Random evolutionary dynamics in predator-prey systems yields large, clustered ecosystems

We study the effect of introducing new species through evolution into communities. We use the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra (LV) equations, also when multiple predator and prey species co-exist. We use a stochastic method to introduce new species in a two-trophic LV system. We find that introducing random evolving species leads to robust ecosystems in which large numbers of species coexist. Crucially, in these large ecosystems an emergent clustering of species is observed, tying functional differences to phylogenetic history.

Neural timescales reflect behavioral demands in freely moving rhesus macaques

Previous work demonstrated a highly reproducible cortical hierarchy of neural timescales at rest, with sensory areas displaying fast, and higher-order association areas displaying slower timescales. The question arises how such stable hierarchies give rise to adaptive behavior that requires flexible adjustment of temporal coding and integration demands. Potentially, this lack of variability in the hierarchical organization of neural timescales could reflect the structure of the laboratory contexts. We posit that unconstrained paradigms are ideal to test whether the dynamics of neural timescales reflect behavioral demands. Here we measured timescales of local field potential activity while male rhesus macaques foraged in an open space. We found a hierarchy of neural timescales that differs from previous work. Importantly, although the magnitude of neural timescales expanded with task engagement, the brain areas' relative position in the hierarchy was stable. Next, we demonstrated that the change in neural timescales is dynamic and contains functionally-relevant information, differentiating between similar events in terms of motor demands and associated reward. Finally, we demonstrated that brain areas are differentially affected by these behavioral demands. These results demonstrate that while the space of neural timescales is anatomically constrained, the observed hierarchical organization and magnitude is dependent on behavioral demands.

Broad environmental adaptation of abundant microbial taxa in Robinia pseudoacacia forests during long-term vegetation restoration

Vegetation restoration has significant impacts on ecosystems, and a comprehensive understanding of microbial environmental adaptability could facilitate coping with ecological challenges such as environmental change and biodiversity loss. Here, abundant and rare soil bacterial and fungal communities were characterized along a 15-45-year chronosequence of forest vegetation restoration in the Loess Plateau region. Phylogenetic-bin-based null model analysis (iCAMP), niche breadth index, and co-occurrence network analysis were used to assess microbial community assembly and environmental adaptation of a Robinia pseudoacacia plantation under long-term vegetation restoration. The drift process governed community assembly of abundant and rare soil fungi and bacteria. With increasing soil total phosphorus content, the relative importance of drift increased, while dispersal limitation and heterogeneous selection exhibited opposite trends for abundant and rare fungi. Rare soil fungal composition dissimilarities were dominated by species replacement processes. Abundant microbial taxa had higher ecological niche width and contribution to ecosystem multifunctionality than rare taxa. Node property values (e.g., degree and betweenness) of abundant microbial taxa were substantially higher than those of rare microbial taxa, indicating abundant species occupied a central position in the network. This study provides insights into the diversity and stability of microbial communities during vegetation restoration in Loess Plateau. The findings highlight that abundant soil fungi and bacteria have broad environmental adaptation and major implications for soil multifunctionality under long-term vegetation restoration.

Rhythm of relationships in a social fish over the course of a full year in the wild

BACKGROUND

Animals are expected to adjust their social behaviour to cope with challenges in their environment. Therefore, for fish populations in temperate regions with seasonal and daily environmental oscillations, characteristic rhythms of social relationships should be pronounced. To date, most research concerning fish social networks and biorhythms has occurred in artificial laboratory environments or over confined temporal scales of days to weeks. Little is known about the social networks of wild, freely roaming fish, including how seasonal and diurnal rhythms modulate social networks over the course of a full year. The advent of high-resolution acoustic telemetry enables us to quantify detailed social interactions in the wild over time-scales sufficient to examine seasonal rhythms at whole-ecosystems scales. Our objective was to explore the rhythms of social interactions in a social fish population at various time-scales over one full year in the wild by examining high-resolution snapshots of a dynamic social network.

METHODS

To that end, we tracked the behaviour of 36 adult common carp, Cyprinus carpio, in a 25 ha lake and constructed temporal social networks among individuals across various time-scales, where social interactions were defined by proximity. We compared the network structure to a temporally shuffled null model to examine the importance of social attraction, and checked for persistent characteristic groups over time.

RESULTS

The clustering within the carp social network tended to be more pronounced during daytime than nighttime throughout the year. Social attraction, particularly during daytime, was a key driver for interactions. Shoaling behavior substantially increased during daytime in the wintertime, whereas in summer carp interacted less frequently, but the interaction duration increased. Therefore, smaller, characteristic groups were more common in the summer months and during nighttime, where the social memory of carp lasted up to two weeks.

CONCLUSIONS

We conclude that social relationships of carp change diurnally and seasonally. These patterns were likely driven by predator avoidance, seasonal shifts in lake temperature, visibility, forage availability and the presence of anoxic zones. The techniques we employed can be applied generally to high-resolution biotelemetry data to reveal social structures across other fish species at ecologically realistic scales.

