Jerome Buhl

From Disorder to Order in Marching Locusts

Recent models from theoretical physics have predicted that mass-migrating animal groups may share group-level properties, irrespective of the type of animals in the group. One key prediction is that as the density of animals in the group increases, a rapid transition occurs from disordered movement of individuals within the group to highly aligned collective motion. Understanding such a transition is crucial to the control of mobile swarming insect pests such as the desert locust. We confirmed the prediction of a rapid transition from disordered to ordered movement and identified a critical density for the onset of coordinated marching in locust nymphs. We also demonstrated a dynamic instability in motion at densities typical of locusts in the field, in which groups can switch direction without external perturbation, potentially facilitating the rapid transfer of directional information.

Inherent noise can facilitate coherence in collective swarm motion

Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending the factors that determine such switches is key to understanding the movement of these groups. Here, we adopt a coarse-grained approach to the study of directional switching in a self-propelled particle model assuming an underlying one-dimensional Fokker–Planck equation for the mean velocity of the particles. We continue with this assumption in analyzing experimental data on locusts and use a similar systematic Fokker–Planck equation coefficient estimation approach to extract the relevant information for the assumed Fokker–Planck equation underlying that experimental data. In the experiment itself the motion of groups of 5 to 100 locust nymphs was investigated in a homogeneous laboratory environment, helping us to establish the intrinsic dynamics of locust marching bands. We determine the mean time between direction switches as a function of group density for the experimental data and the self-propelled particle model. This systematic approach allows us to identify key differences between the experimental data and the model, revealing that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. We give a quantitative description of how locusts use noise to maintain swarm alignment. We discuss further how properties of individual animal behavior, inferred by using the Fokker–Planck equation coefficient estimation approach, can be implemented in the self-propelled particle model to replicate qualitatively the group level dynamics seen in the experimental data.

Ergodic directional switching in mobile insect groups

We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of constituents of the swarm. The stationary probability distribution shows a rich phenomenology including nonmonotonic behavior of several order and disorder transition indicators in noise intensity. This complex behavior arises naturally as a result of the randomness in the system. Its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models. Our results suggest that the collective switches of the groups direction of motion might be due to a random ergodic effect and, as such, they are inherent to group formation.

Information transfer in moving animal groups

Moving animal groups provide some of the most intriguing and difficult to characterise examples of collective behaviour. We review some recent (and not so recent) empirical research on the motion of animal groups, including fish, locusts and homing pigeons. An important concept which unifies our understanding of these groups is that of transfer of directional information. Individuals which change their direction of travel in response to the direction taken by their near neighbours can quickly transfer information about the presence of a predatory threat or food source. We show that such information transfer is optimised when the density of individuals in a group is close to that at which a phase transition occurs between random and ordered motion. Similarly, we show that even relatively small differences in information possessed by group members can lead to strong collective-level decisions for one of two options. By combining the use of self-propelled particle and social force models of collective motion with thinking about the evolution of flocking we aim to better understand how complexity arises within these groups.

Shape and efficiency of wood ant foraging networks

We measured the shape of the foraging trail networks of 11 colonies of the wood ant Formica aquilonia (Formica rufa group). We characterized these networks in terms of their degree of branching and the angles between branches, as well as in terms of their efficiency. The measured networks were compared with idealized model networks built to optimize one of two components of efficiency, total length (i.e., total amount of trail) and route factor (i.e., average distance between nest and foraging site). The analysis shows that the networks built by the ants obtain a compromise between the two modes of efficiency. These results are largely independent of the size of the network or colony size. The ants’ efficiency is comparable to that of networks built by humans but achieved without the benefit of centralized control.

Nutritional ecology beyond the individual: a conceptual framework for integrating nutrition and social interactions.

Over recent years, modelling approaches from nutritional ecology (known as Nutritional Geometry) have been increasingly used to describe how animals and some other organisms select foods and eat them in appropriate amounts in order to maintain a balanced nutritional state maximising fitness. These nutritional strategies profoundly affect the physiology, behaviour and performance of individuals, which in turn impact their social interactions within groups and societies. Here, we present a conceptual framework to study the role of nutrition as a major ecological factor influencing the development and maintenance of social life. We first illustrate some of the mechanisms by which nutritional differences among individuals mediate social interactions in a broad range of species and ecological contexts. We then explain how studying individual- and collective-level nutrition in a common conceptual framework derived from Nutritional Geometry can bring new fundamental insights into the mechanisms and evolution of social interactions, using a combination of simulation models and manipulative experiments.

