Consumption patterns, complexity and enrichment in ... - Europe PMC

Consumption patterns, complexity and enrichment in aquatic food chains Lars-Anders Hansson*, Christer Bro«nmark, Per Nystro«m, Larry Greenberg, Per Lundberg, P. Anders Nilsson, Anders Persson, Lars B. Pettersson, Pia Romare and Lars J. Tranvik{ Department of Ecology, Ecology Building, Lund University, S-223 62 Lund, Sweden The interactions between consumers and prey, and their impact on biomass distribution among trophic levels, are central issues in both empirical and theoretical ecology. In a long-term experiment, where all organisms, including the top predator, were allowed to respond to environmental conditions by reproduction, we tested predictions from `prey-dependent' and `ratio-dependent' models. Prey-dependent models made correct predictions only in the presence of strong interactors in simple food chains, but failed to predict patterns in more complex situations. Processes such as omnivory, consumer excretion, and unsuitable prey-size windows (invulnerable prey) increased the complexity and created patterns resembling ratio-dependent consumption. However, whereas the prey-dependent patterns were created by the mechanisms predicted by the model, ratio-dependent patterns were not, suggesting that they may be `right for the wrong reason'. We show here that despite the enormous complexity of ecosystems, it is possible to identify and disentangle mechanisms responsible for observed patterns in community structure, as well as in biomass development of organisms ranging in size from bacteria to ¢sh. Keywords: food chain; ratio-dependent; prey-dependent; enrichment; omnivory

levels: only every second trophic level in a food chain should respond to changes in K (Fretwell 1977; Oksanen et al. 1981; table 1). This would be true if (i) the system can be viewed as a simple food chain, and (ii) the functional response of all consumers is of a Holling's type II nature. Alternative models, e.g. so-called `ratio-dependent' models of food-chain dynamics, make other assumptions and predictions. Assuming a very di¡erent and controversial functional response of all consumers (Lundberg & Fryxell 1995), such models make no predictions about changes in the dynamic stability properties of the system in response to productivity. Also, the biomasses of all trophic levels are expected to respond to changes in productivity (Arditi et al. 1991a,b; table 1). Here, we report on an experiment where we tested how biomass changes in aquatic food chains of di¡erent length in response to two levels of productivity. We also analyse how the structure of the food chain, such as the number of trophic levels and the number of components per level, as well as consumer-resistant morphologies and omnivory, a¡ect the outcome of food-chain interactions. An important feature of such an experiment is to allow enough time for the highest trophic level to respond via reproduction to alterations in productivity (Yodzis 1988; Osenberg & Mittelbach 1996). Hence, as a top predator we used a ¢sh species with a short generation time (eight weeks; guppy, Poecilia reticulata). Another crucial prerequisite is to allow enough time for the system to approach equilibrium conditions (Yodzis 1988). We employed a 19-week-long experiment, allowing reproduction of two generations at the top trophic level and more

1. INTRODUCTION

A fundamental question in ecology is whether general patterns of abundance, biomass, and interspeci¢c interactions exist, despite the enormous complexity of ecosystems (Hairston & Hairston 1997). An important aspect of this question is how ecosystems respond to increased productivity. Apart from the fact that `productivity' is a rather ambiguous ecological concept, many attempts have been made to predict how dynamical stability properties respond to changes in productivity (Rosenzweig 1971; Nakajima & DeAngelis 1989; DeAngelis 1992; Abrams & Roth 1994; for a review, see Rosenzweig 1995), how food-web structure itself is a¡ected by levels of productivity (Fretwell 1977; Oksanen et al. 1981; DeAngelis et al. 1989; Rosenzweig 1995), and how population interactions within the food web should best be modelled (e.g. the prey- versus ratio-dependent debate: Arditi & Ginzburg 1989; Berryman 1992; Diehl et al. 1992; Ginzburg & Akc°akaya 1992; Oksanen et al. 1992; Sarnelle 1992; Abrams 1994; Lundberg & Fryxell 1995). If we assume that productivity can be represented as the carrying capacity of the lowest trophic level in the system (K), traditional food-chain theory makes a number of predictions about trophic level responses to increased K (e.g. Rosenzweig 1971; Oksanen et al. 1981). The response to increased productivity should di¡er among trophic * Author for correspondence ([email protected]). {Present address: Department of Water and Environmental Studies, Linko«ping University, S-58183 Linko«ping, Sweden.

