Ecology, evolution and 1f-noise

Population dynamics in a time-varying environment with fat-tailed correlations

Temporal environmental noise (EN) is a prevalent natural phenomenon that controls population and community dynamics, shaping the destiny of biological species and genetic types. Conventional theoretical models often depict EN as a Markovian process with an exponential distribution of correlation times, resulting in two distinct qualitative dynamical categories: quenched (long environmental timescales) and annealed (short environmental timescales). However, numerous empirical studies demonstrate a fat-tailed decay of correlation times. Here we study the consequences of power-law correlated EN on the dynamics of isolated and competing populations. We analyze the intermediate region that lies between the quenched and annealed regimes and show that it can widen indefinitely. Within this region, dynamics is primarily driven by rare, yet not exceedingly rare, long periods of almost-steady environmental conditions. For an isolated population, the time to extinction in this region exhibits a power-law scaling with the logarithm of the abundance and also a nonmonotonic dependence on the spectral exponent.

Effects of auditory noise intensity and color on the dynamics of upright stance

Previous work assessing the effect of additive noise on the postural control system has found a positive effect of additive white noise on postural dynamics. This study covers two separate experiments that were run sequentially to better understand how the structure of the additive noise signal affects postural dynamics, while also furthering our knowledge of how the intensity of auditory stimulation of noise may elicit this phenomenon. Across the two experiments, we introduced three auditory noise stimulations of varying structure (white, pink, and brown noise). Experiment 1 presented the stimuli at 35 dB while Experiment 2 was presented at 75 dB. Our findings demonstrate a decrease in variability of the postural control system regardless of the structure of the noise signal presented, but only for high intensity auditory stimulation.

Simulating the Effect of Environmental Change on Evolving Populations

This study uses evolutionary simulations to explore the strategies that emerge to enable populations to cope with random environmental changes in situations where lifetime learning approaches are not available to accommodate them. In particular, it investigates how the average magnitude of change per unit time and the persistence of the changes (and hence the resulting autocorrelation of the environmental time series) affect the change tolerances, population diversities, and extinction timescales that emerge. Although it is the change persistence (often discussed in terms of environmental noise color) that has received most attention in the recent literature, other factors, particularly the average change magnitude, interact with this and can be more important drivers of the adaptive strategies that emerge. Moreover, when running simulations, the choice of change representation and normalization can also affect the outcomes. Detailed simulations are presented that are designed to explore all these issues. They also reveal significant dependences on the associated mutation rates and the extent to which they can evolve, and they clarify how evolution often leads populations into strategies with higher risks of extinction. Overall, this study shows how modeling the effect of environmental change requires more care than may have previously been realized.

From biological data to oscillator models using SINDy

Periodic changes in the concentration or activity of different molecules regulate vital cellular processes such as cell division and circadian rhythms. Developing mathematical models is essential to better understand the mechanisms underlying these oscillations. Recent data-driven methods like SINDy have fundamentally changed model identification, yet their application to experimental biological data remains limited. This study investigates SINDy's constraints by directly applying it to biological oscillatory data. We identify insufficient resolution, noise, dimensionality, and limited prior knowledge as primary limitations. Using various generic oscillator models of different complexity and/or dimensionality, we systematically analyze these factors. We then propose a comprehensive guide for inferring models from biological data, addressing these challenges step by step. Our approach is validated using glycolytic oscillation data from yeast.

Processes governing species richness in communities exposed to temporal environmental stochasticity: A review and synthesis of modelling approaches

Research into the processes governing species richness has often assumed that the environment is fixed, whereas realistic environments are often characterised by random fluctuations over time. This temporal environmental stochasticity (TES) changes the demographic rates of species populations, with cascading effects on community dynamics and species richness. Theoretical and applied studies have used process-based mathematical models to determine how TES affects species richness, but under a variety of frameworks. Here, we critically review such studies to synthesise their findings and draw general conclusions. We first provide a broad mathematical framework encompassing the different ways in which TES has been modelled. We then review studies that have analysed models with TES under the assumption of negligible interspecific interactions, such that a community is conceptualised as the sum of independent species populations. These analyses have highlighted how TES can reduce species richness by increasing the frequency at which a species becomes rare and therefore prone to extinction. Next, we review studies that have relaxed the assumption of negligible interspecific interactions. To simplify the corresponding models and make them analytically tractable, such studies have used mean-field theory to derive fixed parameters representing the typical strength of interspecific interactions under TES. The resulting analyses have highlighted community-level effects that determine how TES affects species richness, for species that compete for a common limiting resource. With short temporal correlations of environmental conditions, a non-linear averaging effect of interspecific competition strength over time gives an increase in species richness. In contrast, with long temporal correlations of environmental conditions, strong selection favouring the fittest species between changes in environmental conditions results in a decrease in species richness. We compare such results with those from invasion analysis, which examines invasion growth rates (IGRs) instead of species richness directly. Qualitative differences sometimes arise because the IGR is the expected growth rate of a species when it is rare, which does not capture the variation around this mean or the probability of the species becoming rare. Our review elucidates key processes that have been found to mediate the negative and positive effects of TES on species richness, and by doing so highlights key areas for future research.

