Constraining nonlinear time series modeling with the metabolic theory of ecology.

Forecasting the response of ecological systems to environmental change is a critical challenge for sustainable management. The metabolic theory of ecology (MTE) posits scaling of biological rates with temperature, but it has had limited application to population dynamic forecasting. Here we use the temperature dependence of the MTE to constrain empirical dynamic modeling (EDM), an equation-free nonlinear machine learning approach for forecasting. By rescaling time with temperature and modeling dynamics on a "metabolic time step," our method (MTE-EDM) improved forecast accuracy in 18 of 19 empirical ectotherm time series (by 19% on average), with the largest gains in more seasonal environments. MTE-EDM assumes that temperature affects only the rate, rather than the form, of population dynamics, and that interacting species have approximately similar temperature dependence. A review of laboratory studies suggests these assumptions are reasonable, at least approximately, though not for all ecological systems. Our approach highlights how to combine modern data-driven forecasting techniques with ecological theory and mechanistic understanding to predict the response of complex ecosystems to temperature variability and trends.

Dryland sensitivity to climate change and variability using nonlinear dynamics.

Primary productivity response to climatic drivers varies temporally, indicating state-dependent interactions between climate and productivity. Previous studies primarily employed equation-based approaches to clarify this relationship, ignoring the state-dependent nature of ecological dynamics. Here, using 40 y of climate and productivity data from 48 grassland sites across Mongolia, we applied an equation-free, nonlinear time-series analysis to reveal sensitivity patterns of productivity to climate change and variability and clarify underlying mechanisms. We showed that productivity responded positively to annual precipitation in mesic regions but negatively in arid regions, with the opposite pattern observed for annual mean temperature. Furthermore, productivity responded negatively to decreasing annual aridity that integrated precipitation and temperature across Mongolia. Productivity responded negatively to interannual variability in precipitation and aridity in mesic regions but positively in arid regions. Overall, interannual temperature variability enhanced productivity. These response patterns are largely unrecognized; however, two mechanisms are inferable. First, time-delayed climate effects modify annual productivity responses to annual climate conditions. Notably, our results suggest that the sensitivity of annual productivity to increasing annual precipitation and decreasing annual aridity can even be negative when the negative time-delayed effects of annual precipitation and aridity on productivity prevail across time. Second, the proportion of plant species resistant to water and temperature stresses at a site determines the sensitivity of productivity to climate variability. Thus, we highlight the importance of nonlinear, state-dependent sensitivity of productivity to climate change and variability, accurately forecasting potential biosphere feedback to the climate system.

Environmental context dependency in species interactions.

Ecological interactions are not uniform across time and can vary with environmental conditions. Yet, interactions among species are often measured with short-term controlled experiments whose outcomes can depend greatly on the particular environmental conditions under which they are performed. As an alternative, we use empirical dynamic modeling to estimate species interactions across a wide range of environmental conditions directly from existing long-term monitoring data. In our case study from a southern California kelp forest, we test whether interactions between multiple kelp and sea urchin species can be reliably reconstructed from time-series data and whether those interactions vary predictably in strength and direction across observed fluctuations in temperature, disturbance, and low-frequency oceanographic regimes. We show that environmental context greatly alters the strength and direction of species interactions. In particular, the state of the North Pacific Gyre Oscillation seems to drive the competitive balance between kelp species, asserting bottom-up control on kelp ecosystem dynamics. We show the importance of specifically studying variation in interaction strength, rather than mean interaction outcomes, when trying to understand the dynamics of complex ecosystems. The significant context dependency in species interactions found in this study argues for a greater utilization of long-term data and empirical dynamic modeling in studies of the dynamics of other ecosystems.

A hybrid empirical and parametric approach for managing ecosystem complexity: Water quality in Lake Geneva under nonstationary futures.

