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.

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.

Hidden similarities in the dynamics of a weakly synchronous marine metapopulation.

Populations of many marine species are only weakly synchronous, despite coupling through larval dispersal and exposure to synchronous environmental drivers. Although this is often attributed to observation noise, factors including local environmental differences, spatially variable dynamics, and chaos might also reduce or eliminate metapopulation synchrony. To differentiate spatially variable dynamics from similar dynamics driven by spatially variable environments, we applied hierarchical delay embedding. A unique output of this approach, the "dynamic correlation," quantifies similarity in intrinsic dynamics of populations, independently of whether their abundance is correlated through time. We applied these methods to 17 populations of blue crab (Callinectes sapidus) along the US Atlantic coast and found that their intrinsic dynamics were broadly similar despite largely independent fluctuations in abundance. The weight of evidence suggests that the latitudinal gradient in temperature, filtered through a unimodal response curve, is sufficient to decouple crab populations. As unimodal thermal performance is ubiquitous in ectotherms, we suggest that this may be a general explanation for the weak synchrony observed at large distances in many marine species, although additional studies are needed to test this hypothesis.

Fast behavioral feedbacks make ecosystems sensitive to pace and not just magnitude of anthropogenic environmental change.

Anthropogenic environmental change is altering the behavior of animals in ecosystems around the world. Although behavior typically occurs on much faster timescales than demography, it can nevertheless influence demographic processes. Here, we use detailed data on behavior and empirical estimates of demography from a coral reef ecosystem to develop a coupled behavioral-demographic ecosystem model. Analysis of the model reveals that behavior and demography feed back on one another to determine how the ecosystem responds to anthropogenic forcing. In particular, an empirically observed feedback between the density and foraging behavior of herbivorous fish leads to alternative stable ecosystem states of coral population persistence or collapse (and complete algal dominance). This feedback makes the ecosystem more prone to coral collapse under fishing pressure but also more prone to recovery as fishing is reduced. Moreover, because of the behavioral feedback, the response of the ecosystem to changes in fishing pressure depends not only on the magnitude of changes in fishing but also on the pace at which changes are imposed. For example, quickly increasing fishing to a given level can collapse an ecosystem that would persist under more gradual change. Our results reveal conditions under which the pace and not just the magnitude of external forcing can dictate the response of ecosystems to environmental change. More generally, our multiscale behavioral-demographic framework demonstrates how high-resolution behavioral data can be incorporated into ecological models to better understand how ecosystems will respond to perturbations.

Ancestral genetic variation in phenotypic plasticity underlies rapid evolutionary changes in resurrected populations of waterfleas.

The role of phenotypic plasticity in adaptive evolution has been debated for decades. This is because the strength of natural selection is dependent on the direction and magnitude of phenotypic responses to environmental signals. Therefore, the connection between plasticity and adaptation will depend on the patterns of plasticity harbored by ancestral populations before a change in the environment. Yet few studies have directly assessed ancestral variation in plasticity and tracked phenotypic changes over time. Here we resurrected historic propagules of Daphnia spanning multiple species and lakes in Wisconsin following the invasion and proliferation of a novel predator (spiny waterflea, Bythotrephes longimanus). This approach revealed extensive genetic variation in predator-induced plasticity in ancestral populations of Daphnia It is unlikely that the standing patterns of plasticity shielded Daphnia from selection to permit long-term coexistence with a novel predator. Instead, this variation in plasticity provided the raw materials for Bythotrephes-mediated selection to drive rapid shifts in Daphnia behavior and life history. Surprisingly, there was little evidence for the evolution of trait plasticity as genetic variation in plasticity was maintained in the face of a novel predator. Such results provide insight into the link between plasticity and adaptation and highlight the importance of quantifying genetic variation in plasticity when evaluating the drivers of evolutionary change in the wild.

Effects of daily thermal fluctuations on the Atlantic silverside, a fish with temperature-dependent sex determination.

Temperature-dependent sex determination (TSD) occurs when the temperature during development affects gonad determination. Historically, most work on TSD in fishes was conducted under constant temperatures, yet daily fluctuating temperatures can significantly alter fish physiology and life history. Thus, we subjected the Atlantic silverside, Menidia menidia (a TSD species), to 28, 28 ± 2 and 28 ± 4°C (a high, masculinizing temperature) and quantified sex ratios and length. We found that the percentage of females increased by 60%-70% when the fish were exposed to daily fluctuating temperatures (from 10% to 16% and 17% under fluctuations).

