Using field data to test locust migratory band collective movement models

Non-local interaction in discrete Ricci curvature-induced biological aggregation

We investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods. We find that even a single effective topological neighbour suffices for significant order in a system with non-local topological interactions. We also explore topological information flow patterns and clustering dynamics using Hodge spectral entropy and mean Forman-Ricci curvature.

An effective hydrodynamic description of marching locusts

A fundamental question in complex systems is how to relate interactions between individual components ('microscopic description') to the global properties of the system ('macroscopic description'). Furthermore, it is unclear whether such a macroscopic description exists and if such a description can capture large-scale properties. Here, we address the validity of a macroscopic description of a complex biological system using the collective motion of desert locusts as a canonical example. One of the world's most devastating insect plagues begins when flightless juvenile locusts form 'marching bands'. These bands display remarkable coordinated motion, moving through semiarid habitats in search of food. We investigated how well macroscopic physical models can describe the flow of locusts within a band. For this, we filmed locusts within marching bands during an outbreak in Kenya and automatically tracked all individuals passing through the camera frame. We first analyzed the spatial topology of nearest neighbors and found individuals to be isotropically distributed. Despite this apparent randomness, a local order was observed in regions of high density in the radial distribution function, akin to an ordered fluid. Furthermore, reconstructing individual locust trajectories revealed a highly aligned movement, consistent with the one-dimensional version of the Toner-Tu equations, a generalization of the Navier-Stokes equations for fluids, used to describe the equivalent macroscopic fluid properties of active particles. Using this effective Toner-Tu equation, which relates the gradient of the pressure to the acceleration, we show that the effective 'pressure' of locusts increases as a linear function of density in segments with the highest polarization (for which the one-dimensional approximation is most appropriate). Our study thus demonstrates an effective hydrodynamic description of flow dynamics in plague locust swarms.

Anisotropic interaction and motion states of locusts in a hopper band

Swarming locusts present a quintessential example of animal collective motion. Juvenile locusts march and hop across the ground in coordinated groups called hopper bands. Composed of up to millions of insects, hopper bands exhibit aligned motion and various collective structures. These groups are well-documented in the field, but the individual insects themselves are typically studied in much smaller groups in laboratory experiments. We present, to our knowledge, the first trajectory data that detail the movement of individual locusts within a hopper band in a natural setting. Using automated video tracking, we derive our data from footage of four distinct hopper bands of the Australian plague locust, Chortoicetes terminifera. We reconstruct nearly 200 000 individual trajectories composed of over 3.3 million locust positions. We classify these data into three motion states: stationary, walking and hopping. Distributions of relative neighbour positions reveal anisotropies that depend on motion state. Stationary locusts have high-density areas distributed around them apparently at random. Walking locusts have a low-density area in front of them. Hopping locusts have low-density areas in front and behind them. Our results suggest novel insect interactions, namely that locusts change their motion to avoid colliding with neighbours in front of them.

Power Bars: Mormon Crickets Get Immunity Boost from Eating Grasshoppers

In addition to feeding on plants, Mormon crickets Anabrus simplex Haldeman, 1852 predate on invertebrates, including one another, which effectively drives their migration. Carnivory derives from lack of dietary protein, with Mormon crickets deprived of protein having less phenoloxidase (PO) available to combat foreign invaders, such as fungal pathogens. Because Mormon crickets commonly occur with grasshoppers that feed on the same plants, we investigated interactions between grasshoppers and Mormon crickets, and hypothesized that if Mormon crickets are predatory on grasshoppers, grasshopper abundance would influence the protein available to Mormon crickets and their immunity. In a field setting, we varied densities of Mormon crickets (0, 10, or 20 per cage) and grasshoppers Melanoplus borealis (0, 15, 30, or 45) in 68 1-m2 cages. After one month, we measured Mormon cricket dietary preferences and PO activity. As predicted, artificial diet consumption shifted away from protein as grasshopper density increased, and immunocompetence, as measured by PO activity, also increased with grasshopper availability. Although nitrogen availability in the vegetation decreased with increasing insect density, predation became an important source of protein for Mormon crickets that enhanced immunity. Grasshoppers can be an important source of dietary protein for Mormon crickets, with prey availability affecting Mormon cricket immunity to diseases.

