Direct Reciprocity in Spatial Populations Enhances R-Reciprocity As Well As ST-Reciprocity

• Kohei Miyaji,

  Affiliation Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka, Japan

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• Jun Tanimoto ,

  * E-mail: zhenwang0@gmail.com (ZW); tanimoto@cm.kyushu-u.ac.jp (JT)

  Affiliation Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka, Japan

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• Zhen Wang ,

  * E-mail: zhenwang0@gmail.com (ZW); tanimoto@cm.kyushu-u.ac.jp (JT)

  Affiliations Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, Center for Nonlinear Studies and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, Hong Kong

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• Aya Hagishima,

  Affiliation Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka, Japan

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• Naoki Ikegaya

  Affiliation Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka, Japan

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