The probabilistic niche model reveals substantial variation in the niche structure of empirical food webs

The structure of food webs, complex networks of interspecies feeding interactions, plays a crucial role in ecosystem resilience and function, and understanding food web structure remains a central problem in ecology. Previous studies have shown that key features of empirical food webs can be reproduced by low-dimensional "niche" models. Here we examine the form and variability of food web niche structure by fitting a probabilistic niche model to 37 empirical food webs, a much larger number of food webs than used in previous studies. The model relaxes previous assumptions about parameter distributions and hierarchy and returns parameter estimates for each species in each web. The model significantly outperforms previous niche model variants and also performs well for several webs where a body-size-based niche model performs poorly, implying that traits other than body size are important in structuring these webs' niche space. Parameter estimates frequently violate previous models' assumptions: in 19 of 37 webs, parameter values are not significantly hierarchical, 32 of 37 webs have nonuniform niche value distributions, and 15 of 37 webs lack a correlation between niche width and niche position. Extending the model to a two-dimensional niche space yields networks with a mixture of one- and two-dimensional niches and provides a significantly better fit for webs with a large number of species and links. These results confirm that food webs are strongly niche-structured but reveal substantial variation in the form of the niche structuring, a result with fundamental implications for ecosystem resilience and function.     

A link between biologically imported particulate organic nutrients and the detritus food web in reef communities

Previous work with planktivorous fishes has shown that they import particulate organic and inorganic material to reefs in the form of fecal pellets, which, in part, are deposited in crevices on the reef where these fishes shelter during their inactive period. Since these feces do not accumulate in fish shelters, we predicted that some of the feces could be rapidly consumed by reef detritivores. We examined the attractiveness of fish feces to potential reef detritivores by placing traps baited with planktivorous fish feces, along with unbaited control traps, in crevices on rocky reefs at Santa Catalina Island, California, USA, between June 1982 and November 1983, and on coral reefs at St. Croix, U.S. Virgin Islands, during June 1983. Significantly more animals (the majority being crustaceans) were trapped in the baited traps compared to the unbaited controls on both reefs. There was also a significant association between the presence of trapped animals and fish feces at Santa Catalina Island (p = 0.009); this association was not quite as strong in St. Croix (p = 0.069). The consumption by shrimp of feces marked with carmine particles and, in turn, the predation on these shrimp by a reef fish demonstrates the links between this type of imported particulate organic and inorganic material and the food web of the reef community.Please address all correspondence and requests for reprints to Dr. Miller at California State University, Long Beach     

The models of niche and their application

Having studied the definitions of niche proposed by different ecologists, I have proposed a quantitative method of niche which can be applied to plants. Accordingly, the niche of an operational taxonomic unit (OTU) has been described by a mapping from its environmental set to the unit interval [0, 1], which enables a model of niche to be mathematically operational. The concepts of fundamental niche, realized niche, time niche, etc., may be described by using mathematical models related to each other, and the geometrical relationships between them can be revealed by a multi-dimensional surface. The uni-factor models are built upon the condition that the other factors are optimal for OTU, which are particular cases of the multi-factor models. The establishment of the quantitative relationship between these two kinds of models makes it possible to find out the plants' fundamental niche by doing uni-factor experiments. This may simplify the experiments in which the parameters in a practically applied model are to be estimated. The niche index introduced in this paper is related to average level and aftereffect of plant responses to the effects of its environment (i.e. “inertia”), thus it should be the basis of the simulation of plant seed yield and of its environmental evaluation. Accordingly, models of niche index, of plant seed yield, of plant growth and of environmental evaluation have been built which can be applied to the environmental evaluation or the prediction and management of plant (crop) production, etc.As an example of application, the models of wheat yield and its environmental assessment have been established and practically tested. The results of testing the model of wheat yield showed that the relative errors are 8% and 7.2%, respectively, in 1984 and 1986. The results of the environmental assessment of wheat reveal the fact that the insufficiency of the soil moisture at the 2th and 3th stages is the main restriction of the production of the wheat in Dinxi, Gansu Province, China.     

