Response of species and stand types to snow/wind damage in a temperate secondary forest,Northeast China

Xiufen Li•Lei Jin•Jiaojun Zhu•Limin Liu•Jinxin Zhang•Yi Wang•Chengyao Zhu

Introduction

According to forecasts,the frequency and intensity of all kinds of snow/wind damage will increase due to the effects of global climate change(Emanuel 1987;Gray 1990;Blennow et al.2010;Kilpela inen et al.2010).The yield of wood harvesting caused by meteorological disasters such as snow/wind damage,accounted for 20% of the total damages in temperate forests and is still rising(Hou 1992;McCarthy et al.2010).For example,four states in the northern USA experienced severe snowstorms in 1998,and the area of the destroyed forest reached 6.88×106ha(Chen and Wu 2008).In 1999,a devastating storm swept through most of Europe,and in Germany,damaged trees represented some 30 million m3,equivalent to two-thirds of the national average cutting volume.In January 2005,a blizzard in southern Sweden blew down or damaged 75 million m3trees,almost equivalent to the country’s annual cutting volume.From the end of 2005 to early 2006,Japan suffered the heaviest snow falls of the past 20 years and damaged forested areas reached 2900 ha(Chen and Wu 2008).In early 2008,most of the provinces in southern China suffered heavy snow sleet storms,and nearly 10% of the forests(18.6 million ha)were affected(Xu et al.2010).Snow/wind disasters may also change the original service function of ecosystems(Vlinger and Fridman 1997;Yang et al.2008;Cao and Chang 2010).For example,light,temperature,moisture and other environmental conditions in forest stands would change after trees were broken or uprooted(Guo and Xue 2012;Veblen et al.2001).Root exposure caused changes in micro terrains,outward appearances of trees,and soil composition.After being injured,trees are vulnerable to diseases and insect pests,and the vegetation structure and composition consequentially changed(Beatty 1984;Schaetzl et al.1989;Baker et al.2002).As a result,these changes may lead to variations in spatial heterogeneity of resource ef fi ciency,and have a major impact on regeneration and distribution patterns of forests(Peterson and Pickett 1995;Veblen et al.2001;Liang et al.2002;Darwin et al.2004;Du et al.2012).Obviously,snow/wind damage is an important natural disturbance factor in forest ecosystems.Therefore,in the current context of high frequency meteorological events,research on snow/wind damage is of considerable importance in order to enhance the ability of stands to withstand natural disasters,to predict succession directions for different forest stands,to reasonably regulate and protect existing forest resources and to guide the management of forests following a severe climatic event.

The degree of snow/wind damage to forest plantations mainly depends on weather conditions,site factors,tree and forest stand characteristics,and the interaction between these factors.Weather conditions and site factors are uncontrollable,while others may be arti fi cially manipulated(Nyka nen et al.1997;Pa a talo et al.1999;Li et al.2005,2007).Numerous studies have focused on the relationships between tree and stand characteristics and snow/wind events in order to reduce losses by regulating stand characteristics(Peltola et al.1999;Chiba 2000;Frey and Thee 2002;Zhu et al.2006;Vyse et al.2008;Gardiner et al.2008;Teste and Lieffers 2011;Ciftci et al.2014).However,these studies were concentrated on plantations,and little is known of the relationships between trees/forest characteristics of natural secondary forests and snow/wind damage(Li et al.2004;Zhu et al.2006).

Secondary forests,regenerated on abandoned agricultural land and pasture or re-established after stand-replacing disturbances,are an important component of terrestrial ecosystems around the world(Kauppi et al.2006).However,as the main type of forests(more than 60% of the world’s forest resources),secondary forests frequently suffer from severe snow/wind damage(Hou 1992;Zhu et al.2006).Therefore,it is of signi fi cance to evaluate the effects of snow/wind storms on secondary forests.The secondary forests in this study were exposed to a once in fi fty-year snow/wind event March 29,2003 in northeast China.The relationship between snow/wind damage and injury characteristics of trees and stands was explored by plot survey in the affected areas.The objectives of this study were:(1)to determine if there were different susceptibilities to the weather event,the amount and types of snow/wind damages(uprooting,snapping,bending)by different tree species;(2)to explore how tree size(height and diameter)affects the susceptibility of trees to snow/wind damage;(3)to examine whether cover types affect the severity and type of snow/wind damage;and,(4)to determine the relationships between stand characteristics and snow/wind damage in a natural secondary forest.

