Branching Pattern Modeling for Psychotoria species and Their Deterministic Algorithm

Abstract

Back Ground: The branching patterns and the subsequent elongations of two shrub Psychotria species, Pyschotoria rubra and Psychotoria manillensis, in Okinawa Island, the Ryukyu Islands, Japan, were examined by Watanabe. His results showed that Hamilton's classi cation for Psychotria species in the South American continent is also applicable to the same species in Okinawa Island. AfterWatanabe's research, the author of the present paper introduced branching pattern models for same species to simulate their branching patterns theoretically. He also determined the branching pattern models in earlier growth stages and calculated their occurrence probabilities. To proceed with the analyses, a systematic construction of the branching pattern models has been required. Aims: To re ne our earlier branching pattern models of P. rubra and P. manillensis in view of vector representation and to introduce a deterministic algorithm which produces the branching pattern models systematically. Methodology: Introducing vector representations, we re ne previous branching pattern models for Psychotria species in Okinawa Island. We also study the properties of branching pattern models in view of computational methods. Finally, we describe a deterministic algorithm for branching pattern models of P. rubra and P. manillensis by a pseudo-code. Results: By studying properties of branching patterns of Psychotria species in mathematical way, we systematize the construction of our branching pattern models as a deterministic algorithm. Running this algorithm, we also succeed in the determination of the third branching pattern models. Conclusion: A systematic determination algorithm which produces the branching pattern models inductively has been successfully established.