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OIKOS 104: 467 /478, 2004 Species loss and the structure and functioning of multitrophic aquatic systems Owen L. Petchey, Amy L. Downing, Gary G. Mittelbach, Lennart Persson, Christopher F. Steiner, Philip H. Warren and Guy Woodward Petchey, O. L., Downing, A. L., Mittelbach, G. G., Persson, L., Steiner, C. F., Warren, P. H. and Woodward, G. 2004. Species loss and the structure and functioning of multitrophic aquatic systems. / Oikos 104: 467 /478. Experiments and theory in single trophic level systems dominate biodiversity and ecosystem functioning research and recent debates. All natural ecosystems contain communities with multiple trophic levels, however, and this can have important effects on ecosystem structure and functioning. Furthermore, many experiments compare assembled communities, rather than examining loss of species directly. We identify three questions around which to organise an investigation of how species loss affects the structure and functioning of multitrophic systems. 1) What is the distribution of species richness among trophic levels; 2) from which trophic levels are species most often lost; and 3) does loss of species from different trophic levels influence ecosystem functioning differently? Our analyses show that: 1) Relatively few high-quality data are available concerning the distribution of species richness among trophic levels. A new data-set provides evidence of a decrease in species richness as trophic height increases. 2) Multiple lines of evidence indicate that species are lost from higher trophic levels more frequently than lower trophic levels. 3) A theoretical model suggests that both the structure of food webs (occurrence of omnivory and the distribution of species richness among trophic levels) and the trophic level from which species are lost determines the impact of species loss on ecosystem functioning, which can even vary in the sign of the effect. These results indicate that, at least for aquatic systems, models of single trophic level ecosystems are insufficient for understanding the functional consequences of extinctions. Knowledge is required of food web structure, which species are likely to be lost, and also whether cascading extinctions will occur. O. L. Petchey and P. H. Warren, Dept of Animal and Plant Sciences, Univ. of Sheffield, Alfred Denny Building, Western Bank, UK, S10 2TN ([email protected]). / A. L Downing, Dept of Zoology Ohio Wesleyan Univ., Delaware, OH 43015, USA. / G. G Mittelbach, W. K. Kellogg Biological Station, Michigan State Univ., Hickory Corners, MI 49060, USA. / L. Persson, Dept of Ecology and Environmental Science, Umeå Univ., SE-901-87 Umeå, Sweden. / C. F. Steiner, Dept of Ecology, Evolution and Natural Resources, 14 College Farm Road, Cook College, Rutgers Univ., New Brunswick, NJ 08901-8511, USA. / G. Woodward, Dept of Zoology, Ecology and Plant Science, Univ. College Cork, Cork, Ireland. Most experiments and virtually all theory about the effects of biodiversity on ecosystem functioning have focused on a single trophic level-primary producers. Yet interactions between trophic levels are integral to the dynamics of most natural ecosystems, especially aquatic ones (Hairston and Hairston 1993, Polis and Strong 1996). Trophic cascades in aquatic systems can affect the biomass of organisms, water clarity and temperature, nutrient dynamics, community structure, and more (Oksanen et al. 1981, Carpenter and Kitchell 1993, Hairston and Hairston 1993). The strength of a trophic cascade depends on the species or functional group Accepted 16 September 2003 Copyright # OIKOS 2004 ISSN 0030-1299 OIKOS 104:3 (2004) 467 composition within a trophic level (Leibold et al. 1997, Persson 1999). Keystone species provide striking examples of how the presence or absence of a species can change biomass flow and storage in ecosystems as well as altering community composition (Paine 1966). The presence or absence of omnivores can have important consequences for ecosystems through their direct and indirect interactions with other species (Diehl 1993). It is clear from a long history of theory, experiments, and observations that trophic interactions affect ecosystems. However, our understanding of how biodiversity per se influences ecosystem functioning in systems where trophic interactions play such a dominant role is only beginning to develop (Raffaelli et al. 2002). Studies investigating how biodiversity influences ecosystem functioning in multitrophic systems have been conducted in terrestrial grasslands (Wardle et al. 1999), soils (Mikola 1998), laboratory microbial communities (McGrady-Steed et al. 1997), freshwater mesocosms (Norberg 2000), and rocky intertidal communities (Paine 2002). These studies have shown that species diversity and especially species composition can have large impacts on ecosystem functioning via direct and indirect pathways (Downing and Leibold 2002). In situations where species diversity changes across more than one trophic level, diversity at adjacent trophic levels can act synergistically to affect ecosystem functioning (Naeem et al. 2000), and the diversity and composition of a community can influence ecosystems through indirect interactions that alter trophic structure (Petchey et al. 1999, Downing and Leibold 2002). Predicting the effects of species extinction is more difficult in multiple trophic level systems compared to single trophic levels for several reasons. First, the more complex community structure makes models involving multiple trophic levels harder to formulate and analyse. Indirect effects in these communities make predicting effects of perturbations difficult (Yodzis 1988). Second, the order in which species are lost will be even more important in multitrophic-level systems than within a single trophic level. For example, unbalanced extinctions among trophic levels can increase or decrease the proportion of species that reside within a particular trophic level depending on the original distribution of species among trophic levels. Such changes in trophic structure may alter the flow of energy through the food web or change food-web stability or both (King and Pimm 1983). For example, it is likely that the loss of a predator will have very different ecosystem consequences than the loss of a herbivore. We focus here upon potential ecosystem-level effects of species loss, rather than the more general question of how biodiversity may influence ecosystem functioning. Species loss is the process by which an extant community becomes a more depauperate community. This impoverishment contrasts with situations in typical biodiversity 468 experiments in which assembled communities with different numbers of species are compared in order to simulate effects of species loss (Symstad et al. 1998). Such purely synthetic experiments cannot show any short-term transient effects of the loss of a species, or, indeed, any long-term historical effects of now extinct species. Species loss is better simulated in removal experiments, though these too have limitations (Dı́az and Chapin 2000). Here we explore aspects of species loss in multitrophic-level systems from an empirical and theoretical perspective. First, we investigate how species richness and extinctions are distributed amongst trophic levels. For example, are there more producer species than consumer species and which will go extinct first? Second, we use a simple food-web model to examine how the loss of species at different trophic levels will affect ecosystem structure and functioning. Most of our examples come from multi-trophic aquatic systems, although many of the issues we cover appear to be common to aquatic and terrestrial systems alike. Patterns of diversity and species loss in natural aquatic ecosystems