamic viewpoint, as static species-distributional viewpoint; adopted in this paper, emphasizes the (2) the dynamic species-distributional relationship of trophic or "energy-avail- viewpoint, with emphasis on successional ing" relationships within the community- phenomena; and (3) the trophic-dynamic unit to the process of succession. From viewpoint. From either species-distri- this viewpoint, which is closely allied to butional viewpoint, a lake, for example, Vernadsky's "biogeochemical" approach might be considered by a botanist as (cf. Hutchinson and Wollack, '40) and containing several distinct plant aggre- to the "oekologische Sicht" of Friederichs gations, such as marginal emergent, ('30), a lake is considered as a primary floating-leafed, submerged, benthic, or ecological unit in its own right, since all phytoplankton communities, some of the lesser "communities" mentioned which might even be considered as above are de~endentuDon other com- "climax" (cf. Tutin, '41). The associ- ponents of the lacustrine food cycle (cf. ated animals would be "biotic factors" figure 1) for their very existence. Upon of the plant environment, tending to further consideration of the trophic cycle, limit or modify the development of the the discrimination between living organ- aquatic plant communities. To a strict isms as parts of the "biotic community" zoologist, on the other hand, a lake would and dead organisms and inorganic nutri- seem to contain animal communities tives as parts of the "environment" roughly coincident with the plant com- seems arbitrary and unnatural. The munities, although the "associated vege- difficulty of drawing clear-cut lines be- tation" would be considered merely as a tween the living communityand the non- part of the environment l of the animal living environment is illustrated by the difficulty of determining the status of a t The term habitat is used by certain ecologists slowly dying pondweed covered with (Clements and Shelford, '39; Haskell, '40; T. Park, '41) as a synonym for environment in the periphytes, some of which are also con- usual sense and as here used, although Park tinually dying. As indicated in figure 1, points out that most biologists understand "hab- much of the non-living nascent ooze is itat" to mean "simply the place or niche that rapidly reincorporated through "dis- an animal or plant occupies in nature" in a species-distributional sense. On the other hand, be hoped that ecologists will shortly be able to Haskell, and apparently also Park, use "environ- reach some sort of agreement on the meanings ment" as synonymous with the cosmos. It is to of these basic terms. i99 400 RAYMOND L. LINDEMAN Ecology, Vol. 23, No. 4 solved nutrients" back into the living magnitude, i.e., the biotic community "biotic community." This constant or- plus its abiotic environment. The con- ganic-inorganic cycle of nutritive sub- cept of the ecosystem is believed by the stance is so completely integrated that writer to be of fundamental importance to consider even such a unit as a lake in interpreting the data of dynamic primarily as a biotic community appears ecology. to force a LLbiological"emphasis upon a more basic functional organization. This concept was perhaps first expressed by Thienemann ('18), as a result Qua1itati.de food-cycle relationships of his extensive limnological studies on the lakes of Korth Germany. Allee ('34) Although certain aspects of food rela- expressed a similar view, stating: "The tions have been known for centuries, picture than finally emerges . . . is of a many processes within ecosystems are sort of superorganismic unity not alone still very incompletely understood. The between the plants and animals to form basic process in trophic dynamics is the biotic communities, but also between the transfer of energy from one part of biota and the environment." Such a the ecosystem to another. All function, concept is inherent in the term ecosystem, and indeed all life, within an ecosystem proposed by Tansley ('35)for the funda- depends upon the utilization of an exter- mental ecological unit.2 Rejecting the nal source of energy, solar radiation. terms "complex organism" and "biotic portion of this incident energy is trans- community," Tansley writes, "But the formed by the process of photosynthesis more fundamental conception is, as it into the structure of living organisms. seems to me, the whole system (in the In the language of community economics sense of physics), including not only the introduced by Thienemann ('26), auto- organism-complex, but also the whole trophic plants are producer organisms, complex of physical factors forming what employing the energy obtained by photo- we call the environment of the biome. synthesis to synthesize complex organic . . . It is the systems so formed which, substances from simple inorganic sub- from the point of view of the ecologist, stances. Although plants again release are the basic units of nature on the face a portion of this potential energy in cata- of the earth. . . . These ecosystems, as bolic processes, a great surplus of organic we may call them, are of the most vari- substance is accumulated. Animals and ous liinds and sizes. They form one heterotrophic plants, as consumer organ- category of the multitudinous physical isms, feed upon this surplus of potential systems of the universe, which range energy, oxidizing a considerable portion from the universe as a whole down to of the consumed substance to release the atom." Tansley goes on to discuss kinetic energy for metabolism, but trans- the ecosystem as a category of rank forming the remainder into the complex equal to the "biome" (Clements, '16), chemical substances of their own bodies. but points out that the term can also Following death, every organism is a be used in a general sense, as is the word potential source of energy for saproph- "community." The ecosystem may be agous organisms (feeding directly on formally defined as the system composed dead tissues), which again may act as of physical-chemical-biological processes energy sources for successive categories active within a space-time unit of any of consumers. Heterotrophic bacteria and fungi, representing the most im- The ecological system composed of the "bio- portant saprophagous consumption of coenosis + biotop " has been termed the holocoen by Friederichs ('30)and the biosystem by Thiene- energy, may be conveniently differenti- mann ('39). ated from animal consumers as special- October, 1942 TROPHIC-DYNAMIC ASPECT OF ECOLOGY 401

Sdar Radiation Solor Radiation

FIG.1. Generalized lacustrine food-cycle relationships (after Lindeman, '4lb). ized decomposers3 of organic substance. solved nutrients once more in resynthe- Waksman ('41) has suggested that cer- sizing complex organic substance, thus tain of these bacteria be further differ- completing the food cycle. entiated as transformers of organic and The careful study of food cycles re- inorganic compounds. The combined veals an intricate pattern of trophic action of animal consumers and bacterial predilections and substitutions underlain decomposers tends to dissipate the po- by certain basic dependencies; food-cycle tential energy of organic substances, diagrams, such as figure 1, attempt to again transforming them to the inorganic portray these underlying relationships. state. From this inorganic state the In general, predators are less specialized autotrophic plants may utilize the dis- in food habits than are their prey. The Thienemann ('26) proposed the term reducers ecological importance of this statement for the heterotrophic bacteria and fungi, but this seems to have been first recognized by term suggests that decomposition is produced Elton ('27), who discussed its effect on solely by chemical reduction rather than oxida- the survival of prey species when predation, which is certainly not the case. The term decomposers is suggested as being more appro- tors are numerous and its effect in priate. enabling predators to survive when their 402 RAYMOND L. LINDEMAN Ecology, VO~.23, NO.4

