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Abstract We analyzed the fine??scale spatial genetic structure of the individuals of Zelkova schneideriana， which were classified by age using the spatial autocorrelation method， to quantify spatial patterns of genetic variation within the population and to explore potential mechanisms that determine genetic variation in population. The spatial autocorrelation coefficient （r） at 13 distance classes was determined on the basis of both geographical distance and genetic distance matrix which was derived from co??dominant SSR data using GenAlEx software. The results showed that all the individuals of Z. schneideriana exhibited significantly positive spatial genetic structure at distance less than 40 m （the X??intercept was 53.568）， indicating that the average length of the smallest genetic patch for the same genotype clustering of the Z. schneideriana Mailing population was about 50 m. Limited seed dispersal is the main factor that leads to the spatial genetic variation within populations. The individuals in age Class II showed significantly positive spatial genetic structure at distance less than 30 m （the X??intercept was 47.882）， while the individuals in age Class I and age Class III showed no significant spatial genetic structure in any of the spatial distance classes. Z. schneideriana is a long??lived perennial plant； the self??thinning resulted from the cohort competition between individuals in the growing process may lead to this certain spatial structure in age Class III of Z. schneideriana population.
Key words Zelkova schneideriana； Spatial autocorrelation analysis； Spatial genetic structure； SSR.
The spatial genetic structure （SGS） is the non??random spatial distribution pattern of genetic variation[1]. The SGS in plants is affected by multiple factors and it is closely related to the propagation mechanism of the species， the dispersal distance of pollen and seeds， population density， self??thinning of cohort， population colonization history and microhabitat selection[2]. The study of population SGS can facilitate the exploration of the roles of various evolutionary factors[3]， and the correct interpretation of the population genetic characteristics[4].
Zelkova schneideriana Hand.??Mazz. is a deciduous tree belonging to the family Ulmaceae. It is found mainly in central and southern China as well as the southeast coast and the southwestern provinces （regions）. It is valued by many countries， including China， because of its high economic， ecological and landscape values. The leaf colour of Z. schneideriana varies with the seasons， showing yellow， red， orange and green in the fall， and this makes it a species of tree with a high ornamental value， and suitable for roadside and courtyard planting. In addition， Z. schneideriana possesses other desirable characteristics. It is fast??growing and its wood is of a high quality， being tough， durable and resistant to corrosion and having attractive markings， making it often the choice to produce high??grade furniture and decorative materials. Before the maturation of mahogany furniture during the Ming and Qing Dynasties， Z. schneideriana was widely used to make traditional furniture in Jiangnan region and owing to its popularity as the furniture??making material there， the tradition of "no Z. schneideriana no furniture" spread throughout Jiangnan. Z. schneideriana is a desired ecological tree species， because of its well??developed root system， which can hold soil and conserve water. It can also be used for paper making because of its high fibre content in its stem bark. With the characteristics of a long lifespan， wind resistance， drought and pest resistance， Z. schneideriana is also easy to popularize. However， these same values lead to excessive deforestation by humans for economic benefits， which in turn， seriously harms the natural population of Z. schneideriana and its habitat， resulting in the gradual depletion of its resources due to its poor capacity for natural regeneration. Consequently， Z. schneideriana has been listed as a level two national key protected wild plant in the first batch of the "List of national key protected wild plants"[5]. Currently， studies of Z. schneideriana are mainly focused on its biological characteristics[6]， breeding technology[7]， afforestation technology[8]， population distribution and dynamics[9-10]， as well as its wood properties[11]， tissue culture for rapid propagation[12] and genetic diversity[13-14]. However， the study of its population genetic structure has not been reported.
Based on the data of SSR （simple sequence repeat） markers， the present study applied the spatial autocorrelation method to analyse the SGS of the Z. schneideriana population， to reveal the spatial distribution pattern of alleles within the Z. schneideriana population and to explore the reasons for its formation and maintenance. In addition， the SGS of different age groups within the Z. schneideriana population was analysed to investigate the spatial distribution pattern and dynamic mode and the spatial??temporal distribution patterns of alleles in the Z. schneideriana population， which provides a scientific basis for resource protection and sustainable utilization of the species.