The distribution of species richness among trophic levels will influence post-extinction trophic structure, for example, if there are few species at a particular trophic level there is an increased likelihood that extinctions will cause loss of this entire group. In addition, the outcome of a species deletion is also influenced by whether the species that goes extinct is high up or low down in the food web (Pimm 1980). Both observations make documenting the patterns of diversity and extinctions across trophic levels important if we are to predict effects of extinctions on ecosystem structure and functioning. The distribution of species among trophic levels Patterns of species richness across trophic levels are generally less well documented than either total abundance or biomass in each trophic level. Studies have mainly drawn on data from detailed species surveys of specific systems (Evans and Murdoch 1968, Moran and Southwood 1982), food web data (Cohen 1977, Briand and Cohen 1984, Sugihara et al. 1989, Martinez 1991, Schoenly et al. 1991a, Havens 1992), or species lists from many different studies (Warren and Gaston 1992). All yield information on the shape of food webs, but interpreting their results is not straightforward for a number of reasons. First, not all types of data have information across all trophic levels (for example, studies of trophic guild structure only examine the faunal component of the community). Second, assignment to trophic position may be based on the recorded feeding OIKOS 104:3 (2004) links in a particular web, but this may not reflect the typical trophic role of the species (for example, a herbivore might appear as a top consumer simply because it is not consumed in a particular web). Thirdly, the food web data in particular have considerable variation in resolution, both of links and taxa, which is not independent of trophic position (for example, top predators are likely to be much better resolved taxonomically than species near the base of the food web). As a result of these problems, early generalizations about trophic richness ratios are unreliable (Polis 1991). Some of the later studies, however, whilst still imperfect, may nonetheless provide useful guidance as to the relative richness of different trophic levels. Systematic cross-community comparisons of food web shape have most extensively been carried out using food web data, classifying species as ‘basal’ (i.e. feed on nothing else in the web), ‘top’ (are fed on by nothing else in the web) and ‘intermediate’ (both feed on, and are fed upon by, others in the web). Studies using this approach suggest that there is a tendency for intermediate species to account for a smaller fraction of the community as diversity is reduced, at least at lower diversity, with the proportions of basal and top species becoming correspondingly larger (Briand and Cohen 1984, Sugihara et al. 1989, Havens 1992, Martinez 1993), though the strength of this effect is subject to debate (Havens 1992, Martinez 1993). Analysis of such data from aquatic food webs produces rather mixed results (Fig. 1). While there is some indication of triangularity in the shape of the web for top and intermediate species, basal species constitute a very variable fraction of the web (Fig. 1). This may genuinely be the case, though there are also two possible artefactual explanations. First, the base Fig. 1. Proportions of basal (B), intermediate (I) and top (T) species from different studies as follows: a) Schoenly et al. (1991b), means from nine insect dominated aquatic food webs; b) Martinez (1991, 1991a) single large lake food web; c) Hall and Raffaelli (1991, 1991a) single large estuarine food web; d) Havens (1992), pelagic food webs from fifty lakes; e) Closs and Lake (1994) stream food webs for different seasons; f) and g) Deb (1995), two pond food webs; h) and i) Thompson and Townsend (2000) means, over season, for two streams. OIKOS 104:3 (2004) of many aquatic food webs, especially in benthic systems, is largely dead organic matter (detritus), and the associated heterotrophic microbes. Taxonomic resolution of these elements of most food webs is notoriously coarse, and so provides little guidance as to taxonomic diversity. Second, even where food webs have a substantial component of basal species, these may be aggregated into broad groups (e.g. ‘periphyton’ or ‘phytoplankton’) rather than resolved to species. These problems make it difficult to judge whether difference in species richness among trophic levels are an artefact, or reflect real differences between types of aquatic systems. In the relatively few food webs where effort has been put explicitly into obtaining good taxonomic resolution in both basal and other levels, the basal level can be as, or more, diverse than the levels above (Havens 1992) though this is not inevitably the case (Martinez 1991). Assignment of species to the other categories is ambiguous. Intermediate species can be second, third or fourth level consumers, provided there is at least one species that (perhaps occasionally) feeds on them. This results in there being almost no true ‘top’ species as food webs become large (Martinez and Lawton 1995), at which point the classification seems of little value. Clearly, estimating the distribution of species richness amongst trophic levels requires both good taxonomic resolution across all trophic levels, and a clear definition of trophic position. Here we present a new compilation of data from a number of studies in benthic freshwater systems, that may suffer less from the problems discussed above. Species richness data were collated from a total of 141 freshwater sites, 91 from running waters, 50 from standing waters. The sites spanned a wide range of systems across a large acidity gradient (pH 4 /8.5) created mostly by variation in geology and land-use. One hundred and twenty-three of the sites were located within the U.K. Eighteen New Zealand streams (Townsend et al. 1998) were also included, to compare the shape of food webs from two regions with very different evolutionary histories. We standardised taxonomic resolution by identifying taxa to the lowest common denominator across studies: i.e. to species where possible, or to the next highest taxonomic level if species could not be distinguished with certainty. This meant that our estimates of species richness are conservative and certain large taxonomic groups whose members are difficult to identify, such as meiofauna and bacteria, were excluded all together. We then sub-divided our communities into trophic levels: because we ignored trophic interactions within the microbial part of the food web (microbial loop), we defined ‘consumer 1’ species as those that eat only at the ‘basal’ level (primary producers, detritus, and associated microbes), ‘consumer 2’ species as invertebrates that eat other metazoans, and ‘consumer 3’ species as vertebrates (fish here) that eat 469 other metazoans (Jeffries and Lawton 1985). Although a large proportion of the consumer 2 species in benthic aquatic systems are traditionally described as ‘detritivores’ (e.g. many stoneflies and caddisflies), many of these are, in fact, facultative grazers (Ledger and Hildrew 2000) as, indeed, are many of the consumer 3 species (Woodward and Hildrew 2002). We further limited our analysis to communities and restricted basal species to include only diatoms because of a lack of sufficiently detailed taxonomic data for cyanobacteria and other algae. Aquatic macrophytes were excluded since they contribute to the food web primarily via the detrital pathway (Hildrew 1992, Jones et al. 1998). Benthic grazers (e.g. some snails and mayflies) feed predominantly on biofilms, which are typically rich in diatoms and coat both mineral and organic surfaces (Hildrew 1992, Jones