Disturbance alters transience but nutrients determine equilibria during grassland succession with multiple global change drivers

Disturbance and environmental change may cause communities to converge on a steady state, diverge towards multiple alternative states or remain in long-term transience. Yet, empirical investigations of successional trajectories are rare, especially in systems experiencing multiple concurrent anthropogenic drivers of change. We examined succession in old field grassland communities subjected to disturbance and nitrogen fertilization using data from a long-term (22-year) experiment. Regardless of initial disturbance, after a decade communities converged on steady states largely determined by resource availability, where species turnover declined as communities approached dynamic equilibria. Species favoured by the disturbance were those that eventually came to dominate the highly fertilized plots. Furthermore, disturbance made successional pathways more direct revealing an important interaction effect between nutrients and disturbance as drivers of community change. Our results underscore the dynamical nature of grassland and old field succession, demonstrating how community properties such as β $$ \beta $$ diversity change through transient and equilibrium states.

Multimodal distribution of transient time of predator extinction in a three-species food chain

The transient dynamics capture the time history in the behavior of a system before reaching an attractor. This paper deals with the statistics of transient dynamics in a classic tri-trophic food chain with bistability. The species of the food chain model either coexist or undergo a partial extinction with predator death after a transient time depending upon the initial population density. The distribution of transient time to predator extinction shows interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. More precisely, the distribution shows a multimodal character when the initial points are located near a basin boundary and a unimodal character when chosen from a location far away from the boundary. The distribution is also anisotropic because the number of modes depends on the direction of the local of initial points. We define two new metrics, viz., homogeneity index and local isotropic index, to characterize the distinctive features of the distribution. We explain the origin of such multimodal distributions and try to present their ecological implications.

Neural timescales reflect behavioral demands in freely moving rhesus macaques

Previous work has demonstrated remarkably reproducible and consistent hierarchies of neural timescales across cortical areas at rest. The question arises how such stable hierarchies give rise to adaptive behavior that requires flexible adjustment of temporal coding and integration demands. Potentially, this previously found lack of variability in the hierarchical organization of neural timescales could be a reflection of the structure of the laboratory contexts in which they were measured. Indeed, computational work demonstrates the existence of multiple temporal hierarchies within the same anatomical network when the input structure is altered. We posit that unconstrained behavioral environments where relatively little temporal demands are imposed from the experimenter are an ideal test bed to address the question of whether the hierarchical organization and the magnitude of neural timescales reflect ongoing behavioral demands. To tackle this question, we measured timescales of local field potential activity while rhesus macaques were foraging freely in a large open space. We find a hierarchy of neural timescales that is unique to this foraging environment. Importantly, although the magnitude of neural timescales generally expanded with task engagement, the brain areas' relative position in the hierarchy was stable across the recording sessions. Notably, the magnitude of neural timescales monotonically expanded with task engagement across a relatively long temporal scale spanning the duration of the recording session. Over shorter temporal scales, the magnitude of neural timescales changed dynamically around foraging events. Moreover, the change in the magnitude of neural timescales contained functionally relevant information, differentiating between seemingly similar events in terms of motor demands and associated reward. That is, the patterns of change were associated with the cognitive and behavioral meaning of these events. Finally, we demonstrated that brain areas were differentially affected by these behavioral demands - i.e., the expansion of neural timescales was not the same across all areas. Together, these results demonstrate that the observed hierarchy of neural timescales is context-dependent and that changes in the magnitude of neural timescales are closely related to overall task engagement and behavioral demands.

Demographic Basis of Spatially Structured Fluctuations in a Threespine Stickleback Metapopulation

AbstractUncovering the demographic basis of population fluctuations is a central goal of population biology. This is particularly challenging for spatially structured populations, which require disentangling synchrony in demographic rates from coupling via movement between locations. In this study, we fit a stage-structured metapopulation model to a 29-year time series of threespine stickleback abundance in the heterogeneous and productive Lake Mývatn, Iceland. The lake comprises two basins (North and South) connected by a channel through which the stickleback disperse. The model includes time-varying demographic rates, allowing us to assess the potential contributions of recruitment and survival, spatial coupling via movement, and demographic transience to the population's large fluctuations in abundance. Our analyses indicate that recruitment was only modestly synchronized between the two basins, whereas survival probabilities of adults were more strongly synchronized, contributing to cyclic fluctuations in the lake-wide population size with a period of approximately 6 years. The analyses further show that the two basins were coupled through movement, with the North Basin subsidizing the South Basin and playing a dominant role in driving the lake-wide dynamics. Our results show that cyclic fluctuations of a metapopulation can be explained in terms of the combined effects of synchronized demographic rates and spatial coupling.

Towards a heuristic understanding of the storage effect

The storage effect is a general explanation for coexistence in a variable environment. Unfortunately, the storage effect is poorly understood, in part because the generality of the storage effect precludes an interpretation that is simultaneously simple, intuitive and correct. Here, we explicate the storage effect by dividing one of its key conditions-covariance between environment and competition-into two pieces, namely that there must be a strong causal relationship between environment and competition, and that the effects of the environment do not change too quickly. This finer-grained definition can explain a number of previous results, including (1) that the storage effect promotes annual plant coexistence when the germination rate fluctuates, but not when the seed yield fluctuates, (2) that the storage effect is more likely to be induced by resource competition than the apparent competition, and (3) why the storage effect arises readily in models with either stage structure or environmental autocorrelation. Additionally, our expanded definition suggests two novel mechanisms by which the temporal storage effect can arise-transgenerational plasticity and causal chains of environmental variables-thus suggesting that the storage effect is a more common phenomenon than previously thought.

Simulation applications to support teaching and research in epidemiological dynamics

BACKGROUND

An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMP ^Ⓡ (Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs.