Life Is Uncertain: Inherent Variability Exhibited by Organisms, and at Higher Levels of Biological Organization

Organisms act stochastically. A not uncommon view in the ecological literature is that this is mainly due to the observer having insufficient information or a stochastic environment-and not partly because organisms themselves respond with inherent unpredictability. In this study, I compile the evidence that contradicts that view. Organisms generate uncertainty internally, which results in irreducible stochastic responses. I consider why: for instance, stochastic responses are associated with greater adaptability to changing environments and resource availability. Over longer timescales, biologically generated uncertainty influences behavior, evolution, and macroecological processes. Indeed, it could be stated that organisms are systems defined by the internal generation, magnification, and record-keeping of uncertainty as inputs to responses. Important practical implications arise if organisms can indeed be defined by an association with specific classes of inherent uncertainty: not least that isolating those signatures then provides a potential means for detecting life, for considering the forms that life could theoretically take, and for exploring the wider limits to how life might become distributed. These are all fundamental goals in astrobiology.

Catastrophic and noncatastrophic population crashes in a bitrophic system with dynamic additional food provision to cooperative predators

In this article we contemplate the dynamics of an additional food-provided prey-predator system. We assume that the behavior of cooperative predators induces fear in prey, which radically affects the prey's birth and death rates. We observe that the structural instability imposed by strong cooperative hunting among predators goes away with higher intensities of fear levels affecting the prey's reproductive output and mortality. High levels of prey refuge are not conducive to the survival of predators. In such a situation, adequate supply of high-quality additional food is favorable regarding the persistence and stability of the system. Interestingly, the system potentially exhibits two stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including saddle-node and backward bifurcations, and associated hysteresis effects with prey refuge along with additional food quantity and quality. In the stochastic environment, the system experiences critical transitions through bifurcation-induced tipping events with time-varying additional food for predators. Enhanced disturbance events promote noise-induced switching and tipping events. Finally, our investigation explores whether impending population crashes resulting from the variability of additional food quantity and quality can reliably be predicted using early warning signals in the context of redshifted noise. Overall, our results may provide insights for finding control strategies in the context of community ecology.

Fractal Phototherapy in Maximizing Retina and Brain Plasticity

The neuroplasticity potential is reduced with aging and impairs during neurodegenerative diseases and brain and visual system injuries. This limits the brain's capacity to repair the structure and dynamics of its activity after lesions. Maximization of neuroplasticity is necessary to provide the maximal CNS response to therapeutic intervention and adaptive reorganization of neuronal networks in patients with degenerative pathology and traumatic injury to restore the functional activity of the brain and retina.Considering the fractal geometry and dynamics of the healthy brain and the loss of fractality in neurodegenerative pathology, we suggest that the application of self-similar visual signals with a fractal temporal structure in the stimulation therapy can reactivate the adaptive neuroplasticity and enhance the effectiveness of neurorehabilitation. This proposition was tested in the recent studies. Patients with glaucoma had a statistically significant positive effect of fractal photic therapy on light sensitivity and the perimetric MD index, which shows that methods of fractal stimulation can be a novel nonpharmacological approach to neuroprotective therapy and neurorehabilitation. In healthy rabbits, it was demonstrated that a long-term course of photostimulation with fractal signals does not harm the electroretinogram (ERG) and retina structure. Rabbits with modeled retinal atrophy showed better dynamics of the ERG restoration during daily stimulation therapy for a week in comparison with the controls. Positive changes in the retinal function can indirectly suggest the activation of its adaptive plasticity and the high potential of stimulation therapy with fractal visual stimuli in a nonpharmacological neurorehabilitation, which requires further study.

Stability of consumer-resource interactions in periodic environments

Periodic fluctuations in abiotic conditions are ubiquitous across a range of temporal scales and regulate the structure and function of ecosystems through dynamic biotic responses that are adapted to these external forces. Research has suggested that certain environmental signatures may play a crucial role in the maintenance of biodiversity and the stability of food webs, while others argue that coupled oscillators ought to promote chaos. As such, numerous uncertainties remain regarding the intersection of temporal environmental patterns and biological responses, and we lack a general understanding of the implications for food web stability. Alarmingly, global change is altering the nature of both environmental rhythms and biological rates. Here, we develop a general theory for how continuous periodic variation in productivity, across temporal scales, influences the stability of consumer-resource interactions: a fundamental building block of food webs. Our results suggest that consumer-resource dynamics under environmental forcing are highly complex and depend on asymmetries in both the speed of forcing relative to underlying dynamics and in local stability properties. These asymmetries allow for environmentally driven stabilization under fast forcing, relative to underlying dynamics, as well as extremely complex and unstable dynamics at slower periodicities. Our results also suggest that changes in naturally occurring periodicities from climate change may lead to precipitous shifts in dynamics and stability.