et al. 2002). Species richness decreased from the lower to the higher trophic levels in both running and standing waters (Fig. 2). In fact, our analysis of empirical data shows that food webs were probably even more triangular than suggested by our results because our basal species category included only diatoms. The New Zealand data exhibited broadly similar patterns to those from the U.K., despite the very different evolutionary histories and environmental conditions of these two regions, suggesting that the trophic structuring of benthic freshwater systems might follow similar ‘rules’ across a wide range of environments. Fig. 2. Variation in numbers of species in each of four trophic levels for the data-set described in the text. See the text also for a description of how species were assigned to the trophic levels. Open circles are UK lakes and ponds; open squares are UK streams and rivers; open triangles are New Zealand (NZ) streams. Bars represent 9/95% CL. Sample sizes are: diatoms: 11 Lakes, 11 UK streams, 18 NZ streams; primary consumers: 40 Lakes, 91 UK streams, 18 NZ streams; invertebrate predators: 40 Lakes, 91 UK streams, 18 NZ streams; fish: 43 Lakes, 59 UK streams, 18 NZ streams. Raw data were provided by the contributors listed below, with the relevant literature cited where appropriate: S. J. Ormerod (Bradley and Ormerod 2001, Bradley and Ormerod 2002); F. Edwards (unpubl.); C. Gjerløv (Gjerløv et al. in press); S. S. C. Harrison (Pretty et al. 2003); J. I. Jones and C. D. Sayer (Jones and Sayer 2003); A. M. J. Lane (Lane 1999); N. Towers (unpubl.); R. Thompson (Townsend et al. 1998); W. Beaumont (UKAWMN 2000); G. Woodward (unpubl.). 470 The distribution of extinctions among trophic levels Multiple factors may predispose for extinction of species at higher trophic levels compared to those at lower ones. The relatively small population sizes of species at higher trophic levels increase their risk of extinction via demographic stochasticity and environmental fluctuations (Lande 1993). Longer generation times and relative rarity of resting stages mean that evolutionary and ecological change will lag further behind altering environments, putting species at higher trophic levels at special risk again. Furthermore, species occupying higher trophic levels depend on the presence of species at lower trophic levels, causing higher extinction risk for species occupying higher trophic levels in simple foodwebs (Fowler and MacMahon 1982, Holt et al. 1999) and perhaps also in more complex webs (Holt et al. 1999). However, effects of trophic dependencies on extinction risk in complex food webs are harder to predict (Pimm 1980, Holt et al. 1999), because species occupying higher trophic levels can promote co-existence of competing species at lower trophic levels (Paine 1966). Nevertheless, disproportionate extinction probabilities among trophic groups, with generally higher extinction rates for species at higher trophic levels seems to be an emerging general pattern (Dickerson and Robinson 1986, Mikkelson 1993, Wright and Coleman 1993, Kruess and Tscharntke 1994, Lawton 1995, Gilbert et al. 1998, Holt et al. 1999). Indeed, it can be difficult to find any combination of species in microbial aquatic communities in microcosms that both include a species at a high trophic level and are persistent (Weatherby et al. 1998). The data we compiled on species richness distributions amongst trophic levels (Fig. 2) were collected from systems spanning a gradient in acidity; they suggest that the species at some trophic levels were more vulnerable to acidification than others. Despite the fact that species richness always increased with pH, the strength of the relationship and the rate of increase varied among trophic levels (Fig. 3). However, there was no evidence that the effect of pH on richness increased with increasing trophic level (p /0.37 for Spearman’s rank correlation between the slopes of the relationships in Fig. 3 and trophic level (1, 2, 3 or 4 corresponding to basal, consumer 1, consumer 2, and consumer 3 levels) for either streams and rivers or ponds and lakes). Our data supported the view that populations of species at high trophic levels (here fish) are often severely reduced, or even extirpated, at low pH (Brown and Sadler 1989, Muniz 1990). This suppression of the consumer 3 species can often lead to release of the large invertebrate consumers at the adjacent trophic level, which can become very abundant (Hildrew et al. 1984). Despite these variations among trophic groups and given that our data were collated from different communities, the positive relationships between pH and species richness OIKOS 104:3 (2004) particular, are sensitive to heavy metal pollution, which typically accompanies acidification in mine tailings (Brown and Sadler 1989). Fishes and amphibians, which occupy the highest trophic levels in many freshwaters, are also susceptible to the effects of climate change; even slight rises in temperature can lead to population crashes and extinctions (Carpenter et al. 1992). Species at higher trophic levels also tend to be most heavily exploited (Pauly and Christensen 1995). Consequently, their extinction resulting from over-harvesting is a very real concern, as is evidenced by the precarious position of the much of the world’s cetacean fauna and the collapse of many marine fisheries (Griffith 2000). Despite the often strong influences of a single environmental stressor, many natural systems are simultaneously affected by multiple stressors (Breitburg et al. 1999, Folt et al. 1999, Vinebrooke et al. 2003), which can induce more complex ecosystem responses. For instance, some of the pH-species richness relationships were altered in the sites with greater nutrient availability (denoted by crosses in Fig. 3): invertebrate species richness in standing waters was unusually low, but phytoplankton were far more speciose under elevated nutrient loadings. In contrast, fish species richness was largely unaffected by nutrient enrichment, as were invertebrates in running waters. These deviations suggest that very different food web configurations can occur when multiple stressors are operating, and that responses can vary among trophic levels and are also systemspecific. Indeed, alternative stable states, transiently maintained by trophic cascades, are well documented in eutrophic shallow lakes (Van de Bund and Van Donk 2002, Jones and Sayer 2003), but are far less prevalent in running waters. Fig. 3. Numbers of species in each of four trophic groups, and chlorophyll a concentration for phytoplankton along a pH gradient in (a) streams and rivers and (b) ponds and lakes. See the text for a description of how species were assigned to the trophic levels. Regression statistics were from log10(x/1) transformed data. Circles denote ‘normal’ water bodies; crosses denote sites that are subject to significant artificial eutrophication resulting from either sewage or agricultural fertiliser input. Open triangles represent freshwater bodies that recently experienced altered productivity or acidity and were excluded from regression analyses. were strong and consistent within most trophic levels and remarkably similar across running and standing waters. Although our analysis of data from running and standing waters focussed on acidification, examples of stressors that lead to disproportionate species loss at high trophic levels are legion. For instance, biomagnification of organochlorine pesticides has been implicated in the impaired reproduction or loss of top predators from many freshwater food webs (Mason 1991) and similar effects have been reported in marine systems (Jarman et al. 1996). Fish in general, and salmonids in OIKOS 104:3 (2004) Modelling multitrophic extinctions and effects on ecosystem