The study included pigs from four genetic lines: Commercial, F1, ML1, and ML2. Both sexes were evaluated, with animals raised under standard commercial housing, management, and feeding conditions on the commercial farm “Los Micos” located in Antioquia, Colombia, between July 2024 and January 2025. Animals were selected through a completely randomized sampling procedure based on optimal health status, age, and body conformation appropriate for their production stage, and ensuring representativeness of the farm population. All animals included in the study were monitored from birth until their transfer to the slaughter plant at 22 to 24 weeks of age. They were clinically evaluated by a veterinarian, who ruled out signs of respiratory, digestive, or locomotor diseases. Field measurements were performed twice a month starting from the ninth week of age and through slaughter. Live weight was recorded using an electronic crate-type livestock scale integrated into the weighing pen for individual animal measurements, equipped with a low-profile galvanized steel platform and a digital indicator with weight-hold stabilization. The nominal capacity of the system was approximately 300–500 kg, with an operating accuracy of about 0.5 kg (≈0.1% of full load). Fat thickness was recorded in millimeters at both the 10th rib (GDD, dorsal backfat thickness at the 10th rib) and the last rib (GDU, dorsal backfat thickness at the last rib), following the longitudinal method described by Cisneros et al. (1996). In vivo ultrasound measurements were performed using a Honda Electronics Co., Ltd. HS–1600 device (Honda Electronics Co., Ltd.) equipped with an HLV-7212M linear probe, following established scanning protocols. The transducer and piezoelectric component were positioned 5 to 7 cm from the midline of the pig’s back, at the level of the 10th and last ribs.

The commercial farm “Los Micos” operates under high biosecurity standards, with high health status, and applies comprehensive management practices. It is free of mandatory notifiable diseases in Colombia, such as rabies, foot-and-mouth disease, classical swine fever, aujeszky and brucellosis, as well as of the porcine reproductive and respiratory syndrome virus (PRRSV). All vaccination and deworming schedules were up to date, and the body development of all individuals was consistent with their growth. An even sex distribution was maintained within each genetic group. Male pigs underwent standardized immunocastration procedures on the farm, following the manufacturer’s protocol. Animals were fed a uniform diet and managed according to the health and biosecurity program of the farm, which included routine vaccination protocols and periodic veterinary monitoring. Two trained technicians performed real-time ultrasound assessments following a standardized protocol to minimize measurement bias. Inter-operator variability was evaluated prior to data collection to ensure consistency and reproducibility of the measurements.

A total of 412 pigs from four genetic lines were included in this study (commercial = 109, F1 = 94, ML1 = 111, and ML2 = 98). Sex distribution within each genetic line was well balanced: Commercial (54 males, 55 females), F1 (47 males, 47 females), ML1 (52 males, 59 females), and ML2 (46 males, 52 females) to support the inclusion of sex as a fixed effect in the statistical models. Each animal was individually identified with a unique consecutive number assigned within its group placed using a visible ear tag. This identification system ensured accurate and consistent tracking of individual animals throughout the experimental period. Two variables were registered twice a month: individual body weight (kg) from birth to slaughter age, and backfat thickness (mm) measured at the tenth and last ribs of the live animal from week 9 of age until slaughter. Backfat measurements began at week 9 because, at earlier ages, the subcutaneous fat layer is still very thin, which may reduce ultrasonographic resolution and increase measurement variability under commercial conditions. At the end of the study period, a total of 4,944 records were collected and summarized, available by line and across four genetic lines (commercial = 1308, F1 = 1128, ML1 = 1332, and ML2 = 1176). Feed consumption was recorded at the pen level under commercial production conditions. Animals had ad libitum access to feed and water throughout the study. Feed intake per pen was calculated daily as the difference between the amount of feed offered and the residual feed weighed the following morning. Average individual feed intake was estimated by dividing pen-level consumption by the number of animals housed in each pen. Feeding phases and supply schedules followed standardized commercial practices typical of Colombian pig production systems; specific diet formulations are proprietary and therefore not disclosed. Details of the commercial diets are provided in Supplementary Table S1.

