Modeling feed intake in lactating sows during summer considering temperature and humidity covariates

Abstract

Heat stress during lactation reduces voluntary feed intake (FI) and milk production in sows, thereby limiting piglet growth. In this context, the main objectives of this study were to compare alternative models for describing daily FI over a 22-d lactation and to evaluate temperature- and humidity-related environmental covariates under commercial conditions. Daily FI records from 898 lactating sows (parity 1: 503, parity 2: 138, parity 3 and higher: 257) were analyzed using mixed-effects models. The generalized Michaelis–Menten (GMM) function was compared against a third-order orthogonal polynomial function using model diagnostic metrics and a sow-level cross-validation. To account for thermal stress, we incorporated daily maximum air temperature (MT), daily maximum dew point (MD), and degree-hours above 24°C (DGH24) into the models. These environmental indicators were evaluated as fixed linear covariates, as interactions with lactation time components, or as proportional modifiers to the base intake curve. The cubic polynomial mixed-effects model (R² = 0.85) demonstrated superior out-of-sample predictive performance relative to the GMM (R² = 0.82) by accommodating late-lactation declines in FI. Parity significantly affected FI dynamics, with multiparous sows exhibiting greater overall FI and steeper early lactation increases than primiparous sows. Modeling environmental variables as interactions with lactation day improved model fit in comparison to fixed linear covariates and proportional modifiers, indicating lactation-day–dependent environmental sensitivity. Among single covariates, MD provided the best fit (AIC = 49,829), and a joint MT + MD interaction model achieved the strongest overall performance (AIC = 49,793). These findings demonstrate that flexible polynomial models combined with multidimensional environmental indicators provide an improved framework for describing lactation FI dynamics. Accounting for parity and moisture-related heat load may enhance precision feeding and environmental management strategies in modern sow production systems.

Flexible polynomial modeling revealed declines in feed intake during late-lactation period with dew point being the stronger predictor of this reduction compared to air temperature.

Introduction

Genetic selection in modern sow lines has substantially increased litter size, milk production, and piglet growth over recent decades (Schinckel et al. 2010; Rodríguez et al. 2023). However, feed intake (FI) during lactation has not increased proportionally (Noblet and Etienne 1987; Revell et al. 1998; Dourmad et al. 2022). This imbalance creates a persistent nutritional gap in which high-producing sows face rapidly increasing energy demands while remaining physiologically constrained in their capacity to consume sufficient feed. Consequently, excessive mobilization of body reserves, prolonged weaning-to-estrus intervals, reduced subsequent litter size, and compromised longevity and welfare remain common challenges in commercial systems (Auldist and King 1995; Revell et al. 1998; Gasa et al. 2023).

FI during lactation is therefore a key determinant of both sow productivity and piglet performance. However, substantial variation in FI trajectories exists among sows due to physiological factors such as parity, body condition, and litter size, as well as environmental and management conditions (Koketsu et al. 1996; Schinckel et al. 2010; Cabezón et al. 2016). Among environmental factors, heat stress exerts a particularly strong suppressive effect on FI. Experimental and field studies consistently demonstrate that elevated ambient temperature reduces FI in lactating sows, often by more than 1 kg/d during hot periods (Quiniou and Noblet 1999; Renaudeau and Noblet 2001; Cabezón et al. 2016). Meta-analyses further indicate that FI is one of the most heat-sensitive traits, with reductions of approximately one-third between thermoneutral and hot conditions, and that much of the decline in milk production under heat stress can be attributed to reduced FI (Ribeiro et al. 2018; Dourmad et al. 2022).

Given the biological and economic importance of the FI of lactation sows, considerable effort has been devoted to modeling FI trajectories. Generalized Michaelis–Menten (GMM) functions have been used to describe the rapid rise and near-plateau in FI during early lactation, but under modern commercial systems with longer lactation lengths, more flexible mixed-model approaches such as polynomial functions may better capture late-lactation deviations, including post-peak declines (Schinckel et al. 2010, Cabezón et al. 2016, 2017). Since environmental heat load results from the combined effects of ambient temperature and humidity, atmospheric moisture conditions may also influence FI trajectories (Guevara et al. 2022). However, most studies have emphasized temperature, whereas humidity-related measures such as dew point remain underrepresented in FI models despite their potential to alter the sow’s effective thermal burden (Renaudeau and Noblet 2001, Cabezón et al. 2016).

We hypothesized that incorporating both temperature- and humidity-related covariates into parametric mixed-effects models would significantly improve the characterization of daily FI trajectories in lactating sows under commercial conditions. Therefore, the objectives of this study were to compare different models for daily FI in lactating sows using multiple parametric mixed-effects and to quantify the contribution of temperature- and humidity-related variables to FI variation. By appropriately modeling daily FI and accounting for environmental variables, this study aims to support climate-adaptive management strategies at the farm level, thereby contributing to improved sow performance and the sustainability of modern production systems.

