Combining generalized modeling and specific modeling in the analysis of ecological networks

The complexity of real food webs involves uncertainty in data and in underlying ecological processes, and modeling approaches deal with these challenges differently. Generalized modeling provides a linear stability analysis without narrow specification of all processes, and conventional dynamical systems models approximate functional forms to discuss trajectories in phase space. This study compares results and ecological interpretations from both methods in four-species ecological networks at steady state. We find that a specific (dynamical systems) model only provides a subset of stability data from the generalized model, which spans many plausible dynamic scenarios, allowing for conflicting results. Nevertheless, both approaches reveal that fixed points become stable when nutrient flows to predators are fettered and even more when the basal growth rate approaches a maximum. The specific model identifies a distinct ecosystem response to bottom-up forcing, the enrichment of lower trophic levels. Enrichment stabilizes a fixed point when basal species are in a resource-deprived environment but destabilizes it if resources become more abundant. The generalized model provides less specific information since infinitely many paths of enrichment are hypothetical. Nevertheless, generalized modeling of ecological systems is a powerful technique that enables a meta analysis of these uncertain complex systems.

Non-linear relationships between density and demographic traits in three Aedes species

Understanding the relationship of population dynamics to density is central to many ecological investigations. Despite the importance of density-dependence in determining population growth, the empirical relationship between density and per capita growth remains understudied in most systems and is often assumed to be linear. In experimental studies of interspecific competition, investigators often evaluate the predicted outcomes by assuming such linear relationships, fitting linear functions, and estimating parameters of competition models. In this paper, we experimentally describe the shape of the relationship between estimated population rate of change and initial density using laboratory-reared populations of three mosquito species. We estimated per capita growth rate for these experimental populations over a 30-fold range of larval densities at a standard resource abundance. We then compared fits of linear models and several different nonlinear models for the relationship of estimated rate of change and density. We find that that the relationship between density and per capita growth is strongly non-linear in Aedes aegypti (Linnaeus), Aedes albopictus (Skuse), and Aedes triseriatus (Say) mosquitoes. Components of population growth (survivorship, development time, adult size) are also nonlinearly related to initial density. The causes and consequences of this nonlinearity are likely to be important issues for population and community ecology.

Stability of generalized ecological-network models

The stability of ecological networks of varying topologies and predator-prey relationships is explored by applying the concept of generalized modeling. The effects of omnivory, complexity, enrichment, number of top predators, and predatory response are discussed. The degree of omnivory plays a large role in governing web stability at steady state. Complexity as measured from connectance and network size is not a perfect indicator of stability; large, highly connected webs can be just as stable as smaller, less connected ones. Learning behavior as expressed in Holling's type III predatory response is stabilizing for food webs and provides exceptions to the paradox of enrichment for some topologies.

Temperature variability alters the stability and thresholds for collapse of interacting species

Temperature variability and extremes can have profound impacts on populations and ecological communities. Predicting impacts of thermal variability poses a challenge, because it has both direct physiological effects and indirect effects through species interactions. In addition, differences in thermal performance between predators and prey and nonlinear averaging of temperature-dependent performance can result in complex and counterintuitive population dynamics in response to climate change. Yet the combined consequences of these effects remain underexplored. Here, modelling temperature-dependent predator-prey dynamics, we study how changes in temperature variability affect population size, collapse and stable coexistence of both predator and prey, relative to under constant environments or warming alone. We find that the effects of temperature variation on interacting species can lead to a diversity of outcomes, from predator collapse to stable coexistence, depending on interaction strengths and differences in species' thermal performance. Temperature variability also alters predictions about population collapse-in some cases allowing predators to persist for longer than predicted when considering warming alone, and in others accelerating collapse. To inform management responses that are robust to future climates with increasing temperature variability and extremes, we need to incorporate the consequences of temperature variation in complex ecosystems. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.