Severe deterioration of water quality in lakes, characterized by overabundance of algae and declining dissolved oxygen in the deep lake (DOB), was one of the ecological crises of the 20th century. Even with large reductions in phosphorus loading, termed "reoligotrophication," DOB and chlorophyll (CHL) have often not returned to their expected pre-20th-century levels. Concurrently, management of lake health has been confounded by possible consequences of climate change, particularly since the effects of climate are not neatly separable from the effects of eutrophication. Here, using Lake Geneva as an iconic example, we demonstrate a complementary alternative to parametric models for understanding and managing lake systems. This involves establishing an empirically-driven baseline that uses supervised machine learning to capture the changing interdependencies among biogeochemical variables and then combining the empirical model with a more conventional equation-based model of lake physics to predict DOB over decadal time-scales. The hybrid model not only leads to substantially better forecasts, but also to a more actionable description of the emergent rates and processes (biogeochemical, ecological, etc.) that drive water quality. Notably, the hybrid model suggests that the impact of a moderate 3°C air temperature increase on water quality would be on the same order as the eutrophication of the previous century. The study provides a template and a practical path forward to cope with shifts in ecology to manage environmental systems for non-analogue futures.

Population impact of fine particulate matter on tuberculosis risk in China: a causal inference.

BACKGROUND: Previous studies have suggested the potential association between air pollution and tuberculosis incidence, but this association remains inconclusive and evidence to assess causality is particularly lacking. We aimed to draw causal inference between fine particulate matter less than 2.5 µm in diameter (PM2.5) and tuberculosis in China. METHODS: Granger causality (GC) inference was performed within vector autoregressive models at levels and/or first-differences using annual national aggregated data during 1982-2019, annual provincial aggregated data during 1982-2019 and monthly provincial aggregated data during 2004-2018. Convergent cross-mapping (CCM) approach was used to determine the backbone nonlinear causal association based on the monthly provincial aggregated data during 2004-2018. Moreover, distributed lag nonlinear model (DLNM) was applied to quantify the causal effects. RESULTS: GC tests identified PM2.5 driving tuberculosis dynamics at national and provincial levels in Granger sense. Empirical dynamic modeling provided the CCM causal intensity of PM2.5 effect on tuberculosis at provincial level and demonstrated that PM2.5 had a positive effect on tuberculosis incidence. Then, DLNM estimation demonstrated that the PM2.5 exposure driven tuberculosis risk was concentration- and time-dependent in a nonlinear manner. This result still held in the multi-pollutant model. CONCLUSIONS: Causal inference showed that PM2.5 exposure driving tuberculosis, which showing a concentration gradient change. Air pollutant control may have potential public health benefit of decreasing tuberculosis burden.

Temperature is a regulator of leaf production in the family Dipterocarpaceae of equatorial Southeast Asia.

PREMISE: Leaf phenology is an essential developmental process in trees and an important component in understanding climate change. However, little is known about the regulation of leaf phenology in tropical trees. METHODS: To understand the regulation by temperature of leaf phenology in tropical trees, we performed daily observations of leaf production under rainfall-independent conditions using saplings of Shorea leprosula and Neobalanocarpus heimii, both species of Dipterocarpaceae, a dominant tree family of Southeast Asia. We analyzed the time-series data obtained using empirical dynamic modeling (EDM) and conducted growth chamber experiments. RESULTS: Leaf production by dipterocarps fluctuated in the absence of fluctuation in rainfall, and the peaks of leaf production were more frequent than those of day length, suggesting that leaf production cannot be fully explained by these environmental factors, although they have been proposed as regulators of leaf phenology in dipterocarps. Instead, EDM suggested a causal relationship between temperature and leaf production in dipterocarps. Leaf production by N. heimii saplings in chambers significantly increased when temperature was increased after long-term low-temperature treatment. This increase in leaf production was observed even when only nighttime temperature was elevated, suggesting that the effect of temperature on development is not mediated by photosynthesis. CONCLUSIONS: Because seasonal variation in temperature in the tropics is small, effects on leaf phenology have been overlooked. However, our results suggest that temperature is a regulator of leaf phenology in dipterocarps. This information will contribute to better understanding of the effects of climate change in the tropics.