properties The discussions above are limited forays into what is clearly a complex problem. Attempting to predict the possible effects of species loss on functional aspects of aquatic systems by piecing together inferences from our current understanding of how such systems work is an important endeavour, but has limitations. In particular, it is difficult to relate insights from specific results in one system to more general principles across different types of system, and it is difficult, from field observations and experiments, to separate the effects of species loss from other confounding factors (Huston 1997). One approach to tackling these problems is to explore the problem in model systems, trading off the advantages of clear comparison of the effects of interest, with the inevitable danger of oversimplification (Morin 1998). Here we take this approach and explored how standard Lotka / Volterra consumer /resource equations respond to loss 471 of species from different trophic levels. For simplicity, the model we present includes three trophic levels and species within a trophic level differ in growth rate and interaction strength. Because of our restriction to three trophic levels, consumer 2 biomass is relatively high because of release from consumption (Oksanen et al. 1981). We focus upon total biomass, a state variable, of each trophic level as the ecosystem-level property of interest. Focusing on total biomass enables direct comparison with the results of experiments that also focused on total autotroph biomass (Tilman 1997, Hector et al. 1999), though we stress that standing biomass may (Leibold et al. 1997) or may not inform about the rate of biomass production, especially in aquatic systems where much of the biomass is quickly consumed. Regardless, the total biomass of a trophic level, especially of primary producers, is a valid and important ecosystem property in its own right. Modelling methods Four different food web structures were simulated; all were composed of three trophic levels: a basal level of autotrophic primary producers (hereafter called basal), a primary consumer level (hereafter called consumer 1), and a secondary consumer level (hereafter called consumer 2). Web structure differed in the level of omnivory (present or absent) and shape (rectangular or triangular) in a 2 /2 design. Omnivory was manipulated by creating webs in which consumers fed only on the trophic level below them (no omnivory) and webs in which consumer 2 species fed on both consumer 1 and basal species. Web shape was either ‘‘rectangular’’, in which each trophic level was composed of an equal number of species (3 species per level for a total of 9) or ‘‘triangular’’, in which fewer species were found at successively higher trophic levels (4 basal species, 3 species at the consumer 1 level, and 2 species at the consumer 2 level, for a total of 9). We modelled rectangular webs in addition to the more realistic triangular webs to explore whether web structure may be a determinant of responses to extinction, but we only show graphs of results from triangular webs, given that in reality food webs are rarely if ever rectangular. All interactions were modelled using Lotka /Volterra consumer /resource equations of the general form: dBi =dtBi f i (B) (1) where f i (B)Bi Sj aij Bj Bi is the biomass of species i, fi is its per biomass rate of increase, and aij is the effect of species j on species i. The state variables of this class of model are often assumed to be the number of individuals in some area or volume 472 (e.g. density of individuals). The models are, strictly speaking, based on biomass conversion equations, however, so that the state variables are the biomasses of species (Berryman 1999). Basal species were self-limited populations exhibiting logistic growth with an intrinsic rate of increase (bi) chosen randomly from a uniform distribution between 0.00001 and 1 and a self-limitation term, aii /bi/K, where K was the carrying capacity set at 10 for all basal species. For simplicity, we did not model interspecific competition among basal species. Consumers were modelled without self-limitation (aii /0). An effect of consumer j on resource i (parameter aij) was chosen randomly from a uniform distribution between 0 and 1. The consumers gain from their resource (aji) was calculated as /aij /cji, where cji was a conversion efficiency (the fraction of consumed prey that is converted into predator biomass) chosen randomly from a uniform distribution between 0.01 and 0.9. Consumer mortality rates (bi) were chosen randomly from a uniform distribution between /0.00001 and /1. We randomly generated 1000 feasible food webs for each of the four web structures. Unlike previous studies that have relied upon asymptotic population stability as a criterion for determining the feasibility of randomly generated communities (Pimm 1982, Moore et al. 1993, Borrvall et al. 2000), we use permanence as our determinant of food-web feasibility following methods in Law and Morton (1996). Permanence is a global property of a model community requiring only that biomasses of all component species are positive and finite (Hofbauer and Sigmund 1988, Law and Morton 1996). Consequently, permanence allows for asymptotically stable communities (local and global) as well as classically unstable systems such as cyclic fluctuations in populations biomass or chaotic states (Law and Morton 1996). Hence, the permanence criterion includes a wider range of dynamics, some of which may occur in natural systems and yet be excluded by less inclusive feasibility criteria. To explore effects of species losses, we subjected each permanent community to a series of species deletions. For the sake of simplicity and tractability, we only consider deletions within single trophic levels. For each trophic level in the rectangular food webs, every possible one-species deletion was performed, followed by every possible two-species combination. Deletions of all three species were performed for the consumer 1 and consumer 2 trophic levels, though not for basal species since this would result in a ‘community with no species’. In the triangular food webs, every possible one-species and two-species deletion was executed for the consumer 2 level and every possible combination of one, two, and three-species deletion was performed for the consumer 1 and basal levels. OIKOS 104:3 (2004) Following each deletion, the resultant community was assessed for permanence. If not permanent, an attracting (permanent and non-invasible) species sub-set was obtained by checking every possible combination of species left following deletion for the properties of permanence and non-invasibility by species not included in the sub-set of interest. For example, consider a web with four species initially (1,2,3,4) from which species 4 is subsequently deleted. The resultant community (1,2,3) is checked for permanence. If not permanent, then every possible sub-set (1), (2), (3), (1,2), (1,3), and (2,3) is checked for permanence and non-invasibility by species from the post-deletion species pool not included in the focal sub-set. Invasibility was determined by calculating the invaders growth rate (fi(x) from Eq. 1) when its biomass was equal to zero and the biomasses of the resident species were set at equilibrium values (Law and Morton 1996). In rare instances (4% of total deletion attempts), a single attracting sub-set could not be obtained or permanence could not be determined. In such cases we relied on numerical integration to determine community composition following species deletions using a 4th/5th order Runge /Kutta solver. The post-deletion community was given initial biomasses equal to their pre-deletion equilibrium values, and dynamics were then allowed to run for 6000 time steps. Visual