Detecting shifts in nonlinear dynamics using Empirical Dynamic Modeling with Nested-Library Analysis.

Abrupt changes in system states and dynamical behaviors are often observed in natural systems; such phenomena, named regime shifts, are explained as transitions between alternative steady states (more generally, attractors). Various methods have been proposed to detect regime shifts from time series data, but a generic detection method with theoretical linkage to underlying dynamics is lacking. Here, we provide a novel method named Nested-Library Analysis (NLA) to retrospectively detect regime shifts using empirical dynamic modeling (EDM) rooted in theory of attractor reconstruction. Specifically, NLA determines the time of regime shift as the cutting point at which sequential reduction of the library set (i.e., the time series data used to reconstruct the attractor for forecasting) optimizes the forecast skill of EDM. We illustrate this method on a chaotic model of which changing parameters present a critical transition. Our analysis shows that NLA detects the change point in the model system and outperforms existing approaches based on statistical characteristics. In addition, NLA empirically detected a real-world regime shift event revealing an abrupt change of Pacific Decadal Oscillation index around the mid-1970s. Importantly, our method can be easily generalized to various systems because NLA is equation-free and requires only a single time series.

Fluctuating interaction network and time-varying stability of a natural fish community.

Ecological theory suggests that large-scale patterns such as community stability can be influenced by changes in interspecific interactions that arise from the behavioural and/or physiological responses of individual species varying over time. Although this theory has experimental support, evidence from natural ecosystems is lacking owing to the challenges of tracking rapid changes in interspecific interactions (known to occur on timescales much shorter than a generation time) and then identifying the effect of such changes on large-scale community dynamics. Here, using tools for analysing nonlinear time series and a 12-year-long dataset of fortnightly collected observations on a natural marine fish community in Maizuru Bay, Japan, we show that short-term changes in interaction networks influence overall community dynamics. Among the 15 dominant species, we identify 14 interspecific interactions to construct a dynamic interaction network. We show that the strengths, and even types, of interactions change with time; we also develop a time-varying stability measure based on local Lyapunov stability for attractor dynamics in non-equilibrium nonlinear systems. We use this dynamic stability measure to examine the link between the time-varying interaction network and community stability. We find seasonal patterns in dynamic stability for this fish community that broadly support expectations of current ecological theory. Specifically, the dominance of weak interactions and higher species diversity during summer months are associated with higher dynamic stability and smaller population fluctuations. We suggest that interspecific interactions, community network structure and community stability are dynamic properties, and that linking fluctuating interaction networks to community-level dynamic properties is key to understanding the maintenance of ecological communities in nature.

Spatiotemporal variations and influential factors affecting reproductive dynamics of Pacific saury in the Northwest Pacific during fishing season.

This study examined the spatial and monthly variations in reproductive dynamics of Pacific saury collected in the high sea (40°N-49°N, 149°E-168°E) of the northwestern Pacific during the fishing season of the Taiwanese stick-held dip-net fisheries (July-November) from 2018 to 2019. Generalized additive mixed-effects models (GAMMs) were applied to explore the relationship between the probability of maturing and spawning occurrence (PMOS ) and the explanatory variables (month, body length, sea-surface temperature [SST] as fixed effects, and fishing set as a random effect) for the age 0 and age 1 fish, respectively. In addition, the impact of the geographical difference in growth rates of age 0 fish, quantified as the radius of the otolith annual ring, on the PMOS of age 1 fish was explored in the GAMMs. Results showed that the mean values of the condition factor (CF) varied by months, and higher mean CFs were observed north of 45°N. However, the mean values of the gonado-somatic index did not show a clear spatiotemporal pattern. The spatial distribution of the ovarian maturation states revealed that the spawning ground of Pacific saury during July-November was broader than that previously known and had partly overlapped with the high-sea fishing ground. The best GAMM showed that the predicted PMOS of the age 0 fish were generally low (mean = 19%, standard deviation [SD] = 10%) and tended to increase with increasing body length. In contrast, the predicted PMOS were relatively higher (mean = 37%, SD = 10%) for the age 1 fish and increased with increasing SST and decreasing latitude. Two candidate GAMMs, which are equally supported as the best model (ΔAIC < 2), provide evidence that a higher growth rate of age 0 fish may result in higher reproductive activity in age 1 fish. This is one of few studies focusing on the reproductive dynamics of Pacific saury during the fishing season; current limitations, future directions, and conservation implications were discussed.

