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Abstract [Objectives] This study was conducted to explore the relationship between morphological traits and body mass trait of Lutraria sieboldii.
[Methods]110 were randomly selected from 120 2nd-instar L. sieboldii collected from the Tieshangang area of Beihai， Guangxi， and 132 were randomly selected from 150 shellfish at the instar of 0.6. Their morphological traits were measured： shell length （SL）， shell height （SH）， shell width （SW）， anterior length （AL）， posterior length （PL）， nose length （NL） in closed shell state， and maximum open shell width （OS） between two shells in closed shell state， and the body mass trait BM was also measured. Statistical methods such as path analysis and multiple regression were used for data analysis， and the effects of these seven morphological traits on the body mass trait were studied， respectively. The correlation between the tested seven quantitative traits and one body mass trait was all positive， all reaching an extremely significant level （P<0.01）.
[Results] The body mass trait of the shellfish at the instar of 2 had the highest correlation coefficient with shell length （0.922）， that is， shell length had the greatest direct impact on the body mass trait; the path coefficient was 0.700; and the final multiple regression equation established was BM=-124.882+1.189SL+1.551 SH+1.035SW+0.119NL， and the total determination coefficient （R2） on body mass was 0.849. The body mass trait of the shellfish at the instar of 0.6 had the highest correlation coefficient with shell length （0.859）， that is， shell length had the greatest direct impact on the body mass trait; the path coefficient was 0.494; and the final multiple regression equation established was BM=-1.917+0.111SL +0.021NL+0.078SW+0.032OS， and the total determination coefficient （R2） on body mass was 0.828. The multivariate regression variance analysis showed that the regression between the morphological traits and body mass trait of the L. sieboldii at the instars of 2 and 0.6 reached an extremely significant level （P<0.01）.
[Conclusions]This study provides a scientific basis for the selection of broodstock in the selection and breeding of L. sieboldii.
Key words Lutraria sieboldi; Morphological traits; Correlation analysis; Multiple regression; Path analysis
Received： March 7， 2021 Accepted： May 1 2021
Supported by Guangxi Key R&D Program （2018AB52002）; National Key R&D Program of China （2018YFD0901406）; Natural Science Foundation of Guangxi （2018GXNSFAA138197， 2021GXNSFAA075008）; General Project of National Natural Science Foundation of China （31873042）; 2021 Key Cultivation Project of Guangxi Key Laboratory of Beibu Gulf Marine Biodiversity Conservation （2021ZB02）; The Basic Ability Improvement Project for Young and Middle-aged Teachers in Guangxi Universities （2018KY0612）. Multiple regression analysis of morphological traits on the body mass trait
According to the analysis results of partial regression coefficients and T test in Table 3， shell length， shell width， shell height， anterior length， posterior length， nose length and open shell width had extremely significant effects on the body mass trait （P<0.01）， indicating that there was an extremely significant linear relationship between the independent variables and the dependent variable. Taking shell morphology as the independent variables and body weight as the dependent variable， the stepwise regression analysis method was used to obtain the multiple regression equations of the morphology and body weight of L. sieboldii： instar of 0.6： BM=-1.917+0.111SL+0.021 NL+0.078SW+0.032OS， R2=0.828; instar of 2： BM=-124.882+1.189SL+1.551SH+1.035SW+0.119NL， R2=0.849. From the results of the analysis of variance of the multiple regression in Table 4， it can be seen that for the instar of 0.6， F=152.435， P=0.000， and for the instar of F=132.343， P=0.000， that is， the regression between various morphological traits and body mass trait reached an extremely significant level （P< 0.01）. According to the prediction by the above equations， the differences between the estimated values and the actual observation values were not significant， indicating that the above equation can be applied to actual production[13]. In this study， the correlation index R2 of the morphological traits and the body mass trait of L. sieboldii was 0.828 and 0.849， respectively， less than 0.850， indicating that the main variables that affect the body mass trait of L. sieboldii include other factors besides the morphological traits， and it may also be related to soft body mass， adductor muscle mass and other factors[19-21].
