Journal of Earth Science  2019, Vol. 30 Issue (2): 387-396   PDF    
Bacterial Diversity in Alpine Lakes:A Review from the Third Pole Region
Adhikari Namita Paudel 1,2,3, Adhikari Subash 2,3,4, Liu Xiaobo 5, Shen Liang 1,2, Gu Zhengquan 1,2,3     
1. Key Laboratory of Alpine Ecology and Biodiversity, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing 100101, China;
2. Key Laboratory of Tibetan Environment Changes and Land Surface Processes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing 100101, China;
3. University of Chinese Academy of Science, Beijing 100049, China;
4. Janapriya Multiple Campus, Tribhuvan University, Pokhara 33700, Nepal;
5. Kathmandu Center for Research and Education, CAS-TU, Kathmandu 44618, Nepal
ABSTRACT: Microorganisms are unique among all of the living organisms because of their high population size, advanced genetic diversity, short generation time, and quick response to the small change in environmental conditions. Remote alpine lakes of the Third Pole region provide the unique habitat for microorganisms acting as a natural laboratory and offering the information about the ecological roles of microorganisms. Many researchers focused on microbial communities as well as the impact of physicochemical, biological and hydrological parameters in lakes of this region since decades but the comprehensive review focusing on bacterial diversity and the role of environmental parameters still lacks. Here we reviewed bacterial diversity in lakes of the Third Pole region by analyzing 16S rRNA clone libraries accessed from previous research findings. A total of 5 388 bacterial 16S rRNA gene sequences were analyzed and classified into different phylogenetic groups. The average relative abundance of dominant taxa includes Betaproteobacteria (19%), Bacteroidetes (18%), Gammaproteobacteria (16%), Actinobacteria (15%), Alphaproteobacteria (14%), Cyanobacteria (7%), and Firmicutes (5%). Several adaptational strategies were adopted by these dominant bacterial groups in order to accommodate in the respective habitat. Nevertheless, lake water properties like temperature, pH, salinity, incident UV radiation, turbidity, and nutrients also played role in bacterial diversity.
KEY WORDS: bacterial diversity    alpine lakes    16S rRNA    Third Pole region    

The Third Pole region comprises of the Tibetan Plateau and adjoining mountains with approximate ice storage of 100 000 km2 and 46 000 glaciers (Zhang et al., 2015; Yao et al., 2012; Qiu, 2008). It occupies several youngest, highest, and largest geomorphological units which are considered to play a dynamic role in earth's aquatic and terrestrial ecosystems (Guan et al., 2013). Many of the big rivers such as Ganges, Indus, and Brahmaputra originate from the Third Pole region also called as water tower of Asia, supporting the livelihood of about 1.3 billion people. Glaciers are the prime source of nutrients and water (Hood et al., 2009) for underlying system, and interconnect the cryosphere, the hydrosphere, the pedosphere, and the biosphere. This region also harbors several lentic water bodies with different sizes, which were mostly formed by the deposition of glacial ice and snow meltwater. A recent study (Zhang et al., 2015) supports the consensus that the number and size of glacial lakes in this region are increasing due to the rapid melting of glaciers triggered by global warming. This mechanism alters the lentic environment and ecosystem which has a direct impact on the bacterial community of respective lakes (Liu et al., 2014). Although lakes and reservoirs occupy nearly 3% of the world's aggregate land surface territory (Downing et al., 2006), they assume to be a crucial part as sentinels, integrators, and controllers of environmental change and global carbon budget (Cole et al., 2007).

Microorganisms are very special among all the organisms due to their advanced genetic diversity, huge population size, rapid multiplication, and cosmopolitan in distribution (Zhang et al., 2013). Headwater bodies are considered as the habitat of dynamic microbial communities (Peter and Sommaruga, 2016), and the identification and characterization of the bacterial communities provide the information about ecological history, functional, and evolutionary diversity of bacteria. Bacteria are the most important components of microbial communities (Llirós et al., 2014). As microorganisms can be displaced from one habitat to another via different routes, the presence of a type of bacteria in a particular community has no compulsion that it grows and thrives in that environment (Zwart et al., 2002).