Materials and methods

Study sites

This study was conducted at the Qingyuan Forest CERN,Chinese Academy of Sciences,located in a mountainous region of Liaoning Province(41°51′N,124°54′E,500–1100 m a.s.l.).The climate is a continental monsoon with a humid,rainy summer,and a cold,dry winter.Mean annual temperature is 4.7°C with minimum and maximum temperatures of-37.6 °C in January and 36.5 °C in July.The annual precipitation ranges 700–850 mm,with 80%falling during June–August.The frost-free period is 130 days,with an early frost in October and a late frost in April(Zhu et al.2010).

The study site had been covered primarily by mixed broadleaf Korean pine(Pinus koraiensisSiebold and Zuccarini)forests before the 1930s and thereafter had been subject to unregulated timber removal for decades.Massive control burns were used in the early 1950s for clearing the original forest.The study area gradually changed to secondary forest with a tree layer ofFraxinus rhynchophyllaHance.,Juglans mandshuricaMaxim.,Phellodendron amurenseRupr.,Quercus mongolicaFisch.Ex Ledeb andAcer pictum subsp.mono(Maxim.)H.Ohashi;a shrub layer ofAcer mandshricumMaxim.,Acer triforiumKom.,Acer tegmentosumMaxim.andSyringa reticulatesubsp.AmurensisRupr.;and an herbaceous layer ofCardamine leucantha(Tausch)O.E.Schulz,AlliummonanthumMaxim.,Arisaema amurenseMaxim.AndPolygonatum involucratum(Franchet and Savatier)Maximoulicz.In the 1960s,the secondary forest was partially cleared,and patches were planted to larch(Larix gmelinii(Rupr.)Rupr.)that contained a shrub layer ofA.tegmentosum,Acer pseudosieboldianum(Pax)Komarov.,Schisandra chinensis(Turcz.)Baill.,Syringa wol fi iSchneid,andAcanthopanax senticosus(Rupr.and Maxim.)Marms and an herbaceous layer includingC.leucantha,Rubia sylvatica(Maxim.)Naki,andSpuriopimpinella brachycarp(Naki)Kitag.(Yang and Zhu 2015).The soil is a typical brown forest soil with texture in the larch plantations and the secondary forest similar,namely,on average 25.6%sand,51.2%silt and 23.2%clay(Yan et al.2016).

In the early spring(March 29)of 2003,serious forest damage occurred in the secondary forests in Dasuhe District(41°51′6.1′′N,124°54′32.6′′E),Qingyuan County in the northeastern part of China.The total forest area of Dasuhe District is more than 10,000 ha,of which,about 1000 ha belongs to Qingyuan Forest CERN,Chinese Academy of Sciences(QYF CERN,CAS).More than 15% of the total area in QYF CERN was damaged from bending,snapping and uprooting of trees.The damage fi rst occurred since records began from 1958.

Field investigation

Stand-level analysis complements work that was based on the investigation to relate damage occurrence and damage patterns to climatic factors,site indices and topographic characteristics(Li et al.2004;Zhu et al.2006).

To investigate how the traits of individual trees and stand structure might in fl uence the type and severity of snow/wind damage, fi eld investigations were carried out during the spring and autumn of 2003 and 2004.For viewing the overall damage,sixty-nine 20 m×20 m sample plots were established with four 10 m×10 m subplots in each.In each sub-plot,damage types(i.e.,undamaged vs.damaged),uprooting,and breakage(stem or canopy snap or bend)were determined.Diameter at breast height(DBH)and tree heights(DBH＞4 cm)were measured,species recorded,and assigned a damage value.The sample plots met the following criteria:

1. Each plot was at least 100 m from the damage boundary.

2. Each plot contained different damage types.

3. Sample plots had similar site conditions(elevation 900–1000 m;slope 20°–30°;and aspect).

In order to examine the in fl uence of stand structure on the extent and severity of storm damage,the stand type of each plot was determined according to the importance value(Iv)of the species.Ivwas calculated as following:whereRarepresents the relative abundance(i.e.,number of one tree species/total number of trees in a plot),Rfthe relative frequency(i.e.,sub-plot number of one tree species appearance/total number of sub-plots in a plot),andSdthe signi fi cant degree(i.e.,basal area of one tree species/total basal area in a plot of one tree species(including the damaged trees))(Hao et al.2002,2003).The importance value ranged from 0 to 100.

