## 4 Materials and Methods  
### Data Description  
In this paper, we consider a dataset collected from the study by [PERSON] et al. (2018) [17]. The dataset targets the growth data of 9600 northern abalone (Haliiotis discus hannai) and disk abalone (H. discus discus) cultured at the Abalone Research Institute (Department of Fisheries Seed) of the Jeonnam Marine and Fisheries Science Institute in Wando, Jeolanam-do. The abalones were spawned through artificial fertilization into four breeds (northern \(\times\) northern cross, northern \(\times\) disk cross, disk \(\times\) disk cross, disk \(\times\) northern cross), and then cultured in land-based tanks for 250 days. From these, individuals with a shell length of over 30 mm were selected, totaling 9600 across the breeds, and transferred to sea cages in Wando County, where their growth was monitored over 967 days. Each cage, measuring 2.4 m in length, 1.2 m in width, and 2 m in height, housed 800 abalones, utilizing a total of 12 cages. The abalones' feed consisted of cultured wakame (Undaria pinnatifida) and kelp (Laminaria japonica), including wakame stems, supplied every two weeks at 40 kg. To evaluate the impact of environmental factors on abalone growth, water temperature (water.temp), salinity (salt), dissolved oxygen (DO), nutrient supply (NS), and pH were measured every two weeks over a 967-day cultivation period, resulting in 61 sets of environmental data. These variables are listed in Table 1. To minimize the impact of rearing management on growth, no other work such as selection or net cleaning was performed, except for one net change on the 600 th day. Summary statistics for these factors are presented in Table 2, and the patterns of water temperature and DO is plotted in Figure 1. In the table, Q2 is the median value, and Q1 and Q3 represent the 25 th percentile and the 75 th percentile, respectively. From the figure, we can see that water temperature showed a clear seasonal pattern, while dissolved oxygen levels generally decreased in summer and increased in winter, without showing a consistent overall pattern. In contrast, salinity and pH did not show significant changes during the same period. Salinity was maintained at 32-34 psu regardless of seasonal or rainy season effects, and pH also maintained a value between 7 and 9. \begin{table}
\begin{tabular}{p{113.8 pt} p{227.6 pt}} \hline \hline
**Variable** & **Description** \\ \hline Water temperature (°C) & Measured at two-week intervals for 950 days using marine environmental survey equipment (YSI 5908, Xylem, Yellow Springs, OH, USA). \\ \hline DO (mg/L) & Dissolved oxygen levels in the water. \\ \hline pH & Acidity or alkalinity of the water. \\ \hline Salinity (psu) & Salinity levels in the water. \\ \hline Nutrient supply (kg) & Supply of 40 kg of seaweed (_Undaria pinnatifida_), kelp (_Laminaria japonica_), and seaweed stems cultivated in nearby areas every two weeks. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of potential variables used in predictions. Figure 1: Temperature and DO values over time. The growth of abalones was assessed every 50 days by randomly sampling 90 individuals per breed and measuring shell length, width, height, and weight. Growth data were collected 16 times over the 967-day period, and we focus specifically on weight, as it is the most important factor for understanding growth based on economic value. The growth and environmental data were integrated by matching measurement dates, with the closest environmental data used when exact matches were unavailable. Prior to conducting the analysis, we performed additional data preprocessing. This involved removing missing values for abalone weight and eliminating outliers from the abalone weight measurements at each time point. Outliers were identified using the criterion of Q1 \(\pm\) 1.5 IQR, where IQR is the interquartile range. This resulted in the removal of 109 data points. Figure 2 shows scatter plots of the dataset before and after outlier removal.