Global environmental drivers of influenza.

In temperate countries, influenza outbreaks are well correlated to seasonal changes in temperature and absolute humidity. However, tropical countries have much weaker annual climate cycles, and outbreaks show less seasonality and are more difficult to explain with environmental correlations. Here, we use convergent cross mapping, a robust test for causality that does not require correlation, to test alternative hypotheses about the global environmental drivers of influenza outbreaks from country-level epidemic time series. By moving beyond correlation, we show that despite the apparent differences in outbreak patterns between temperate and tropical countries, absolute humidity and, to a lesser extent, temperature drive influenza outbreaks globally. We also find a hypothesized U-shaped relationship between absolute humidity and influenza that is predicted by theory and experiment, but hitherto has not been documented at the population level. The balance between positive and negative effects of absolute humidity appears to be mediated by temperature, and the analysis reveals a key threshold around 75 °F. The results indicate a unified explanation for environmental drivers of influenza that applies globally.

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.

Predicting coastal algal blooms in southern California.

The irregular appearance of planktonic algae blooms off the coast of southern California has been a source of wonder for over a century. Although large algal blooms can have significant negative impacts on ecosystems and human health, a predictive understanding of these events has eluded science, and many have come to regard them as ultimately random phenomena. However, the highly nonlinear nature of ecological dynamics can give the appearance of randomness and stress traditional methods-such as model fitting or analysis of variance-to the point of breaking. The intractability of this problem from a classical linear standpoint can thus give the impression that algal blooms are fundamentally unpredictable. Here, we use an exceptional time series study of coastal phytoplankton dynamics at La Jolla, CA, with an equation-free modeling approach, to show that these phenomena are not random, but can be understood as nonlinear population dynamics forced by external stochastic drivers (so-called "stochastic chaos"). The combination of this modeling approach with an extensive dataset allows us to not only describe historical behavior and clarify existing hypotheses about the mechanisms, but also make out-of-sample predictions of recent algal blooms at La Jolla that were not included in the model development.

Causal effect of air pollution and meteorology on the COVID-19 pandemic: A convergent cross mapping approach.

Environmental factors have been suspected to influence the propagation and lethality of COVID-19 in the global population. However, most of the studies have been limited to correlation analyses and did not use specific methods to address the dynamic of the causal relationship between the virus and its external drivers. This work focuses on inferring and understanding the causal effect of critical air pollutants and meteorological parameters on COVID-19 by using an Empirical Dynamic Modeling approach called Convergent Cross Mapping. This technique allowed us to identify the time-delayed causation and the sign of interactions. Considering its remarkable urban environment and mortality rate during the pandemic, Quito, Ecuador, was chosen as a case study. Our results show that both urban air pollution and meteorology have a causal impact on COVID-19. Even if the strength and the sign of the causality vary over time, a general trend can be drawn. NO2, SO2, CO and PM2.5 have a positive causation for COVID-19 infections (ρ > 0.35 and ∂ > 9.1). Contrary to current knowledge, this study shows a rapid effect of pollution on COVID-19 cases (1 < lag days <24) and a negative impact of O3 on COVID-19-related deaths (ρ = 0.53 and ∂ = -0.3). Regarding the meteorology, temperature (ρ = 0.24 and ∂ = -0.4) and wind speed (ρ = 0.34 and ∂ = -3.9) tend to mitigate the epidemiological consequences of SARS-CoV-2, whereas relative humidity seems to increase the excess deaths (ρ = 0.4 and ∂ = 0.05). A causal network is proposed to synthesize the interactions between the studied variables and to provide a simple model to support the management of coronavirus outbreaks.

Long-term occurrence, resistance risk and chaotic characteristics of antibiotic resistance genes in sludge anaerobic digestion system.