Seasonal dynamics of phytoplankton in the northern part of Suez Gulf, Egypt

This study was conducted to evaluate the seasonal variability of phytoplankton in the northern part of the Gulf of Suez (Suez Bay), considering the contribution of physicochemical parameters of bay water in shaping the dynamics, and eutrophication assessment. Water and phytoplankton samples were collected seasonally at nine stations in the Suez Bay during the period from the winter to autumn of 2012. A total of 423 phytoplankton species were identified, comprised mainly of 224 diatoms, 127 dinoflagellates, 33 cyanophytes, 20 chlorophytes, and 9 euglenophytes; the rest of the species (10 species) belong to other six groups. Of these, 28 species were potentially harmful. The total phytoplankton abundance exhibits a significant seasonal variation, with the autumn being the most fertile season, followed by the winter due to the proliferation of diatom species Thalassionema nitzschioides and Proboscia alata f. gracillima, respectively. While the seasonal species richness indicates that the winter attained the highest number of species, followed by summer. Generally, the major diatom genera were Chaetoceros (16 species), Navicula (15 species), Nitzschia (15 species), and Amphora (14 species), while dinoflagellates were principally composed of the genera Protoperidinium (34 species), and Tripos (26 species). Water temperature, pH, salinity, nitrate, and nitrite were the most important explanatory parameters in regard to phytoplankton abundance and chlorophyll a concentration. In addition, the phytoplankton stability exhibited a significant positive relationship with the mean values of dissolved oxygen and biological oxygen demand and the variability of salinity and phosphate, while a negative relationship was observed with ammonia and nitrite and the variability of nitrate. Based on the trophic index (TRIX), the bay water was classified as mesotrophic (moderately polluted) for almost the entire year except in the autumn as it turned eutrophic. The results explored the potential importance of the environmental heterogeneity in the bay as a key structuring mechanism of phytoplankton abundance and biomass, influenced by anthropogenic activities.

Research on key acoustic characteristics of soundscapes of the classical Chinese gardens

Soundscapes have played an important role in the design and building of classical Chinese gardens. In Chinese classical poetry, biophonies such as bird calls, and geophonies such as wind, are the preferable sound sources. Although these major sound sources have been categorized and summarized by scholars extensively, little research has been conducted to analyze the physical characteristics and preference matrix of these preferred sound sources. Moreover, the perceived loudness of sound in classical Chinese gardens has received more attention from scholars than acoustic frequency. In this study, we selected 12 sound sources that are most typically present in classical Chinese gardens based on extensive literature research on Chinese classical poetry, and acquired respective audio samples from the BBC's library of Sound Effects. Through the spectrogram analyses, pitch detection algorithm and LSTM audio classification methods, the sound sources were classified into discrete sound sources with pitch variation and continuous sound sources with spectral characteristics of white noise or pink noise. The reasoning behind the preference for these two types of sound sources was then discussed from physical and mental healing perspectives, which aims to help provide perspectives on the associated implications in the planning of urban green spaces.

Effects of gamma frequency binaural beats on attention and anxiety

Binaural beats (BB) are an auditory phenomenon produced from a combination of two sine waves with slightly different frequencies presented to each ear. Previous research has implicated the role of BBs through brainwave entrainment in potentially giving rise to benefits ranging from enhanced memory and attention to reduced anxiety and stress. Here, we investigated the effect of gamma (40-Hz) BBs on attention using the attention network test (ANT), a previously unused task that assesses three subtypes of attention: Alerting, Orienting, and Executive Control. Fifty-eight healthy adults performed the ANT remotely under the exposure of 340-Hz BBs and a 380-Hz control tone. All completed a rating scale for levels of anxiety before and after each exposure. Performance on the ANT task (reaction time and error rates) between BB and control groups was evaluated using Wilcoxon signed-rank tests. We found no significant differences in Reaction Time (RT), Error Rate (ER), or the efficacy of the Attention Networks (AN) between the experimental and control conditions (p > 0.05). We found no effect of BB on self-rated measures of anxiety. Our findings do not provide evidence for improvement in attention with gamma BB.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12144-023-04681-3.

The color of environmental noise in river networks

Despite its far-reaching implications for conservation and natural resource management, little is known about the color of environmental noise, or the structure of temporal autocorrelation in random environmental variation, in streams and rivers. Here, we analyze the geography, drivers, and timescale-dependence of noise color in streamflow across the U.S. hydrography, using streamflow time series from 7504 gages. We find that daily and annual flows are dominated by red and white spectra respectively, and spatial variation in noise color is explained by a combination of geographic, hydroclimatic, and anthropogenic variables. Noise color at the daily scale is influenced by stream network position, and land use and water management explain around one third of the spatial variation in noise color irrespective of the timescale considered. Our results highlight the peculiarities of environmental variation regimes in riverine systems, and reveal a strong human fingerprint on the stochastic patterns of streamflow variation in river networks.