Path analysis of morphological traits to the body mass trait
According to the correlation coefficients between morphological traits and the body mass trait of L. sieboldii， the path coefficients of L. sieboldii morphology and body mass were obtained by the linear stepwise regression method， as shown in Table 5 and Table 6. It can be seen from the data in Table 5 that the morphological trait that had the greatest direct effect on BM of the shellfish at the instar of 0.6 was SL （0.700）， and that with the smallest effect was OS （0.102）; and SH had the largest indirect effect on BM through SL （0.520）， while NL had the smallest indirect effect on BM through OS （0.005）. And the indirect effect of SH on BM was the largest （0.586）. From the data in Table 6， it can be seen that the morphological trait that had the greatest direct effect on the BM of the 2nd-instar shellfish was SL （0.494）， and that with the smallest effect was NL （0.089）; and SW had the greatest indirect effect on BM through SL （0.437）， while NL had the smallest indirect effect on BM through OS （-0.006）. And the indirect effect of SH on BM was the largest （0.599）. The results are similar to the results of other economic shellfish research. Zhang et al.[22] studied Patinopecten yessoensis and found that shell length had the greatest direct impact on the body mass trait. Yang et al.[23] studied Cyclina sinensis and found that the most important factor affecting body mass traits was shell length. Xue et al.[24] studied different-month-old Sinonovacula constricta new variety "Shenzhe 1" and found that the traits had the largest direct impacts on body weight traits were shell length， shell width and shell height. Du et al.[25] found that shell length had the greatest direct effect on the wet mass of the 1st-instar Chlamys farreri， and shell height had the greatest direct effect on the wet mass of the 2nd-instar C. farreri. However， some research results are different. For example， Wei et al.[8] studied C. erycina and found that shell width had the greatest direct effects on body mass traits， and Wu et al.[18] studied Tapes dorsatus and found that shell width had the greatest direct effects on its body mass traits.
Analysis of the degree of determination of morphological traits on body mass trait
Table 7 and Table 8 show the determination coefficients of various morphological traits of L. sieboldii on the body weight trait. In the tables， the diagonal line lists the determination coefficient of each trait on the body mass trait， and the part above the diagonal line lists the indirect determination coefficients of two traits in pairs on the body mass trait. It can be seen from Table 7 that for the 2nd-instar shellfish， SL alone had the largest coefficient of determination on BM （0.490）， followed by SH （0.202）， while OS alone had the smallest coefficient of determination on BM （0.002）; and paired SL and SH showed the largest codetermination coefficient on BM （0.038）， while NL and OS showed the smallest value （0.002）. It can be seen from Table 8 that for the shellfish at the instar of 0.6， SL alone had the largest coefficient of determination on BM （0.248）， and NL alone had the smallest coefficient of determination on BM （-0.001）; and the two traits showing the largest codetermination coefficient on BM were SL and SH （0.244）， while SH and NL exhibited the smallest value （-0.001）. The results were basically consistent with the results of path analysis， and both results indicated that shell length was the main morphological trait that affected the body mass trait of L. sieboldii.
