Trophic structure and dynamical complexity in simple ecological models

We study the dynamical complexity of five non-linear deterministic predator–prey model systems. These simple systems were selected to represent a diversity of trophic structures and ecological interactions in the real world while still preserving reasonable tractability. We find that these systems can dramatically change attractor types, and the switching among different attractors is dependent on system parameters. While dynamical complexity depends on the nature (e.g., inter-specific competition versus predation) and degree (e.g., number of interacting components) of trophic structure present in the system, these systems all evolve principally on intrinsically noisy limit cycles. Our results support the common observation of cycling and rare observation of chaos in natural populations. Our study also allows us to speculate on the functional role of specialist versus generalist predators in food web modeling.     

Measuring ecological complexity

Complexity is an elusive term in ecology that is often used in different ways to describe the state of an ecosystem. Ecological complexity has been linked to concepts such as ecological integrity, diversity and resilience and has been put forth as a candidate ecological orientor. In this article, the concept of complexity as a system attribute is presented and candidate measures of ecological complexity are reviewed. The measures are distinguished by their ability to characterize the spatial, temporal, structural or spatiotemporal signatures of an ecosystem. Many of these measures have been adapted from disciplines such as physics and information theory that have a long history of quantifying complexity, however more work needs to be done to develop techniques adapted to ecological data. It is argued that if appropriate measures are developed and validated for ecosystems, ecological complexity could become a key ecological indicator.     

Navigating the complexity of ecological stability

Human actions challenge nature in many ways. Ecological responses are ineluctably complex, demanding measures that describe them succinctly. Collectively, these measures encapsulate the overall ‘stability’ of the system. Many international bodies, including the Intergovernmental Science‐Policy Platform on Biodiversity and Ecosystem Services, broadly aspire to maintain or enhance ecological stability. Such bodies frequently use terms pertaining to stability that lack clear definition. Consequently, we cannot measure them and so they disconnect from a large body of theoretical and empirical understanding. We assess the scientific and policy literature and show that this disconnect is one consequence of an inconsistent and one‐dimensional approach that ecologists have taken to both disturbances and stability. This has led to confused communication of the nature of stability and the level of our insight into it. Disturbances and stability are multidimensional. Our understanding of them is not. We have a remarkably poor understanding of the impacts on stability of the characteristics that define many, perhaps all, of the most important elements of global change. We provide recommendations for theoreticians, empiricists and policymakers on how to better integrate the multidimensional nature of ecological stability into their research, policies and actions.     