Chaos theory discloses triggers and drivers of plankton dynamics in stable environment

Despite the enticing discoveries of chaos in nature, triggers and drivers of this phenomenon remain a classical enigma which needs irrefutable empirical evidence. Here we analyze results of the yearlong replicated mesocosm experiment with multi-species plankton community that allowed revealing signs of chaos at different trophic levels in strictly controlled abiotic environment. In mesocosms without external stressors, we observed the “paradox of chaos” when biotic interactions (internal drivers) were acting as generators of internal abiotic triggers of complex plankton dynamics. Chaos was registered as episodes that vanished unpredictably or were substituted by complex behaviour of other candidates when longer time series were considered. Remarkably, episodes of chaos were detected even in the most abiotically stable conditions. We developed the Integral Chaos Indicator to validate the results of the Lyapunov exponent analysis. These findings are essential for modelling and forecasting behaviour of a variety of natural and other global systems.

Bacterial social interactions and the emergence of community-intrinsic properties

Bacterial communities are dominated and shaped by social interactions, which facilitate the emergence of properties observed only in the community setting. Such community-intrinsic properties impact not only the phenotypes of cells in a community, but also community composition and function, and are thus likely to affect a potential host. Studying community-intrinsic properties is, therefore, important for furthering our understanding of clinical, applied and environmental microbiology. Here, we provide recent examples of research investigating community-intrinsic properties, focusing mainly on community composition and interactions in multispecies biofilms. We hereby wish to emphasize the importance of studying social interactions in settings where community-intrinsic properties are likely to emerge.

A new dimension: Evolutionary food web dynamics in two dimensional trait space

Species within a habitat are not uniformly distributed. However this aspect of community structure, which is fundamental to many conservation activities, is neglected in the majority of models of food web assembly. To address this issue, we introduce a model which incorporates a second dimension, which can be interpreted as space, into the trait space used in evolutionary food web models. Our results show that the additional trait axis allows the emergence of communities with a much greater range of network structures, similar to the diversity observed in real ecological communities. Moreover, the network properties of the food webs obtained are in good agreement with those of empirical food webs. Community emergence follows a consistent pattern with spread along the second trait axis occurring before the assembly of higher trophic levels. Communities can reach either a static final structure, or constantly evolve. We observe that the relative importance of competition and predation is a key determinant of the network structure and the evolutionary dynamics. The latter are driven by the interaction-competition and predation-between small groups of species. The model remains sufficiently simple that we are able to identify the factors, and mechanisms, which determine the final community state.

Evolutionary and plastic rescue in multitrophic model communities

Under changing environmental conditions, intraspecific variation can potentially rescue populations from extinction. There are two principal sources of variation that may ultimately lead to population rescue: genetic diversity and phenotypic plasticity. We compared the potential for evolutionary rescue (through genetic diversity) and plastic rescue (through phenotypic plasticity) by analysing their differential ability to produce dynamical stability and persistence in model food webs. We also evaluated how rescue is affected by the trophic location of variation. We tested the following hypotheses: (i) plastic communities are more likely to exhibit stability and persistence than communities in which genetic diversity provides the same range of traits. (ii) Variation at the lowest trophic level promotes stability and persistence more than variation at higher levels. (iii) Communities with variation at two levels have greater probabilities of stability and persistence than communities with variation at only one level. We found that (i) plasticity promotes stability and persistence more than genetic diversity; (ii) variation at the second highest trophic level promotes stability and persistence more than variation at the autotroph level; and (iii) more than variation at two trophic levels. Our study shows that proper evaluation of the rescue potential of intraspecific variation critically depends on its origin and trophic location.

The dynamics of spatially coupled food webs

The dynamics of ecological systems include a bewildering number of biotic interactions that unfold over a vast range of spatial scales. Here, employing simple and general empirical arguments concerning the nature of movement, trophic position and behaviour we outline a general theory concerning the role of space and food web structure on food web stability. We argue that consumers link food webs in space and that this spatial structure combined with relatively rapid behavioural responses by consumers can strongly influence the dynamics of food webs. Employing simple spatially implicit food web models, we show that large mobile consumers are inordinately important in determining the stability, or lack of it, in ecosystems. More specifically, this theory suggests that mobile higher order organisms are potent stabilizers when embedded in a variable, and expansive spatial structure. However, when space is compressed and higher order consumers strongly couple local habitats then mobile consumers can have an inordinate destabilizing effect. Preliminary empirical arguments show consistency with this general theory.

