Real Ecological Systems Research Articles

Resilience of hybrid herbivore-plant-pollinator networks.

The concept of network resilience has gained increasing attention in the last few decades owing to its great potential in strengthening and maintaining complex systems. From network-based approaches, researchers have explored resilience of real ecological systems comprising diverse types of interactions, such as mutualism, antagonist, and predation, or mixtures of them. In this paper, we propose a dimension-reduction method for analyzing the resilience of hybrid herbivore-plant-pollinator networks. We qualitatively evaluate the contribution of species toward maintaining resilience of networked systems, as well as the distinct roles played by different categories of species. Our findings demonstrate that the strong contributors to network resilience within each category are more vulnerable to extinction. Notably, among the three types of species in consideration, plants exhibit a higher likelihood of extinction, compared to pollinators and herbivores.

Complexity-stability trade-off in empirical microbial ecosystems.

May's stability theory, which holds that large ecosystems can be stable up to a critical level of complexity, a product of the number of resident species and the intensity of their interactions, has been a central paradigm in theoretical ecology. So far, however, empirically demonstrating this theory in real ecological systems has been a long-standing challenge with inconsistent results. Especially, it is unknown whether this theory is pertinent in the rich and complex communities of natural microbiomes, mainly due to the challenge of reliably reconstructing such large ecological interaction networks. Here we introduce a computational framework for estimating an ecosystem's complexity without relying on a priori knowledge of its underlying interaction network. By applying this method to human-associated microbial communities from different body sites and sponge-associated microbial communities from different geographical locations, we found that in both cases the communities display a pronounced trade-off between the number of species and their effective connectance. These results suggest that natural microbiomes are shaped by stability constraints, which limit their complexity.

ДВОСЕКТОРНА МОДЕЛЬ ЕКОНОМІКИ В УМОВАХ ЕКОЛОГІЗАЦІЇ ВИРОБНИЦТВА ТА СПОЖИВАННЯ

The urgency of the problem of ecologization of the economy and of other spheres of human life is revealed. This problem is one of the most acute and priority problems of the modern world, as the consequences of negative anthropogenic impact on the environment are environmental crises of regional and global scale, including climate change, which threatens not only socio-economic development of human civilization but also its existence. In this regard, not only the greening of the economy is relevant, but also the greening of consumption, education, culture, upbringing, and so on. The research of the stated and many other issues related to the greening of human activities requires the use of many scientific tools. The multifaceted nature of the object and subject of research is analyzed, which actually leads to the use of a set of conceptual, methodological and methodological approaches. The efficiency of the modeling method and the necessity of constructing the ecological economy models for the purpose to research conceptual bases and admissible scenarios of its formation and development are substantiated. The differential dynamic The urgency of the problem of ecologization of the economy and of other spheres of human life is revealed. This problem is one of the most acute and priority problems of the modern world, as the consequences of negative anthropogenic impact on the environment are environmental crises of regional and global scale, including climate change, which threatens not only socio-economic development of human civilization but also its existence. In this regard, not only the greening of the economy is relevant, but also the greening of consumption, education, culture, upbringing, and so on. The research of the stated and many other issues related to the greening of human activities requires the use of many scientific tools. The multifaceted nature of the object and subject of research is analyzed, which actually leads to the use of a set of conceptual, methodological and methodological approaches. The efficiency of the modeling method and the necessity of constructing the ecological economy models for the purpose to research conceptual bases and admissible scenarios of its formation and development are substantiated. The differential dynamic The urgency of the problem of ecologization of the economy and of other spheres of human life is revealed. This problem is one of the most acute and priority problems of the modern world, as the consequences of negative anthropogenic impact on the environment are environmental crises of regional and global scale, including climate change, which threatens not only socio-economic development of human civilization but also its existence. In this regard, not only the greening of the economy is relevant, but also the greening of consumption, education, culture, upbringing, and so on. The research of the stated and many other issues related to the greening of human activities requires the use of many scientific tools. The multifaceted nature of the object and subject of research is analyzed, which actually leads to the use of a set of conceptual, methodological and methodological approaches. The efficiency of the modeling method and the necessity of constructing the ecological economy models for the purpose to research conceptual bases and admissible scenarios of its formation and development are substantiated. The differential dynamic model of a two-sector economy in the conditions of greening of production and consumption processes has been developed, in which one sector is engaged in the production of the main aggregate product, and the other – in utilization of environmentally hazardous production and consumption residues. A specific feature of the model is also taking into account the socio-economic clustering of society, which allows in a sense to reflect both environmental, economic and social aspects of the economy uder the study. Spatial variables of the model are liquid savings or liquid capital of production owners and workers in each sector, the price of the main aggregate product, the tariff for waste disposal, the amount of environmental pollution. The proposed model serves as a theoretical basis for building models of ecological and economic dynamics and the basis for some of its modifications, taking into account the specifics of behavioral functions and parameters, and is designed for experimental research in computer simulation of major trends and features of real ecological and economic systems. The results of such a study with models of this class also provide an opportunity to analyze acceptable environmental standards of production and consumption, test and improve the relevant information support, detail the fundamentally important requirements for the functions and parameters used in formalizing the model and ultimately create a valuable information base for systems support of management decisions on forecasting and implementation of ecological and economic processes.