Fig. 2 shows the determination coefficients of the morphological traits of L. sieboldii on its yield trait. NL-NL， OS-OS， SH-SH， SL-SL and SW-SW represented the coefficients of determination of single independent variables on yield trait， and SL-SH， NL-OS， NL-SW， SH-NL， SH-SW， SL-NL， SL-OS， SL-SW， SW-NL and SW-OS represented the determination coefficients of two independent variables on yield trait. Among the determining effects of individual morphological traits on the BM of L. sieboldii， SL had the largest independent determining effects on the shellfish the instars of 0.6 and and the corresponding coefficients of determination were 0.828 and 0.849， respectively. Discussion and Conclusions
Shellfish have different morphologies， but there is a certain correlation between shellfish morphological traits and body mass traits. The yield of shellfish is controlled by multiple genes， and has close genetic links with other traits， and they influence each other[29]. Phenotypic traits as quantitative traits are the main content of shellfish genetic breeding research. A certain morphological trait may have a major impact on body mass traits. Therefore， to carry out the selection and breeding of L. sieboldii， starting with the determining effect of each morphological trait on the target trait can realize the screening of the best mass trait. Through the correlation analysis of shell type and growth index， the shell type closely related to economic traits can be screened out， which is of great significance in the genetic improvement， artificial breeding and breeding of shellfish[15]. In the process of selection and breeding， if body mass traits are used as the indexes of direct selection， large systematic errors may occur due to the interference of environmental factors， while identifying the main traits that affect body mass traits by the path analysis method and performing indirect selection can minimize the errors[27]. Therefore， correlation and path analysis are used to find out the relationship between shellfish morphological traits and yield traits， as well as the effects of morphological traits on yield traits， so as to find out the main morphological traits that affect body mass traits. Furthermore， the purpose of obtaining high-yield shellfish can be achieved through direct selection of morphological traits[3，13，25].
In shellfish breeding， shell morphology （shell length， shell height， shell width） and body mass （living body mass， soft body mass） are important measurement indicators for shellfish[23]. Therefore， clarify the relationship between morphological traits and body weight traits by path analysis and multiple regression analysis had very important practical significance for selective breeding. Path analysis can determine the correlation between traits， and split the correlation coefficient between traits into direct effects and indirect effects produced through other traits[30]. The main factor affecting the body mass trait of L. sieboldii at the instar of 0.6 was shell length， followed by shell width， while the main factor affecting the body mass trait of L. sieboldii at the instar of 2 was the shell length， followed by shell height. The coefficients of variation of shell morphology traits （shell height， shell length and shell width） were larger， and the coefficient of variation of the body weight trait was smaller. And the values of L. sieboldii at the instar of 0.6 were greater than those of the shellfish at the instar of 2. The coefficient of variation is the key reference basis for selection and breeding， and when the variation is large， the potential of selection is also greater， and the value of carrying out selective breeding is also higher. The reason for the above results might be that there was a transitional period from the growth of juvenile L. sieboldii to adult growth， or L. sieboldii grew faster in the early stage and slower in the later period， leading to large morphological variation[25-26]. The shell length and shell width increased the fastest in the early growth stage， and the shell length and shell height mainly increased in the later period. It is consistent with the result obtained by Lin et al.[12] that the maximum growth line of Pteria penguin before the 6-month age was mainly along the width of the shell， and when it developed to the age of 8 months， it gradually began to grow in the direction of shell height， that is， the growth rate in the direction of shell height was greater than the growth rate in the direction of shell width， and the maximum growth line started to change from the shell width direction to the shell height direction. It is also consistent with the result obtained by Zou et al.[10] that both shell mass and shell length traits could have a significant impact on the body mass traits of the selected population of L. sieboldii. The difference is that they chose shell length that is easy to measure as the preferred selection trait， and then strengthened the collaborative selection of shell mass. The biological characteristics of different shellfish are different， they all have their specific genetic genes， morphological characteristics， and the living habits， living environment， and growth stages of each species of shellfish can affect the differences of their morphological traits on body mass traits[8，11，18]. We compared the orders of the growth traits of L. sieboldii at different stages， and the families with fast growth in the early stage also had certain growth advantages in the middle and late stages. Therefore， it is possible to combine the characteristics of the stages during the growth of L. sieboldii to screen the traits in the juvenile stage and the adult stage， so as to screen out excellent individuals that can be used for genetic selection. During artificial selection of L. sieboldii and its reservation for breeding， the selection of corresponding traits should be combined with different shell ages. When taking body mass traits as high-yield breeding targets， the shell length and shell width traits should be considered first in individuals at the instar of 0.6， and shell length and shell height traits should be considered first in individuals at the instar of 2.