Forecasting in the face of ecological complexity: Number and strength of species interactions determine forecast skill in ecological communities.

The potential for forecasting the dynamics of ecological systems is currently unclear, with contrasting opinions regarding its feasibility due to ecological complexity. To investigate forecast skill within and across systems, we monitored a microbial system exposed to either constant or fluctuating temperatures in a 5-month-long laboratory experiment. We tested how forecasting of species abundances depends on the number and strength of interactions and on model size (number of predictors). We also tested how greater system complexity (i.e. the fluctuating temperatures) impacted these relations. We found that the more interactions a species had, the weaker these interactions were and the better its abundance was predicted. Forecast skill increased with model size. Greater system complexity decreased forecast skill for three out of eight species. These insights into how abundance prediction depends on the connectedness of the species within the system and on overall system complexity could improve species forecasting and monitoring.

A latitudinal gradient in thermal transgenerational plasticity and a test of theory.

Transgenerational plasticity (TGP) occurs when phenotypes are shaped by the environment in both the current and preceding generations. Transgenerational responses to rainfall, CO2 and temperature suggest that TGP may play an important role in how species cope with climate change. However, little is known about how TGP will evolve as climate change continues. Here, we provide a quantitative test of the hypothesis that the predictability of the environment influences the magnitude of the transgenerational response. To do so, we take advantage of the latitudinal decrease in the predictability of temperatures in near shore waters along the US East Coast. Using sheepshead minnows (Cyprinodon variegatus) from South Carolina, Maryland, and Connecticut, we found the first evidence for a latitudinal gradient in thermal TGP. Moreover, the degree of TGP in these populations depends linearly on the decorrelation time for temperature, providing support for the hypothesis that thermal predictability drives the evolution of these traits.

Trophic control changes with season and nutrient loading in lakes.

Experiments have revealed much about top-down and bottom-up control in ecosystems, but manipulative experiments are limited in spatial and temporal scale. To obtain a more nuanced understanding of trophic control over large scales, we explored long-term time-series data from 13 globally distributed lakes and used empirical dynamic modelling to quantify interaction strengths between zooplankton and phytoplankton over time within and across lakes. Across all lakes, top-down effects were associated with nutrients, switching from negative in mesotrophic lakes to positive in oligotrophic lakes. This result suggests that zooplankton nutrient recycling exceeds grazing pressure in nutrient-limited systems. Within individual lakes, results were consistent with a 'seasonal reset' hypothesis in which top-down and bottom-up interactions varied seasonally and were both strongest at the beginning of the growing season. Thus, trophic control is not static, but varies with abiotic conditions - dynamics that only become evident when observing changes over large spatial and temporal scales.

Reverse-engineering ecological theory from data.

Ecologists have long sought to understand the dynamics of populations and communities by deriving mathematical theory from first principles. Theoretical models often take the form of dynamical equations that comprise the ecological processes (e.g. competition, predation) believed to govern system dynamics. The inverse of this approach-inferring which processes and ecological interactions drive observed dynamics-remains an open problem in ecology. Here, we propose a way to attack this problem using a machine learning method known as symbolic regression, which seeks to discover relationships in time-series data and to express those relationships using dynamical equations. We found that this method could rapidly discover models that explained most of the variance in three classic demographic time series. More importantly, it reverse-engineered the models previously proposed by theoretical ecologists to describe these time series, capturing the core ecological processes these models describe and their functional forms. Our findings suggest a potentially powerful new way to merge theory development and data analysis.

Estimating partial regulation in spatiotemporal models of community dynamics.

Niche-based approaches to community analysis often involve estimating a matrix of pairwise interactions among species (the "community matrix"), but this task becomes infeasible using observational data as the number of modeled species increases. As an alternative, neutral theories achieve parsimony by assuming that species within a trophic level are exchangeable, but generally cannot incorporate stabilizing interactions even when they are evident in field data. Finally, both regulated (niche) and unregulated (neutral) approaches have rarely been fitted directly to survey data using spatiotemporal statistical methods. We therefore propose a spatiotemporal and model-based approach to estimate community dynamics that are partially regulated. Specifically, we start with a neutral spatiotemporal model where all species follow ecological drift, which precludes estimating pairwise interactions. We then add regulatory relations until model selection favors stopping, where the "rank" of the interaction matrix may range from zero to the number of species. A simulation experiment shows that model selection can accurately identify the rank of the interaction matrix, and that the identified spatiotemporal model can estimate the magnitude of species interactions. A 40-yr case study for the Gulf of St. Lawrence marine community shows that recovering grey seals have an unregulated and negative relationship with demersal fishes. We therefore conclude that partial regulation is a plausible approximation to community dynamics using field data and hypothesize that estimating partial regulation will be expedient in future analyses of spatiotemporal community dynamics given limited field data. We conclude by recommending ongoing research to add explicit models for movement, so that meta-community theory can be confronted with data in a spatiotemporal statistical framework.