inspection of haphazardly selected cases showed that transient dynamics generally disappeared within the first 500 time steps. Any species with biomass greater than an arbitrary lower limit (1/10 6) at the end of the simulation were retained and equilibrium population biomasses were calculated as the average over the final 1000 time steps. Once a permanent attracting subsystem was found, the community composition was saved and response variables were calculated. We recorded the total biomass of basal species and the incidence of cascading extinctions (losses of species other than those deleted). To calculate biomasses, we relied upon equilibrium values (i.e. we set Eq. 1 to zero and solved for Bi). Though nonequilibrium dynamics were possible, equilibrium population biomasses derived from linear Lotka /Volterra equations are equivalent to biomasses averaged through time (Hofbauer and Sigmund 1988, Law and Morton 1996). number of species deleted on basal biomass, we used repeated-measures analysis of variance (rm-ANOVA) with the number of species deleted modelled as a within-subjects effect. Statistical significance should not be over-interpreted since it is a partly a function of the number of replicates chosen. We ran separate repeated-measures analyses for deletions within the basal, consumer 1, and consumer 2 trophic levels. Because some trophic levels experienced different levels of species deletion in rectangular versus triangular webs, we focused only on 0, 1 and 2 species deletion combinations in our statistical analyses to ease comparisons. We log10(100/B/1) transformed all values for both statistical analyses and graphical depiction. We multiplied biomass by 100 before adding the constant to reduce the influence of the constant. All statistical analyses were performed using Systat Version 8.0. Modelling results Focusing first on basal species deletions, biomass at all trophic levels decreased as a function of increasing losses of basal species (Fig. 4A, 4B). Declines in basal biomass Analyses of modelling results For analyses of simulation results, we considered each randomly generated food web to be an experimental unit. Because multiple combinations of a level of species deletion were performed within a trophic level, biomass responses to these multiple combinations were averaged to obtain a single response for a given community. To explore effects of omnivory, food web shape, and the OIKOS 104:3 (2004) Fig. 4. Effects of deletions of basal species (A, B), consumer 1 species (C, D) and consumer 2 species (E, F) on total biomass of basal species (triangles), consumers 1 (squares) and consumers 2 (diamonds). Food webs either excluded (A, C, E) or included (B, D, F) omnivory. Shown are means and standard deviations. Symbols are slightly displaced along the x-axis to increase clarity. 473 were generally steeper in webs without omnivory (p B/ 0.0001, omnivory /number deleted within-subjects effect). Loss of biomass with increasing numbers of basal species deletions was greatest in rectangular webs without omnivory, as indicated by a significant three-way interaction between number of species deleted, food web shape, and omnivory (p B/0.0001, within-subjects effect). Cascading extinctions of basal species were infrequent (Fig. 5A, 5B). However, cascading extinctions of consumer 1 and consumer 2 species occurred in the majority of food webs, regardless of food web shape or omnivory (Fig. 5A). The exception was consumer 2 in triangular webs without omnivory. Basal biomass increased as more consumer 1 species were deleted (Fig. 4C, pB/0.0001, within-subjects effect). However, this effect was weaker in food webs with omnivory (p B/0.0001, omnivory/number deleted effect). Consumer 1 biomass decreased with increasing numbers of extinctions (Fig. 4C), while the effect on consumer 2 biomass depended on the presence of omnivory (Fig. 4C, 4D). Compared to deletions of basal species, consumer 1 deletions tended to increase the frequency of cascading extinctions of basal species (Fig. 5C, 5D). These basal species extinctions were more frequent in webs with omnivory and were most common in triangular webs with omnivory, occurring in greater than 50% of the communities. Cascading extinctions were relatively rare in the consumer 1 trophic level (Fig. 5C). However, cascading extinctions of consumer 2 species were very frequent in webs without omnivory, but less so in food webs with omnivory (Fig. 5C, 5D). Species deletions within the consumer 2 trophic level caused basal biomass to decrease (Fig. 4E, pB/0.0001, within subjects effect of number deleted). This effect was more pronounced in food webs without omnivory and was especially strong in triangular webs without omnivory as indicated by a significant within-subjects interaction between web shape, omnivory and number of consumer 2 species deleted (pB/0.0001). The deletions increased consumer 1 biomass and decreased consumer 2 biomass (Fig. 4E). Increasing losses of consumer 2 species also resulted in large increases in the frequency of cascading extinctions within the basal trophic level (Fig. 5E). Triangular webs were particularly prone to cascading extinctions. Model conclusions Fig. 5. Effects of deletions of basal species (A, B), consumer 1 species (C, D) and consumer 2 species (E, F) on the frequency of cascading extinctions of basal species (triangles), consumers 1 (squares) and consumers 2 (diamonds). Food webs either excluded (A, C, E) or included (B, D, F) omnivory. Shown are means and standard deviations. Symbols are slightly displaced along the x-axis to increase clarity. 474 Simplistic community models suggest that basal (e.g. primary producer) species extinctions can only reduce total biomass at the basal level (Tilman et al. 1997, Loreau 1998). In contrast, extinctions from our multitrophic model can either increase or decrease the total biomass within a trophic level. In general, our simple model exploration shows that effects of species loss from multitrophic systems depend on how many species are lost, from which trophic level species are lost, and also on food web shape (triangular or rectangular). The effects of extinctions were, however, suggestive of a simple consumer /resource dynamic. As more species are removed from a trophic level, the more their resources are freed from top-down control. This can then cascade to lower trophic levels as those intermediate species exert stronger control of their resources, the basal species (as seen in the consumer 2 deletions). It is not unexpected that losses of consumer species may influence basal species either directly or indirectly through consumptive effects, assuming that feeding links are not donor-controlled. These relatively intuitive changes in total biomass within a trophic level (an aggregate ecosystem property) contrast with the indeterminate effects of species loss on abundances of individual species (Yodzis 1988). This mirrors the qualitatively different responses of population-level and community-level stability to change in biodiversity (McNaughton 1977). However, this simplistic interpretation disregards the impacts of species extinctions that may cascade through a food web as the result of species deletions. Our results OIKOS 104:3 (2004) indicate that loss of a focal species or group of species commonly results in further species extinctions in adjacent and non-adjacent trophic levels. Though previous studies have examined such phenomena in model food webs, revealing important effects of species richness and food web structure (Pimm 1980, Borrvall et al. 2000, Lundberg et al. 2000, Dunne et al. 2002), these studies did not expose the precise distribution of extinctions within the food web or their consequences for ecosystem properties. Some cascading extinctions are expected based