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[Methods]110 were randomly selected from 120 2nd-instar L. sieboldii collected from the Tieshangang area of Beihai， Guangxi， and 132 were randomly selected from 150 shellfish at the instar of 0.6. Their morphological traits were measured： shell length （SL）， shell height （SH）， shell width （SW）， anterior length （AL）， posterior length （PL）， nose length （NL） in closed shell state， and maximum open shell width （OS） between two shells in closed shell state， and the body mass trait BM was also measured. Statistical methods such as path analysis and multiple regression were used for data analysis， and the effects of these seven morphological traits on the body mass trait were studied， respectively. The correlation between the tested seven quantitative traits and one body mass trait was all positive， all reaching an extremely significant level （P<0.01）.
[Results] The body mass trait of the shellfish at the instar of 2 had the highest correlation coefficient with shell length （0.922）， that is， shell length had the greatest direct impact on the body mass trait; the path coefficient was 0.700; and the final multiple regression equation established was BM=-124.882+1.189SL+1.551 SH+1.035SW+0.119NL， and the total determination coefficient （R2） on body mass was 0.849. The body mass trait of the shellfish at the instar of 0.6 had the highest correlation coefficient with shell length （0.859）， that is， shell length had the greatest direct impact on the body mass trait; the path coefficient was 0.494; and the final multiple regression equation established was BM=-1.917+0.111SL +0.021NL+0.078SW+0.032OS， and the total determination coefficient （R2） on body mass was 0.828. The multivariate regression variance analysis showed that the regression between the morphological traits and body mass trait of the L. sieboldii at the instars of 2 and 0.6 reached an extremely significant level （P<0.01）.
[Conclusions]This study provides a scientific basis for the selection of broodstock in the selection and breeding of L. sieboldii.
Key words Lutraria sieboldi; Morphological traits; Correlation analysis; Multiple regression; Path analysis
Received： March 7， 2021 Accepted： May 1 2021
Supported by Guangxi Key R&D Program （2018AB52002）; National Key R&D Program of China （2018YFD0901406）; Natural Science Foundation of Guangxi （2018GXNSFAA138197， 2021GXNSFAA075008）; General Project of National Natural Science Foundation of China （31873042）; 2021 Key Cultivation Project of Guangxi Key Laboratory of Beibu Gulf Marine Biodiversity Conservation （2021ZB02）; The Basic Ability Improvement Project for Young and Middle-aged Teachers in Guangxi Universities （2018KY0612）. Multiple regression analysis of morphological traits on the body mass trait
According to the analysis results of partial regression coefficients and T test in Table 3， shell length， shell width， shell height， anterior length， posterior length， nose length and open shell width had extremely significant effects on the body mass trait （P<0.01）， indicating that there was an extremely significant linear relationship between the independent variables and the dependent variable. Taking shell morphology as the independent variables and body weight as the dependent variable， the stepwise regression analysis method was used to obtain the multiple regression equations of the morphology and body weight of L. sieboldii： instar of 0.6： BM=-1.917+0.111SL+0.021 NL+0.078SW+0.032OS， R2=0.828; instar of 2： BM=-124.882+1.189SL+1.551SH+1.035SW+0.119NL， R2=0.849. From the results of the analysis of variance of the multiple regression in Table 4， it can be seen that for the instar of 0.6， F=152.435， P=0.000， and for the instar of F=132.343， P=0.000， that is， the regression between various morphological traits and body mass trait reached an extremely significant level （P< 0.01）. According to the prediction by the above equations， the differences between the estimated values and the actual observation values were not significant， indicating that the above equation can be applied to actual production[13]. In this study， the correlation index R2 of the morphological traits and the body mass trait of L. sieboldii was 0.828 and 0.849， respectively， less than 0.850， indicating that the main variables that affect the body mass trait of L. sieboldii include other factors besides the morphological traits， and it may also be related to soft body mass， adductor muscle mass and other factors[19-21].
