, INTERNATIONALE VEREINIGUNG v ä FÜR THEORETISCHE U N D ANGEWANDTE LIMNOLOGIE ^

INTERNATIONAL ASSOCIATION 3 OF THEORETICAL A N D APPLIED LIMNOLOGY

ASSOCIATION INTERNATIONALE ' DE LIMNOLOGIE THEORIQÜE ET ÄPPLIQUEE

Verhandlungen • Pröceedings • Travaux

Cöngress in Munichr1989

Volume 24 • Part 5 -

Edited for,the Association by V. Sladecek and A'.SladeSkovd

World List Abbreviatipn: Verh. int. Ver. L i m n o l .

DIN 1502 Abkürzung: Verh. Internat. Verein. L i m n o l .

Stuttgart 1991 v

E. Schweizerbart'sche Verlagsbuchhandlung

, (Nägefe u. Qhermiller)

INTERNATIONALE VEREINIGUNG FÜR THEORETISCHE UND ANGEWANDTE LIMNOLOGIE

INTERNATIONAL ASSOCIATION OF THEORETICAL A N D APPLIED LIMNOLOGY

ASSOCIATION INTERNATIONALE DE LIMNOLOGIE THEORIQUE ET ÄPPLIQUEE

Verhandlungen • Proceedings • Travaux

Congress in Munich 1989

Volume 24 • Part 5

Edited for the Association by V. Sladecek and A. Sladeckovä

World List Abbreviation: Verh. int. Ver. L i m n o l .

DIN 1502 Abkürzung: Verh. I n t e r n a t . V e r e i n . L i m n o l .

Stuttgart 1991

E. Schweizerbart'sche Verlagsbuchhandlung

(Nägele u. Obermiller)

Contents of Part 5

XII. Ecology of Aquatic Organisms. 2. Algae and Macrophyta (continued)

V A N DER D O E S , J . & K L I N K , F . J . : Excessive growth of Lemnaceae and A z o l l a in ditches observed by false colour teledetection 2683

K O K , C . J . & V A N D E L A A R , B. J . : Influence of p H and buffering capacity o n the decomposition of N y m p h a e a alba L . detritus i n laboratory experiments: A possible explanation for the inhibi t ion of decomposi­t ion at low alkalinity 2689

V A N D E N B R I N K , F . W . B., M A E N E N , M . M . J . , V A N D E R V E L D E , G . & D E V A A T E , A . B.: The (semi-) aquatic Vege­tation of still waters w i t h i n the floodplains of the rivers R h i n e and Meuse i n The Netherlands: Historical changes and the role of inundation 2693

V A N V I E R S S E N , W . & H O O T S M A N S , M . J . M . : O n the or ig in of macrophyte population dynamics during lake recovery aftereutrophication 2700

H O O T S M A N S , M . J . M . & V A N V I E R S S E N , W . : C o m p u t e r simulations of macrophyte population dynamics during lake recovery after eutrophication 2703

C O O P S , H . & SMIT, H : Effects of various water depths o n S c i r p u s m a r i t i m u s L . : F ie ld and experimental ob-servations 2706

C L E V E R I N G , O . A . & v. G U L I K , W . J . M . : T h e establishment of S c i r p u s l a c u s t r i s ssp. l a c u s t r i s and S. m a r i t i m u s i n the northern Delta area, The Netherlands 2711

G A C I A , E . & BALLESTEROS, E . : T w o methods to estimate leaf product ion i n Isoetes l a c u s t r i s L . : A critical assess-ment 2714

V I A R O L I , P . & F U M A G A L L I , I.: Regeneration of dissolved reactive silica during decomposition of recalcitrant plant tissues in temporary shallow-water environments 2717

B R E E N , C . M . & S T O K M A N N S , C . - H : Observations o n the growth and production of C y p e r u s p a p y r u s L . in a sub-tropical swamp 2722

XII. Ecology of Aquatic Organisms. 3. Animals

M E I S T E R F E L D , R.: Vertical distribution of D i f f l u g i a b y d r o s t a t i c a (Protozoa, Rhizopoda) 2726 O C A N A , A . & P I C A Z O , J . S.: Study on nematode species encountered i n the M o n a c h i l River (Granada,