Taming the complexity of large models

There are many complex biological models that fit the data perfectly and yet do not reflect the cellular reality. The process of validating a large model should therefore be viewed as an ongoing mission that refines underlying assumptions by improving low-confidence areas or gaps in the model''s construction.At its most basic, science is about models. Natural phenomena that were perplexing to ancient humans have been systematically illuminated as scientific models have revealed the mathematical order underlying the natural world. But what happens when the models themselves become complex enough that they too must be interpreted to be understood?In 2012, Jonathan Karr, Markus Covert and colleagues at the University of California, San Diego (USA) produced a bold new biological model that attempts to simulate an entire cell: iMg [1]. iMg merges 28 sub-modules of processes within Mycobacterium genitalium, one of the simplest organisms known to man. As a systems biology big-data model, iMg is unique in its scope and is an undeniable paragon of good craft. Because it is probable that this landmark paper will soon be followed by other whole cell models, we feel it is timely to examine this important endeavour, its challenges and potential pitfalls.Building a model requires making many decisions, such as which processes to glaze over and which to reconstruct in detail, how many and what kinds of connections to forge between the model''s constituents, and how to determine values for the model''s parameters. The standard practice has been to tune a model''s parameters and its structure to a best fit with the available data. But this approach breaks down when building a large whole cell model because the number of decisions inflates with the model''s size, and the amount of data required for these decisions to be unequivocal becomes huge. This problem is fundamental, not merely technical, and is rooted in the principle of frugality that underlies all science: Occam''s razor.The problem posed by Occam''s razor is that there are vastly more potential large models that can successfully predict and explain any given body of data than there are small ones. As we can tweak increasingly complex models in an increasing number of ways, we can produce many large models that fit the data perfectly and yet do not reflect the cellular reality. Even if a model fits all the data well, the chance of it happening to be the ‘correct'' model—in other words the one that reflects correctly the underlying cellular architecture and relevant enzymatic parameters—is inversely related to its complexity. A sophisticated large model such as iMg, which has been fitted to many available datasets, will certainly recapture many behaviours of the real system. But it could also recapture many other potentially wrong ones.How do we test a model''s correctness in the sense just mentioned? The intuitive way is to make and test predictions about previously uncharted phenomena. But validating a large biological model is an inherently different challenge than the common practice of “predict, test and validate” customary with smaller ones. Validation using phenotypic ‘emerging'' predictions would require such large amounts of data that it would be highly inefficient and costly at this scale, especially as many of these predictions will turn out to be false leads, with negative results yielding little insight. Rather, the correctness of a whole-cell model is perhaps best validated by using a complementary paradigm: direct testing of the basic decisions that went into the model''s construction. For example, enzymatic rate constants that were fitted in order to make the model behave properly could be experimentally scrutinized for later versions. Performing extensive sensitivity analyses and incorporating known confidence levels of modelling decisions, or harnessing more advanced methods such as ‘active learning'' should all be used in conjunction to determine which parameters to focus on in the future. The process of validating a large model should thus be viewed as an ongoing mission that aims to produce more refined and accurate drafts by improving low-confidence areas or gaps in the model''s construction. Step by step, this paradigm should increase a model''s reliability and ability to make valid new predictions.An open discussion of the potential pitfalls and benefits of building complex biological models could not be timelier, as both the EU and the US have just committed more than a combined 1.4 billion dollars to explicitly model the human brain. Massive data collection and big data analysis are the new norm in most fields, and big models are following closely behind. Their cost, usefulness and application remain open for discussion, but we certainly laud the spirit of the effort. For what is certain is this: only by building these models will we know what usefulness we can attribute to them. Paraphrasing Paul Cezzane, these efforts might be indeed justified and worthy, so long as one is “more or less master of his model”.     

The socioecological complexity of ecological restoration in Mexico

Almost half of Mexican territory has been classified as environmentally degraded. The main response for the last 60 years has been reforestation to combat soil erosion and loss of forest cover, mostly carried out on private lands where negotiations with local stakeholders were critical. Despite four legal instruments referring to ecological restoration, no specific instrument that defines basic concepts, criteria and standards, required actions, or regulations to implement and evaluate ecological restoration exists. The Ministry of the Environment and Natural Resources is now solely in charge of restoration and only recently have external scientists been invited to be part of the process. Following important national and international events in Latin America and the Caribbean region, the First Mexican Symposium on Ecological Restoration was held in November, 2014. This historic event was the first action undertaken in Mexico to meet Objective 3 of the Global Strategy of Plant Conservation, coordinated in Mexico by the National Council for the Use and Knowledge of Biodiversity. Although mangrove ecosystems are the most endangered ecosystem type in Mexico, they were not well represented at the symposium. In contrast, several other ecosystem types, such as tropical dry forest and islands, have received increased attention. Overall, while the Symposium and above‐cited policy initiatives are important steps, Mexico needs to increase its institutional capacities and social organization of the rural sector with regard to ecological restoration. Better integration of social and natural scientists and increased participation of Mexico internationally is also needed.     

