caa a22 4500 605497419 CHVBK 20210128100541.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10441-015-9254-z doi (NATIONALLICENCE)springer-10.1007/s10441-015-9254-z How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos? [Elektronische Daten] [Jorge Duarte, Carla Rodrigues, Cristina Januário, Nuno Martins, Josep Sardanyés] Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable. Springer Science+Business Media Dordrecht, 2015 Adaptive dynamics nationallicence Chaos nationallicence Coevolution nationallicence Ecology nationallicence Predator-prey nationallicence Predictability nationallicence Red Queen nationallicence Duarte Jorge Department of Mathematics, ISEL - Engineering Superior Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1949-014, Lisbon, Portugal aut Rodrigues Carla Department of Mathematics, ESTS - Technology Superior School of Setubal, Campus do IPS, Rua Vale de Chaves, Estefanilha, 2914-761, Setubal, Portugal aut Januário Cristina Department of Mathematics, ISEL - Engineering Superior Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1949-014, Lisbon, Portugal aut Martins Nuno Mathematics Department, Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisbon, Portugal aut Sardanyés Josep ICREA-Complex Systems Lab, Universitat Pompeu Fabra (UPF), Parc de Recerca Biomèdica de Barcelona (PRBB), Dr. Aiguader, 88, 08003, Barcelona, Spain aut Acta Biotheoretica Springer Netherlands 63/4(2015-12-01), 341-361 0001-5342 63:4<341 2015 63 10441 https://doi.org/10.1007/s10441-015-9254-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10441-015-9254-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Duarte Jorge Department of Mathematics, ISEL - Engineering Superior Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1949-014, Lisbon, Portugal aut NATIONALLICENCE 700 1- Rodrigues Carla Department of Mathematics, ESTS - Technology Superior School of Setubal, Campus do IPS, Rua Vale de Chaves, Estefanilha, 2914-761, Setubal, Portugal aut NATIONALLICENCE 700 1- Januário Cristina Department of Mathematics, ISEL - Engineering Superior Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1949-014, Lisbon, Portugal aut NATIONALLICENCE 700 1- Martins Nuno Mathematics Department, Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisbon, Portugal aut NATIONALLICENCE 700 1- Sardanyés Josep ICREA-Complex Systems Lab, Universitat Pompeu Fabra (UPF), Parc de Recerca Biomèdica de Barcelona (PRBB), Dr. Aiguader, 88, 08003, Barcelona, Spain aut NATIONALLICENCE 773 0- Acta Biotheoretica Springer Netherlands 63/4(2015-12-01), 341-361 0001-5342 63:4<341 2015 63 10441