Persistence increases with diversity and connectance in trophic metacommunities

BACKGROUND

We are interested in understanding if metacommunity dynamics contribute to the persistence of complex spatial food webs subject to colonization-extinction dynamics. We study persistence as a measure of stability of communities within discrete patches, and ask how do species diversity, connectance, and topology influence it in spatially structured food webs.

METHODOLOGY/PRINCIPAL FINDINGS

We answer this question first by identifying two general mechanisms linking topology of simple food web modules and persistence at the regional scale. We then assess the robustness of these mechanisms to more complex food webs with simulations based on randomly created and empirical webs found in the literature. We find that linkage proximity to primary producers and food web diversity generate a positive relationship between complexity and persistence in spatial food webs. The comparison between empirical and randomly created food webs reveal that the most important element for food web persistence under spatial colonization-extinction dynamics is the degree distribution: the number of prey species per consumer is more important than their identity.

CONCLUSIONS/SIGNIFICANCE

With a simple set of rules governing patch colonization and extinction, we have predicted that diversity and connectance promote persistence at the regional scale. The strength of our approach is that it reconciles the effect of complexity on stability at the local and the regional scale. Even if complex food webs are locally prone to extinction, we have shown their complexity could also promote their persistence through regional dynamics. The framework we presented here offers a novel and simple approach to understand the complexity of spatial food webs.

Predator foraging behaviour drives food-web topological structure

1. The structure and dynamics of prey populations are shaped by the foraging behaviours of their predators. Yet, there is still little documentation on how distinct predator foraging types control biodiversity, food-web architecture and ecosystem functioning. 2. We experimentally compared the effects of model fish species of two major foraging types of lake planktivores: a size-selective visual feeder (bluegill), and a filter feeder (gizzard shad). The visual feeder forages on individually captured consumer prey, whereas the filter feeder forages on various prey simultaneously, not only consumers but also primary producers. We ran a 1-month mesocosm experiment cross-classifying a biomass gradient of each predator type. We analysed the effect of each fish on food-web architecture by computing major topological descriptors over time (connectance, link density, omnivory index, etc.). These descriptors were computed from 80 predator-prey binary matrices, using taxa mostly identified at the species level. 3. We found that the visual feeder induced more trophic cul-de-sac (inedible) primary-producer species, lower link density and connectance, and lower levels of food-web omnivory and generalism than the filter feeder. Yet, predator biomass did not affect food-web topology. 4. Our results highlight that top-predator foraging behaviour is a key functional trait that can drive food-web topology and ultimately ecosystem functioning.

Rapid contemporary evolution and clonal food web dynamics

Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most readily explored in systems with short generations and simple genetics. Asexual and cyclically parthenogenetic organisms such as microalgae, cladocerans and rotifers, which frequently dominate freshwater plankton communities, meet these requirements. Multiple clonal lines can coexist within each species over extended periods, until either fixation occurs or a sexual phase reshuffles the genetic material. When clones differ in traits affecting interspecific interactions, within-species clonal dynamics can have major effects on the population dynamics. We first consider a simple predator-prey system with two prey genotypes, parametrized with data from a well-studied experimental system, and explore how the extent of differences in defence against predation within the prey population determine dynamic stability versus instability of the system. We then explore how increased potential for evolution affects the community dynamics in a more general community model with multiple predator and multiple prey genotypes. These examples illustrate how microevolutionary 'details' that enhance or limit the potential for heritable phenotypic change can have significant effects on contemporaneous community-level dynamics and the persistence and coexistence of species.