How Communities of Marine Stramenopiles Varied with Environmental and Biological Variables in the Subtropical Northwestern Pacific Ocean.

MArine STramenopiles (MASTs) have been recognized as parts of heterotrophic protists and contribute substantially to protist abundances in the ocean. However, little is known about their spatiotemporal variations with respect to environmental and biological factors. The objectives of this study are to use canonical correspondence analysis to investigate how MASTs communities are shaped by environmental variables, and co-occurrence networks to examine their potential interactions with prokaryotic communities. Our dataset came from the southern East China Sea (sECS) in the subtropical northwestern Pacific, and involved 14 cruises along a coastal-oceanic transect, each of which sampled surface water from 4 to 7 stations. MASTs communities were revealed by metabarcoding of 18S rDNA V4 region. Most notably, MAST-9 had a high representation in warm waters in terms of read number and diversity. Subclades of MAST-9C and -9D showed slightly different niches, with MAST-9D dominating in more coastal waters where concentrations of nitrite and Synechococcus were higher. MAST-1C was a common component of colder water during spring. Overall, canonical correspondence analysis showed that MASTs communities were significantly influenced by temperature, nitrite and Synechococcus concentrations. The co-occurrence networks showed that certain other minor prokaryotic taxa can influence MAST communities. This study provides insight into how MASTs communities varied with environmental and biological variables.

Reconstructing large interaction networks from empirical time series data.

Reconstructing interactions from observational data is a critical need for investigating natural biological networks, wherein network dimensionality is usually high. However, these pose a challenge to existing methods that can quantify only small interaction networks. Here, we proposed a novel approach to reconstruct high-dimensional interaction Jacobian networks using empirical time series without specific model assumptions. This method, named "multiview distance regularised S-map," generalised the state space reconstruction to accommodate high dimensionality and overcome difficulties in quantifying massive interactions with limited data. When evaluating this method using time series generated from theoretical models involving hundreds of interacting species, estimated strengths of interaction Jacobians were in good agreement with theoretical expectations. Applying this method to a natural bacterial community helped identify important species from the interaction network and revealed mechanisms governing the dynamical stability of a bacterial community. The proposed method overcame the challenge of high dimensionality in large natural dynamical systems.

Body Size, Light Intensity, and Nutrient Supply Determine Plankton Stoichiometry in Mixotrophic Plankton Food Webs.

Trophic strategy determines stoichiometry of plankton. In general, heterotrophic zooplankton have lower and more stable C∶N and C∶P ratios than photoautotrophic phytoplankton, whereas mixotrophic protists, which consume prey and photosynthesize, have stoichiometry between zooplankton and phytoplankton. As trophic strategies change with cell size, body size may be a key trait influencing eukaryotic plankton stoichiometry. However, the relationship between body size and stoichiometry remains unclear. Here we measured plankton size-fractionated C∶N ratios under different intensities of light and nutrient supply in subtropical freshwater and marine systems. We found a unimodal body size-C∶N ratio pattern, with a maximum C∶N ratio at ∼50 µm diameter in marine and freshwater systems. Moreover, the variation in C∶N ratios is explained mainly by body size, followed by light intensity and nutrient concentration. To investigate the mechanisms behind this unimodal pattern, we constructed a size-based plankton food web model in which the trophic strategy and C∶N ratio are an emerging result. Our model simulations reproduce the unimodal pattern with a C∶N ratio of photoautotrophs ≤50 µm increasing with body size due to increase of photosynthetic carbon, whereas C∶N ratios of organisms >50 µm decrease with size due to decreasing photoautotrophic but increasing heterotrophic uptake. Based on our field observations and simulation, we extend the classic "light-nutrient" theory that determines plankton C∶N ratio to include body size and trophic strategy dependency. We conclude that body size and size-dependent uptake of resources (light, nutrients, and prey) determine plankton stoichiometry at various light and nutrient supplies.