Proc. R. Soc. Lond. B (1998) 265, 901^906 Received 5 January 1998 Accepted 29 January 1998

901

& 1998 The Royal Society

902

L.-A. Hansson and others

Aquatic food-chain dynamics

Table 1. Predicted response in biomass to nutrient enrichment according to ratio-dependent and prey-dependent models with di¡erent food-chain compositions (+ strong response and 7 weak response; `ratio' and `prey' refer to ratio-dependent and prey-dependent models; treatments A, B and C are di¡erent food-chain compositions. In prey-dependent models, the functional response of consumers in the food chain is a function of prey density only. In ratio-dependent models, the functional response is dependent on the ratio between prey and predator density.) trophic level

food chain A food chain B food chain C ratio prey ratio prey ratio prey

bacteria £agellates and algae zooplankton ¢sh

+ + +

+ 7 +

+ + +

+ 7 +

+ + + +

7 + 7 +

than ten generations at lower trophic levels. Moreover, to avoid stochastic extinctions of speci¢c populations among replicates, we retrieved 1% of the volume from all replicates within each treatment once a week, mixing the water in a separate tank before returning an identical volume to each replicate. 2. METHODS The experiment was done in a greenhouse from 21 November 1995 to 2 April 1996 (133 days). A 2 3 factorial design was used with low and high nutrient concentrations crossed with three di¡erent food chains. The basic food chain (A) included bacteria, heterotrophic £agellates, algae, and small grazers (small cladocerans and rotifers, mainly Chydorus sp. and Lecane sp.; ¢gure 1). The B and C chains also included large grazers (mainly Daphnia magna), and in the C chain, two adult guppy ¢sh (Poecilia reticulata) of each sex were added to each tank (¢gure 1). To ensure ¢sh reproduction throughout the experiment, a minimum of one ¢sh of each sex was always present in each tank. The B and C chains were contained in 400 l cylindrical tanks (height, 1.0 m; diameter, 0.74 m). For the A chain, 80 l cylindrical tanks were used (height, 0.70 m; diameter, 0.46 m). Each treatment was replicated six times, resulting in a total of 36 experimental tanks, to which treatments were randomly assigned. To increase the habitat complexity, four arti¢cial macrophytes were added to each tank (untwined polypropylene ropes extending from the bottom to the surface). In chains with zooplankton and ¢sh, complexity was further increased by introducing two mesh cylinders as refugia for ¢sh larvae and zooplankton (mesh size, 2 mm; total volume of 36 l). Once a week and prior to sampling, refugia, polypropylene ropes and tank walls were scrubbed and the water thoroughly mixed. The water in each tank was continuously aerated and the temperature was 23 3 8C throughout the experiment. Arti¢cial light optimized for plant growth (Osram Vialox Planta-T, 400 W) was used between 0600 and 2200 during periods when sunlight decreased below approximately 150 mmol of photons m72 s71. Hence, light intensity was always above 150 mmol m72 s71 during 16 h per day. At the start of the experiment, the total phosphorus concentrations were 28.7 (3.8) and 30.6 (5.9) mg l71 (means 1 s.d.) in the low-nutrient and high-nutrient treatments, respectively (t34 1.15; Proc. R. Soc. Lond. B (1998)

