Ryunosuke Minami,¹ Chiaki Sato,¹ Yumi Yamahama,² Hideo Kubo,³ Takahiko Hariyama,² Ken-ichi Kimura<sup>1,*

1</sup>1Laboratory of Biology, Hokkaido University of Education, Sapporo Campus, Sapporo 002-8502, Japan
²2Department of Biology, Hamamatsu University School of Medicine, Hamamatsu 431-3192, Japan
³3Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

^*Corresponding author.Tel.:+81-11-778-0347; Fax:+81-11-778-0347; E-mail:kimura.kenichi@s.hokkyodai.ac.jp