Path analysis of morphological traits to the body mass trait
According to the correlation coefficients between morphological traits and the body mass trait of L. sieboldii， the path coefficients of L. sieboldii morphology and body mass were obtained by the linear stepwise regression method， as shown in Table 5 and Table 6. It can be seen from the data in Table 5 that the morphological trait that had the greatest direct effect on BM of the shellfish at the instar of 0.6 was SL （0.700）， and that with the smallest effect was OS （0.102）; and SH had the largest indirect effect on BM through SL （0.520）， while NL had the smallest indirect effect on BM through OS （0.005）. And the indirect effect of SH on BM was the largest （0.586）. From the data in Table 6， it can be seen that the morphological trait that had the greatest direct effect on the BM of the 2nd-instar shellfish was SL （0.494）， and that with the smallest effect was NL （0.089）; and SW had the greatest indirect effect on BM through SL （0.437）， while NL had the smallest indirect effect on BM through OS （-0.006）. And the indirect effect of SH on BM was the largest （0.599）. The results are similar to the results of other economic shellfish research. Zhang et al.[22] studied Patinopecten yessoensis and found that shell length had the greatest direct impact on the body mass trait. Yang et al.[23] studied Cyclina sinensis and found that the most important factor affecting body mass traits was shell length. Xue et al.[24] studied different-month-old Sinonovacula constricta new variety "Shenzhe 1" and found that the traits had the largest direct impacts on body weight traits were shell length， shell width and shell height. Du et al.[25] found that shell length had the greatest direct effect on the wet mass of the 1st-instar Chlamys farreri， and shell height had the greatest direct effect on the wet mass of the 2nd-instar C. farreri. However， some research results are different. For example， Wei et al.[8] studied C. erycina and found that shell width had the greatest direct effects on body mass traits， and Wu et al.[18] studied Tapes dorsatus and found that shell width had the greatest direct effects on its body mass traits.
Analysis of the degree of determination of morphological traits on body mass trait
Table 7 and Table 8 show the determination coefficients of various morphological traits of L. sieboldii on the body weight trait. In the tables， the diagonal line lists the determination coefficient of each trait on the body mass trait， and the part above the diagonal line lists the indirect determination coefficients of two traits in pairs on the body mass trait. It can be seen from Table 7 that for the 2nd-instar shellfish， SL alone had the largest coefficient of determination on BM （0.490）， followed by SH （0.202）， while OS alone had the smallest coefficient of determination on BM （0.002）; and paired SL and SH showed the largest codetermination coefficient on BM （0.038）， while NL and OS showed the smallest value （0.002）. It can be seen from Table 8 that for the shellfish at the instar of 0.6， SL alone had the largest coefficient of determination on BM （0.248）， and NL alone had the smallest coefficient of determination on BM （-0.001）; and the two traits showing the largest codetermination coefficient on BM were SL and SH （0.244）， while SH and NL exhibited the smallest value （-0.001）. The results were basically consistent with the results of path analysis， and both results indicated that shell length was the main morphological trait that affected the body mass trait of L. sieboldii.