RESULTS

We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that 'burn' through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive value R₀, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value of R₀>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality.

CONCLUSION

Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.

Fast environmental change and eco-evolutionary feedbacks can drive regime shifts in ecosystems before tipping points are crossed

Anthropogenic environmental changes are altering ecological and evolutionary processes of ecosystems. The possibility that ecosystems can respond abruptly to gradual environmental change when critical thresholds are crossed (i.e. tipping points) and shift to an alternative stable state is a growing concern. Here I show that fast environmental change can trigger regime shifts before environmental stress exceeds a tipping point in evolving ecological systems. The difference in the time scales of coupled ecological and evolutionary processes makes ecosystems sensitive not only to the magnitude of environmental changes, but also to the rate at which changes are imposed. Fast evolutionary change mediated by high trait variation can reduce the sensitivity of ecosystems to the rate of environmental change and prevent the occurrence of rate-induced regime shifts. This suggests that management measures to prevent rate-induced regime shifts should focus on mitigating the effects of environmental change and protecting phenotypic diversity in ecosystems.

A resilience concept based on system functioning: A dynamical systems perspective

We introduce a new framework for resilience, which is traditionally understood as the ability of a system to absorb disturbances and maintain its state, by proposing a shift from a state-based to a system functioning-based approach to resilience, which takes into account that several different coexisting stable states could fulfill the same functioning. As a consequence, not every regime shift, i.e., transition from one stable state to another, is associated with a lack or loss of resilience. We emphasize the importance of flexibility-the ability of a system to shift between different stable states while still maintaining system functioning. Furthermore, we provide a classification of system responses based on the phenomenological properties of possible disturbances, including the role of their timescales. Therefore, we discern fluctuations, shocks, press disturbances, and trends as possible disturbances. We distinguish between two types of mechanisms of resilience: (i) tolerance and flexibility, which are properties of the system, and (ii) adaptation and transformation, which are processes that alter the system's tolerance and flexibility. Furthermore, we discuss quantitative methods to investigate resilience in model systems based on approaches developed in dynamical systems theory.

Evaluating the performance of multivariate indicators of resilience loss

Various complex systems, such as the climate, ecosystems, and physical and mental health can show large shifts in response to small changes in their environment. These 'tipping points' are notoriously hard to predict based on trends. However, in the past 20 years several indicators pointing to a loss of resilience have been developed. These indicators use fluctuations in time series to detect critical slowing down preceding a tipping point. Most of the existing indicators are based on models of one-dimensional systems. However, complex systems generally consist of multiple interacting entities. Moreover, because of technological developments and wearables, multivariate time series are becoming increasingly available in different fields of science. In order to apply the framework of resilience indicators to multivariate time series, various extensions have been proposed. Not all multivariate indicators have been tested for the same types of systems and therefore a systematic comparison between the methods is lacking. Here, we evaluate the performance of the different multivariate indicators of resilience loss in different scenarios. We show that there is not one method outperforming the others. Instead, which method is best to use depends on the type of scenario the system is subject to. We propose a set of guidelines to help future users choose which multivariate indicator of resilience is best to use for their particular system.

New forms of structure in ecosystems revealed with the Kuramoto model

Ecological systems, as is often noted, are complex. Equally notable is the generalization that complex systems tend to be oscillatory, whether Huygens' simple patterns of pendulum entrainment or the twisted chaotic orbits of Lorenz' convection rolls. The analytics of oscillators may thus provide insight into the structure of ecological systems. One of the most popular analytical tools for such study is the Kuramoto model of coupled oscillators. We apply this model as a stylized vision of the dynamics of a well-studied system of pests and their enemies, to ask whether its actual natural history is reflected in the dynamics of the qualitatively instantiated Kuramoto model. Emerging from the model is a series of synchrony groups generally corresponding to subnetworks of the natural system, with an overlying chimeric structure, depending on the strength of the inter-oscillator coupling. We conclude that the Kuramoto model presents a novel window through which interesting questions about the structure of ecological systems may emerge.

Management implications of long transients in ecological systems

The underlying biological processes that govern many ecological systems can create very long periods of transient dynamics. It is often difficult or impossible to distinguish this transient behaviour from similar dynamics that would persist indefinitely. In some cases, a shift from the transient to the long-term, stable dynamics may occur in the absence of any exogenous forces. Recognizing the possibility that the state of an ecosystem may be less stable than it appears is crucial to the long-term success of management strategies in systems with long transient periods. Here we demonstrate the importance of considering the potential of transient system behaviour for management actions across a range of ecosystem organizational scales and natural system types. Developing mechanistic models that capture essential system dynamics will be crucial for promoting system resilience and avoiding system collapses.

How long do population level field experiments need to be? Utilising data from the 40-year-old LTER network

We utilise the wealth of data accessible through the 40-year-old Long-Term Ecological Research (LTER) network to ask if aspects of the study environment or taxa alter the duration of research necessary to detect consistent results. To do this, we use a moving-window algorithm. We limit our analysis to long-term (> 10 year) press experiments recording organismal abundance. We find that studies conducted in dynamic abiotic environments need longer periods of study to reach consistent results, as compared to those conducted in more moderated environments. Studies of plants were more often characterised by spurious results than those on animals. Nearly half of the studies we investigated required 10 years or longer to become consistent, where all significant trends agreed in direction, and four studies (of 100) required longer than 20 years. Here, we champion the importance of long-term data and bolster the value of multi-decadal experiments in understanding, explaining and predicting long-term trends.