Field bands of marching locust juveniles show carbohydrate, not protein, limitation

Locusts are grasshoppers that migrate en masse and devastate food security, yet little is known about the nutritional needs of marching bands in nature. While it has been hypothesized that protein limitation promotes locust marching behavior, migration is fueled by dietary carbohydrates. We studied South American Locust (Schistocerca cancellata) bands at eight sites across Argentina, Bolivia, and Paraguay. Bands ate most frequently from dishes containing carbohydrate artificial diets and minimally from balanced, protein, or control (vitamins and salts) dishes-indicating carbohydrate hunger. This hunger for carbohydrates is likely explained by the observation that local vegetation was generally protein-biased relative to locusts' preferred protein to carbohydrate ratio. This study highlights the importance of studying the nutritional ecology of animals in their environment and suggests that carbohydrate limitation may be a common pattern for migrating insect herbivores.

Velocity correlations in jackdaw flocks in different ecological contexts

Velocity correlation is an important feature for animal groups performing collective motions. Previous studies have mostly focused on the velocity correlation in a single ecological context. It is unclear whether correlation characteristics vary in a single species in different contexts. Here, we studied the velocity correlations in jackdaw flocks in two different contexts: transit flocks where birds travel from one location to another, and mobbing flocks where birds respond to an external stimulus. We found that in both contexts, although the interaction rules are different, the velocity correlations remain scale-free, i.e. the correlation length (the distance over which the velocity of two individuals is similar) increases linearly with the group size. Furthermore, we found that the correlation length is independent of the group density for transit flocks, but increases with increasing group density in mobbing flocks. This result confirms a previous observation that birds obey topological interactions in transit flocks, but switch to metric interactions in mobbing flocks. Finally, in both contexts, the impact of group polarization on correlation length is not significant. Our results suggest that wild animals are always able to respond coherently to perturbations regardless of context.

Modelling foraging competition between solitarious and gregarious organisms in increasingly heterogeneous environments

Density dependent phase polyphenism is the exhibiting of two or more distinct phenotypes from a single genotype depending on local population density. The most well known insect to exhibit this phenomenon is the locust, with whom the profound effect on behaviour leads to the classification of the two phases; solitarious, where locusts actively avoid other locusts, and gregarious, where locusts are strongly attracted to other locusts. It has been shown that food distributions at both small and large scales have an effect on the process of gregarisation. While gregarisation offers advantages, such as greater predator avoidance, the relationship between phase polyphenism and potential foraging benefits is still not fully understood. In this paper, we explore the effect of gregarisation on foraging within increasingly heterogeneous environments using a partial differential equation model. We first consider a single two dimensional simulation of a spatially heterogeneous environment to understand the mechanics of gregarious/solitarious foraging. We then look at the steady state foraging advantage (measured as the ratio of per-capita contact with food) in environments ranging from homogeneous to very spatially heterogeneous. Finally, we perform a parameter sensitivity analysis to find which model parameters have the greatest effect on foraging advantage. We find that during the aggregation stage, prior to the onset of marching (which we do not model here), in increasingly heterogeneous food environments it is better to be gregarious than solitarious. In addition, we find that this is intrinsic to the gregarious/solitarious behavioural dynamic as it occurs almost regardless of the model parameters. That is to say, it doesn't matter how fast the organisms disperse or how strong their long range interactions as long as there is the solitarious/gregarious behaviour the gregarious foraging advantage will exist.

A journey towards an integrated understanding of behavioural phase change in locusts

Behavioural phase change initiates and functionally couples the suite of traits that comprise density-dependent polyphenism in locusts. Here I provide a semi-expurgated account of my 25-year research journey studying behavioural phase transition in the desert locust. The journey spans continents, involves a cast of extraordinary colleagues, and travels across levels of biological organisation from deep within the nervous system of individual locusts to mass migration and the evolution and population dynamics of swarming.

