Measuring complexity to infer changes in the dynamics of ecological systems under stress

Despite advances in our mechanistic understanding of ecological processes, the inherent complexity of real-world ecosystems still limits our ability in predicting ecological dynamics especially in the face of on-going environmental stress. Developing a model is frequently challenged by structure uncertainty, unknown parameters, and limited data for exploring out-of-sample predictions. One way to address this challenge is to look for patterns in the data themselves in order to infer the underlying processes of an ecological system rather than to build system-specific models. For example, it has been recently suggested that statistical changes in ecological dynamics can be used to infer changes in the stability of ecosystems as they approach tipping points. For computer scientists such inference is similar to the notion of a Turing machine: a computational device that could execute a program (the process) to produce the observed data (the pattern). Here, we make use of such basic computational ideas introduced by Alan Turing to recognize changing patterns in ecological dynamics in ecosystems under stress. To do this, we use the concept of Kolmogorov algorithmic complexity that is a measure of randomness. In particular, we estimate an approximation to Kolmogorov complexity based on the Block Decomposition Method (BDM). We apply BDM to identify changes in complexity in simulated time-series and spatial datasets from ecosystems that experience different types of ecological transitions. We find that in all cases, K_BDM complexity decreased before all ecological transitions both in time-series and spatial datasets. These trends indicate that loss of stability in the ecological models we explored is characterized by loss of complexity and the emergence of a regular and computable underlying structure. Our results suggest that Kolmogorov complexity may serve as tool for revealing changes in the dynamics of ecosystems close to ecological transitions.     

Measuring complexity of environmental gradients

Analysis of vegetation response to environmental gradients should take into account the spatial complexity of the environmental property itself. Whether a gradient exists on the landscape or in abstract space, the spatial variability of environmental factors often invalidates the implicit assumption that the gradient is continuous. There is a need to know how variable the spatial pattern of a gradient is and how much deviation from the general trend may be expected. Geostatistics is shown to provide a useful method for analyzing spatial variability. If the assumptions for its use can be met, the fractal dimension can be used in combination with geostatistics to provide a quantitative index of gradient complexity. An example is given, showing that an hypothesized gradient of shoreline erosion disturbance along Delaware Bay either does not exist or is so complicated by short-range, local factors that any longer-range gradient is relatively unimportant. Such complex environmental patterns are thought to be common in nature. Geostatistics, fractals, or similar spatial methods can be utilized to detect and measure such complexity.This work was conducted while the author was a research assistant at the Center for Coastal and Environmental Studies, Rutgers University, New Brunswick, N.J. The support of the Center is gratefully acknowledged.     

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.     

Mapping the complexity of ecological models

We propose to define the complexity of an ecological model as the statistical complexity of the output it produces. This allows for a direct comparison between data and model complexity. Working with univariate time series, we show that this measure ‘blindly’ discriminates among the different dynamical behaviours a model can exhibit. We then search a model parameter space in order to segment it into areas of different dynamical behaviour and calculate the maximum complexity a model can generate. Given a time series, and the problem of choosing among a number of ecological models to study it, we suggest that models whose maximum complexity is lower than the time series complexity should be disregarded because they are unable to reconstruct some of the structures contained in the data. Similar reasoning could be used to disregard models’ subdomains as well as areas of unnecessary high complexity. We suggest that model complexity so defined better captures the difficulty faced by a user in managing and understanding the behaviour of an ecological model than measures based on a model ‘size’.     

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.     

Measuring genetic diversity in ecological studies

There is an increasing interest in how genetic diversity may correlate with and influence community and ecosystem properties. Genetic diversity can be defined in multiple ways, and currently lacking in ecology is a consensus on how to measure genetic diversity. Here, we examine two broad classes of genetic diversity: genotype-based and genome-based measures. Genotype-based measures, such as genotypic richness, are more commonly used in ecological studies, and often it is assumed that as genotypic diversity increases, genomic diversity (the number of genetic polymorphisms and/or genomic dissimilarity among individuals) also increases. However, this assumption is rarely assessed. We tested this assumption by investigating correlations between genotype- and genome-based measures of diversity using two plant population genetic datasets: one observational with data collected at Konza Prairie, KS, and the other based on simulated populations with five levels of genotypic richness, a typical design of genetic diversity experiments. We found conflicting results for both datasets; we found a mismatch between genotypic and genomic diversity measures for the field data, but not the simulated data. Last, we tested the consequences of this mismatch and found that correlations between genetic diversity and community/ecosystem properties depended on metric used. Ultimately, we argue that genome-based measures should be included in future studies alongside genotypic-based measures because they capture a greater spectrum of genetic differences among individuals.     

Measuring information-based complexity across scales using cluster analysis

Scaling of ecological data can present a challenge firstly because of the large amount of information contained in an ecological data set, and secondly because of the problem of fitting data to models that we want to use to capture structure. We present a measure of similarity between data collected at several scales using the same set of attributes. The measure is based on the concept of Kolmogorov complexity and implemented through minimal message length estimates of information content and cluster analysis (the models). The similarity represents common patterns across scales, within the model class. We thus provide a novel solution to the problem of simultaneously considering data structure, model fit and scale. The methods are illustrated in application to an ecological data set.     

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.     

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.     

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.     

