scholarly journals Non-classical phase diagram for virus bacterial coevolution mediated by clustered regularly interspaced short palindromic repeats

2017 ◽  
Vol 14 (127) ◽  
pp. 20160905 ◽  
Author(s):  
Pu Han ◽  
Michael W. Deem
Keyword(s):  
Phase Diagram ◽  
Evolutionary Biology ◽  
Bacterial Population ◽  
Genetic Material ◽  
Extinction Probability ◽  
Exposure Rate ◽  
Parameter Region ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Two Phases

CRISPR is a newly discovered prokaryotic immune system. Bacteria and archaea with this system incorporate genetic material from invading viruses into their genomes, providing protection against future infection by similar viruses. The condition for coexistence of prokaryots and viruses is an interesting problem in evolutionary biology. In this work, we show an intriguing phase diagram of the virus extinction probability, which is more complex than that of the classical predator–prey model. As the CRISPR incorporates genetic material, viruses are under pressure to evolve to escape recognition by CRISPR. When bacteria have a small rate of deleting spacers, a new parameter region in which bacteria and viruses can coexist arises, and it leads to a more complex coexistence patten for bacteria and viruses. For example, when the virus mutation rate is low, the virus extinction probability changes non-montonically with the bacterial exposure rate. The virus and bacteria coevolution not only alters the virus extinction probability, but also changes the bacterial population structure. Additionally, we show that recombination is a successful strategy for viruses to escape from CRISPR recognition when viruses have multiple proto-spacers, providing support for a recombination-mediated escape mechanism suggested experimentally. Finally, we suggest that the re-entrant phase diagram, in which phages can progress through three phases of extinction and two phases of abundance at low spacer deletion rates as a function of exposure rate to bacteria, is an experimentally testable phenomenon.

scholarly journals Nonclassical phase diagram for virus bacterial co-evolution mediated by CRISPR

2017 ◽  
Author(s):  
Pu Han ◽  
Michael W. Deem
Keyword(s):  
Phase Diagram ◽  
Evolutionary Biology ◽  
Bacterial Population ◽  
Genetic Material ◽  
Extinction Probability ◽  
Exposure Rate ◽  
Parameter Region ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Two Phases

CRISPR is a newly discovered prokaryotic immune system. Bacteria and archaea with this system incorporate genetic material from invading viruses into their genomes, providing protection against future infection by similar viruses. The conditions for coexistence of prokaryots and viruses is an interesting problem in evolutionary biology. In this work, we show an intriguing phase diagram of the virus extinction probability, which is more complex than that of the classical predator-prey model. As the CRISPR incorporates genetic material, viruses are under pressure to evolve to escape the recognition by CRISPR. When bacteria have a small rate of deleting spacers, a new parameter region in which bacteria and viruses can coexist arises, and it leads to a more complex coexistence patten for bacteria and viruses. For example, when the virus mutation rate is low, the virus extinction probability changes non-montonically with the bacterial exposure rate. The virus and bacteria co-evolution not only alters the virus extinction probability, but also changes the bacterial population structure. Additionally, we show that recombination is a successful strategy for viruses to escape from CRISPR recognition when viruses have multiple proto-spacers, providing support for a recombination-mediated escape mechanism suggested experimentally. Finally, we suggest that the reentrant phase diagram, in which phages can progress through three phases of extinction and two phases of abundance at low spacer deletion rates as a function of exposure rate to bacteria, is an experimentally testable phenomenon.

scholarly journals Spatiotemporal Dynamics in a Predator–Prey Model with Functional Response Increasing in Both Predator and Prey Densities

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 17
Author(s):  
Ruizhi Yang ◽  
Qiannan Song ◽  
Yong An
Keyword(s):  
Phase Diagram ◽  
Hopf Bifurcation ◽  
Functional Response ◽  
Dynamic Properties ◽  
Equation System ◽  
Turing Instability ◽  
Bifurcation Curve ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Characteristic Roots

In this paper, a diffusive predator–prey system with a functional response that increases in both predator and prey densities is considered. By analyzing the characteristic roots of the partial differential equation system, the Turing instability and Hopf bifurcation are studied. In order to consider the dynamics of the model where the Turing bifurcation curve and the Hopf bifurcation curve intersect, we chose the diffusion coefficients d1 and β as bifurcating parameters. In particular, the normal form of Turing–Hopf bifurcation was calculated so that we could obtain the phase diagram. For parameters in each region of the phase diagram, there are different types of solutions, and their dynamic properties are extremely rich. In this study, we have used some numerical simulations in order to confirm these ideas.

Phase diagram of a cyclic predator-prey model with neutral-pair exchange

2013 ◽  
Vol 88 (2) ◽  
Author(s):  
Nara C. Guisoni ◽  
Ernesto S. Loscar ◽  
Mauricio Girardi
Keyword(s):  
Phase Diagram ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pair Exchange

scholarly journals Dynamics of an Eco-Epidemic Predator–Prey Model Involving Fractional Derivatives with Power-Law and Mittag–Leffler Kernel

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 785
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Isnani Darti
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Derivative ◽  
Equilibrium Point ◽  
Power Law ◽  
Equilibrium Points ◽  
Essential Difference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Infected Prey

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana–Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag–Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.

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