Additionally,stem density was calculated according to the number of trees in a plot.

Data analyses

To test the differences between the susceptibilities of species to various types of snow/wind damage(uprooted,snapped,bent),we compared the damage ratios for each damage type.The damage ratio is de fi ned as the ratio of the number of damaged stems to the total number of stems in a plot.Damage ratios were calculated separately for each species.To avoid confusion of the effects of species with those of tree size,we compared canopy trees and subcanopy trees separately(Liu 2004).Canopy trees includedBetula costata Trautvetter,Q.mongolica,Acer monoandFraxinusmandshurica;J.mandshurica,A.pseudosieboldianum,Carpinus cordataandA.tegmentosumwere classi fi ed as subcanopy trees.Canopy trees included 666B.costata,223Q.mongolica,143F.mandshuricaand 110J.mandshurica.Subcanopy trees included 738A.pseudosieboldianum,728A.mono,109C.cordataand 202A.tegmentosum.The basal area of these eight species accounted for 90.2% of the total basal area of all 32 species found in the study plots.Chi square analysis of 2×4 contingency tables was used to statistically evaluate the differences in damage ratios among the four canopy species and the four subcanopy species.Separate analyses were conducted for each damage type.Tests were not carried out if the expected frequency in any cell of the contingency table was less than fi ve(Veblen et al.2001).

The in fl uence of tree height on susceptibility to snow/wind damage was examined by comparing the median heights of each species.Statistical signi fi cance in median height was evaluated using one-way analysis of variance(ANOVA)based on ranks;pairwise comparisons were made using Dunn’s method(Veblen et al.2001).

Possible differences in susceptibility to snow/wind damage between cover types were examined by comparing the meanpercentageofeachdegreeofdamageinstandsthathad six cover types.Cover types were determined by clustering sample plots according to the importance value(Iv)of the species.The six cover types were:A.pseudosieboldianumdominatedstands(I),Q.mongolica-dominatedstands(II),A.mono-dominated stands (III),J.mandshurica-F.mandshuricadominated stands(IV),B.costata-dominated stands(V),andU.laciniata-dominated stands(VI).Due to onlytwoplotsforU.laciniata-dominatedstands,differences in susceptibility to snow/wind damage between other fi ve cover types were evaluated using Kruskal–Wallis one-way ANOVA;pairwise comparisons were made using Dunn’s method(statistical analyses were not conducted for type VI because only two plots contained this type).

To evaluate the in fl uence of stand-level attributes on susceptibility to snow/wind storms,best-subset regression was used to identify potential predictors of damage.The dependent variable was the percentage of trees totally damaged,snapped or bent.Independent variables were trees per hectare,mean tree height,total basal area and importance value(Iv)of each species.Some independent variables were excluded because of their collinearity.Multiple linear regressions were used to relate variation of each dependent variable to the remaining independent variables that had low collinearity.All variables used in regression analyses passed tests of normality and homogeneity of variance.Statistical analyses were performed using SPSS 22.0.

Results

Tree attributes and snow/wind damage

Among the 3144 individual trees included in the 69 sampled plots,4.5%were uprooted,35.4%were broken,18.5%were bent,and 41.6%were not damaged.There were 32 tree species in the sampled plots.

Differences in the susceptibility of species to snow/wind damage were investigated separately for canopy and subcanopy trees,as shown in Fig.1.The percentages of uprooted trees in each category were low,and the numbers too small(80 canopy and 54 subcanopy trees)for statistical evaluation(Fig.1a,e).Among the canopy trees,B.costataandJ.mandshuricawere most susceptible to uprooting,whereasQ.mongolicawas the least susceptible.Subcanopy trees were less susceptible than canopy trees.Among subcanopy trees,A.pseudosieboldianumwas the least susceptible to uprooting.Both canopy and subcanopy species differed signi fi cantly in their susceptibility to breakage (χ2=26.57,p＜0.005 and χ2=83.71,p＜0.001 for canopy and subcanopy trees,respectively;Fig.1b,f).Among the canopy trees,Q.mongolicaandB.costatawere more susceptible to breakage thanF.mandshuricaandJ.mandshurica.Subcanopy trees were less susceptible to breakage but more susceptible to bending than canopy trees.Among subcanopy trees,A.pseudosieboldianumhad the highest ratio andA.monothe lowest of bending. The differences between the susceptibility of subcanopy trees to bending were signi ficant(χ2=17.68,p＜0.005,Fig.1g).B.costatawas more susceptible to bending than other canopy species.Chi square analyses were not conducted because there were too fewJ.mandshurica(only 4 trees;Fig.1c).The percentage of undamaged canopy trees was lower than that of subcanopy trees and differed between species both in the canopy and subcanopy (χ2=51.74,p＜0.005;χ2=38.19,p＜0.005,respectively;Fig.1d,h).