Microplastics reduce soil microbial network complexity and ecological deterministic selection

Microplastics have been proposed as emerging threats for terrestrial systems as they may potentially alter the physicochemical/biophysical soil environments. Due to the variety of properties of microplastics and soils, the microplastic-induced effects in soil ecosystems are greatly manifold. Here, we studied effects of three polymer microplastics (polyamide-6, polyethylene, and polyethylene terephthalate) on soil properties with four different soil types. The success patterns, interaction relationships, and assembly processes of soil bacterial communities were also studied. Microplastics have the potential to promote CO₂ emissions and enhance the soil humification. Even though microplastics did not significantly alter the diversity and composition of the soil microbial community, the application of microplastics decreased the network complexity and stability, including network size, connectivity, and the number of module and keystone species. The bacterial community assembly was governed by deterministic selection (77.3%–90.9%) in all treatments, while microplastics increased the contribution of stochastic processes from 9.1% in control to 13.6%–22.7%. The neutral model results also indicated most of the bacterial taxa were present in the predicted neutral region (approximately 98%), suggesting the importance of stochastic processes. These findings provided a fundamental insight in understanding the effects of microplastics on soil ecosystems.     

Measuring the number of co-dominants in ecological communities

We suggest a concept that allows the objective determination of the number of co-dominants in a community. We define co-dominants as a subset of species that are more abundant and more uniformly distributed than other species in a given sample. We compare the sample with a model community and use Simpsons diversity index to estimate the apparent number of co-dominants. Dominant species determined in this way are responsible for 70–90% of the total measure of abundance in the sample. The statistical significance of the apparent number of co-dominants may be assessed by a randomization test.     

Limits on ecosystem trophic complexity: insights from ecological network analysis

Articulating what limits the length of trophic food chains has remained one of the most enduring challenges in ecology. Mere counts of ecosystem species and transfers have not much illumined the issue, in part because magnitudes of trophic transfers vary by orders of magnitude in power‐law fashion. We address this issue by creating a suite of measures that extend the basic indexes usually obtained by counting taxa and transfers so as to apply to networks wherein magnitudes vary by orders of magnitude. Application of the extended measures to data on ecosystem trophic networks reveals that the actual complexity of ecosystem webs is far less than usually imagined, because most ecosystem networks consist of a multitude of weak connections dominated by a relatively few strong flows. Although quantitative ecosystem networks may consist of hundreds of nodes and thousands of transfers, they nevertheless behave similarly to simpler representations of systems with fewer than 14 nodes or 40 flows. Both theory and empirical data point to an upper bound on the number of effective trophic levels at about 3–4 links. We suggest that several whole‐system processes may be at play in generating these ecosystem limits and regularities.     

社会-生态系统恢复力的测量方法综述

恢复力和社会-生态系统研究的理论及实践近年来在西方较为流行,然而经过几十年发展,学术界仍旧没有对恢复力的概念达成一致,相应的测量方法更是多种多样。基于恢复力理论对系统相对稳定状态和边界的假设以及恢复力概念3个阶段的演变和理论的发展,总结了测量恢复力的5种方法,得出恢复力测量的3个发展现状或趋势:阈值和断裂点方法依旧是量化恢复力的基本方法;恢复力测量从关注时间转向空间,关注生态转向社会和社会-生态;复杂学和多学科融合的方法是未来发展的主要方向。     

Measuring morphological complexity of segmented animals: centipedes as model systems

In segmented animals it is possible to define morphological complexity as the degree of morphological differentiation of segments. A quantitative method for measuring morphological complexity of segmental patterns was devised by McShea in 1992, who introduced three geometrical indices. Here, we introduce a new index of morphological complexity and emphasize the possible decoupling between segmentation and segment differentiation and illustrate different patterns of variation within segmental series and how these could affect morphological evolution and evolvability. Concepts are illustrated by contrasting the segmental models of two groups of centipedes (Chilopoda): the elongate Geophilomorpha and the short‐bodied Lithobiomorpha. A preliminary application of the new metric provides no evidence of macroevolutionary increase in morphological complexity of centipede segmental organization.     

Capturing ecological complexity: OCI,a novel combination of ecological indices as applied to benthic marine habitats

The novel Overall Complexity Index (OCI) is proposed to measure ecological complexity, incorporating four complexity indices: (1) exergy and (2) throughput as extensive metrics, (3) specific exergy and (4) information as intensive metrics. Exergy and specific exergy estimate structural complexity while throughput and information functional complexity. OCI was applied to benthic habitats in a coastal marine tract encompassing a Marine Protected Area (MPA) in north-western Italy. The four individual indices did not always show homogeneous results in assigning complexity to different habitats. On the contrary, the additive measure provided by OCI showed that seagrass meadows and coralligenous reefs are in all the most complex habitats. Applying OCI provided results consistent with traditional approaches based on expert judgement, which usually attach more interest to seagrass meadows and hard bottoms with respect to soft bottoms, but expressed a synthetic, objective and quantitative approach. OCI can be mapped for management purposes, resolving the discordances evidenced by the individual indices. Ecological complexity in the study area is concentrated in some hot spots, as mapped by OCI, while the greatest part of the seafloor is occupied by low complexity habitats. Only some of these complexity hotspots are included within the Marine Protected Area, while this study suggests that high complexity areas, adjacent to the existing MPA, should be considered for protection possibly reshaping MPA's limits.     

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.