Spain): Response to organic pol lut ion 2729 W A R N E R , B. G . & C H E N G A L A T H , R.: H a b r o t r o c b a a n g u s t i c o l l i s (Bdelloidea, Rotifera): A new paleoecological

indicator in Holocene peat deposits i n Canada 273 8 D E M A N U E L , J . : Distr ibution of Brachionidae (Rotifera: Monogononta) i n Spanish reservoirs 2741 E S P A R C I A , A . , A R M E N G O L , J . , V I C E N T E , E . & M I R A C L E , M . R.: Vert ical distribution of Anuraeopsis species as

related to oxygen depletion in two stratified lakes 2745 W A L Z , N . & R O T H B U C H E R , F . : Effect of food concentration on body size, egg size, and population

dynamics of B r a c h i o n u s a n g u l a r i s (Rotatoria) 2750 C A R M O N A , M . J . & SERRA, M . : Comparative total protein and demographic patterns of mictic and amictic fe-

malerotifers 2754 R O T H H A U P T , K . O . : The influence of toxic and filamentous blue-green algae on feeding and population

growth of the rotifer B r a c h i o n u s r u b e n s (Abstract) 2760 M A T V E E V A , L . K . : C a n pelagic rotifers be used as indicators of lake t rophic State? 2761 B O N A C I N A , C , B O N O M I , G . , D i C O L A , G . & M O N T I , C : A n improved model for the study of population

dynamics in T u b i f e x t u b i f e x (Oligochaeta, Tubificidae) 2764 V I J V E R B E R G , J . & K O E L E W I J N , H . P. : Size dependent mortal i ty and production of D i a p h a n o s o m a b r a c h y u r u m

( L I E V E N ) in an eutrophic lake 2768 H E R Z I G , A . & A U E R , B.: The feeding behaviour of Leptoäora k i n d t i and its impact on the Zooplank­

ton Community of Neusiedler See (Austria) (Abstract) 2772 SIEBECK, O . & B Ö H M , U . : U V - B effects on aquatic animals 2773 D U N C A N , A . & DOS S A N T O S , L . C : C o h o r t analysis i n three species of D a p h n i a in the L o n d o n reser­

voirs 2778 G E R R I T S E N , J . J . : The influence of phosphorus-limited g r o w n algae on grazing of D a p h n i a m a g n a

(Abstract) 2783 G A B R I E L , W . & T A Y L O R , B. E . : O p t i m a l resource allocation in cladocerans 2784 G I A N I , A . : The nutritive value of different algae as food for two D a p h n i a species 2788

X X X V I

F U H L E N D O R F , D . C : Measuring seasonal patterns of food l imitat ion in D a p h n i a - an experimental study . . . . 2792 B E R B E R O V I C - J U N G E , R. : Starvation resistance of two coexisting D a p h n i a species under temperature con-

ditions simulating vertical migration behaviour (Abstract) 2794 G L I W I C Z , M . Z . : F o o d thresholds, resistance to starvation, and cladoceran body size 2795 W O L F , H . G . & W E I D E R , L . J . : D O life-history parameters of D a p h n i a as determined i n the laboratory cor-

rectly predict species successions i n the field? 2799 T O L L R I A N , R. : Some aspects i n the costs of cyclomorphosis i n D a p h n i a c u c u l l a t a 2802 R I N G E L B E R G , J . : The relation between ultimate and proximate aspects of diel vertical migration i n D a p h n i a

h y a l i n a 2804 L E H T O V A A R A , A . & S A L O N E N , K . : D i e l vertical migration of D a p h n i a l o n g i s p i n a in a humic lake w i t h steep

thermal and oxygen stratification (Abstract) 2808 G O R B I , G . , PARIS , G . M . , M O R O N I , F . & B A C H I O R R I , A . : Differences i n population dynamics of D a p h n i a magna

clones 2809 B A C H I O R R I , A . , ROSSI , V . , B O N A C I N A , C . & M E N O Z Z I , P . : Enzymatic variability of a colonizing population of

D a p h n i a ohtusa K U R Z (Crustacea, Cladocera) i n Lake O r t a (Italy) 2813 ROSSI, V . , R O Z Z I , M . C . & M E N O Z Z I , P . : Life strategy differences among electrophoretic clones of H e t e r o c y p r i s

i n c o n g r u e n s (Crustacea, Ostracoda) 2816 C H A P M A N , M . A . , G R E E N , J . D . & N O R T H C O T E , T . G . : The enigma o t D i a p t o m u s connexus (Copepoda) i n M a -

honey Lake: O n e or two populations? (Abstract) 2820 H A R T M A N N , H . J . : In situ predation on planktonic ciliates by copepods, measured w i t h diffusion exclosures