The characteristic time of ecological communities

A simple description of temporal dynamics of ecological communities may help us understand how community assembly proceeds, predict ecological responses to environmental disturbances, and improve the performance of biological conservation actions. Although community changes take place at multiple temporal scales, the variation of species composition and richness over time across communities and habitats shows general patterns that may potentially reveal the main drivers of community dynamics. We used the simplest stochastic model of island biogeography to propose two quantities to characterize community dynamics: the community characteristic time, as a measure of the typical time scale of species‐richness change, and the characteristic Jaccard index, as a measure of temporal β diversity, that is, the variation of community composition over time. In addition, the community characteristic time, which sets the temporal scale at which null, noninteracting species assemblages operate, allowed us to define a relative sampling frequency (to the characteristic time). Here we estimate these quantities across microbial and macroscopic species assemblages to highlight two related results. First, we illustrated both characteristic time and Jaccard index and their relation with classic time‐series in ecology, and found that the most thoroughly sampled communities, relative to their characteristic time, presented the largest similarity between consecutive samples. Second, our analysis across a variety of habitats and taxa show that communities span a large range of species turnover, from potentially very fast (short characteristic times) to rather slow (long characteristic times) communities. This was in agreement with previous knowledge, but indicated that some habitats may have been sampled less frequently than required. Our work provides new perspectives to explore the temporal component in ecological studies and highlights the usefulness of simple approximations to the complex dynamics of ecological communities.

Mitigating long transient time in deterministic systems by resetting

How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest and has stimulated a lot of activities in dynamical and stochastic systems where the metric of this estimation is often known as the transient or first passage time. In nonlinear systems, one often experiences long transients due to their underlying dynamics. We apply resetting or restart, an emerging concept in statistical physics and stochastic process, to mitigate the detrimental effects of prolonged transients in deterministic dynamical systems. We show that resetting the intrinsic dynamics intermittently to a spatial control line that passes through the equilibrium point can dramatically expedite its completion, resulting in a huge reduction in mean transient time and fluctuations around it. Moreover, our study reveals the emergence of an optimal restart time that globally minimizes the mean transient time. We corroborate the results with detailed numerical studies on two canonical setups in deterministic dynamical systems, namely, the Stuart-Landau oscillator and the Lorenz system. The key features-expedition of transient time-are found to be very generic under different resetting strategies. Our analysis opens up a door to control the mean and fluctuations in transient time by unifying the original dynamics with an external stochastic or periodic timer and poses open questions on the optimal way to harness transients in dynamical systems.

Genes and environments, development and time

A now substantial body of science implicates a dynamic interplay between genetic and environmental variation in the development of individual differences in behavior and health. Such outcomes are affected by molecular, often epigenetic, processes involving gene-environment (G-E) interplay that can influence gene expression. Early environments with exposures to poverty, chronic adversities, and acutely stressful events have been linked to maladaptive development and compromised health and behavior. Genetic differences can impart either enhanced or blunted susceptibility to the effects of such pathogenic environments. However, largely missing from present discourse regarding G-E interplay is the role of time, a "third factor" guiding the emergence of complex developmental endpoints across different scales of time. Trajectories of development increasingly appear best accounted for by a complex, dynamic interchange among the highly linked elements of genes, contexts, and time at multiple scales, including neurobiological (minutes to milliseconds), genomic (hours to minutes), developmental (years and months), and evolutionary (centuries and millennia) time. This special issue of PNAS thus explores time and timing among G-E transactions: The importance of timing and timescales in plasticity and critical periods of brain development; epigenetics and the molecular underpinnings of biologically embedded experience; the encoding of experience across time and biological levels of organization; and gene-regulatory networks in behavior and development and their linkages to neuronal networks. Taken together, the collection of papers offers perspectives on how G-E interplay operates contingently within and against a backdrop of time and timescales.

The macroecology of the COVID-19 pandemic in the Anthropocene

Severe acute respiratory syndrome coronavirus 2, the virus that causes coronavirus disease 2019 (COVID-19), has expanded rapidly throughout the world. Thus, it is important to understand how global factors linked with the functioning of the Anthropocene are responsible for the COVID-19 outbreak. We tested hypotheses that the number of COVID-19 cases, number of deaths and growth rate of recorded infections: (1) are positively associated with population density as well as (2) proportion of the human population living in urban areas as a proxies of interpersonal contact rate, (3) age of the population in a given country as an indication of that population's susceptibility to COVID-19; (4) net migration rate and (5) number of tourists as proxies of infection pressure, and negatively associated with (5) gross domestic product which is a proxy of health care quality. Data at the country level were compiled from publicly available databases and analysed with gradient boosting regression trees after controlling for confounding factors (e.g. geographic location). We found a positive association between the number of COVID-19 cases in a given country and gross domestic product, number of tourists, and geographic longitude. The number of deaths was positively associated with gross domestic product, number of tourists in a country, and geographic longitude. The effects of gross domestic product and number of tourists were non-linear, with clear thresholds above which the number of COVID-19 cases and deaths increased rapidly. The growth rate of COVID-19 cases was positively linked to the number of tourists and gross domestic product. The growth rate of COVID-19 cases was negatively associated with the mean age of the population and geographic longitude. Growth was slower in less urbanised countries. This study demonstrates that the characteristics of the human population and high mobility, but not population density, may help explain the global spread of the virus. In addition, geography, possibly via climate, may play a role in the pandemic. The unexpected positive and strong association between gross domestic product and number of cases, deaths, and growth rate suggests that COVID-19 may be a new civilisation disease affecting rich economies.