usual prey are only periodically abun- figure 1) indicates that the terrestrial dant. This ability on the part of preda- food cycle is essentially "mono-cyclic" tors, which tends to make the higher with macrophytic producers, while the trophic levels of a food cycle less discrete lacustrine cycle, with two "life-forms" than the lower, increases the difficulties of producers, may be considered as "bi- of analyzing the energy relationships in cyclic." The marine cycle, in which this portion of the food cycle, and may plankters are the only producers of any also tend to "shorten the food-chain." consequence, may be considered as Fundamental food-cycle variations in "mono-cyclic" with microphytic pro- different ecosystems may be observed ducers. The relative absence of massive by comparing lacustrine and terrestrial supporting tissues in plankters and the cycles. Although dissolved nutrients in very rapid completion of their life cycle the lake water and in the ooze corre- exert a great influence on the differential spond directly with those in the soil, the productivities of terrestrial and aquatic autotrophic producers differ considerably systems. The general convexity of ter- in form. Lacustrine producers include restrial systems as contrasted with the macrophytic pondweeds, in which mas- concavity of aquatic substrata results in sive supporting tissues are at a minimum, striking trophic and successional differ- and microphytic phytoplankters, which ences, which will be discussed in a later in larger lakes definitely dominate the section. production of organic substance. Ter- Productivity restrial producers are predominantly multicellular plants containing much Dejinitions.-The quantitative aspects cellulose and lignin in various types of of trophic ecology have been commonly supporting tissues. Terrestrial herbi- expressed in terms of the productivity vores, belonging to a great number of of the food groups concerned. Produc- specialized food groups, act as primary tivity has been rather broadly defined consumers (sensu Jacot, '40) of organic as the general rate of production (Riley, substance; these groups correspond to '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 pro- as more remote (secondary, tertiary, ductivity as related to biotic dynamics quaternary, etc.) consumers, according has been critically analyzed by G. E. to whether they prey upon herbivores or Hutchinson ('42) in his recent book on upon other predators; these correspond limnological principles. The two follow- roughly to the benthic predators and ing paragraphs are quoted from Hutchin- swimming predators, respectively, of a son's chapter on "The Dynamics of lake. Bacterial and fungal decomposers Lake Biota": in terrestrial systems are concentrated The dynamics of lake biota is here treated as in the humus layer of the soil; in lakes, primarily a problem of energy transfer . . . the where the "soil" is overlain by water, biotic utilization of solar energy entering the decomposition takes place both in the lake surface. Some of this energy is transformed water, as organic particles slowly settle, by photosynthesis into the structure of phytoplankton organisms, representing an energy con- and in the benthic "soil." Nutrient salts tent which may be expressed as At (first level). are thus freed to be reutilized by the Some of the phytoplankters will be eaten by autotrophic plants of both ecosystems. plankton. This concept appears to have a nuin- The striking absence of terrestrial her of adherents in this country. The author "life-forms" analogous to plankters * (cf. feels that this analogy is misleading, as the edaphon, which has almost no producers, repre- Franc6 ('13) developed the concept of the sents only a dependent side-chain of the terres- edaphon, in which the soil microbiota was repre- trial cycle, and is much more comparable to the sented as the terrestrial equivalent of aquatic lacustrine microbenthos than to the plankton. October, 1942 TROPHIC-DYh-.-\3IIC ASPECT OF ECOLOGY 403 zooplankters (energy content .I?). \vhich again Sunierous estimates of average respi- \\.ill be eaten by plankton predators (energy ration for photosynthetic producers may content .i3). The various successive le\rels (i.e., stages6) of the food cycle are thus seen to have be obtained from tlie literature. For successively different energy contents (.11, '12, '13, terrestrial plants, estimates range from etc ). 15 per cent (Putter, re Spoelir, '26) to Considering any food-clcle level .I,,, energy is 43 per cent (Lundeg5rdl1, '24) under enterlng the lc\el and is leaving it. The rate of various types of natural conditions. For t hange of the energy content .intherefore may be divided into a positive and a negative part: aquatic producers, Hicks ('34) reported d,I,, a coefficient of about 15 per cent for - = A,, + A,,', dt Lemna under certain conditions. IYim- penny ('41) has indicated that the respi- \\.here A,, is 11). definition positive and represents the rate of contribution of energy from 1\,-1 (the ratory coefficient of marine producers in previous le\rcl) to A,,, \vhile A,,' is negative and polar regions (diatoms) is probably much rrpresents the sum of the rate of energy dissi- less than that of tlie more "animal-like" pated from .I,and the rate of energy content producers (peridinians and coccolitho- handed on to the follo\ving level A,,+I. The more interesting quantity is A,, ~vhichis defined as the phorids) of lvarnler seas, and that teni- true prodzictiz'ity of level A,,. In practice, it is perature may be an important factor in necessar!. to use mean rates over finite periods determining respiratory coefficients in of time as approsirnations to the mean rates general. Juday ('40), after conducting Ao, A,, A?. . . . numerous experiments lvith Alanning In the follo\ving pages we shall con- and others on the respiration of phyto- sider the quantitative relationships of tlie plankters in Trout Lake, IYisconsin, folloxving productivities: Xo (rate of inci- concluded that under average conditions dent solar radiation), XI (rate of plioto- these producers respire about % of the synthetic production), X2 (rate of primary organic matter lvliich they synthesize. or herbivorous consumption), Xg (rate of This latter value, 33 per cent, is prob- secondary consumption or primary pre- ably the best available respiratory co- dation), and XI irate, of tertiary con- efficient for lacustrine producers. sumption). The. total aniount of organic Information on the respiration of structure forrnctl pcr >~'arfor any level aquatic primary consumers is obtained Ai,, which is comnionly elpressed as the from an illuminating study by Ivlev annual "yiclcl," actually represents a ('39a) on the energy relationships of value uncorrected for dissipation of Tubifex. By means of ingenious tech- energy by (1) rcspiration, (2) pred a t'ion, niques, he determined calorific values and (3) post-mortem decomposition. for assimilation and gro\vtli in eleven Let us nolv consider the cluantitative series of experiments. Using the aver- aspects of these losses. ages of his calorific values, we can make Respiraiory corrections.-The amount the follolving simple calculations: assimi- of energy lost from food levels by cata- lation (16.77 cal.) - growth (10.33 cal.) bolic processes (respiration) varies con- = respiration (6.44 cal.), so that respira- siderably for the different stages in the 6.44 tion in terms of growth = -- 62.30 life histories of individuals, for different 10.33 levels in the food cvcle and for differ- per cent. As a check on tlie growth ent seasonal temperatures. In terrns of stage of these worms, \ye find that annual production, however, individual growth deviates cancel out and respiratory dif- = 61.7 per cent, a value in assirnilation ferences between footl groups may be observed. good agreement with tlie classical conclusions of Needliam ('31, 111, p. 1655) The term stage, in some respects preferable with respect to embryos: the efficiency to the term lez'el, cannot he used in this trophic sense because of its long-established usage as a of all developing embryos is numerically successional term (cf. p. 23). similar, between 60 and 70 per cent, and 404 RAYMOND L. LINDEMAN Ecology, Vol. 23, No. 4 independent of temperature \vithin the have a higher- rate of res~irationthan range of biological tolerance. We may the more sluggish herbivorous species; therefore conclude that the worms were the respiratory rate of Esox under resting growing at nearly maximal efficiency, so conditions at 20°C. was 39 times that that the above respiratory coefficient is of Cyprinus. The form of piscian growth nearly minimal. In the absence of fur- curves (cf. Hile, '41) suggests that the ther data, we shall tentatively accept respiratory coefficient is much higher for 62 Der cent as the best available res~ira- fishes towards the end of their normal tory coefficient for aquatic herbivores. life-span. Since the value obtained from The respiratory coefficient for aquatic Ivlev (above) is based on more extensive predators can be approximated from data than those of Moore, we shall ten- data of another important study by tatively accept 140 per cent as an aver- Ivlev ('39b), on the energy transforma- age respiratory coefficient for aquatic tions in predatory yearling carp. Treat- predators. ing his calorific values as in the preceding Considering that predators are usually paragraph, we find that ingestion (1829 more active than their herbivorous prey, 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 surprising to find that respiration with that respiration in terms of growth respect to growth in producers (33 per 802 cent), in primary consumers (62 per cent) - 140 per cent, a much higher 573 - and in secondary consumers ( >100 per coefficient than that found for the pri- cent) increases progressively. These mary consumer, Tubifex. A rough check differences probably reflect a trophic on this coefficient was obtained by cal- principle of wide application: the per- orific analysis of data on the growth of centage loss of energy due to respiration yearling green sunfishes (Lepomis cy- is progressively greater for higher levels anellus) published by W. G. Moore ('41), in the food cycle. which indicate a respiratory coefficient Predation corrections.