Band movement and thermoregulation in Schistocerca cancellata

At high density, juvenile locusts create marching hopper bands. Understanding the roles of temperature and vegetation on the movement of these bands shall allow to better forecast and control them. Following a hopper band in North Argentina in November 2019, we explored the thermoregulation behaviours of the South American locust, Schistocerca cancellata. Gut-content samples informed about the feeding status at different time of the day. Hoppers' body temperature was above cold air temperature in the mornings during basking and group-basking activities and before the onset of marching behaviour. Marching by walking or hopping was dominant at body temperatures close to 40 °C. Jumping, stilting, shading and perching on plants were seen as thermoregulatory behaviours to avoid ground temperatures above 50 °C. Feeding was observed throughout the day with continuous high gut contents despite an intermittent pattern of feeding-resting-marching. Speed and daily travelled distance of the front of the hopper band was depending on the type of encountered vegetation. Daily behavioural patterns, thermoregulatory behaviours, walking speed and daily travelled distances of S. cancellata were similar to the ones observed for the Desert locust, S. gregaria, in Africa. High air temperatures recorded during the observation times could explain the continuous feeding patterns. These species may have evolved behaviours of alternating consuming a bit and marching as a migration strategy to avoid staying where no food is available after the havoc left behind large hopper bands. Recommendations made for the control of Desert locust hopper bands can be extended to South American locust ones.

Modelling locust foraging: How and why food affects group formation

Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local population density. These are: solitarious, where they will actively avoid other locusts, and gregarious where they will seek them out. It is in this gregarious state that locusts can form massive and destructive flying swarms or plagues. However, these swarms are usually preceded by the aggregation of juvenile wingless locust nymphs. In this paper we attempt to understand how the distribution of food resources affect the group formation process. We do this by introducing a multi-population partial differential equation model that includes non-local locust interactions, local locust and food interactions, and gregarisation. Our results suggest that, food acts to increase the maximum density of locust groups, lowers the percentage of the population that needs to be gregarious for group formation, and decreases both the required density of locusts and time for group formation around an optimal food width. Finally, by looking at foraging efficiency within the numerical experiments we find that there exists a foraging advantage to being gregarious.

Non-local interactions in collective motion

The collective motion of animal groups often exhibits velocity-velocity correlations between nearest neighbours, with the strongest velocity correlations observed at the shortest inter-animal spacings. This may have been a motivational factor in the development of models based primarily on short-ranged interactions. Here we ask whether such observations necessarily mean that the interactions are short-ranged. We develop a minimal model of collective motion capable of supporting interactions of arbitrary range and show that it represents a counterexample: the strongest velocity correlations emerge at the shortest distances, even when the interactions are explicitly non-local.

Detection and characterization of chemotaxis without cell tracking

Swarming has been observed in various biological systems from collective animal movements to immune cells. In the cellular context, swarming is driven by the secretion of chemotactic factors. Despite the critical role of chemotactic swarming, few methods to robustly identify and quantify this phenomenon exist. Here, we present a novel method for the analysis of time series of positional data generated from realizations of agent-based processes. We convert the positional data for each individual time point to a function measuring agent aggregation around a given area of interest, hence generating a functional time series. The functional time series, and a more easily visualized swarming metric of agent aggregation derived from these functions, provide useful information regarding the evolution of the underlying process over time. We extend our method to build upon the modelling of collective motility using drift-diffusion partial differential equations (PDEs). Using a functional linear model, we are able to use the functional time series to estimate the drift and diffusivity terms associated with the underlying PDE. By producing an accurate estimate for the drift coefficient, we can infer the strength and range of attraction or repulsion exerted on agents, as in chemotaxis. Our approach relies solely on using agent positional data. The spatial distribution of diffusing chemokines is not required, nor do individual agents need to be tracked over time. We demonstrate our approach using random walk simulations of chemotaxis and experiments investigating cytotoxic T cells interacting with tumouroids.