Diversity is generally explained in three perspectives, i.e., alpha (α) diversity, beta (β) diversity and gamma (γ) diversity. Alpha diversity or local diversity is the mean of species pool, Beta diversity is the difference in community composition between communities, and Gamma diversity is the diversity of entire landscape (Zhang et al., 2014). Species diversity comprises two independent components i.e. richness and evenness. Richness explains the number of types that a set of observed entities are classified into, and usually concerns the presence or absence of species, while the evenness explains the number of effective species for each dataset (Tuomisto, 2012). Shannon diversity index and Simpson Index are the most commonly used diversity indices in previous studies in the Third Pole region (Yadav et al., 2016; Liu et al., 2014, 2013a, b; Wang et al., 2011; Xing et al., 2009). Shannon diversity index provides information about microbial biodiversity, higher the value, greater the richness and so on. Simpson Index is the similarity index i.e. higher value indicates lower biodiversity and so on (Tuomisto, 2012).

As the average elevation of the Third Pole region is 4 000 m above sea level (Yao et al., 2012), most of the lakes in this region are remote and alpine with very little anthropogenic influences, while the microorganisms should adapt to minimal nutrient conditions, low temperature, and strong UV radiation (Sommaruga and Casamayor, 2009; Xing et al., 2009). Similarly, these lakes act as an early warning framework for identifying the natural response to warming temperature being very sensitive to anthropogenic influences and climate change (Nelson, 2009). Due to these reasons, lakes in this region act as the natural laboratory and provide a suitable habitat for microbiological studies.

This paper takes an account of the studies on bacterial diversity in lakes of the Third Pole region and the impact of major environmental parameters. We analyzed the sequence data available from 58 lakes (some lakes were common for two or more studies) including 6 lakes from Nepal Himalaya, 4 from Indian Himalaya and 48 from the Tibetan Plateau, China. All the lakes were from the alpine region with extreme environmental conditions i.e. low temperature, high incident UV radiation, and oligotrophic nutrient status. For the location of studied lakes, refer Fig. 1.

Figure 1. Location map of analyzed lakes in the Third Pole region for studying bacterial diversity.

Methodologies applied as a part of the environmental assessment of the Third Pole lakes are changing with new strategies in the world. Global advancement of technology has a direct effect on methods used in microbiological studies in the Third Pole region (Table 1).

Table 1 Review table illustrating methods used and major bacterial groups revealed during the study in the Third Pole lakes
1.1 Culture-Based Method

Culture-based method, i.e. the conventional method in microbiology includes the inoculation of the appropriate volume of sample onto solidified culture medium, repeated streaking to get the pure culture followed by colony characterization based on cultural characteristics (Liu et al., 2009; Berg et al., 2008). Microorganisms can be cultivated only if their physiological niche in natural habitat can be maintained in the laboratory, which is the most challenging job leaving the vast portion of microorganisms unidentifiable. That is why, this method was considered to be biased for ecological studies (Stahl, 1995; Ward et al., 1990; Stahl et al., 1988).

One of the pioneer studies in this region by Jiang et al. (2006) used the culture-based method in order to study the physiological characteristics of the isolates recovered from water and sediments of saline Chaka Lake. Some authors employed culture-based methods followed by sequencing and analysis of 16S rRNA for the studies in Indian lakes (Yadav et al., 2016; Sahay et al., 2013), while some incorporated both cultivation and clone library method independently, and reported the significant difference in dominant groups recovered by two methods (Liu et al., 2009).

1.2 16S rRNA Gene Library

Direct extraction of bacterial DNA from environmental samples followed by sequencing and classification in different taxa provide better coverage than culture-based methods. However, the degree of resistance of bacteria in the natural environment serves an issue in direct extraction of DNA which is the major demerit of non-culture methods (Casamayor et al., 2000). Given that different methodologies may produce different results, the choice of method seems to have a critical influence on the final result. Therefore, we should optimize our methodology so as to obtain the exact picture of bacterial diversity in the study area.

16S rRNA gene of microorganisms represents consensus sequences. Using these highly conserved sequences for the study of microorganisms in natural habitat replaced the conventional culture-based methods (Dunbar et al., 1999; Hengstmann et al., 1999; Ward et al., 1990). In addition, 16S rRNA gene libraries of bacterial isolates recovered by cultivation method can be constructed and analyzed together with the library of uncultured ones, making this method a good choice for several researchers (Ward et al., 1990).

