How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement

Jager, Monique de; Bartumeus, Frederic; Kölzsch, Andrea; Weissing, Franz J.; Hengeveld, G.M.; Nolet, Bart A.; Herman, Peter M. J.; Koppel, Johan van de

doi:10.1098/rspb.2013.2605

Cited by 65 publications

(100 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We use the notationr 2 M to represent mussel movement, which is modelled explicitly as random walks of individual mussels 13 . Statistical analysis of experimental movement trails revealed that the distances covered by the mussels during 1 min could be approximated by an exponential distribution 13,33 , where the frequency h of occurrence decreased with movement distance r; h(r, b) ¼ (1/b) exp( À r/b). Here, the scaling parameter b is a function of the densities of mussels in the neighbourhood.…”

Section: Methodsmentioning

confidence: 99%

Pattern formation at multiple spatial scales drives the resilience of mussel bed ecosystems

et al. 2014

Self Cite

View full text Add to dashboard Cite

Self-organized complexity at multiple spatial scales is a distinctive characteristic of biological systems. Yet, little is known about how different self-organizing processes operating at different spatial scales interact to determine ecosystem functioning. Here we show that the interplay between self-organizing processes at individual and ecosystem level is a key determinant of the functioning and resilience of mussel beds. In mussel beds, self-organization generates spatial patterns at two characteristic spatial scales: small-scale net-shaped patterns due to behavioural aggregation of individuals, and large-scale banded patterns due to the interplay of between-mussel facilitation and resource depletion. Model analysis reveals that the interaction between these behavioural and ecosystem-level mechanisms increases mussel bed resilience, enables persistence under deteriorating conditions and makes them less prone to catastrophic collapse. Our analysis highlights that interactions between different forms of self-organization at multiple spatial scales may enhance the intrinsic ability of ecosystems to withstand both natural and human-induced disturbances.

show abstract

Section: Methodsmentioning

confidence: 99%

Pattern formation at multiple spatial scales drives the resilience of mussel bed ecosystems

et al. 2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…In our non-Markovian model, the role of the collision and repulsion rate γ ± is drastically changed. This term is responsible for the shift from the superdiffusive Lévy walk to diffusion as the density increases [39]. The nonlinear equations for the structural densities n + (x,t,τ ) and n − (x,t,τ ) can be written as…”

mentioning

confidence: 99%

“…Motivated by the recent experiments [19,39], we introduce microscopic mean-field kinetic equations in which we combine two key ingredients: (1) the turning rate that depends on alignment and collision interactions between individuals and (2) non-Markovian effects. The crucial problem here is how to incorporate nonlinear interactions into non-Markovian superdiffusion.…”

mentioning

confidence: 99%

Emergence of Lévy walks in systems of interacting individuals

Fedotov¹,

Korabel²

2017

Phys. Rev. E

View full text Add to dashboard Cite

We propose a model of superdiffusive Lévy walk as an emergent nonlinear phenomenon in systems of interacting individuals. The aim is to provide a qualitative explanation of recent experiments [G. Ariel et al., Nat. Commun. 6, 8396 (2015)] revealing an intriguing behavior: swarming bacteria fundamentally change their collective motion from simple diffusion into a superdiffusive Lévy walk dynamics. We introduce microscopic mean-field kinetic equations in which we combine two key ingredients: (1) alignment interactions between individuals and (2) non-Markovian effects. Our interacting run-and-tumble model leads to the superdiffusive growth of the mean-squared displacement and the power-law distribution of run length with infinite variance. The main result is that the superdiffusive behavior emerges as a cooperative effect without using the standard assumption of the power-law distribution of run distances from the inception. At the same time, we find that the collision and repulsion interactions lead to the density-dependent exponential tempering of power-law distributions. This qualitatively explains the experimentally observed transition from superdiffusion to the diffusion of mussels as their density increases [M. [15][16][17][18]. Recently an intriguing behavior of swarming bacteria was found: they fundamentally change their collective motion from simple diffusion into a superdiffusive Lévy walk dynamics [19]. The extraordinary feature of this movement is that the emergence of a superdiffusive motility is a result of the interactions between bacteria rather than the standard mechanism of controlling the individual frequency of tumbling. However, it is still an open question how Lévy walks emerge in systems of interacting self-propelled particles. The current theory of Lévy walk [8] assumes noninteracting particles and power-law distribution of traveled distances from the inception.The collective behavior of large groups of interacting individuals such as bird flocks, fish schools, and the collective migration of cells or bacteria is another rapidly growing area of active matter research [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. There exist two main types of models used for a collective behavior: (1) Lagrangian models describing the movements of self-propelled particles in terms of nonlinear equations for the positions and velocities of all particles [20][21][22][23], and (2) kinetic models involving partial differential equations for the population densities [24][25][26][27][28][29][30]. In this Rapid Communication we are only concerned with the nonlinear kinetic and macroscopic equations. They have been used to describe interactions between individuals and investigate the formation of a large variety of spatiotemporal self-organized aggregations. Most of these models converge to the density-dependent diffusive transport and do not lead to non-Markovian Lévy walks.In this Rapid Communication we propose a kinetic nonlinear Lévy walk model for interacting individuals in which...

show abstract

“…We modelled the movement of individuals in correspondance to natural mussel movements, using a heavy-tailed step length distribution (a Lévy walk with l = 2; de Jager et al 2011), where steps are made in random directions and their lengths are drawn from a power law distribution. A mussel ends its step prematurely when it encounters a conspecific (de Jager et al 2014). In our model, mussels cooperate after (and not during) pattern formation; therefore the attachment of byssus threads does not impair mussel movement.…”

Section: Methods An Individual-based Model Of Self-organized Patterningmentioning

confidence: 99%

Why mussels stick together: spatial self-organization affects the evolution of cooperation

2017

Self Cite

View full text Add to dashboard Cite

Cooperation with neighbours may be crucial for the persistence of populations in stressful environments. Yet, cooperation is often not evolutionarily stable, since noncooperative individuals can reap the benefits of cooperation without having to pay the costs associated with cooperation. Here we show that active aggregation leading to self-organized spatial pattern formation can promote the evolution of cooperativeness. To this end, we study the effect of movement strategies on the evolution of cooperation in mussel beds. Mussels cooperate by attaching themselves to neighbours via byssal threads, thereby providing mutual protection. Using an individual-based model for mussel bed formation, we first demonstrate that the spatial pattern and the corresponding number of neighbours strongly depends on the movement strategies of the mussels. With an evolutionary model, we then show that this has important implications for the evolution of cooperation, since the evolved level of cooperativeness (the number of byssus threads produced) strongly depends on the number of neighbours and on the harshness and variability of the environment. Our results suggest that spatial aggregation, abundantly found in self-organized ecosystems, may promote the evolution of cooperation.

show abstract

How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement

Cited by 65 publications

References 27 publications

Pattern formation at multiple spatial scales drives the resilience of mussel bed ecosystems

Pattern formation at multiple spatial scales drives the resilience of mussel bed ecosystems

Emergence of Lévy walks in systems of interacting individuals

Why mussels stick together: spatial self-organization affects the evolution of cooperation

Contact Info

Product

Resources

About