Figure 1. An outline of possible interactions between components included in the study showing strong (thick arrows) and weak (thin arrows) interactions. The ¢gure illustrates that grazers feed on several trophic levels (omnivory), that some consumer^prey links are more important than others owing to unsuitable prey-size windows, and that excretion from higher trophic levels (DOC and nutrients; dotted lines) may stimulate bacterial growth; these factors have been identi¢ed as creating patterns resembling ratio-dependent consumption. p40.1). Nutrient solution (proportions: phosphate^ phosphorus, 1%; ammonium ^ N, 2%; nitrate ^ N, 3.1%; by weight) was added to all treatments, corresponding to an increase in phosphorus concentration of 125 mg l71 in high-nutrient treatments and 12.5 mg l71 in low nutrient treatments. This addition was repeated after three weeks. Thereafter, the high-nutrient treatments received the same nutrient addition ¢ve times at intervals of three weeks, whereas no more nutrients were added to the low-nutrient treatments. The ¢nal concentration of total phosphorus in the low-nutrient treatment was 29.1 (4.8) mg l71 (mean 1 s.d.), and in the high-nutrient treatment the concentration was 69.7 (32.3) mg l71 (t34 5.28; p50.001). At the end of the experiment, all ¢sh were counted, measured (total length), and weighed (dry weight, 65 8C, 48 h). Fish stomachs were analysed using a dissecting microscope, and the presence of crustaceans, rotifers, algal and ¢sh remains were noted. We acknowledge that stomach analysis only gives information on what the ¢sh had eaten during the last hours, which may not mirror diet changes during the experiment. Water samples were taken from surface to bottom with a Plexiglas tube after thorough mixing of the water column. Zooplankters were concentrated from 10 l from each tank by ¢ltration through a 55 mm mesh and preserved with Lugol's solution. One litre from each tank was subsampled for determination of heterotrophic £agellate and bacterial abundances as well as phytoplankton biomass and dissolved organic carbon (DOC). The concentration of DOC of ¢ltered (Whatman GF/F) samples was measured on a Shimadzu TOC-5000 analyser after acidi¢cation and purging to remove inorganic carbon. Algal samples were preserved with Lugol's solution and permanent slides were made using 2-hydroxypropyl-metacrylate (HPMA) (Crumpton 1987). Algae were counted at 200 magni¢cation, and 20 individuals of each species were measured, and biovolumes were calculated using formulae for approximate geometrical ¢gures. Algae were separated into èdible' algae, of which the genera Scenedesmus and Monoraphidium accounted for



903

Table 2. Two-way ANOVA table comparing the total biomass of bacteria, £agellates, algae and zooplankton in relation to nutrient level (low or high) and food-web structure (A, B or C) source bacteria nutrient level food web nutrient level food web error £agellates nutrient level food web nutrient level food web error algae nutrient level food web nutrient level food web error zooplankton nutrient level food web nutrient level food web error

d.f.

MS

F

1 2 2 30

2.612 0.085 0.949 0.179

14.601 0.476 5.302

0.0006 0.6257 0.0107

1 2 2 30

0.032 1.238 0.614 0.194

0.163 6.385 3.165

0.6890 0.0049 0.0566

1 2 2 29

8.567 5.801 11.731 0.279

30.746 20.819 42.103

50.0001 50.0001 50.0001

1 2 2 30

0.645 0.127 0.014 0.022

29.989 5.889 0.645

50.0001 0.0070 0.5316

95% (by numbers), and `¢lamentous' algae. More than 95% (by numbers) of the latter group consisted of Oscillatoria, Tribonema, Anabaena and Pseudanabaena. Èdible' algae were assumed to be suitable food for all herbivores, whereas `¢lamentous' forms were assumed to be eaten exclusively by Daphnia (Sterner 1989; ¢gure 1). Bacteria and heterotrophic £agellates were preserved with the Lugol/formaldehyde/thiosulphate method of Sherr & Sherr (1993) and counted by epi£uorescence microscopy after staining with 4',6-Diamidino-2-phenylindole (Porter & Feig 1980). Herbivorous zooplankton were divided into `large' (Daphnia spp.) and `small' grazers (Chydorus spp., copepods and rotifers). The biomass of zooplankton was estimated using the length ^ weight regressions presented by Bottrell et al. (1976). The rotifer community was dominated by Lecane spp., for which a constant individual body dry weight of 0.2 mg was used (Bottrell et al. 1976). The e¡ect of food-chain structure (A, B or C) and nutrient level (low or high) on the ¢nal biomasses of bacteria, £agellates, algae and zooplankton was evaluated by a two-way ANOVA. The e¡ect of enrichment on the ¢nal biomass of ¢sh in the C chain was analysed by a one-way ANOVA. Di¡erences in DOC concentration among treatments were tested with a one-way ANOVA, and Tukey's post hoc test was used to reveal di¡erences between treatment means. All data except DOC and ¢sh biomass were log-transformed before analysis. 3. RESULTS AND DISCUSSION

