## 1 Introduction  
Terpenoids are the largest and a structurally diverse group of natural products in plants [1]. To date, more than 80,000 terpenoid compounds, including monoterpenes, sesquiterpenes, and diterpenes, have been identified [2, 3]. Terpenoids play important roles in both primary and secondary metabolism of plants. For example, gibberellin, brassinosterol, and carotenoid are well characterized terpenoids, which play important roles in plant growth and development as plant hormones and photosynthetic pigments [4]. Compared to the small amount of terpenoids involved in primary metabolism, the majority of terpenoids are classified as secondary metabolites. Although they are not involved in the basic growth and development of plants, they still have some physiological functions and a wide range of applications, including plant defense response, pharmacological compounds, and fragrance and aroma constituents [5; 6; 7]. Although the number of terpenoids is huge, they are all derived biosynthetically from common precursors, dimethylallyl diphosphate (DMAPP) and isopentenyl diphosphate (IPP) [8]. These precursors are produced by two biosynthetic pathways, the methylerythtitol phosphate pathway (MEP) in the chloroplast and the mevalonate pathway (MVA) in the cytosol [9]. The condensation reaction of DMAPP and IPP catalyzed by prenyltransferases produces the direct precursors geranyl diphosphate (GPP C10), famresyl diphosphate (FPP C15), and geranylgeranyl pyrophosphate (GGPP C20). Subsequently, terpene syntheses (TPSs) catalyze the precursors to form a variety of terpenoids, including hemiterpene (C5), monoterpene (C10), sesquiterpene (C15), and diterpene (C20) [10; 11]. The products of TPS can be further modified by other enzymatic reaction, such as dehydrogenation, isomerization, and group transfer. In the biosynthetic pathway of terpenoids, TPSs is positioned at the branch point and is a key enzyme for terpenoid biosynthesis. Each full-length TPS is characterized by two conserved domains with Pfam ID PF01397 (N-terminal) and PF03936 (C-terminal) [1]. The N-terminal domain has a conserved RRX8W motif, and the C-terminal domain has a conserved DDXXD motif and NSE/DTE motif [12]. _TPSs_ constitute a mid-size gene family, the number of which varies greatly in different plants [12]. To date, _TPS_ gene families have been genome-widely identified in various plant species, ranging from spermatophytes to mosses [13]. According to the phylogenetic analysis, the plant _TPS_ family can be classified into seven subfamilies (TPS-a, TPS-b, TPS-c, TPS-d, TPS-e/f, TPS-g, and TPS-h) [12; 13]. Different subfamily genes also encode terpene synthase with different functions, for example, TPS-a subfamily genes encode sesquiterpene synthases, while TPS-b and TPS-g subfamily genes encode monoterpene synthases [14]. TPS-d is a gymnosperm-specific subfamily, which performs several functions, such as diterpene, monoterpene, and sesquiterpene synthases [15]. The _TPS_ genes could also been classified into different classes according to their genomic structure, including class I (13-15 exons), class II (10 exons), and class III (7 exons) [16]. The genus _Mentha_ encompasses mint species cultivated for their essential oils, which are widely used in the flavor, fragrance, and aromatherapy industries [17]. The major constituents of mint essential oils are monoterpenes, including (\(-\))-menthol, (\(+\))-neomethol, (\(+\))-isomenthol, (\(+\))-carvone, and (\(+\))-menthofuran [18; 19]. The biosynthetic pathway of the most abundant oil constituents has been well illustrated in peppermint (_Mentha_\(\times\)_piperita_ L) and spearmint (_Mentha spicata_ L.) [20; 21]. Limited by the complex polyploidy, the genome research of peppermint and spearmint has been progressing slowly. The horse mint (_Mentha longifolia_) is an ancestor species of the genus _Mentha_, which has been developed as a model species for mint genomics because of its diploid genome structure, relatively small genome, and other genetics features [22]. The genome sequencing of _M.