Differences in susceptibility to snow/wind damage between different sizes of trees were examined by comparing median heights of the trees within each species which were snapped,bent or left standing(Table 1).For all eight species,broken trees were signi fi cantly taller than those bent or undamaged trees.Dunn’s pairwise comparisons showed that within each tree species there were signi fi cant differences in the median heights between broken and bent,and between broken and undamaged trees.Median heights of bent trees did not differ from those of undamaged ones for all species(p＞0.05),except forA.pseudosieboldianum.

Although the median heights of the snapped and bent trees were different,data on DBH were more complete to evaluate the in fl uence of tree size on susceptibility to snow/wind damage because the burial of the tops of many trees permitted estimates of only minimum heights.Comparison of the percentages of trees with different diameters that were snapped or bent indicates that size in fl uences susceptibility to the type of snow/wind damage.Box plots compared DBH of damaged trees(uprooted,snapped,bent)to those of undamaged ones.This analysis was conducted for the four canopy and subcanopy trees(Fig.2).The DBHs of uprooted and broken trees were greater than that of bent and undamaged trees for all with the exception ofJ.mandshurica.

Stand attributes and snow/wind damage

At the stand level,there were signi fi cant differences in damage between cover types(Table 2).The median percentage of damaged trees differed signi fi cantly amongst the fi ve cover types(Kruskal–Wallis one-way ANOVA on ranks,p=0.009).The median percentage of damaged trees in each cover type were ranked as:II(75.02%)＞V(68.19%)＞III(53.58%)＞IV (49.26%)＞I(42.85%).Pairwise comparisons showed that there were signi fi cant differences in the median percentage between cover types I and II,I and V,II and IV,and III and V.The median percentage of snapped trees signi fi cantly differed among the fi ve cover types(p=0.000)and were ranked as:II(55.92%)＞V (38.78%)＞III (37.36%)＞IV(29.63%)＞I(9.09%).There were signi fi cant differences in the median percentage of snapped trees between covertypes I and II and between I and V.Similarly,the median percentage of bent trees differed signi fi cantly among the fi ve cover types(p=0.002)and were ranked as:I(31.31%)＞V (21.37%)＞III (11.31%)＞II(10.19%)＞IV(9.09%).The median percentage of bent trees in cover type I differed signi fi cantly from that of cover type IV.

Fig.1 Percentage of canopy and subcanopy species uprooted,snapped,bent or remained undamaged after wind and snow damage in 2003

Multiple regressions showed that the percentage of damaged trees was positively related to the importance value ofB.costataand negatively related to stand density(p=0.000;adjustedr2=0.416).The percentage of snapped or broken trees was positively related to mean tree height and the importance value ofB.costataand negatively related to the importance value ofJ.mandshurica(p=0.000;adjustedr2=0.586).The percentage of bent trees was positively related to the important value ofB.costataandA.pseudosieboldianum(p=0.000;adjustedr2=0.453).

Discussion and conclusions

Numerous studies have demonstrated that trees at high altitudes and on steep slopes are susceptible to wind and snow damages(Pa a talo et al.1999;Jalkanen and Mattila 2000;Li et al.2004;Mayer et al.2005;Zhu et al.2006;Kilpela inen et al.2010;Martínez et al.2013).Our results are in agreement with these studies.Moreover,they show that the severity and type of damage differ signi fi cantly between stands of trees on the same site conditions(elevation,900–1000 m;slope,20°–30°).This indicated that the pattern of snow/wind damage was signi fi cantly in fl uenced by species composition and structure of forest patches.

