Optimal sampling of spatial patterns improves deep learning-based early warning signals of critical transitions.

Complex spatio-temporal systems like lakes, forests and climate systems exhibit alternative stable states. In such systems, as the threshold value of the driver is crossed, the system may experience a sudden (discontinuous) transition or smooth (continuous) transition to an undesired steady state. Theories predict that changes in the structure of the underlying spatial patterns precede such transitions. While there has been a large body of research on identifying early warning signals of critical transitions, the problem of forecasting the type of transitions (sudden versus smooth) remains an open challenge. We address this gap by developing an advanced machine learning (ML) toolkit that serves as an early warning indicator of spatio-temporal critical transitions, Spatial Early Warning Signal Network (S-EWSNet). ML models typically resemble a black box and do not allow envisioning what the model learns in discerning the labels. Here, instead of naively relying upon the deep learning model, we let the deep neural network learn the latent features characteristic of transitions via an optimal sampling strategy (OSS) of spatial patterns. The S-EWSNet is trained on data from a stochastic cellular automata model deploying the OSS, providing an early warning indicator of transitions while detecting its type in simulated and empirical samples.

Spatial structure could explain the maintenance of alternative reproductive tactics in tree cricket males.

Trait polymorphisms are widespread in nature, and explaining their stable co-existence is a central problem in ecology and evolution. Alternative reproductive tactics, in which individuals of one or more sex exhibit discrete, discontinuous traits in response to reproductive competition, represent a special case of trait polymorphism in which the traits are often complex, behavioural, and dynamic. Thus, studying how alternative reproductive tactics are maintained may provide general insights into how complex trait polymorphisms are maintained in populations. We construct a spatially explicit individual-based model inspired from extensively collected empirical data to address the mechanisms behind the co-existence of three behavioural alternative reproductive tactics in males of a tree cricket (Oecanthus henryi). Our results show that the co-existence of these tactics over ecological time scales is facilitated by the spatial structure of the landscape they inhabit, which serves to equalise the otherwise unequal mating benefits of the three tactics. We also show that this co-existence is unlikely if spatial aspects of the system are not considered. Our findings highlight the importance of spatial dynamics in understanding ecological and evolutionary processes and underscore the power of integrative approaches that combine models with empirical data.

Multi-Object Tracking in Heterogeneous environments (MOTHe) for animal video recordings.

Aerial imagery and video recordings of animals are used for many areas of research such as animal behaviour, behavioural neuroscience and field biology. Many automated methods are being developed to extract data from such high-resolution videos. Most of the available tools are developed for videos taken under idealised laboratory conditions. Therefore, the task of animal detection and tracking for videos taken in natural settings remains challenging due to heterogeneous environments. Methods that are useful for field conditions are often difficult to implement and thus remain inaccessible to empirical researchers. To address this gap, we present an open-source package called Multi-Object Tracking in Heterogeneous environments (MOTHe), a Python-based application that uses a basic convolutional neural network for object detection. MOTHe offers a graphical interface to automate the various steps related to animal tracking such as training data generation, animal detection in complex backgrounds and visually tracking animals in the videos. Users can also generate training data and train a new model which can be used for object detection tasks for a completely new dataset. MOTHe doesn't require any sophisticated infrastructure and can be run on basic desktop computing units. We demonstrate MOTHe on six video clips in varying background conditions. These videos are from two species in their natural habitat-wasp colonies on their nests (up to 12 individuals per colony) and antelope herds in four different habitats (up to 156 individuals in a herd). Using MOTHe, we are able to detect and track individuals in all these videos. MOTHe is available as an open-source GitHub repository with a detailed user guide and demonstrations at: https://github.com/tee-lab/MOTHe-GUI.

Data-driven discovery of stochastic dynamical equations of collective motion.

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, the size of many real flocks falls within 'mesoscopic' scales (10 to 100 individuals), where stochasticity arising from the finite flock sizes is important. Previous studies on mesoscopic models have typically focused on non-spatial models. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models that explicitly account for space. To address this gap, here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple, spatial, self-propelled particle (SPP) model of collective motion. In the spatial model, a focal individual can interact withkrandomly chosen neighbours within an interaction radius. We considerk = 1 (called stochastic pairwise interactions),k = 2 (stochastic ternary interactions), andkequalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). For the stochastic pairwise interaction model, the data-driven mesoscopic equations reveal that the collective order is driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, models yield collective order driven by a combination of deterministic and stochastic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasises the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies.

