Modelling Size Structured Food Webs Using a Modified Niche Model with Two Predator Traits

The structure of food webs is frequently described using phenomenological stochastic models. A prominent example, the niche model, was found to produce artificial food webs resembling real food webs according to a range of summary statistics. However, the size structure of food webs generated by the niche model and real food webs has not yet been rigorously compared. To fill this void, I use a body mass based version of the niche model and compare prey-predator body mass allometry and predator-prey body mass ratios predicted by the model to empirical data. The results show that the model predicts weaker size structure than observed in many real food webs. I introduce a modified version of the niche model which allows to control the strength of size-dependence of predator-prey links. In this model, optimal prey body mass depends allometrically on predator body mass and on a second trait, such as foraging mode. These empirically motivated extensions of the model allow to represent size structure of real food webs realistically and can be used to generate artificial food webs varying in several aspects of size structure in a controlled way. Hence, by explicitly including the role of species traits, this model provides new opportunities for simulating the consequences of size structure for food web dynamics and stability.     

Predicting trophic relations in ecological networks: A test of the Allometric Diet Breadth Model

Few food web theory hypotheses/predictions can be readily tested using likelihoods of reproducing the data. Simple probabilistic models for food web structure, however, are an exception as their likelihoods were recently derived. Here I test the performance of a more complex model for food web structure that is grounded in the allometric scaling of interactions with body size and the theory of optimal foraging (Allometric Diet Breadth Model—ADBM). This deterministic model has been evaluated by measuring the fraction of trophic relations it correctly predicts. I contrasted this value with that produced by simpler models based on body sizes and found that the quantitative information on allometric scaling and optimal foraging does not significantly increase model fit. Also, I present a method to compute the p-value for the fraction of trophic interactions correctly predicted by the ADBM, or any other model, with respect to three probabilistic models. I find that the ADBM predicts significantly more links than random graphs, but other models can outperform it. Although optimal foraging and allometric scaling may improve our understanding of food webs, the ADBM needs to be modified or replaced to find support in the data.     

Adaptive foraging does not always lead to more complex food webs

Recent modeling studies exploring the effect of consumers’ adaptivity in diet composition on food web complexity invariably suggest that adaptivity in foraging decisions of consumers makes food webs more complex. That is, it allows for survival of a higher number of species when compared with non-adaptive food webs. Population-dynamical models in these studies share two features: parameters are chosen uniformly for all species, i.e. they are species-independent, and adaptive foraging is described by the search image model. In this article, we relax both these assumptions. Specifically, we allow parameters to vary among the species and consider the diet choice model as an alternative model of adaptive foraging. Our analysis leads to three important predictions. First, for species-independent parameter values for which the search image model demonstrates a significant effect of adaptive foraging on food web complexity, the diet choice model produces no such effect. Second, the effect of adaptive foraging through the search image model attenuates when parameter values cease to be species-independent. Finally, for the diet choice model we observe no (significant) effect of adaptive foraging on food web complexity. All these observations suggest that adaptive foraging does not always lead to more complex food webs. As a corollary, future studies of food web dynamics should pay careful attention to the choice of type of adaptive foraging model as well as of parameter values.     

Relevance of evolutionary history for food web structure

Explaining the structure of ecosystems is one of the great challenges of ecology. Simple models for food web structure aim at disentangling the complexity of ecological interaction networks and detect the main forces that are responsible for their shape. Trophic interactions are influenced by species traits, which in turn are largely determined by evolutionary history. Closely related species are more likely to share similar traits, such as body size, feeding mode and habitat preference than distant ones. Here, we present a theoretical framework for analysing whether evolutionary history--represented by taxonomic classification--provides valuable information on food web structure. In doing so, we measure which taxonomic ranks better explain species interactions. Our analysis is based on partitioning of the species into taxonomic units. For each partition, we compute the likelihood that a probabilistic model for food web structure reproduces the data using this information. We find that taxonomic partitions produce significantly higher likelihoods than expected at random. Marginal likelihoods (Bayes factors) are used to perform model selection among taxonomic ranks. We show that food webs are best explained by the coarser taxonomic ranks (kingdom to class). Our methods provide a way to explicitly include evolutionary history in models for food web structure.     