Avoiding a crisis of motivation for ocean management under global environmental change.

Climate change and ocean acidification are altering marine ecosystems and, from a human perspective, creating both winners and losers. Human responses to these changes are complex, but may result in reduced government investments in regulation, resource management, monitoring and enforcement. Moreover, a lack of peoples' experience of climate change may drive some towards attributing the symptoms of climate change to more familiar causes such as management failure. Taken together, we anticipate that management could become weaker and less effective as climate change continues. Using diverse case studies, including the decline of coral reefs, coastal defences from flooding, shifting fish stocks and the emergence of new shipping opportunities in the Arctic, we argue that human interests are better served by increased investments in resource management. But greater government investment in management does not simply mean more of "business-as-usual." Management needs to become more flexible, better at anticipating and responding to surprise, and able to facilitate change where it is desirable. A range of technological, economic, communication and governance solutions exists to help transform management. While not all have been tested, judicious application of the most appropriate solutions should help humanity adapt to novel circumstances and seek opportunity where possible.

Predicting life history parameters for all fishes worldwide.

Scientists and resource managers need to know life history parameters (e.g., average mortality rate, individual growth rate, maximum length or mass, and timing of maturity) to understand and respond to risks to natural populations and ecosystems. For over 100 years, scientists have identified "life history invariants" (LHI) representing pairs of parameters whose ratio is theorized to be constant across species. LHI then promise to allow prediction of many parameters from field measurements of a few important traits. Using LHI in this way, however, neglects any residual patterns in parameters when making predictions. We therefore apply a multivariate model for eight variables (seven parameters and temperature) in over 32,000 fishes, and include taxonomic structure for residuals (with levels for class, order, family, genus, and species). We illustrate that this approach predicts variables probabilistically for taxa with many or few data. We then use this model to resolve three questions regarding life history parameters in fishes. Specifically we show that (1) on average there is a 1.24% decrease in the Brody growth coefficient for every 1% increase in maximum size; (2) the ratio of natural mortality rate and growth coefficient is not an LHI but instead varies systematically based on the timing of maturation, where movement along this life history axis is predictably correlated with species taxonomy; and (3) three variables must be known per species to precisely predict remaining life history variables. We distribute our predictive model as an R package, FishLife, to allow future life history predictions for fishes to be conditioned on taxonomy and life history data for fishes worldwide. This package also contains predictions (and predictive intervals) for mortality, maturity, size, and growth parameters for all described fishes.

Predator-driven brain size evolution in natural populations of Trinidadian killifish (Rivulus hartii).

Vertebrates exhibit extensive variation in relative brain size. It has long been assumed that this variation is the product of ecologically driven natural selection. Yet, despite more than 100 years of research, the ecological conditions that select for changes in brain size are unclear. Recent laboratory selection experiments showed that selection for larger brains is associated with increased survival in risky environments. Such results lead to the prediction that increased predation should favour increased brain size. Work on natural populations, however, foreshadows the opposite trajectory of evolution; increased predation favours increased boldness, slower learning, and may thereby select for a smaller brain. We tested the influence of predator-induced mortality on brain size evolution by quantifying brain size variation in a Trinidadian killifish, Rivulus hartii, from communities that differ in predation intensity. We observed strong genetic differences in male (but not female) brain size between fish communities; second generation laboratory-reared males from sites with predators exhibited smaller brains than Rivulus from sites in which they are the only fish present. Such trends oppose the results of recent laboratory selection experiments and are not explained by trade-offs with other components of fitness. Our results suggest that increased male brain size is favoured in less risky environments because of the fitness benefits associated with faster rates of learning and problem-solving behaviour.

Tracking and forecasting ecosystem interactions in real time.

