Pattern formation in animals and plants, or morphogenesis, is an extremely important subject in developmental biology. It is fascinating to see the process leading from a fertilized egg with a relatively simple structure to the extremely complicated three-dimensional structures of the adult body with its numerous organs. However problems of pattern formation are not restricted to developmental biology, but exist in all the branches of the biological sciences. This special issue of Forma entitled "biological pattern formation" includes seven articles, the subjects of which range from phenomena at the cellular and organismal level to pattern formation at the ecological scale, such as the spatial spread of invader species in a novel habitat.
The seven papers in the special issue are based on more than 30 oral presentations made in a three-day symposium of mathematical topics in biology, which was held on November 6-8th 1995, in the School of Mathematical Sciences, University of Tokyo, at the annual meeting of the Japanese Association for Mathematical Biology. Papers suitable for Forma were encouraged to contribute to this special issue.
This issue includes a range of subjects: it starts with a fascinating review article of pattern formation of visual cortical maps, followed by two papers on developmental pattern formation, and then by a paper on optimal design in plant morphology, and finishes with three papers on spatial pattern formation in population biology. The papers also differ in the methods used to analyze biological pattern formation—some emphasize rigorous mathematical analysis, as exemplified by Yamada's article of reaction-diffusion systems, while others are based on neural network computation of genetic switching, or on the optimal design of biological forms. On the other hand, it is also illuminating to notice that the same modeling technique has been adopted for vastly different biological phenomena, exemplified by the cellular automata models used for modeling visual cortical map formation, cell-sorting experiments, and prey-predator dynamics.
The subject of biological pattern formation is a very rich field, and has great potential to quickly increase its importance in the biological sciences. The need to develop a basic understanding of biological pattern formation will become stronger in light of the vast amount of knowledge becoming available due to the recent advances of molecular biology. An array of biological phenomena are now waiting for new concepts and the further development of tools to examine spatial pattern formation.
We would like to thank Professor Masayasu Mimura, University of Tokyo for providing the venue for the symposium. We also thank the Editor-in-Chief of Forma, Professor Ryuji Takaki, for agreeing to publish this special issue of Forma.
June 1996
Y. Iwasa1, H. Matsuda1, A. Sasaki1 and T. Sekimura2
1Kyushu University, Fukuoka, Japan
2Chubu University, Kasugai, Japan