Food web framework for size-structured populations

We synthesise traditional unstructured food webs, allometric body size scaling, trait-based modelling, and physiologically structured modelling to provide a novel and ecologically relevant tool for size-structured food webs. The framework allows food web models to include ontogenetic growth and life-history omnivory at the individual level by resolving the population structure of each species as a size-spectrum. Each species is characterised by the trait ‘size at maturation’, and all model parameters are made species independent through scaling with individual body size and size at maturation. Parameter values are determined from cross-species analysis of fish communities as life-history omnivory is widespread in aquatic systems, but may be reparameterised for other systems. An ensemble of food webs is generated and the resulting communities are analysed at four levels of organisation: community level, species level, trait level, and individual level. The model may be solved analytically by assuming that the community spectrum follows a power law. The analytical solution provides a baseline expectation of the results of complex food web simulations, and agrees well with the predictions of the full model on biomass distribution as a function of individual size, biomass distribution as a function of size at maturation, and relation between predator-prey mass ratio of preferred and eaten food. The full model additionally predicts the diversity distribution as a function of size at maturation.     

The role of fish life histories in allometrically scaled food‐web dynamics

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A modified niche model for generating food webs with stage‐structured consumers: The stabilizing effects of life‐history stages on complex food webs

1. Almost all organisms grow in size during their lifetime and switch diets, trophic positions, and interacting partners as they grow. Such ontogenetic development introduces life‐history stages and flows of biomass between the stages through growth and reproduction. However, current research on complex food webs rarely considers life‐history stages. The few previously proposed methods do not take full advantage of the existing food web structural models that can produce realistic food web topologies.
2. We extended the niche model developed by Williams and Martinez (Nature, 2000, 404, 180–183) to generate food webs that included trophic species with a life‐history stage structure. Our method aggregated trophic species based on niche overlap to form a life‐history structured population; therefore, it largely preserved the topological structure of food webs generated by the niche model. We applied the theory of allometric predator–prey body mass ratio and parameterized an allometric bioenergetic model augmented with biomass flow between stages via growth and reproduction to study the effects of a stage structure on the stability of food webs.
3. When life‐history stages were linked via growth and reproduction, more food webs persisted, and persisting food webs tended to retain more trophic species. Topological differences between persisting linked and unlinked food webs were small to modest. The slopes of biomass spectra were lower, and weak interaction links were more prevalent in the linked food webs than the unlinked ones, suggesting that a life‐history stage structure promotes characteristics that can enhance stability of complex food webs.
4. Our results suggest a positive relationship between the complexity and stability of complex food webs. A life‐history stage structure in food webs may play important roles in dynamics of and diversity in food webs.

     

Exploring the evolutionary signature of food webs' backbones using functional traits

Increasing evidence suggests that an appropriate model for food webs, the network of feeding links in a community of species, should take into account the inherent variability of ecological interactions. Harnessing this variability, we will show that it is useful to interpret empirically observed food webs as realisations of a family of stochastic processes, namely random dot‐product graph models. These models provide an ideal extension of food‐web models beyond the limitations of current deterministic or partially probabilistic models. As an additional bene?t, our RDPG framework enables us to identify the pairwise distance structure given by species' functional food‐web traits: this allows for the natural emergence of ecologically meaningful species groups. Lastly, our results suggest the notion that the evolutionary signature in food webs is already detectable in their stochastic backbones, while the contribution of their ?ne wiring is arguable. Synthesis Food webs are influenced by many stochastic processes and are constantly evolving. Here, we treat observed food webs as realisations of random dot‐product graph models (RDPG), extending food‐web modelling beyond the limitations of current deterministic or partially probabilistic models. Our RDPG framework enables us to identify the pairwise‐distance structure given by species' functional food‐web traits, which in turn allows for the natural emergence of ecologically meaningful species groups. It also provides a way to measure the phylogenetic signal present in food webs, which we find is strongest in webs' low‐dimensional backbones.     