Long-term warming destabilizes aquatic ecosystems through weakening biodiversity-mediated causal networks.

Understanding how ecosystems will respond to climate changes requires unravelling the network of functional responses and feedbacks among biodiversity, physicochemical environments, and productivity. These ecosystem components not only change over time but also interact with each other. Therefore, investigation of individual relationships may give limited insights into their interdependencies and limit ability to predict future ecosystem states. We address this problem by analyzing long-term (16-39 years) time series data from 10 aquatic ecosystems and using convergent cross mapping (CCM) to quantify the causal networks linking phytoplankton species richness, biomass, and physicochemical factors. We determined that individual quantities (e.g., total species richness or nutrients) were not significant predictors of ecosystem stability (quantified as long-term fluctuation of phytoplankton biomass); rather, the integrated causal pathway in the ecosystem network, composed of the interactions among species richness, nutrient cycling, and phytoplankton biomass, was the best predictor of stability. Furthermore, systems that experienced stronger warming over time had both weakened causal interactions and larger fluctuations. Thus, rather than thinking in terms of separate factors, a more holistic network view, that causally links species richness and the other ecosystem components, is required to understand and predict climate impacts on the temporal stability of aquatic ecosystems.

Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling.

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner-recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts.

Abundant and rare picoeukaryotic sub-communities present contrasting patterns in the epipelagic waters of marginal seas in the northwestern Pacific Ocean.

In this work, they compared patterns of abundant and rare picoeukaryotic sub-communities in the epipelagic waters (surface and 40-75 m depth subsurface layers) of the East and South China Seas across seasons via 454 pyrosequencing of the V4 region of 18S rDNA. They also examined the relative effects of environmental filtering, dispersal limitations and seasonality on community assembly. Their results indicated that (i) in the surface layer, abundant taxa are primarily influenced by dispersal limitations and rare taxa are primarily influenced by environmental filtering, whereas (ii) in the subsurface layer, both abundant and rare sub-communities are only weakly influenced by environmental filtering but are strongly influenced by dispersal limitations. Moreover, (iii) abundant taxa exhibit stronger temporal variability than rare taxa. They also found that abundant and rare sub-communities display similar spatial richness patterns that are negatively correlated with latitude and chlorophyll a and positively correlated with temperature. In summary, environmental filtering and dispersal limitations have different effects on abundant and rare picoeukaryotic sub-communities in different layers. Thus, depth appears as an essential variable that governs the structuring patterns of picoeukaryotic communities in the oceans and should be thoroughly considered to develop a more comprehensive understanding of oceanic microbial assemblages.

Infections of Wolbachia may destabilize mosquito population dynamics.

Recent efforts in controlling mosquito-borne diseases focus on biocontrol strategies that incapacitate pathogens inside mosquitoes by altering the mosquito's microbiome. A case in point is the introduction of Wolbachia into natural mosquito populations in order to eliminate Dengue virus. However, whether this strategy can successfully control vector-borne diseases is debated; particularly, how artificial infection affects population dynamics of hosts remains unclear. Here, we show that natural Wolbachia infections are associated with unstable mosquito population dynamics by contrasting Wolbachia-infected versus uninfected cage populations of the Asian tiger mosquito (Aedes albopictus). By analyzing weekly data of adult mosquito abundances, we found that the variability of the infected populations is significantly higher than that of the uninfected. The elevated population variability is explained by increased instability in dynamics, as quantified by system nonlinearity (i.e., state-dependence). In addition, predictability of infected populations is substantially lower. A mathematical model analysis suggests that Wolbachia may alter mosquito population dynamics by modifying larval competition of hosts. These results encourage examination for effects of artificial Wolbachia establishment on mosquito populations, because an enhancement of population variability with reduced predictability could pose challenges in management. Our findings have implications for application of microbiome alterations in biocontrol programs.