-In considering of 120 per cent with respect to growth, the predation losses from each level, it suggesting that these fishes were growing is most convenient to begin with the more efficiently than those studied by highest level, A,. In a mechanically Ivlev. Since Moore's fishes were fed on perfect food cycle composed of organ- a highly concentrated food (liver), this ically discrete levels, this loss by preda- greater growth efficiency is not sur- tion obviously would be zero. Since no prising. If the maximum growth effi- natural food cycle is so mechanically growth constituted, some "cannibalism" within ciency would occur when assimilation such an arbitrary level can be expected, = 60-70 per cent (AEE of Needham, so that the actual value for predation '31), the AEE of Moore's data (about loss from An probably will be somewhat 50 per cent) indicates that the minimum above zero. The predation loss from respiratory coefficient with respect to level An-l will represent the total amount growth might be as low as 100 per cent of assimilable energy passed on into the for certain fishes. Food-conversion data higher level (i.e., the true productivity, from Thompson ('41) indicate a mini- A,), plus a quantity representing the mum respiratory coefficient of less than average content of substance killed but 150 per cent for young black bass (Huro not assimilated by the predator, as will salmoides) at 70' F., the exact percent- be discussed in the following section. age depending upon how much of the The predation loss from level A,-2 will ingested food (minnows) was assimilated. likewise represent the total amount of Krogh ('41) showed that predatory fishes assimilable energy passed on to the next October, 1942 TROPHIC-DYNAMIC ASPECT OF ECOLOGY 405 level (i.e., A,-I), plus a similar factor for saprophages, whose metabolic products unassimilated material, as illustrated by provide simple inorganic and organic the data of tables I1 and 111. The solutes reavailable to photosynthetic various categories of parasites are some- producers. These saprophages may also what comparable to those of predators, serve as energy sources for successive but the details of their energy relation- levels of consumers, often considerably ships have not yet been clarified, and supplementing the normal diet of herbi- cannot be included in this preliminary vores (ZoBell and Feltham, '38). Jacot account. ('40) considered saprophage-feeding or Decomposition corrections. -In con- coprophagous animals as "low" primary formity with the principle of Le Chate- consumers, but the writer believes that lier, the energy of no food level can be in the present state of our knowledge a completely extracted by the organisms quantitative subdivision of primary con- which feed upon it. In addition to the sumers is unwarranted. energy represented by organisms which Application.-The value of these the- survive to be included in the "annual oretical energy relationships can be illus- yield," much energy is contained in trated by analyzing data of the three "killed" tissues which the predators are ecosvstems for which relativelv comDre- unable to digest and assimilate. Aver- hensive productivity values have been age coefficients of indigestible tissues, published (table I). The summary ac- based largely of the calorific equivalents TABLEI. Productivities of food-groups in of the "crude fiber" fractions in the three aquatic ecosystems, as g-cal/cm2/year, uncor- chemical analyses of Birge and Juday rected for losses due to respiration, predation and decomposition. Data from Brujewicz ('39),Juday ('22), are as follows: ('40) and Lindeman ('41b). Nannoplankters...... ca. 5% Algal mesoplankters...... 5-35% Caspian Cedar Bog Mature pondweeds...... ca. 20% 1 sea / dota Lake Primary consumers...... ca. 10% - Phytoplankters: A,...... 59.5 25.8 Secondary consumers...... ca. 8% Phytobenthos: A,...... 0.3 44.6 Predatory fishes...... ca. 5% Zooplankters: Az...... 20.0 6.1 Benthic browsers: Az...... 0.8 Benthic predators: ha...... 20.6 0.2 Corrections for terrestrial producers Plankton predators: A3...... 0.8 Forage" fishes: Aa(+Az?) ...... 0.6 0.3 would certainly be much higher. Al- Sarp: Aa(+ Az?) ...... 0.0 0.0 Game" fishes: Ad(+ Aa?) ...... 0.6 0.0 though the data are insufficient to war- Seals: A6...... 0.01 0.0 rant ;generalization, these values suggest increasing digestibility of the higher food * Roughly assuming that 2/5 of the bottom fauna is herbivorous (cf. Juday, '22). levels, particularly for the benthic components of aquatic cycles. count of Brujewicz ('39) on "the dy- The loss of energy due to premature namics of living matter in the Caspian death from non-predatory causes usually Sea" leaves much to be desired, as must be neglected, since such losses are bottom animals are not differentiated exceedingly difficult to evaluate and into their relative food levels, and the under normal conditions probably repre- basis for determining the annual pro- sent relatively small components of the duction of phytoplankters (which on annual production. However, consider- theoretical grounds appears to be much ing that these losses may assume con- too low) is not clearly explained. Fur- siderable proportions at any time, the thermore, his values are stated in terms above "decomposition coefficients" must of thousands of tons of dry weight for be regarded as correspondingly minimal. the Caspian Sea as a whole, and must Following non-predated death, every be roughly transformed to calories per organism is a potential source of energy square centimeter of surface area. The for myriads of bacterial and fungal data for Lake Mendota, Wisconsin, are 406 RAYMOND L. LINDEMAN Ecology, Val. 23, No. 4 taken directly from a general summary TABLE111. Productivity values for the Lake Mendota food cycle, in g-cal/cm2/year, as corrected (Juday, '40) of the many productivity by using coeficients derived in the preceding sec- studies made on that eutrophic lake. tions, and as given by Juday ('40). The data for Cedar Bog Lake, Minnesota, are taken from the author's four-year Uncor- Car- Juday's rected Res- Pre- rected analysis (Lindeman, '41b) of its food- Trophic Level pro- pira- da- ZG- produc- tion tion due- pro- cycle dynamics. The calorific values in tivity tivity table I, representing annual production ------$,";; Producers: AI. 321* 107 42 10 480 428 of organic matter, are uncorrected for Primary con- sumerS:Aa. 24 15 2.3 0.3 41.6 144 energy losses. Secondary consumers: TABLE11. Productivity values for the Cedar A3 ...... lt 1 0.3 0.0 2.3 6 Tertiary con- Bog Lake food cycle, in g-cal/cm2/year,as corrected sumers: Aa. 0.12 0.2 0.0 0.0 0.3 0.7 by using the coeficients derived in the preceding sections. * Hutchinson ('42) gives evidence that this 4 8 value is probably too high and may actually be Cor- as low as 250. t Apparently such organisms as small I' forage" fishes are not included in any part of Juday's balance sheet: The inclusion of these forms might be expected to increase considerably the Producers:A~ 70.4110.14 23.4 14.8 2.8 111.3 productivity of secondary consumption. Primary consumers: A2 7.011.07 4.4 3.1 0.3 14.8 Secondary ing-capacity" of lakes containing mostly consumers: Aa 1.3f 0.43* 1.8 0.0 0.0 3.1 carp and other "coarse" fishes (primarily As), was about 500 per cent that of lakes * This value includes the productivity of the containing mostly "game" fishes (pri- small cyprinoid fishes found in the lake. marily A4), and concluded that "this Correcting for the energy losses due difference must be about one complete to respiration, predation and decomposi- link in the food chain, since it usually tion, as discussed in the preceding sec- requires about five pounds of food to