Materials and methods

Ethics statement

This study used retrospective production records collected under routine commercial management practices. No experimental interventions were applied to animals for the purposes of this research. Therefore, Institutional Animal Care and Use Committee (IACUC) approval was not required.

Animals, housing, and management 

Daily lactation FI records were obtained from Large White × Landrace crossbred sows housed in a commercial farrowing facility located in Washington, Iowa, USA. The facility consisted of individual farrowing crates equipped with electronic sow feeders (GESTAL Individual Sow Feeders, Jyga Technologies Inc., St-Lambert-de-Lauzon, QC, Canada) and evaporative cooling cells. Sows had ad libitum access to feed throughout lactation according to standard farm management practices.

A total of 899 sows farrowing between May and July 2024 were included. After data quality control (described below), 898 sows remained in the final dataset, including 503 parity 1 (P1), 138 parity 2 (P2), and 257 parity 3 and higher (P3+). The average lactation length was 20.1 ± 0.97 days, ranging from 1 to 25 days. Daily FI was continuously recorded using an automated feeding system (GESTAL Solo, JYGA Technologies Inc., Quebec, QC, Canada). A total of 17,190 daily FI observations were initially available.

The experimental unit for all analyses was the sow-lactation record, with repeated daily FI observations within sow treated as longitudinal measurements.

Data quality control

Quality control was performed in the initial dataset and included removal of records with negative daily FI values (n = 3) or incomplete entries on the final lactation day (n = 72). One sow lacking a valid farrowing date was excluded. Because few sows had observations beyond lactation day 22 (n = 10), data were truncated at day 22 to avoid imbalance in recording period length across individuals. Summary statistics for daily FI and environmental covariates are provided in Table 1.

Table 1.

Descriptive statistics for daily feed intake and environmental variables.

Variable, unit	Mean ± standard deviation (range)
	Overall	Parity 1	Parity2	Parity 3+
N (sow-days)	17,190	9609	2638	4943
Daily feed intake, kg	6.62 ± 2.33 (0.23–13.71)	5.87 ± 1.98 (0.23–12.71)	7.14 ± 2.29 (0.43–13.07)	7.82 ± 2.41 (0.44–13.71)
Daily maximum air temperature, °C	28.50 ± 2.70 (22.31–33.92)	28.64 ± 2.72 (22.31–33.92)	28.35 ± 2.69 (22.31–33.92)	28.32 ± 2.67 (22.31–33.92)
Daily maximum dew point, °C	20.96 ± 3.49 (12.03–26.85)	21.06 ± 3.50 (12.03–26.85)	20.91 ± 3.47 (12.03–26.85)	20.81 ± 3.46 (12.03–26.85)
Degree-hours above 24°C, h	11.14 ± 5.20 (0–24)	11.32 ± 5.32 (0–24)	10.99 ± 5.06 (0–24)	10.89 ± 5.01 (0–24)

Environmental data

Hourly ambient and dew point temperatures were retrieved from the NASA POWER database (NASA Langley Research Center, Hampton, VA, USA; https://power.larc.nasa.gov/api/temporal/hourly/point) using the farm’s geographical coordinates. From hourly records, three daily environmental indicators were derived: daily maximum air temperature (MT); daily maximum dew point (MD); and degree-hours above 24°C (DGH24), which was calculated as the number of hourly temperatures exceeding 24°C within a 24-hour period (Cabezón et al. 2017). Environmental variables were inspected for missing values, but none were detected. Prior to statistical modeling, MT, MD, and DGH24 were mean-centered and scaled to unit variance to improve numerical stability and to allow coefficients to represent effects per one standard deviation change.

Statistical modeling

Daily FI trajectories were modeled using two alternative functional forms (ie frameworks): a Bayesian GMM function and a third-order orthogonal polynomial mixed model.

The GMM function was defined as:

$${\mathit{DFI}}_{i,t}={\mathit{DFI}}_0+\frac{\left({\mathit{DFI}}_A-{\mathit{DFI}}_0\right){\left(\frac{t}{K}\right)}^C}{1+{\left(\frac{t}{K}\right)}^C}$$

Where DFI₀ is the FI at lactation day 0; DFI_A is the asymptotic daily FI, i denotes sow i; t is the day of lactation; K represents the day at which half of the increase from DFI₀ to DFI_A is achieved; and C is a dimensionless parameter controlling the rate of intake increase (Lopez et al. 2000). Random effects were evaluated on DFI₀, DFI_A, and C, depending on model specification, resulting in 5 GMM different models (Table 2).

Table 2.

Parameters for daily feed intake (kg/d) fitted to the generalized Michaelis-Menten function.