Nutrient pulses driven by internal solitary waves enhance heterotrophic bacterial growth in the South China Sea.

This study demonstrated the potential effects of internal waves (IWs) on heterotrophic bacterial activities for the first time. Nine anchored studies were conducted from 2009-2012 in the South China Sea areas with different physical conditions, i.e. areas subjected to elevation IWs, to depression IWs, and to weak/no IWs. The latter two areas were treated as the Control sites. Field survey results indicated that within the euphotic zone, the minima of the depth-averaged bacterial production (IBP; ∼1.0 mgC m-3 d-1 ) and growth rate (IBµ; ∼0.1 d-1 ) at all sites were similar. Except for one case, the maxima of IBP (6-12 mgC m-3 d-1 ) and IBµ (0.55-1.13 d-1 ) of the elevation IWs areas were ∼fivefolds higher than those of the Control sites (IBP 1.7-2.1 mgC m-3 d-1 ; IBµ 0.13-0.24 d-1 ). Replicate surveys conducted at the north-western area of the Dongsha atoll during spring-to-neap (NW1 survey) and neap-to-spring (NW2 survey) tide periods showed a great contrast to each other. Low variation and averages of IBµ in NW1 survey were similar to those of the Control sites, while those in NW2 were similar to the other elevation IWs sites with larger variation and higher averages of IBµ. This finding suggests that bacterial activities may be a function of the lunar fortnightly (14-day) cycle. Enrichment experiments suggested more directly that the limiting inorganic nutrients introduced by the elevation waves (EIWs) may contribute a higher IBµ within the euphotic zone.

Prey size diversity hinders biomass trophic transfer and predator size diversity promotes it in planktonic communities.

Body size exerts multiple effects on plankton food-web interactions. However, the influence of size structure on trophic transfer remains poorly quantified in the field. Here, we examine how the size diversity of prey (nano-microplankton) and predators (mesozooplankton) influence trophic transfer efficiency (using biomass ratio as a proxy) in natural marine ecosystems. Our results support previous studies on single trophic levels: transfer efficiency decreases with increasing prey size diversity and is enhanced with greater predator size diversity. We further show that communities with low nano-microplankton size diversity and high mesozooplankton size diversity tend to occur in warmer environments with low nutrient concentrations, thus promoting trophic transfer to higher trophic levels in those conditions. Moreover, we reveal an interactive effect of predator and prey size diversities: the positive effect of predator size diversity becomes influential when prey size diversity is high. Mechanistically, the negative effect of prey size diversity on trophic transfer may be explained by unicellular size-based metabolic constraints as well as trade-offs between growth and predation avoidance with size, whereas increasing predator size diversity may enhance diet niche partitioning and thus promote trophic transfer. These findings provide insights into size-based theories of ecosystem functioning, with implications for ecosystem predictive models.

Life history traits and exploitation affect the spatial mean-variance relationship in fish abundance.