How pulse disturbances shape size-abundance pyramids

Ecological pyramids represent the distribution of abundance and biomass of living organisms across body-sizes. Our understanding of their expected shape relies on the assumption of invariant steady-state conditions. However, most of the world's ecosystems experience disturbances that keep them far from such a steady state. Here, using the allometric scaling between population growth rate and body-size, we predict the response of size-abundance pyramids within a trophic guild to any combination of disturbance frequency and intensity affecting all species in a similar way. We show that disturbances narrow the base of size-abundance pyramids, lower their height and decrease total community biomass in a nonlinear way. An experimental test using microbial communities demonstrates that the model captures well the effect of disturbances on empirical pyramids. Overall, we demonstrate both theoretically and experimentally how disturbances that are not size-selective can nonetheless have disproportionate impacts on large species.

Influence of protogynous sex change on recovery of fish populations within marine protected areas

Marine protected areas (MPAs) are increasingly implemented as a conservation tool worldwide. In many cases, they are managed adaptively: the abundance of target species is monitored, and observations are compared to some model-based expectation for the trajectory of population recovery to ensure that the MPA is achieving its goals. Most previous analyses of the transient (short-term) response of populations to the cessation of fishing inside MPAs have dealt only with gonochore (fixed-sex) species. However, many important fishery species are protogynous hermaphrodites (female-to-male sex-changing). Because size-selective harvest will predominantly target males in these species, harvesting not only reduces abundance but also skews the sex ratio toward females. Thus the response to MPA implementation will involve changes in both survival and sex ratio, and ultimately reproductive output. We used an age-structured model of a generic sex-changing fish population to compare transient population dynamics after MPA implementation to those of an otherwise similar gonochore population and examine how different features of sex-changing life history affect those dynamics. We examined both demographically open (most larval recruitment comes from outside the MPA) and demographically closed (most larval recruitment is locally produced) dynamics. Under both scenarios, population recovery of protogynous species takes longer when fishing was more intense pre-MPA (as in gonochores), but also depends heavily on the mating function, the degree to which the sex ratio affects reproduction. If few males are needed and reproduction is not affected by a highly female-biased sex ratio, then population recovery is much faster; if males are a limiting resource, then increases in abundance after MPA implementation are much slower than for gonochores. Unfortunately, the mating function is largely unknown for fishes. In general, we expect that most protogynous species with haremic mating systems will be in the first category (few males needed), though there is at least one example of a fish species (though not a sex-changing species) for which males are limiting. Thus a better understanding of the importance of male fish to population dynamics is needed for the adaptive management of MPAs.

Differentiation strategies of soil rare and abundant microbial taxa in response to changing climatic regimes

Despite the important roles of soil microbes, especially the most diverse rare taxa in maintaining community diversity and multifunctionality, how different climate regimes alter the stability and functions of the rare microbial biosphere remains unknown. We reciprocally transplanted field soils across a latitudinal gradient to simulate climate change and sampled the soils annually after harvesting the maize over the following 6 years (from 2005 to 2011). By sequencing microbial 16S ribosomal RNA gene amplicons, we found that changing climate regimes significantly altered the composition and dynamics of soil microbial communities. A continuous succession of the rare and abundant communities was observed. Rare microbial communities were more stable under changing climatic regimes, with lower variations in temporal dynamics, and higher stability and constancy of diversity. More nitrogen cycling genes were detected in the rare members than in the abundant members, including amoA, napA, nifH, nirK, nirS, norB and nrfA. Random forest analysis and receiver operating characteristics analysis showed that rare taxa may act as potential contributors to maize yield under changing climatics. The study indicates that the taxonomically and functionally diverse rare biosphere has the potential to increase functional redundancy and enhance the ability of soil communities to counteract environmental disturbances. With ongoing global climate change, exploring the succession process and functional changes of rare taxa may be important in elucidating the ecosystem stability and multifunctionality that are mediated by microbial communities.

Effects of density dependence and climatic factors on population dynamics of Cricetulus barabensis: a 25-year field study

Rodents often act as keystone species in communities and play important roles in shaping structures and functions of many ecosystems. Understanding the underlying mechanisms of population fluctuation in rodents is therefore of great interest. Using the data from a 25-year field survey carried out in Inner Mongolia, China, we explored the effects of density dependence, local climatic factors, and a large-scale climatic perturbation (El Niño–Southern Oscillation) on the population dynamics of the striped hamster (Cricetulus barabensis), a rodent widely distributed in northern China. We detected a strong negative density-dependent effect on the population dynamics of C. barabensis. Rainfall had a significant positive effect on population change with a 1-year lag. The pregnancy rate of C. barabensis was negatively affected by the annual mean temperature in the current year, but positively associated with the population density in the current year and the annual Southern Oscillation Index in the previous year. Moving-window analyses suggested that, with a window length of 12 years, there was a significant interaction between rainfall and density dependence, with increasing rainfall alleviating the negative effect of density dependence. As C. barabensis often causes agricultural damage and can transmit zoonotic diseases to human beings, our results also have implications for pest and disease control.

