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It was known through the efforts of many works that the generating functions in the closed Gromov–Witten theory of K P 2 are meromorphic quasi-modular forms (Coates and Iritani in Kyoto J Math 58(4):695–864, 2018; Lho and Pandharipande in Adv Math 332:349–402, 2018; Coates and Iritani in Gromov–Witten invariants of local P 2 and modular forms, arXiv:1804.03292 [math.AG], 2018) basing on the B-model predictions (Bershadsky et al. in Commun Math Phys 165:311–428, 1994; Aganagic et al. in Commun Math Phys 277:771–819, 2008; Alim et al. in Adv Theor Math Phys 18(2):401–467, 2014). In this article, we extend the modularity phenomenon to K P 1 × P 1 , K W P [ 1 , 1 , 2 ] , K F 1 . More importantly, we generalize it to the generating functions in the open Gromov–Witten theory using the theory of Jacobi forms where the open Gromov–Witten parameters are transformed into elliptic variables. [ABSTRACT FROM AUTHOR]

• Diameter growth rate of three species of street trees was analyzed using tree rings. • Diameter growth equation was developed for three of four street tree species. • Diameter growth of street trees was lower than that of nursery-grown trees. • Diameter growth of street trees was lower than that of street trees in the USA. Tree growth equations are indispensable for modeling tree functions for ecosystem services. However, knowledge about the growth rates of street trees in Japan remains limited. This study aimed to examine the growth characteristics of street trees (Zelkova serrata, Platanus orientalis , and Prunus yedoensis) in Japan to generate growth equations of the diameter at breast height (DBH) based on measurements of tree rings. Specifically, diameter growth was used and compared against nursery-grown trees used in previous studies in Japan and street trees in the USA. The diameter growth rate per year of Z. serrata ranged from 0.43 cm to 1.12 cm, with peak growth occurring at 17.8 years of age. For P. orientalis , the diameter growth rate per year ranged from 0.25 cm to 1.59 cm, with peak growth occurring at 7.4 years of age. For P. yedoensis , the diameter growth rate per year ranged from 0.68 cm to 1.65 cm, with no apparent peak growth. The Chapman-Richards growth function generated the best fit as a diameter growth equation for all three species out of three tested theoretical growth equations (Chapman-Richards, Gompertz, and Logistic function). For 25-year old trees, the estimated DBH of Z. serrata and P. orientalis grown as street trees was 68 % and 84 % of that of nursery-grown trees, respectively. For street trees 25 years after planting, the estimated DBH of Z. serrata, P. orientalis , and P. yedoensis in Kyoto City was 62 %, 63 %, and 56 % of that of street trees in the USA. The diameter growth of street trees in Kyoto was substantially lower than that of nursery-grown trees and street trees in the USA. Therefore, region-specific growth equations must be developed for street trees when the planting environment and management approaches are different. [ABSTRACT FROM AUTHOR]