## 2 Results
### Root Length Per Depth Is Influenced over Time by Bacterial Inoculation and High Temperature  
The depth of the agar plate was divided into 20 horizontal layers, which are referred to here as \"depths\" from the top or exposed agar surface (0 cm), which divides the root and shoot. The software allowed us to extract the exact length of the primary and lateral roots in each of these \"depths\" and to evaluate the system distribution across the root types over depth and time (Figure 4). The plants from all of the treatments started growing lateral roots from 5 DAI, but a large difference between the treatments was not found until 9 DAI when the inoculated plants under the ambient condition showed the highest total root length (5.6 cm) which was initially 1 cm below the open-top plate surface (Figure 4a). At 12 DAI, the effect of bacterial inoculation already started manifesting under the high temperature as well at the depths between 1 and 4 cm. Shortly after (from around 14 to 16 DAI), the high temperature started decreasing the root length distribution from 4 to 8 cm. At the same timepoints, the bacterial stimulation effect on the total root lengths from the upper depths (1 to 9 cm) increased under both of the temperature regimes (Figure 4a). This effect was also shown in the 1 st-order lateral root lengths (Figure 4b). For the 2 nd-order laterals, the effect of the inoculation was first observed at 16 DAI under the high temperature between 1 and 3 cm (Figure 4c). At 19 DAI, the stimulation effect of the bacteria on the root lengths (at 1 to 10 cm depth) were more pronounced under the high temperature when they were compared to those under the ambient temperature (Figure 4a). This can be attributed to the positive responses of both 1 st- and 2 nd-order laterals under the high temperature (Figure 4b,c). At the end of the growing period (21 DAI), the effect of the inoculation on the total root lengths under both the ambient and high-temperature condition was prominent from the top of them down to a 15 cm depth (Figure 4a). This effect was mainly due to the differential effects of the two lateral roots (Figure 4b,c). While the effect of the bacteria on the 1 st-order laterals diminished under the ambient condition, its effect on the 2 nd-order laterals increased towards the lower depths (from 5 to 13 cm). On the other hand, under the high temperature, the bacterial inoculation caused the 1 st- and 2 nd-order lateral roots to display greater root length distributions than the control plants did, with an almost bimodal curve (Figure 4b,c).  
Overall, these results show that at all of the stages and root types, the bacterial inoculation increased the root length per depth under both of the temperatures. While the effect of the inoculation for the 1 st-order lateral roots under the ambient condition declined through time, the opposite was found for the late-emerging 2 nd-order laterals. This mainly accounted for the difference between the inoculated and control under the ambient condition. On the other hand, the effect of the bacteria under the high temperature can be summed up from the combined effects of the 1 st- and 2 nd-order laterals.