Deterministic and Stochastic Holling-Tanner Prey-Predator Models

A modified version of the so called Holling-Tanner prey-predator models with prey dependent functional response is introduced. We improved some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems and studied the stability of this model in the deterministic and stochastic environments. The study was focused on three types of stability, namely, stable node, spiral node, and center. The numerical schemes are employed to get the approximated solutions of the differential equations. We have used Euler scheme to solve the deterministic prey-predator model and we used Euler-Maruyama scheme to solve stochastic prey-predator model.

Information limitation and the dynamics of coupled ecological systems.

The dynamics of large ecological systems result from vast numbers of interactions between individual organisms. Here, we develop mathematical theory to show that the rate of such interactions is inherently limited by the ability of organisms to gain information about one another. This phenomenon, which we call 'information limitation', is likely to be widespread in real ecological systems and can dictate both the rates of ecological interactions and long-run dynamics of interacting populations. We show how information limitation leads to sigmoid interaction rate functions that can stabilize antagonistic interactions and destabilize mutualistic ones; as a species or type becomes rare, information on its whereabouts also becomes rare, weakening coupling with consumers, pathogens and mutualists. This can facilitate persistence of consumer-resource systems, alter the course of pathogen infections within a host and enhance the rates of oceanic productivity and carbon export. Our findings may shed light on phenomena in many living systems where information drives interactions.

The role of spatial scale in organism\u2013environment positive feedback

Organism–environment positive feedback (i.e., ecosystem self-modification or facilitation) will incur bistability, which is often disadvantageous to biological conservation and ecosystem restoration. Using a spatially correlated equation based on pair approximation and simulation, we found that the feature of bistability in the positive feedback system strongly depends on spatial scale of organism–environment feedback. It will mitigate and even disappear when the interaction between organisms and environment is localized spatially, while the population will lessen globally when dispersal colonization is limited. As the spatially local influence is a basic property of real ecological systems (especially for sessile organisms), but classical ecological models based on mean-field assumption (or mass action) does not consider the impact of spatial scale. This implies that spatial configuration and local facilitation could be essential process for the stability and maintenance of ecosystem.

Interactive effects of multiple climate change variables on food web dynamics: Modeling the effects of changing temperature, CO2, and water availability on a tri-trophic food web

Predicting food web responses to climate change can be difficult because of the potentially complex interplay between co-occurring climate variables and multiple interacting species across trophic levels. The large majority of research in this field has focused on understanding the effects of single climate variables on species at one or two trophic levels, implicitly assuming that simultaneous shifts across multiple climate variables will have additive effects on food web dynamics. We constructed a tri-trophic food web model and varied temperature, CO2, and water availability both alone and in concert to test this assumption. We found that population biomass does indeed respond additively across trophic levels when temperature, CO2, and water availability all increase simultaneously to moderate levels; however, if water availability decreases, like in a drought scenario, all three trophic levels respond antagonistically. We also found that interaction effect magnitude is highly dependent on temperature and water availability. Decreases in water availability led to 54–74% declines in population biomass across trophic levels when temperatures were within normal organismal operating ranges, but dry conditions coupled with high temperatures led to the extinction of the highest trophic level. Our results suggest that studying simplified versions of climate change and food webs will not be sufficient to predict the responses of real ecological systems. Therefore climate change ecology experiments and models must incorporate more complexity into their structure.