Material and Methods
Plant materials
The experimental station at Mailing Town， Fuchuan County， Guangxi， is located at 25??05??N and 111??17??E at an altitude of about 410 m. The vegetation type of the region is evergreen broad??leaved forest with Z. schneideriana as the primary dominant and constructive species. In March 2015， 26 Z. schneideriana plants were collected in the station， and GPS was used to locate each individual. The diameter of the tree trunk was determined for each plant， and the one??year old leaves were collected， desiccated with silica gel， sealed in bags and brought back to the laboratory. After desiccation， leaf samples were stored in a freezer at -20 ??. The spatial distribution of each plant in the Z. schneideriana population is shown in Fig. 1.
The 26 Z. schneideriana individuals were grouped into three age classes based on their trunk diameter at breast height （dbh）： eight in Class I， all of which were classified as seedlings （dbh??1.0 cm）， 10 in Class II （1.030.0 cm）.
DNA extraction and SSR amplification
The total genome was extracted from the silica gel dried Z. schneideriana leaf using an adapted CTAB method. PCR was performed on all samples using 13 SSR primers with a 10 ??l reaction system， and the primer sequences were included in the reference[15]. The 10 ??l PCR reaction system was as follows： 1 ??l 10??PCR Buffer， 0.8 ??l MgCl2， 0.8 ??l dNTPs， 0.1 ??l Taq DNA polymerase， 0.4 ??l of each primer， 5 ng DNA template and 6 ??l ddH2O. PCR amplification was performed using a PCT??220PCR thermocycler （Bio??Rad， Hercules， CA， USA） with the program as follows： 95 ?? for 5 min， then 30 cycles of 95 ?? for 30 s， annealing at primer??specific temperature for 30 s and 72 ?? for 45 s， followed by 72 ?? for 10 min. PCR products were then stored at 4 ?? and electrophoresis was performed on a 1.4% agarose gel （1.4 g agarose， 100 ml 0.5??TBE） with voltage of 100 V and power of 50 W for about 1 h. The electrophoresis products were analysed using a gel imaging system （Bio??Rad）.
Data analysis
The same migration rate for the same primers represents the same allele， based on all the electrophoresis bands being read manually and labelled as A， B， C， D， E ???? from the smallest to the largest bands. The homozygotes were labelled with the same letter， such as "AA" or "BB"， and the heterozygotes were labelled with different letters， such as "AB".
The spatial autocorrelation analysis of plant population genetic structure is an effective method for studying the spatial structure of genetic variation[16]. The spatial autocorrelation coefficient provides a measure of genetic similarity among individuals who fall within a specific distance level. In the present study， a spatial autocorrelation coefficient r of genetic distance matrix at the corresponding distance level， calculated by GenAlEx 6 software[17] was used， which ranged from -1 to 1 to indicate the genetic similarity between paired individuals under different distance levels. When there is no SGS， r = 0. A two??tailed 95% confidence interval was constructed using 1 000 random samplings， and a significant difference was found when r falls out of the 95% confidence interval[18]. When significantly positive SGS is present， the estimated r value will be significantly higher than the +95% confidence interval， but it reduces with the increase in geographical distance levels[19].
Results and Analysis
SGS of all the individuals of the Z. schneideriana population in Mailing Town
The distance level was set at 20 m and there were 13 levels in total. The results of the spatial autocorrelation analysis are shown in Fig. 2a. A significantly positive SGS was observed when the spatial distance was less than 40 m among individuals of the Z. schneideriana population in Mailing Town. When the distance level was 20 cm， the spatial autocorrelation coefficient r was 0.085， and the intercept on the X??axis was 53.568. No significant SGS was observed when the spatial distance was over 40 m. The SGS of individuals from different age classes of Z. schneideriana population in Mailing town
Spatial autocorrelation analysis of individuals from different age classes of the Z. schneideriana population in Mailing Town is shown in Fig. 2b， c and d. A significantly positive SGS was observed in age Class II when the spatial distance was less than 30 m. At a distance level of 20 m， its spatial autocorrelation coefficient was 0.270 and the X??axis intercept was 47.882. No substantial SGS was seen at any tested spatial distance levels in individuals of age Class I and Class III.
