Systematics of the genus Neocaridina
Many studies suggest that species should fulfil two criteria, monophyly and distinctness [33-35]. In the present study, the freshwater shrimp Neocaridina in Taiwan formed four monophyletic clades (clades 1, 6, 9 and 12; Fig. 2), and the mean genetic distance among these four clades was 6.64% (ranging 5.74% to 7.50%; Table 2). The range of the pairwise genetic distance between these 13 clades of Neocaridina (Fig. 2) was from 2.87% (between N. davidi and N. denticulata) to 15.23% (between N. sp. in Japan and N. spinose), and the average pairwise distance was 8.19% (Table 2). Robe et al.  evaluated the utility of mtDNA COI in the identification of species of Palaemonidae (Crustacea, Decapoda) and found that the mean genetic distances between the species within the genus Macrobrachium ranged from 0.000 to 0.312 (mean = 0.198). Hebert et al.  suggested that the best threshold for distinguishing intra- from interspecific divergence was approximately 3% sequence divergence, although this value was later modified approximately ten times by many studies [37-40]. Thus, the present study suggested that the four clades in Taiwan corresponded to four species: N. davidi, N. saccam, N. ketagalan and one undescribed species (N. sp. in Taiwan) (Fig. 2; Table 2). Our study provides a table comparing the morphologic characteristics among these four Neocaridina species in Taiwan and their identification keys (Table 4).
Recently, Shih et al.  proposed the third endemic species of Neocaridina known from Taiwan. This new species of land-locked freshwater shrimp, N. fonticulata, is described from Kenting, Hengchun Peninsula, and southern Taiwan . However, although our study sampled specimens from 35 localities in Taiwan, which covers almost all rivers within the island, we did not sample any specimens in the Hengchun Peninsula (Fig. 1). After comparing the morphological characteristics (Table 4 and Shih et al. ), our study found that N. sp. in Taiwan may be synonymous with N. fonticulata. However, the molecular data of N. fonticulata have not been released. Therefore, this question needs to be confirmed in the future.
Moreover, our study found that the systematics of N. davidi were unclear. Neocaridina davidi, once named N. denticulate sinensis , and Shih et al.  suggested that it was synonymous with N. davidi. However, our study found that the genetic distance between N. davidi and N. denticulata was the smallest (2.87%). Thus, we could not suggest that “N. davidi in Taiwan” was a species, subspecies or population. The systematics and distribution area of N. denticulata were also unclear. Moreover, our study also found that there were many questions about the systematics of the genus Neocaridina in East Asia. For example, clade 11 (name: Nak; accession no. LC324777) was named N. aff. koreana , but it is not close to N. koreana (clade 3; Fig. 2) (name: Nkr; accession no. LC324768 in Shih et al. ). Furthermore, undescribed Neocaridina species were found not only in our study (Fig. 2; clade 4, N. sp. in China, and clade 9, N. sp. in Taiwan) but also in the study of Shih et al.  (clade 10, N. sp. in Japan). Our study suggests that the systematics and species diversity of the genus Neocaridina in East Asia need revisions in future studies.
As described above, the diversity of the genus Neocaridina is outside of our understanding. The distribution of the shared haplotypes (Table 1) and NST (Table 3) within each species showed high population differentiation. These results suggested weak migrating potential in the Neocaridina species. Thus, their distribution patterns were restricted (Fig. 2), and the ancestral populations were easily isolated. These results were also supported by the DIYABC analysis (Fig. 3). The four species did not colonize Taiwan by one colonization route (scenario E, Fig. 3e) because the ancestral populations could not disperse over the entire island. Thus, these four Neocaridina species in Taiwan may have colonized the islands through four different groups of ancestral populations.
Multiple origins of the genus Neocaridina in Taiwan
Our study found four Neocaridina species in Taiwan. The distribution ranges of the three species, N. saccam, N. ketagalan and N. sp., were restricted, and only N. davidi was widely distributed (Fig. 2). The phylogenetic analysis of Neocaridina species in the world revealed that these four species in Taiwan were polytomous (Fig. 2). The TMRCA of these four Taiwanese species were different (Table 3). Moreover, the results of the DIYABC analysis demonstrated that these four Neocaridina species colonized Taiwan during four colonization events (Fig. 3). Chang et al.  also found that two endemic Microphysogobio species colonized Taiwan from two origins and through two colonization centres. Previous studies [9, 19, 42] propose that due to the geological history of Taiwan Island, the different colonization times shaped the different distribution patterns. These present results of the genus Neocaridina in Taiwan agreed with those of previous studies [9, 19, 42]. The four Neocaridina species in Taiwan displayed different distribution patterns, and they may have colonized the islands at different times.