The spectral color of natural and anthropogenic time series and its impact on the statistical significance of cross correlation

The cross-correlation between time series is a common tool to study and quantify the impact of climatic and anthropogenic changes on ecosystems. The traditional method for estimating the statistical significance of correlation relies on the assumption that the data are independent, but time series found in nature are often strongly auto-correlated because of low-frequency environmental variability and ecosystem inertia. Previous authors have used Monte Carlo simulations to study the impact of serial auto-correlation on the significance of cross-correlations. Most studies have used random time series that are often a poor representation of those found in nature, e.g., low-order auto-regressive models with normally distributed noise. Moreover, we are not aware of any tests of the applicability of those methods to anthropogenic time series. Here, we study the effect of serial auto-correlation on the performance of two methods for estimating the significance of cross-correlations determined from Monte Carlo simulations with time series that are generated synthetically based on power-law specification of spectral characteristics. Such time series have an auto-correlation structure defined by a single parameter, their spectral "color", and are generally more convenient representations of natural time series than the autoregressive models. Our results show that one of the two methods considered here accurately reproduces prescribed error rates for the wide range of spectral colors representative of climatic, ecological and anthropogenic time series. For this, we characterized roughly 1800 observational records in different categories of spectral colors, including climate variability, abundance of vertebrate species, and pollution. We specifically focus on time series with annual sampling over data records of at least 40 years, which are particularly relevant for climate studies. The methodology advocated in this study provides a simple and realistic assessment of the significance of sample estimates of cross correlation for time series with any sample interval and record length.

Laplace's demon in biology: Models of evolutionary prediction

Our ability to predict natural phenomena can be limited by incomplete information. This issue is exemplified by "Laplace's demon," an imaginary creature proposed in the 18th century, who knew everything about everything, and thus could predict the full nature of the universe forward or backward in time. Quantum mechanics, among other things, has cast doubt on the possibility of Laplace's demon in the full sense, but the idea still serves as a useful metaphor for thinking about the extent to which prediction is limited by incomplete information on deterministic processes versus random factors. Here, we use simple analytical models and computer simulations to illustrate how data limits can be captured in a Bayesian framework, and how they influence our ability to predict evolution. We show how uncertainty in measurements of natural selection, or low predictability of external environmental factors affecting selection, can greatly reduce predictive power, often swamping the influence of intrinsic randomness caused by genetic drift. Thus, more accurate knowledge concerning the causes and action of natural selection is key to improving prediction. Fortunately, our analyses and simulations show quantitatively that reasonable improvements in data quantity and quality can meaningfully increase predictability.

Effect of Environmental Change Distribution on Artificial Life Simulations

It is already well known that environmental variation has a big effect on real evolution, and similar effects have been found in evolutionary artificial life simulations. In particular, a lot of research has been carried out on how the various evolutionary outcomes depend on the noise distributions representing the environmental changes, and how important it is for models to use inverse power-law distributions with the right noise colour. However, there are two distinct factors of relevance-the average total magnitude of change per unit time and the distribution of individual change magnitudes-and misleading results may emerge if those factors are not properly separated. This article makes use of an existing agent-based artificial life modeling framework to explore this issue using models previously tried and tested for other purposes. It begins by demonstrating how the total magnitude and distribution effects can easily be confused, and goes on to show how it is possible to untangle the influence of these interacting factors by using correlation-based normalization. It then presents a series of simulation results demonstrating that interesting dependencies on the noise distribution remain after separating those factors, but many effects involving the noise colour of inverse power-law distributions disappear, and very similar results arise across restricted-range white-noise distributions. The average total magnitude of change per unit time is found to have a substantial effect on the simulation outcomes, but the distribution of individual changes has very little effect. A robust counterexample is thereby provided to the idea that it is always important to use accurate environmental change distributions in artificial life models.

Ergodic descriptors of non-ergodic stochastic processes

The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far-from-equilibrium. Far-from-equilibrium, non-ergodicity reigns. Non-ergodicity implies that the average outcome for a group/ensemble (i.e. of representative organisms/minds) is not necessarily a reliable estimate of the average outcome for an individual over time. However, the scientific interest in causal inference suggests that we somehow aim at stable estimates of the cause that will generalize to new individuals in the long run. Therefore, the valid analysis must extract an ergodic stationary measure from fluctuating physiological data. So the challenge is to extract statistical estimates that may describe or quantify some of this non-ergodicity (i.e. of the raw measured data) without themselves (i.e. the estimates) being non-ergodic. We show that traditional linear statistics such as the standard deviation, coefficient of variation and root mean square can break ergodicity. Time series of statistics addressing sequential structure and its potential nonlinearity: fractality and multi-fractality, change in a time-independent way and fulfil the ergodic assumption. Complementing traditional linear indices with fractal and multi-fractal indices would empower the study of stochastic far-from-equilibrium biological and psychological dynamics.