The long-term occurrence, dynamics and risk of antibiotic resistance genes (ARGs) in anaerobic digestion (AD) of excess sludge (ES) are not fully understood. Therefore, 13-month metagenomic monitoring was carried out in a full-scale AD plant. The highest ARG abundance and risk scores were observed in spring. AD achieved a 35 % removal rate for the total ARG abundance, but the risk score of AD sludge was not always lower than ES samples, because of the higher proportion of Rank I ARGs in AD sludge. ARGs showed less obvious patterns under linear models compared with microbial community, implying their chaotic dynamics, which was further confirmed by nonlinearity tests. Empirical dynamic modeling performed better than the autoregressive integrated moving average model for ARG dynamics, especially for those with simple and nonlinear dynamics. This study highlighted spring for its higher ARG abundance and risk, and recommended nonlinear models for revealing the dynamics of ARGs.

The size of the susceptible pool differentiates climate effects on seasonal epidemics of bacillary dysentery.

OBJECTIVES: At present, some studies have pointed out several possible climate drivers of bacillary dysentery. However, there is a complex nonlinear interaction between climate drivers and susceptible population in the spread of diseases, which makes it challenging to detect climate drivers at the size of susceptible population. METHODS: By using empirical dynamic modeling (EDM), the climate drivers of bacillary dysentery dynamic were explored in China's five temperature zones. RESULTS: We verified the availability of climate drivers and susceptible population size on bacillary dysentery, and used this information for bacillary dysentery dynamic prediction. Moreover, we found that their respective effects increased with the increase of temperature and relative humidity, and their states (temperature and relative humidity) were different when they reached their maximum effects, and the negative effect between the effect of temperature and disease incidence increased with the change of temperature zone (from temperate zone to warm temperate zone to subtropical zone) and the climate driving effect of the temperate zone (warm temperate zone) was greater than that of the colder (temperate zone) and warmer (subtropics) zones. When we viewed from single temperature zone, the climatic effect arose only when the size of the susceptible pool was large. CONCLUSIONS: These results provide empirical evidence that the climate factors on bacillary dysentery are nonlinear, complex but dependent on the size of susceptible populations and different climate scenarios.

Sub-monthly prediction of harmful algal blooms based on automated cell imaging.

Harmful algal blooms (HABs) are an increasing threat to global fisheries and human health. The mitigation of HABs requires management strategies to successfully forecast the abundance and distribution of harmful algal taxa. In this study, we attempt to characterize the dynamics of 2 phytoplankton genera (Pseudo-nitzschia spp. and Dinophysis spp.) in Narragansett Bay, Rhode Island, using empirical dynamic modeling. We utilize a high-resolution Imaging FlowCytobot dataset to generate a daily-resolution time series of phytoplankton images and then characterize the sub-monthly (1-30 days) timescales of univariate and multivariate prediction skill for each taxon. Our results suggest that univariate predictability is low overall, different for each taxon and does not significantly vary over sub-monthly timescales. For all univariate predictions, models can rely on the inherent autocorrelation within each time series. When we incorporated multivariate data based on quantifiable image features, we found that predictability increased for both taxa and that this increase was apparent on timescales >7 days. Pseudo-nitzschia spp. has distinctive predictive dynamics that occur on timescales of around 16 and 25 days. Similarly, Dinophysis spp. is most predictable on timescales of 25 days. The timescales of prediction for Pseudo-nitzschia spp. and Dinophysis spp. could be tied to environmental drivers such as tidal cycles, water temperature, wind speed, community biomass, salinity, and pH in Narragansett Bay. For most drivers, there were consistent effects between the environmental variables and the phytoplankton taxon. Our analysis displays the potential of utilizing data from automated cell imagers to forecast and monitor harmful algal blooms.

Alternative stable states, nonlinear behavior, and predictability of microbiome dynamics.