Cryptic population dynamics: rapid evolution masks trophic interactions

Trophic relationships, such as those between predator and prey or between pathogen and host, are key interactions linking species in ecological food webs. The structure of these links and their strengths have major consequences for the dynamics and stability of food webs. The existence and strength of particular trophic links has often been assessed using observational data on changes in species abundance through time. Here we show that very strong links can be completely missed by these kinds of analyses when changes in population abundance are accompanied by contemporaneous rapid evolution in the prey or host species. Experimental observations, in rotifer-alga and phage-bacteria chemostats, show that the predator or pathogen can exhibit large-amplitude cycles while the abundance of the prey or host remains essentially constant. We know that the species are tightly linked in these experimental microcosms, but without this knowledge, we would infer from observed patterns in abundance that the species are weakly or not at all linked. Mathematical modeling shows that this kind of cryptic dynamics occurs when there is rapid prey or host evolution for traits conferring defense against attack, and the cost of defense (in terms of tradeoffs with other fitness components) is low. Several predictions of the theory that we developed to explain the rotifer-alga experiments are confirmed in the phage-bacteria experiments, where bacterial evolution could be tracked. Modeling suggests that rapid evolution may also confound experimental approaches to measuring interaction strength, but it identifies certain experimental designs as being more robust against potential confounding by rapid evolution.

The presence and strength of interactions between species has frequently been inferred from observational data on changes in species abundance. For example, correlated cycles in potential predator and prey species may be interpreted as evidence that the species interact, while the absence of such coupled oscillations might be interpreted as evidence for lack of interaction. Here we show that prey abundance can be decoupled from changes in predator abundance when there is genetic variability in the prey for antipredator defense traits, allowing rapid evolutionary changes in prey defense levels. It then appears that the two species are not interacting, when in fact they are. We deduce this from studies of two laboratory microcosm systems, one with algae consumed by rotifers and the other with bacteria attacked by phage. In each, when the prey vary genetically for defense traits and undefended genotypes are superior competitors, defended and undefended prey frequencies evolve in a cyclical way that is almost exactly counterbalancing, so that total prey density remains nearly constant. We show mathematically that these “cryptic cycles” occur whenever conditions are right for predator-prey cycles, when prey vary genetically for defense traits, and when prey defense against predation is effective but inexpensive to produce. Under these conditions, observations of predator and prey population dynamics cannot be trusted to be informative about the strength or even the existence of interspecific trophic links.

Contemporary rapid evolution in prey and pathogen species masks strong tropic interactions with predators and hosts. These "cryptic dynamics" reveal a need for a new approach to measuring interaction strengths in food webs.

Effects of dynamics on ecological networks

Ecological food webs define the feeding patterns of interacting species. The architecture of such networks may be affected by dynamical processes operating within them, ultimately influencing the capacity of the networks to persist. As yet relatively little is known about these effects. We compared the architecture of ecological networks with a fixed number of species, constructed in four contrasting ways: (I) topological networks, which required only that species had prey to eat; (II) persistent networks, in which species had also to persist under a simple model of population dynamics; (III) assembled networks, built up by sequential addition of species with dynamical persistence at each step in the sequence; (IV) evolved networks where, in addition to dynamical persistence, body size of species was determined by a simple mutation-selection process. Dynamics had fundamental effects on architecture, the networks of classes II, III and IV being restricted to a small number of trophic levels, in contrast to the non-dynamic, topological class I networks. Class III assembled networks tended to have fewer trophic levels and a more pyramidal biomass distribution than networks of classes II and IV. In evolved class IV networks, the smallest consumers converged to similar body sizes, whereas larger consumers evolved more slowly and did not show such convergence. The results indicate that dynamics affect the architecture of food webs, and that assumptions about simultaneous arrival, sequential arrival and evolution lead to different outcomes. Sequential assembly was shown to have a special property of finding rare sets of persistent species in a small number of steps, suggesting that the rarity of stable communities is not a serious problem in the development of complex communities.

Pattern formation, outbreaks, and synchronization in food chains with two and three species

We study the dynamics of populations of predators and preys using a mean field approach and a spatial model. The mean field description assumes that the individuals are homogeneously mixed and interact with one another with equal probability, so that space can be ignored. In the spatial model, on the other hand, predators can prey only in a certain neighborhood of their spatial location. We show that the size of these predation neighborhoods has dramatic effects on the dynamics and on the organization of the species in space. In the case of a three species food chain, in particular, the populations of predators display a sequence of apparently irregular outbreaks when the predation neighborhood has intermediate values, as compared to the size of the available space. Nonetheless, further increasing their size makes the outbreaks disappear and the dynamics approach that of the mean field model. Our study of synchronization also shows that the periodic behavior displayed by the average populations in a spatially extended system may hide the existence of patches that oscillate out of phase in a highly coordinated fashion.

