## 3 Results
### Cell Structure of Fruit Stalks on Gridled Bearing Branches at Different LFRs  
The changes in the anatomical structures of the fruit stalk cells were similar for each LFR over time according to the microscopy observations. However, the anatomical structures of the fruit stalks substantially differed among the LFR treatments. The fruit stalk was anatomically more developed at the higher LFRs. The pitch of the fruit stalk gradually degenerates and disappears as walnuts grow and develop; therefore, only a few tissues are shown in Figure 7.  
The length of Xylem (XL), Phloem (FSPL), Cambium (CL), Cortex (FSCL), long with Pith (PL) and the width of Pith (PW) in the cross-section of fruit stalk showed the same trend with the change of LFRs, most reaching a maximum value when the fruit quantity was high: (1-5)L:3F! (1-5)L:2F! (1-5)L:1F (Figure 8). The PL was significantly longer at 3L:3F than at the other LFRs (_p_! 0.05; Figure 8A). The PW was significantly wider at 5L:3F than at the other LFRs (_p_! 0.05, Figure 8B). The XL did not significantly differ between the 5L:3F and 1L:2F treatments but was significantly higher in these two treatments than in the other LFR treatments (_p_! 0.05, Figure 8C). The CL was the significantly longer at 5L:3F compared with that for the other LFRs (_p_! 0.05, Figure 8D). The FSPL was the shortest at 1L:1F, but the difference in the phloem length among the LFRs was small (Figure 8E). The cortex was significantly shorter at 1L:1F than at the other LFRs (_p_! 0.05, Figure 8F).  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Response Variable** & _df_ & _SS_ & _MS_ & _F Value_ & _p Value_ \\ \hline Area of fruit stalk & 14 & 0.382 & 0.027 & 5.799 & 0.000 \\ Phloem (FSPA) & & & & & \\ \hline \end{tabular}
\end{table}
Table 2: ANOVA results of the effect of LFR on fruit stalk trait.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**LFR** & 1L:1F & 2L:1F & 3L:1F & 4L:1F & 5L:1F \\ \hline FSPA & & & & & \\ (10\({}^{5}\)\(\upmu\)m\({}^{2}\)) & 1.05 \(\pm\) 0.04 c & 1.04 \(\pm\) 0.03 c & 1.06 \(\pm\) 0.10 c & 1.08 \(\pm\) 0.07 c & 1.05 \(\pm\) 0.04 c \\
**LFR** & 1L:2F & 2L:2F & 3L:2F & 4L:2F & 5L:2F \\ FSPA & & & & & \\ (10\({}^{5}\)\(\upmu\)m\({}^{2}\)) & 1.15 \(\pm\) 0.04 bc & 1.25 \(\pm\) 0.09 ab & 1.17 \(\pm\) 0.10 bc & 1.26 \(\pm\) 0.10 ab & 1.23 \(\pm\) 0.04 ab \\
**LFR** & 1L:3F & 2L:3F & 3L:3F & 4L:3F & 5L:3F \\ FSPA & & & & & \\ (10\({}^{5}\)\(\upmu\)m\({}^{2}\)) & 1.23 \(\pm\) 0.05 ab & 1.25 \(\pm\) 0.11 ab & 1.26 \(\pm\) 0.01 ab & 1.23 \(\pm\) 0.05 ab & 1.31 \(\pm\) 0.02 a \\ \hline \end{tabular} Note: Different lowercase letters denote significant differences (_p_! 0.05) between treatments for the same index.  
\end{table}
Table 3: Results of multiple comparisons of phloem area of fruit stalk of girdled branches for different leaf-to-fruit ratio (LFR) (mean \(\pm\) SD, \(n\) = 10). FSPA is area of fruit stalk phloem.  
Figure 8: Differences in the anatomical structures of the main leaf vein on the bearing branches among the different LFR treatments: (**A**) pitch length, (**B**) pit width, (**C**) xylem length, (**D**) cambium length, (**E**) fruit stalk phloem length, and (**F**) fruit stalk cortex length. Note: Different lowercase letters denote significant differences (\(p<0.05\)) between treatments for the same index.  
Figure 7: Microstructure of transverse section of fruit stalk at walnut fruit maturity: (**A–F**) 1L:1F, 1L:2F, 1L:3F, 5L:1F, 5L:2F and 5L:3F, respectively. The image was captured with a 5\(\times\) objective lens. FSCL, fruit stalk cortex length; FSPL, fruit stalk phloem length; CL, cambium length; XL, xylem length.