Evidence shows that species interactions are not constant but change as the ecosystem shifts to new states. Although controlled experiments and model investigations demonstrate how nonlinear interactions can arise in principle, empirical tools to track and predict them in nature are lacking. Here we present a practical method, using available time-series data, to measure and forecast changing interactions in real systems, and identify the underlying mechanisms. The method is illustrated with model data from a marine mesocosm experiment and limnologic field data from Sparkling Lake, WI, USA. From simple to complex, these examples demonstrate the feasibility of quantifying, predicting and understanding state-dependent, nonlinear interactions as they occur in situ and in real time--a requirement for managing resources in a nonlinear, non-equilibrium world.

Local adaptation in transgenerational responses to predators.

Environmental signals can induce phenotypic changes that span multiple generations. Along with phenotypic responses that occur during development (i.e. 'within-generation' plasticity), such 'transgenerational plasticity' (TGP) has been documented in a diverse array of taxa spanning many environmental perturbations. New theory predicts that temporal stability is a key driver of the evolution of TGP. We tested this prediction using natural populations of zooplankton from lakes in Connecticut that span a large gradient in the temporal dynamics of predator-induced mortality. We reared more than 120 clones of Daphnia ambigua from nine lakes for multiple generations in the presence/absence of predator cues. We found that temporal variation in mortality selects for within-generation plasticity while consistently strong (or weak) mortality selects for increased TGP. Such results provide us the first evidence for local adaptation in TGP and argue that divergent ecological conditions select for phenotypic responses within and across generations.

Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data.

Accurate predictions of species abundance remain one of the most vexing challenges in ecology. This observation is perhaps unsurprising, because population dynamics are often strongly forced and highly nonlinear. Recently, however, numerous statistical techniques have been proposed for fitting highly parameterized mechanistic models to complex time series, potentially providing the machinery necessary for generating useful predictions. Alternatively, there is a wide variety of comparatively simple model-free forecasting methods that could be used to predict abundance. Here we pose a rather conservative challenge and ask whether a correctly specified mechanistic model, fit with commonly used statistical techniques, can provide better forecasts than simple model-free methods for ecological systems with noisy nonlinear dynamics. Using four different control models and seven experimental time series of flour beetles, we found that Markov chain Monte Carlo procedures for fitting mechanistic models often converged on best-fit parameterizations far different from the known parameters. As a result, the correctly specified models provided inaccurate forecasts and incorrect inferences. In contrast, a model-free method based on state-space reconstruction gave the most accurate short-term forecasts, even while using only a single time series from the multivariate system. Considering the recent push for ecosystem-based management and the increasing call for ecological predictions, our results suggest that a flexible model-free approach may be the most promising way forward.

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.

Predator-induced phenotypic plasticity within- and across-generations: a challenge for theory?

Much work has shown that the environment can induce non-genetic changes in phenotype that span multiple generations. Theory predicts that predictable environmental variation selects for both increased within- and across-generation responses. Yet, to the best of our knowledge, there are no empirical tests of this prediction. We explored the relationship between within- versus across-generation plasticity by evaluating the influence of predator cues on the life-history traits of Daphnia ambigua. We measured the duration of predator-induced transgenerational effects, determined when transgenerational responses are induced, and quantified the cues that activate transgenerational plasticity. We show that predator exposure during embryonic development causes earlier maturation and increased reproductive output. Such effects are detectable two generations removed from predator exposure and are similar in magnitude in response to exposure to cues emitted by injured conspecifics. Moreover, all experimental contexts and traits yielded a negative correlation between within- versus across-generation responses. That is, responses to predator cues within- and across-generations were opposite in sign and magnitude. Although many models address transgenerational plasticity, none of them explain this apparent negative relationship between within- and across-generation plasticities. Our results highlight the need to refine the theory of transgenerational plasticity.

On estimating the reliability of ecological forecasts.

Recent work has highlighted the utility of nonparametric forecasting methods for predicting ecological time series (Perretti et al., 2013. Proc. Natl. Acad. Sci. U.S.A. 110, 5253-5257). However, one topic that has received considerably less attention is the quantification of uncertainty in nonparametric forecasts. This important topic was brought to the forefront in the recent work by Jabot (2014. J. Theor. Biol.). Here, we add to this emerging discussion by reviewing the available methods for quantifying forecast uncertainty in nonparametric models. We conclude with a demonstration of one such method using the simulation model of Jabot (2014. J. Theor. Biol.). We find that nonparametric forecast error is accurately estimated with as few as 10 observations in the time series.