scholarly journals Self-organized pattern formation increases functional diversity

2020 ◽  
Author(s):  
Janne Hülsemann ◽  
Toni Klauschies ◽  
Christian Guill
Keyword(s):  
Pattern Formation ◽  
Functional Diversity ◽  
Continuous Distribution ◽  
Stabilizing Selection ◽  
Chain Model ◽  
Self Organized ◽  
Local Functional ◽  
Spatio Temporal ◽  
Alternative Community ◽  
Food Chain Model

AbstractSelf-organized formation of spatial patterns is known from a variety of different ecosystems, yet little is known how these patterns affect functional diversity of local and regional communities. Here we use a food chain model in which autotroph diversity is described by a continuous distribution of a trait that affects both growth rate and defense against a heterotroph. On a single patch, stabilizing selection always promotes the dominance of a single autotroph species. Two alternative community states, with either defended or undefended species, are possible. In a metacommunity context, dispersal can destabilize these states, and complex spatio-temporal patterns emerge. This creates varying selection pressures on the local autotroph communities, which feed back on the trait dynamics. Local functional diversity increases ten-fold compared to a situation without self-organized pattern formation, thereby maintaining the adaptive potential of communities in an environment threatened by fragmentation and global change.

Movement, competition and pattern formation in a two prey–one predator food chain model

2017 ◽  
Vol 37 (3) ◽  
pp. 2445-2459 ◽  
Author(s):  
P. M. Tchepmo Djomegni ◽  
K. S. Govinder ◽  
E. F. Doungmo Goufo
Keyword(s):  
Pattern Formation ◽  
Food Chain ◽  
Chain Model ◽  
Food Chain Model

scholarly journals Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lei Zhang
Keyword(s):  
Pattern Formation ◽  
Equilibrium Point ◽  
Food Chain ◽  
Reaction Diffusion ◽  
Evolution Process ◽  
Chain Model ◽  
Reaction Diffusion Model ◽  
Model Dynamics ◽  
Ratio Dependent ◽  
Food Chain Model

Predator-prey models describe biological phenomena of pursuit-evasion interaction. And this interaction exists widely in the world for the necessary energy supplement of species. In this paper, we have investigated a ratio-dependent spatially extended food chain model. Based on the bifurcation analysis (Hopf and Turing), we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point(u2*,v2*,w2*), and find that the model dynamics exhibits complex pattern replication. For fixed parameters, on increasing the control parameterc1, the sequence “holes→holes-stripe mixtures→stripes→spots-stripe mixtures→spots” pattern is observed. And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication. Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point(u1*,v1*,0), and find that the model dynamics exhibits stripes-spots pattern replication. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.

scholarly journals Cross Diffusion Induced Turing Patterns in a Tritrophic Food Chain Model with Crowley-Martin Functional Response

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 229 ◽  
Author(s):  
Nitu Kumari ◽  
Nishith Mohan
Keyword(s):  
Pattern Formation ◽  
Positive Solution ◽  
Functional Response ◽  
Food Chain ◽  
Turing Patterns ◽  
Chain Model ◽  
Self Diffusion ◽  
Cross Diffusion ◽  
Wide Range ◽  
Food Chain Model

Diffusion has long been known to induce pattern formation in predator prey systems. For certain prey-predator interaction systems, self diffusion conditions ceases to induce patterns, i.e., a non-constant positive solution does not exist, as seen from the literature. We investigate the effect of cross diffusion on the pattern formation in a tritrophic food chain model. In the formulated model, the prey interacts with the mid level predator in accordance with Holling Type II functional response and the mid and top level predator interact via Crowley-Martin functional response. We prove that the stationary uniform solution of the system is stable in the presence of diffusion when cross diffusion is absent. However, this solution is unstable in the presence of both self diffusion and cross diffusion. Using a priori analysis, we show the existence of a inhomogeneous steady state. We prove that no non-constant positive solution exists in the presence of diffusion under certain conditions, i.e., no pattern formation occurs. However, pattern formation is induced by cross diffusion because of the existence of non-constant positive solution, which is proven analytically as well as numerically. We performed extensive numerical simulations to understand Turing pattern formation for different values of self and cross diffusivity coefficients of the top level predator to validate our results. We obtained a wide range of Turing patterns induced by cross diffusion in the top population, including floral, labyrinth, hot spots, pentagonal and hexagonal Turing patterns.

scholarly journals Pattern Formation in Tri-Trophic Ratio-Dependent Food Chain Model

2011 ◽  
Vol 02 (12) ◽  
pp. 1507-1514 ◽  
Author(s):  
Dawit Melese ◽  
Sunita Gakkhar
Keyword(s):  
Pattern Formation ◽  
Food Chain ◽  
Chain Model ◽  
Ratio Dependent ◽  
Food Chain Model

scholarly journals Pattern Formation in Spatially Extended Tritrophic Food Chain Model Systems: Generalist versus Specialist Top Predator

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Nitu Kumari
Keyword(s):  
Pattern Formation ◽  
Food Chain ◽  
Model System ◽  
Model Systems ◽  
Subsurface Water ◽  
Chain Model ◽  
Top Predator ◽  
Top Predators ◽  
Spatially Extended ◽  
Food Chain Model

The complex dynamics of two types of tritrophic food chain model systems when the species undergo spatial movements, modeling two real situations of marine ecosystem, are investigated in this study analytically and using numerical simulations. The study has been carried out with the objective to explore and compare the competitive effects of fish and molluscs species being the top predators, when phytoplankton and zooplankton species are undergoing spatial movements in the subsurface water. Reaction diffusion systems have been used to represent temporal evolution and spatial interaction among the species. The two model systems differ in an essential way that the top predators are generalist and specialist, respectively, in two models. “Wave of Chaos” mechanism is found to be the responsible factor for the pattern (non-Turing) formation in one dimension seen in the food chain ending with top generalist predator. In the present work we have reported WOC phenomenon, for the first time in the literature, in a three-species spatially extended food chain model system. The numerical simulation leads to spontaneous and interesting pattern formation in two dimensions. Constraints on different parameters under which Turing and non-Turing patterns may be observed are obtained analytically. Diffusion-driven analysis is carried out, and the effect of diffusion on the chaotic dynamics of the model systems is studied. The existence of chaotic attractor and long-term chaotic behavior demonstrate the effect of diffusion on the dynamics of the model systems. It is observed from numerical study that food chain model system with top predator as generalist has very rich dynamics and shows very interesting patterns. An ecosystem having top predator as specialist leads to the stability of the system.

Pattern formation in an explosive food chain model: the case of “apparent” mutualism

2021 ◽  
Vol 136 (4) ◽  
Author(s):  
Saikat Batabyal ◽  
Debaldev Jana ◽  
Rana D. Parshad ◽  
Aladeen Al Basheer ◽  
Ranjit Kumar Upadhyay
Keyword(s):  
Pattern Formation ◽  
Food Chain ◽  
Chain Model ◽  
Food Chain Model

scholarly journals Perspective: network-guided pattern formation of neural dynamics

2014 ◽  
Vol 369 (1653) ◽  
pp. 20130522 ◽  
Author(s):  
Marc-Thorsten Hütt ◽  
Marcus Kaiser ◽  
Claus C. Hilgetag
Keyword(s):  
Pattern Formation ◽  
Network Architecture ◽  
Brain Connectivity ◽  
Activity Patterns ◽  
Neural Dynamics ◽  
Self Organized ◽  
Topological Features ◽  
Small Set ◽  
Spatio Temporal

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings and lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatio-temporal pattern formation and propose a novel perspective for analysing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.

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