Agricultural Biotechnology 2018Discussion
Spatial autocorrelation analysis is an effective method of studying the spatial structure of genetic variation， especially in a small??scale space[20]. The spatial distribution of genetic variation can be obtained via the spatial autocorrelation analysis of genetic variation to determine the existence of SGS[21].
The spatial distribution pattern of the species?? genetic variation is closely related to the population habitat heterogeneity and reproductive biological characteristics， such as the reproductive system and the seed dispersal mode[22-23]. Although the pollen distribution pattern may affect plant SGS， the seed gravity dissemination pattern leads to the gathering of individuals from the same maternal plant around the mother tree and so the SGS of plant population within a short distance is not influenced by the pollen dispersal distance， even a very large one[24]. Therefore， limited seed dispersal is the main factor to induce the spatial structure of genetic variation in populations. In the present study， spatial autocorrelation analysis was applied to show the significantly positive SGS of the Z. schneideriana population in Mailing town within a distance of less than 40 m. Z. schneideriana is an anemophilous flower with a relatively large pollen dispersal distance， but seed distribution is merely reliant on gravity， which results in the significantly positive SGS of the Z. schneideriana population within a short distance scale.
The SGS of the Z. schneideriana Mailing population in different age classes demonstrated the significantly positive SGS in age Class II within a short distance （< 30 m）， but not over a large distance scale. No significant SGS was observed for age Class I or Class III at any tested distance levels. In age Class III， the SGS of the Z. schneideriana population no longer existed. The tree species exhibiting SGS at seed and seedling stages may eliminate the adjacent relative individuals to reduce the intensity of genetic structure in its adult stage due to the self??thinning resulting from the cohort competition in the growing process[25]. This self??thinning might be the main reason for the disappearance of SGS from the age Class III Z. schneideriana population. Some studies indicated an aggregated SGS in seedlings[26]， but no significant SGS was seen in the age Class I Z. schneideriana population， which is not consistent with previous results. We believe that the seedling recruitment of Z. schneideriana is reduced by adverse environmental and human activities， which may lead to the non??significant SGS in age Class I Z. schneideriana population. When the genetic patch is irregular， the intercept on the X??axis is the average shortest length of the genetic patch， which can be used to indicate the spatial scope of the autocorrelation. The intercept on the X??axis was 53.568 from the spatial autocorrelation analysis of all individuals from the Z. schneideriana population in Mailing Town， indicating that the average length of the smallest genetic patch for the same genotype clustering of the Z. schneideriana Mailing population was about 50 m. The intercept of the X??axis was 47.882 for the age Class II Z. schneideriana population， which is close to 50 m. Currently， the field distribution of Z. schneideriana populations are rare， and most of the individuals are isolated， so it is hard to find a contiguous Z. schneideriana population， which is unfavourable to its propagation and the increase of heterozygosity in its offspring. Consequently， it is of great urgency that we carry out the in??situ conservation and ex??situ conservation work for the tree species. The present study reveals that the individual distance should be greater than 50 m to reduce the genetic similarity of the samples when collecting ex??situ conservation materials. In addition， the gene flow should be artificially promoted in the in??situ conservation process to lower the risk of inbreeding.
In order to further understand the survival and maintenance mechanism of the Z. schneideriana population， further investigation of its reproductive system and the dispersal pattern of its seeds and pollen is needed.
References
[1] LOVELESS MD， Hamrick JL. Ecological determinants of genetic structure in plant populations[J]. Annual Review of Ecology and Systematics， 1984， 15： 65-95.