Most of the authors utilized 16S rRNA gene library and associated methods during their studies in the lakes of the Third Pole, for instance, Wang et al. (2011) and Sommaruga and Casamayor (2009) used DGGE of 16S rRNA genes, Zhang et al. (2013) used 16S rRNA gene-based phylochip. Similarly, Liu Y Q et al.(2014, 2013a, b), Liu X B et al. (2010) and Xing et al. (2009) used 16S rRNA gene clone library approach.

1.3 Next-Generation Sequencing (NGS) Methods

Sequencing of the small and highly variable regions (e.g., V3, V4, V5 or V6) of 16S rRNA gene using high throughput methods provide the highest possible coverage as it can resolve the rare bacterial population from environmental samples (Staley et al., 2013; Sogin et al., 2006). Sequencing by using NGS methods use several platforms, viz. Roche 454, Illumina MiSeq, Illumina HiSeq, Life Technologies SOLiD4, Life Technologies Ion Proton, and Pacific Biosciences SMRT (Shokralla et al., 2012). Our review reflects that recent microbiological studies in the Third Pole lakes used several platforms of NGS methods (e.g., Liu et al., 2017, 2016; Dai et al., 2016; Zhong et al., 2016).


Literature was searched in Google Scholar from July to November of 2017 for multiple keywords (i.e., bacteria, diversity, alpine lake). 16S rRNA gene sequences of both the cultured isolates as well as uncultured bacteria were accessed based on accession numbers provided on literature through NCBI ( Sequences were imported to Mega version 7 (Kumar et al., 2016) in order to generate the corresponding FAS file. The taxonomy of respective sequences was determined by online RDP classifier tool (Wang et al., 2007) and the number of OTUs for each taxon was counted upon analysis. A total of 5 388 sequences were classified into several bacterial taxa and only the taxon with the average relative abundance of more than 0.5% was used for data interpretation. The detailed information regarding the number of sequences from each literature and the length of sequences is listed in Table 2. As the physicochemical and environmental parameters in sediments and water are not identical, the 16S rRNA sequences only from the lake water were analyzed. Similarly, the metagenomic data generated by NGS platform was also not used for the analysis because the sequences were not from the same region making the analysis tough and inadequate as well.

Table 2 Number of sequences from each study and length of sequences

Researchers revealed various bacterial group in the Third Pole lakes. The properties, ecology and adaptational mechanisms of seven most dominant bacterial groups (Fig. 2) revealed by the analysis of 16S rRNA gene sequences (as mentioned earlier) are discussed below.

Figure 2. Relative abundance of dominant bacterial taxa in lakes of the Third Pole region based on the analysis of 16S rRNA gene clone library.
3.1 Betaproteobacteria

Based on our analysis in the Third Pole lakes, Betaproteobacteria was the most dominant taxon with the average relative abundance of 19%. Bacteria in this class are gram negative with diverse metabolic functions which are the attribute of phylum Proteobacteria. Betaproteobacteria is the most abundant class of Phylum Proteobacteria in the topmost layer of lakes. This taxon is also regarded as the most dominant bacterial group among all classes of Proteobacteria in several freshwater lakes which may be due to very short generation time that helps to maintain the high count in short duration of time (Jezbera et al., 2012). It has been observed that phylum Betaproteobacteria is mainly driven by the high amount of carbon, nitrate and Cyanobacterial load. However, bacteria in this class are vulnerable to grazing pressure (Newton et al., 2011).

3.2 Bacteroidetes

Bacteroidetes was the second most dominant phylum in the Third Pole lakes with the average relative abundance of 18%. This phylum was previously known as Cytophaga Flexibacter Bacteroides (CFB) group and endorses gram-negative, rod-shaped, non-sporing, aerobic or anaerobic, with both terrestrial as well as aquatic habitat. This phylum is very important for the biodegradation of high molecular weight organic matter, especially carbohydrates and proteins in human gut as well as in the environment (Wang et al., 2017; Thomas et al., 2011; Kirchman et al., 2004).

Many bacteria in this phylum are capable of genetic rearrangement in order to accommodate in extreme environmental conditions. Production of various types of pigments is the survival strategy against strong UV radiation in high altitude (Xing et al., 2009). The elongated shape assists them to escape from seasonal grazing. One of the literatures of freshwater microbial ecology highlighted that Bacteroidetes proliferated in the period of high heterotrophic activity, algal blooms, and seasonal grazing in lakes (Newton et al., 2011).