Building Resilience Against Climate-Driven Shifts in a Temperate Reef System: Staying Away from Context-Dependent Ecological Thresholds

As climate-driven environmental changes and anthropogenic perturbations increasingly affect ecological systems, the number of abrupt phase shifts in ecosystem dynamics is rising, with far-reaching ecological, economic and social effects. These shifts are notoriously difficult to study, anticipate and manage. Although indicators of impending phase shifts in ecosystems have been described theoretically, they have only been observed empirically either after the fact or under controlled experiments. Here we demonstrate the usefulness of case-specific simulation models to estimate tipping points in the dynamics of real ecological systems, characterise how these thresholds may vary depending on local conditions and derive safe management targets associated with low risk of undesirable phase shifts. Under the combined effects of ocean changes and fishing, inshore rocky reefs in eastern Tasmania can transition from dense seaweed beds to sea urchin ‘barrens’ habitat, realising severe local loss of habitat, productivity and valuable fisheries. Using Monte-Carlo simulations with a validated model that realistically captures reef dynamics, we characterise the hysteresis in community dynamics and the variability in ecological thresholds along the gradient of environmental conditions. Simulation suggests that prevention of ongoing sea urchin destructive grazing of macroalgal beds is achievable but the yet-to-be-observed restoration of seaweed beds from extensive sea urchin barrens is highly unlikely. To guide management against undesirable phase shifts, we define target points associated with low risk of widespread barrens formation and show that, along with sea urchin culling, recognising the role of lobsters in mitigating sea urchin destructive grazing through predation is key to maintain reef productivity.

Spirals and coarsening patterns in the competition of many species: a complex Ginzburg–Landau approach

In order to model real ecological systems one has to consider many species that interact in complex ways. However, most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions. The few studies dealing with larger number of species and/or more complex interaction schemes are mostly restricted to numerical explorations. In this paper we determine, starting from the deterministic mean-field rate equations, for large classes of systems the space of coexistence fixed points at which biodiversity is maximal. For systems with a single coexistence fixed point we derive complex Ginzburg–Landau equations that allow to describe space-time pattern realized in two space dimensions. For selected cases we compare the theoretical predictions with the pattern observed in numerical simulations.

Mobility-dependent selection of competing strategy associations

Standard models of population dynamics focus on the interaction, survival, and extinction of the competing species individually. Real ecological systems, however, are characterized by an abundance of species (or strategies, in the terminology of evolutionary-game theory) that form intricate, complex interaction networks. The description of the ensuing dynamics may be aided by studying associations of certain strategies rather than individual ones. Here we show how such a higher-level description can bear fruitful insight. Motivated from different strains of colicinogenic Escherichia coli bacteria, we investigate a four-strategy system which contains a three-strategy cycle and a neutral alliance of two strategies. We find that the stochastic, spatial model exhibits a mobility-dependent selection of either the three-strategy cycle or of the neutral pair. We analyze this intriguing phenomenon numerically and analytically.

Single species models with logistic growth and dissymmetric impulse dispersal

In this paper, two classes of single-species models with logistic growth and impulse dispersal (or migration) are studied: one model class describes dissymmetric impulsive bi-directional dispersal between two heterogeneous patches; and the other presents a new way of characterizing the aggregate migration of a natural population between two heterogeneous habitat patches, which alternates in direction periodically. In this theoretical study, some very general, weak conditions for the permanence, extinction of these systems, existence, uniqueness and global stability of positive periodic solutions are established by using analysis based on the theory of discrete dynamical systems. From this study, we observe that the dynamical behavior of populations with impulsive dispersal differs greatly from the behavior of models with continuous dispersal. Unlike models where the dispersal is continuous in time, in which the travel losses associated with dispersal make it difficult for such dispersal to evolve e.g., [25,26,28], in the present study it was relatively easy for impulsive dispersal to positively affect populations when realistic parameter values were used, and a rich variety of behaviors were possible. From our results, we found impulsive dispersal seems to more nicely model natural dispersal behavior of populations and may be more relevant to the investigation of such behavior in real ecological systems.

Phase portraits, Hopf bifurcations and limit cycles of the Holling–Tanner models for predator–prey interactions

The phase portraits, existence and uniqueness of stable limit cycles and Hopf bifurcations of the well-known Holling–Tanner models for predator–prey interactions are studied. The ranges of the parameters involved are provided under which the unique interior equilibrium can be determined to be a stable (or an unstable) node or focus. The Hopf bifurcations and the existence and uniqueness of stable limit cycles of the models are obtained by computing the Lyapunov number involved. Our results confirm some previous results observed and suggested from the real ecological systems.