[2] FUCHS EJ， HAMRICK JL. Genetic diversity in the endangered tropical tree， Guaiacum sanctum （Zygophyllaceae）[J]. Journal of Heredity. 2010， 101： 284-291.
[3] Epperson BK. Recent advances in correlation studies of spatial patterns of genetic variation[J]. Evolutionary Biology， 1993， 27： 95-155.
[4] WANG Y， SHEN Y. Spatial autocorrelation methods and application[J]. Chinese Journal of Health Statistics， 2008， 25： 443-445.
[5] WANG LD， ZHANG RQ. Research advances on Zelkova schneideriana[J]. Guangxi Forestry Science， 2005， 34： 188-191.
[6] JIN XL. Study on biological character and micro??reproduction technology on Zelkova schneideriana Hand. Mazz[D]. Zhuzhou： Central??South Forestry University， 2003. [7] DOU QQ， ZHONG L， ZHANG M， et al. Study on the classification of seedling quality of Zelkova schneideriana[J]. Journal of Jiangsu Forestry Science & Technology， 2009， 36：1-4， 14.
[8] CHEN D， LI JP AND WANG XJ. Studies on the effects of different silvicultural techniques on growth of young Zelkova schneideriana plantations[J]. Central South Forest Inventory and Planning， 2004， 23： 56-57.
[9] CHENG HM.A dynamic study of Zelkova schneideriana population quantity in Mountain Dashu[J]. Journal of Central South University of Forestry &Technology， 2009， 29： 65-69.
[10] FANG YP， LIU SJ， XIANG J， et al. Study on the natural population distribution of Zelkova schneideriana in Hubei[J]. Resources and Environment in the Yangtze Basin. 2007， 16： 744-747.
[11] ZHAO WT， GAN XH， DING YL. An Anatomic Study on the Wood Development of Zelkova schneideriana[J]. Journal of Nanjing Forestry University（Natural Sciences Edition）， 2003， 27： 39-43.
[12] WANG LD， ZHANG RQ， JIN XL. Phyllogen induction and cluster bud multiplication of Zelkova schneideriana Hand.??Mazz[J]. Journal of Central South University of Forestry & Technology， 2010， 30： 75-79.
[13] LIU H L， ZHANG RQ， ZHU JY， et al. Chloroplast analysis of Zelkova schneideriana （Ulmaceae）： genetic diversity， population structure， and conservation implication[J]. Genet. Mol. Res.， 2016， 15： 1-9.
[14] LIU XC， LI YY， CHEN SY. Genetic diversity of Zelkova schneideriana from different populations by ISSR analysis[J]. J. West China Forest. Sci.， 2005， 34： 43-47.
[15] LIU HL， ZHANG RQ， ZHU JY， et al. Isolation and characterization of polymorphic microsatellite loci from Zelkova schneideriana Hand.??Mazz[J]. Genet. Mol. Res.， 2014， 13： 10062-10066.
[16] LI JM， DONG M. Fine??scale clonal structure and diversity of invasive plant Mikania micrantha H. B. K. and its plant parasite Cuscuta campestris Yunker[J]. Biological Invasions， 2009， 11： 687-695.
[17] PEAKALL R， SMOUSE PE. GENALEX 6： genetic analysis in Excel. Population genetic software for teaching and research[J]. Molecular Ecology Notes， 2006， 6： 288-295.
[18] TRAPNELL DW， SCHMIDT JP， HAMRICK J. Spatial genetic structure of the Southeastern North American endemic， Ceratiola ericoides （Empetraceae）[J]. Journal of Heredity， 2008， 99： 604-609.
[19] PEAKALL R， RUIBAL M LINDENMAYER DB. Spatial autocorrelation analysis offers new insights into gene flow in the Australian bush rat， Rattus fuscipes[J]. Evolution， 2003， 57： 1182-1195. [20] SOKAL RR， ODEN NL. Spatial autocorrelation in biology， 1. Methodology[J]. Biological Journal of the Linnean Society， 1978， 10： 199-228.