tions, casts a very different light on the produce one pound of fish." While such relative productivities of food levels. high "metabolic losses" may hold for The calculation of corrections for the tertiary and quaternary predators under Cedar Bog Lake values for producers, certain field conditions, the physiologi- primary consumers and secondary con- cal experiments previously cited indi- sumers are given in table 11. The appli- cate much lower respiratory coefficients. cation of similar corrections to the energy Even when predation and decomposition values for the food levels of the Lake corrections are included, the resultant Mendota food cycle given by Juday productivity values are less than half ('40), as shown in table 111, indicates those obtained by using Juday's coeffi- that Lake Mendota is much more pro- cient. Since we have shown that the ductive of producers and primary con- necessary corrections vary progressively sumers than is Cedar Bog Lake, while with the different food levels, it seems the production of secondary consumers probable that Juday's "coefficient of is of the same order of magnitude in the metabolism" is much too high for pri- two lakes. mary and secondary consumers. In calculating total productivity for Lake Mendota, Juday ('40) used a Biological eficiency blanket correction of 500 per cent of the annual production of all consumer levels The quantitative relationships of any for "metabolism," which presumably in- food-cycle level may be expressed in cludes both respiration and predation. terms of its efficiency with respect to Thompson ('41) found that the "carry- lower levels. Quoting Hutchinson's ('42) October, 1942 TROPHIC-DYNAMIC ASPECT OF ECOLOGY 407 definition, "the efficiency of the produc- of the Lake Mendota productivities, no tivity of any level (A,) relative to the definite conclusions can be drawn from productivity of any previous level (Am) their relative efficiencies. The Cedar An Bog Lake ratios, however, indicate that is defined as - If the rate of ''Iar Am the progressive efficiencies increase from energy entering the ecosystem is denoted about 0.10 per cent for production, to as Ao, the efficiencies of all levels may be 13.3 per cent for primary consumption, referred back to this quantity 10." In and to 22.3 Per cent for secondary con- general, however, the most interesting sumption. An uncorrected efficiency of efficiencies are those referred to the pre- tertiary consumption of 37.5 per cent vious level's productivity (Anp1),or those f 3.0 per cent (for the weight ratios of An 'l~arni~~r~~~"to "forage" fishes in Ala- expressed as -100. These latter may bama ponds) is indicated in data pub- An-1 be termed the progressive e&ciencies of lished by Swing1e and Smith ('40). the various food-cycle levels, indicating These progressively increasing efficiencies for each level the degree of utilization may well represents fundamental tro~hic of its potential food supply or energy principle, namely, that the consumers at source. All efficiencies discussed in the ~'og'essively higher levels in the following pages are progressive effi- cycle are progressively more efficient in ciencies, expressed in terms of relative the their food At first sight, this generalization of productivities (--An 100) . It is impor- increasing efficiency in higher consumer An-1 groups would appear to contradict the to remember that efficiency and previous generalization that the loss of productivity are not synonymous. Pro- energy due to respiration is progressively ductivity is a rate (i.e., in the units here greater for higher levels in the food used, cal/cm2/year), while efficiency, be- cycle. These can be reconciled by re- ing a ratio, is a dimensionless number. membering that increased activity of The points of reference for any efficiency predators considerably increases the value should always be clearly stated. chances of encountering suitable prey. The efficiencies The ultimate effect of such antagonistic principles would present a picture of a the trophic levels of Cedar Lake predator completely wearing itself out and Lake Mendota, as obtained from in the process of completely extermi- the productivities derived in tables I1 nating its prey, a very improbable situa- and 111, are presented in table IV. In to However, Elton ('27) pointed out view of the uncertainties concerning some that food-cycles rarely have more than TABLEIV. Productivities and progressive efi- five trophic levels. Among the ciencies in the Cedar Bog Lake and Lake factors involved, increasing respiration Meendota food cycles, as g-cal/cm2/year of successive levels of predators contrasted with their successively increasing Cedar Bog Lake Lake Mendota efficiency of predation appears to be important in restricting the number of Produc- Effi- Produc- Effi- ----tivity clency tivity ciency trophic levels in a food cycle. Radiation...... 1118,872 118,872 The effect of increasing temperature Producers: AI...... 111.3 0.10% 480* 0.40% Primary consumers: is alleged by Wimpenny ('41) to cause a A2 ...... 14.8 13.3% 41.6 8.7% Secondary decreasing consumer/producer ratio, pre- consumers: A3.. . . 3.1 22.3% 2'3t '.'% Tertiary sumably because he believes that the consumers: A4.. . . - - 0.3 13.0% "acceleration of vital velocities" of con- * Probably too high; see footnote of table 111. sumers at increasing temperatures is t Probably too low; see footnote of table 111. more rapid than that of ~roducers. He 408 RAYMOND L. LINDEMAN Ecology, Vol. 23, No. 4 cites as evidence Lohmann's ('12) data at the base of a food-chain are relatively for relative numbers (not biomass) of abundant while those toward the end are Protophyta, Protozoa and Metazoa in progressively fewer in number. The re- the centrifuge plankton of "cool" seas sulting arrangement of sizes and num- (741:73 :1) as contrasted with tropical bers of animals, termed the pyramid of areas (458 :24:1). Since Wimpenny him- Numbers by Elton, is now commonly self emphasizes that many metazoan known as the Eltonian Pyramid. Wil- plankters are larger in size toward the liams ('41), reporting on the "floor poles, these data do not furnish con- fauna" of the Panama rain forest, has vincing proof of the allegation. The recently published an interesting ex- data given in table IV, since Cedar Bog ample of such a pyramid, which is Lake has a much higher mean annual reproduced in figure 2. water temperature than Lake Mendota, The Eltonian Pyramid may also be appear to contradict Wimpenny's gener- expressed in terms of biomass. The alization that consumer/producer ratios weight of all predators must always be fall as the temperature increases. much lower than that of all food animals, and the total weight of the latter much The Eltonian pyramid lower than the plant production (Boden- heimer, '38). To the human ecologist, The general relationships of higher it is noteworthy that the population den- food-cycle levels to one another and to sity of the essentially vegetarian Chinese, community structure were greatly clari- for example, is much greater than that fied following recognition (Elton, '27) of the more carnivorous English. of the importance of size and of numbers The principle of the Eltonian Pyra- in the animals of an ecosystem. Begin- mid has been redefined in terms of pro- ning with primary consumers of various ductivity by Hutchinson (unpublished) sizes, there are as a rule a number of in the following formalized terms: the food-chains radiating outwards in which rate of production cannot be less and the probability is that predators will be- will almost certainly be greater than the come successively larger, while parasites rate of primary consumption, which in and hyper-parasites will be progressively turn cannot be less and will almost cer- smaller than their hosts. Since small tainly be greater than the rate of second- primary consumers can increase faster ary consumption, which in turn . . . , than larger secondary consumers and are etc. The energy-relationships of this so able to support the latter, the animals principle may be epitomized by means

FIG.2. Eltonian pyramid of numbers, for floor-fauna invertebrates of the Panama rain forest (from Williams, '41). October, 1942 TROPHIC-DYNAMIC ASPECT OF ECOLOGY 409

of the productivity symbol A, as follows: fluence of some combination of limiting factors, which, until they are overcome by species-substitution, etc., tend to This rather obvious generalization is decrease the acceleration of productivity confirmed by the data of all ecosystems and maintain it at a more constant rate. analyzed to date. This tendency towards stage-equilibrium of productivity will be discussed in the following pages.