The role of body mass in diet contiguity and food-web structure

1. The idea that species occupy distinct niches is a fundamental concept in ecology. Classically, the niche was described as an n-dimensional hypervolume where each dimension represents a biotic or abiotic characteristic. More recently, it has been hypothesised that a single dimension may be sufficient to explain the system-level organization of trophic interactions observed between species in a community. 2. Here, we test the hypothesis that species body mass is that single dimension. Specifically, we determine how the intervality of food webs ordered by body size compares to that of randomly ordered food webs. We also extend this analysis beyond the community level to the effect of body mass in explaining the diets of individual species. 3. We conclude that body mass significantly explains the ordering of species and the contiguity of diets in empirical communities. 4. At the species-specific level, we find that the degree to which body mass is a significant explanatory variable depends strongly on the phylogenetic history, suggesting that other evolutionarily conserved traits partly account for species' roles in the food web. 5. Our investigation of the role of body mass in food webs thus helps us to better understand the important features of community food-web structure and the evolutionary forces that have led us to the communities we observe.     

Complex life cycles in a pond food web: effects of life stage structure and parasites on network properties,trophic positions and the fit of a probabilistic niche model

Most food webs use taxonomic or trophic species as building blocks, thereby collapsing variability in feeding linkages that occurs during the growth and development of individuals. This issue is particularly relevant to integrating parasites into food webs because parasites often undergo extreme ontogenetic niche shifts. Here, we used three versions of a freshwater pond food web with varying levels of node resolution (from taxonomic species to life stages) to examine how complex life cycles and parasites alter web properties, the perceived trophic position of organisms, and the fit of a probabilistic niche model. Consistent with prior studies, parasites increased most measures of web complexity in the taxonomic species web; however, when nodes were disaggregated into life stages, the effects of parasites on several network properties (e.g., connectance and nestedness) were reversed, due in part to the lower trophic generality of parasite life stages relative to free-living life stages. Disaggregation also reduced the trophic level of organisms with either complex or direct life cycles and was particularly useful when including predation on parasites, which can inflate trophic positions when life stages are collapsed. Contrary to predictions, disaggregation decreased network intervality and did not enhance the fit of a probabilistic niche model to the food webs with parasites. Although the most useful level of biological organization in food webs will vary with the questions of interest, our results suggest that disaggregating species-level nodes may refine our perception of how parasites and other complex life cycle organisms influence ecological networks.     

Predicting the effects of temperature on food web connectance

Few models concern how environmental variables such as temperature affect community structure. Here, we develop a model of how temperature affects food web connectance, a powerful driver of population dynamics and community structure. We use the Arrhenius equation to add temperature dependence of foraging traits to an existing model of food web structure. The model predicts potentially large temperature effects on connectance. Temperature-sensitive food webs exhibit slopes of up to 0.01 units of connectance per 1°C change in temperature. This corresponds to changes in diet breadth of one resource item per 2°C (assuming a food web containing 50 species). Less sensitive food webs exhibit slopes down to 0.0005, which corresponds to about one resource item per 40°C. Relative sizes of the activation energies of attack rate and handling time determine whether warming increases or decreases connectance. Differences in temperature sensitivity are explained by differences between empirical food webs in the body size distributions of organisms. We conclude that models of temperature effects on community structure and dynamics urgently require considerable development, and also more and better empirical data to parameterize and test them.     

Emergence of complexity in evolving niche-model food webs

We have analysed mechanisms that promote the emergence of complex structures in evolving model food webs. The niche model is used to determine predator-prey relationships. Complexity is measured by species richness as well as trophic level structure and link density. Adaptive dynamics that allow predators to concentrate on the prey species they are best adapted to lead to a strong increase in species number but have only a small effect on the number and relative occupancy of trophic levels. The density of active links also remains small but a high number of potential links allows the network to adjust to changes in the species composition (emergence and extinction of species). Incorporating effects of body size on individual metabolism leads to a more complex trophic level structure: both the maximum and the average trophic level increase. So does the density of active links. Taking body size effects into consideration does not have a measurable influence on species richness. If species are allowed to adjust their foraging behaviour, the complexity of the evolving networks can also be influenced by the size of the external resources. The larger the resources, the larger and more complex is the food web it can sustain. Body size effects and increasing resources do not change size and the simple structure of the evolving networks if adaptive foraging is prohibited. This leads to the conclusion that in the framework of the niche model adaptive foraging is a necessary but not sufficient condition for the emergence of complex networks. It is found that despite the stabilising effect of foraging adaptation the system displays elements of self-organised critical behaviour.     