Integrating the underlying structure of stochasticity into community ecology

Stochasticity is a core component of ecology, as it underlies key processes that structure and create variability in nature. Despite its fundamental importance in ecological systems, the concept is often treated as synonymous with unpredictability in community ecology, and studies tend to focus on single forms of stochasticity rather than taking a more holistic view. This has led to multiple narratives for how stochasticity mediates community dynamics. Here, we present a framework that describes how different forms of stochasticity (notably demographic and environmental stochasticity) combine to provide underlying and predictable structure in diverse communities. This framework builds on the deep ecological understanding of stochastic processes acting at individual and population levels and in modules of a few interacting species. We support our framework with a mathematical model that we use to synthesize key literature, demonstrating that stochasticity is more than simple uncertainty. Rather, stochasticity has profound and predictable effects on community dynamics that are critical for understanding how diversity is maintained. We propose next steps that ecologists might use to explore the role of stochasticity for structuring communities in theoretical and empirical systems, and thereby enhance our understanding of community dynamics.

Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations

Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and numerical studies have demonstrated that improved differential equations for mean and variance of infected individuals reproduce certain regimes of the SIS epidemic model. Here, we show they form a dynamical system that follows Hamilton’s equations, which allow us to understand the role of fluctuations and their effects on epidemics. Our findings show the Hamiltonian is a constant of motion for large population sizes. For small populations, finite size effects break the temporal symmetry and induce a power-law decay of the Hamiltonian near the outbreak onset, with a parameter-free exponent. Away from the onset, the Hamiltonian decays exponentially according to a constant relaxation time, which we propose as a metric when fluctuations cannot be neglected.

Heterogeneous local dynamics revealed by classification analysis of spatially disaggregated time series data

Time series data provide a crucial window into infectious disease dynamics, yet their utility is often limited by the spatially aggregated form in which they are presented. When working with time series data, violating the implicit assumption of homogeneous dynamics below the scale of spatial aggregation could bias inferences about underlying processes. We tested this assumption in the context of the 2015-2016 Zika epidemic in Colombia, where time series of weekly case reports were available at national, departmental, and municipal scales. First, we performed a descriptive analysis, which showed that the timing of departmental-level epidemic peaks varied by three months and that departmental-level estimates of the time-varying reproduction number, R(t), showed patterns that were distinct from a national-level estimate. Second, we applied a classification algorithm to six features of proportional cumulative incidence curves, which showed that variability in epidemic duration, the length of the epidemic tail, and consistency with a cumulative normal density curve made the greatest contributions to distinguishing groups. Third, we applied this classification algorithm to data simulated with a stochastic transmission model, which showed that group assignments were consistent with simulated differences in the basic reproduction number, R₀. This result, along with associations between spatial drivers of transmission and group assignments based on observed data, suggests that the classification algorithm is capable of detecting differences in temporal patterns that are associated with differences in underlying drivers of incidence patterns. Overall, this diversity of temporal patterns at local scales underscores the value of spatially disaggregated time series data.

Influence of aggregation on benthic coral reef spatio-temporal dynamics

Spatial patterning of coral reef sessile benthic organisms can constrain competitive and demographic rates, with implications for dynamics over a range of time scales. However, techniques for quantifying and analysing reefscape behaviour, particularly at short to intermediate time scales (weeks to decades), are lacking. An analysis of the dynamics of coral reefscapes simulated with a lattice model shows consistent trends that can be categorized into four stages: a repelling stage that moves rapidly away from an unstable initial condition, a transient stage where spatial rearrangements bring key competitors into contact, an attracting stage where the reefscape decays to a steady-state attractor, and an attractor stage. The transient stage exhibits nonlinear dynamics, whereas the other stages are linear. The relative durations of the stages are affected by the initial spatial configuration as characterized by coral aggregation-a measure of spatial clumpiness, which together with coral and macroalgae fractional cover, more completely describe modelled reefscape dynamics. Incorporating diffusional processes results in aggregated patterns persisting in the attractor. Our quantitative characterization of reefscape dynamics has possible applications to other spatio-temporal systems and implications for reef restoration: high initial aggregation patterns slow losses in herbivore-limited systems and low initial aggregation configurations accelerate growth in herbivore-dominated systems.

Tropical forests can maintain hyperdiversity because of enemies

Explaining the maintenance of tropical forest diversity under the countervailing forces of drift and competition poses a major challenge to ecological theory. Janzen-Connell effects, in which host-specific natural enemies restrict the recruitment of juveniles near conspecific adults, provide a potential mechanism. Janzen-Connell is strongly supported empirically, but existing theory does not address the stable coexistence of hundreds of species. Here we use high-performance computing and analytical models to demonstrate that tropical forest diversity can be maintained nearly indefinitely in a prolonged state of transient dynamics due to distance-responsive natural enemies. Further, we show that Janzen-Connell effects lead to community regulation of diversity by imposing a diversity-dependent cost to commonness and benefit to rarity. The resulting species-area and rank-abundance relationships are consistent with empirical results. Diversity maintenance over long time spans does not require dispersal from an external metacommunity, speciation, or resource niche partitioning, only a small zone around conspecific adults in which saplings fail to recruit. We conclude that the Janzen-Connell mechanism can explain the maintenance of tropical tree diversity while not precluding the operation of other niche-based mechanisms such as resource partitioning.