(Abstract) 2821 F E R R A R I , I., F A R A B E G O L I , A . , P U G N E T T I , A . & S T E L L A , E . : The occurrence of a calanoid Australasian species,

Boeckeila t r i a r t i c u l a t a ( T H O M S O N ) , i n fish ponds of N o r t h e r n Italy 2822 M A L Y , E . J . : Dispersal ability and its relation to incidence and geographic distribution of Australian

centropagid copepods 2828 B U R N S , C . W . & X u , Z . : U t i l i z a t i o n of cyanobacteria (blue-green algae) as food by freshwater calanoid co­

pepods (Abstract) 2833 V I L L A L O B O S , L . & Z U N I G A , L . : Latitudinal gradient and morphological variability of copepods in C h i l e :

BoeckellagracilipesDADAY 2834 W Y N G A A R D , G . A . : Evidence of food l imitation i n a subtropical copepod population 2839 E L G M O R K , K . : Winter reproduction strategies i n freshwater cyclopoids 2844 H A L V O R S E N , G . : The ecology of Cyclops abyssorum t a t r i c u s K O Z M I N S K I i n N o r w a y (Abstract) 2847 V A N D E N B O S C H , F . & G A B R I E L , W . : The impact of cannibalism on the population dynamics of cyclopoid

copepods 2848 S A N T E R , B . : The role of food l imitation i n summer diapause of cyclopoid copepods (Abstract) 2851 A D R I A N , R.: The feeding behaviour of Cyclops kolensis and C v i c i n u s (Crustacea, Copepoda) 2852 G R O S S N I C K L E , N . E . : Comparative feeding study of the Opossum shrimp, M y s i s r e l i c t a , in Trout Lake,

Wisconsin, U S A , Lake Pääjärvi, F in land, and Lake Jonsvatn, N o r w a y 2864 Y O U N G , L . B . & H A R V E Y , H . H . : The influence of lake p H and crayfish size on carapace elemental compo-

sition in Orconectes spp. and Camharus spp 2869 C H A I S E M A R T I N , C : Respiratory rates and adenylate energy charge in healthy and parasitized muscles of cray­

fish (A u s t r o p o t a m o b i u s p a l l i p e s ) 2873 S C H M I D T - H A L E W I C Z , S. & B A U E R , J . : Response of the macroinvertebrate Community in N T A - , phosphate-

and copper-charged freshwater ponds 2877 A L L A N , J . D . , F L E C K E R , A . S. & K O H L E R , S. L . : D i e l changes in epibenthic activity and gut fullness of some

mayf lynymphs 2881 Z W I C K , P . : G r o w t h and emergence of L e u c t r a p r i m a (Plecoptera): Habitat - species interactions 2886 N E U M A N N , P . : The egg development of B r a c h y p t e r a seticomis (Insecta, Plec.) (Abstract) 2891 R U P P R E C H T , R . & F R I S C H , S.: The sensitivity of N e m u r e l l a p i c t e t i i (Insecta: Plecoptera) to acidity 2892 M A L M Q V I S T , B . : Stonefly functional responses: Influence of Substrate heterogeneity and predator interac-

t ion 2895 A U R I C H , M . , W A G N E R , R., R E D E R , E . & V E I T H , R. : Defensive behaviour of the larva of A p a t a n i a fimhriata

(PICTET) (Abstract) 2901

M U O T K A , T. : Life history patterns of Rhyacophila o b l i t e r a t a in northern F in land (Abstract) 2902 J A C K S O N , J . K . & R E S H , V . H : Use of cellulose acetate electrophoresis to examine population gene-

tics of the caddisfly Helicopsyche borealis 2903 E R L A N D S S O N , A . : G r o u p dynamics i n the water cricket V e l i a caprai (Hemiptera) 2908 G I S L A S O N , G . M . & J Ö H A N N S S O N , V . : Effects of food and temperature on the life cycle of S i m u l i u m

v i t t a t u m Z E T T . (Diptera: Simuliidae) i n the River Laxa, N-Iceland 2912