Species loss and secondary extinctions in simple and complex model communities

1. The loss of a species from an ecological community can trigger a cascade of secondary extinctions. Here we investigate how the complexity (connectance) of model communities affects their response to species loss. Using dynamic analysis based on a global criterion of persistence (permanence) and topological analysis we investigate the extent of secondary extinctions following the loss of different kinds of species. 2. We show that complex communities are, on average, more resistant to species loss than simple communities: the number of secondary extinctions decreases with increasing connectance. However, complex communities are more vulnerable to loss of top predators than simple communities. 3. The loss of highly connected species (species with many links to other species) and species at low trophic levels triggers, on average, the largest number of secondary extinctions. The effect of the connectivity of a species is strongest in webs with low connectance. 4. Most secondary extinctions are due to direct bottom-up effects: consumers go extinct when their resources are lost. Secondary extinctions due to trophic cascades and disruption of predator-mediated coexistence also occur. Secondary extinctions due to disruption of predator-mediated coexistence are more common in complex communities than in simple communities, while bottom-up and top-down extinction cascades are more common in simple communities. 5. Topological analysis of the response of communities to species loss always predicts a lower number of secondary extinctions than dynamic analysis, especially in food webs with high connectance.

Using community viability analysis to identify fragile systems and keystone species

Owing to interdependences among species in ecological communities, the loss of one species can trigger a cascade of secondary extinctions with potentially dramatic effects on the functioning and stability of the community. It is, therefore, important to assess the risk and likely extent of secondary extinctions. Community viability analysis is a new technique that can be used to accomplish this goal. The analysis can also be used to identify fragile community structures and keystone species and, hence, to provide guidelines for conservation priorities. Here, we describe the principles underlying community viability analysis and review its contributions to our understanding of the response of ecological communities to species loss.

Adaptive omnivory and species coexistence in tri-trophic food webs

The commonness of omnivory in natural communities is puzzling, because simple dynamic models of tri-trophic systems with omnivory are prone to species extinction. In particular, the intermediate consumer is frequently excluded by the omnivore at high levels of enrichment. It has been suggested that adaptive foraging by the omnivore may facilitate coexistence, because the intermediate consumer should persist more easily if it is occasionally dropped from the omnivore's diet. We explore theoretically how species permanence in tri-trophic systems is affected if the omnivore forages adaptively according to the "diet rule", i.e., feeds on the less profitable of its two prey species only if the more profitable one is sufficiently rare. We show that, compared to systems where omnivory is fixed, adaptive omnivory may indeed facilitate 3-species persistence. Counter to intuition, however, facilitation of 3-species coexistence requires that the intermediate consumer is a more profitable prey than the basal resource. Consequently, adaptive omnivory does not facilitate persistence of the intermediate consumer but enlarges the persistence region of the omnivore towards parameter space where a fixed omnivore would be excluded by the intermediate consumer. Overall, the positive effect of adaptive omnivory on 3-species persistence is, however, small. Generally, whether omnivory is fixed or adaptive, 3-species permanence is most likely when profitability (=conversion efficiency into omnivores) is low for basal resources and high for intermediate consumers.

Complex dynamics in a three-level trophic system with intraspecies interaction

In this paper, we present a three-level trophic food chain, including intraspecies interaction. In contrast with other analyses, we consider the effect on the third trophic level by the first-level parameters. The model shows complex, as well as, chaotic oscillations. Bifurcation diagrams show period doubling route to chaos and crises. Also from the forward and backwards sections of the bifurcation diagrams, we find hysteresis. This result implies the coexistence of attractors for the same parameter values. In particular, we consider the coexistence of a chaotic and a P1 attractors. Our results show that the regulation in the food chain is not exclusive to either a food-prey or prey-predator interaction, but to a more subtle food-prey-predator interaction, where, for some parameter values, a food-prey or a prey-predator regulation may dominate the system's dynamics. Finally, we consider the impact of the intraspecies interaction in the overall dynamics of the food chain.