Fishing is expected to alter the spatial heterogeneity of fishes. As an effective index to quantify spatial heterogeneity, the exponent b in Taylor's power law (V = aMb) measures how spatial variance (V) varies with changes in mean abundance (M) of a population, with larger b indicating higher spatial aggregation potential (i.e., more heterogeneity). Theory predicts b is related with life history traits, but empirical evidence is lacking. Using 50-yr spatiotemporal data from the California Current Ecosystem, we examined fishing and life history effects on Taylor's exponent by comparing spatial distributions of exploited and unexploited fishes living in the same environment. We found that unexploited species with smaller size and generation time exhibit larger b, supporting theoretical prediction. In contrast, this relationship in exploited species is much weaker, as the exponents of large exploited species were higher than unexploited species with similar traits. Our results suggest that fishing may increase spatial aggregation potential of a species, likely through degrading their size/age structure. Results of moving-window cross-correlation analyses on b vs. age structure indices (mean age and age evenness) for some exploited species corroborate our findings. Furthermore, through linking our findings to other fundamental ecological patterns (occupancy-abundance and size-abundance relationships), we provide theoretical arguments for the usefulness of monitoring the exponent b for management purposes. We propose that age/size-truncated species might have lower recovery rate in spatial occupancy, and the spatial variance-mass relationship of a species might be non-linear. Our findings provide theoretical basis explaining why fishery management strategy should be concerned with changes to the age and spatial structure of exploited fishes.

Predicting climate effects on Pacific sardine.

For many marine species and habitats, climate change and overfishing present a double threat. To manage marine resources effectively, it is necessary to adapt management to changes in the physical environment. Simple relationships between environmental conditions and fish abundance have long been used in both fisheries and fishery management. In many cases, however, physical, biological, and human variables feed back on each other. For these systems, associations between variables can change as the system evolves in time. This can obscure relationships between population dynamics and environmental variability, undermining our ability to forecast changes in populations tied to physical processes. Here we present a methodology for identifying physical forcing variables based on nonlinear forecasting and show how the method provides a predictive understanding of the influence of physical forcing on Pacific sardine.

Linking secondary structure of individual size distribution with nonlinear size-trophic level relationship in food webs.

Existing individual size distribution (ISD) theories assume that the trophic level (TL) of an organism varies as a linear function of its log-transformed body size. This assumption predicts a power-law distribution of the ISD, i.e., a linear relationship between size and abundance in log space. However, the secondary structure of ISD (nonlinear dome shape structures deviating from a power-law distribution) is often observed. We propose a model that extends the metabolic theory to link the secondary structure of ISD to the nonlinear size-TL relationship. This model is tested with empirical data collected from a subtropical reservoir. The empirical ISD and size-TL relationships were constructed by FlowCAM imaging analysis and stable isotope analyses, respectively. Our results demonstrate that the secondary structure of ISD can be predicted from the nonlinear function of size-TL relationship and vice versa. Moreover, these secondary structures arise due to (1) zooplankton omnivory and (2) the trophic interactions within microbial food webs.

Why fishing magnifies fluctuations in fish abundance.

It is now clear that fished populations can fluctuate more than unharvested stocks. However, it is not clear why. Here we distinguish among three major competing mechanisms for this phenomenon, by using the 50-year California Cooperative Oceanic Fisheries Investigations (CalCOFI) larval fish record. First, variable fishing pressure directly increases variability in exploited populations. Second, commercial fishing can decrease the average body size and age of a stock, causing the truncated population to track environmental fluctuations directly. Third, age-truncated or juvenescent populations have increasingly unstable population dynamics because of changing demographic parameters such as intrinsic growth rates. We find no evidence for the first hypothesis, limited evidence for the second and strong evidence for the third. Therefore, in California Current fisheries, increased temporal variability in the population does not arise from variable exploitation, nor does it reflect direct environmental tracking. More fundamentally, it arises from increased instability in dynamics. This finding has implications for resource management as an empirical example of how selective harvesting can alter the basic dynamics of exploited populations, and lead to unstable booms and busts that can precede systematic declines in stock levels.

Increasing zooplankton size diversity enhances the strength of top-down control on phytoplankton through diet niche partitioning.