X X X V I I

R E I D E L B A C H , J . : Studies on population dynamics of blackflies (Diptera: Simuliidae) i n a grassland stream (Abstract) 2917

SMIT, H . , K L A R E N , P . & S N O E K , W . : L i p i n i e l l a a r e n i c o l a S H I L O V A (Diptera: Chironomidae) on a sandy flat i n the Rhine-Meuse estuary: Dis t r ibut ion , population structure, biomass and production of larvae in relation to periodical drainage 2918

H E I N I S , F . : The relation between oxygen regimes and distribution patterns of the larvae of C h i r o n o m i ­dae (Abstract) 2924

C U R E , V . : Structure and ecological role of phytophilous chironomids f rom some Danubian ecosystems in Romania 2925

S A V A G E , H . M . , R E J M Ä N K O V Ä , E . , A R R E D O N D O - J I M E N E Z , J . L , R O B E R T S , D . R. & R O D R I G U E Z , M . H . : Prel iminary

l imnological and botanical characterization of larval habitats for two primary malarial vectors, A n -opheles a l b i m a n u s and A n . p s e u d o p u n c t i p e n n i s , in coastal areas of Chiapas State, Mexico (Abstract) . . . . 2930

W O L F , B . A . M . : Some aspects of the nutrit ional ecology of a detritus-feeding Diptera larva: P t y c h o p t e r a pa-l u d o s a (Abstract) 2931

Y A M E O G O , L . , C A L A M A R I , D . , G R U N E W A L D , J . & F A I R H U R S T , C . P. : The aquatic monitoring and bioassay com-

ponent of the W H O Onchocerciasis C o n t r o l Programme in West Afr ica 2932 A L O I , J . E . & B R Ö N M A R K , C : Effects of snail density on snail growth and periphyton 2936 J O K I N E N , E . H . : The malacofauna of the acid and non-acid lakes and rivers of the Adirondack M o u n ­

tains and surrounding lowlands, N e w Y o r k State, U S A 2940 D O R G E L O , J . : G r o w t h , food and respiration i n the prosobranch snail P o t a m o p y r g u s j e n k i n s i (E. A .

S M I T H ) (Hydrobi idae, Mollusca) 2947 Y I P P , M . W . : The relationship between hydrological factors and distribution of freshwater gastropods i n

H o n g K o n g 2954 R I C C A R D I , N . , M A N G O N I , M . & P I V A , A . : The elemental ( C , H , N , O , S) and biochemical composition of

U n i o m a n c u s (PFEIFFER) and A n o d o n t a cygnea L 2960 T O K E S H I , M . : Aggregation, habitat characteristics and species coexistence (Abstract) 2964 F R A N C E , R . L . & W E L B O U R N , P . M . : Abundance of R a n a c l a m i t a n s tadpoles in Canadian Shield lakes 2965 M E I L I , M . : In situ assessment of trophic levels and transfer rates i n aquatic food webs, using chronic

(Hg) and pulsed ( C h e r n o b y l 1 3 7 C s ) contaminants 2970

XIII. Sediments

C U R T I S , P . J . : P and Fe release f r o m anoxic Precambrian Shield lake Sediments mediated by addition of Fe(II)-insoluble and Fe(II)-soluble bases 2976

R O W A N , D . J . & K A L F F , J . : The l imnological implications of catchment sediment load 2980 C A R A C O , N . F . , C O L E , J . J . & L I K E N S , G . E . : Phosphorus release f rom anoxic Sediments: Lakes that break

therules 2985 N O R T O N , S. A . , V E R T A , M . & K A H L , J . S.: Relative contributions to lake sediment chemistry by atmo-

spheric deposition 2989 E K H O L M , P . , Y L I - H A L L A , M . & K Y L M Ä L Ä , P . : Avai labi l i ty of phosphorus in suspended Sediments

estimated by chemical extraction and bioassay 2994 H U P F E R , M . & U H L M A N N , D . : M i c r o b i a l l y mediated phosphorus exchange across the mud-water interface . . . 2999 K J E N S M O , J . : Bio-geochemical composition of recent Sediments f rom the mixo- and the m o n i m o l i m n i o n of