Dynamic processes within an ecosys- Productivity in hydrarch succession tem, over a period of time, tend to produce certain obvious changes- in its The descriptive dynamics of hydrarch species-composition, soil characteristics succession is well known. Due to the and productivity. Change, according to essentially concave nature of the sub- Cooper ('26), is the essential criteriop of stratum, lake succession is internally succession. From the trophic-dynamic complicated by a rather considerable viewpoint, succession is the process of influx of nutritive substances from the development in an ecosystem, brought drainage basin surrounding the lake. about primarily by the effects of the The basins of lakes are gradually filled organisms on the environment and upon with sediments, largely organogenic, upon each other, towards-a relatively stable which a series of vascular plant stages condition of equilibrium. successively replace one another until a It is well known that in the initial more or less stable (climax) stage is phases of hydrarch succession (oligo- attained. We are concerned here, how- trophy -+ eutrophy) productivity in- ever, primarily with the productivity cresses rapidly; it is equally apparent aspects of the successional process. that the colonization of a bare terrestrial Eutrophication. -Thienemann ('26) area represents a similar acceleration in presented a comprehensive theoretical productivity. In the later phases of discussion of the relation between lake succession, productivity increases much succession and productivity, as follows: more slowly. As Hutchinson and Wol- In oligotrophy, the pioneer phase, pro- lack ('40) pointed out, these generalized ductivity is rather low, limited by the changes in the rate of production may amount of dissolved nutrients in the lake be expressed as a sigmoid curve showing water. Oxygen is abundant at all times, a rough resemblance to the growth curve almost all of the synthesized organic of an organism or of a homogeneous matter is available for animal food; bac- population. teria release dissolved nutrients from the Such smooth logistic growth, of course, remainder. Oligotrophy thus has a very is seldom found in natural succession, "thrifty" food cycle, with a relatively except possibly in such cases as bare high "efficiency" of the consumer popu- areas developing directly to the climax lations. With increasing influx of nutri- vegetation type in the wake of a retreat- tives from the surrounding drainage basin ing glacier. Most successional seres con- and increasing primary productiGity (XI), sist of a number of stages ("recognizable, oligotrophy is gradually changed through clearly-marked subdivisions of a given mesotrophy to eutrophy, in which con- sere1'-W. S. Coower),. ,. so that their dition the production of organic matter productivity growth-curves will contain (XI) exceeds that which can be oxidized undulations corresponding in distinctness (XI') by respiration, predation and bacte- to the distinctness of the stages. The rial decomposition. The oxygen supply presence of stages in a successional sere of the hypolimnion becomes depleted, apparently represents the persistent in- with disastrous effects on the oligotroph- 410 RAYMOND L. LINDEMAN Ecology, Vol. 23, NO.4 conditioned bottom fauna. Organisms- auantitative value for lakes with com- especially adapted to endure temporary parable edaphic nutrient supplies being anaerobiosis replace the oligotrophic spe- dependent on the morphometry (mean cies, accompanied by anaerobic bacteria depth). Since deep lakes have a greater which during the stagnation period cause depth range for plankton photosynthe- reduction rather than oxidation of the sis, abundant oxygen and more chance organic detritus. As a result of this for decomposition of the plankton detri- process, semi-reduced organic ooze, or tus before reaching the bottom, such gyttja, accumulates on the bottom. As deep lakes may be potentially as pro- oxygen supply thus becomes a limiting ductive as shallower lakes. in terms of factor of productivity, relative efficiency unit surface area. Factors tending to of the consumer groups in utilizing the lessen the comparative productivity of synthesized organic substance becomes deep lakes are (1) lower temperature for correspondingly lower. the lake as a whole, and (2) greater The validity of Thienemann's inter- dilution of nutrients in terms of volume pretation, particularly regarding the of the illuminated "trophogenic zone" of trophic mechanisms, has recently been the lake. During eutrophication in a challenged by Hutchinson ('41, '42), who deep lake, the phosphorus content of the states that three distinct factors are sediment falls and nitrogen rises, until a involved : (1) the edaphic factor, repre- NIP ratio of about 4011 is established. senting the potential nutrient supply "The decomposition of organic matter (primarily phosphorus) in the surround- presumably is always liberating some of ing drainage basin; (2) the age of the this phosphorus and nitrogen. Within lake at any stage, indicating the degree limits, the more organic matter present of utilization of the nutrient supply; and the easier will be such regeneration. It (3) the morphometric character at any is probable that benthic animals and stage, dependent on both the original anion exchange play a part in such morphometry of the lake basin and the processes" (Hutchinson, '42). The pro- age of the lake, and presumably influ- gressive filling of the lake basin with encing the oxygen concentration in the sediments makes the lake shallower. so hypolimnion. He holds that true eu- that the oxygen supply of the hypo- trophication takes place only in regions limnion is increasingly, and finally com- well supplied with- nutrients, lakes in pletely, exhausted during summer stag- other regions developing into "ideotrophic nation. Oxidation of the sediments is types." The influx of phosphorus is less complete, but sufficient phosphorus probably very great in the earliest phases, is believed to be regenerated from the much greater than the supply of nitro- ooze surface so that productivity in gen, as indicated by very low NIP ratios terms of surface area remains relatively 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- tending to maintain the productivity of soluble, as a com~onentof such mineral a lake in stage-equilibrium (typological particles as apatite, etc., although cer- equilibrium of Hutchinson) during the tainly some of it is soluble. The supply eutrophic stage of its succession. of available nitrogen increases somewhat The concept of eutrophic stage-equi- more slowly, being largely dependent librium seems to be partially confused upon the fixation of nitrogen by micro- (cf. .Thienemann, '26; Hutchinson and organisms either in the lake or in the Wollack, '40) with the theoretically ideal surrounding soils. The photosynthetic condition of complete trophic equilibrium, productivity (XI) 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 41 1 utilization and regeneration of chemical energy which is lost from the food cycle, nutrients in an ecosystem, without loss is derived largely from level hl, as plant or gain from the outside, under a peri- structures in general are decomposed odically constant energy source-such as less easily than animal structures. The might be found