A comparison of ecological and eco-evolutionary system with rapid predator evolution
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A comparison of ecological and eco-evolutionary system with rapid predator evolution Sukumar Samanta1 · Banshidhar Sahoo2 · Barun Das1 Received: 14 May 2020 / Revised: 19 September 2020 / Accepted: 27 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Evolution takes place in ecological system which involves interactions with other species. To describe such evolution, the modeling of predator-prey system is essential with simultaneous evolution of interacting species. In this paper, a predatorprey system with rapid predator evolution is proposed and studied. Rapid evolution is considered to affect the outcomes of simultaneous ecological change of dieting. The change of such diet is fast compared to the timescale of ecological system. We introduce a timescale difference parameter between the dynamics of a predator trait and the ecological system. The model is analyzed in terms of theoretical as well as numerical point of view. The comparisons are shown in between ecological and evolutionary dynamics. Simulated results illustrate that evolution causes chaotic dynamics and it will be controlled to periodic orbits, and stable steady state by increasing parameter values. On the other hand, the ecological system has only limit cycle and steady state dynamics with the variation of parameters. Therefore, the evolution makes the predator-prey dynamics to more complex. The proposed model is applicable in large population size, short generation times, and well-changed environment system. More preciously, the system has the suitable applicability in plankton system. Keywords Ecological dynamics · Eco-evolutionary dynamics · Rapid predator evolution · Chaos · Order
1 Introduction Evolution in ecosystem is one of the most important ecological processes for creating and disappearing species stability or diversity. If evolution takes place in population system, then it can be expressed as an evolutionary change in traits (i.e., properties that affect how well an individual performs as an organism via genomic changes of a predator and/or prey) (e.g. see [1,2]). If such an evolution happens on a timescale of about 1000 generations and can be observed in laboratory conditions, it is called a ‘rapid’ evolutionary change of traits (see [1]). Rapid evolutionary changes
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Sukumar Samanta [email protected] Banshidhar Sahoo [email protected] Barun Das [email protected]
1
Department of Applied Mathematics, S.K.B. University, Purulia, West Bengal, India
2
Department of Mathematics, Hiralal Bhakat College, Nalhati, Birbhum, West Bengal, India
have been reported in a wide variety of organisms, ranging from mammals to bacteria [3,4], from prey to predator (e.g. see [5,6]). A list of reports [7,8] on rapid evolution in predator-prey populations has been generated a great interest for two distinct reasons. Firstly, calculated rates of change seem very fast relative to typical rates of evolution. Secondly, rapid trait changes have the potential measure to affect the outcomes of simultaneous ecological
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