Lekking as collective behaviour.

Lekking is a spectacular mating system in which males maintain tightly organized clustering of territories during the mating season, and females visit these leks for mating. Various hypotheses-ranging from predation dilution to mate choice and mating benefit-offer potential explanations for the evolution of this peculiar mating system. However, many of these classic hypotheses rarely consider the spatial dynamics that produce and maintain the lek. In this article, we propose to view lekking through the perspective of collective behaviour, in which simple local interactions between organisms, as well as habitat, likely produce and maintain lekking. Further, we argue that interactions within the leks change over time, typically over a breeding season, to produce many broad-level as well as specific collective patterns. To test these ideas at both proximate and ultimate levels, we argue that the concepts and tools from the literature on collective animal behaviour, such as agent-based models and high-resolution video tracking that enables capturing fine-scale spatio-temporal interactions, could be useful. To demonstrate the promise of these ideas, we develop a spatially explicit agent-based model and show how simple rules such as spatial fidelity, local social interactions and repulsion among males can potentially explain the formation of lek and synchronous departures of males for foraging from the lek. On the empirical side, we discuss the promise of applying the collective behaviour approach to blackbuck (Antilope cervicapra) leks-using high-resolution recordings via a camera fitted to unmanned aerial vehicles and subsequent tracking of animal movements. Broadly, we suggest that a lens of collective behaviour may provide novel insights into understanding both the proximate and ultimate factors that shape leks. This article is part of a discussion meeting issue 'Collective behaviour through time'.

Abnormalities in the migration of neural precursor cells in familial bipolar disorder.

Cellular migration is a ubiquitous feature that brings brain cells into appropriate spatial relationships over time; and it helps in the formation of a functional brain. We studied the migration patterns of induced pluripotent stem cell-derived neural precursor cells (NPCs) from individuals with familial bipolar disorder (BD) in comparison with healthy controls. The BD patients also had morphological brain abnormalities evident on magnetic resonance imaging. Time-lapse analysis of migrating cells was performed, through which we were able to identify several parameters that were abnormal in cellular migration, including the speed and directionality of NPCs. We also performed transcriptomic analysis to probe the mechanisms behind the aberrant cellular phenotype identified. Our analysis showed the downregulation of a network of genes, centering on EGF/ERBB proteins. The present findings indicate that collective, systemic dysregulation may produce the aberrant cellular phenotype, which could contribute to the functional and structural changes in the brain reported for bipolar disorder. This article has an associated First Person interview with the first author of the paper.

Modelling the first wave of COVID-19 in India.

Estimating the burden of COVID-19 in India is difficult because the extent to which cases and deaths have been undercounted is hard to assess. Here, we use a 9-component, age-stratified, contact-structured epidemiological compartmental model, which we call the INDSCI-SIM model, to analyse the first wave of COVID-19 spread in India. We use INDSCI-SIM, together with Bayesian methods, to obtain optimal fits to daily reported cases and deaths across the span of the first wave of the Indian pandemic, over the period Jan 30, 2020 to Feb 15, 2021. We account for lock-downs and other non-pharmaceutical interventions (NPIs), an overall increase in testing as a function of time, the under-counting of cases and deaths, and a range of age-specific infection-fatality ratios. We first use our model to describe data from all individual districts of the state of Karnataka, benchmarking our calculations using data from serological surveys. We then extend this approach to aggregated data for Karnataka state. We model the progress of the pandemic across the cities of Delhi, Mumbai, Pune, Bengaluru and Chennai, and then for India as a whole. We estimate that deaths were undercounted by a factor between 2 and 5 across the span of the first wave, converging on 2.2 as a representative multiplier that accounts for the urban-rural gradient. We also estimate an overall under-counting of cases by a factor of between 20 and 25 towards the end of the first wave. Our estimates of the infection fatality ratio (IFR) are in the range 0.05-0.15, broadly consistent with previous estimates but substantially lower than values that have been estimated for other LMIC countries. We find that approximately 35% of India had been infected overall by the end of the first wave, results broadly consistent with those from serosurveys. These results contribute to the understanding of the long-term trajectory of COVID-19 in India.

The absence of alternative stable states in vegetation cover of northeastern India.