Fig. 2 shows the determination coefficients of the morphological traits of L. sieboldii on its yield trait. NL-NL， OS-OS， SH-SH， SL-SL and SW-SW represented the coefficients of determination of single independent variables on yield trait， and SL-SH， NL-OS， NL-SW， SH-NL， SH-SW， SL-NL， SL-OS， SL-SW， SW-NL and SW-OS represented the determination coefficients of two independent variables on yield trait. Among the determining effects of individual morphological traits on the BM of L. sieboldii， SL had the largest independent determining effects on the shellfish the instars of 0.6 and and the corresponding coefficients of determination were 0.828 and 0.849， respectively. Discussion and Conclusions
Shellfish have different morphologies， but there is a certain correlation between shellfish morphological traits and body mass traits. The yield of shellfish is controlled by multiple genes， and has close genetic links with other traits， and they influence each other[29]. Phenotypic traits as quantitative traits are the main content of shellfish genetic breeding research. A certain morphological trait may have a major impact on body mass traits. Therefore， to carry out the selection and breeding of L. sieboldii， starting with the determining effect of each morphological trait on the target trait can realize the screening of the best mass trait. Through the correlation analysis of shell type and growth index， the shell type closely related to economic traits can be screened out， which is of great significance in the genetic improvement， artificial breeding and breeding of shellfish[15]. In the process of selection and breeding， if body mass traits are used as the indexes of direct selection， large systematic errors may occur due to the interference of environmental factors， while identifying the main traits that affect body mass traits by the path analysis method and performing indirect selection can minimize the errors[27]. Therefore， correlation and path analysis are used to find out the relationship between shellfish morphological traits and yield traits， as well as the effects of morphological traits on yield traits， so as to find out the main morphological traits that affect body mass traits. Furthermore， the purpose of obtaining high-yield shellfish can be achieved through direct selection of morphological traits[3，13，25].
In shellfish breeding， shell morphology （shell length， shell height， shell width） and body mass （living body mass， soft body mass） are important measurement indicators for shellfish[23]. Therefore， clarify the relationship between morphological traits and body weight traits by path analysis and multiple regression analysis had very important practical significance for selective breeding. Path analysis can determine the correlation between traits， and split the correlation coefficient between traits into direct effects and indirect effects produced through other traits[30]. The main factor affecting the body mass trait of L. sieboldii at the instar of 0.6 was shell length， followed by shell width， while the main factor affecting the body mass trait of L. sieboldii at the instar of 2 was the shell length， followed by shell height. The coefficients of variation of shell morphology traits （shell height， shell length and shell width） were larger， and the coefficient of variation of the body weight trait was smaller. And the values of L. sieboldii at the instar of 0.6 were greater than those of the shellfish at the instar of 2. The coefficient of variation is the key reference basis for selection and breeding， and when the variation is large， the potential of selection is also greater， and the value of carrying out selective breeding is also higher. The reason for the above results might be that there was a transitional period from the growth of juvenile L. sieboldii to adult growth， or L. sieboldii grew faster in the early stage and slower in the later period， leading to large morphological variation[25-26]. The shell length and shell width increased the fastest in the early growth stage， and the shell length and shell height mainly increased in the later period. It is consistent with the result obtained by Lin et al.[12] that the maximum growth line of Pteria penguin before the 6-month age was mainly along the width of the shell， and when it developed to the age of 8 months， it gradually began to grow in the direction of shell height， that is， the growth rate in the direction of shell height was greater than the growth rate in the direction of shell width， and the maximum growth line started to change from the shell width direction to the shell height direction. It is also consistent with the result obtained by Zou et al.[10] that both shell mass and shell length traits could have a significant impact on the body mass traits of the selected population of L. sieboldii. The difference is that they chose shell length that is easy to measure as the preferred selection trait， and then strengthened the collaborative selection of shell mass. The biological characteristics of different shellfish are different， they all have their specific genetic genes， morphological characteristics， and the living habits， living environment， and growth stages of each species of shellfish can affect the differences of their morphological traits on body mass traits[8，11，18]. We compared the orders of the growth traits of L. sieboldii at different stages， and the families with fast growth in the early stage also had certain growth advantages in the middle and late stages. Therefore， it is possible to combine the characteristics of the stages during the growth of L. sieboldii to screen the traits in the juvenile stage and the adult stage， so as to screen out excellent individuals that can be used for genetic selection. During artificial selection of L. sieboldii and its reservation for breeding， the selection of corresponding traits should be combined with different shell ages. When taking body mass traits as high-yield breeding targets， the shell length and shell width traits should be considered first in individuals at the instar of 0.6， and shell length and shell height traits should be considered first in individuals at the instar of 2.
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