on first principles. For instance, in rectangular food webs without omnivory, loss of a single consumer 1 species will result in three consumer 2 species feeding on only two consumer 1 species, a case in which stable coexistence is unlikely under constant environmental conditions. Omnivory can buffer consumer 2 populations from this effect, as can triangular food web configurations (compare Fig. 5C, D). Potentially more complex are extinctions that cascade down trophic levels. If consumers mediate coexistence of their resources (e.g. by feeding on competitive dominants, curtailing competitive exclusion), then deletions of those consumers can cause extinctions among the resource species. This is a plausible explanation for consumer 1 extinctions following consumer 2 removals (Fig. 5E, F). However, this cannot explain extinctions of basal species following consumer 1 deletions (Fig. 5C, D), as competitive interactions were not modelled for basal species. If we had modelled interspecific competition among basal species, it is likely that extinctions at the basal level would have been even more frequent in this case. Finally, consumer 2 deletions vividly illustrate how extinctions may cascade to non-adjacent trophic levels (Fig. 5E, F). The high frequency of cascading extinctions among basal species was likely to be due to apparent competition following the release of consumer 1 species from consumer 2 control. If true, this illustrates how coexistence of species within trophic levels may be indirectly mediated by consumers in higher, non-adjacent trophic levels, a balance that may be easily disrupted. As with any model, our study required a number of simplifying assumptions and abstractions to maintain tractability. Consequently, there are several caveats that deserve mentioning. First, strong consumer effects were due to our use of Lotka /Volterra equations with recipient control. Incorporation of donor-control or ratio-dependent functional responses should weaken consumer effects (direct and indirect) on basal species. Secondly, we modelled basal species without interspecific competition. This implicitly assumes no overlap in resource requirements of basal species (i.e. in the absence of consumers, basal biomass is a linear, increasing function of basal species richness). Hence, losses of basal species will have a greater impact on basal biomass compared to situations in which species display some degree of niche overlap and can exhibit density compenOIKOS 104:3 (2004) sation following competitive release (note, however, that there may be a greater tendency for competitive exclusion and cascading extinctions in this scenario). Our models have focussed on food webs where primary producer species form the basal food resource. However, in some freshwater ecosystems, allochthonous, rather than autochthonous, inputs can dominate the basal resources (Wallace et al. 1997). In these systems, dependence on terrestrial subsidies results in a predominance of donor-controlled interactions between basal species and consumers. Donor-control (e.g. semi-chemostat dynamics in basal resource) can produce qualitatively different effects from Lotka /Volterra dynamics with logistic growth, and may serve to stabilise food web structure (Polis and Strong 1996). It seems possible, though clear answers would require further investigation, that the models above are appropriate if we consider the detritivores as the basal trophic level; organisms that feed on detritivores would then occupy the consumer 1 level, and organisms that consume these would occupy the consumer 2 level. Extinctions within our model were random within trophic levels. Future models could simulate extinctions that correspond to generalism (e.g. connectedness, as in Dunne et al. 2002), interaction strength, vulnerability to predation, and competitive ability (though note that any cascading extinctions must have resulted from these kinds of difference among species). Because we modelled all consumers as generalists (every species within a consumer trophic level fed on every species in their resource trophic level) extinctions were not ordered by generalism. However, simulated extinctions from food webs differ in effect depending on whether more or less connected species go extinct (Dunne et al. 2002). For simplicity also, our simulated extinctions occurred without regard to aij or aji (Borrvall et al. 2000). Loss of species that are more vulnerable to predation might have qualitatively different effects than the loss of species that resist predation. If invulnerable species are lost, more nutrients will be passed to consumers via vulnerable species. Another complexity that we chose not to include in the model was that of ontogenic shifts in the trophic level occupied by a species. Often species in aquatic systems occupy one trophic level while young and another trophic level in the adult stage (Wu and Culver 1992), and large ontogenetic shifts in trophic position can occur even among insect larvae (Woodward and Hildrew 2002). The occurrence of ontogenetic niche shifts could have several implications for the effect of extinctions on ecosystem properties. Extinction of a single species might remove a component of two trophic levels simultaneously and consequently have greater effects than otherwise. Finally, we chose not to allow the replacement of the extinct species with a different species. This contrasts with observations of some aquatic 475 systems, where species replacements along an environmental gradient are common and also important in regulating trophic structure (Leibold et al. 1997). Further modeling that includes ontogenic shifts and a regional pool of species that could replace extinct species could inform about how species replacements might temper the functional consequences of extinctions. Future directions Our multi-trophic level model shows how effects of species deletions may depend critically on food web shape and omnivorous links (independent of species richness). This is perhaps not surprising when considering species losses amongst consumers. Yet, even losses of basal species affect species at other trophic levels, with ultimate impacts on total production being linked to consumers, food-web shape, and degree of omnivory. We argue that there is little un-biased and or reliable information about the shape of food webs, though they are generally though to be triangular; a proposition that is supported by the new compilation of data that we present. New high-resolution studies of food webs provide a method for assessing the consequences of extinction in very complex food webs with realistic structure (Dunne et al. 2002). Linking this work to ecosystem functioning would scale up from the study of small modules of interacting species (used here) to much more complex and realistic food web structures. The model also shows that where in the food web species loss is focused can be crucial for eventual impacts on ecosystem functioning. We argue that multiple mechanisms will increase the extinction risk of species at higher trophic levels. Assessing the relative importance of these mechanisms (e.g. is trophic position per se important, Lawton 1995) would be an interesting academic exercise. Nevertheless, future research could focus more closely on the consequences of extinctions at high trophic levels. For example, loss of consumer 2 are the most context-dependent (Fig. 4); is this model prediction borne out in empirical data? Ultimately, predicting a system’s capacity to maintain fundamental properties will at least require knowledge of the prevalence of omnivory, the manner in which species richness is partitioned among trophic levels within the community, and from where in the food web species are lost. Total biodiversity loss and changes in