Lake Svinsjoen 3004 H O R I , R. , H j . I K H S A N , S. B I N , W O O D , A B D . K . B I N & A B U B A K A R , M D . Y . B I N : N e u t r o n activation analysis of

the sediment of Kelang River , Malaysia 3009 SAGER, M . : Detection of environmental mobilities of nutrients and heavy metals in Sediments 3012 O S B O R N E , P . L . & T O T O M E , R . G . : Sediment deposition in Lake K u t u b u , Papua N e w Guinea 3018 T A T U R , A . , D E L V A L L E , R . & P A Z D U R , M . : Lake Sediments in maritime Antarctic zone: A record of land-

scape and biota evolution: prel iminary report 3022 G O L T E R M A N , H . L . : Influence of FeS on denitrification in shallow waters 3025 D E G R O O T , C. - J . : The influence of FeS on the inorganic phosphate System in Sediments 3029 K O Y A M A , T . : Biochemical reduction process in the lake sediment-water interface. O n the basis of

laboratory experiments 3036 M A R X S E N , J . & F I E B I G , D . : Measurement of bacterial production in stream-bed Sediments (Abstract) 3044 T O M A S Z E K , J . : Oxygen consumption by bottom Sediments 3045 W A S M U N D , N . : Microautoradiographic determination of the viabil i ty of algae in deep sediment layers (Ab­

stract) 3050 A N D E R S E N , F . 0 . & J E N S E N , H . S.: The influence of chironomids on decomposition of organic matter and

nutrient exchange i n a lake sediment 3051

X X X V I I I

I W A K U M A , T . & O T S U K I , A . : Role of chironomid larvae in reducing rate of nutrient release from lake sediment: Evaluation by a mathematical model 3056

S C H R O E D E R , F . , K L A G E S , D . & K N A U T H , H . - D . : Contributions of Sediments to the nitrogen budget of the Elbe

estuary 3063 K E R N E R , M . : The coupling of microbial respiration processes w i t h i n the two-dimensional spatial structure

of an intertidal mud flat sediment of the Elbe Estuary 3067 W I L T S H I R E , K . H . : Experimental procedures for the fractionation of phosphorus in Sediments with emphasis

on anaerobic techniques 3073

X I V . Received too late for Classification

H E R R M A N N , J . : Bioindication of nutrient and organic pol lut ion by benthic stream invertebrates - pitfalls and problems (Abstract) 3079

M U N A W A R , M . , L E P P A R D , G . G . & M U N A W A R , I. F . : Ecotoxicology of stressed environments: Structural and functional strategy 3080

W A R D , J . V . & S T A N F O R D , J . : Benthic faunal patterns along the longitudinal gradient of a R o c k y Mountain river System 3087

O V E R B E C K , J . : Plenary lecture: Initial, present and future aim of l imnology 3095

Societas Internationalis Limnologiae: Twenty-Fourth Congress, Munich/Federal Republic of Germany, 1989 3102

Officers and list of members 3137 Contents of volume 24 (completely) (1)

Verh. Internat. Verein. L i m n o l . 24 2784-2787 Stuttgart, Dezember 1991

Optimal resource allocation in cladocerans

Wilfried Gabriel and Barbara E. Taylor

Introduction The natural pattern for growth and reproduction of cla­docerans results i n continued growth during most or all of adult life. This reproductive strategy is not wel l understood because optimal control theory predicts simultaneous growth and reproduction only under very special conditions (SIBLY et al. 1985) w h i c h are unl ikely to obtain for cladocerans. Theoretically preferred is the "bang-bang" strategy: no Investment into reproduction until an optimal switching point is reached, then no fur­ther growth. T A Y L O R & G A B R I E L (1985) showed that in-determinate growth of D a p h n i a pulex and D . p u l i c a r i a is suboptimal under the assumption of constant mortal-ity. T o explain w h y Simocephalus v e t u l u s ( M Ü L L E R ) , an-other daphniid cladoceran, is not a "bang-bang strat-egist", P E R R I N et al. (1987) proposed that structural con-straints such as size of the brood chamber could require continued growth after first reproduction.

Because reproductive Output is among the most important components of fitness, one can expect that the resource allocation pattern has been shaped by strong selection pressure during evolution. But there are many plausible excuses for disagreements between theory and nature. Genetic, developmental, phy-siological, or other factors that could constrain an organism from achieving optimal allocation are poor ly known and thus difficult to include i n a model. Before invoking such constraints to reconcile nature to theory in the case of resource allocation for D a p h n i a , we deci-ded to analyse the problem further. F r o m laboratory data for D a p h n i a pulex, we constructed a model in which adult growth and reproduction are functions of resource allocation. W e numerically solved the model for optimal resource allocation patterns under various con­ditions. These optimal patterns are more similar to natu­ral patterns than previous analyses led us to expect, and they indicate how selection may have shaped the life histories of cladocerans.