The effects of seston food quality on planktonic food web patterns

In planktonic food webs, the conversion rate of plant material to herbivore biomass is determined by a variety of factors such as seston biochemical/elemental composition, phytoplankton cell morphology, and colony architecture. Despite the overwhelming heterogeneity characterizing the plant–animal interface, plankton population models usually misrepresent the food quality constraints imposed on zooplankton growth. In this study, we reformulate the zooplankton grazing term to include seston food quality effects on zooplankton assimilation efficiency and examine its ramifications on system stability. Using different phytoplankton parameterizations with regards to growth strategies, light requirements, sinking rates, and food quality, we examined the dynamics induced in planktonic systems under varying zooplankton mortality/fish predation, light conditions, nutrient availability, and detritus food quality levels. In general, our analysis suggests that high food quality tends to stabilize the planktonic systems, whereas unforced oscillations (limit cycles) emerge with lower seston food quality. For a given phytoplankton specification and resource availability, the amplitude of the plankton oscillations is primarily modulated from zooplankton mortality and secondarily from the nutritional quality of the alternative food source (i.e., detritus). When the phytoplankton community is parameterized as a cyanobacterium-like species, conditions of high nutrient availability combined with high zooplankton mortality led to phytoplankton biomass accumulation, whereas a diatom-like parameterization resulted in relatively low phytoplankton to zooplankton biomass ratios highlighting the notion that high phytoplankton food quality allows the zooplankton community to sustain relatively high biomass and to suppress phytoplankton biomass to low levels. During nutrient and light enrichment conditions, both phytoplankton and detritus food quality determine the extent of the limit cycle region, whereas high algal food quality increases system resilience by shifting the oscillatory region towards lower light attenuation levels. Detritus food quality seems to regulate the amplitude of the dynamic oscillations following enrichment, when algal food quality is low. These results highlight the profitability of the alternative food sources for the grazer as an important predictor for the dynamic behavior of primary producer–grazer interactions in nature.     

Bridging biogeochemical and food web models for an End-to-End representation of marine ecosystem dynamics: The Venice lagoon case study

The simultaneous accounting of effects of natural and anthropogenic changes within a common framework calls for the development of new comprehensive tools capable of integrating biological processes that span a huge range of scales, from viruses to fishes, in addition to their interactions with physical–chemical environmental properties, i.e. End-to-End models.     

Simple predator–prey interactions control dynamics in a plankton food web model

A plankton food web model is analysed using interaction parameter values appropriate to the upper mixed layer of the high latitude oceans. The dynamics of this four-variable system are analysed in terms of the dynamics of much simpler two-variable predator–prey subsystems. Thus, the food web's robust, periodic, four-dimensional dynamics are explained by means of two-dimensional spirals and limit cycles. These dynamical subsystems are coupled by means of an omnivore that transfers control of the dynamics between the two predator–prey subsystems. The food web may substantially decouple the predator–prey subsystems so that the oscillating phytoplankton/zooplankton blooms exhibit population collapses when bacterial ‘breathers’ briefly dominate after growing dramatically from low background levels. This regular bloom/breather behaviour becomes benignly chaotic when the system is mildly forced by the annual cycle of the sun's irradiance.     

Temperature-dependent ranges of coexistence in a model of a two-prey-one-predator microbial food web

The objective of our study was to analyze the effects of temperature on the population dynamics of a three-species food web consisting of two prey bacteria (Pedobacter sp. and Acinetobacter johnsonii) and a protozoan predator (Tetrahymena pyriformis) as model organisms. We assessed the effects of temperature on the growth rates of all three species with the objective of developing a model with four differential equations based on the experimental data. The following hypotheses were tested at a theoretical level: Firstly, temperature changes can affect the dynamic behavior of a system by temperature-dependent parameters and interactions and secondly, food web response to temperature cannot be derived from the single species temperature response. The main outcome of the study is that temperature changes affect the parameter range where coexistence is possible within all three species. This has significant consequences on our ideas regarding the evaluation of effects of global warming.     