3.3 Gammaproteobacteria

The average relative abundance of Gammaproteobacteria based on our analysis in the Third Pole lakes was 16%. Gammaproteobacteria is the class of Proteobacteria that ascribes medically, ecologically, and scientifically important gram-negative bacteria. Thus, this class of bacteria is the most studied among all bacteria. Bacteria of class Gammaproteobacteria possess a high amount of unsaturated fatty acid in their cell membrane and can produce various extracellular hydrolytic enzymes (Margesin and Miteva, 2011).

Several Genus of class Gammaproteobacteria can be used as bioindicators for water pollution as they are fugacious members and can be transported to water bodies from anthropogenic or zoonotic sources (Newton et al., 2011). A high proportion of bacteria in anthalosaline lake of the northernmost Tibetan Plateau belonged to class Gammaproteobacteria (Yang et al., 2016). Similarly, Liu et al. (2014) reported the high abundance and diversity of Gammaproteobacteria in littoral and pelagic part of the Bangongco Lake in the western Tibetan Plateau justifying that members of the class of Gammaproteobacteria are actively blooming rather than being ephemeral. As the anthropogenic influences in this region is very less, we can suggest that these bacteria have been transported to the Third Pole lakes through local and long-range transport either by summer monsoon or by winter westerly, which are the major sources of precipitation in this region (Dong et al., 2010; Sommaruga and Casamayor, 2009). A large number of the Third Pole lakes are reported to be saline (Hu et al., 2010) and these bacteria have the ability to flourish in saline water (Liu et al., 2014). Similarly, the abundance of the members of the class Gammaproteobacteria was higher with the increase in salinity (Wu et al., 2006).

3.4 Actinobacteria

The average relative abundance of Actinobacteria in the Third Pole lakes based on our analysis was 15%. Phylum Actinobacteria includes high (G+C) gram-positive bacteria of both terrestrial as well as aquatic origin. Actinobacteria are fungi like bacteria as they produce slender mycelium. This phylum is very popular for the production of antibiotics and enzymes like cellulase, lipase, protease, catalase, and chitinase used for the biodegradation of wastes. This ability makes them the major participant in organic matter turnover and carbon cycle (Newton et al., 2011; Arifuzzaman et al., 2010; Warnecke et al., 2005).

Sporulation provides the best adaptational mechanism for Actinobacteria in saline, oligotrophic lakes with subzero temperature typical for the Third Pole lakes (Cao et al., 2017; Jiang et al., 2006). Production of pigments and high G+C content in the genome has been reported as another adaptational feature of Actinobacteria against strong UV radiation (Warnecke et al., 2005), making them an abundant group in the upper layer of water.

3.5 Alphaproteobacteria

The average relative abundance of Alphaproteobacteria based on our analysis in the Third Pole lakes was 14%. It is one of the important taxonomic classes of phylum Proteobacteria which consists of gram-negative bacteria. Presence of highly diverse bacterial species sharing the common ancestor is the special property of this class. Members of class Alphaproteobacteria are also the hub of global nitrogen budget as some symbiotic bacteria of genus Rhizobium are associated with fixation of atmospheric nitrogen into nitrites and nitrates (Newton et al., 2011).

Alphaproteobacteria can display prostheses, a unique extension to increase the surface to volume ratio which helps them to survive in minimal nutrient conditions. One of the recent studies in Kalakuli Lake also endorsed this fact (Liu et al., 2017). Similarly, members of this class can utilize both organic and inorganic nutrient sources equally, which enables them to flourish in oligotrophic lakes (Eiler et al., 2003). A study (Xiong et al., 2012) detailed the expanded plenitude of Alphaproteobacteria with the increase in pH of lake sediment.

3.6 Cyanobacteria

The average relative abundance of Cyanobacteria based on our analysis was 7%. Phylum Cyanobacteria, commonly regarded as Blue Green Algae (BGA) incorporates morphologically and ecologically heterogeneous photosynthetic bacteria. Cyanobacteria are pioneers in succession of both terrestrial as well as aquatic ecosystems and have the imperative role in the global nitrogen and carbon cycle. Moreover, Cyanobacteria have the ability to produce special types of toxins in order to resist predation (Catherine et al., 2013).