in a perfectly balanced quantity of energy passed on into con- aauarium or terrarium. Natural eco- sumer levels can onlv be surmised from systems may tend to approach a state of undecomposed fragments of organisms trophic equilibrium under certain con- which are believed to occupy those levels. ditions, but it is doubtful if any are Several tvDesa of animal "microfossils" sufficiently autochthonous to attain, or occur rather consistently in lake sedi- maintain, true trophic equilibrium for ments, such as the carapaces and post- any length of time. The biosphere as a abdomens of certain cladocerans, chiron- whole, however, as Vernadsky ('29, '39) omid head-capsules, fragments of the so vigorously asserts, may exhibit a high phantom-midge larva Chaoborus, snail degree of true trophic equilibrium. shells, polyzoan statoblasts, sponge spic- The existence of prolonged eutrophic ules and rhizopod shells. Deevey ('42), stage-equilibrium was first suggested as after making comprehensive microfossil a result of a study on the sediments of and chemical analyses of the sediments of Grosser Ploner See in Germany (Gro- Linsley Pond, suggested that the abun- schopf, '36). Its significance was recog- dant half-carapaces of the planktonic nized by Hutchinson and Wollack ('40), browser Bosmina afford "a reasonable who based their critical discussion on estimate of the quantity of zooplankton chemical analyses (ibid.) and pollen produced" and that "the total organic analyses (Deevey, '39) of the sediments matter of the sediment is a reasonable of Linsley Pond, Connecticut. They estimate of the organic matter produced reported a gradual transition from oligo- by phytoplankton and littoral vegeta- trophy to eutrophy (first attained in the tion." He found a striking similarity oak-hemlock pollen period), in which in the shape of the curves representing stage the lake has remained for a very Bosmina content and total organic- mat- long time, perhaps more than 4000 years. ter plotted against depth, which, when They report indications of a comparable plotted logarithmically against each eutrophic stage-equilibrium in the sedi- other, showed a linear relations hi^ ex- ments of nearby Upper Linsley Pond pressed by an empirical power equition. (Hutchinson and Wollack, unpublished). Citing Hutchinson and Wollack ('40) to Similar attainment of stage-equilibrium the effect that the developmental curve is indicated in a preliminary report on for organic matter was analogous to that the sediments of Lake Windermere in for the development of an organism, he England (Jenkin, Mortimer and Pen- pressed the analogy further by suggest- nington, '41). Every stage of a sere ing that the increase of zooplankton is believed to possess a similar stage- (Bosmina) with reference to the increase equilibrium of variable duration, al- of organic matter (XI) fitted the formula though terrestrial stages have not yet y = bxk for allometric growth (Huxley, been defined in terms of productivity. '32), "where y = Bosmina, x = total The trophic aspects of eutrophication organic matter, b = a constant giving cannot be determined easily from the the value of y when x = 1, and k = the sediments. In general, however, the 'allometry constant,' or the slope of the ratio of organic matter to the silt washed line when a double log plot is made." into the lake from the margins affords If we represent the organic matter pro- an approximation of the photosynthetic duced as XI and further assume that productivity. This undecomposed or- Bosmina represents the primary con- ganic matter, representing the.amou11t of sumers (Xz), neglecting benthic browsers, 412 RAYMOND L. LINDEMAN Ecology, Vol. 23, NO.4

the formula becomes X2 = bXlk. Whether continuing, at a rate corresponding to this formula would express the relation- the rate of sediment accumulation. In ship found in other levels of the food the words of Hutchinson and Wollack cycle, the development of other stages, ('40), "this means that during the equi- or other ecosystems, remains to be dem- librium period the lake, through the on~trated.~Stratigraphic analyses in internal activities of its biocoenosis, is Cedar Bog Lake (Lindeman and Linde- continually approaching a condition when man, unpublished) suggest a roughly it ceases to be a lake." similar increase of both organic matter Senescence.-As a result of long-con- and Bosmina carapaces in the earliest tinued sedimentation, eutrophic lakes sediments. In the modern senescent attain senescence, first manifested in lake, however, double logarithmic plot- bays and wind-protected areas. Senes- tings of the calorific values for XI against cence is usuallv characterized bv such X2, and X2 against Xs, for the four years pond-like conditions as (1) tremendous studied, show no semblance of linear increase in shallow littoral area popu- relationship, i.e., do not fit any power lated with pondweeds and (2) increased equation. If Deevey is correct in his marginal invasion of terrestrial stages. interpretation of the Linsley Pond micro- Cedar Bog Lake, which the author has fossils, allometric growth would appear studied for several vears. is in late senes- to characterize the phases of pre-equilib- cence, rapidly changing to the terrestrial rium succession as the term "growth" stages of its succession. On casual indeed implies. ins~ection,the massed verdure of ~ond- The relative duration of eutrophic weeds and' epiphytes, together witi spo- stage-equilibrium is not yet completely radic algal blooms, appears to indicate understood. As exemplified by Linsley great photosynthetic productivity. As Pond, the relation of stage-equilibrium pointed out by Wesenberg-Lund ('12), to succession is intimately concerned littoral areas of lakes are virtual hot- with the trophic processes of (1) external houses, absorbing more radiant energy influx and efflux (partly controlled by per unit volume than deeper areas. At climate), (2) photosynthetic productiv- the present time the entire aquatic area ity, (3) sedimentation (partly by physio- of Cedar Bog Lake is essentially littoral graphic silting) and (4) regeneration of in nature, and its productivity per cubic nutritives from the sediments. These meter of water is probably greater than processes apparently maintain a rela- at any time in its history. However, tively constant ratio to each other during since radiant energy (XO) enters a lake the extended equilibrium period.- Yet only from the surface, productivity must the food cycle is not in true trophic equi- be defined in terms of surface area. In librium, and continues to fill the lake these terms, the present photosynthetic with organic sediments. Succession is productivity pales into insignificance when compared with less advanced lakes It should be mentioned in this connection in similar edaphic regions; for instance, that Meschkat ('37) found that the relationship of population density of tubificids to organic X1 is less than % that of Lake Mendota, matter in the bottom of a polluted "Buhnen- Wisconsin (cf. table IV). These facts feld" could be expressed by the formula y = az, attest the essential accuracy of Welch's where y represents the population density, x is ('35) generalization that productivity the "determining environmental factor," and a is a constant. He pointed out that for such an declines greatly during senescence. 