Systematics of the genus Neocaridina
Many studies suggest that species should fulfil two criteria, monophyly and distinctness [33, 34, 35]. In the present study, the freshwater shrimp Neocaridina in Taiwan formed into four monophyletic clades (1, 6 9 and 12; Figure 2), and the mean genetic distance among these four clades was 6.64% (ranging 5.74% to 7.50%). The range of the pairwise genetic distance between these 13 clades of Neocaridina (Figure 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 species identification of Palaemonidae (Crustacea, Decapoda) and found that the mean genetic distances between 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 about ten times by many studies (e.g., [37, 38, 39, 40]). Thus, the present study suggested that the four clades in Taiwan corresponded to four species including N. davidi, N. saccam, N. ketagalan and one undescribed species (N. sp. in Taiwan) (Figure 2; Table 2).
Moreover, our study found that the systematics of N. davidi unidentified. Neocaridina davidi once named N. denticulate sinensis , and Shih et al.  suggested that it is synonymous to 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” is a species or subspecies. Moreover, the systematics and distribution area of N. denticulata also unidentified. Accordingly, our study could not suggest the geological origin of N. davidi as other three endemic species, N. saccam, N. ketagalan and N. sp. in Taiwan. Our study suggested that the systematics and species diversity of the genus Neocaridina need revisions in future studies.
Multiple origins of the genus Neocaridina in Taiwan
Our study found four Neocaridina species in Taiwan. The distribution ranges of three species, N. saccam, N. ketagalan and N. sp., were restricted, and only N. davidi was widely distributed (Figure 2). The phylogenetic analysis of Neocaridina species in the world displayed that these four species in Taiwan are polytomous (Figure 2). The TMRCA of these four Taiwan species were different (Table 3). Moreover, the results of the DIYABC demonstrated that these four Neocaridina species colonized Taiwan in four colonization events (Figure 3). Chang et al. (2016)  also found that two endemic Microphysogobio species colonized Taiwan from two origins and through two colonization centres. Previous studies (e.g., [9, 19, 41]) 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 are agreement with those of previous studies (e.g., [9, 19, 41]).
Many studies (e.g., [9, 18, 19, 41]) suggested that when the freshwater species colonized Taiwan after the island reached its present shape, their distribution range were restricted. Among these four Taiwan species, N. sp. was restricted in East Taiwan. However, the distribution patterns of freshwater fishes and phylogeographic studies (e.g., [10, 19]) indicate that the Central Range have acted as a barrier to dispersal between the western and eastern populations of species. Thus, many freshwater species were not distributed in East Taiwan, and some species were distributed in East Taiwan by human activities . Thus, the freshwater species in East Taiwan colonized before that in West Taiwan, or originated from populations in West Taiwan by human activities. The results of TMRCA estimated displayed N. sp. colonized before other species (Table 3). Based on the substitution rate of 1.1 % per millions of years , the TMRCA of N. sp. was 2.180 mya, before the Central Range in Taiwan formed (ca. 2 mya). Moreover, the phylogenetic analysis of the genus Neocaridina displayed that N. sp. in Taiwan did not close to other species in Taiwan (Figure 2); and three N. sp. populations all have private haplotypes. Besides, 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 island reached its shape, and the TMRCA based on the substitution rate of 1.1 % per millions of years is likely a proper estimate.
According to previous studies (e.g., [9, 17, 18, 20, 26]), the freshwater species colonized Taiwan through five colonization centres, two in the south of Formosa Bank, two in the north of Formosa Bank and the south of Miaoli Plateau, and one in the north of Miaoli Plateau. In the phylogeny of the genus Neocaridina (Figure 2), N. ketagalan grouped with N. aff. koreana and N. sp. in Japan as monophyletic. The pairwise p-distance between 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 in north of Taoyuan Plateau (Figure 5b). Thus, this study suggests N. ketagalan originated from Japan. Neocaridina saccam was only distributed south of Miaoli Plateau, and the results of the S-DIVA analysis demonstrated that the ancestral populations of N. saccam were distributed south- and north of Formosa Bank (Figures 1 and 5c). Based on these results, N. saccam did not colonize from Japan. According to the geographic locations, our study suggests that the N. saccam may have colonized from mainland China. Besides, although the S-DIVA analyses showed that the ancestral populations of N. davidi were distributed in northern Taiwan and the phylogenetic analysis displayed that N. davidi was close to N. denticulata in Japan, our study could not suggest the geographical origin because the systematics status of this species is unidentified (see DISCUSSION: Systematics of the genus Neocaridina). Accordingly, this study suggests that the Neocaridina species in Taiwan colonized through multiple geographical and temporal origins, but the deterministic geographical sources need more studies.
Population history of N. sp. in Taiwan
Our study found that N. sp. was only distributed in East Taiwan, and was distributed in three adjacent rivers only: SK, SM and WL (Figures 2 and 5d). Although the NST in this species was smaller than those in other species, only this species displayed the GST was higher than NST (Table 3). These results suggested that most related haplotypes were found in different populations. However, the depth of the sea around East Taiwan was deeper than the depth in West Taiwan (Taiwan Strait), and even during glaciations, these oceans around East Taiwan were not exposed. The previous studies displayed the amphidromous fish R. giurinus  and shrimp Caridina pseudodenticulata , larva survived in seawater, could not cross this deep sea. How did N. sp. colonize 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. Thus, our study suggests that this species colonized Taiwan before this island reached its shape and then was isolated by the Central Range. Finally, it diverged by river diversion recently.