This characteristic makes them one of the dominant phyla in several lakes of the Third Pole region. Numerous genera of Cyanobacteria were reported by Liu et al. (2016) in Namco Lake during their study in vertical gradient. Cyanobacteria also support the growth of other heterotrophic bacteria by releasing a large amount of organic matter (Newton et al., 2011). However, the toxins produced by Cyanobacteria have the antagonistic effect on some bacterial groups.

3.7 Firmicutes

The average relative abundance of Firmicutes in the Third Pole lakes was 5%. This phylum comprises gram-positive, heterotrophic bacteria with 50% G+C content. The normal habitat of these bacteria is terrestrial environment rather than the aquatic ecosystem. However, bacteria belonging to this group were reported in several lakes of the Third Pole region (Liu et al., 2017; Dai et al., 2016; Zhang et al., 2013; Xiong et al., 2012; Sommaruga and Casamayor, 2009) providing the best evidence of bacterial cosmopolitanism and transport through atmospheric circulation.

The ability to produce endospores during abnormal environmental conditions provides them the best adaptational strategy in the extreme environment of the Third Pole lakes (Sommaruga and Casamayor, 2009). Bacteria in this phylum are also famous for the production of various extracellular enzymes and pigments of different colors (Newton et al., 2011). Because of such type of adaptations, Firmicutes was also reported as the dominant phylum in glaciers of the Tibetan Plateau (Shen et al., 2012; Dong et al., 2010; Zhang et al., 2008).


Numerous factors affect the bacterial diversity of lakes i.e., abiotic environmental factors (physicochemical factors), hydrological status as well as the ecological factors (phytoplankton grazing and viral lysis). Organisms inhabiting in alpine lakes and associated ecosystem need to adapt to various environmental conditions (Fig. 3) such as low nutrients, low temperature, high incident UV radiation, short developing seasons (3-5 months), and vast changes in light conditions between the ice-covered as well as ice-free season (Sommaruga, 2001). Here are some important environmental factors that affect the bacterial diversity in alpine lakes of the Third Pole region.

Figure 3. Interaction of microbes with the environment in alpine lakes.
4.1 Temperature

Water temperature is one of the important environmental variables affecting the bacterial diversity in the alpine ecosystem (Lindström et al., 2005), as it is often associated with the metabolic rates and the affinity of bacteria with available substrates (Nedwell, 1999). The rate of metabolism increases exponentially with the expansion in temperature until the temperature reaches to inhibitory condition (Williamson et al., 2008).

As most of the alpine lakes are characterized by subzero temperature during winter, bacteria inhabiting in this region are psychrophiles which adapt to the low temperature by modulating membrane fluidity and regulating gene expression at low temperatures to produce heat shock and anti-freeze protein (Yadav et al., 2016; Margesin and Miteva, 2011).

Lake water temperature was reported as one of the important environmental parameters to shape out the community composition in Tibetan Plateau lakes, for instance, Lake Namco (Liu et al., 2010) and Lake Bangongco (Liu et al., 2014).

4.2 pH

Water pH is the important environmental factor affecting the community composition and diversity in alpine lakes (Klug et al., 2000) as it is an important controller of biogeochemical cycles. Similarly, it reflects the impact of topography and hydrogeochemistry. pH not only mediates the availability of ions and trace metals which acts as growth enhancer and suppressor (Yannarell and Triplett, 2005) but also be altered by the number of input nutrients from the atmosphere.

On consideration in the Third Pole region, pH was an important environmental parameter for the community composition of ammonia-oxidizing bacteria (Yang et al., 2016) and sediment bacterial assemblages (Xiong et al., 2012). Recently, Liu et al. (2017) suggested pH as the imperative environmental parameter for bacterioplankton community composition in Kalakuli Lake.

4.3 Turbidity

Turbidity co-varies with other environmental conditions i.e. temperature, nutrients, incident ultraviolet (UV) radiation, as well as biotic factors such as primary production, and the relative abundance of grazers. Turbid lakes are also beneficial for the proliferation of UV sensitive bacteria in alpine lakes. So, it is one of the important environmental factor affecting bacterial diversity in alpine lakes (Peter and Sommaruga, 2016). Significant positive correlation of lake water turbidity with the bacterial community was reported in high altitude lakes of Khumbu region, southern slope of Himalaya (Sommaruga and Casamayor, 2009).