Agent-based and continuous models of hopper bands for the Australian plague locust: How resource consumption mediates pulse formation and geometry

Locusts are significant agricultural pests. Under favorable environmental conditions flightless juveniles may aggregate into coherent, aligned swarms referred to as hopper bands. These bands are often observed as a propagating wave having a dense front with rapidly decreasing density in the wake. A tantalizing and common observation is that these fronts slow and steepen in the presence of green vegetation. This suggests the collective motion of the band is mediated by resource consumption. Our goal is to model and quantify this effect. We focus on the Australian plague locust, for which excellent field and experimental data is available. Exploiting the alignment of locusts in hopper bands, we concentrate solely on the density variation perpendicular to the front. We develop two models in tandem; an agent-based model that tracks the position of individuals and a partial differential equation model that describes locust density. In both these models, locust are either stationary (and feeding) or moving. Resources decrease with feeding. The rate at which locusts transition between moving and stationary (and vice versa) is enhanced (diminished) by resource abundance. This effect proves essential to the formation, shape, and speed of locust hopper bands in our models. From the biological literature we estimate ranges for the ten input parameters of our models. Sobol sensitivity analysis yields insight into how the band's collective characteristics vary with changes in the input parameters. By examining 4.4 million parameter combinations, we identify biologically consistent parameters that reproduce field observations. We thus demonstrate that resource-dependent behavior can explain the density distribution observed in locust hopper bands. This work suggests that feeding behaviors should be an intrinsic part of future modeling efforts.

Local interactions and their group-level consequences in flocking jackdaws

As one of nature's most striking examples of collective behaviour, bird flocks have attracted extensive research. However, we still lack an understanding of the attractive and repulsive forces that govern interactions between individuals within flocks and how these forces influence neighbours' relative positions and ultimately determine the shape of flocks. We address these issues by analysing the three-dimensional movements of wild jackdaws ( Corvus monedula) in flocks containing 2-338 individuals. We quantify the social interaction forces in large, airborne flocks and find that these forces are highly anisotropic. The long-range attraction in the direction perpendicular to the movement direction is stronger than that along it, and the short-range repulsion is generated mainly by turning rather than changing speed. We explain this phenomenon by considering wingbeat frequency and the change in kinetic and gravitational potential energy during flight, and find that changing the direction of movement is less energetically costly than adjusting speed for birds. Furthermore, our data show that collision avoidance by turning can alter local neighbour distributions and ultimately change the group shape. Our results illustrate the macroscopic consequences of anisotropic interaction forces in bird flocks, and help to draw links between group structure, local interactions and the biophysics of animal locomotion.

Locust and Grasshopper Management

Locusts and grasshoppers (Orthoptera: Acridoidea) are among the most dangerous agricultural pests. Their control is critical to food security worldwide and often requires governmental or international involvement. Although locust and grasshopper outbreaks are now better controlled and often shorter in duration and reduced in extent, large outbreaks, often promoted by climate change, continue to occur in many parts of the world. While some locust and grasshopper control systems are still curative, the recognition of the damage these pests can cause and the socioeconomic consequences of locust and grasshopper outbreaks have led to an increasing paradigm shift from crop protection to preventive management. Effective preventive management strategy relies on an improved knowledge of the pest biology and ecology and more efficient monitoring and control techniques.

Sounds and hydrodynamics of polar active fluids

Spontaneously flowing liquids have been successfully engineered from a variety of biological and synthetic self-propelled units^1-11. Together with their orientational order, wave propagation in such active fluids has remained a subject of intense theoretical studies^12-17. However, the experimental observation of this phenomenon has remained elusive. Here, we establish and exploit the propagation of sound waves in colloidal active materials with broken rotational symmetry. We demonstrate that two mixed modes, coupling density and velocity fluctuations, propagate along all directions in colloidal-roller fluids. We then show how the six material constants defining the linear hydrodynamics of these active liquids can be measured from their spontaneous fluctuation spectrum, while being out of reach of conventional rheological methods. This active-sound spectroscopy is not specific to synthetic active materials and could provide a quantitative hydrodynamic description of herds, flocks and swarms from inspection of their large-scale fluctuations^18-21.