The fundamental prediction from ratio-dependent models is a proportional e¡ect of enrichment at all trophic levels, and no e¡ect of food-chain composition or interactive e¡ects of nutrients and food-chain composition. Our results revealed that for all trophic levels there were e¡ects of food-chain composition or interactions between food chain and enrichment (table 2). Hence, our experiment failed to corroborate predictions from ratiodependence models. However, the biomass accumulations at di¡erent trophic levels in the three food chains were also Proc. R. Soc. Lond. B (1998)

p

not in complete agreement with predictions from preydependent models. All top consumers (small and large zooplankton in chains A and B, respectively, and ¢sh in chain C; F1,10 28.869; p50.001) responded to enrichment with an increase in ¢nal biomass (¢gure 2), which is in accordance with the predictions from both prey- and the ratio-dependent models (table 1). Presumably, owing to grazing by the unregulated zooplankton assemblage, algae and heterotrophic £agellates in the B chain showed no increase in biomass in response to enrichment, which is in accordance with prey-dependent, but not ratio-dependent models (¢gure 2). Similarly, in the A chain, with only small grazers, £agellates showed no response to enrichment (¢gure 2). However, total phytoplankton biomass in the A chain increased in response to enrichment, most probably owing to the dominance of ¢lamentous algae; a size fraction too large to be ingested by these small grazers (Leibold 1989; Sterner 1989; ¢gure 2). Similar results were obtained in a recent study of a much simpler food chain, including a bacteriophage and two strains of bacteria, one of which was resistant to predation by the bacteriophage. Here, the bacteria shifted from primarily being regulated by predation to resource regulation (Bohannan & Lenski 1997). The weak bacterial response to enrichment in the A and B chains, in spite of consumer regulation of the heterotrophic £agellates, was probably due to feeding on bacteria by small (Christo¡ersen et al. 1990; Porter 1996) and large (Christo¡ersen et al. 1990; Pace et al. 1990; Jeppesen et al. 1992; Ju«rgens & Gu«de 1994) zooplankters, respectively (¢gure 1). In the C chain, ¢sh removed all Daphnia, which were replaced by smaller, less vulnerable, but also less e¤cient herbivores (Chydorus and rotifers). Although these grazers were able to respond to enrichment, they were a¡ected by the ¢sh, as indicated by the high abundances of both Chydorus and the dominant rotifer Lecane in ¢sh stomachs, as well as by their lower biomass in the C chain than in the A chain (with and

904



Figure 2. Final mean values 1 s.e. at low (L) and high (H) nutrient concentrations in treatments A, B and C for biomass of ¢sh and of `small' (shaded) and `large' (dotted) zooplankton, biovolume of èdible' (shaded) and ¢lamentous (striped) algae, number of heterotrophic £agellates and bacteria, and concentration of DOC. Note that for algae and zooplankton, the standard error is based on total biomass, and that standard errors for DOC in some cases are too small to be visible in the ¢gure. Proc. R. Soc. Lond. B (1998)