Globally, forests and savannah are shown to be alternative stable states for intermediate rainfall regimes. This has implications for how these ecosystems respond to changing rainfall conditions. However, we know little about the occurrence of alternative stable states in forest ecosystems in India. In this study, we investigate the possibility of alternative stable states in the vegetation cover of northeastern India, which is a part of the Eastern Himalaya and the Indo-Burma biodiversity hotspots. To do so, we construct the so-called state diagram, by plotting frequency distributions of vegetation cover as a function of mean annual precipitation (MAP). We use remotely sensed satellite data of the enhanced vegetation index (EVI) as a proxy for vegetation cover (at 1 km resolution). We find that EVI exhibits unimodal distribution across a wide range of MAP. Specifically, EVI increases monotonically in the range 1000-2000 mm of MAP, after which it plateaus. This range of MAP corresponds to the vegetation transitional zone (1200-3700 m), whereas MAP greater than 2000 mm covers the larger extent of the tropical forest (less than or equal to 1200 m) of northeast India. In other words, we find no evidence for alternative stable states in vegetation cover or forest states at coarser scales in northeast India.

Randomness in the choice of neighbours promotes cohesion in mobile animal groups.

Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group-level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real organisms; for example, fish stochastically align towards only one randomly chosen neighbour and yet the schools are highly polarized. Here, we ask-how do organisms maintain group cohesion? Using a spatially explicit model, inspired from empirical investigations, we show that group cohesion can be achieved in finite groups even when organisms randomly choose only one neighbour to interact with. Cohesion is maintained even in the absence of local averaging that requires interactions with many neighbours. Furthermore, we show that choosing a neighbour randomly is a better way to achieve cohesion than interacting with just its closest neighbour. To understand how cohesion emerges from these random pairwise interactions, we turn to a graph-theoretic analysis of the underlying dynamic interaction networks. We find that randomness in choosing a neighbour gives rise to well-connected networks that essentially cause the groups to stay cohesive. We compare our findings with the canonical averaging models (analogous to the Vicsek model). In summary, we argue that randomness in the choice of interacting neighbours plays a crucial role in achieving cohesion.

Noise-induced effects in collective dynamics and inferring local interactions from data.

In animal groups, individual decisions are best characterized by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so-called intrinsic noise at the group level. Theory predicts that the strength of intrinsic noise is not a constant but often depends on the collective state of the group; hence, it is also called a state-dependent noise or a multiplicative noise. Surprisingly, such noise may produce collective order. However, only a few empirical studies on collective behaviour have paid attention to such effects owing to the lack of methods that enable us to connect data with theory. Here, we demonstrate a method to characterize the role of stochasticity directly from high-resolution time-series data of collective dynamics. We do this by employing two well-studied individual-based toy models of collective behaviour. We argue that the group-level noise may encode important information about the underlying processes at the individual scale. In summary, we describe a method that enables us to establish connections between empirical data of animal (or cellular) collectives and the phenomenon of noise-induced states, a field that is otherwise largely limited to the theoretical literature. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Dispersal Increases the Resilience of Tropical Savanna and Forest Distributions.

Global change may induce changes in savanna and forest distributions, but the dynamics of these changes remain unclear. Classical biome theory suggests that climate is predictive of biome distributions, such that shifts will be continuous and reversible. This view, however, cannot explain the overlap in the climatic ranges of tropical biomes, which some argue may result from fire-vegetation feedbacks, maintaining savanna and forest as bistable states. Under this view, biome shifts are argued to be discontinuous and irreversible. Mean-field bistable models, however, are also limited, as they cannot reproduce the spatial aggregation of biomes. Here we suggest that both models ignore spatial processes, such as dispersal, which may be important when savanna and forest abut. We examine the contributions of dispersal to determining biome distributions using a 2D reaction-diffusion model, comparing results qualitatively to empirical savanna and forest distributions in sub-Saharan Africa. We find that the diffusion model resolves both the aforementioned limitations of biome models. First, local dispersive spatial interactions, with an underlying precipitation gradient, can reproduce the spatial aggregation of biomes with a stable savanna-forest boundary. Second, the boundary is determined not only by the amount of precipitation but also by the geometrical shape of the precipitation contours. These geometrical effects arise from continental-scale source-sink dynamics, which reproduce the mismatch between biome and climate. Dynamically, the spatial model predicts that dispersal may increase the resilience of tropical biome in response to global change: the boundary continuously tracks climate, recovering following disturbances, unless the remnant biome patches are too small.