Collective movement in ecology: from emerging technologies to conservation and management

Recent advances in technology and quantitative methods have led to the emergence of a new field of study that stands to link insights of researchers from two closely related, but often disconnected disciplines: movement ecology and collective animal behaviour. To date, the field of movement ecology has focused on elucidating the internal and external drivers of animal movement and the influence of movement on broader ecological processes. Typically, tracking and/or remote sensing technology is employed to study individual animals in natural conditions. By contrast, the field of collective behaviour has quantified the significant role social interactions play in the decision-making of animals within groups and, to date, has predominantly relied on controlled laboratory-based studies and theoretical models owing to the constraints of studying interacting animals in the field. This themed issue is intended to formalize the burgeoning field of collective movement ecology which integrates research from both movement ecology and collective behaviour. In this introductory paper, we set the stage for the issue by briefly examining the approaches and current status of research in these areas. Next, we outline the structure of the theme issue and describe the obstacles collective movement researchers face, from data acquisition in the field to analysis and problems of scale, and highlight the key contributions of the assembled papers. We finish by presenting research that links individual and broad-scale ecological and evolutionary processes to collective movement, and finally relate these concepts to emerging challenges for the management and conservation of animals on the move in a world that is increasingly impacted by human activity.This article is part of the theme issue 'Collective movement ecology'.

Understanding how animal groups achieve coordinated movement

Moving animal groups display remarkable feats of coordination. This coordination is largely achieved when individuals adjust their movement in response to their neighbours' movements and positions. Recent advancements in automated tracking technologies, including computer vision and GPS, now allow researchers to gather large amounts of data on the movements and positions of individuals in groups. Furthermore, analytical techniques from fields such as statistical physics now allow us to identify the precise interaction rules used by animals on the move. These interaction rules differ not only between species, but also between individuals in the same group. These differences have wide-ranging implications, affecting how groups make collective decisions and driving the evolution of collective motion. Here, I describe how trajectory data can be used to infer how animals interact in moving groups. I give examples of the similarities and differences in the spatial and directional organisations of animal groups between species, and discuss the rules that animals use to achieve this organisation. I then explore how groups of the same species can exhibit different structures, and ask whether this results from individuals adapting their interaction rules. I then examine how the interaction rules between individuals in the same groups can also differ, and discuss how this can affect ecological and evolutionary processes. Finally, I suggest areas of future research.

Both Nearest Neighbours and Long-term Affiliates Predict Individual Locations During Collective Movement in Wild Baboons

In many animal societies, groups of individuals form stable social units that are shaped by well-delineated dominance hierarchies and a range of affiliative relationships. How do socially complex groups maintain cohesion and achieve collective movement? Using high-resolution GPS tracking of members of a wild baboon troop, we test whether collective movement in stable social groups is governed by interactions among local neighbours (commonly found in groups with largely anonymous memberships), social affiliates, and/or by individuals paying attention to global group structure. We construct candidate movement prediction models and evaluate their ability to predict the future trajectory of focal individuals. We find that baboon movements are best predicted by 4 to 6 neighbours. While these are generally individuals’ nearest neighbours, we find that baboons have distinct preferences for particular neighbours, and that these social affiliates best predict individual location at longer time scales (>10 minutes). Our results support existing theoretical and empirical studies highlighting the importance of local rules in driving collective outcomes, such as collective departures, in primates. We extend previous studies by elucidating the rules that maintain cohesion in baboons ‘on the move’, as well as the different temporal scales of social interactions that are at play.

Mechanisms underpinning aggregation and collective movement by insect groups

Collective movement behaviours range from temporary aggregations to coordinated mass migrations with synchronous movement. Models show how complex collective patterns can arise from simple rules regulating local interactions between individuals. However, it is not always clear how these rules are implemented by real insects: even simple abstract rules contain non-trivial assumptions about the perceptual abilities of individuals. Here we review the underlying mechanisms of simple forms of aggregation and collective movement focussing on locusts using them as an example of system in which analyses of the underlying molecular and neural mechanisms have become feasible. These and similar studies promise to reveal the physiological rules governing these behaviours.