Many studies [9, 18, 19, 42] have suggested that when the freshwater species colonized Taiwan after the island reached its present shape, their distribution range was restricted. Among the four species in Taiwan, N. sp. was restricted to eastern Taiwan. However, the distribution patterns of the freshwater fishes and the phylogeographic studies [10, 19] indicate that the Central Range has acted as a barrier to dispersal between the western and eastern populations of species. Thus, many freshwater species were not distributed in eastern Taiwan, and some species were distributed in eastern Taiwan by human activities . Thus, the freshwater species in eastern Taiwan colonized before those in western Taiwan or originated from populations in western Taiwan through human activities. The results of TMRCA estimated that N. sp. colonized before other species (Table 3). Based on the substitution rate of 1.1% per million years , the TMRCA of N. sp. was 2.180 mya, which was before the Central Range in Taiwan formed (ca. 2 mya). In addition, the results of the DIYABC analysis also supported that the genus Neocaridina colonized Taiwan through four colonization events. Thus, this study suggested that N. sp. colonized Taiwan before the island reached its current shape, and the TMRCA based on the substitution rate of 1.1% per million years was likely an appropriate estimate.
According to previous studies [9, 17, 18, 20, 26], the freshwater species colonized Taiwan through five colonization centres: two to the south of the Formosa Bank, two to the north of the Formosa Bank and the south of the Miaoli Plateau, and one to the north of the Miaoli Plateau. In the phylogeny of the genus Neocaridina (Fig. 2), N. ketagalan was grouped with N. aff. koreana and N. sp. in Japan as monophyletic. The pairwise p-distance between the clades of Neocaridina suggested that N. ketagalan was close to N. aff. koreana in Japan (Table 2). Moreover, the S-DIVA analyses showed that the ancestral populations of N. ketagalan were distributed north of the Taoyuan Plateau (Fig. 5b). Our study found that M. brevirostris and N. ketagalan had the same distribution area, but Chang et al.  proposed that M. brevirostris might have originated from mainland China. However, in a study by Chang et al. , we found that M. brevirostris was close to M. koreensis from South Korea. Moreover, Chiu et al.  found that the freshwater snail in northern Taiwan originated from Japan. Thus, this study considered that the freshwater species in northern Taiwan might not have colonized from mainland China and suggested that N. ketagalan originated from Japan (Fig. 1).
Neocaridina saccam was only distributed south of the Miaoli Plateau, and the results of the S-DIVA analysis demonstrated that the ancestral populations of N. saccam were distributed south and north of the Formosa Bank (Figs 1 and 5c). Based on these results, N. saccam did not colonize Japan. According to the geographic locations, our study suggested that N. saccam originated from mainland China (Fig. 1). Actually, this colonization route was the most common to Taiwan Island [17, 23, 32, 43]. In addition, our study found that N. sp. in eastern Taiwan may be synonymous with N. fonticulata in the Hengchun Peninsula (Fig. 1). If this hypothesis is supported, N. sp. was also distributed in southern Taiwan. This distribution pattern was similar to that of two freshwater fishes, Spinibarbus hollandi and Onychostoma alticorpus. Chiang et al.  proposed that these two fishes colonized the island in the southern region of the Kaoping foreland basins, followed by eastern and northward dispersal. Thus, our study considered that N. sp. in Taiwan (N. fonticulata) may have colonized mainland China (Fig. 1).
In addition, although the S-DIVA analyses showed that the ancestral populations of N. davidi were distributed in northern Taiwan, this species is widely distributed around the world. Moreover, the phylogenetic analysis showed that N. davidi was close to N. denticulata in Japan. Neocaridina davidi may have colonized Japan (Fig. 1). However, our study could not suggest a geographical origin because the systematic status of this species was unidentified. Accordingly, this study suggested that the Neocaridina species in Taiwan colonized the area from multiple geographical and temporal origins, but the deterministic geographical sources need further study.
Population history of N. sp. in eastern Taiwan
Our study found that N. sp. was distributed only in three adjacent rivers: SK, SM and WL (Figs 2 and 5d). Although the NST in this species was smaller than those in other species, only this species displayed a higher GST than NST (Table 3). These results suggested that most related haplotypes were found in different populations. However, the depth of the sea around eastern Taiwan was deeper than the depth in western Taiwan (Taiwan Strait), and even during the glaciations, these oceans around eastern Taiwan were not exposed. Previous studies have demonstrated that the amphidromous fish R. giurinus  and shrimp Caridina pseudodenticulata  larvae survived in seawater and could not cross this deep sea. How did N. sp. colonize or migrate among these three rivers? The geological study of Taiwan Island  proposed that these three adjacent rivers belonged to one river, the paleo-Siuguluan River (paleo-SK), and separated after the middle Pleistocene.