Two modeling approaches were applied: 1) Generalized Additive Models (GAMs), employed to capture nonlinear relationships between the predictor and the response variable, as proposed by Hastie and Tibshirani (1990), fitted with penalized splines using the mgcv package in R version 4.3.3 (R Core Team, 2024). Analyses were performed separately for each genetic line, sex, and trait; and 2) optimization functions, the optimal slaughter point was defined as the week and weight corresponding to the commercial peak backfat thickness, before a consistent decline in performance (Derringer and Suich, 1980). The multi-objective optimization using the desirability function was implemented in Python employing the pandas library to process and analyze the productive data for each animal.

The analysis using GAMs provided a precise and flexible description of growth trajectories and backfat deposition throughout the production cycle across the four evaluated genetic lines. The fitted curves demonstrated a remarkable ability to capture nonlinear variations, revealing phases of acceleration and deceleration that were not always evident in linear or segmented models. Overall, Commercial and F1 lines reached their peaks in daily weight gain and backfat deposition at earlier ages, followed by a plateau and gradual decline, suggesting a relatively narrow optimal slaughter window. In contrast, ML1 and ML2 lines exhibited more prolonged curves with performance peaks shifted to older ages, particularly in males, indicating an extended growth potential before efficiency losses occur. This differential behavior across lines and sexes highlights the usefulness of GAMs for optimizing slaughter scheduling in a line- and sex-specific manner, considering not only final weight but also the joint dynamics of weight gain and fat deposition.

Figure 2 presents the smoothed trajectories of backfat thickness (BDD) as a function of age (days) for each line (rows) × sex (columns) combination (GAM with k=3; REML). The Blue line is the smoothed prediction; the shaded area is the 95% CI of the prediction. A nonlinear increase with progressive deceleration was observed in all groups, consistent with an initial phase of more rapid lipid deposition followed by a plateau as slaughter age approaches. The basis dimension (k = 3) was selected to favor smooth, biologically plausible trajectories and to reduce the risk of overfitting, given the temporal resolution of the data. This choice is consistent with previous applications of GAMs in similar pig production systems, where dominant nonlinear biological patterns occur at low frequencies and do not require highly flexible smoothers (Herrera et al., 2026). Smoothness selection was controlled via REML penalization.

Among lines, Commercial and F1 show earlier increases and an earlier stabilization (≈110–140 days), whereas ML1 and ML2 show a more prolonged increase and shifted plateaus to older ages (≈135–160 days), suggesting later maturation profiles. The differences by sex are consistent; females tend to flatten the curve earlier and have slightly lower terminal values compared to males of the same line, consistent with the growth peaks observed in the weight curves. The uncertainty bands (95% CI of the prediction) are narrow in the central age range, where there are more observations, and widen at the extremes, reflecting lower data density.

Figure 2 focuses on the purebred maternal lines (ML1 and ML2). The GAM weight curves (k = 3) show sigmoid trajectories with the later peak daily gain (ADG) than those observed in the terminal/commercial lines; in ML2, the peak is located practically at the same point for both sexes (~165 days, ≈23.5 weeks), while in ML1 it occurs later (males ~177 days and females ~176 days, ≈25 weeks). This chronology suggests a later productive maturity and a more extended finishing phase, especially in ML1. At the top of the curve, males tend to project somewhat higher terminal weights than females, although the difference in peak age is small (≈1 day in ML1 and zero in ML2). Operationally, these profiles support later exit-scheduling windows than in Commercial/F1. For ML2, the target window is around 22–24 weeks (just after peak ADG) and, for ML1, around 24–26 weeks, prioritizing dispatch when the curve slope begins to flatten.