Reconstructing historical marine ecosystems using food web models: Northern British Columbia from Pre-European contact to present

Mass-balance trophic models (Ecopath with Ecosim) are developed for the marine ecosystem of northern British Columbia (BC) for the historical periods 1750, 1900, 1950 and 2000 AD. Time series data are compiled for catch, fishing mortality and biomass using fisheries statistics and literature values. Using the assembled dataset, dynamics of the 1950-based simulations are fitted to agree with observations over 50 years to 2000 through the manipulation of trophic flow parameters and the addition of climate factors: a primary production anomaly and herring recruitment anomaly. The predicted climate anomalies reflect documented environmental series, most strongly sea surface temperature and the Pacific Decadal Oscillation index. The best-fit predator–prey interaction parameters indicate mixed trophic control of the ecosystem. Trophic flow parameters from the fitted 1950 model are transferred to the other historical periods assuming stationarity in density-dependent foraging tactics. The 1900 model exhibited an improved fit to data using this approach, which suggests that the pattern of trophic control may have remained constant over much of the last century. The 1950 model is driven forward 50 years using climate and historical fishing drivers. The resulting ecosystem is compared to the 2000 model, and the dynamics of these models are compared in a predictive forecast to 2050. The models suggest similar restoration trajectories after a hypothetical release from fishing.     

An inverse model for the analysis of the Venice lagoon food web

A steady-state model of the Venice lagoon food web was constructed, based on a comprehensive set of data, which were collected in the years 2001-2005. Energy flows were estimated by means of an inverse methodology of constrained optimization based on the Minimum Norm criterion, i.e. on the minimization of both the sum of squares of the residuals and of the sum of squares of energy flows. The solution was constrained by a set inequalities, which were derived from general eco-physiological knowledge and site specific data on energy flows. The trophic network was represented by thirty-two nodes, including single-species compartments for the species of high economical or ecological relevance. Mass balance equations were weighted, in order to obtain meaningful results in presence of large differences, up to 5 orders of magnitude, among biomasses. A perturbation technique was applied, with the purpose of reducing the risk of finding solutions heavily affected by the set of constraints and of obtaining a more robust representation of the energy flows. The main patterns of energy flow are consistent with those obtained in previous attempts at modelling the Venice lagoon food web. Micro- and macro-phytobenthos account for the largest fraction of the primary production. Energy is then transferred towards higher trophic levels by means of two main pathways: the recycling of dead biomass through the detritus compartment and the direct consumption by grazers. The first pathway is the most important and accounts for approximately two/thirds of the energy transferred to the second trophic level.     

Optimal foraging: Some simple stochastic models

Summary Some simple stochastic models of optimal foraging are considered. Firstly, mathematical renewal theory is used to make a general model of the combined processes of search, encounter, capture and handling. In the case where patches or prey items are encountered according to a Poisson process the limiting probability distribution of energy gain is found. This distribution is found to be normal and its mean and variance are specified. This result supports the use of Holling's disc equation to specify the rate of energy intake in foraging models. Secondly, a model based on minimization of the probability of death due to an energetic shortfall is presented. The model gives a graphical solution to the problem of optimal choices when mean and variance are related. Thirdly, a worked example using these results is presented. This example suggests that there may be natural relationships between mean and variance which make solutions to the problems of energy maximization and minimization of the probability of starvation similar. Finally, current trends in stochastic modeling of foraging behavior are critically discussed.     