ecosystem functioning are not simply a product of a focal group of species that are especially prone to extinction (whatever the cause). Effects of losing such species may cascade through food webs, leading to more extinctions. It follows that impacts of species losses on ecosystem processes such as primary production will ultimately be the product of both trophic interactions (a release or intensification of consumer effects) and extinctions that 476 cascade through the food web. The challenge for future research will be to link all of these potential consequences of species loss to produce a general and predictive framework for the consequences of species loss in multitrophic system. Acknowledgements / This manuscript is a product of the Biodiversity in Multitrophic Systems Working Group at the Aquatic Biodiversity and Ecosystem Functioning Workshop, 4 /7 April 2002, Ascona, Switzerland, funded by LINKECOL (European Science Foundation; ESF), the US National Science Foundation (NSF), DIVERSITAS, the Swiss National Science Foundation (SNF), and the Swiss Federal Institute of Environmental Science and Technology (EAWAG). Order of authorship does not necessarily represent individuals’ relative contributions. CFS performed the modelling and thanks Richard Law for his expert advice on determining permanence. GW compiled the data presented in Fig. 2 and 3 and thanks especially W. Beaumont and M. Lane for assistance. GGM acknowledges support during manuscript preparation from the National Center for Ecological Analysis and Synthesis, a Center funded by the US NSF (Grant #DEB-0072909), the University of California, and the Santa Barbara campus. OLP was funded by a NERC Fellowship. Mark Gessner and Pablo Inchausti commented on previous drafts of this article and made significant improvements possible. References Berryman, A. A. 1999. Alternative perspectives on consumer / resource dynamics: a reply to Ginzburg. / J. Anim. Ecol. 68: 1263 /1266. Borrvall, C., Ebenman, B. and Jonsson, T. 2000. Biodiversity lessens the risk of cascading extinction in model food webs. / Ecol. Lett. 3: 131 /136. Bradley, D. C. and Ormerod, S. J. 2001. Community persistence among stream invertebrates tracks the North Atlantic oscillation. / J. Anim. Ecol. 70: 987 /996. Bradley, D. C. and Ormerod, S. J. 2002. Long-term effects of catchment liming on invertebrates in upland streams. / Freshwater Biol. 47: 161 /171. Breitburg, D. L., Sanders, J. G., Gilmour, C. C. et al. 1999. Variability in responses to nutrients and trace elements, and transmission of stressor effects through an estuarine food web. / Limnol. Oceanogr. 44: 837 /863. Briand, F. and Cohen, J. E. 1984. Community food webs have scale-invariant structure. / Nature 307: 264 /267. Brown, D. J. A. and Sadler, K. 1989. Fish survival in acidic waters. / In: Morris, R., Taylor, E. W., Brown, D. J. A. et al. (eds), Acid toxicity and aquatic animals. Soc. Exp. Biol, pp. 31 /44. Carpenter, S. R. and Kitchell, J. F. 1993. The trophic cascade in lakes. / Cambridge Univ. Press. Carpenter, S. R., Fisher, S.G., Grimm, N. B. et al. 1992. Global climate change and freshwater ecosystems. / Annu. Rev. Ecol. Syst. 23: 119 /139. Closs, G. P. and Lake, P. S. 1994. Spatial and temporal variation in the structure of an intermittent stream food web. / Ecology 64: 1 /21. Cohen, J. E. 1977. Ratio of prey to predators in community food webs. / Nature 270: 165 /167. Deb, D. 1995. Scale-dependence of food web structures: tropical ponds as paradigm. / Oikos 72: 245 /262. Dı́az, S. and Chapin, F. S. 2000. Network of removal experiments on the role of biodiversity in ecosystem functioning. / GCTE News 15: 10. Dickerson, J. E. J. and Robinson, J. V. 1986. The controlled assembly of microcosmic communities: the selective extinction hypothesis. / Oecologia 71: 12 /17. OIKOS 104:3 (2004) Diehl, S. 1993. Relative consumer sizes and the strengths of direct and indirect interactions in omnivorous feeding relationships. / Oikos 68: 151 /157. Downing, A. L. and Leibold, M. A. 2002. Ecosystem consequences of species richness and composition in pond food webs. / Nature 416: 837 /841. Dunne, J. A., Williams, R. J. and Martinez, N. D. 2002. Network structure and biodiversity loss in food webs: robustness increases with connectance. / Ecol. Lett. 5: 558 /567. Evans, F.-C. and Murdoch, W. W. 1968. Taxonomic composition, trophic structure and seasonal occurrence in a grassland insect community. / J. Anim. Ecol. 37: 259 /273. Folt, C. L., Chen, C. Y., Moore, M. V. et al. 1999. Synergism and antagonism among multiple stressors. / Limnol. Oceanogr. 44: 864 /877. Fowler, C. W. and MacMahon, J. A. 1982. Selective extinction and speciation: their influence on the structure and functioning of communities and ecosystems. / Am. Nat. 119: 480 /498. Gilbert, F., Gonzalez, A. and Evans-Freke, I. 1998. Corridors maintain species richness in the fragmented landscape of a microecosystem. / Proc. R. Soc. Lond. Ser. B, Biol. Sci. 265: 577 /582. Gjerløv, C., Hildrew, A. G. and Jones, J. I. in press. Mobility of stream invertebrates in relation to disturbance and refugia: a test of habitat template theory. / J. N. Am. Benthol. Soc. 22: 207 /223. Griffith, M. H. 2000. Long-term trends in catch and effort of commercial linefish off South Africa’s Cape Province: snapshots of the 20th century. / S. Afr. J. Mar. Sci. 22: 81 /110. Hairston, N. G. J. and Hairston, N. G. S. 1993. Cause-effect relationships in energy flow, trophic structure and interspecific interactions. / Am. Nat. 142: 379 /411. Hall, S. J. and Raffaelli, D. G. 1991. Food web patterns: lessons from a species rich web. / J. Anim. Ecol. 60: 823 /841. Havens, K. E. 1992. Scale and structure in natural food webs. / Science 257: 1107 /1109. Hector, A., Schmid, B., Beierkuhnlein, C. et al. 1999. Plant diversity and productivity experiments in European grassland. / Science 286: 1123 /1127. Hildrew, A. G. 1992. Food webs and species interactions. / In: Calow, P. and Petts, G. E. (eds), The rivers handbook. Blackwell Sciences, pp. 309 /330. Hildrew, A. G., Townsend, C. R. and Francis, J. 1984. Community structure in some southern English streams: the influence of species interactions. / Freshwater Biol. 14: 297 /310. Hofbauer, J. and Sigmund, K. 1988. Theory of evolution and dynamical systems. / Cambridge Univ. Press. Holt, R. D., Lawton, J. H., Polis, G. A. et al. 1999. Trophic rank and the species-area relationship. / Ecology 80: 1495 /1504. Huston, M. A. 1997. Hidden treatments in ecological experiments: re-evaluating the ecosystem function of biodiversity. / Oecologia 110: 449 /460. Jarman, W. M., Hobson, K. A., Sydeman, W. J. et al. 1996. Influence of trophic position and feeding location on contaminant levels in the Gulf of the Farallones food web revealed by stable isotope analysis. / Environmental Science 30: 654 /660. Jeffries, M. J. and Lawton, J. H. 1985. Predator /prey ratios in communities of freshwater invertebrates: the role of enemy free space. / Freshwater Biol. 15: 105 /112. Jones, J. I. and Sayer, C. 2003. Does the fish /invertebrate / periphyton cascade precipitate plant loss in shallow lakes? / Ecology 84: 2155 /2167. Jones, J. I., Young, J. O., Eaton, J. W. et al. 2002. The influence of nutrient loading, dissolved inorganic carbon and higher trophic levels on the interaction between submerged plants and periphyton. / J. Ecol. 90: 12 /24. Jones, R. I., Grey, J., Sleep, D. et al. 1998. An assessment, using stable isotopes, of the importance of allochthonous organic OIKOS 104:3 (2004) carbon sources to the pelagic food web in Loch Ness. / Proc. R. Soc. Lond. Ser. B, Biol. Sci. 265: 105 /111. King, A. W. and Pimm, S. L. 1983. Complexity, diversity, and stability: a reconciliation of theoretical and empirical results. / Am. Nat. 122: 229 /239. Kruess, A. and Tscharntke, T. 