Evolution of dispersal in spatial population models with multiple timescales

We study the evolutionary stability of dispersal strategies, including but not limited to those that can produce ideal free population distributions (that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium). The environment is assumed to be variable in space but constant in time. We assume that there is a separation of times scales, so that dispersal occurs on a fast timescale, evolution occurs on a slow timescale, and population dynamics and interactions occur on an intermediate timescale. Starting with advection-diffusion models for dispersal without population dynamics, we use the large time limits of profiles for population distributions together with the distribution of resources in the environment to calculate growth and interaction coefficients in logistic and Lotka-Volterra ordinary differential equations describing population dynamics. We then use a pairwise invasibility analysis approach motivated by adaptive dynamics to study the evolutionary and/or convergence stability of strategies determined by various assumptions about the advection and diffusion terms in the original advection-diffusion dispersal models. Among other results we find that those strategies which can produce an ideal free distribution are evolutionarily stable.

Transient phenomena in ecology

The importance of transient dynamics in ecological systems and in the models that describe them has become increasingly recognized. However, previous work has typically treated each instance of these dynamics separately. We review both empirical examples and model systems, and outline a classification of transient dynamics based on ideas and concepts from dynamical systems theory. This classification provides ways to understand the likelihood of transients for particular systems, and to guide investigations to determine the timing of sudden switches in dynamics and other characteristics of transients. Implications for both management and underlying ecological theories emerge.

Propagule size and structure, life history, and environmental conditions affect establishment success of an invasive species

Population dynamics of species that are recently introduced into a new area, e.g., invasive species and species of conservation concern that are translocated to support global populations, are likely to be dominated by short-term, transient effects. Wild pigs (Sus scrofa, or wild boar) are pulsed-resource consumers of mast nuts that are commonly introduced into new areas. We used vital rate data (i.e., survival and fecundity) for wild pigs in Germany under varying forage conditions to simulate transient population dynamics in the 10-years following introduction into a new environment. In a low forage environment (i.e., conditions similar to their native range), simulated wild pig populations maintained a stable population size with low probability of establishment, while in environments with better quality forage (i.e., conditions similar to parts of their invasive range), high juvenile fecundity and survival facilitated rapid population growth and establishment probability was high. We identified a strategy for simulating population dynamics of species whose reproduction and survival depend on environmental conditions that fluctuate and for predicting establishment success of species introduced into a new environment. Our approach can also be useful in projecting near-term transient population dynamics for many conservation and management applications.

Abrupt Change in Ecological Systems: Inference and Diagnosis

Abrupt ecological changes are, by definition, those that occur over short periods of time relative to typical rates of change for a given ecosystem. The potential for such changes is growing due to anthropogenic pressures, which challenges the resilience of societies and ecosystems. Abrupt ecological changes are difficult to diagnose because they can arise from a variety of circumstances, including rapid changes in external drivers (e.g., climate, or resource extraction), nonlinear responses to gradual changes in drivers, and interactions among multiple drivers and disturbances. We synthesize strategies for identifying causes of abrupt ecological change and highlight instances where abrupt changes are likely. Diagnosing abrupt changes and inferring causation are increasingly important as society seek to adapt to rapid, multifaceted environmental changes.

Inferring genetic connectivity in real populations, exemplified by coastal and oceanic Atlantic cod

Estimates of migration are important for understanding the dynamics of natural populations. A statistic known as F_ST is often used to measure levels of genetic differentiation among natural populations. Equations that translate F_ST into estimates of migration are based on “ideal” populations, which are subject to many simplifying assumptions compared with real populations. Therefore, theoretical estimates of migration might not be realistic. We modeled populations of Atlantic cod in the North Sea and the adjacent Skagerrak region to compare how migration is related to the complexities of real populations, and how actual migration compares with predictions based on theory. Results are intended to help apply population genetic theory to practical situations.

Genetic data are commonly used to estimate connectivity between putative populations, but translating them to demographic dispersal rates is complicated. Theoretical equations that infer a migration rate based on the genetic estimator F_ST, such as Wright’s equation, F_ST ≈ 1/(4N_em + 1), make assumptions that do not apply to most real populations. How complexities inherent to real populations affect migration was exemplified by Atlantic cod in the North Sea and Skagerrak and was examined within an age-structured model that incorporated genetic markers. Migration was determined under various scenarios by varying the number of simulated migrants until the mean simulated level of genetic differentiation matched a fixed level of genetic differentiation equal to empirical estimates. Parameters that decreased the N_e/N_t ratio (where N_e is the effective and N_t is the total population size), such as high fishing mortality and high fishing gear selectivity, increased the number of migrants required to achieve empirical levels of genetic differentiation. Higher maturity-at-age and lower selectivity increased N_e/N_t and decreased migration when genetic differentiation was fixed. Changes in natural mortality, fishing gear selectivity, and maturity-at-age within expected limits had a moderate effect on migration when genetic differentiation was held constant. Changes in population size had the greatest effect on the number of migrants to achieve fixed levels of F_ST, particularly when genetic differentiation was low, F_ST ≈ 10⁻³. Highly variable migration patterns, compared with constant migration, resulted in higher variance in genetic differentiation and higher extreme values. Results are compared with and provide insight into the use of theoretical equations to estimate migration among real populations.