In commercial lines (Commercial and F1), the GAM weight curves (k = 3; REML) show a clear sigmoid pattern with maximum daily gain concentrated around 164–165 days in both sexes (dotted vertical lines in the figures). Between ~90 and 140 days, the slope is steepest, reflecting the phase of greatest growth efficiency; from ~160 days onwards, the curvature softens and marginal gain decreases, anticipating the onset of the plateau. Although the timing of the peak is very similar between sexes, females tend to flatten the curve slightly earlier, while males reach slightly higher terminal weights towards the right end. Compared with maternal lines (ML1/ML2), whose peaks occur later (~176–177 days), Commercial and F1 mature earlier and present an earlier and relatively narrow profit window.

Operationally, these patterns, along with the average weight and consumption curves, are combined to propose the optimal schedule for slaughter plant release by line and sex, i.e., allow for defining benefit windows when the slope (dGDD/age) begins to decline steadily, when the GDD reaches the flock reference threshold, or both. In the current study, this occurs earlier in commercial/F1 and later in ML1/ML2, consistent with the differences in biological maturity described in relation to live weight. Because weight flattening typically coincides with a relative acceleration in fat deposition, it is appropriate to accompany these windows with close monitoring of GDD/GDU and, if necessary, dietary energy density adjustments as the upper limit is approached, to capture the target weight without penalties for excess fat. Operationally, the results support scheduling release between 22 and 24 weeks (≈154–168 days), fine-tuning by sex: females closer to 22–23 weeks and males closer to 23–24 weeks, and synchronizing with backfat thresholds (GDD/GDU) and the average intake trajectory to avoid overshooting the fattening target once the ADG peak is passed.

The GAM curves for average feed intake showed a clear nonlinear (saturating) pattern in all genetic lines and both sexes. Intake increased rapidly from the start of the growing–finishing period and then tended to level off, with the 95% prediction bands becoming narrower in the age range with the highest data density (≈70–140 d). Commercial lines (commercial and F1) reached the plateau earlier, around 120–130 days, with mean intakes close to 2.8–3.0 kg/d, whereas the maternal lines (ML1 and ML2) maintained a rising trajectory for longer and stabilized later (≈140–160 d), indicating a more prolonged intake capacity. Within each line, females tended to plateau slightly earlier and at a marginally lower intake than males, consistent with their earlier growth peaks described for body weight and backfat. These trajectories support the intake ranges used in the desirability optimization (≈2.7–3.2 kg/d) and confirm that, by the time the slaughter windows predicted by the GAMs (22–23 weeks) are reached, most line and sex groups are already in the flat part of the intake curve, so additional days on feed contribute more to cost than to biological gain. (Figure 3).

Figure 4 shows the weekly evolution of the mean global desirability value T(d) for each genetic line (F1, ML1, ML2, and commercial), separating trajectories for males (M) and females (F). In all lines, D(t) remained close to zero (0) up to approximately week 18 and then increased sharply from week 19 onwards, indicating that the most favorable combinations of live weight, backfat thickness, and feed intake are only reached during the last weeks of the growing–finishing cycle. A noticeable sex effect was observed in the F1 line, where the biological optima differed between males and females, with females reaching high t(d) values slightly earlier than males. In contrast, the trajectories of ML1, ML2, and commercial pigs showed almost overlapping curves for both sexes, with the highest desirability peaks concentrated around week 23, where the biological optimal week (t*D) was located for most groups.

Table 2 summarizes the biological optimal slaughter week (t*D) estimated for each genetic line and sex combination, along with the mean live weight, backfat thickness, and desirability values reached at that week. The results indicate that the biologically optimal slaughter window is, on average, located between weeks 20 and 22, with modest shifts depending on genetic background and sex. However, the live weight values registered at t*D remain below current market specifications for slaughter pigs, indicating that this biologically optimal point does not necessarily coincide with market-driven targets. This confirms that most groups achieve the best technical balance, i.e., adequate weight, backfat within the target range, and acceptable intake, before the economic optimum, and that the model can differentiate slightly earlier optimal in the more precocious commercial and crossbred lines and in females.