[21] LI A， LUO YB， GE S. Spatial autocorrelation study of population genetic structure of two orchid species[J]. Biodiversity Science， 2002， 10： 249-257.
[22] CHUNG MG， CHUNG JM， CHUNG MY， et al. Spatial distribution of allozyme polymorphisms following clonal and sexual reproduction in populations of Rhus javanica （Anacardiaceae）. Heredity， 2000， 84： 178-185.
[23] MARQUARDT PE， EPPERSON BK. Spatial and population genetic structure of microsatellites in white pine[J]. Molecular Ecology， 2004， 13： 3305-3315.
[24] TORIMARU T， TANI N TSUMURA Y， et al. Effects of kin??structured seed dispersal on the genetic structure of the clonal dioecious shrub Ilex Leucoclada[J]. Evolution， 2007， 61： 1289-1300.
[25] UENO S， T OMARU N， YOSHIMARU H， et al. Size??class differences in genetic structure and individual distribution of Camellia japonica L. in a Japanese old??growth evergreen forest[J]. Heredity， 2002， 89： 120-126.
[26] CHUNG MY， EPPERSON BK， CHUNG MG. Genetic structure of age classes in Camellia japonica （Theaceae）[J]. Evolution， 2003， 57： 62-73.
Key words Zelkova schneideriana； Spatial autocorrelation analysis； Spatial genetic structure； SSR.
The spatial genetic structure （SGS） is the non??random spatial distribution pattern of genetic variation[1]. The SGS in plants is affected by multiple factors and it is closely related to the propagation mechanism of the species， the dispersal distance of pollen and seeds， population density， self??thinning of cohort， population colonization history and microhabitat selection[2]. The study of population SGS can facilitate the exploration of the roles of various evolutionary factors[3]， and the correct interpretation of the population genetic characteristics[4].
Zelkova schneideriana Hand.??Mazz. is a deciduous tree belonging to the family Ulmaceae. It is found mainly in central and southern China as well as the southeast coast and the southwestern provinces （regions）. It is valued by many countries， including China， because of its high economic， ecological and landscape values. The leaf colour of Z. schneideriana varies with the seasons， showing yellow， red， orange and green in the fall， and this makes it a species of tree with a high ornamental value， and suitable for roadside and courtyard planting. In addition， Z. schneideriana possesses other desirable characteristics. It is fast??growing and its wood is of a high quality， being tough， durable and resistant to corrosion and having attractive markings， making it often the choice to produce high??grade furniture and decorative materials. Before the maturation of mahogany furniture during the Ming and Qing Dynasties， Z. schneideriana was widely used to make traditional furniture in Jiangnan region and owing to its popularity as the furniture??making material there， the tradition of "no Z. schneideriana no furniture" spread throughout Jiangnan. Z. schneideriana is a desired ecological tree species， because of its well??developed root system， which can hold soil and conserve water. It can also be used for paper making because of its high fibre content in its stem bark. With the characteristics of a long lifespan， wind resistance， drought and pest resistance， Z. schneideriana is also easy to popularize. However， these same values lead to excessive deforestation by humans for economic benefits， which in turn， seriously harms the natural population of Z. schneideriana and its habitat， resulting in the gradual depletion of its resources due to its poor capacity for natural regeneration. Consequently， Z. schneideriana has been listed as a level two national key protected wild plant in the first batch of the "List of national key protected wild plants"[5]. Currently， studies of Z. schneideriana are mainly focused on its biological characteristics[6]， breeding technology[7]， afforestation technology[8]， population distribution and dynamics[9-10]， as well as its wood properties[11]， tissue culture for rapid propagation[12] and genetic diversity[13-14]. However， the study of its population genetic structure has not been reported.
Based on the data of SSR （simple sequence repeat） markers， the present study applied the spatial autocorrelation method to analyse the SGS of the Z. schneideriana population， to reveal the spatial distribution pattern of alleles within the Z. schneideriana population and to explore the reasons for its formation and maintenance. In addition， the SGS of different age groups within the Z. schneideriana population was analysed to investigate the spatial distribution pattern and dynamic mode and the spatial??temporal distribution patterns of alleles in the Z. schneideriana population， which provides a scientific basis for resource protection and sustainable utilization of the species.