Table 1 Median heights(m)of each species in different damage categories

Of the types of damage,the highest percentage of damage was snapped or broken trees,whereas the lowest percentage was uprooted trees.This suggests that trees are more likely to be snapped than uprooted.This result is consistent with other studies(Jones 1983;Peltola et al.1993,2000;Pa a talo et al.1999;Achim et al.2005).Trees are more likely to be snapped and broken than uprooted because the soil was frozen when the storm occurred.Frozen soil enhances root system resistance to uprooting(Petty and Worrell 1981;Coutts 1983;Valinger and Lundqvist 1992;Nyka nen et al.1997;Peltola et al.1997).On the other hand,the water content of the trees is relatively low in early spring when the damage occurred,which in turn,causes the branches and the crown of the trees to be more frangible and easily snapped(Li et al.2004).Canopy trees are more susceptible to uprooting and snapping damage than subcanopy trees,whereas subcanopy trees are more likely to be bent or remain undamaged.This may be due to greater snow accumulation and wind stress on the crown of canopy trees,while subcanopy trees are sheltered(Veblen et al.2001;Quine and Gardiner 2007).The relatively high percentage of bent subcanopy trees may be due to a domino effect caused by uprooted and snapped canopy trees(Li et al.2004).

When individual canopy species were compared independent of site and stand,B.costataexhibited much more damage than the other species.This is consistent with previous studies(Nyka nen et al.1997;Peltola et al.1999)and may be due to crowns with high density of fi ne branches(Li et al.2004),and thus much more snow is accumulated on them.In addition,the wood ofB.costatais brittle(Li et al.2004).Quercus mongolicahad a relatively high ratio of snapped trees because of its deep root system,but its branches are frangible(Hales et al.2013;Song et al.2012).Therefore,Q.mongolicamay be more susceptible to wind damage compared with other tree species and thus exhibits a high ratio of snapped trees.Among subcanopy trees,A.pseudosieboldianumhas the lowest damage ratio and this may be because it is a small,deciduous species and sheltered by canopy trees(Li et al.2004).In addition,the pliable stem ofA.pseudosieboldianumis easily bent when loaded with snow (Ren 1997).Therefore,A.pseudosieboldianumis not readily susceptible to wind/snow damage compared with other species.

The size(DBH;height)of trees plays an important role in the type of damage induce by snow and wind(Webb 1988;Peterson and Pickett 1991;Peltola et al.1999;Valinger and Fridman 1999;Karlsson and Novell 2005;Zhu et al.2006;Hlásny et al.2011;Teste and Lieffers 2011).In our study,tall,thick trees were more susceptible to wind and snow damage than shorter slender ones.Because larger trees in general have larger crowns,areas that bear snow and wind are larger and therefore these trees are more easily uprooted or broken.However,these results are inconsistent with those of other studies which reported that intermediate-sized trees were most susceptible to snow and wind damage(Everham and Brokaw 1996;Peterson 2004).The inconsistency may be due to the research taking place in a natural secondary forest formed after a disturbance to the original virgin forest,and there were few large-diameter trees(Zhu 2002;Zhang et al.2003).

At the stand level,signi fi cant differences in the degree of damage are observed among the different cover types.Stands dominated byQ.mongolicaandB.costataexhibited higher damage ratios and had more broken trees than otherstands.Stands dominated byA.pseudosieboldianumhad the lowest snapping ratio and were most likely to contain bent trees(Table 2).The reasons are correlated with the differences in tree species characteristics as noted.

Fig.2 Within-species comparison of the DBH of uprooted,snapped,bent and undamaged trees

Multiple regression analyses showed that some tree and stand characteristics,such as importance values of the species,stand density and mean tree height,play an important role in damage severity and type,which is consistent with other studies(Klopcic et al.2009;Zhang et al.2010;Teste and Lieffers 2011).In this study,the percentage of total damage was negatively related to stand density,which is inconsistent with the results of other studies(Cremer et al.1982;Putz and Sharitz 1991;Jalkanen and Mattila 2000;Hlásny et al.2011).This inconsistency may be induced by the differences in forest types,i.e.,the secondary forests in our study rather than plantations or old-growth forests in other studies.These secondary forests,formed by sprout regeneration from oldgrowth forests after heavy disturbances,are distributed along the ridge steep slope with low stem densities(Zhang et al.2003).

