Binary interaction algorithms for the simulation of flocking and swarming dynamics

Microscopic models of flocking and swarming takes in account large numbers of interacting individ- uals. Numerical resolution of large flocks implies huge computational costs. Typically for $N$ interacting individuals we have a cost of $O(N^2)$. We tackle the problem numerically by considering approximated binary interaction dynamics described by kinetic equations and simulating such equations by suitable stochastic methods. This approach permits to compute approximate solutions as functions of a small scaling parameter $\varepsilon$ at a reduced complexity of O(N) operations. Several numerical results show the efficiency of the algorithms proposed

Refining self-propelled particle models for collective behaviour

Swarming, schooling, flocking and herding are all names given to the wide variety of collective behaviours exhibited by groups of animals, bacteria and even individual cells. More generally, the term swarming describes the behaviour of an aggregate of agents (not necessarily biological) of similar size and shape which exhibit some emergent property such as directed migration or group cohesion. In this paper we review various individual-based models of collective behaviour and discuss their merits and drawbacks. We further analyse some one-dimensional models in the context of locust swarming. In specific models, in both one and two dimensions, we demonstrate how varying the parameters relating to how much attention individuals pay to their neighbours can dramatically change the behaviour of the group. We also introduce leader individuals to these models with the ability to guide the swarm to a greater or lesser degree as we vary the parameters of the model. We consider evolutionary scenarios for models with leaders in which individuals are allowed to evolve the degree of influence neighbouring individuals have on their subsequent motion

Similarities in social calls during autumn swarming may facilitate interspecific communication between Myotis bat species

Bats employ a variety of social calls for communication purposes. However, for most species, social calls are far less studied than echolocation calls and their specific function often remains unclear. We investigated the function of in-flight social calls during autumn swarming in front of a large hibernaculum in Northern Germany, whose main inhabitants are two species of Myotis bats, Natterer’s bats (Myotis nattereri) and Daubenton’s bats (Myotis daubentonii). We recorded social calls in nights of high swarming activity and grouped the calls based on their spectro-temporal structure into ten types and verified our visual classification by a discriminant function analysis. Whenever possible, we subsequently assigned social calls to either M. daubentonii or M. nattereri by analyzing the echolocation calls surrounding them. As many bats echolocate at the same time during swarming, we did not analyze single echolocation calls but the “soundscape” surrounding each social call instead, encompassing not only spectral parameters but also the timbre (vocal “color”) of echolocation calls. Both species employ comparatively similar social call types in a swarming context, even though there are subtle differences in call parameters between species. To additionally gain information about the general function of social calls produced in a swarming context, we performed playback experiments with free-flying bats in the vicinity of the roost, using three different call types from both species, respectively. In three out of six treatments, bat activity (approximated as echolocation call rate) increased during and after stimulus presentation, indicating that bats inspected or approached the playback site. Using a camera trap, we were sometimes able to identify the species of approaching bats. Based on the photos taken during playbacks, we assume one call type to support interspecific communication while another call type works for intraspecific group cohesion

Towards Swarm Calculus: Urn Models of Collective Decisions and Universal Properties of Swarm Performance

Methods of general applicability are searched for in swarm intelligence with the aim of gaining new insights about natural swarms and to develop design methodologies for artificial swarms. An ideal solution could be a `swarm calculus' that allows to calculate key features of swarms such as expected swarm performance and robustness based on only a few parameters. To work towards this ideal, one needs to find methods and models with high degrees of generality. In this paper, we report two models that might be examples of exceptional generality. First, an abstract model is presented that describes swarm performance depending on swarm density based on the dichotomy between cooperation and interference. Typical swarm experiments are given as examples to show how the model fits to several different results. Second, we give an abstract model of collective decision making that is inspired by urn models. The effects of positive feedback probability, that is increasing over time in a decision making system, are understood by the help of a parameter that controls the feedback based on the swarm's current consensus. Several applicable methods, such as the description as Markov process, calculation of splitting probabilities, mean first passage times, and measurements of positive feedback, are discussed and applications to artificial and natural swarms are reported

The soundscape of swarming: Proof of concept for a noninvasive acoustic species identification of swarming Myotis bats

Bats emit echolocation calls to orientate in their predominantly dark environment. Recording of species‐specific calls can facilitate species identification, especially when mist netting is not feasible. However, some taxa, such as Myotis bats can be hard to distinguish acoustically. In crowded situations where calls of many individuals overlap, the subtle differences between species are additionally attenuated. Here, we sought to noninvasively study the phenology of Myotis bats during autumn swarming at a prominent hibernaculum. To do so, we recorded sequences of overlapping echolocation calls (N = 564) during nights of high swarming activity and extracted spectral parameters (peak frequency, start frequency, spectral centroid) and linear frequency cepstral coefficients (LFCCs), which additionally encompass the timbre (vocal “color”) of calls. We used this parameter combination in a stepwise discriminant function analysis (DFA) to classify the call sequences to species level. A set of previously identified call sequences of single flying Myotis daubentonii and Myotis nattereri, the most common species at our study site, functioned as a training set for the DFA. 90.2% of the call sequences could be assigned to either M. daubentonii or M. nattereri, indicating the predominantly swarming species at the time of recording. We verified our results by correctly classifying the second set of previously identified call sequences with an accuracy of 100%. In addition, our acoustic species classification corresponds well to the existing knowledge on swarming phenology at the hibernaculum. Moreover, we successfully classified call sequences from a different hibernaculum to species level and verified our classification results by capturing swarming bats while we recorded them. Our findings provide a proof of concept for a new noninvasive acoustic monitoring technique that analyses “swarming soundscapes” by combining classical acoustic parameters and LFCCs, instead of analyzing single calls. Our approach for species identification is especially beneficial in situations with multiple calling individuals, such as autumn swarming

State-space modelling of the drivers of movement behaviour in sympatric species

Understanding animal movement behaviour is key to furthering our knowledge on intra- and inter-specific competition, group cohesion, energy expenditure, habitat use, the spread of zoonotic diseases or species management. We used a radial basis function surface approximation subject to minimum description length constraint to uncover the state-space dynamical systems from time series data. This approximation allowed us to infer structure from a mathematical model of the movement behaviour of sheep and red deer, and the effect of density, thermal stress and vegetation type. Animal movement was recorded using GPS collars deployed in sheep and deer grazing a large experimental plot in winter and summer. Information on the thermal stress to which animals were exposed was estimated using the power consumption of mechanical heated models and meteorological records of a network of stations in the plot. Thermal stress was higher in deer than in sheep, with less differences between species in summer. Deer travelled more distance than sheep, and both species travelled more in summer than in winter; deer travel distance showed less seasonal differences than sheep. Animal movement was better predicted in deer than in sheep and in winter than in summer; both species showed a swarming behaviour in group cohesion, stronger in deer. At shorter separation distances swarming repulsion was stronger between species than within species. At longer separation distances inter-specific attraction was weaker than intra-specific; there was a positive density-dependent effect on swarming, and stronger in deer than in sheep. There was not clear evidence which species attracted or repelled the other; attraction between deer at long separation distances was stronger when the model accounted for thermal stress, but in general the dynamic movement behaviour was hardly affected by the thermal stress. Vegetation type affected intra-species interactions but had little effect on inter-species interactions. Our modelling approach is useful in interpreting animal interactions, in order to unravel complex cooperative or competitive behaviours, and to the best of our knowledge is the first modelling attempt to make predictions of multi-species animal movement under different habitat mosaics and abiotic environmental conditions