Natural Length Scales of Ecological Systems: Applications at Community and Ecosystem Levels

The characteristic, or natural, length scales of a spatially dynamic ecological landscape are the spatial scales at which the deterministic trends in the dynamic are most sharply in focus. Given recent development of techniques to determine the characteristic length scales (CLSs) of real ecological systems, I explore the potential for using CLSs to address three important and vexing issues in applied ecology, viz. (i) determining the optimum scales to monitor ecological systems, (ii) interpreting change in ecological communities, and (iii) ascertaining connectivity between species in complex ecologies. In summarizing the concept of characteristic length scales as system-level scaling thresholds, I emphasize that the primary CLS is, by definition, the optimum scale at which to monitor a system if the objective is to observe its deterministic dynamics at a system level. Using several different spatially explicit individual-based models, I then explore predictions of the underlying theory of CLSs in the context of interpreting change and ascertaining connectivity among species in ecological systems. Analysis of these models support predictions that systems with strongly fluctuating community structure, but an otherwise stable long-term dynamic defined by a stationary attractor, indicate an invariant length scale irrespective of community structure at the time of analysis, and irrespective of the species analyzed. In contrast, if changes in the underlying dynamic are forcibly induced, the shift in dynamics is reflected by a change in the primary length scale. Thus, consideration of the magnitude of the CLS through time enables distinguishing between circumstances where there are temporal changes in community structure but not in the long-term dynamic, from that where changes in community structure reflect some kind of fundamental shift in dynamics. In this context, CLSs emerge as a diagnostic tool to identify phase shifts to alternative stable states associated with loss of resilience in ecological systems and thus provide a means to interpret change in community composition. By extension, comparison of the CLSs of ostensibly similar communities at different points in space can reveal whether they experience similar underlying dynamics. Analysis of these models also reveals that species in the same community whose dynamics are largely independent indicate different length scales. These examples demonstrate the potential to apply CLSs in a decision-support role in determining scales for monitoring, interpreting whether change in community structure reflects a shift in underlying dynamics and therefore may warrant management intervention, and determining connectivities among species in complex ecological systems.

Effects of time delay on symmetric two-species competition subject to noise

Noise and time delay act simultaneously on real ecological systems. The Lotka-Volterra model of symmetric two-species competition with noise and time delay was investigated in this paper. By means of stochastic simulation, we find that (i) the time delay induces the densities of the two species to periodically oscillate synchronously; (ii) the stationary probability distribution function of the two-species densities exhibits a transition from multiple to single stability as the delay time increases; (iii) the characteristic correlation time for the sum of the two-species densities squared exhibits a nonmonotonic behavior as a function of delay time. Our results have the implication that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems.

Evolutionary or Ecological Dynamics among Individuals or Colonies on a Lattice-Structured Population

The lattice model, which has been used in physics, is a convenient model to describe the nearest-neighbors interactions between individuals. The ecological dynamics has no equations like physics and is modeled to fit the real ecological systems. Therefore, different assumptions produce different ecological dynamics, which makes modeling in ecology interesting. Here I show that different birth and death processes, influenced by social interactions between neighbors, lead to different outcomes of the competition for space in a lattice. Moreover, I show the ecological dynamics caused by the competition for space between individuals is also different from that of colonies.

Sudden Shifts in Ecological Systems: Intermittency and Transients in the Coupled Ricker Population Model

Many real ecological systems show sudden changes in behavior, phenomena sometimes categorized as regime shifts in the literature. The relative importance of exogenous versus endogenous forces producing regime shifts is an important question. These forces' role in generating variability over time in ecological systems has been explored using tools from dynamical systems. We use similar ideas to look at transients in simple ecological models as a way of understanding regime shifts. Based in part on the theory of crises, we carefully analyze a simple two patch spatial model and begin to understand from a mathematical point of view what produces transient behavior in ecological systems. In particular, since the tools are essentially qualitative, we are able to suggest that transient behavior should be ubiquitous in systems with overcompensatory local dynamics, and thus should be typical of many ecological systems.

Ambiguous, circular and polysemous: students' definitions of the “balance of nature” metaphor

The “balance of nature” metaphor has been used to explain the functioning of natural systems from ancient times and continues to be invoked in popular culture, in spite of controversy regarding its use in the scientific community. We demonstrate that undergraduate students in the United States believe this term is descriptive of real ecological systems, and continue to do so after instruction in ecological science. A content analysis of students' definitions of the “balance of nature” and its causes varied widely with multiple, often contradictory, interpretations. A second survey confirmed that the range of definitions generated by students was representative of the larger educated population. Common responses included population regulation, species interactions, absence of disturbance and Nature. We speculate that the lack of a fixed meaning for the balance of nature term could lead to problems in education, public policy, and the transmission of ecological concepts to the general public.