The enemy of my enemy: multiple interacting selection pressures lead to unexpected anti-predator responses.

Despite being a major selective force, predation can induce puzzling variability in anti-predator responses-from lack of predator aversion to lifelong predator-induced fear. This variability is hypothesised to result from variation in the trade-offs associated with avoiding predators. But critical information on fitness outcomes of these trade-offs associated with anti-predator behaviours is lacking. We tested this trade-off hypothesis in Aedes aegypti, by examining oviposition site selection decisions in response towards larval predation risk and comprehensively measuring the fitness implications of trade-offs of avoiding larval predators, using three fitness measures: larval survival, development time and size. In a field study, we find that adult females show a surprisingly variable response to predators, ranging from attraction to avoidance. This variation is explained by fitness outcomes of oviposition along a predation-risk gradient that we measured in the laboratory. We show that ovipositing females could gain fitness benefits from ovipositing in pools with a low density of predators, rather than in predator-free pools, as predators provide a release from negative density effects of conspecific larvae that might co-occur in a pool. Interacting selection pressures may thus explain diverse prey responses. We suggest other systems in which similarly unexpected prey behaviour is likely to occur.

Inferring critical thresholds of ecosystem transitions from spatial data.

Ecosystems can undergo abrupt transitions between alternative stable states when the driver crosses a critical threshold. Dynamical systems theory shows that when ecosystems approach the point of loss of stability associated with these transitions, they take a long time to recover from perturbations, a phenomenon known as critical slowing down. This generic feature of dynamical systems can offer early warning signals of abrupt transitions. However, these signals are qualitative and cannot quantify the thresholds of drivers at which transition may occur. Here, we propose a method to estimate critical thresholds from spatial data. We show that two spatial metrics, spatial variance and autocorrelation of ecosystem state variable, computed along driver gradients can be used to estimate critical thresholds. First, we investigate cellular-automaton models of ecosystem dynamics that show a transition from a high-density state to a bare state. Our models show that critical thresholds can be estimated as the ecosystem state and the driver values at which spatial variance and spatial autocorrelation of the ecosystem state are maximum. Next, to demonstrate the application of the method, we choose remotely sensed vegetation data (Enhanced Vegetation Index, EVI) from regions in central Africa and northeast Australia that exhibit alternative states in woody cover. We draw transects (8 × 90 km) that span alternative stable states along rainfall gradients. Our analyses of spatial variance and autocorrelation of EVI along transects yield estimates of critical thresholds. These estimates match reasonably well with those obtained by an independent method that uses large-scale (250 × 200 km) spatial data sets. Given the generality of the principles that underlie our method, our method can be applied to a variety of ecosystems that exhibit alternative stable states.

Fission-fusion dynamics and group-size-dependent composition in heterogeneous populations.

Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behavior, however, typically assume that groups and populations consist of identical individuals. In this paper, using the mathematical framework of the coagulation-fragmentation process, we develop and analyze a model of merge and split group dynamics, also called fission-fusion dynamics, for heterogeneous populations that contain two types (or species) of individuals. We assume that more heterogeneous groups experience higher split rates than homogeneous groups, forming two daughter groups whose compositions are drawn uniformly from all possible partitions. We analytically derive a master equation for group size and compositions and find mean-field steady-state solutions. We predict that there is a critical group size below which groups are more likely to be homogeneous and contain the abundant type or species. Despite the propensity of heterogeneous groups to split at higher rates, we find that groups are more likely to be heterogeneous but only above the critical group size. Monte Carlo simulation of the model show excellent agreement with these analytical model results. Thus, our model makes a testable prediction that composition of flocks are group-size-dependent and do not merely reflect the population level heterogeneity. We discuss the implications of our results to empirical studies on flocking systems.

Demographic noise and cost of greenbeard can facilitate greenbeard cooperation.

Cooperation among organisms, where cooperators suffer a personal cost to benefit others, is ubiquitous in nature. Greenbeard is a key mechanism for the evolution of cooperation, where a single gene or a set of linked genes codes for both cooperation and a phenotypic tag (metaphorically called "green beard"). Greenbeard cooperation is typically thought to decline over time since defectors can also evolve the tag. However, models of tag-based cooperation typically ignore two key realistic features: populations are finite, and that phenotypic tags can be costly. We develop an analytical model for coevolutionary dynamics of two evolvable traits in finite populations with mutations: costly cooperation and a costly tag. We show that an interplay of demographic noise and cost of the tag can induce coevolutionary cycling, where the evolving population does not reach a steady state but spontaneously switches between cooperative tag-carrying and noncooperative tagless states. Such dynamics allows the tag to repeatedly reappear even after it is invaded by defectors. Thus, we highlight the surprising possibility that the cost of the tag, together with demographic noise, can facilitate the evolution of greenbeard cooperation. We discuss implications of these findings in the context of the evolution of quorum sensing and multicellularity.