Phylogeography of N. saccam and N. ketagalan
Neocaridina ketagalan and N. saccam are allopatric distribution (Figure 2). Neocaridina ketagalan was only distributed west of Central Rang and north of the Wu River (excluding) (Figures 1 and 2), and the results of S-DIVA analysis showed the ancestral populations of N. ketagalan were distributed north of the Taoyuan Plateau (A1 region; Figure 5b). Neocaridina saccam was only distributed west of Central Rang, south of the Wu River (excluding), and north of Kaoping foreland basins (Figures 1 and 2). The S-DIVA analysis displayed that the ancestral populations of N. saccam were distributed in north of Formosa Bank (C1) and south of Formosa Bank (C3) (Figure 5c). Based on the distribution pattern and phylogeny of Neocaridina, (Figure 2), the results of the DIYABC analysis (Figure 3) and the results of previous studies (e.g., [17, 18]), N. ketagalan and N. saccam may have originated from Japan Islands and mainland China, respectively. The colonization routes of these two Neocaridina species, N. ketagalan and N. saccam, were similar to two clades of Semisulcospira libertina in Taiwan . The populations in North Taiwan originated from Japan; the populations in South Taiwan may have originated from South China or South Asia.
Neocaridina saccam divided into two lineages, NS1 and NS2 (Figure 3c), exhibiting a southern and northern distribution, south- and north of Formosa Bank. The S-DIVA analysis displayed that the ancestral populations of N. saccam were distributed in south- and north of Formosa Bank (Figure 5c). Moreover, only two populations JS, the northernmost population, and ER, the southernmost population, have private haplotypes (Table 1; Figure 1). These results seem to reveal that the colonization route divided into two routes by Formosa Bank. The Formosa Bank is located at the south of Taiwan Strait. Previous studies (e.g., [9, 17, 19, 44]) have suggested that the Formosa Bank divided the glacial land bridge in the Taiwan Strait; however, the role of Formosa Bank on the population dispersion within the island has not been described. Ju et al.  proposed that during the maximum glacial periods, the ridge lifted from Formosa Bank to present coastal line of Taiwan Island. Therefore, during maximum glaciation, the dispersions between two sides of the bank through the exposed continental shelves of the island were broken. After N. saccam colonized island, the northward dispersal route was broken by the Miaoli Plateau, and the southward dispersal route was broken by the Kaoping foreland basins (Figure 1).
Neocaridina ketagalan can be divided into three lineages (NK1-NK3, Figure 5b). Lineage NK3 was restricted north of the Taoyuan Plateau; lineage NK1 was restricted in north of Miaoli Plateau; lineage NK2 was restricted north of Formosa Bank (Figures 1 and 5b). The S-DIVA analysis displayed that its ancestral populations were distributed in north of Taoyuan Plateau, and then southward (A1 region; Figure 5b). Finally, the population structure was shaped by Taoyuan Plateau, Miaoli Plateau and Formosa Bank. Taoyuan Plateau located in Northwest Taiwan (Figure 1). Some freshwater fishes, e.g., O. evolans, Squalids argentatus, Sinigrama macrops and Hemibarbus labeo, were only distributed Tamsui River, north of Taoyuan Plateau (excluding). Chang et al.  and Hsu et al.  also found that Taoyuan Plateau divided the populations of M. brevirostris and Semisulcospria libertina as different lineages. Thus, the lineage NK3 was restricted in north of Taoyuan Plateau. Moreover, many studies suggest that the Miaoli Plateau isolated the dispersions of freshwater fishes [9, 19]. Thus, when Miaoli Plateau emerged, the populations were isolated and divergent (lineage NK1). Lastly, as the descriptions above, during maximum glaciation Formosa Bank and interrupted the migrations of N. saccam and N. ketagalan.
Population history of N. davidi in Taiwan
Among four Neocaridina species in Taiwan, the distribution range of N. davidi was wider than others (Figure 2). According to the previous study (e.g., [9, 18]), the widely distributed species colonized the Taiwan Island before the restriction species. However, the results of the TMRCA analysis showed that N. davidi colonized island after other species (Table 3). Besides, our study also found this species distributed widely in 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 result in the introduction to the wild by aquarium stocks.
Neocaridina davidi in Taiwan can be divided into three lineages (ND-ND3, Figure 5a). The lineage ND2 was only distributed in north of Miaoli Plateaus; lineage ND3 was almost distributed Northeast Taiwan; lineage ND1 was distributed widely. The results of the S-DIVA revealed that the ancestral populations were distributed in north of Formosa Bank and Northeast Taiwan. Moreover, our study found some populations did not have private haplotypes, and these populations were not distributed in ancestral areas, excluding population FG (Table 3; Figures 1 and 5a). Besides, the shared haplotypes of other three species were only distributed in neighbor populations, and the shared haplotypes of N. davidi, excluding D9 and D10, were also distributed neighbor populations (Table 1). Thus, we suggest the distribution widely haplotype and the discontinuous distribution might result in the introduction to the wild by aquarium stocks, and the transformations among wild population by human are rarer than the introduction to the wild by aquarium stocks.
In conclusion, our study considered the ancestral populations of N. davidi were distributed in north of Formosa Bank and Northeast Taiwan (Figure 5a), and then isolated and divergent by Central Rang and Miaoli Plateau. Finally, the lineages ND1-ND3 were restricted in Northeast Taiwan (E region), north of Miaoli Plateau (A region), and south of Miaoli Plateau and north of Formosa Bank (B region), respectively. We suggested the populations in regions C and D were might result in the introduction from aquarium stocks to the wild by human (Figure 5a).