The Importance of Noise Colour in Simulations of Evolutionary Systems

Simulations of evolutionary dynamics often employ white noise as a model of stochastic environmental variation. Whilst white noise has the advantages of being simply generated and analytically tractable, empirical analyses demonstrate that most real environmental time series have power spectral densities consistent with pink or red noise, in which lower frequencies contribute proportionally greater amplitudes than higher frequencies. Simulated white noise environments may therefore fail to capture key components of real environmental time series, leading to erroneous results. To explore the effects of different noise colours on evolving populations, a simple evolutionary model of the interaction between life-history and the specialism-generalism axis was developed. Simulations were conducted using a range of noise colours as the environments to which agents adapted. Results demonstrate complex interactions between noise colour, reproductive rate, and the degree of evolved generalism; importantly, contradictory conclusions arise from simulations using white as opposed to red noise, suggesting that noise colour plays a fundamental role in generating adaptive responses. These results are discussed in the context of previous research on evolutionary responses to fluctuating environments, and it is suggested that Artificial Life as a field should embrace a wider spectrum of coloured noise models to ensure that results are truly representative of environmental and evolutionary dynamics.

Evolution of anticipatory effects mediated by epigenetic changes

Anticipatory effects mediated by epigenetic changes occur when parents modify the phenotype of their offspring by making epigenetic changes in their gametes, guided by information from an environmental cue. To investigate when do anticipatory effects mediated by epigenetic changes evolve in a fluctuating environment, I use an individual-based simulation model with explicit genetic architecture. The model allows for the population to respond to environmental changes by evolving plasticity, bet hedging, or by tracking the environment with genetic adaptation, in addition to the evolution of anticipatory effects. The results show that anticipatory effects evolve when the environmental cue provides reliable information about the environment and the environment changes at intermediate rates, provided that fitness costs of anticipatory effects are rather low. Moreover, evolution of anticipatory effects is quite robust to different genetic architectures when reliability of the environmental cue is high. Anticipatory effects always give smaller fitness benefits than within-generation plasticity, suggesting a possible reason for generally small observed anticipatory effects in empirical studies.

Natural selection for imprecise vertical transmission in host-microbiota systems

How and when the microbiome modulates host adaptation remains an evolutionary puzzle, despite evidence that the extended genetic repertoire of the microbiome can shape host phenotypes and fitness. One complicating factor is that the microbiome is often transmitted imperfectly across host generations, leading to questions about the degree to which the microbiome contributes to host adaptation. Here, using an evolutionary model, we demonstrate that decreasing vertical transmission fidelity can increase microbiome variation, and thus phenotypic variation, across hosts. When the most beneficial microbial genotypes change unpredictably from one generation to the next (for example, in variable environments), hosts can maximize fitness by increasing the microbiome variation among offspring, as this improves the chance of there being an offspring with the right microbial combination for the next generation. Imperfect vertical transmission can therefore be adaptive in varying environments. We characterize how selection on vertical transmission is shaped by environmental conditions, microbiome changes during host development and the contribution of other factors to trait variation. We illustrate how environmentally dependent microbial effects can favour intermediate transmission and set our results in the context of examples from natural systems. We also suggest research avenues to empirically test our predictions. Our model provides a basis to understand the evolutionary pathways that potentially led to the wide diversity of microbe transmission patterns found in nature.

The Dynamic Hypercube as a Niche Community Model

Different models of community dynamics, such as the MacArthur–Wilson theory of island biogeography and Hubbell’s neutral theory, have given us useful insights into the workings of ecological communities. Here, we develop the niche-hypervolume concept of the community into a powerful model of community dynamics. We describe the community’s size through the volume of the hypercube and the dynamics of the populations in it through the fluctuations of the axes of the niche hypercube on different timescales. While the community’s size remains constant, the relative volumes of the niches within it change continuously, thus allowing the populations of different species to rise and fall in a zero-sum fashion. This dynamic hypercube model reproduces several key patterns in communities: lognormal species abundance distributions, 1/f-noise population abundance, multiscale patterns of extinction debt and logarithmic species-time curves. It also provides a powerful framework to explore significant ideas in ecology, such as the drift of ecological communities into evolutionary time.