Methods and model T o describe growth and reproduction of cladocerans we used laboratory data for D a p h n i a pulex ( T A Y L O R 1985). F r o m these measurements we estimated the various functions and parameters of the model, including net production as a function of body size and food concen-tration. Production is modelled as a continuous process

during the intermolt; reproduction and change in body size are implemented as discrete events at instar tran-sitions. F o r each adult instar A the allocation a\ of net production P A to reproduction determines growth and reproduction: the number of eggs produced is propor­tional to C * A P A a n a * t n e weight increment is proport ional to ( 1 - Q ! A ) P A . Measured values of « A were used i n this model to describe the natural allocation pattern. T o find the optimal resource allocation patterns, we chose in-trinsic growth rate r as our measure of fitness. F o r any specified size dependent mortality scheme, the life history parameters l x (survival probability) and m x (re­production) are constants or functions of the CKA'S. Therefore, the discrete f o r m of the renewal equation

1 = £ l x m x e x p ( - r x )

can be used to calculate numerically those «A-values which maximize r. W e assume three simple cases of mor­tality: i) size-independent, ii) survivorship linearly de-creasing w i t h body length to model a fish-like predation, and iii) survivorship linearly increasing w i t h body length to represent invertebrate predation. F o r the re­sults presented, the size-independent mortality is as-sumed to be 10 % per adult instar and the size-dependent mortality is calculated as increasing or decreasing linear­ly w i t h body length so that at 0.75 m m or 3.5 m m the mortality becomes 10% or 60%. A more detailed de-scription of the model w i l l be given elsewhere ( T A Y L O R & G A B R I E L 1992).

Results and discussion

The natural pattern of growth and reproduction at abundant food is given in Fig. 1 a. The frequency histogram below the figure represents the part a A

of net production that is allocated to reproduc­tion. We count the last juvenile instar where al­location to reproduction can Start as A = 1. (The eggs resulting from this allocation are laid at the beginning of instar 2 and hatch at end of instar 2.) At this instar already 76 % of net production is de-voted to reproduction. This allocation increases to over 95 % at adult instar 10, resulting in small but continuous growth after first egg production. This natural pattern is contrasted by the model results in Fig. 1 b - d . With size-independent mortality

0368-0770/91/0024-2784 $ 1.00 © 1991 E . Schweizerbart'sche Verlagsbuchhandlung, D-7000 Stuttgart 1

W . Gabrie l & B. E . Taylor , O p t i m a l resource allocation in cladocerans

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2786 X I I . Ecology of Aquatic Organisms. 3. Animals

Table 1. Intrinsic growth rates r for the best "bang-bang strategy" and comparison of r under natural resource allocation w i t h the optimal values achievable for assu-med size-independent mortality, fish-like and inverte-brate-like predation risks under abundant and limited food conditions. food predation optimal natural difference bang-bang

r [ d - ' ] r f d " 1 ] abs. rel. [%] r [ d - ' ]

high independent 0.3412 0.3368 0.0044 1.3 0.3389 high fish 0.2710 0.2592 0.0118 4.3 0.2702 invertebrate 0.1909 0.1460 0.0449 23.5 0.1897

low independent 0.2314 0.2247 0.0067 2.9 0.2313 fish 0.1665 0.1607 0.0058 3.5 0.1648 invertebrate 0.0873 0.0183 0.0690 79.0 0.0864

(Fig. 1 b) the optimal strategy is to cease growing after one intermediate allocation to reproduction. Qualitatively the same is predicted if the mortality increases with body length (Fig. 1 c), but the first intermediate allocation to reproduction is higher and consequently the final body size is smaller than for size-independent mortality. Under inver­tebrate predation (Fig. 1 d) it is optimal to post-pone the first reproduction by one instar and to have four intermediate allocations before inves-ting all into reproduction. The largest final body size would be attained with this allocation pattern.