Material and Methods
Plant materials
The experimental station at Mailing Town， Fuchuan County， Guangxi， is located at 25??05??N and 111??17??E at an altitude of about 410 m. The vegetation type of the region is evergreen broad??leaved forest with Z. schneideriana as the primary dominant and constructive species. In March 2015， 26 Z. schneideriana plants were collected in the station， and GPS was used to locate each individual. The diameter of the tree trunk was determined for each plant， and the one??year old leaves were collected， desiccated with silica gel， sealed in bags and brought back to the laboratory. After desiccation， leaf samples were stored in a freezer at -20 ??. The spatial distribution of each plant in the Z. schneideriana population is shown in Fig. 1.
The 26 Z. schneideriana individuals were grouped into three age classes based on their trunk diameter at breast height （dbh）： eight in Class I， all of which were classified as seedlings （dbh??1.0 cm）， 10 in Class II （1.030.0 cm）.
DNA extraction and SSR amplification
The total genome was extracted from the silica gel dried Z. schneideriana leaf using an adapted CTAB method. PCR was performed on all samples using 13 SSR primers with a 10 ??l reaction system， and the primer sequences were included in the reference[15]. The 10 ??l PCR reaction system was as follows： 1 ??l 10??PCR Buffer， 0.8 ??l MgCl2， 0.8 ??l dNTPs， 0.1 ??l Taq DNA polymerase， 0.4 ??l of each primer， 5 ng DNA template and 6 ??l ddH2O. PCR amplification was performed using a PCT??220PCR thermocycler （Bio??Rad， Hercules， CA， USA） with the program as follows： 95 ?? for 5 min， then 30 cycles of 95 ?? for 30 s， annealing at primer??specific temperature for 30 s and 72 ?? for 45 s， followed by 72 ?? for 10 min. PCR products were then stored at 4 ?? and electrophoresis was performed on a 1.4% agarose gel （1.4 g agarose， 100 ml 0.5??TBE） with voltage of 100 V and power of 50 W for about 1 h. The electrophoresis products were analysed using a gel imaging system （Bio??Rad）.
Data analysis
The same migration rate for the same primers represents the same allele， based on all the electrophoresis bands being read manually and labelled as A， B， C， D， E ???? from the smallest to the largest bands. The homozygotes were labelled with the same letter， such as "AA" or "BB"， and the heterozygotes were labelled with different letters， such as "AB".
The spatial autocorrelation analysis of plant population genetic structure is an effective method for studying the spatial structure of genetic variation[16]. The spatial autocorrelation coefficient provides a measure of genetic similarity among individuals who fall within a specific distance level. In the present study， a spatial autocorrelation coefficient r of genetic distance matrix at the corresponding distance level， calculated by GenAlEx 6 software[17] was used， which ranged from -1 to 1 to indicate the genetic similarity between paired individuals under different distance levels. When there is no SGS， r = 0. A two??tailed 95% confidence interval was constructed using 1 000 random samplings， and a significant difference was found when r falls out of the 95% confidence interval[18]. When significantly positive SGS is present， the estimated r value will be significantly higher than the +95% confidence interval， but it reduces with the increase in geographical distance levels[19].
Results and Analysis
SGS of all the individuals of the Z. schneideriana population in Mailing Town
The distance level was set at 20 m and there were 13 levels in total. The results of the spatial autocorrelation analysis are shown in Fig. 2a. A significantly positive SGS was observed when the spatial distance was less than 40 m among individuals of the Z. schneideriana population in Mailing Town. When the distance level was 20 cm， the spatial autocorrelation coefficient r was 0.085， and the intercept on the X??axis was 53.568. No significant SGS was observed when the spatial distance was over 40 m. The SGS of individuals from different age classes of Z. schneideriana population in Mailing town
Spatial autocorrelation analysis of individuals from different age classes of the Z. schneideriana population in Mailing Town is shown in Fig. 2b， c and d. A significantly positive SGS was observed in age Class II when the spatial distance was less than 30 m. At a distance level of 20 m， its spatial autocorrelation coefficient was 0.270 and the X??axis intercept was 47.882. No substantial SGS was seen at any tested spatial distance levels in individuals of age Class I and Class III.
