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.

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).

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.

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.

Chaos is not rare in natural ecosystems.

Chaotic dynamics are thought to be rare in natural populations but this may be due to methodological and data limitations, rather than the inherent stability of ecosystems. Following extensive simulation testing, we applied multiple chaos detection methods to a global database of 172 population time series and found evidence for chaos in >30%. In contrast, fitting traditional one-dimensional models identified <10% as chaotic. Chaos was most prevalent among plankton and insects and least among birds and mammals. Lyapunov exponents declined with generation time and scaled as the -1/6 power of body mass among chaotic populations. These results demonstrate that chaos is not rare in natural populations, indicating that there may be intrinsic limits to ecological forecasting and cautioning against the use of steady-state approaches to conservation and management.

Recurrent neural networks for partially observed dynamical systems.

Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables. Here we provide an algebraic approach to delay embedding that permits explicit approximation of error. We also provide the asymptotic dependence of the first-order approximation error on the system size. More importantly, this formulation of delay embedding can be directly implemented using a recurrent neural network (RNN). This observation expands the interpretability of both delay embedding and the RNN and facilitates principled incorporation of structure and other constraints into these approaches.

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.

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.

Thermal transgenerational effects remain after two generations.

Transgenerational plasticity (TGP) is increasingly recognized as a mechanism by which organisms can respond to environments that change across generations. Although recent empirical and theoretical studies have explored conditions under which TGP is predicted to evolve, it is still unclear whether the effects of the parental environment will remain beyond the offspring generation. Using a small cyprinodontid fish, we explored multigenerational thermal TGP to address two related questions. First (experiment 1), does the strength of TGP decline or accumulate across multiple generations? Second (experiment 2), how does the experience of a temperature novel to both parents and offspring affect the strength of TGP? In the first experiment, we found a significant interaction between F1 and F2 temperatures and juvenile growth, but no effect of egg diameter. The strength of TGP between F0 and F1 generations was similar in both experiments but declined in subsequent generations. Further, experience of a novel temperature accelerated the decline. This pattern, although similar to that found in other species, is certainly not universally observed, suggesting that theoretical and empirical effort is needed to understand the multigenerational dynamics of TGP.

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.

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.

Circularity in fisheries data weakens real world prediction.

The systematic substitution of direct observational data with synthesized data derived from models during the stock assessment process has emerged as a low-cost alternative to direct data collection efforts. What is not widely appreciated, however, is how the use of such synthesized data can overestimate predictive skill when forecasting recruitment is part of the assessment process. Using a global database of stock assessments, we show that Standard Fisheries Models (SFMs) can successfully predict synthesized data based on presumed stock-recruitment relationships, however, they are generally less skillful at predicting observational data that are either raw or minimally filtered (denoised without using explicit stock-recruitment models). Additionally, we find that an equation-free approach that does not presume a specific stock-recruitment relationship is better than SFMs at predicting synthesized data, and moreover it can also predict observational recruitment data very well. Thus, while synthesized datasets are cheaper in the short term, they carry costs that can limit their utility in predicting real world recruitment.

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.

Contrasting genomic shifts underlie parallel phenotypic evolution in response to fishing.

Humans cause widespread evolutionary change in nature, but we still know little about the genomic basis of rapid adaptation in the Anthropocene. We tracked genomic changes across all protein-coding genes in experimental fish populations that evolved pronounced shifts in growth rates due to size-selective harvest over only four generations. Comparisons of replicate lines show parallel allele frequency shifts that recapitulate responses to size-selection gradients in the wild across hundreds of unlinked variants concentrated in growth-related genes. However, a supercluster of genes also rose rapidly in frequency and dominated the evolutionary dynamic in one replicate line but not in others. Parallel phenotypic changes thus masked highly divergent genomic responses to selection, illustrating how contingent rapid adaptation can be in the face of strong human-induced selection.

A function-valued trait approach to estimating the genetic basis of size at age and its potential role in fisheries-induced evolution.

Natural selection is inherently a multivariate phenomenon. The selection pressure on size (natural and artificial) and the age at which selection occurs is likely to induce evolutionary changes in growth rates across the entire life history. However, the covariance structure that will determine the path of evolution for size at age has been studied in only a few fish species. We therefore estimated the genetic covariance function for size throughout ontogeny using Atlantic silversides (Menidia menidia) as the model system. Over a 3-year period, a total of 542 families were used to estimate the genetic covariance in length at age from hatch through maturity. The function-valued trait approach was employed to estimate the genetic covariance functions. A Bayesian hierarchical model was used to account for the unbalanced design, unequal measurement intervals, unequal sample sizes, and family-aggregated data. To improve mixing, we developed a two-stage sampler using a Gibbs sampler to generate the posterior of a well-mixing approximate model followed by an importance sampler to draw samples from posterior of the completely specified model. We found that heritability of length is age-specific and there are strong genetic correlations in length across ages that last 30 days or more. We used these estimates in a hypothetical model predicting the evolutionary response to harvesting following a single generation of selection under both sigmoidal and unimodal patterns of gear selectivity to illustrate the potential outcomes of ignoring the genetic correlations. In these scenarios, genetic correlations were found to have a strong effect on both the direction and magnitude of the response to harvest selection.

Trait variation in extreme thermal environments under constant and fluctuating temperatures.

Climate change is increasingly exposing populations to rare and novel environmental conditions. Theory suggests that extreme conditions will expose cryptic phenotypes, with a concomitant increase in trait variation. Although some empirical support for this exists, it is also well established that physiological mechanisms (e.g. heat shock protein expression) change when organisms are exposed to constant versus fluctuating temperatures. To determine the effect of common, rare and novel temperatures on the release of hidden variation, we exposed fathead minnows, Pimephales promelas, to five fluctuating and four constant temperature regimes (constant treatments: 23.5, 25, 28.5 and 31°C; all fluctuating treatments shared a minimum temperature of 22°C at 00.00 and a maximum of 25, 28, 31, 34 or 37°C at 12.00). We measured each individual's length weekly over 60 days, critical thermal maximum (CTmax), five morphometric traits (eye anterior-posterior distance, pelvic fin length, pectoral fin length, pelvic fin ray count and pectoral fin ray count) and fluctuating asymmetry (FA, absolute difference between left and right morphometric measurements; FA is typically associated with stress). Length-at-age in both constant and fluctuating conditions decreased with temperature, and this trait's variance decreased with temperature under fluctuating conditions but increased and then decreased in constant temperatures. CTmax in both treatments increased with increasing water temperature, while its variance decreased in warmer waters. No consistent pattern in mean or variance was found across morphometric traits or FA. Our results suggest that, for fathead minnows, variance can decrease in important traits (e.g. length-at-age and CTmax) as the environment becomes more stressful, so it may be difficult to establish comprehensive rules for the effects of rarer or stressful environments on trait variation. This article is part of the theme issue 'The role of plasticity in phenotypic adaptation to rapid environmental change'.

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.

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.

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.