A Multiscale Approach to Timescale Analysis: Isolating Diel Signals from Solute Concentration Time Series

Solute concentration time series reflect hydrological and biological drivers through various frequencies, phases, and amplitudes of change. Untangling these signals facilitates the understanding of dynamic ecosystem conditions and transient water quality issues. A case in point is the inference of biogeochemical processes from diel solute concentration variations. This analysis requires approaches capable of isolating subtle diel signals from background variability at other scales. Conventional time series analyses typically assume stationary or deterministic background variability; however, most rivers do not respect such niceties. We developed a time-series filtering method that uses empirical mode decomposition to decompose a measured solute concentration time series into intrinsic mode frequencies. Based on externally supplied mechanistic knowledge, we then filter these modes by periodicity, phase, and coherence with neighboring days. This method is tested on three synthetic series that incorporate environmental variability and sensor noise and on a year of 15 min sampled concentration time series from three hydrologically and ecologically distinct rivers in the eastern United States. The proposed method successfully isolated signals in the measured data sets that corresponded with variability in gross primary productivity. The strength the diel signal isolated through this method was smaller compared to the true signal in the synthetic series; however, uncertainty analysis showed that the process-model-based estimates derived from these signals were similar to other inference methods. This signal decomposition method retains information that can be used for further process modeling while making different assumptions about the data than Fourier and wavelet analyses.

Resonance in Physiologically Structured Population Models

Ecologists have long sought to understand how the dynamics of natural populations are affected by the environmental variation those populations experience. A transfer function is a useful tool for this purpose, as it uses linearization theory to show how the frequency spectrum of the fluctuations in a population's abundance relates to the frequency spectrum of environmental variation. Here, we show how to derive and to compute the transfer function for a continuous-time model of a population that is structured by a continuous individual-level state variable such as size. To illustrate, we derive, compute, and analyze the transfer function for a size-structured population model of stony corals with open recruitment, parameterized for a common Indo-Pacific coral species complex. This analysis identifies a sharp multi-decade resonance driven by space competition between existing coral colonies and incoming recruits. The resonant frequency is most strongly determined by the rate at which colonies grow, and the potential for resonant oscillations is greatest when colony growth is only weakly density-dependent. While these resonant oscillations are unlikely to be a predominant dynamical feature of degraded reefs, they suggest dynamical possibilities for marine invertebrates in more pristine waters. The size-structured model that we analyze is a leading example of a broader class of physiologically structured population models, and the methods we present should apply to a wide variety of models in this class.

Higher airborne pollen concentrations correlated with increased SARS-CoV-2 infection rates, as evidenced from 31 countries across the globe

Pollen exposure weakens the immunity against certain seasonal respiratory viruses by diminishing the antiviral interferon response. Here we investigate whether the same applies to the pandemic severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which is sensitive to antiviral interferons, if infection waves coincide with high airborne pollen concentrations. Our original hypothesis was that more airborne pollen would lead to increases in infection rates. To examine this, we performed a cross-sectional and longitudinal data analysis on SARS-CoV-2 infection, airborne pollen, and meteorological factors. Our dataset is the most comprehensive, largest possible worldwide from 130 stations, across 31 countries and five continents. To explicitly investigate the effects of social contact, we additionally considered population density of each study area, as well as lockdown effects, in all possible combinations: without any lockdown, with mixed lockdown-no lockdown regime, and under complete lockdown. We found that airborne pollen, sometimes in synergy with humidity and temperature, explained, on average, 44% of the infection rate variability. Infection rates increased after higher pollen concentrations most frequently during the four previous days. Without lockdown, an increase of pollen abundance by 100 pollen/m3 resulted in a 4% average increase of infection rates. Lockdown halved infection rates under similar pollen concentrations. As there can be no preventive measures against airborne pollen exposure, we suggest wide dissemination of pollen-virus coexposure dire effect information to encourage high-risk individuals to wear particle filter masks during high springtime pollen concentrations.

Scaling up biodiversity-ecosystem functioning relationships: the role of environmental heterogeneity in space and time

The biodiversity and ecosystem functioning (BEF) relationship is expected to be scale-dependent. The autocorrelation of environmental heterogeneity is hypothesized to explain this scale dependence because it influences how quickly biodiversity accumulates over space or time. However, this link has yet to be demonstrated in a formal model. Here, we use a Lotka-Volterra competition model to simulate community dynamics when environmental conditions vary across either space or time. Species differ in their optimal environmental conditions, which results in turnover in community composition. We vary biodiversity by modelling communities with different sized regional species pools and ask how the amount of biomass per unit area depends on the number of species present, and the spatial or temporal scale at which it is measured. We find that more biodiversity is required to maintain functioning at larger temporal and spatial scales. The number of species required increases quickly when environmental autocorrelation is low, and slowly when autocorrelation is high. Both spatial and temporal environmental heterogeneity lead to scale dependence in BEF, but autocorrelation has larger impacts when environmental change is temporal. These findings show how the biodiversity required to maintain functioning is expected to increase over space and time.