Adaptations in a hierarchical food web of southeastern Lake Michigan

Two issues in ecological network theory are: (1) how to construct an ecological network model and (2) how do entire networks (as opposed to individual species) adapt to changing conditions? We present a novel method for constructing an ecological network model for the food web of southeastern Lake Michigan (USA) and we identify changes in key system properties that are large relative to their uncertainty as this ecological network adapts from one time point to a second time point in response to multiple perturbations. To construct our food web for southeastern Lake Michigan, we followed the list of seven recommendations outlined in Cohen et al. [Cohen, J.E., et al., 1993. Improving food webs. Ecology 74, 252–258] for improving food webs. We explored two inter-related extensions of hierarchical system theory with our food web; the first one was that subsystems react to perturbations independently in the short-term and the second one was that a system's properties change at a slower rate than its subsystems’ properties. We used Shannon's equations to provide quantitative versions of the basic food web properties: number of prey, number of predators, number of feeding links, and connectance (or density). We then compared these properties between the two time-periods by developing distributions of each property for each time period that took uncertainty about the property into account. We compared these distributions, and concluded that non-overlapping distributions indicated changes in these properties that were large relative to their uncertainty. Two subsystems were identified within our food web system structure (p < 0.001). One subsystem had more non-overlapping distributions in food web properties between Time 1 and Time 2 than the other subsystem. The overall system had all overlapping distributions in food web properties between Time 1 and Time 2. These results supported both extensions of hierarchical systems theory. Interestingly, the subsystem with more non-overlapping distributions in food web properties was the subsystem that contained primarily benthic taxa, contrary to expectations that the identified major perturbations (lower phosphorous inputs and invasive species) would more greatly affect the subsystem containing primarily pelagic taxa. Future food-web research should employ rigorous statistical analysis and incorporate uncertainty in food web properties for a better understanding of how ecological networks adapt.     

Midwater food web in McMurdo Sound,Ross Sea,Antarctica

The trophic structure of the midwater ecosystem of McMurdo Sound, Ross Sea, Antarctica in February, 1983 was examined through diet analysis of 35 species of zooplankton and micronekton. Ten feeding groups were suggested through cluster analysis. The two largest clusters consisted of small-particle grazers and omnivore generalists; the eight remaining clusters were of carnivores specializing on one or several types of metazoan prey. Diet composition often shifted with ontogeny and though exceptions occurred, diet diversity usually increased either during early growth or throughout development. Comparison with a krill-dominated area along the Antarctic Penisula (Croker Passage) indicated that species common to the two areas occupied approximately the same trophic position. Biomass in McMurdo Sound was much lower than in Croker Passage and large-sized particle grazers such as krill and salps were trophically less dominant in McMurdo Sound. Krill in Croker Passage in the fall entered the midwater food web primarily as detritus (molts); in McMurdo Sound it was mostly as live furcilia. Sampling in McMurdo Sound was during a plankton bloom and calculations of grazing rates suggest that much of the primary production settled through the water column uneaten.     

Immunological methods for food web analysis in a soft-bottom benthic community

Basic to nearly any prediction concerning the behavior and structure of entire communities or of their components is knowledge of trophic connections among species. A major impediment to such understanding of soft-bottom benthos is methodological. Because none of the routinely available methods of food web analysis (e.g. visual gut content analysis, direct observation of feeding, tracer techniques) is generally suitable for examining all trophic interactions of benthic infauna, we rought to evaluate the potential of immunological methods for identifying predatorprey relationships in one typical, estuarine, intertidal sand flat. Whole-organism extracts of individual macro- and meiofaunal taxa were injected into rabbits to produce antisera of varying specificity. Double immunodiffusion precipitin tests of antiserum specificity revealed both phyletic and trophic relationships among 20 taxa. Using relatively unspecific antisera, preliminary analysis of the stomach contents of a few surface deposit-feeders and particle browsers was successful, giving positive identification of several trophic links which would otherwise have gone undetected. The production of taxon-specific antisera is expected to provide the methodological tool necessary to document the breadth of trophic connections in a marine benthic food web.     

Including model uncertainty in estimating variances in multiple capture studies

We present bootstrap-based methods which incorporate model uncertainty in estimating variances in multiple capture studies. Each of our three methods has a specific set of properties, and we discuss when each method should be used. Our first method can be used in any multiple capture setting, but it gives an estimate of the variance conditional on the number of observed animals. Our other two methods yield estimates of the unconditional variance; they require good estimates of part or all of the specific probability model, respectively. Smoothed estimated cell probabilities are utilized by the latter method. We contrast the three methods on a real-life data set, and then conduct simulations for a simple setting. Finally, we detail the use of our methodology for specific settings and discuss adaptations for tag-return studies.     