The natural allocation pattern seems to be quite independent of food level (TAYLOR 1985, L Y N C H 1989), and it seems to be mainly a function of weight and/or age. At least for the D a p h n i a p u l e x clone used in the experiments by TAYLOR, the natural a A values are a function only of the instar number. Therefore, limited food implies retarded growth and fewer eggs without any qualitative change in the natural allocation pattern (Fig. 2 a). The optimal strategy under size-independent mor­tality delays reproduction by one instar (Fig. 2 b), as compared to the high food Situation. Food shortage does not change the optimal strategy under fish predation very much (Fig. 2 c), but the intermediate a A is lower, i.e. allocation gives a higher proportion to growth, so that the final body size is similar. Under invertebrate predation

the optimal strategy strongly depends on the food level. Optimization with limited food postpones the first reproduction further, and there is only one intermediate allocation before reaching the final body size, which is larger than under abun­dant food.

Table 1 compares the intrinsic growth rates for natural and optimal allocations and the best "bang-bang" allocation for various predation schedules and food levels. The simple optimal con-trol model obviously does not predict inter­mediate allocations and its "bang-bang strategy" can result in higher r values than natural alloca­tion. The fitness under this strategy is very close but always below the Optimum which our model reaches with intermediate allocations. The natural resource allocation seems to be suboptimal under all conditions tested. Invertebrate predation produces the largest deviations from the optimal values. In most cases, however, the realized fitness is very close to its maximum, so that inde-terminate growth seems not to be very expensive. Similar results are obtained with more com-plicated predation schedules, such as arctangent or parabolic functions. A weak point of any such op­timization is the underlying assumption of con-stant environmental conditions within and be­tween gener ations.

But ponds and lakes are temporally variable, and thus cladocerans perceive a variety of environ-ments even during one growing season. One can question whether the intrinsic growth rate is the appropriate fitness measure under variable en­vironmental conditions. Optimizing the total re­productive Output can lead to indeterminate growth as shown by GABRIEL (1982) in a different model approach. Other measures of fitness will be discussed elsewhere in detail; e.g. for non-over-wintering cladocerans the number of adults able to produce resting eggs at the end of the season might be a better fitness measure.

If the environment changes from generation to generation one has to maximize the geometric mean fitness over successive generations. The re-

Fig . 1. Body size (= triangles) and fecundity (= circles) at abundant food resulting f rom allocation a A of net produc­t ion to reproduction (histogram below figure) for adult instars A starting w i t h A = 1 as the last juvenile instar where first allocation to reproduction can occur. a) Natural allocation. b - d) M o d e l results under the assumption of size-in­dependent mortality (b), fish (c), and invertebrate predation (d).

Fig. 2. Same as F ig . 1 but for l imited food (30 % below the incipient l imi t ing level).

W . Gabriel & B. E . Taylor , O p t i m a l resource allocation in cladocerans 2787

b

0 3 6 9 Adult Instar

Fig . 3. Opt imal resource allocation C*A of net production to reproduction if mortality varies between generations. a) Equal probability is assumed for fish and invertebrate predation at abundant food. b) A s a) but w i t h size-inde­pendent mortality as a third equal probable predation schedule. c) A s b) but for limited food (30 % below the incipient l imit ing level).

sulting optimal resource allocation is then not just a superposition of the results under constant con­ditions. This is demonstrated in Fig. 3 for the sim­ple case that food is always constant but predation changes between generations. In reality we must of course consider that food conditions and kind and intensity of predation may change between generations and as well within generations. De-pending on the frequency of the various environ-ments this probably can result in almost any optimal resource allocation pattern.

More detailed measurements on resource alloca­tions and its correlation with other life history parameters of different clones and species would be helpful to gain more insight into the selective forces shaping the observed growth and reproduc­tion patterns. From our model we conclude: The natural resource allocation pattern with its con-sequences of indeterminate growth is suboptimal for any constant environment, but it can be under-

stood as adaptive to variable environments which change between generations in food availability and predation risk.

Acknowledgements B E T was supported in part by contract D E - A C - 0 9 -7 6 S R 0 0 8 1 9 between the U . S. Dept. of Energy and the Research Foundation of the Universi ty of Georgia and in part by a research fellowship from the Max-Planck-Gesellschaft.

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Authors ' address:

M a x Planck Institute for L imnology , Department of Physiological Ecology, Postfach 165, D-2320 Plön, F R G .

Present address of B. E . T A Y L O R : Savannah River Ecology Laboratory, Drawer E , A i k e n , South Carol ina 29801, U . S . A .