Smartphone-enabled road condition monitoring: from accelerations to road roughness and excess energy dissipation

We develop a framework to address the shortcomings of current smartphone-based approaches for road roughness sensing and monitoring through combining vehicle dynamics, random vibration theory and a two-layer inverse analysis. The proposed approach uses in-cabin recordings of the vehicle’s vertical acceleration measured by a smartphone positioned inside the car for the estimation of road roughness. The mechanistic road roughness–vehicle interaction model at the core of the proposed framework links the frequency spectrum of the vehicle’s vertical acceleration to the road roughness power spectral density and lends itself to the quantitative characterization of roughness-induced energy dissipation. We demonstrate that the measure of roughness provided by the stochastic model of car dynamics interacting with a rough road is fully compatible, in a statistical sense, with the spatial but deterministic definition of road roughness, and validate the identification strategy that originates from it against laser measurements of road roughness. The critical crowdsourcing features of the proposed framework, such as the marginal impact of phone position and transferability, are examined and its utility to meld with big data analytics to identify the class of vehicles travelling on a roadway network is demonstrated.

Long-term consistency despite cross-seasonal changes in personality traits of common waxbills

Tests of long-term consistency in personality differences are not abundant. We studied personality in common waxbills (Estrilda astrild) from one Autumn to the next, and also from Autumn to a subsequent Spring, using a behavioural assay for their proactive-reactive personality axis (mirror test) and for tonic immobility. From one Autumn to the next, individual differences were consistent and the population median behaviours did not change, indicating long-term stability of personality differences. From Autumn to Spring, behavioural differences remained consistent, despite the population shifting to more proactive behaviour and individual differences being accentuated in the proactive-reactive personality axis. This increase in personality differences was not found between the two previous Autumns, suggesting a seasonal rather than longitudinal change, and a possible role for personality differences during the Spring breeding season. We conclude that waxbill personality differences are stable in the long term, despite changes in behaviour between Autumn and Spring.

Complex interactions can create persistent fluctuations in high-diversity ecosystems

When can ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where many species populations fluctuate without going to extinction? We show that high-diversity spatially heterogeneous systems can exhibit chaotic dynamics which persist for extremely long times. We develop a theoretical framework, based on dynamical mean-field theory, to quantify the conditions under which these fluctuating states exist, and predict their properties. We uncover parallels with the persistence of externally-perturbed ecosystems, such as the role of perturbation strength, synchrony and correlation time. But uniquely to endogenous fluctuations, these properties arise from the species dynamics themselves, creating feedback loops between perturbation and response. A key result is that fluctuation amplitude and species diversity are tightly linked: in particular, fluctuations enable dramatically more species to coexist than at equilibrium in the very same system. Our findings highlight crucial differences between well-mixed and spatially-extended systems, with implications for experiments and their ability to reproduce natural dynamics. They shed light on the maintenance of biodiversity, and the strength and synchrony of fluctuations observed in natural systems.

A case for environmental statistics of early-life effects

There is enduring debate over the question of which early-life effects are adaptive and which ones are not. Mathematical modelling shows that early-life effects can be adaptive in environments that have particular statistical properties, such as reliable cues to current conditions and high autocorrelation of environmental states. However, few empirical studies have measured these properties, leading to an impasse. Progress, therefore, depends on research that quantifies cue reliability and autocorrelation of environmental parameters in real environments. These statistics may be different for social and non-social aspects of the environment. In this paper, we summarize evolutionary models of early-life effects. Then, we discuss empirical data on environmental statistics from a range of disciplines. We highlight cases where data on environmental statistics have been used to test competing explanations of early-life effects. We conclude by providing guidelines for new data collection and reflections on future directions.

This article is part of the theme issue ‘Developing differences: early-life effects and evolutionary medicine'.

Population variability under stressors is dependent on body mass growth and asymptotic body size

The recruitment and biomass of a fish stock are influenced by their environmental conditions and anthropogenic pressures such as fishing. The variability in the environment often translates into fluctuations in recruitment, which then propagate throughout the stock biomass. In order to manage fish stocks sustainably, it is necessary to understand their dynamics. Here, we systematically explore the dynamics and sensitivity of fish stock recruitment and biomass to environmental noise. Using an age-structured and trait-based model, we explore random noise (white noise) and autocorrelated noise (red noise) in combination with low to high levels of harvesting. We determine the vital rates of stocks covering a wide range of possible body mass (size) growth rates and asymptotic size parameter combinations. Our study indicates that the variability of stock recruitment and biomass are probably correlated with the stock's asymptotic size and growth rate. We find that fast-growing and large-sized fish stocks are likely to be less vulnerable to disturbances than slow-growing and small-sized fish stocks. We show how the natural variability in fish stocks is amplified by fishing, not just for one stock but for a broad range of fish life histories.