Initiation and spread of escape waves within animal groups.

The exceptional reactivity of animal collectives to predatory attacks is thought to be owing to rapid, but local, transfer of information between group members. These groups turn together in unison and produce escape waves. However, it is not clear how escape waves are created from local interactions, nor is it understood how these patterns are shaped by natural selection. By startling schools of fish with a simulated attack in an experimental arena, we demonstrate that changes in the direction and speed by a small percentage of individuals that detect the danger initiate an escape wave. This escape wave consists of a densely packed band of individuals that causes other school members to change direction. In the majority of cases, this wave passes through the entire group. We use a simulation model to demonstrate that this mechanism can, through local interactions alone, produce arbitrarily large escape waves. In the model, when we set the group density to that seen in real fish schools, we find that the risk to the members at the edge of the group is roughly equal to the risk of those within the group. Our experiments and modelling results provide a plausible explanation for how escape waves propagate in nature without centralized control.

Cannibalism in the lifeboat — collective movement in Australian plague locusts

Mass migration of locusts is an economically devastating and poorly understood phenomenon. Locust mass migration often follows rapid population growth because individuals must move to find new sources of locally depleted resources. In Mormon crickets and Desert locusts, cannibalistic interactions have been revealed as the driving force behind collective mass movement. Locusts are known to compensate for nutrient deficiencies and they themselves are a good source of nutrients such as protein. However, direct empirical evidence for an adaptive benefit of cannibalism in migratory bands has been lacking. Here, we first show that Australian plague locusts, Chortoicetes terminifera, will cannibalise vulnerable conspecifics to compensate for protein deprivation, supporting the notion that cannibalistic interactions among nutritionally deprived individuals drives collective mass movement. We then show that individuals in a group with the opportunity to cannibalise survive longer and move more than individuals without the opportunity to cannibalise. These results provide empirical support for the ‘lifeboat mechanism’, which proposes that cannibalism offers the dual benefits to individuals in a group of surviving longer and travelling farther than a solitary individual without the opportunity to cannibalise.

Modelling nutrition across organizational levels: from individuals to superorganisms

The Geometric Framework for nutrition has been increasingly used to describe how individual animals regulate their intake of multiple nutrients to maintain target physiological states maximizing growth and reproduction. However, only a few studies have considered the potential influences of the social context in which these nutritional decisions are made. Social insects, for instance, have evolved extreme levels of nutritional interdependence in which food collection, processing, storage and disposal are performed by different individuals with different nutritional needs. These social interactions considerably complicate nutrition and raise the question of how nutrient regulation is achieved at multiple organizational levels, by individuals and groups. Here, we explore the connections between individual- and collective-level nutrition by developing a modelling framework integrating concepts of nutritional geometry into individual-based models. Using this approach, we investigate how simple nutritional interactions between individuals can mediate a range of emergent collective-level phenomena in social arthropods (insects and spiders) and provide examples of novel and empirically testable predictions. We discuss how our approach could be expanded to a wider range of species and social systems.

Evolving Nutritional Strategies in the Presence of Competition: A Geometric Agent- Based Model

Access to nutrients is a key factor governing development, reproduction and ultimately fitness. Within social groups, contest-competition can fundamentally affect nutrient access, potentially leading to reproductive asymmetry among individuals. Previously, agent-based models have been combined with the Geometric Framework of nutrition to provide insight into how nutrition and social interactions affect one another. Here, we expand this modelling approach by incorporating evolutionary algorithms to explore how contest-competition over nutrient acquisition might affect the evolution of animal nutritional strategies. Specifically, we model tolerance of nutrient excesses and deficits when ingesting nutritionally imbalanced foods, which we term ‘nutritional latitude’; a higher degree of nutritional latitude constitutes a higher tolerance of nutritional excess and deficit. Our results indicate that a transition between two alternative strategies occurs at moderate to high levels of competition. When competition is low, individuals display a low level of nutritional latitude and regularly switch foods in search of an optimum. When food is scarce and contest-competition is intense, high nutritional latitude appears optimal, and individuals continue to consume an imbalanced food for longer periods before attempting to switch to an alternative. However, the relative balance of nutrients within available foods also strongly influences at what levels of competition, if any, transitions between these two strategies occur. Our models imply that competition combined with reproductive skew in social groups can play a role in the evolution of diet breadth. We discuss how the integration of agent-based, nutritional and evolutionary modelling may be applied in future studies to further understand the evolution of nutritional strategies across social and ecological contexts.