Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.
Diffusion-induced instabilities promote cooperation in eco-evolutionary networks
Bagchi School of Public Health, Ahmedabad University（艾哈迈达巴德大学巴吉公共卫生学院）；Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata（印度科学教育与研究学院加尔各答分校物理科学系）；Department of Mathematics and Namur Institute for Complex Systems - naXys, University of Namur（南纳尔大学数学与南纳尔复杂系统研究所-naXys）；Faculty of Natural Sciences and Mathematics, University of Maribor（马里博尔大学自然科学与数学学院）；Community Healthcare Center Dr. Adolf Drolc Maribor（马里博尔阿道夫·德罗尔克博士社区健康中心）；Department of Physics, Kyung Hee University（庆熙大学物理系）；University College, Korea University（韩国大学综合研究生院）；Physics and Applied Mathematics Unit, Indian Statistical Institute（印度统计物理学与应用数学单元）
Emergence of cooperation in nonlinear higher-order public goods games
Institute for Cross-disciplinary Physics and Complex Systems IFISC (CSIC-UIB)（交叉物理与复杂系统研究所）；Department of Network and Data Science, Central European University Vienna（中欧大学维也纳网络与数据科学系）；Human Evolutionary Ecology Group, Department of Evolutionary Anthropology, University of Zurich（苏黎世大学生物人类学系人类进化生态组）；Center for Networks and Complexity, Luiss University of Rome（罗马LUISS大学网络与复杂性中心）；Department of AI, Data and Decision Sciences, Luiss University of Rome（罗马LUISS大学人工智能、数据与决策科学系）
Stable cooperation emerges in stochastic multiplicative growth
International School for Advanced Studies (SISSA)（国际高等研究院）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克科学促进研究所数学系）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）