Empirical patterns of environmental variation favor adaptive transgenerational plasticity

Effects of parental environment on offspring traits have been well known for decades. Interest in this transgenerational form of phenotypic plasticity has recently surged due to advances in our understanding of its mechanistic basis. Theoretical research has simultaneously advanced by predicting the environmental conditions that should favor the adaptive evolution of transgenerational plasticity. Yet whether such conditions actually exist in nature remains largely unexplored. Here, using long-term climate data, we modeled optimal levels of transgenerational plasticity for an organism with a one-year life cycle at a spatial resolution of 4 km2 across the continental United States. Both annual temperature and precipitation levels were often autocorrelated, but the strength and direction of these autocorrelations varied considerably even among nearby sites. When present, such environmental autocorrelations render offspring environments statistically predictable based on the parental environment, a key condition for the adaptive evolution of transgenerational plasticity. Results of our optimality models were consistent with this prediction: High levels of transgenerational plasticity were favored at sites with strong environmental autocorrelations, and little-to-no transgenerational plasticity was favored at sites with weak or nonexistent autocorrelations. These results are among the first to show that natural patterns of environmental variation favor the evolution of adaptive transgenerational plasticity. Furthermore, these findings suggest that transgenerational plasticity is likely variable in nature, depending on site-specific patterns of environmental variation.

Selective Sweep at a QTL in a Randomly Fluctuating Environment

Adaptation is mediated by phenotypic traits that are often near continuous, and undergo selective pressures that may change with the environment. The dynamics of allelic frequencies at underlying quantitative trait loci (QTL) depend on their own phenotypic effects, but also possibly on other polymorphic loci affecting the same trait, and on environmental change driving phenotypic selection. Most environments include a substantial component of random noise, characterized both by its magnitude and its temporal autocorrelation, which sets the timescale of environmental predictability. I investigate the dynamics of a mutation affecting a quantitative trait in an autocorrelated stochastic environment that causes random fluctuations of an optimum phenotype. The trait under selection may also exhibit background polygenic variance caused by many polymorphic loci of small effects elsewhere in the genome. In addition, the mutation at the QTL may affect phenotypic plasticity, the phenotypic response of given genotype to its environment of development or expression. Stochastic environmental fluctuations increase the variance of the evolutionary process, with consequences for the probability of a complete sweep at the QTL. Background polygenic variation critically alters this process, by setting an upper limit to stochastic variance of population genetics at the QTL. For a plasticity QTL, stochastic fluctuations also influences the expected selection coefficient, and alleles with the same expected trajectory can have very different stochastic variances. Finally, a mutation may be favored through its effect on plasticity despite causing a systematic mismatch with optimum, which is compensated by evolution of the mean background phenotype.

Performance in a variable world: using Jensen's inequality to scale up from individuals to populations

Body temperature affects plants' and animals' performance, but these effects are complicated by thermal variation through time within an individual and variation through space among individuals in a population. This review and synthesis describes how the effects of thermal variation-in both time and space-can be estimated by applying a simple, nonlinear averaging scheme. The method is first applied to the temporal variation experienced by an individual, providing an estimate of the individual's average performance. The method is then applied to the scale-dependent thermal variation among individuals, which is modelled as a 1/f-noise phenomenon. For an individual, thermal variation reduces average performance, lowers the temperature of maximum performance (Topt ) and contracts the range of viable temperatures. Thermal variation among individuals similarly reduces performance and lowers Topt , but increases the viable range of average temperatures. These results must be viewed with caution, however, because they do not take into account the time-dependent interaction between body temperature and physiological plasticity. Quantifying these interactions is perhaps the largest challenge for ecological and conservation physiologists as they attempt to predict the effects of climate change.

A functional trait approach to identifying life history patterns in stochastic environments

Temporal variation in demographic processes can greatly impact population dynamics. Perturbations of statistical coefficients that describe demographic rates within matrix models have, for example, revealed that stochastic population growth rates (log(λ s)) of fast life histories are more sensitive to temporal autocorrelation of environmental conditions than those of slow life histories. Yet, we know little about the mechanisms that drive such patterns. Here, we used a mechanistic, functional trait approach to examine the functional pathways by which a typical fast life history species, the macrodetrivore Orchestia gammarellus, and a typical slow life history species, the reef manta ray Manta alfredi, differ in their sensitivity to environmental autocorrelation if (a) growth and reproduction are described mechanistically by functional traits that adhere to the principle of energy conservation, and if (b) demographic variation is determined by temporal autocorrelation in food conditions. Opposite to previous findings, we found that O. gammarellus log(λ s) was most sensitive to the frequency of good food conditions, likely because reproduction traits, which directly impact population growth, were most influential to log(λ s). Manta alfredi log(λs ) was instead most sensitive to temporal autocorrelation, likely because growth parameters, which impact population growth indirectly, were most influential to log(λ s). This differential sensitivity to functional traits likely also explains why we found that O. gammarellus mean body size decreased (due to increased reproduction) but M. alfredi mean body size increased (due to increased individual growth) as food conditions became more favorable. Increasing demographic stochasticity under constant food conditions decreased O. gammarellus mean body size and increased log(λ s) due to increased reproduction, whereas M. alfredi mean body and log(λ s) decreased, likely due to decreased individual growth. Our findings signify the importance of integrating functional traits into demographic models as this provides mechanistic understanding of how environmental and demographic stochasticity affects population dynamics in stochastic environments.