Agricultural Biotechnology 2018Discussion
Spatial autocorrelation analysis is an effective method of studying the spatial structure of genetic variation， especially in a small??scale space[20]. The spatial distribution of genetic variation can be obtained via the spatial autocorrelation analysis of genetic variation to determine the existence of SGS[21].
The spatial distribution pattern of the species?? genetic variation is closely related to the population habitat heterogeneity and reproductive biological characteristics， such as the reproductive system and the seed dispersal mode[22-23]. Although the pollen distribution pattern may affect plant SGS， the seed gravity dissemination pattern leads to the gathering of individuals from the same maternal plant around the mother tree and so the SGS of plant population within a short distance is not influenced by the pollen dispersal distance， even a very large one[24]. Therefore， limited seed dispersal is the main factor to induce the spatial structure of genetic variation in populations. In the present study， spatial autocorrelation analysis was applied to show the significantly positive SGS of the Z. schneideriana population in Mailing town within a distance of less than 40 m. Z. schneideriana is an anemophilous flower with a relatively large pollen dispersal distance， but seed distribution is merely reliant on gravity， which results in the significantly positive SGS of the Z. schneideriana population within a short distance scale.
The SGS of the Z. schneideriana Mailing population in different age classes demonstrated the significantly positive SGS in age Class II within a short distance （< 30 m）， but not over a large distance scale. No significant SGS was observed for age Class I or Class III at any tested distance levels. In age Class III， the SGS of the Z. schneideriana population no longer existed. The tree species exhibiting SGS at seed and seedling stages may eliminate the adjacent relative individuals to reduce the intensity of genetic structure in its adult stage due to the self??thinning resulting from the cohort competition in the growing process[25]. This self??thinning might be the main reason for the disappearance of SGS from the age Class III Z. schneideriana population. Some studies indicated an aggregated SGS in seedlings[26]， but no significant SGS was seen in the age Class I Z. schneideriana population， which is not consistent with previous results. We believe that the seedling recruitment of Z. schneideriana is reduced by adverse environmental and human activities， which may lead to the non??significant SGS in age Class I Z. schneideriana population. When the genetic patch is irregular， the intercept on the X??axis is the average shortest length of the genetic patch， which can be used to indicate the spatial scope of the autocorrelation. The intercept on the X??axis was 53.568 from the spatial autocorrelation analysis of all individuals from the Z. schneideriana population in Mailing Town， indicating that the average length of the smallest genetic patch for the same genotype clustering of the Z. schneideriana Mailing population was about 50 m. The intercept of the X??axis was 47.882 for the age Class II Z. schneideriana population， which is close to 50 m. Currently， the field distribution of Z. schneideriana populations are rare， and most of the individuals are isolated， so it is hard to find a contiguous Z. schneideriana population， which is unfavourable to its propagation and the increase of heterozygosity in its offspring. Consequently， it is of great urgency that we carry out the in??situ conservation and ex??situ conservation work for the tree species. The present study reveals that the individual distance should be greater than 50 m to reduce the genetic similarity of the samples when collecting ex??situ conservation materials. In addition， the gene flow should be artificially promoted in the in??situ conservation process to lower the risk of inbreeding.
In order to further understand the survival and maintenance mechanism of the Z. schneideriana population， further investigation of its reproductive system and the dispersal pattern of its seeds and pollen is needed.
References
[1] LOVELESS MD， Hamrick JL. Ecological determinants of genetic structure in plant populations[J]. Annual Review of Ecology and Systematics， 1984， 15： 65-95.