1. The biodiversity-ecosystem functioning debate is a central topic in ecology. Recently, there has been a growing interest in size diversity because body size is sensitive to environmental changes and is one of the fundamental characteristics of organisms linking many ecosystem properties. However, how size diversity affects ecosystem functioning is an important yet unclear issue. 2. To fill the gap, with large-scale field data from the East China Sea, we tested the novel hypothesis that increasing zooplankton size diversity enhances top-down control on phytoplankton (H1) and compared it with five conventional hypotheses explaining the top-down control: flatter zooplankton size spectrum enhances the strength of top-down control (H2); nutrient enrichment lessens the strength of top-down control (H3); increasing zooplankton taxonomic diversity enhances the strength of top-down control (H4); increasing fish predation decreases the strength of top-down control of zooplankton on phytoplankton through trophic cascade (H5); increasing temperature intensifies the strength of top-down control (H6). 3. The results of univariate analyses support the hypotheses based on zooplankton size diversity (H1), zooplankton size spectrum (H2), nutrient (H3) and zooplankton taxonomic diversity (H4), but not the hypotheses based on fish predation (H5) and temperature (H6). More in-depth analyses indicate that zooplankton size diversity is the most important factor in determining the strength of top-down control on phytoplankton in the East China Sea. 4. Our results suggest a new potential mechanism that increasing predator size diversity enhances the strength of top-down control on prey through diet niche partitioning. This mechanism can be explained by the optimal predator-prey body-mass ratio concept. Suppose each size group of zooplankton predators has its own optimal phytoplankton prey size, increasing size diversity of zooplankton would promote diet niche partitioning of predators and thus elevates the strength of top-down control.

Dynamics of phytoplankton communities under photoinhibition.

We analyzed a model of phytoplankton competition for light in a well-mixed water column. The model, proposed by Gerla et al. (Oikos 120:519-527, 2011), assumed inhibition of photosynthesis at high irradiance (photoinhibition). We described the global behavior through mathematical analyses, providing a general solution to the multi-species competition for light with photoinhibition. We classified outcomes of 2- and 3-species competitions as examples, and evaluated feasibility of the theoretical predictions using empirical relationships between photosynthetic production and irradiance. Numerical simulations with published p-I curves indicate that photoinhibition may often lead to strong Allee effects and competitive facilitation among species. Hence, our results suggest that photoinhibition may play a major role in organizing phytoplankton communities.

Deterministic Assembly Processes Strengthen the Effects of ß-Diversity on Community Biomass of Marine Bacterioplankton.

The presence of more species in the community of a sampling site (α diversity) typically increases ecosystem functions via nonrandom processes like resource partitioning. When considering multiple communities, we hypothesize that higher compositional difference (ß diversity) increases overall functions of these communities. Further, we hypothesize that the ß diversity effect is more positive when ß diversity is increased by nonrandom assembly processes. To test these hypotheses, we collected bacterioplankton along a transect of 6 sampling sites in the southern East China Sea in 14 cruises. For any pairs of the 6 sites within a cruise, we calculated the Bray-Curtis index to represent ß diversity and summed bacterial biomass as a proxy to indicate the overall function of the two communities. We then calculated deviation of observed mean pairwise phylogenetic similarities among species in two communities from random to represent the influences of nonrandom processes. The bacterial ß diversity was found to positively affect the summed bacterial biomass; however, the effect varied among cruises. Cross-cruise comparison indicated that the ß diversity effect increased with the nonrandom processes selecting for phylogenetically dissimilar species. This study extends biodiversity-ecosystem functioning research to the scale of multiple sites and enriches the framework by considering community assembly processes. IMPORTANCE The implications of our analyses are twofold. First, we emphasize the importance of studying ß diversity. We expanded the current biodiversity-ecosystem functioning framework from single to multiple sampling sites and investigated the influences of species compositional differences among sites on the overall functioning of these sites. Since natural ecological communities never exist alone, our analyses allow us to more holistically perceive the role of biodiversity in natural ecosystems. Second, we took community assembly processes into account to attain a more mechanistic understanding of the impacts of biodiversity on ecosystem functioning.