A discrete particle model reproducing collective dynamics of a bee swarm

Abstract

In this article, we present a microscopic discrete mathematical model describing collective dynamics of a bee swarm. More specifically, each bee is set to move according to individual strategies and social interactions, the former involving the desire to reach a target destination, the latter accounting for repulsive/attractive stimuli and for alignment processes. The insects tend in fact to remain sufficiently close to the rest of the population, while avoiding collisions, and they are able to track and synchronize their movement to the flight of a given set of neighbors within their visual field. The resulting collective behavior of the bee cloud therefore emerges from non-local short/long-range interactions. Differently from similar approaches present in the literature, we here test different alignment mechanisms (i.e., based either on an Euclidean or on a topological neighborhood metric), which have an impact also on the other social components characterizing insect behavior. A series of numerical realizations then shows the phenomenology of the swarm (in terms of pattern configuration, collective productive movement, and flight synchronization) in different regions of the space of free model parameters (i.e., strength of attractive/repulsive forces, extension of the interaction regions). In this respect, constraints in the possible variations of such coefficients are here given both by reasonable empirical observations and by analytical results on some stability characteristics of the defined pairwise interaction kernels, which have to assure a realistic crystalline configuration of the swarm. An analysis of the effect of unconscious random fluctuations of bee dynamics is also provided.

A particle model analysing the behavioural rules underlying the collective flight of a bee swarm towards the new nest

“…These assumptions have been previously implemented in a number of approaches dealing with the collective dynamics of swarms, as commented in the conclusive section of this paper and reviewed by Carrillo and coworkers in [9]. We have also employed such phenomenological rules in a previous work [2], that has .d how a single leader bee is able to transmit the direction of movement to the rest of the population. In particular, we have therein tested alternative alignment hypotheses, i.e.…”

“…The exact form of h group is taken such that its maximum is given by the positive coefficient f group ∈ (0, +∞), which has units m/s, and located in the middle of the interval (d avoid , d group ). Analogous attraction functions has been used in the case of other particle models relative to bee and cell dynamics, see [2,[11][12][13] and references therein. It is also useful to underline that, according to the above-introduced kernels h avoid and h group , which are plotted in Figure 3(b), and to the corresponding interaction sets N avoid and N group , two individuals do not interact (i) when they do not see each other and (ii) when they are exactly at the comfort distance d avoid .…”

Nonlocal Flocking Dynamics: Learning the Fractional Order of PDEs from Particle Simulations

“…Although this collective dynamics are at very different scales and levels of complexity, the mechanism of self-organization, where local interactions for the individuals lead to a coherent group motion, is very general and transcends the detailed objects [8]. To this end, simulation and modeling of both physical [9] and biological [10] systems have driven a rich field of research to explore how individual behavior engenders large scale collective motion. There are generally two different approaches to investigate the underlying mechanics: 1) at the microscopic level, agent-based models are developed to simulate dynamics of each individual in flocks, such as swarms, tori, and polarized groups; 2) at the macroscopic level, the mathematical modeling approach is based on continuum models described by partial differential equations (PDEs).…”

An interdisciplinary approach to investigate collective cell migration in neural crest

“…Collective migration is a common phenomenon that is observed to arise at many different length scales ranging from the micron level to kilometers. For example, in embryonic development many processes rely on cells moving collectively either in sheets or as individuals; in humans, a major area of research is the understanding of crowd dynamics; in insects, the phenomenon of swarm dynamics is well‐studied . These are only a small sample of the vast number of examples of this phenomenon.…”

“…For example, in embryonic development many processes rely on cells moving collectively either in sheets or as individuals 1,2 ; in humans, a major area of research is the understanding of crowd dynamics [3][4][5] ; in insects, the phenomenon of swarm dynamics is well-studied. [6][7][8] These are only a small sample of the vast number of examples of this phenomenon. In this Critical Commentary, we narrow our focus to one example, namely, cranial neural crest (NC) cell migration in chick and illustrate how an interdisciplinary approach combining experiments and computational modeling has enabled us to investigate a number of key biological questions concerning this collective behaviour.…”