Epidemicity thresholds for water-borne and water-related diseases

Determining the conditions that favor pathogen establishment in a host community is key to disease control and eradication. However, focusing on long-term dynamics alone may lead to an underestimation of the threats imposed by outbreaks triggered by short-term transient phenomena. Achieving an effective epidemiological response thus requires to look at different timescales, each of which may be endowed with specific management objectives. In this work we aim to determine epidemicity thresholds for some prototypical examples of water-borne and water-related diseases, a diverse family of infections transmitted either directly through water infested with pathogens or by vectors whose lifecycles are closely associated with water. From a technical perspective, while conditions for endemicity are determined via stability analysis, epidemicity thresholds are defined through generalized reactivity analysis, a recently proposed method that allows the study of the short-term instability properties of ecological systems. Understanding the drivers of water-borne and water-related disease dynamics over timescales that may be relevant to epidemic and/or endemic transmission is a challenge of the utmost importance, as large portions of the developing world are still struggling with the burden imposed by these infections.

Transient synchrony among populations of five foliage-feeding Lepidoptera

Studies of transient population dynamics have largely focused on temporal changes in dynamical behaviour, such as the transition between periods of stability and instability. This study explores a related dynamic pattern, namely transient synchrony during a 49-year period among populations of five sympatric species of forest insects that share host tree resources. The long time series allows a more comprehensive exploration of transient synchrony patterns than most previous studies. Considerable variation existed in the dynamics of individual species, ranging from periodic to aperiodic. We used time-averaged methods to investigate long-term patterns of synchrony and time-localized methods to detect transient synchrony. We investigated transient patterns of synchrony between species and related these to the species' varying density dependence structures; even species with very different density dependence exhibited at least temporary periods of synchrony. Observed periods of interspecific synchrony may arise from interactions with host trees (e.g., induced host defences), interactions with shared natural enemies or shared impacts of environmental stochasticity. The transient nature of synchrony observed here raises questions both about the identity of synchronizing mechanisms and how these mechanisms interact with the endogenous dynamics of each species. We conclude that these patterns are the result of interspecific interactions that act only temporarily to synchronize populations, after which differences in the endogenous population dynamics among the species acts to desynchronize their dynamics.

Predicting tipping points in mutualistic networks through dimension reduction

Complex systems in many fields, because of their intrinsic nonlinear dynamics, can exhibit a tipping point (point of no return) at which a total collapse of the system occurs. In ecosystems, environmental deterioration can lead to evolution toward a tipping point. To predict tipping point is an outstanding and extremely challenging problem. Using complex bipartite mutualistic networks, we articulate a dimension reduction strategy and establish its general applicability to predicting tipping points using a large number of empirical networks. Not only can our reduced model serve as a paradigm for understanding the tipping point dynamics in real world ecosystems for safeguarding pollinators, the principle can also be extended to other disciplines to address critical issues, such as resilience and sustainability.

Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a “point of no return”) at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability.

How ecosystems recover from pulse perturbations: A theory of short- to long-term responses

Quantifying stability properties of ecosystems is an important problem in ecology. A common approach is based on the recovery from pulse perturbations, and posits that the faster an ecosystem return to its pre-perturbation state, the more stable it is. Theoretical studies often collapse the recovery dynamics into a single quantity: the long-term rate of return, called asymptotic resilience. However, empirical studies typically measure the recovery dynamics at much shorter time scales. In this paper we explain why asymptotic resilience is rarely representative of the short-term recovery. First, we show that, in contrast to asymptotic resilience, short-term return rates depend on features of the perturbation, in particular on the way its intensity is distributed over species. We argue that empirically relevant predictions can be obtained by considering the median response over a set of perturbations, for which we provide explicit formulas. Next, we show that the recovery dynamics are controlled through time by different species: abundant species tend to govern the short-term recovery, while rare species often dominate the long-term recovery. This shift from abundant to rare species typically causes short-term return rates to be unrelated to asymptotic resilience. We illustrate that asymptotic resilience can be determined by rare species that have almost no effect on the observable part of the recovery dynamics. Finally, we discuss how these findings can help to better connect empirical observations and theoretical predictions.

Interpreting beta-diversity components over time to conserve metacommunities in highly dynamic ecosystems

The concept of metacommunity (i.e., a set of local communities linked by dispersal) has gained great popularity among community ecologists. However, metacommunity research mostly addresses questions on spatial patterns of biodiversity at the regional scale, whereas conservation planning requires quantifying temporal variation in those metacommunities and the contributions that individual (local) sites make to regional dynamics. We propose that recent advances in diversity-partitioning methods may allow for a better understanding of metacommunity dynamics and the identification of keystone sites. We used time series of the 2 components of beta diversity (richness and replacement) and the contributions of local sites to these components to examine which sites controlled source-sink dynamics in a highly dynamic model system (an intermittent river). The relative importance of the richness and replacement components of beta diversity fluctuated over time, and sample aggregation led to underestimation of beta diversity by up to 35%. Our literature review revealed that research on intermittent rivers would benefit greatly from examination of beta-diversity components over time. Adequately appraising spatiotemporal variability in community composition and identifying sites that are pivotal for maintaining biodiversity at the landscape scale are key needs for conservation prioritization and planning. Thus, our framework may be used to guide conservation actions in highly dynamic ecosystems when time-series data describing biodiversity across sites connected by dispersal are available.