Aquatic food-chain dynamics without ¢sh, respectively; ¢gure 2). Hence, the grazing pressure in the C chain was low, partly explaining the positive responses of both heterotrophic £agellates and edible algae to enrichment (¢gure 2). A complementary explanation to the positive response of heterotrophic £agellates to enrichment relates to the twofold greater bacterial abundance in the C chain than in the other enriched chains (¢gure 2). Most likely, this a¡ected heterotrophic £agellates by providing a higher resource base, compensating for the grazing pressure, and also by providing an alternative food resource for the small cladocerans. The probable cause for the higher bacterial biomass in enriched tanks with ¢sh (C chain), is the 30% higher concentration of DOC in this chain than in any other chain (¢gure 2; ANOVA, F5,30 10.175, p50.001; Tukey's post hoc test, p50.008), providing a higher amount of energy for bacterial growth (Tranvik 1988). This higher carbon content in the presence of ¢sh is in line with the recent ¢nding that planktivorous ¢sh increase the carbon input from the atmosphere to primary producers of aquatic ecosystems (Schindler et al. 1997). The carbon is then transferred from primary producers to higher trophic levels by feeding, and part of it is, together with other nutrients, excreted and again made available to lower trophic levels (Vanni et al. 1997). Hence, positive e¡ects of excretion from consumers on lower trophic levels, in combination with ine¤cient grazing from small zooplankters, are likely mechanisms behind the pattern resembling ratio-dependent predation in the C chain (¢gure 2). The overall pattern revealed from this experiment is that large, e¤cient grazers create patterns in accordance with prey-dependent models (¢gure 2). When small, less e¤cient herbivores dominate, there is still a tendency towards prey-dependent patterns, although invulnerable resources, such as ¢lamentous algae, respond as predicted by ratio-dependent models. When ¢sh were added, they strongly suppressed the large grazers, and depressed the small grazers to some degree, as well as increased the input of atmospheric carbon into the water (Schindler et al. 1997), stimulating bacterial growth (¢gure 1). In this way ¢sh stimulate lower trophic levels, both by predation on herbivores and by donating resources, thereby creating patterns predicted by ratio-dependent models. Ratio-dependent patterns obviously occur both in experimental and in natural situations. However, our experiment shows that they may not be generated by interference or resource sharing (Akc°akaya et al. 1995), but by other mechanisms, such as unsuitable prey-size windows, consumer excretion and omnivory, suggesting that ratiodependent models may be `right for the wrong reason'. On the other hand, the prey-dependent models failed to predict biomass patterns other than in simple food chains with strong interactors, and may therefore be viewed as too simple to be as generally applicable, as is indicated by their widespread use (Lundberg & Fryxell 1995; Polis & Strong 1996). Although we recognize that our experiment is only a simple version of natural, more complex systems, it is obvious that even our simple and controlled environment was more complex than can be accommodated in present models. As long as important processes of food-chain complexity, like the ones pointed out in this study, are not Proc. R. Soc. Lond. B (1998)