Evaluating the ecological realism of plant species distribution models with ecological indicator values

Species distribution models (SDMs) are routinely applied to assess current as well as future species distributions, for example to assess impacts of future environmental change on biodiversity or to underpin conservation planning. It has been repeatedly emphasized that SDMs should be evaluated based not only on their goodness of fit to the data, but also on the realism of the modeled ecological responses. However, possibilities for the latter are hampered by limited knowledge on the true responses as well as a lack of quantitative evaluation methods. Here we compared modeled niche optima obtained from European-scale SDMs of 1476 terrestrial vascular plant species with empirical ecological indicator values indicating the preferences of plant species for key environmental conditions. For each plant species we first fitted an ensemble SDM including three modeling techniques (GLM, GAM and BRT) and extracted niche optima for climate, soil, land use and nitrogen deposition variables with a large explanatory power for the occurrence of that species. We then compared these SDM-derived niche optima with the ecological indicator values by means of bivariate correlation analysis. We found weak to moderate correlations in the expected direction between the SDM-derived niche optima and ecological indicator values. The strongest correlation occurred between the modeled optima for growing degree days and the ecological indicator values for temperature. Correlations were weaker for SDM-derived niche optima with a more distal relationship to ecological indicator values (notably precipitation and soil moisture). Further, correlations were consistently highest for BRT, followed by GLM and GAM. Our method gives insight into the ecological realism of modeled niche optima and projected core habitats and can be used to improve SDMs by making a more informed selection of environmental variables and modeling techniques.     

Detecting behaviours in ecological models

Given an ecological model, I address the question of how to identify the different dynamical behaviours it can exhibit. This requires three steps: the discrimination of different behaviours, the detection of novel behaviours in the model space given current knowledge on model behaviour and the display of the results for visual inspection. I propose simple heuristic algorithms to carry out these steps in the case of models generating time series. I test the method on three models of increasing complexity, analysing both local and global structures in the time series and demonstrating the flexibility of the approach.     

Food-web complexity emerging from ecological dynamics on adaptive networks

Food webs are complex networks describing trophic interactions in ecological communities. Since Robert May's seminal work on random structured food webs, the complexity-stability debate is a central issue in ecology: does network complexity increase or decrease food-web persistence? A multi-species predator-prey model incorporating adaptive predation shows that the action of ecological dynamics on the topology of a food web (whose initial configuration is generated either by the cascade model or by the niche model) render, when a significant fraction of adaptive predators is present, similar hyperbolic complexity-persistence relationships as those observed in empirical food webs. It is also shown that the apparent positive relation between complexity and persistence in food webs generated under the cascade model, which has been pointed out in previous papers, disappears when the final connection is used instead of the initial one to explain species persistence.     

Stage structure alters how complexity affects stability of ecological networks

Resolving how complexity affects stability of natural communities is of key importance for predicting the consequences of biodiversity loss. Central to previous stability analysis has been the assumption that the resources of a consumer are substitutable. However, during their development, most species change diets; for instance, adults often use different resources than larvae or juveniles. Here, we show that such ontogenetic niche shifts are common in real ecological networks and that consideration of these shifts can alter which species are predicted to be at risk of extinction. Furthermore, niche shifts reduce and can even reverse the otherwise stabilizing effect of complexity. This pattern arises because species with several specialized life stages appear to be generalists at the species level but act as sequential specialists that are hypersensitive to resource loss. These results suggest that natural communities are more vulnerable to biodiversity loss than indicated by previous analyses.     

Neural hierarchical models of ecological populations

Neural networks are increasingly being used in science to infer hidden dynamics of natural systems from noisy observations, a task typically handled by hierarchical models in ecology. This article describes a class of hierarchical models parameterised by neural networks – neural hierarchical models. The derivation of such models analogises the relationship between regression and neural networks. A case study is developed for a neural dynamic occupancy model of North American bird populations, trained on millions of detection/non‐detection time series for hundreds of species, providing insights into colonisation and extinction at a continental scale. Flexible models are increasingly needed that scale to large data and represent ecological processes. Neural hierarchical models satisfy this need, providing a bridge between deep learning and ecological modelling that combines the function representation power of neural networks with the inferential capacity of hierarchical models.     

Periodic solutions of some ecological models

A result is given on the existence of an asymptotically stable periodic solution of a class of systems of periodic ordinary differential equations. The result is applied to a lake eutrophication model with seasonal effects, and some suggestions are made for the solution of such models.     