Locust Collective Motion and Its Modeling

Over the past decade, technological advances in experimental and animal tracking techniques have motivated a renewed theoretical interest in animal collective motion and, in particular, locust swarming. This review offers a comprehensive biological background followed by comparative analysis of recent models of locust collective motion, in particular locust marching, their settings, and underlying assumptions. We describe a wide range of recent modeling and simulation approaches, from discrete agent-based models of self-propelled particles to continuous models of integro-differential equations, aimed at describing and analyzing the fascinating phenomenon of locust collective motion. These modeling efforts have a dual role: The first views locusts as a quintessential example of animal collective motion. As such, they aim at abstraction and coarse-graining, often utilizing the tools of statistical physics. The second, which originates from a more biological perspective, views locust swarming as a scientific problem of its own exceptional merit. The main goal should, thus, be the analysis and prediction of natural swarm dynamics. We discuss the properties of swarm dynamics using the tools of statistical physics, as well as the implications for laboratory experiments and natural swarms. Finally, we stress the importance of a combined-interdisciplinary, biological-theoretical effort in successfully confronting the challenges that locusts pose at both the theoretical and practical levels.

Intermittent collective dynamics emerge from conflicting imperatives in sheep herds

Among the many fascinating examples of collective behavior exhibited by animal groups, some species are known to alternate slow group dispersion in space with rapid aggregation phenomena induced by a sudden behavioral shift at the individual level. We study this phenomenon quantitatively in large groups of grazing Merino sheep under controlled experimental conditions. Our analysis reveals strongly intermittent collective dynamics consisting of fast, avalanche-like regrouping events distributed on all experimentally accessible scales. As a proof of principle, we introduce an agent-based model with individual behavioral shifts, which we show to account faithfully for all collective properties observed. This offers, in turn, an insight on the individual stimulus/response functions that can generate such intermittent behavior. In particular, the intensity of sheep allelomimetic behavior plays a key role in the group's ability to increase the per capita grazing surface while minimizing the time needed to regroup into a tightly packed configuration. We conclude that the emergent behavior reported probably arises from the necessity to balance two conflicting imperatives: (i) the exploration of foraging space by individuals and (ii) the protection from predators offered by being part of large, cohesive groups. We discuss our results in the context of the current debate about criticality in biology.

Sardine cycles, krill declines, and locust plagues: revisiting 'wasp-waist' food webs

'Wasp-waist' systems are dominated by a mid trophic-level species that is thought to exert top-down control on its food and bottom-up control on its predators. Sardines, anchovy, and Antarctic krill are suggested examples, and here we use locusts to explore whether the wasp-waist concept also applies on land. These examples also display the traits of mobile aggregations and dietary diversity, which help to reduce the foraging footprint from their large, localised biomasses. This suggests that top-down control on their food operates at local aggregation scales and not at wider scales suggested by the original definition of wasp-waist. With this modification, the wasp-waist framework can cross-fertilise marine and terrestrial approaches, revealing how seemingly disparate but economically important systems operate.

On the duality between interaction responses and mutual positions in flocking and schooling

Recent research in animal behaviour has contributed to determine how alignment, turning responses, and changes of speed mediate flocking and schooling interactions in different animal species. Here, we propose a complementary approach to the analysis of flocking phenomena, based on the idea that animals occupy preferential, anysotropic positions with respect to their neighbours, and devote a large amount of their interaction responses to maintaining their mutual positions. We test our approach by deriving the apparent alignment and attraction responses from simulated trajectories of animals moving side by side, or one in front of the other. We show that the anisotropic positioning of individuals, in combination with noise, is sufficient to reproduce several aspects of the movement responses observed in real animal groups. This anisotropy at the level of interactions should be considered explicitly in future models of flocking and schooling. By making a distinction between interaction responses involved in maintaining a preferred flock configuration, and interaction responses directed at changing it, our work provides a frame to discriminate movement interactions that signal directional conflict from interactions underlying consensual group motion.