The fear of being eaten reduces energy transfer in a simple food chain

Food chain length is an important property of ecosystems, but the mechanisms maintaining it remain elusive. Classical views suggest that energetic inefficiencies (the "energy-flow hypothesis") limit food chain length, but others have argued that better explanations reside in more complex scenarios that consider the stability of food webs or the combined effects of productivity and ecosystem size. We argue that abandonment of the energy-flow hypothesis is premature. For a simple tritrophic rocky intertidal food chain, we show that the efficiency of energy transfer is strongly influenced by predation risk and consumer density. Effects tied to predation risk were particularly strong, explaining 32% of the variation in growth efficiency (compared to 15% for density effects) and reducing it by 44-76%. Hence, the stress (fear of being eaten) that predators impose on prey may be instrumental in limiting energy transfer up the food chain and thus contribute to the shortening of food chains.     

Analysing sperm competition data: simple models for predicting mechanisms

Summary Prospective models are developed for analysing sperm competition data so as to predict the underlying mechanisms determining paternity in multiply mated females. The models require: 1) estimations of proportion of offspring sired by the last male to mate (P ₂), 2) knowledge of the number of sperm transferred by each male, and 3) knowledge of the sperm storage capacity of the female, should this be limited. They will distinguish between raffles (sperm mixing without displacement) and sperm displacement mechanisms. The sensitivity of the techniques can be increased by manipulating the number of sperm transferred by each male. Typically, this can be done by manipulating copula duration or number of ejaculations, given a knowledge of the rate of sperm transfer. Data from two contrasting insect species are fitted to the models to demonstrate the techniques. These models are prospective only, and their limitations are discussed. The principal limitation is that we assume that sperm used for fertilization mix randomly in a fertilization set immediately prior to fertilization; in reality this may be difficult to identify. When sperm mixing is very rapid, the fertilization set will often be equivalent to the sperm stores, but with slow mixing, the fertilization set may be equivalent to a much more restricted zone and may change with time. Offprint requests to: G.A. Parker     

Macroinvertebrate production and food web energetics in an industrially contaminated stream.

This study examines secondary production and periphyton-invertebrate food web energetics at two sites in an industrially contaminated, nutrient-enriched stream. Secondary production data and data from the literature were used to calculate potential amounts of mercury transferred from periphyton to chironomid larvae and into terrestrial food webs with emerging adults. The nutritional quality of periphyton was characterized using energy content, chlorophyll a, protein, ash-free dry mass (AFDM), and percentage of organic matter. Chironomid larvae (Orthocladiinae: Cricotopus spp.) comprised 96% of all macroinvertebrates collected from stones at the two sites. Cricotopus production was extremely high: production was 59.5 g AFDM x m(-2) x yr(-1) at the site upstream of a 1-ha settling basin and 32.4 g AFDM x m(-2) x yr(-1) at the site below the basin. Apparent differences in annual secondary production were associated with reduced organic content (i.e., nutritional quality) of the periphyton matrix under different loading of total suspended solids. The periphyton matrix at both sites was contaminated with inorganic (Hg(II)) and methyl (MeHg) mercury. The amount of Hg(II) potentially ingested by Cricotopus was calculated to be 49 mg Hg(II) x m(-1) x yr(-1) at the upstream site and 19 mg Hg(II)x m(-2) x yr(-1) at the downstream site. Mercury ingestion by Cricotopus at the downstream site was calculated to be 2% of the estimated annual deposition of particulate-bound Hg(II) to the stream bed. Emergence of adult Cricotopus was calculated to remove 563 microg Hg(II)x m(-2) x yr(-1) from the stream at the upstream site and 117 microg Hg(II) x m(-2) x yr(-1) at the downstream site, which amounted to 4.1 g Hg(II)/yr for the 2.1-km reach of stream included in this study. The ratio of metal export in emergence production to surface area for the study stream was 10 to 10(3) times higher than ratios calculated for lakes using data from the literature. This study is the first well-documented example of extremely high aquatic insect production in an industrially contaminated, nutrient-enriched stream, and it highlights the application of production measurements to examine the role of aquatic insect production in the trophic transfer of energy and persistent contaminants in aquatic food webs and into terrestrial food webs.     