1994. Habitat fragmentation, species loss and biological control. / Science 264: 1581 / 1584. Lande, R. 1993. Risks of population extinction from demographic and environmental stochasticity and random catastrophes. / Am. Nat. 142: 911 /922. Lane, A. M. J. 1999. ECN data reporting /freshwater measurements. / The U.K. Environ. Change Network: protocols for standard measurements at freshwater sites, I.T.E., U.K. Law, R. and Morton, R. D. 1996. Permanence and the assembly of ecological systems. / Ecology 77: 762 /775. Lawton, J. H. 1995. Population dynamic principles. / In: Lawton, J. H. and May, R. M. (eds), Extinction rates. Oxford Univ. Press, pp. 145 /163. Ledger, M. E. and Hildrew, A. G. 2000. Herbivory in an acid stream. / Freshwater Biol. 43: 545 /556. Leibold, M. A., Chase, J. M., Shurin, J. B. et al. 1997. Species turnover and the regulation of trophic structure. / Annu. Rev. Ecol. Syst. 28: 467 /494. Loreau, M. 1998. Biodiversity and ecosystem functioning: a mechanistic model. / Proc. Natl Acad. Sci. USA 95: 5632 / 5636. Lundberg, P., Ranta, E. and Kaitala, V. 2000. Species loss leads to community closure. / Ecol. Lett. 3: 465 /468. Martinez, N. D. 1991. Artifacts of attributes? Effects of resolution on the Little Rock lake food web. / Ecol. Monogr. 61: 367 /392. Martinez, N. D. 1993. Effect of scale on food web structure. / Science 260: 242 /243. Martinez, N. D. and Lawton, J. H. 1995. Scale and food-web structure-from local to global. / Oikos 73: 148 /154. Mason, C. F. 1991. Biology of freshwater pollution. / Longman Scientific & Technical. McGrady-Steed, J., Harris, P. M. and Morin, P. J. 1997. Biodiversity regulates ecosystem predictability. / Nature 390: 162 /165. McNaughton, S. J. 1977. Diversity and stability of ecological communities: a comment on the role of empiricism in ecology. / Am. Nat. 111: 515 /525. Mikkelson, G. M. 1993. How do food webs fall apart? A study of changes in trophic structure during relaxation on habitat fragments. / Oikos 67: 539 /547. Mikola, J. 1998. Effects of microbivore species composition and basal resource enrichment on trophic-level biomasses in an experimental microbial-based soil food web. / Oecologia 117: 396 /403. Moore, J. C., de Ruiter, P. C. and Hunt, H. W. 1993. Influence of productivity on the stability of real model ecosystems. / Science 261: 906 /908. Moran, V. C. and Southwood, T. R. E. 1982. The guild composition of arthropod communities in trees. / J. Anim. Ecol. 51: 289 /306. Morin, P. J. 1998. Realism, precision, and generality in experimental ecology. / In: Resetarits, W. J. J. and Bernardo, J. (eds), Experimental ecology. Issues and perspectives. Oxford Univ. Press, pp. 236 /253. Muniz, P. 1990. Fresh water acidification / its effects on species and communities of fresh-water microbes, plants and animals. / Proc. R. Soc. Edinburgh Ser. B, Biol. Sci. 97: 227 /254. Naeem, S., Hahn, D. R. and Schuurman, G. 2000. Producerdecomposer co-dependency influences biodiversity effects. / Nature 403: 762 /764. Norberg, J. 2000. Resource-niche complementarity and autotrophic compensation determines ecosystem-level responses to Cladoceran species richness. / Oecologia 122: 264 /272. 477 Oksanen, L., Fretwell, S. D., Arruda, J. et al. 1981. Exploitation ecosystems in gradients of primary productivity. / Am. Nat. 118: 240 /261. Paine, R. T. 1966. Food web complexity and species diversity. / Am. Nat. 100: 65 /75. Paine, R. T. 2002. Trophic control of production in a rocky intertidal community. / Science 296: 736 /739. Pauly, D. and Christensen, V. 1995. Primary production required to sustain global fisheries. / Nature 374: 255 /257. Persson, L. 1999. Trophic cascades: abiding heterogeneity and the trophic level concept at the end of the road. / Oikos 85: 385 /397. Petchey, O. L., McPhearson, P. T., Casey, T. M. et al. 1999. Environmental warming alters food-web structure and ecosystem function. / Nature 402: 69 /72. Pimm, S. L. 1980. Food web design and the effect of species deletion. / Oikos 35: 139 /149. Pimm, S. L. 1982. Food webs. / Chapman and Hall. Polis, G. A. 1991. Complex trophic interactions in deserts: an empirical critique of food web ecology. / Am. Nat. 138: 123 /155. Polis, G. A. and Strong, D. R. 1996. Food web complexity and community dynamics. / Am. Nat. 147: 813 /846. Pretty, J. L., Harrison, S. S. C., Sheperd, D. J. et al. 2003. River rehabilitation and fish populations: assessing the benefit of instream structures. / J. Appl. Ecol. 40: 251 /265. Raffaelli, D., van der Putten, W. H., Persson, L. et al. 2002. Multi-trophic processes and ecosystem functioning. / In: Loreau, M., Naeem, S. and Inchausti, P. (eds), Biodiversity and ecosystem functioning: syntheses and perspectives. Oxford Univ. Press, pp. 147 /154. Schoenly, K., Beaver, R. A. and Heumer, T. A. 1991a. On the trophic relations of insects: a food web approach. / Am. Nat. 137: 597 /638. Schoenly, K., Beaver, R. A. and Heumier, T. A. 1991b. On the trophic relations of insects: a food web approach. / Am. Nat. 137: 597 /638. Sugihara, G., Schoenly, K. and Trombla, A. 1989. Scale invariance in food-web properties. / Science 245: 48 /52. Symstad, A. J., Tilman, D., Willson, J. et al. 1998. Species loss and ecosystem functioning: effects of species identity and community composition. / Oikos 81: 389 /397. Thompson, R. M. and Townsend, C. R. 2000. Is resolution the solution? the effect of taxonomic resolution on the calculated properties of three stream food webs. / Freshwater Biol. 44: 413 /422. 478 Tilman, D. 1997. Distinguishing between the effects of species diversity and species composition. / Oikos 80: 185. Tilman, D., Lehman, C. L. and Thomson, K. T. 1997. Plant diversity and ecosystem productivity: theoretical considerations. / Proc. Natl Acad. Sci. USA 94: 1857 /1861. Townsend, C. R., Thompson, R. M., McIntosh, A. R. et al. 1998. Disturbance, resource supply and food-web architecture in streams. / Ecol. Lett. 1: 200 /209. UKAWMN (ed.). 2000. 10 year report: analysis and interpretation of resutls, April 1988 /March 1998. / ENSIS Publishing. Van de Bund, W. J. and Van Donk, E. 2002. Short-term and long-term effects of zooplanktivorous fish removal in a shallow lake: a synthesis of 15 years of data from Lake Zwemlust. / Freshwater Biol. 47: 2380 /2387. Vinebrooke, R. D., Cottingham, K. L., Norberg, J. et al. 2003. Cumulative impacts of multiple stressors on biodiversity and ecosystem functioning: the role of species tolerances. / Oikos 104: 451 /457. Wallace, J. B., Eggert, S. L., Meyer, J. L. et al. 1997. Multiple trophic levels of a forest stream linked to terrestrial litter inputs. / Science 277: 102 /104. Wardle, D. A., Bonner, K. I., Barker, G. M. et al. 1999. Plant removals in perennial grasslands: vegetation dynamics, decomposers, soil biodiversity, and ecosystem properties. / Ecol. Monogr. 69: 535 /568. Warren, P. H. and Gaston, K. J. 1992. Predator /prey ratios: a special case of a general pattern? / Philos. Trans. R. Soc. Lond. B, Biol. Sci. 338: 113 /130. Weatherby, A. J., Warren, P. H. and Law, R. 1998. Coexistence and collapse: an experimental investigation of the persistent communities of a protist species pool. / J. Anim. Ecol. 67: 554 /566. Woodward, G. and Hildrew, A. G. 2002. Body-size determinants of niche overlap and intraguild predation with a complex food web. / J. Anim. Ecol. 71: 1063 /1074. Wright, D. H. and Coleman, D. C. 1993. Patterns of survival and extinction of nematodes in isolated soil. / Oikos 67: 563 /572. Wu, L. and Culver, D. A. 1992. Ontogenic diet shifts in Lake Erie age-0 yellow perch (Perca flavescens ) / a size-related response to zooplankton density. / Can. J. Fish. Aquat. Sci. 49: 1932 /1937. Yodzis, P. 1988. The indeterminacy of ecological interactions as perceived through perturbation experiments. / Ecology 69: 508 /515. OIKOS 104:3 (2004)