BACKGROUND: Microbiome dynamics are both crucial indicators and potential drivers of human health, agricultural output, and industrial bio-applications. However, predicting microbiome dynamics is notoriously difficult because communities often show abrupt structural changes, such as "dysbiosis" in human microbiomes. METHODS: We integrated theoretical frameworks and empirical analyses with the aim of anticipating drastic shifts of microbial communities. We monitored 48 experimental microbiomes for 110 days and observed that various community-level events, including collapse and gradual compositional changes, occurred according to a defined set of environmental conditions. We analyzed the time-series data based on statistical physics and non-linear mechanics to describe the characteristics of the microbiome dynamics and to examine the predictability of major shifts in microbial community structure. RESULTS: We confirmed that the abrupt community changes observed through the time-series could be described as shifts between "alternative stable states" or dynamics around complex attractors. Furthermore, collapses of microbiome structure were successfully anticipated by means of the diagnostic threshold defined with the "energy landscape" analysis of statistical physics or that of a stability index of nonlinear mechanics. CONCLUSIONS: The results indicate that abrupt microbiome events in complex microbial communities can be forecasted by extending classic ecological concepts to the scale of species-rich microbial systems. Video Abstract.

Reconstruction of a Soil Microbial Network Induced by Stress Temperature.

The microbial community is viewed as a network of diverse microorganisms connected by various interspecific interactions. While the stress gradient hypothesis (SGH) predicts that positive interactions are favored in more stressful environments, the prediction has been less explored in complex microbial communities due to the challenges of identifying interactions. Here, by applying a nonlinear time series analysis to the amplicon-based diversity time series data of the soil microbiota cultured under less stressful (30°C) or more stressful (37°C) temperature conditions, we show how the microbial network responds to temperature stress. While the genera that persisted only under the less stressful condition showed fewer positive effects, the genera that appeared only under the more stressful condition received more positive effects, in agreement with SGH. However, temperature difference also induced reconstruction of the community network, leading to an increased proportion of negative interactions at the whole-community level. The anti-SGH pattern can be explained by the stronger competition caused by increased metabolic rate and population densities. IMPORTANCE By combining amplicon-based diversity survey with recently developed nonlinear analytical tools, we successfully determined the interaction networks of more than 150 natural soil microbial genera under less or more temperature stress and explored the applicability of the stress gradient hypothesis to soil microbiota, shedding new light on the well-known hypothesis.

Differences in initial abundances reveal divergent dynamic structures in Gause's predator-prey experiments.

Improved understanding of complex dynamics has revealed insights across many facets of ecology, and has enabled improved forecasts and management of future ecosystem states. However, an enduring challenge in forecasting complex dynamics remains the differentiation between complexity and stochasticity, that is, to determine whether declines in predictability are caused by stochasticity, nonlinearity, or chaos. Here, we show how to quantify the relative contributions of these factors to prediction error using Georgii Gause's iconic predator-prey microcosm experiments, which, critically, include experimental replicates that differ from one another only in initial abundances. We show that these differences in initial abundances interact with stochasticity, nonlinearity, and chaos in unique ways, allowing us to identify the impacts of these factors on prediction error. Our results suggest that jointly analyzing replicate time series across multiple, distinct starting points may be necessary for understanding and predicting the wide range of potential dynamic types in complex ecological systems.

Intraseasonal predictability of natural phytoplankton population dynamics.

It is difficult to make skillful predictions about the future dynamics of marine phytoplankton populations. Here, we use a 22-year time series of monthly average abundances for 198 phytoplankton taxa from Station L4 in the Western English Channel (1992-2014) to test whether and how aggregating phytoplankton into multi-species assemblages can improve predictability of their temporal dynamics. Using a non-parametric framework to assess predictability, we demonstrate that the prediction skill is significantly affected by how species data are grouped into assemblages, the presence of noise, and stochastic behavior within species. Overall, we find that predictability one month into the future increases when species are aggregated together into assemblages with more species, compared with the predictability of individual taxa. However, predictability within dinoflagellates and larger phytoplankton (>12 µm cell radius) is low overall and does not increase by aggregating similar species together. High variability in the data, due to observational error (noise) or stochasticity in population growth rates, reduces the predictability of individual species more than the predictability of assemblages. These findings show that there is greater potential for univariate prediction of species assemblages or whole-community metrics, such as total chlorophyll or biomass, than for the individual dynamics of phytoplankton species.