Untangling ecological complexity on different scales of space and time

Ecological systems are complex and essentially unpredictable, because of the multitude of interactions among their constituents. However, there are general statistical patterns emerging on particular spatial and temporal scales, which indicate the existence of some universal principles behind many ecological phenomena, and which can even be used for the prediction of phenomena occurring on finer scales of resolution. These generalities comprise regular frequency distributions of particular macroscopic variables within higher taxa (body size, abundance, range size), relationships between such variables, and general patterns in species richness. All the patterns are closely related to each other and although there are only a few major explanatory principles, there are plenty of alternative explanations. Reconciliation of different approaches cannot be obtained without careful formulation of testable hypotheses and rigorous quantitative empirical research. Two especially promising ways of untangling ecological complexity comprise: (1) analysis of invariances, i.e. universal quantitative relationships observed within many different systems, and (2) detailed analysis of the anatomy of macroecological phenomena, i.e. explorations of how emergent multispecies patterns are related to regular patterns concerning individual species.

Zusammenfassung

Ökologische Systeme sind komplex und im Wesentlichen aufgrund der Vielzahl von Interaktionen zwischen ihren Bestandteilen nicht vorhersagbar. Dennoch gibt es allgemeine statistische Muster, die in bestimmten räumlichen und zeitlichen Skalen auftreten. Dies weist auf die Existenz von einigen universellen Prinzipien hinter diesen ökologischen Phänomenen hin, die sogar für die Vorhersage von Phänomenen genutzt werden können, die auf kleineren Skalen auftreten. Diese Allgemeingültigkeiten bestehen aus Häufigkeitsverteilungen von bestimmten makroskopischen Variablen innerhalb höherer Taxa (Körpergröße, Abundanz, Arealgröße), den Beziehungen zwischen diesen Variablen und allgemeinen Mustern des Artenreichtums. Alle Muster stehen in enger Beziehung zueinander und obwohl es nur wenige bedeutende Erklärungsprinzipien gibt, existieren viele alternative Erklärungen. Die Abstimmung zwischen verschiedenen Ansätzen kann ohne eine sorgfältige Formulierung von testbaren Hypothesen und rigorose quantitative empirische Forschung nicht erreicht werden. Zwei besonders vielversprechende Wege ökologische Komplexität zu entwirren beinhalten (1) die Analyse von Invarianten, d.h. universellen quantitativen Beziehungen, die innerhalb verschiedener Systeme beobachtet werden, und (2) detaillierte Analysen der Anatomie von makroökologischen Phänomenen, d.h. Untersuchungen darüber, in welcher Beziehung die auftauchenden Muster von Multi-Arten-Systemen zu regulären Mustern individueller Arten stehen.     

Cognitive landscape and information: new perspectives to investigate the ecological complexity

Landscape ecology deals with ecological processes in their spatial context. It shares with ecosystem ecology the primate of emergent ecological disciplines. The aim of this contribution is to approach the definition of landscapes using cognitive paradigms. Neutral-based landscape (NbL), individual-based landscape (IbL) and observed-based landscape (ObL) are defined to explore the cognitive mechanisms. NbL represents the undecoded component of the cognitive matrix. The IbL is the portion of landscape perceived by the biological sensors. ObL is the part of the cognitive matrix perceived using the cultural background of the observer. The perceived landscape (PL) is composed by the sum of these three approaches of landscape perception. Two further types of information (sensu Stonier) are recognized in this process of perception: the compressed information, as it is present inside the cognitive matrix, and the decompressed information that will structure the PL when a semiotic relationship operates between the organisms and the cognitive matrix. Scaling properties of these three PL components are recognized in space and time. In NbL scale seems irrelevant, in IbL the perception is filtered by organismic scaling and in ObL the spatio-temporal scale seems of major importance. Definitively, perception is scale-dependent. A combination of the cognitive approach with information paradigms to study landscapes opens new perspectives in the interpretation of ecological complexity.