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 during late lake senescence general to the relationship between populations of marine plankton and the "controlling factor" of productivity (A,) is increasingly influ- their environment. enced by climatic factors, acting through October, 1942 TROPHIC-DYNAMIC ASPECT OF ECOLOGY 413 water level chaoges, drainage, duratioll thus subject to a certain nutrient loss by of winter ice, 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 food groups in the lake. nutrients as can be extracted from the Terrestrial stages.-As an aquatic eco- "C" soil horizon. system passes into terrestrial phases, Successional productivity curves.-In fluctuations in atmospheric factors in- recapitulating the probable photosyn- creasingly affect its productivity,. As thetic productivity relationships in hy- succession proceeds, both the species- drarch succession, we shall venture to composition and the productivity of an diagram (figure 3) a hypothetical hydro- ecosystem increasingly reflect the effects sere, developing from a moderately deep of the regional climate. Qualitatively, lake in a fertile cold temperate region these climatic effects are known for soil under relatively constant climatic condi- morphology (Joffe, '36), autotrophicvege- tions. The initial period of oligotrophy tation (Clements, '16), fauna (Clements is believed to be relatively short (Hutch- and Shelford, '39) and soil microbiota inson and Wollack, '40; Lindeman (Braun-Blanquet, '32), in fact for every '41a), with productivity rapidly increas- important component of the food cycle. ing until eutrophic stage-equilibrium is Quantitatively, these effects have been attained. The duration of high eu- so little studied that generalizations are trophic productivity depends 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 fluctuates about a high eutrophic mean maturity. Clements and Shelford ('39, until the lake becomes too shallow for p. 116) assert that both plant and animal maximum growth of phytoplankton or productivity is generally greatest in the regeneration of nutrients from the ooze. subclimax, except possibly in the case of As the lake becomes shallower and more grasslands. Terrestrial ecosystems are senescent, productivity is increasingly primarily convex topographically and influenced by climatic fluctuations and

TIME 4 FIG.3. Hypothetical productivity growth-curve of a hydrosere, developing from a deep lake to climax in a fertile, cold-temperate region. 414 RAYMOND L. LINDEMAN Ecology, Val. 23, No. 4 gradually declines to a minimum as the original observations, but are probably lake is completely filled with sediments. of the correct order of magnitude. The The terrestrial aspects of hydrarch mean photosynthetic efficiency for the succession in cold temperate regions sea is given as 0.31 per cent (after Riley, usually follow sharply defined, distinc- '41). The mean photosynthetic effi- tive stages. In lake basins which are ciency for terrestrial areas of the earth poorly drained, the first stage consists is given as 0.09 per cent f 0.02 per cent of a mat, often partly floating, made up (after Noddack, '37), for forests as 0.16 primarily of sedges and grasses or (in per cent, for cultivated lands as 0.13 per more coastal regions) such heaths as cent, for steppes as 0.05 per cent, and Chamaedaphne and Kalfnia with certain for deserts as 0.004 per cent. The mean species of sphagnum moss (cf. Rigg, '40). photosynthetic efficiency for the earth The mat stage is usually followed by a as a whole is given as 0.25 per cent. bog forest stage, in which the dominant Hutchinson has suggested (cf. Hutchin- species is Larix laricina, Picea mariana son and Lindeman, '41) that numerical or Thuja occidentalis. The bog forest efficiency values may provide "the most stage may be relatively permanent fundamental ~ossible classification of ("edaphic" climax) or succeeded to a biological formations and of their devel- greater or lesser degree by the regional opmental stages." climax vegetation. The stage-produc- Almost nothing is known concerning tivities indicated in figure 3 represent the efficiencies of consumer groups in only crude relative estimates, as practi- succession. The general chronological cally no quantitative data are available. increase in numbers of Bosmina carapaces with respect to organic matter and Eficiency relationships in succession of Chaoborus fragments with respect to Bosmina carapaces in the sediments of The successional changes of photosyn- Linsley Pond (Deevey, '42) suggests thetic efficiency in natural areas (with progressively increasing efficiencies of respect to solar radiation, i.e., 100) zooplankters and plankton predators. A0 On the other hand, Hutchinson ('42) have not been intensively studied. 1n concludes from a com~arisonof the P : Z lake succession, photosynthetic efficiency (phytoplankton : zooplankton) biomass would be expected to follow the same ratios of several oligotrophic alpine lakes, course deduced for productivity, rising ca 1 : 2 (Ruttner, '37), as compared with to a more or less constant value during the ratios for Linsley Pond, 1 : 0.22 eutrophic stage-equilibrium, and declin- (Riley, '40) and three eutrophic Bava- ing during senescence, as suggested by a rian lakes, 1 : 0.25 (Heinrich, '34), that photosynthetic efficiency of at least 0.27 "as the phytoplankton crop is increased per cent for ,eutrophic Lake Mendota the zooplankton by 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 meso- terrestrial hydrosere, efficiency would trophic (Connecticut) and eutrophic likewise follow a curve similar to that regions (southern Wisconsin), indicate postulated for productivity. that the deeper or morphometrically Rough estimates of photosynthetic "younger" lakes have a lower ratio of efficiency for various climatic regions of bottom fauna to the standing crop of 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, corrected for eutrophic equilibrium (22-27 per cent). respiration, do not appear to be very The ratios for senescent Cedar Bog Lake, reliable because of imperfections in the while not directly comparable because October, 1942 TROPHIC-DYNAMIC ASPECT OF ECOLOGY 415

of its essentially littoral nature, are even sumers, secondary consumers, etc., each higher. These meager data suggest that successively dependent upon the preced- the efficiencies of consumer groups may ing level as a source of energy, with the increase throughout the aquatic phases producers (Al) directly dependent upon of succession. the rate of incident solar radiation (pro- For terrestrial stages, no consumer ductivity Ao) as a source of energy. efficiency data are available. A sug- 3. The more remote an organism is gestive series of species-frequencies in from the initial source of energy (solar mesarch succession was published by radiation), the less probable that it will Vera Smith-Davidson ('32), which in- be dependent solely upon the preceding dicated greatly increasing numbers of trophic level as a source of energy. arthropods in successive stages approach- 4. The progressive energy relation- ing the regional climax. Since the pho- ships of the food levels of an "Eltonian tosynthetic productivity of the stages Pyramid" may be epitomized in terms of probably also increased, it is impossible the productivity symbol A, as follows: to determine progressive efficiency relationships. The problems of biological A0 > A1 > A2 . . . > A,. efficiencies present a practically virgin 5. The percentage loss of energy due field, which appears to offer abundant to respiration is progressively greater for rewards for studies guided by a trophic- higher levels in the food cycle. Respira- dynamic viewpoint. tion with respect to growth is 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 principles indi- per cent for secondary consumers. cated in the following.