905

included in predator^ prey models, the use of such models and the debate regarding which of them is least £awed, may not be very fruitful. Instead, the major challenge for future studies, theoretical as well as empirical, will be to embrace this complexity in consumer ^ prey models. Recent identi¢cation of potentially important mechanisms, including prey size refuges (Mittelbach et al. 1988; Leibold 1989; Hambright et al. 1991; this study), spatial and temporal refuges (Sih 1987), omnivory (Diehl 1993; Porter 1996), and increased resource base induced by consumers (Vanni et al. 1997), are promising hints for the creation of future models of consumer ^ prey interactions and food-chain dynamics. It is tempting to clump such processes into terms like `noisy complexity' and simply conclude that communities are too complex to show general patterns (Polis & Strong 1996). However, we show here, in line with the suggestion by Hairston & Hairston (1993, 1997), that despite this complexity it is possible to disentangle processes causing observed patterns in food chains. We thank Haªkan Bjo«rklund for counting the bacteria and £agellates. The study was supported by the Swedish Natural Science Research Council (NFR; to L.A.H, L.J.T and P.L.) and the Swedish Board for Agriculture and Forestry Research (SJFR; to C.B.). P. A. Abrams, N. G. Hairston Jr, and S. Cooper made valuable comments on an earlier version of the paper. REFERENCES Abrams, P. A. 1994 The fallacies of `ratio-dependent' predation. Ecology 75, 1842^1850. Abrams, P. A. & Roth, J. 1994 The responses of unstable food chains to enrichment. Evol. Ecol. 8, 150^171. Akc°akaya, H. R., Arditi, R. & Ginzburg, L. R. 1995 Ratiodependent predation: an abstraction that works. Ecology 76, 995^1004. Arditi, R. & Ginzburg, L. R. 1989 Coupling predator ^ prey dynamics: ratio dependence. J.Theor. Biol. 139, 311^326. Arditi, R., Ginzburg, L. R., & Akc°akaya, H.R. 1991a Variation in plankton densities among lakes: a case for ratio-dependent predation models. Am. Nat. 138, 1287^1296. Arditi, R., Perrin, N. & Saah, H. 1991b Functional responses and heterogenities: an experimental test with cladocerans. Oikos 60, 69^75. Berryman, A. A. 1992 The origins and evolution of predator ^ prey theory. Ecology 73, 1530^1535. Bohannan, B. J. & Lenski, R. E. 1997 E¡ect of resource enrichment on a chemostat community of bacteria and bacteriophage. Ecology 78, 2303^2315. Bottrell, H. H., Duncan, A., Gliwicz, Z. M., Grygierek, E., Herzig, A., Hillbricht-Ilkowska, A., Kurasawa, H., Larsson, P. & Weglenska, T. 1976 A review of some problems in zooplankton production studies. Norw. J. Zool. 24, 419^456. Christo¡ersen, K. Riemann, B., Hansen, L., Klysner, A. & SÖrensen, H. B. 1990 Qualitative importance of the microbial loop and plankton community structure in a eutrophic lake during a bloom of cyanobacteria. Microb. Ecol. 20, 253^272. Crumpton, W. 1987 A simple and reliable method for making permanent mounts of phytoplankton for light and £uorescence microscopy. Limnol. Oceanogr. 32, 1154^1159. DeAngelis, D. L. 1992 Dynamics of nutrient cycling and food webs. New York: Chapman & Hall. DeAngelis, D. L., Bartell, S. M. & Brenkert, A. L. 1989 E¡ects of nutrient recycling and food-chain length on resilience. Am. Nat. 134, 778^805.

906



Diehl, S. 1993 Relative consumer sizes and the strengths of direct and indirect interactions in omnivorous feeding relationships. Oikos 68, 151^157. Diehl, S., Lundberg, P. A., Gardfjell, H., Oksanen, L. & Persson, L. 1992 Daphnia ^ phytoplankton interactions in lakes: is there a need for ratio-dependent consumer ^ resource models ? Am. Nat. 142, 1052^1061. Fretwell, S. D. 1977 The regulation of plant communities by the food chains exploiting them. Perspect. Med. Biol. 20, 169^185. Ginzburg, L. R. & Akc°akaya, H. R. 1992 Consequences of ratiodependent predation for steady-state properties of ecosystems. Ecology 73, 1536^1543. Hairston, N. G. Jr & Hairston, N. G. Sr 1993 Cause ^ e¡ect relationships in energy £ow, trophic structure and interspeci¢c interactions. Am. Nat. 142, 379^411. Hairston, N. G. Jr & Hairston, N. G. Sr 1997 Does food web complexity eliminate trophic-level dynamics ? Am. Nat. 149, 1001^1007. Hambright, K. D., Drenner, R. D., McComas, S. R. & Hairston, N. G. Jr 1991 Gape limited piscivores, planktivore size refuges, and the trophic cascade hypothesis. Arch. Hydrobiol. 121, 389^404. Jeppesen, E., Sortkjer, O, SÖndergaard, M. & Erlandsen, M. 1992 Impact of a trophic cascade on heterotrophic bacterioplankton production in two shallow ¢sh-manipulated lakes. Arch. Hydrobiol. Beih. Ergebn. Limnol. 37, 219^231. Ju«rgens, K. & Gu«de, H. 1994 The potential importance of grazing-resistant bacteria in planktonic systems. Mar. Ecol. Prog. Ser. 112, 169^188. Leibold, M. A. 1989 Resource edibility and the e¡ects of predators and productivity on the outcome of trophic interactions. Am. Nat. 134, 922^949. Lundberg, P. & Fryxell, J. M. 1995 Expected population density versus productivity in ratio-dependent and prey-dependent models. Am. Nat. 146, 153^161. Mittelbach, G. G., Osenberg, C. W. & Leibold, M. A. 1988 Trophic relations and ontogenetic niche shifts in aquatic ecosystems. In Size structured populations (ed. B. Ebenman & L. Persson), pp 219^235. Berlin: Springer-Verlag. Nakajima, H. & DeAngelis, D. L. 1989 Resilience and local stability in a nutrient-limited resource ^ consumer system. Bull. Math. Biol. 51, 501^510. Oksanen, L., Fretwell, S. D., Arruda, J. & Niemela, P. 1981 Exploitation ecosystems in gradients of primary productivity. Am. Nat. 118, 240^261. Oksanen, L., Moen, J. & Lundberg, P. A. 1992 The time-scale problem in exploiter^ victim models: does the solution lie in ratio-dependent predation? Am. Nat. 140, 938^960.