[2] FUCHS EJ， HAMRICK JL. Genetic diversity in the endangered tropical tree， Guaiacum sanctum （Zygophyllaceae）[J]. Journal of Heredity. 2010， 101： 284-291.
[3] Epperson BK. Recent advances in correlation studies of spatial patterns of genetic variation[J]. Evolutionary Biology， 1993， 27： 95-155.
[4] WANG Y， SHEN Y. Spatial autocorrelation methods and application[J]. Chinese Journal of Health Statistics， 2008， 25： 443-445.
[5] WANG LD， ZHANG RQ. Research advances on Zelkova schneideriana[J]. Guangxi Forestry Science， 2005， 34： 188-191.
[6] JIN XL. Study on biological character and micro??reproduction technology on Zelkova schneideriana Hand. Mazz[D]. Zhuzhou： Central??South Forestry University， 2003. [7] DOU QQ， ZHONG L， ZHANG M， et al. Study on the classification of seedling quality of Zelkova schneideriana[J]. Journal of Jiangsu Forestry Science & Technology， 2009， 36：1-4， 14.
[8] CHEN D， LI JP AND WANG XJ. Studies on the effects of different silvicultural techniques on growth of young Zelkova schneideriana plantations[J]. Central South Forest Inventory and Planning， 2004， 23： 56-57.
[9] CHENG HM.A dynamic study of Zelkova schneideriana population quantity in Mountain Dashu[J]. Journal of Central South University of Forestry &Technology， 2009， 29： 65-69.
[10] FANG YP， LIU SJ， XIANG J， et al. Study on the natural population distribution of Zelkova schneideriana in Hubei[J]. Resources and Environment in the Yangtze Basin. 2007， 16： 744-747.
[11] ZHAO WT， GAN XH， DING YL. An Anatomic Study on the Wood Development of Zelkova schneideriana[J]. Journal of Nanjing Forestry University（Natural Sciences Edition）， 2003， 27： 39-43.
[12] WANG LD， ZHANG RQ， JIN XL. Phyllogen induction and cluster bud multiplication of Zelkova schneideriana Hand.??Mazz[J]. Journal of Central South University of Forestry & Technology， 2010， 30： 75-79.
[13] LIU H L， ZHANG RQ， ZHU JY， et al. Chloroplast analysis of Zelkova schneideriana （Ulmaceae）： genetic diversity， population structure， and conservation implication[J]. Genet. Mol. Res.， 2016， 15： 1-9.
[14] LIU XC， LI YY， CHEN SY. Genetic diversity of Zelkova schneideriana from different populations by ISSR analysis[J]. J. West China Forest. Sci.， 2005， 34： 43-47.
[15] LIU HL， ZHANG RQ， ZHU JY， et al. Isolation and characterization of polymorphic microsatellite loci from Zelkova schneideriana Hand.??Mazz[J]. Genet. Mol. Res.， 2014， 13： 10062-10066.
[16] LI JM， DONG M. Fine??scale clonal structure and diversity of invasive plant Mikania micrantha H. B. K. and its plant parasite Cuscuta campestris Yunker[J]. Biological Invasions， 2009， 11： 687-695.
[17] PEAKALL R， SMOUSE PE. GENALEX 6： genetic analysis in Excel. Population genetic software for teaching and research[J]. Molecular Ecology Notes， 2006， 6： 288-295.
[18] TRAPNELL DW， SCHMIDT JP， HAMRICK J. Spatial genetic structure of the Southeastern North American endemic， Ceratiola ericoides （Empetraceae）[J]. Journal of Heredity， 2008， 99： 604-609.
[19] PEAKALL R， RUIBAL M LINDENMAYER DB. Spatial autocorrelation analysis offers new insights into gene flow in the Australian bush rat， Rattus fuscipes[J]. Evolution， 2003， 57： 1182-1195. [20] SOKAL RR， ODEN NL. Spatial autocorrelation in biology， 1. Methodology[J]. Biological Journal of the Linnean Society， 1978， 10： 199-228.
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