Friendship across species borders: factors that facilitate and constrain heterospecific sociality.

Our understanding of animal sociality is based almost entirely on single-species sociality. Heterospecific sociality, although documented in numerous taxa and contexts, remains at the margins of sociality research and is rarely investigated in conjunction with single-species sociality. This could be because heterospecific and single-species sociality are thought to be based on fundamentally different mechanisms. However, our literature survey shows that heterospecific sociality based on mechanisms similar to single-species sociality is reported from many taxa, contexts and for various benefits. Therefore, we propose a conceptual framework to understand conspecific versus heterospecific social partner choice. Previous attempts, which are all in the context of social information, model partner choice as a trade-off between information benefit and competition cost, along a single phenotypic distance axis. Our framework of partner choice considers both direct grouping benefits and information benefits, allows heterospecific and conspecific partners to differ in degree and qualitatively, and uses a multi-dimensional trait space analysis of costs (competition and activity matching) and benefits (relevance of partner and quality of partner). We conclude that social partner choice is best-viewed as a continuum: some social benefits are obtainable only from conspecifics, some only from dissimilar heterospecifics, while many are potentially obtainable from conspecifics and heterospecifics.This article is part of the theme issue 'Collective movement ecology'.

Rising Variability, Not Slowing Down, as a Leading Indicator of a Stochastically Driven Abrupt Transition in a Dryland Ecosystem.

Complex systems can undergo abrupt state transitions near critical points. Theory and controlled experimental studies suggest that the approach to critical points can be anticipated by critical slowing down (CSD), that is, a characteristic slowdown in the dynamics. The validity of this indicator in field ecosystems, where stochasticity is important in driving transitions, remains unclear. We analyze long-term data from a dryland ecosystem in the Shapotou region of China and show that the ecosystem underwent an abrupt transition from a nearly bare to a moderate grass cover state. Prior to the transition, the system showed no (or weak) signatures of CSD but exhibited expected increasing trends in the variability of the grass cover, quantified by variance and skewness. These surprising results are consistent with the theoretical expectation of stochastically driven abrupt transitions that occur away from critical points; indeed, a driver of vegetation-annual rainfall-showed rising variance prior to the transition. Our study suggests that rising variability can potentially serve as a leading indicator of stochastically driven transitions in real-world ecosystems.

Mobility can promote the evolution of cooperation via emergent self-assortment dynamics.

The evolution of costly cooperation, where cooperators pay a personal cost to benefit others, requires that cooperators interact more frequently with other cooperators. This condition, called positive assortment, is known to occur in spatially-structured viscous populations, where individuals typically have low mobility and limited dispersal. However many social organisms across taxa, from cells and bacteria, to birds, fish and ungulates, are mobile, and live in populations with considerable inter-group mixing. In the absence of information regarding others' traits or conditional strategies, such mixing may inhibit assortment and limit the potential for cooperation to evolve. Here we employ spatially-explicit individual-based evolutionary simulations to incorporate costs and benefits of two coevolving costly traits: cooperative and local cohesive tendencies. We demonstrate that, despite possessing no information about others' traits or payoffs, mobility (via self-propulsion or environmental forcing) facilitates assortment of cooperators via a dynamically evolving difference in the cohesive tendencies of cooperators and defectors. We show analytically that this assortment can also be viewed in a multilevel selection framework, where selection for cooperation among emergent groups can overcome selection against cooperators within the groups. As a result of these dynamics, we find an oscillatory pattern of cooperation and defection that maintains cooperation even in the absence of well known mechanisms such as kin interactions, reciprocity, local dispersal or conditional strategies that require information on others' strategies or payoffs. Our results offer insights into differential adhesion based mechanisms for positive assortment and reveal the possibility of cooperative aggregations in dynamic fission-fusion populations.

Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk.

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

Early warning signals of ecological transitions: methods for spatial patterns.

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.