Proc. R. Soc. Lond. B (1998)

Osenberg, C. W. & Mittelbach, G. G. 1996 The relative importance of resource limitation and predator limitation in food chains. In Food webs, integration of patterns and dynamics (ed. G. A. Polis & K. O. Winemiller), pp. 134^148. New York: Chapman & Hall. Pace, M. L., McManus, G. B. & Findlay, E. G. 1990 Planktonic community structure determines the fate of bacteria production in a temperate lake. Limnol. Oceanogr. 35, 795^808. Polis, G. A. & Strong, D. R. 1996 Food web complexity and community dynamics. Am. Nat. 147, 813^846. Porter, K. 1996 Integrating the microbial loop and the classic food chain to a realistic planktonic food web. In Food webs, integration of patterns and dynamics (ed. G. A. Polis & K. O. Winemiller), pp. 51^59. New York: Chapman & Hall. Porter, K. G. & Feig, Y. S. 1980 The use of DAPI for identifying and counting aquatic micro£ora. Limnol. Oceanogr. 25, 943^948. Rosenzweig, M. L. 1971 Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171, 385^387. Rosenzweig, M. L. 1995 Species diversity in space and time. Cambridge University Press. Sarnelle, O. 1992 Nutrient enrichment and grazer e¡ects on phytoplankton in lakes. Ecology 73, 551^560. Schindler, D. E., Carpenter, S. R., Cole, J. J., Kitchell, J. F. & Pace, M. L. 1997 In£uence of food web structure on carbon exchange between lakes and the atmosphere. Science 277, 248^251. Sherr, E. B. & Sherr, B. E. 1993 Preservation and storage of samples for enumeration of heterotrophic protists. In Handbook of methods in aquatic microbial ecology (ed. P. F. Lemp, B. E. Sherr, E. B. Sherr & J. J. Cole), pp. 207^212. Boca Raton: Lewis. Sih, A. 1987 Predators and prey lifestyles: an evolutionary and ecological overview. In Predation ö direct and indirect impacts on aquatic communities (ed. C. W. Kerfoot & A. Sih), pp. 203^224. Hanover and London: University Press of New England. Sterner, R. W. 1989 The role of grazers in phytoplankton succession. In Plankton ecology (ed. U. Sommer), pp. 107^170. New York: Brock/Springer. Tranvik, L. J. 1988 Availability of dissolved organic carbon for planktonic bacteria in oligotrophic lakes of di¡ering humic content. Microb. Ecol. 16, 311^322. Vanni, M. J., Layne, C. & Arnott, S. 1997 `Top-down' trophic interactions in lakes: e¡ects of ¢sh on nutrient dynamics. Ecology 78, 1^20. Yodzis, P. 1988 The indeterminacy of ecological interactions as perceived through perturbation experiments. Ecology 69, 508^515.