Figure 5 shows the weekly evolution of mean accumulated profit Π(t) by genetic line and sex. In all groups, Π(t) increases steadily across the finishing period, indicating that the economic value of the pigs grows with age as live weight and projected carcass yield improve. Profit trajectories display very similar slopes between males (M) and females (F) within each line, although males tend to reach slightly higher values in most cases, particularly in the ML1 and ML2 lines, likely due to their higher final weights. The F1 and Commercial lines exhibit the highest profit levels around week 23, whereas ML1 and ML2 show comparatively lower values. Across all genetic lines, the economic optimal slaughter weeks (t*P) fall within a narrow 21–23-week window, indicating that this interval represents the point at which the economic return is maximized.

Table 3 reports the optimal economic slaughter week (t*P) for each genetic line and sex combination, along with the mean profit, live weight, and backfat thickness reached that week. Across all groups, the economic optimum was located between 22 and 23 weeks, with low dispersion (SD ≈ 0.5–1.2 weeks), indicating a very consistent point of maximum profitability. Differences between sexes were small; males tended to achieve slightly higher economic returns and heavier final weights, whereas females showed slightly lower backfat values. Overall, the results confirm that week 23 is the highest point of economic return for all genetic lines, providing a balanced combination of target weight, acceptable backfat, and accumulated feed intake. The lower variability of tP relative to tD is expected, as economic optimization integrates cost price constraints that restrict the optimal window and dampen biological variability.

Table 4 compares the optimal biological slaughter week (tD) and the optimal economic slaughter week (tP) for each genetic line and sex, including the mean difference and its standard deviation. In all groups, the economic week tP occurred after the biological week tD, with an average lag of 1 to 3 weeks, indicating that animals reach their best biological balance earlier than they do their maximum profitability.

The Pareto-type plot displays the relationship between live weight and backfat thickness, with points colored according to the global desirability value T(d). This visualization allows seeing the trade-off between weight gain and fat accumulation, and identifying the region where desirability is highest.

The general Pareto plot (Figure 6) shows the relationship between live weight and dorsal backfat of all animals in the study, with point color reflecting the global desirability T(d). This indicator combines the biological and economic objectives of the model (higher weight, lower backfat, and lower cumulative intake), so lighter/brighter colors represent animals closer to the optimal balance. The horizontal dashed lines that limit a transparent pink area mark the reference range of 13–16 mm of backfat, where values below 13 mm are considered ideal, 13–16 mm acceptable, and >16 mm are higher than desired.

The plot shows an upward trend, with backfat increasing progressively as body weight increases. However, most animals are clustered in a favorable zone, between 70 and 120 kg of live weight and 5 to 12 mm of backfat, which corresponds to the area where the highest desirability values were observed. This confirms that the optimization procedure is aligned with commercial slaughter ranges and that most animals reached the target phenotype before being sent to the slaughter plant.

Figure 7 shows Pareto-type plots for each genetic line (F1, ML1, ML2, and Commercial), relating live weight to backfat thickness, with point color representing the overall desirability value D(t). Across all groups, there is an upward trend between weight and fat, reflecting the expected relationship between growth and adipose deposition. The color scale shows that the highest desirability values concentrate in animals that reach higher market weights while keeping backfat within the desired range (<13 mm). The F1 line shows the widest spread of data at higher weights (up to ~130 kg) and a cluster of points with backfat between 8 and 12 mm associated with the highest desirability. This indicates very good efficiency in animals that achieve high weight without excessive fat. ML1 displays a pattern similar to F1, though with a slight tendency toward higher backfat at the same live weight. Even so, a good number of points remain within the desired fat range (≈13–16 mm). ML2 shows greater variability and a few outliers with higher backfat, although most animals group between 80–100 kg and 7–12 mm of fat. Moreover, the commercial animals show the most concentrated pattern, with low dispersion and high desirability in animals weighing 90–110 kg and with 6–10 mm of backfat, standing out for their uniformity.