Chaos far away from the edge of chaos: A recurrence quantification analysis of plankton time series

Chaotic turnover of rare and abundant species in a strongly interacting model community

The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species toward rarity or abundance is crucial to assessing ecosystem resilience and adaptation to changing environmental conditions. In plankton communities in particular, large temporal fluctuations in species abundances have been associated with chaotic dynamics. On the other hand, microbial diversity is overwhelmingly sustained by a "rare biosphere" of species with very low abundances. We consider here the possibility that interactions within a species-rich community can relate both phenomena. We use a Lotka-Volterra model with weak immigration and strong, disordered, and mostly competitive interactions between hundreds of species to bridge single-species temporal fluctuations and abundance distribution patterns. We highlight a generic chaotic regime where a few species at a time achieve dominance but are continuously overturned by the invasion of formerly rare species. We derive a focal-species model that captures the intermittent boom-and-bust dynamics that every species undergoes. Although species cannot be treated as effectively uncorrelated in their abundances, the community's effect on a focal species can nonetheless be described by a time-correlated noise characterized by a few effective parameters that can be estimated from time series. The model predicts a nonunitary exponent of the power-law abundance decay, which varies weakly with ecological parameters, consistent with observation in marine protist communities. The chaotic turnover regime is thus poised to capture relevant ecological features of species-rich microbial communities.

Wide ecological niches ensure frequent harmful dinoflagellate blooms

Harmful algal blooms (HABs) and their consequences cause multiple devastating effects in various freshwater, brackish and marine ecosystems. However, HAB species at moderate population densities have positive ecological roles as primary producers of organic matter and food for zooplankton and fish. They also enhance benthic-pelagic coupling and participate in the biogeochemical cycles. The consequences of HABs are transported across the conventional environmental boundaries by numerous cascade effects in the food webs and beyond. Meanwhile, forecasts of bloom events are still limited, largely because of scarcity of reliable information on ecological niches of the bloom-forming algae. To fill up this knowledge gap, this study focused on dinoflagellates, a diverse group of mostly photosynthesizing protists (unicellular eukaryotes) capable of mixotrophy, since they play a key role in primary production and formation of blooms in marine and brackish waters worldwide. In this study, ecological niches of 17 abundant bloom-forming dinoflagellate species from coastal regions of the southern Baltic Sea were identified for the first time. It was hypothesized that wider ecological niches ensure more frequent dinoflagellate blooms compared to the species with narrower niches. This hypothesis was verified using the long-term (44 years) database on phytoplankton abundance and physical-chemical characteristics of the environment. It were analyzed 4534 datasets collected from 1972 to 2016. Fourteen abiotic parameters (water temperature, salinity, Secchi depth, pH, Chl a, and concentration of basic nutrients) were considered as ecological niche dimensions. The Principal Component Analysis presented the dissolved inorganic nitrogen, total nitrogen, Chl a, and temperature as principal niche dimensions of dinoflagellates. The algal bloom criteria were refined. It was for the first time proved statistically that HAB frequency of dinoflagellate species robustly correlated with the width of their ecological niches.

Direct input of monitoring data into a mechanistic ecological model as a way to identify the phytoplankton growth-rate response to temperature variations

We present an approach (knowledge-and-data-driven, KDD, modeling) that allows us to get closer to understanding the processes that affect the dynamics of plankton communities. This approach, based on the use of time series obtained as a result of ecosystem monitoring, combines the key features of both the knowledge-driven modeling (mechanistic models) and data-driven (DD) modeling. Using a KDD model, we reveal the phytoplankton growth-rate fluctuations in the ecosystem of the Naroch Lakes and determine the degree of phase synchronization between fluctuations in the phytoplankton growth rate and temperature variations. More specifically, we estimate a numerical value of the phase locking index (PLI), which allows us to assess how temperature fluctuations affect the dynamics of phytoplankton growth rates. Since, within the framework of KDD modeling, we directly include the time series obtained as a result of field measurements in the model equations, the dynamics of the phytoplankton growth rate obtained from the KDD model reflect the behavior of the lake ecosystem as a whole, and PLI can be considered as a holistic parameter.

Intermittent instability is widespread in plankton communities

Chaotic dynamics appear to be prevalent in short-lived organisms including plankton and may limit long-term predictability. However, few studies have explored how dynamical stability varies through time, across space and at different taxonomic resolutions. Using plankton time series data from 17 lakes and 4 marine sites, we found seasonal patterns of local instability in many species, that short-term predictability was related to local instability, and that local instability occurred most often in the spring, associated with periods of high growth. Taxonomic aggregates were more stable and more predictable than finer groupings. Across sites, higher latitude locations had higher Lyapunov exponents and greater seasonality in local instability, but only at coarser taxonomic resolution. Overall, these results suggest that prediction accuracy, sensitivity to change and management efficacy may be greater at certain times of year and that prediction will be more feasible for taxonomic aggregates.

Rethinking the Prevalence and Relevance of Chaos in Ecology

Chaos was proposed in the 1970s as an alternative explanation for apparently noisy fluctuations in population size. Although readily demonstrated in models, the search for chaos in nature proved challenging and led many to conclude that chaos is either rare or nigh impossible to detect. However, in the intervening half-century, it has become clear that ecosystems are replete with the enabling conditions for chaos. Chaos has been repeatedly demonstrated under laboratory conditions and has been found in field data using updated detection methods. Together, these developments indicate that the apparent rarity of chaos was an artifact of data limitations and overreliance on low-dimensional population models. We invite readers to reevaluate the relevance of chaos in ecology, and we suggest that chaos is not as rare or undetectable as previously believed.

Insights from the study of complex systems for the ecology and evolution of animal populations

Populations of animals comprise many individuals, interacting in multiple contexts, and displaying heterogeneous behaviors. The interactions among individuals can often create population dynamics that are fundamentally deterministic yet display unpredictable dynamics. Animal populations can, therefore, be thought of as complex systems. Complex systems display properties such as nonlinearity and uncertainty and show emergent properties that cannot be explained by a simple sum of the interacting components. Any system where entities compete, cooperate, or interfere with one another may possess such qualities, making animal populations similar on many levels to complex systems. Some fields are already embracing elements of complexity to help understand the dynamics of animal populations, but a wider application of complexity science in ecology and evolution has not occurred. We review here how approaches from complexity science could be applied to the study of the interactions and behavior of individuals within animal populations and highlight how this way of thinking can enhance our understanding of population dynamics in animals. We focus on 8 key characteristics of complex systems: hierarchy, heterogeneity, self-organization, openness, adaptation, memory, nonlinearity, and uncertainty. For each topic we discuss how concepts from complexity theory are applicable in animal populations and emphasize the unique insights they provide. We finish by outlining outstanding questions or predictions to be evaluated using behavioral and ecological data. Our goal throughout this article is to familiarize animal ecologists with the basics of each of these concepts and highlight the new perspectives that they could bring to variety of subfields.

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.

Recurrence quantification analysis of a three level trophic chain model

Recurrence plots and recurrence quantification analysis based measures - recurrence rate, determinism, divergence, entropy, laminarity and trapping time, are used to detect transitions between periodic and chaotic states and also the laminar states of the complex three species food web model with improved growth rate function and predatory ability. The study of dynamical equation of such a complex biological system with transients in terms of these measures results in localization of bifurcation behavior of the system.