The inverse niche model for food webs with parasites

Although parasites represent an important component of ecosystems, few field and theoretical studies have addressed the structure of parasites in food webs. We evaluate the structure of parasitic links in an extensive salt marsh food web, with a new model distinguishing parasitic links from non-parasitic links among free-living species. The proposed model is an extension of the niche model for food web structure, motivated by the potential role of size (and related metabolic rates) in structuring food webs. The proposed extension captures several properties observed in the data, including patterns of clustering and nestedness, better than does a random model. By relaxing specific assumptions, we demonstrate that two essential elements of the proposed model are the similarity of a parasite’s hosts and the increasing degree of parasite specialization, along a one-dimensional niche axis. Thus, inverting one of the basic rules of the original model, the one determining consumers’ generality appears critical. Our results support the role of size as one of the organizing principles underlying niche space and food web topology. They also strengthen the evidence for the non-random structure of parasitic links in food webs and open the door to addressing questions concerning the consequences and origins of this structure.     

Niche separation in Varecia variegata rubra and Eulemur fulvus albifrons: II. Intraspecific patterns

Based on a year-long field study in northeastern Madagascar, I summarize annual patterns of niche use (food patch size, diet, forest height, and forest site) in two sympatric lemurs, Varecia variegata rubra and Eulemur fulvus albifrons. Furthermore, I examine intraspecific patterns of niche use according to sex, season, and reproductive stage in these two lemurs that differ in terms of energetic investment in reproduction. Lemurs as a group provide a special opportunity to test hypotheses concerning sex differences in niche use. Due to their body size monomorphism and seasonal, synchronous pattern of breeding, it is possible to directly evaluate whether sex differences in diet reflect high energetic investment in reproduction by females. Results confirm the hypothesis that intraspecific variation in niche use (e.g., sex differences, seasonal differences) would be more pronounced in V. v. rubra than in E. f. albifrons, due in large measure to the former's relatively high energetic investment in reproduction: 1a) Dietary sex differences in V. v. rubra are most pronounced during costly reproductive stages and involve acquisition of low-fiber, high-protein plant foods. Females of both species consume more seasonally available low-fiber protein (young leaves, flowers) relative to conspecific males during the hot dry season, but only in V. v. rubra females is this pattern also evident during gestation and lactation. 1b) The diets of female V. v. rubra and female E. f. albifrons are more similar to each other than are the diets of conspecific males and females in the case of V. v. rubra. This is not uniformly the case for female E. f. albifrons. This finding confirms a hypothesis put forward in Vasey ([2000] Am J Phys Anthropol 112:411-431) that energetic requirements of reproductive females drive niche separation more than do the energetic requirements of males. 1c) Both species synchronize most or all of lactation with seasonal food abundance and diversity. E. f. albifrons shows a more protracted period of synchrony, and this may contribute to its wide biogeographic distribution in Madagascar. 2) Sex differences and seasonal differences in microhabitat use reflect intraspecific patterns of thermoregulation, predator avoidance, and in the case of V. v. rubra, reproduction. One important factor selecting for body size monomorphism in lemurs appears to be the tight synchrony between lactation and periods of food abundance afforded by annual, seasonal breeding.     

Indirect Energy Flows in Niche Model Food Webs: Effects of Size and Connectance

Indirect interactions between species have long been of interest to ecologists. One such interaction type takes place when energy or materials flow via one or more intermediate species between two species with a direct predator-prey relationship. Previous work has shown that, although each such flow is small, their great number makes them important in ecosystems. A new network analysis method, dynamic environ approximation, was used to quantify the fraction of energy flowing from prey to predator over paths of length greater than 1 (flow indirectness or FI) in a commonly studied food web model. Web structure was created using the niche model and dynamics followed the Yodzis-Innes model. The effect of food web size (10 to 40 species) and connectance (0.1 to 0.48) on FI was examined. For each of 250 model realizations run for each pair of size and connectance values, the FI of every predator-prey interaction in the model was computed and then averaged over the whole network. A classification and regression tree (CART) analysis was then used to find the best predictors of FI. The mean FI of the model food webs is 0.092, with a standard deviation of 0.0279. It tends to increase with system size but peaks at intermediate connectance levels. Of 27 potential predictor variables, only five (mean path length, dominant eigenvalue of the adjacency matrix, connectance, mean trophic level and fraction of species belonging to intermediate trophic levels) were selected by the CART algorithm as best accounting for variation in the data; mean path length and the dominant eigenvalue of the adjacency matrix were dominant.     

