Spatial structure arising from chase-escape interactions with crowding

Abstract

Movement of individuals, mediated by localised interactions, plays a key role in numerous processes including cell biology and ecology. In this work, we investigate an individual-based model accounting for various intraspecies and interspecies interactions in a community consisting of two distinct species. In this framework we consider one species to be chasers and the other species to be escapees, and we focus on chase-escape dynamics where the chasers are biased to move towards the escapees, and the escapees are biased to move away from the chasers. This framework allows us to explore how individual-level directional interactions scale up to influence spatial structure at the macroscale. To focus exclusively on the role of motility and directional bias in determining spatial structure, we consider conservative communities where the number of individuals in each species remains constant. To provide additional information about the individual-based model, we also present a mathematically tractable deterministic approximation based on describing the evolution of the spatial moments. We explore how different features of interactions including interaction strength, spatial extent of interaction, and relative density of species influence the formation of the macroscale spatial patterns. Introduction 1Movement of, and interaction between individuals is fundamental to various processes in cell biology and ecology 1-3 .2 These interactions are generated by a number of factors such as the release and detection of chemical signals, 3 mechanical forces, as well as chase and escape dynamics between animals 4-7 , and such interactions can be associated 4 with attractive or repulsive bias 8, 9 . Typically, chase-escape interactions in animal communities involve interspecies 5 interactions between two species where the chasers are biased to move towards the escapees, and the escapees 6 are biased to move away from the chasers 7, 10 . Such chase-escape interactions are relevant to the development of 7 skin patterns in zebrafish involving the movement of two types of pigment cells: melanophores and xanthophores. 8Here, melanophores tend to move away from xanthophores as xanthophores pursue the melanophores 11 . An 9 example of chase-escape interaction among a single species is in the case of locusts. Cannibalism within the 10 population is an important source of nutrients for locusts. Here, individual locusts tend to escape in response to 11 the threat of being attacked by its conspecifics. Concurrently, they pursue others in the migratory band in search of 12 nutrients 12-14 . Another example of chase-escape dynamics includes herding behaviour, such as in the case of dogs 13 herding sheep [15][16][17] . Neighbour dependent movement and directional bias can act in unison to generate distinct spatial 14 patterns in the cell population such as cellular aggregation 18 . Similarly, interactions in animal herds or bird flocks 15 can also lead to the creation of spatial patterns 19 . These observations suggest that individual level i...

Spatial population dynamics: Beyond the Kirkwood superposition approximation by advancing to the Fisher–Kopeliovich ansatz

“…Finally, let us introduce a scheme for the time integration of the coupled system of autonomous ordinary differential equations ( 21)- (23). We first cast them in the following compact form…”

“…For overcoming drawbacks of existing PD models, over the last two decades there has been an increasing interest in developing spatial moment dynamics (SMD) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In SMD the populations are described by time-dependent spatial moments (aka reduced distribution [13] or correlation [15,20,24] functions).…”

“…Using the principle of constrained maximum entropy, a corrected KSA has been introduced, too, in the context of PD [43]. A high efficiency of the original KSA closure has been proven not only for spatially homogeneous PD systems in continuous space [10,19,21,23], but for homogeneous [44][45][46] as well as inhomogeneous lattice [47,48] and off-lattice [49,50] models. Quite recently [51], the KSA ansatz has been applied to spatially inhomogeneous birth-death models in continuous space.…”

“…Being good for the description of segregated states, it performs comparatively poorly in strongly aggregated spatial patterns [10,12,21,43]. Some what better results can be achieved by artificially modifying the power-2 closure [10,11,21,23]. However, this modification destroys properties of symmetry for the triplet correlation function and can lead, in general, to unphysical negative values for the density of the system.…”

Population dynamics with spatial structure and an Allee effect

“…This work shows that spatial structure has a strong impact on the carrying capacity density. More recently, the spatial logistic model has been extended to consider other relevant mechanisms including interspecies and intraspecies interactions, neighbour-dependent motility bias, predator–prey dynamics and chase–escape interactions [43–46].…”