Does past evolutionary history under different mating regimes influence the demographic dynamics of interspecific competition?

Interspecific interactions are contingent upon organism phenotypes, and thus phenotypic evolution can modify interspecific interactions and affect ecological dynamics. Recent studies have suggested that male-male competition within a species selects for capability to reproductively interfere with a closely related species. Here, we examine the effect of past evolutionary history under different mating regimes on the demographic dynamics of interspecific competition in Callosobruchus seed beetles. We used previously established experimental evolution lines of Callosobruchus chinensis that evolved under either forced lifelong monogamy or polygamy for 17 generations, and examined the demographic dynamics of competition between these C. chinensis lines and a congener, Callosobruchus maculatus. Callosobruchus chinensis was competitively excluded by C. maculatus in all trials. Time series data analyses suggested that reproductive interference from C. chinensis was relatively more important in the trials involving polygamous C. chinensis than those involving monogamous C. chinensis, in accordance with the potentially higher reproductive interference capability of polygamous C. chinensis. However, the estimated signs and magnitudes of interspecific interactions were not fully consistent with this explanation, implying the evolution of not only reproductive interference but also other interaction mechanisms. Our study thus suggests multifaceted effects of sexually selected traits on interspecific competitive dynamics.

Causality analysis and prediction of 2-methylisoborneol production in a reservoir using empirical dynamic modeling.

2-Methylisobornel (MIB) is one of the most widespread and problematic biogenic compounds causing taste-and-odor problems in freshwater. To investigate the causes of MIB production and develop models to predict the MIB concentration, we have applied empirical dynamic modeling (EDM), a nonlinear approach based on Chaos theory, to the long-term water quality dataset of Kamafusa Reservoir in Japan. The study revealed the dynamic nature of MIB production in the reservoir, and determined causal variables for MIB production, including water temperature, pH, transparency, light intensity, and Green Phormidium. Moreover, EDM established that the system is three-dimensional, and the approach found elevated nonlinearity (from 1.5 to 3) across the whole study period (1996-2015). By taking only one or two candidate predictors with varying time lags, multivariate models for predicting MIB production (best model: r = 0.83, p < 0.001, root mean squared error = 3.1 ng/L) were successfully established. The modeling approach used in this study is a powerful tool for causality identification and odor prediction, thus making important contributions to reservoir management.

Rapid evolution leads to differential population dynamics and top-down control in resurrected Daphnia populations.

There is growing evidence of rapid genetic adaptation of natural populations to environmental change, opening the perspective that evolutionary trait change may subsequently impact ecological processes such as population dynamics, community composition, and ecosystem functioning. To study such eco-evolutionary feedbacks in natural populations, however, requires samples across time. Here, we capitalize on a resurrection ecology study that documented rapid and adaptive evolution in a natural population of the water flea Daphnia magna in response to strong changes in predation pressure by fish, and carry out a follow-up mesocosm experiment to test whether the observed genetic changes influence population dynamics and top-down control of phytoplankton. We inoculated populations of the water flea D. magna derived from three time periods of the same natural population known to have genetically adapted to changes in predation pressure in replicate mesocosms and monitored both Daphnia population densities and phytoplankton biomass in the presence and absence of fish. Our results revealed differences in population dynamics and top-down control of algae between mesocosms harboring populations from the time period before, during, and after a peak in fish predation pressure caused by human fish stocking. The differences, however, deviated from our a priori expectations. An S-map approach on time series revealed that the interactions between adults and juveniles strongly impacted the dynamics of populations and their top-down control on algae in the mesocosms, and that the strength of these interactions was modulated by rapid evolution as it occurred in nature. Our study provides an example of an evolutionary response that fundamentally alters the processes structuring population dynamics and impacts ecosystem features.