OPTIMAL SCALES TO OBSERVE HABITAT DYNAMICS: A CORAL REEF EXAMPLE

A new technique to estimate the characteristic length scales (CLSs) of real ecological systems provides an objective means to identify the optimal scale(s) of observation to best detect underlying dynamical trends. Application of the technique to natural systems has focused on identifying appropriate scales to measure the dynamics of species as descriptors of community and ecosystem dynamics. However, ecosystem monitoring is often based not on assessing single species, but on species assemblages, functional groups, or habitat types. We asked whether the concept of CLSs based on dynamic interactions among species could be extended to examine interactions among habitat types and thus to identify optimal scales for observing habitat dynamics. A time series of three spatial maps of benthic habitats on a Caribbean coral reef was constructed from aerial photographs, Compact Airborne Spectrographic Imager (CASI) images, and IKONOS satellite images, providing the short time sequence required for this technique. We estimated the CLS based on the dynamics of three distinct habitat types: dense stands of seagrass, sparse stands of seagrass, and Montastrea patch reefs. Despite notable differences in the areal extent of and relative change in these habitats over the 21-year observation period, analyses based on each habitat type indicated a similar CLS of -300 m. We interpret the consistency of CLSs among habitats to indicate that the dynamics of the three habitat types are linked. The results are encouraging, and they indicate that CLS techniques can be used to identify the appropriate scale at which to monitor ecosystem trends on the basis of the dynamics of only one of a disparate suite of habitat types.

Control theory and the management of ecosystems

Summary Control theory is a well‐developed branch of mathematics and engineering that identifies optimal control policies for dynamic systems. While it should be useful for managing ecosystems, it is currently used only in certain fields of ecology and resource management, and only certain aspects of the theory are applied. Where optimal control policies have been determined, such as oceanic fisheries, the control policy often fails. The goals of this study were to determine why control theory has not been used very much and why it fails, and also to improve its applicability to natural resource management. Control theory methods and assumptions were reviewed, and applications to agriculture, forestry and fisheries summarized. A comparison was made between control theory assumptions and the real ecological systems to which the method was applied. A fisheries example was developed to illustrate some improvements to the application of this technique. It was shown that the paradoxical aspects of control theory in resource management result from the points of divergence of real systems from the assumptions of control theory. Because of non‐linearities, noise, sampling difficulties, policy implementation error and other issues, ecosystems are neither readily observable nor easily controllable. This means that even theoretically correct control policies can lead to failure. The fisheries example showed that measurement error and management lags can of themselves lead to the collapse of a fishery. It was shown that the costs of acquiring information and managing the system need to be incorporated explicitly into the control problem as decision variables. The solution to the fisheries control problem prevented extinction of the fishery by reducing sampling error and management lags to reasonable but non‐zero levels. Other suggestions are made for applying control theory with more success. By taking into account the deviations between the idealized control model and real systems, better resource management can be achieved. Control theory could also profitably be applied to the design of monitoring programmes, to model parameter estimation, and to other aspects of ecology and resource management where it is currently not being utilized. Synthesis and applications. Control theory needs to be re‐evaluated for its utility in natural resource management. It offers the potential for providing effective management policies. To achieve this potential, techniques borrowed from engineering must be expanded to incorporate the effects of state uncertainty (measurement error), environmental fluctuations (stochasticity), parameter uncertainty and policy implementation error.

Habitat selection and population regulation in temporally fluctuating environments.

Understanding and predicting the distribution of organisms in heterogeneous environments lies at the heart of ecology, and the theory of density-dependent habitat selection (DDHS) provides ecologists with an inferential framework linking evolution and population dynamics. Current theory does not allow for temporal variation in habitat quality, a serious limitation when confronted with real ecological systems. We develop both a stochastic equivalent of the ideal free distribution to study how spatial patterns of habitat use depend on the magnitude and spatial correlation of environmental stochasticity and also a stochastic habitat selection rule. The emerging patterns are confronted with deterministic predictions based on isodar analysis, an established empirical approach to the analysis of habitat selection patterns. Our simulations highlight some consistent patterns of habitat use, indicating that it is possible to make inferences about the habitat selection process based on observed patterns of habitat use. However, isodar analysis gives results that are contingent on the magnitude and spatial correlation of environmental stochasticity. Hence, DDHS is better revealed by a measure of habitat selectivity than by empirical isodars. The detection of DDHS is but a small component of isodar theory, which remains an important conceptual framework for linking evolutionary strategies in behavior and population dynamics.