Phylogeography of N. saccam and N. ketagalan
Neocaridina saccam were divided into two lineages, NS1 and NS2 (Fig. 5c), and exhibited a southern and northern distribution, which were to the south and to the north of the Formosa Bank. The S-DIVA analysis showed that the ancestral populations of N. saccam were distributed to the south and north of Formosa Bank (Fig. 5c). Moreover, only two populations, JS, the northernmost population, and ER, the southernmost population, had private haplotypes (Table 1; Fig. 1). These results seemed to reveal that the colonization route was divided into two routes by the Formosa Bank. The Formosa Bank is located in the southern part of the Taiwan Strait. Previous studies [9, 17, 19, 45] have suggested that the Formosa Bank divided the glacial land bridge in the Taiwan Strait; however, the role of the Formosa Bank on the population dispersion within the island was rarely described. Ju et al.  proposed that during the maximum glacial periods, the ridge lifted from Formosa Bank to the present coastline of Taiwan Island. Therefore, during the maximum glaciation, the dispersal between the two sides of the bank through the exposed continental shelves of the island were prevented. After N. saccam colonized the island, the northward dispersal route was interrupted by the Miaoli Plateau, and the southward dispersal route was fragmented by the Kaoping foreland basins (Fig. 1).
Neocaridina ketagalan can be divided into three lineages (NK1-NK3, Fig. 5b). Lineage NK3 was restricted to the northern region of the Taoyuan Plateau, lineage NK1 was restricted to the north region of the Miaoli Plateau, and lineage NK2 was restricted to the north region of the Formosa Bank (Figs 1 and 5b). The S-DIVA analysis displayed that its ancestral populations were distributed north of the Taoyuan Plateau and then southward (A1 region; Fig. 5b). Finally, the population structure was shaped by the Taoyuan Plateau, Miaoli Plateau and Formosa Bank. The Taoyuan Plateau is located in northwestern Taiwan (Fig. 1). Some freshwater fishes, e.g., O. evolans, Squalidus argentatus, Sinibrama macrops and Hemibarbus labeo, were only distributed in the Tamsui River north of the Taoyuan Plateau (excluding). Chang et al.  and Hsu et al.  also found that the Taoyuan Plateau divided the populations of M. brevirostris and Semisulcospira libertina into different lineages. Thus, the lineage NK3 was restricted to the northern region of the Taoyuan Plateau. Moreover, many studies suggest that the Miaoli Plateau prevented the dispersal of the freshwater fishes [9, 19]. Thus, when the Miaoli Plateau emerged, the populations were isolated and diverged (lineage NK1). Last, as described above, during the maximum glaciation, the Formosa Bank interrupted the migrations of N. saccam and N. ketagalan.
Population history of N. davidi in Taiwan
Among the four Neocaridina species in Taiwan, the distribution range of N. davidi was wider than those of the others (Fig. 2). According to a previous study [9, 18], this widely distributed species colonized Taiwan Island before the species with restricted ranges. However, the results of the TMRCA analysis showed that N. davidi colonized the islands after the other species (Table 3). In addition, our study also found that this species was widely distributed throughout the world. Neocaridina davidi is known to be an invasive species due to its importance in the aquarium trade (Englund and Cai  for Hawaii; Jabłońska et al.  for Poland; Klotz et al.  for Germany). Thus, some populations might have resulted from introduction into the wild from aquarium stocks.
Neocaridina davidi in Taiwan can be divided into three lineages (ND-ND3, Fig. 5a). Lineage ND2 was only distributed north of the Miaoli Plateaus, lineage ND3 was mostly distributed in northeastern Taiwan, and lineage ND1 was widely distributed. The results of the S-DIVA revealed that the ancestral populations were distributed north of the Formosa Bank and in northeastern Taiwan. Moreover, our study found that some populations did not have private haplotypes, and these populations were not distributed in ancestral areas, excluding population FG (Table 1; Figs 1 and 5a). In addition, the shared haplotypes of the other three species were only distributed in the neighbour populations, and the shared haplotypes of N. davidi, excluding D9 and D10, were also distributed in the neighbour populations (Table 1). Thus, we suggest that the distribution of the widespread haplotype and the discontinuous distribution might have resulted from introductions to the wild from aquarium stocks, and the human-caused transformations among the wild population were rarer than the introductions of individuals to the wild from aquarium stocks.
In conclusion, our study considered that the ancestral populations of N. davidi were distributed north of the Formosa Bank and in northeastern Taiwan (Fig. 5a) and then isolated and divergent by the Central Range and Miaoli Plateau. Finally, the ND1-ND3 lineages were restricted to northeastern Taiwan (E region), north of the Miaoli Plateau (A region), south of the Miaoli Plateau and north of the Formosa Bank (B region). We suggested that the populations in regions C and D might have resulted from the introduction from aquarium stocks to the wild by humans (Fig. 5a).