- summary cannot 6. The consumers at progressively be expected to hold for every single case, higher levels in the food cycle appear to in accord with the known facts of bio- be progressively more efficient in the use logical variability. h priori, however, of their food supply. This generaliza- these principles appear to be valid for tion can be reconciled with the preceding the vast majority of cases, and may be one by remembering that increased ac- expected to possess a statistically signifi- tivity of predators considerably increases cant probability of validity for any case the chances of encountering suitable selected at random. Since the available prey. data summarized in this paper are far 7. Productivity and efficiency increase too meager to establish such generaliza- during the early phases of successional tions on a statistical basis, it is highly development. In lake succession, pro- important that further studies be initi- ductivity and photosynthetic efficiency ated to test the validity of these and increase from oligotrophy to a prolonged other trophic-dynamic principles. eutrophic stage-equilibrium and decline with lake senescence, rising again in the terrestrial stages of hydrarch succession. 1. Analyses of food-cycle relationships 8. The progressive efficiencies of con- indicate that a biotic community cannot sumer levels, on the basis of very meager be clearly differentiated from its abiotic data, apparently tend to increase through- environment; the ecosystem is hence re- out the aquatic phases of succession. garded as the more fundamental ecological unit. 2. The organisms within an ecosystem may be grouped into a series of more or The author is deeply indebted to Professor G. E. Hutchinson of Yale University, who has less discrete trophic levels (Al, A2, A3, stimulated many of the trophic concepts devel- . . . A,) as producers, primary con- oped here, generously placed at the author's 416 RAYMOND L., LINDEMAN Ecology, Val. 23, No. 4

disposal several unpublished manuscripts, given -. 1941. Limnological studies in Connecti- valuable counsel, and aided the final development cut: VI. The quantity and composition of the of this paper in every way possible. Many of bottom fauna. Ecol. Monogr., 11: 413-455. the concepts embodied in the successional sec- -. 1942. Studies on Connecticut lake sedi- tions of this paper were developed independently ments: 111. The biostratonomy of Linsley by Professor Hutchinson at Yale and by the Pond. Amer. Jour. Sci., 240: 233-264, 313- author as a graduate student at the University 338. of Minnesota. Subsequent to an exchange of Elton, C. 1927. Animal Ecology. N. Y. notes, a joint preliminary abstract was published Macmillan Co. (Hutchinson and Lindeman, '41). The author Franc6, R. H. 1913. Das Edaphon, Unter- wishes to express gratitude to the mentors and suchungen zur Oekologie der bodenbewohnen- friends at the University of Minnesota who den Mikroorganismen. Deutsch. Mikrolog. encouraged and helpfully criticized the initial Gesellsch., Arbeit. aus d. Biol. Inst., No. 2. development of these concepts, particularly Drs. Munich. W. S. Cooper, Samuel Eddy, A. C. Hodson, Friederichs, K. 1930. Die Grundfragen und D. B. Lawrence and J. B. Moyle, as well as Gesetzmassigkeiten der land- und forstwirt- other members of the local Ecological Discussion schaftlichen Zoologie. 2 vols. Berlin. Ver- Group. The author is also indebted to Drs. schlag. Paul Parey. J. R. Carpenter, E. S. Deevey, H. J. Lutz, Groschopf, P. 1936. Die postglaziale Ent- A. E. Parr, G. A. Riley and V. E. Shelford, as wicklung des Grosser Ploner Sees in Ost- well as the persons mentioned above, for critical holstein auf Grund pollenanalytischer Sedi- reading of preliminary manuscripts. Grateful mentuntersuchungen. Arch. Hydrobiol., 30: acknowledgment is made to the Graduate School, 1-84. Yale University, for the award of a Sterling Heinrich, K. 1934. Atmung und Assimilation Fellowship in Biology during 1941-1942. im freien Wasser. Internat. Rev. ges. Hy- drobiol. u. Hydrogr., 30: 387-410. Hentschel, E. 1933-1936. Allgemeine Biologie des Siidatlantischen Ozeans. Wiss. Ergebn. Allee, W. C. 1934. Concerning the organiza- Deutsch. Atlant. Exped. a. d. Forschungs- u. tion of marine coastal communities. Ecol. Vermessungsschiff "Meteor" 1925-1927. Bd. Monogr., 4: 541-554. XI. Birge, E. A., and C. Juday. 1922. The inland Hicks, P. A. 1934. Interaction of factors in lakes of Wisconsin. The plankton. Part I. the growth of Lemna: V. Some preliminary Its quantity and chemical composition. Bull. observations upon the interaction of tem- Wisconsin Geol. Nat. Hist. Surv., 64: 1-222. perature and light on the growth of Lemna. Bodenheimer, F. S. 1938. Problems of Animal Ann. Bot., 48: 515-523. Ecology. London. Oxford University Press. Hile, R. 1941. Age and growth of the rock Braun-Blanquet, J. 1932. Plant Sociology. bass Ambloplites rupestris (Rafinesque) in N. Y. McGraw-Hill Co. Nebish Lake, Wisconsin. Trans. Wisconsin Brujewicz, S. W. 1939. Distribution and dy- Acad. Sci., Arts, Lett., 33: 189-337. namics of living matter in the Caspian Sea. Hutchinson, G. E. 1941. Limnological studies Compt. Rend. Acad. Sci. URSS, 25: 138-141. in Connecticut: IV. Mechanism of interme- Carpenter, J. R. 1939. The biome. Amer. diary metabolism in stratified lakes. Ecol. Midl. Nat., 21: 75-91. Monogr., 11: 21-60. -. 1940. The grassland biome. Ecol. -. 1942. Recent Advances in Limnology Monogr., 10: 617-687. (in manuscript). Clements, F. E. 1916. Plant Succession. Car- -and R. L. Lindeman. 1941. Biological negie Inst. Washington Publ., No. 242. --- and V. E. Shelford. 1939. Bio-Ecology. efficiency in succession (Abstract). Bull. Ecol. Soc. Amer., 22: 44. N. Y. John Wiley & Co. Cooper, W. S. 1926. The fundamentals of --- and Anne Wollack. 1940. Studies on vegetational change. Ecology, 7: 391-413. Connecticut lake sediments: 11. Chemical Cowles, H. C. 1899. The ecological relations analyses of a core from Linsley Pond, North of the vegetation of the sand dunes of Lake Branford. Amer. Jour. Sci., 238: 493-517. Michigan. Bot. Gaz., 27: 95-391. Huxley, J. S. 1932. Problems of Relative Davidson, V. S. 1932. The effect of seasonal Growth. N. Y. Dial Press. variability upon animal species in a decidu- Ivlev, V. S. 1939a. ~rans'formationof energy ous forest succession. Ecol. Monogr., 2: by aquatic animals. Internat. Rev. ges. 305-334. Hydrobiol. u. Hydrogr., 38: 449-458. Deevey, E. S. 1939. Studies on Connecticut ---. 1939b. Balance of energy in carps. lake sediments: I. A postglacial climatic chro- Zool. Zhurn. Moscow, 18: 303-316. nology for southern New England. Amer. Jacot, A. P. 1940. The fauna of the soil. Jour. Sci., 237: 691-724. Quart. Rev. Biol., 15: 28-58. October, 1942 TROPHIC-DYNAMIC ASPECT OF ECOLOGY 417

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