## 3 Results
### Genetic Network of Significant QTLs
The taproot length genetic effects network (**d**) versus the lateral root length genetic effects network (**f**) in the salt-stress group. (**e**) Bar charts depict activating/inhibitory links and outgoing/incoming nodes for taproot length and lateral root length networks in the salt-stressed group. Each node symbolizes a QTL. The lines between nodes illustrate QTL interactions, with dotted lines indicating inhibition and solid lines denoting facilitation. Red, orange, and blue nodes indicate that this QTL has a stimulatory or inhibitory effect on other QTLs. The red nodes are hub QTLs, the orange nodes are secondary hub QTLs, and the blue nodes are tertiary hub QTLs. cooperative interactions, coordinating and assisting each other to regulate root growth and confer resistance to adverse environmental influences. Additionally, we deconstructed QTL structures in the networks, investigating their direct effects on root growth regulation and their epistatic effects influenced by other QTLs. As shown in Figure 5, although both Q2434 and Q8011 regulate root development under control and salt-stressed conditions, their modes of action differ. With regard to taproot growth, Q2434 exhibits shallow independent effects, and its regulatory impact mainly arises from the facilitating effects of other QTLs. In contrast, for lateral roots, Q2434 itself has a certain level of independent effects and is simultaneously influenced by the activating effects of other QTLs. The regulatory effect of Q8011 on the taproot is also enhanced by itself and other loci. However, regarding lateral root growth, its independent direct effects closely align with the overall effects, especially under saline stress, where the epistatic effects induced by Q4608 are close to zero. The regulatory effects of the two QTLs above on the root system are activated by the epistatic effects of other QTLs. Figure 5: Genetic effect curves for specific QTLs in the genetic network for control taproot length (**a**), control lateral root length (**b**), salt-stressed taproot length (**c**), and salt-stressed lateral root length (**d**). The net genetic effect (red line) is divided into independent effects (blue line) and dependent effects (green line) due to regulation by other QTLs. Moreover, within the network structure, certain QTLs, like Q849, play a significant role in the control group. Q849 exhibits a high independent effect in regulating the taproot but is suppressed by Q8246 during the root-growth process. Furthermore, it can be observed in the network structure that the overall regulatory effects on growth, induced by the activation or inhibition from other QTLs, are not consistent. For example, in regulating lateral roots under control conditions, Q7816 is facilitated by Q7186 and inhibited by Q825, resulting in a mutual counteracting effect. If the adverse inhibitory effects are effectively silenced through genetic breeding, Q7816 could enhance root growth and development in _Populus euphratica_, potentially improving its resilience to adverse conditions. However, it is pertinent to note that genetic improvement may introduce collateral effects on the Gene Regulatory Network (GRN), with many interactions remaining cryptic. Thus, the overall impact on plant physiology remains uncertain, necessitating a careful consideration of genetic modifications within the complex GRN framework.