Evidence supporting the importance of terrestrial carbon in a large-river food web

Algal carbon has been increasingly recognized as the primary carbon source supporting large-river food webs; however, many of the studies that support this contention have focused on lotic main channels during low-flow periods. The flow variability and habitat-heterogeneity characteristic of these systems has the potential to significantly influence food web structure and must be integrated into models of large-river webs. We used stable-isotope analysis and IsoSource software to model terrestrial and algal sources of organic carbon supporting consumer taxa in the main channel and oxbow lakes of the Brazos River, Texas, USA, during a period of frequent hydrologic connectivity between these habitat types. Standardized sampling was conducted monthly to collect production sources and consumer species used in isotopic analysis. Predictability of hydrologic connections between habitat types was based on the previous 30 years of flow data. IsoSource mixing models identified terrestrial C3 macrophytes (riparian origin) as the primary carbon source supporting virtually all consumers in the main channel and most consumers in oxbow lakes. Small-bodied consumers (<100 mm) in oxbow lakes assimilated large fractions of algal carbon whereas this pattern was not apparent in the main channel. Estimates of detritivore trophic positions based on delta15N values indicated that terrestrial material was likely assimilated via invertebrates rather than directly from detritus. High flows in the river channel influenced algal standing stock, and differences in the importance of terrestrial and algal production sources among consumers in channel vs. oxbow habitats were associated with patterns of flooding. The importance of terrestrial material contradicts the findings of recent studies of large-river food webs that have emphasized the importance of algal carbon and indicates that there can be significant spatial, temporal, and taxonomic variation in carbon sources supporting consumers in large rivers.     

Nutrient enrichment reduces constraints on material flows in a detritus-based food web

Most aquatic and terrestrial ecosystems are experiencing increased nutrient availability, which is affecting their structure and function. By altering community composition and productivity of consumers, enrichment can indirectly cause changes in the pathways and magnitude of material flows in food webs. These changes, in turn, have major consequences for material storage and cycling in the ecosystem. Understanding mechanisms and predicting consequences of nutrient-induced changes in material flows requires a quantitative food web approach that combines information on consumer energetics and consumer-resource stoichiometry. We examined effects of a whole-system experimental nutrient enrichment on the trophic basis of production and the magnitude and pathways of carbon (C), nitrogen (N), and phosphorus (P) flows in a detritus-based stream food web. We compared the response of the treated stream to an adjacent reference stream throughout the study. Dietary composition and elemental flows varied considerably among invertebrate functional feeding groups. During nutrient enrichment, increased flows of leaf litter and amorphous detritus to shredders and gatherers accounted for most of the altered flows of C from basal resources to consumers. Nutrient enrichment had little effect on patterns of material flows but had large positive effects on the magnitude of C, N, and P flows to consumers (mean increase of 97% for all elements). Nutrient-specific food webs revealed similar flows of N and P to multiple functional groups despite an order of magnitude difference among groups in consumption of C. Secondary production was more strongly related to consumption of nutrients than C, and increased material flows were positively related to the degree of consumer-resource C:P and C:N imbalances. Nutrient enrichment resulted in an increased proportion of detrital C inputs consumed by primary consumers (from -15% to 35%) and a decreased proportion of invertebrate prey consumed by predators (from -80% to 55%). Our results demonstrate that nutrient enrichment of detritus-based systems may reduce stoichiometric constraints on material flows, increase the contribution of consumers to C, N, and P cycling, alter the proportion of C inputs metabolized by consumers, and potentially lead to reduced ecosystem-level storage of C.