v er t yp es c o d am ag ed t re es b y o f e p er ce nt ag e t h s o f c om pa ri so n l ti pl e a nd m u a na ly si s b le 2 K-W v ar ia nc e T a B en t a pp ed S n T ot al s Ulmu)inus ian%rp Ca e d(m D am ag e Acerento sum tegm Acer mono Acer pseudo ecies(IV)Fraxinus s sp glan e of Ju valu s portance Quercu la Im Betu o f o un t A m p at ch es v er t yp e C o.31a 2 31 10 11.19ac.31ac 9.09bc.37 ac 2 1 0.00 a 9.0 9 2 b 5 5.9 6 ab 3 7.3 3 ab 2 9.6 8 b 3 8.7 0.000.85a 9 42 75 53 49 68.02b.58ab.26ac.19bd 0.00 0–13 0–7 0–8 0–24 0–22 49–70 3 0–0–0–0–0–2 5 16 70 6 0–0–0–0–0–0–2 551 72 4–20 0–10 4–6 23 0–29 34 0–0–51 1 2 2 3 4–19 0–3 0–32 0–0 4 0–6 0–4 0–13 10–3 0–13 0 12 0–0 0–14 0–6–12–36 15 10 8 1 0–3 3 5 0–8 0–30 0 0–23 0 4–25 0–14 0–27 0–22 20–63 10–14 941 073 72 do pseu Acer mono s p t ofQuercus Acer Betula Ulmu onen t of t of t of t of mp onen onen onen e co mp mpFraxinus mp mponen L ar g e c o L ar g e c o L ar g Juglanse c o L ar g e c o L ar g I I IIII IVV VI pes(statistical analyses t cover ty II,III,IV and V represent differen I,0.0 5).o th er(P＜e a n o n t f ro m d if fe re n i f i c an tl y a re n ot s ig n V I)t yp e t o lumnnged c o t he s am e o p lo ts b el o t w i n w it h l et te r e s am e V Ibecause only t h b y e d l lo w u ct ed f or type Medians fo n ot c on d w er e

Our fi ndings have important implications for the management of temperate secondary forests.In addition to natural factors,of secondary forest structures(composition,size and stand characteristics)are the main reason for stand damage.Secondary forests are often prone to severe disturbances(human and natural)in mountainous regions.Moreover,therationalmanagementforexistingsecondary forests is lacking,resulting in secondary forests with large areas not timely nursed,and thus their instability to resist disaster.This leads to the existing forest ecosystems that are vulnerable to natural disasters.In addition,according to meteorologists and climate models predictions,the frequency and intensity of various types of wind/snow disasters will increase in the future under global climate change(Li et al.2005).Therefore,measures should be adopted to reduce the effect of wind/snow disasters.For example,harvesting should be strictly forbidden at high altitudes and on steep slopes.In addition,low-growing species with deep root systems,hard,dense wood with good bending and compression resistance should be planted to increase the stand density.Furthermore,larger trees with partial crown ratios and height-diameter ratios should be removed by thinning to reduce the possibility of snow/wind damage.For forests that suffer from heavier damage,such as ones dominated byB.costataandQ.mongolica,compositionshouldbeadjustedbytendingand improvement measures to enhance their ability to resist natural disasters.

In summary,our stand-level analysis of individual tree and stand attributes permits us to draw conclusions about the effects of tree size,species andstem density type on the degree and type of snow/wind damage.Relationships between tree attributes and snow/wind damage indicate thatB.costataandQ.mongolicaexhibited higher damage ratios,whileA.pseudo-sieboldianumshowed the lowest.Shorter trees with smaller DBHs are more likely to be bent or remained undamaged than taller ones larger diameters.Stands dominated byQ.mongolicaandB.costatahave the highest damage ratios,but the stands dominated byA.pseudo-sieboldianumthe lowest snapping or breakage ratio.Stem density plays an important role in affecting the snow/wind damage.Overall,the response patterns of individual tree traits to snow/wind damage are similar to that of stand attributes.These additional insights into the factorspredisposingtheforesttowinddamagedemonstrate the bene fi ts of investigating ecological processes,even large and severe disturbance events,across a range of spatial scales.

AcknowledgementsWe thank Dr.Li-ning Song,Dr.Qiao-ling Yan,Dr.Ming-cai Li and Dr.Tao Yan for their helpful suggestions on the earlier versions of this manuscript.

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