Linking intraspecific variability in trophic and functional niches along an environmental gradient

1. Intraspecific trophic variability has important ecological and evolutionary implications, and is driven by multiple interacting factors. Functional traits and environmental conditions are important in mediating the trophic niche of individuals because they determine their ability to consume certain prey, their energetic requirements, and resource availability. In this study, we aimed at investigating the interacting effects of functional traits and environmental conditions on several attributes of trophic niche in natural populations.
2. Here, we quantified intraspecific variability in the trophic niche of 12 riverine populations of European minnow (Phoxinus phoxinus) using stable isotope analyses. Functional traits (i.e. morpho-anatomical traits) and environmental conditions (i.e. upstream–downstream gradient, forest cover) were quantified to identify the determinants of (1) trophic position and resource origin, (2) trophic niche size, and (3) trophic differentiation (β-diversity) among populations.
3. We demonstrated that trophic position and resource origin covaried with functional traits related to body size and locomotion performance, and that the strength and shape of these relationships varied according to local environmental conditions. The trophic niche size also differed among populations, although no determinant was identified. Finally, trophic β-diversity was correlated to environmental differentiation among sites.
4. Overall, the determinants of intraspecific variability in trophic niche appeared highly context-dependent, and related to the interactions between functional traits and environmental conditions. Because populations are currently facing important environmental changes, understanding this context-dependency is important for predicting food web structure and ecosystem dynamics in a changing world.

     

Ontogenetic and individual diet variation in amphibian larvae across an environmental gradient

1. Variation among individuals within size or age classes can have profound effects on community dynamics and food‐web structure. We investigated the potential influence of habitat disturbance on intrapopulation niche variation. 2. Amphibians occupy a range of lentic habitats from short‐hydroperiod intermittent ponds to long‐hydroperiod permanent ponds. We quantified ontogenetic diet variation and individual specialisation in wood frog tadpoles (Lithobates sylvaticus) and blue‐spotted salamander larvae (Ambystoma laterale) to investigate the influence of hydroperiod on population niche width across a natural hydroperiod gradient using stable isotope and gut content analyses. In one of the few tests using larval forms, we tested the niche variation hypothesis, which predicts that populations with larger niche widths also have increased individual variation. 3. Our results support the niche variation hypothesis, indicating that more generalised populations exhibit higher within‐individual diet variation. We report gradual changes in the relative importance of diet items, decreased dietary overlap and increased trophic position in L. sylvaticus throughout development. A. laterale became more enriched in δ¹³C and increased in δ¹⁵N throughout its larval period. We did not find a relationship between hydroperiod and niche parameters, indicating that niches are conserved across heterogeneous habitats. In contrast to most documented cases, we estimated low levels of individual specialisation in amphibian larvae. 4. Amphibians are an important link between aquatic and terrestrial ecosystems, whereby diet shifts can influence food‐web structure by altering energy flow pathways and the trophic position of higher consumers, ultimately changing food‐chain length.     

Predicting the consequences of species loss using size‐structured biodiversity approaches

Understanding the consequences of species loss in complex ecological communities is one of the great challenges in current biodiversity research. For a long time, this topic has been addressed by traditional biodiversity experiments. Most of these approaches treat species as trait‐free, taxonomic units characterizing communities only by species number without accounting for species traits. However, extinctions do not occur at random as there is a clear correlation between extinction risk and species traits. In this review, we assume that large species will be most threatened by extinction and use novel allometric and size‐spectrum concepts that include body mass as a primary species trait at the levels of populations and individuals, respectively, to re‐assess three classic debates on the relationships between biodiversity and (i) food‐web structural complexity, (ii) community dynamic stability, and (iii) ecosystem functioning. Contrasting current expectations, size‐structured approaches suggest that the loss of large species, that typically exploit most resource species, may lead to future food webs that are less interwoven and more structured by chains of interactions and compartments. The disruption of natural body‐mass distributions maintaining food‐web stability may trigger avalanches of secondary extinctions and strong trophic cascades with expected knock‐on effects on the functionality of the ecosystems. Therefore, we argue that it is crucial to take into account body size as a species trait when analysing the consequences of biodiversity loss for natural ecosystems. Applying size‐structured approaches provides an integrative ecological concept that enables a better understanding of each species' unique role across communities and the causes and consequences of biodiversity loss.