## 4 Results and Discussion  
The target of this study was to build a prediction model to quantitatively describe the biomass development path along with each phase of the waterowl-like production lifecycle. That is, we attempted to build a prediction function:  
\[\text{Y}=\text{F}(x_{i}),\text{ where }x_{i}\in\text{key characteristics of hatching rate}\]  
where Y is the predicted hatching rate. The duck farmer could use this function to quantitatively describe the biomass development path, i.e., the hatching rate, and provide sufficient customized care along with each phase of the waterowl-like production lifecycle and the corresponding environment settings. Figure 7 is the classification tree of Model 1. We applied 18 features to construct this model, including the egg size, weight, surface temperature at different stages, and weight loss. In the first stage of the incubation, and with the temperature, humidity, and air quality held constant, three conditions were discovered to have key influences on the hatching results: a long diameter less than 6.65 cm, a weight loss less than 1.45 g between days 0 and 7, and an average eggshell temperature higher than 41.36 \({}^{\circ}\)C between days 7 and 14. Figure 5: (**a**) Features based on the Duck Production System Manual; (**b**) Duck farm of the site visits of this study (captured by this study). Figure 6: (**a**) Thermal image of the eggs; (**b**) a chart of temperature change. Figure 8 is the classification tree result of Model 2. We applied 11 features to establish this model, including the egg size, weight, surface temperature at different stages, and weight loss. In the second stage of the incubation, and with the temperature, humidity, and air quality held constant, two conditions were found to influence the hatching result: a shape coefficient greater than 0.6715 and an average eggshell temperature higher than 41.07 \({}^{\circ}\)C between days 14 and 31. In addition to the analysis results of the classification trees, some crucial data were obtained from the final state of the egg tray (Figure 9). Nine of the eighteen eggs stopped developing during the last 3 days of the incubation. Judging from the positional relationship of these eggs, some mutual influences might exist among them. The strikethroughs in Figure 8 indicate abnormal data during the three egg candling examinations, which we regarded as manual marking errors. Hence, the data of B15, B32, B36, B60, and B64 were excluded. Figure 8: Classification tree result of Model 2. Figure 7: Classification tree result of Model 1. Area A, random duck eggs placed to fill the remaining spaces; area B, 66 Muscovy duck fertilized eggs; strikethrough, data error; baseline, unfertilized duck eggs; grayed out boxes, duck eggs that have stopped growing; blacked out boxes, duck eggs that died in the tray. Based on the above results, we explored four characteristics out of 25 characteristics and built a model to quantitatively predict the survivability of black Muscovy duck egg. The key characteristics include the weight loss percent of an egg, the average eggshell temperature in different phases of the product lifecycle, and the shape coefficient of an egg. Therefore, the prediction function based on the XGBoost algorithm is:  
\[\mathrm{Y}=\mathrm{F}(x_{1},x_{2},x_{3},x_{4})\]  
where Y is the predicted hatching rate, \(x_{1}\) is the weight loss percent of an egg, \(x_{2}\) is the average eggshell temperature in different phases of the product lifecycle, \(x_{3}\) is the shape coefficient of an egg, \(x_{4}\) is the long diameter of an egg. The duck farmer can use the thermal camera to automatically measure the four characteristics to quantitatively describe the biomass development path, i.e., the hatching rate, and provide sufficient customized care along with each phase of the waterowl-like production lifecycle and the corresponding environment settings.