4.4 Salinity

Salinity is a factor that determines ionic strength of solutions and it is an important factor driving bacterial diversity (Oren, 2001). Nearly half of inland water ecosystem in the world is saline (Yang et al., 2016). The Third Pole region also harbors a large number of saline lakes and the salinity value increases from south to north (Xiong et al., 2012). There are two mechanisms contributing to the saline nature of high altitude lakes: relatively lower precipitation and higher evaporation (Diego et al., 2015).

Salinity was observed as the important environmental factor in bacterial community composition and diversity of the Third Pole lakes by several authors (Hu et al., 2010; Jiang et al., 2006). Study of Wang et al. (2011) in several lakes of the Tibetan Plateau reported that bacterial abundance expanded at salinity lower than 1%, however, no extra clear diminishment was observed with higher salinities.

4.5 UV Radiation

Alpine lakes receive the higher amount of incident UV radiation than lowland lakes due to their proximity to the atmosphere, and low concentration of dissolved organic matter in water. The intensity of solar UV radiation increases by 20%-30% per 1 000 m rise in elevation (Xing et al., 2009). Owing to short generation time and tiny size, microorganisms are at high risk concerning the impact of UV radiation in comparison to higher organisms (Karentz et al., 1994). Nevertheless, microorganisms have their own adaptation strategies contrary to UV radiation by producing amino acids like Scytonemin, mycosporine, and carotenoids which can absorb incident UV radiation (Sommaruga, 2001).

The study by Sommaruga and Casamayor (2009) in alpine lakes of Nepal reported that turbid lakes host more diverse communities than transparent ones which may be due to the lower amount of incident UV radiation.

4.6 Nutrients

Unlike lowland lakes, alpine lakes are usually oligotrophic with low primary productivity (Sánchez-Hernández et al., 2015). They are supplied with local and long-range nutrients via atmospheric circulation which influences both the lake primary productivity and plankton species composition. Microorganisms are very sensitive to small changes in the supply of either nitrogen or phosphorous (Brahney et al., 2015; Bergström, 2010). Carbon is another important source of nutrients available in the form of dissolved organic carbon (DOC) in the water column of lakes. DOC is often associated with the microbial ecology of alpine lakes as it is the fixed carbon source for bacterial food web and also absorbs the harmful UV radiation (Williamson et al., 2008).

The Third Pole lakes are also characterized as oligotrophic lakes with low primary productivity (Liu et al., 2014), the concentration of nutrients is an important environmental factor influencing bacterial diversity. Study of Liu et al. (2017), in Kalakuli Lake, reported the predominance shifting from Proteobacteria to Actinobacteria group relating to raising carbon to nitrogen ratio (C : N).


The information about bacterial diversity in the pristine natural environment provides the information about evolutionary history, functional and ecological diversity. This review will assist to broaden the knowledge about the microbial ecology of pristine natural lakes. This review concluded that Actinobacteria, Alphaproteobacteria, Bacteroidetes, Betaproteobacteria, Cyanobacteria, Firmicutes, and Gammaproteobacteria were the most dominant bacterial groups. These bacteria have a strong affinity with environmental parameters like nutrients, pH, salinity, and incident UV radiation. Dominant bacterial groups followed various adaptational strategies to survive in abnormal environmental conditions. We also remarked that different biological analysis methods with different resolution revealed different results. The exact picture of the bacterial community in such alpine lakes can only be conspicuously explored by using the latest high coverage methodology and considering major environmental variables which signify the ecological dynamics of the bacterial community.

This is a general approach to review bacterial diversity in the Third Pole lakes using 16S rRNA clone libraries from published papers. We observed that most of the works focused primarily in the eastern part of Tibetan Plateau. Intensive studies in various region of Third Pole emphasizing on specific bacterial groups and their relationships with environmental parameters (physical, chemical and biological) can be conducted. As this region is located in the highly elevated pristine environment and experiences more effect of climate change, bacterial diversity cannot remain unaffected. So, the use of the latest methods with high coverage value in previously studied lakes may reveal significantly different result and bacterial shifts.


This work was financially supported by the National Natural Science Foundation of China (No. 41425004). The final publication is available at Springer via

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