Itema	Estimate	SE	l–95% CI	u-95% CIb	R 2	RSDc	WAICd
Fixed effects model
DFIA	9.74	0.16	9.45	10.07	0.54	1.58	64,494
DFI0	3.44	0.07	3.28	3.57
C	2.31	0.12	2.07	2.56
K	9.71	0.18	9.40	10.10
Var(e)	2.51	0.03	–	–
One random effect model (dfiAi)
DFIA	12.32	0.23	11.89	12.77	0.79	1.06	51,747
DFI0	2.11	0.08	1.96	2.26
C	1.20	0.03	1.14	1.27
K	11.66	0.34	11.02	12.35
SD (dfiAi)	2.48	0.07	2.35	2.63
Var(e)	1.13	0.01	–	–
One random effect model (dfi0i)
DFIA	15.85	0.14	15.57	16.14	0.75	1.17	54,899
DFI0	2.06	0.13	1.81	2.29
C	0.97	0.03	0.92	1.02
K	20.10	0.34	19.43	20.76
SD (dfi0i)	1.60	0.04	1.52	1.68
Var(e)	1.37	0.02	–	–
Two random effect model (dfiAiand dfi0i)
DFIA	10.20	0.14	9.94	10.49	0.82	0.99	49,870
DFI0	3.35	0.06	3.24	3.47
C	2.05	0.07	1.92	2.19
K	10.21	0.16	9.93	10.53
SD (dfiAi)	1.91	0.06	1.80	2.03
SD (dfi0i)	0.95	0.03	0.90	1.01
Var(e)	0.97	0.01	–	–
Two random effect model with C as linear function ofdfiAi
DFIA	10.03	0.12	9.81	10.27	0.82	0.98	49,748
DFI0	3.48	0.05	3.38	3.57
C	2.35	0.07	2.21	2.48
K	10.18	0.12	9.96	10.42
b	−0.16	0.01	−0.18	−0.13
SD (dfiAi)	2.16	0.06	2.05	2.28
SD (dfi0i)	0.85	0.03	0.08	0.91
Var(e)	0.97	0.01	–	–

^aDFI_A is the asymptotic daily FI; DFI₀ is the FI at lactation day 0; C is a dimensionless parameter controlling the rate of intake increase; K represents the day at which half of the increase from DFI₀ to DFI_A is achieved; e represents residual error.

^bl–95% CI, lower bound of the 95% confidence interval; u-95% CI, upper lower bound of the 95% confidence interval.

^cRSD, residual standard deviation.

^dWAIC, Watanabe–Akaike information criterion.

The polynomial model was defined as:

$${\mathit{DFI}}_{i,t}=b_0+b_1{t}_1+b_2{t}_2+b_3{t}_3$$

Where b₀ is the intercept; b₁, b₂, and b₃ are the regression coefficients; and t₁, t₂, and t₃ are the first-, second-, and third-degree orthogonal polynomial transformations of lactation day generated using R (R Core Team 2024) to eliminate collinearity across terms.

Random effects were evaluated by sequentially adding a random intercept (b₀), linear (b₁), and quadratic (b₂) terms, resulting in 4 different polynomial model structures (Table 3). This allowed evaluation of alternative variance structures. Random effects were assumed to follow multivariate normal distributions.

Table 3.

Parameters for daily feed intake (kg/d) fitted to the third-order orthogonal polynomial function.

Itema	Estimate	SE	P-value	R 2	RSDb	AICc
Fixed effects model
b 0	6.62	0.01	<0.001	0.54	1.58	64,400
b 1	219.48	1.58	<0.001
b 2	−45.42	1.58	<0.001
b 3	−15.39	1.58	<0.001
Var(e)	12.10	0.03	–
One random effect model (b0i)
b 0	6.62	0.04	<0.001	0.78	1.08	54,277
b 1	218.80	1.09	<0.001
b 2	−45.20	1.09	<0.001
b 3	−15.60	1.09	<0.001
Var(b0i)	1.32	–	–
Var(e)	1.17	0.01	–
Two random effect model (b0i, b1i)
b 0	6.62	0.04	<0.001	0.82	0.98	52,164
b 1	218.80	2.23	<0.001
b 2	−45.39	1.00	<0.001
b 3	−14.96	1.01	<0.001
Var(b0i)	1.33	–	–
Var(b1i)	3595.50	–	–
Cov(b0i, b1i)	36.63	–	–
Var(e)	0.95	0.01	–
Three random effect model (b0i, b1i, b2i)
b 0	6.62	0.04	<0.001	0.85	0.91	50,671
b 1	218.80	2.27	<0.001
b 2	−45.76	1.80	<0.001
b 3	−15.36	0.97	<0.001
Var(b0i)	1.32	–	–
Var(b1i)	3836.20	–	–
Var(b2i)	2087.80	–	–
Cov(b0i, b1i)	36.34	–	–
Cov(b0i, b2i)	−33.65	–	–
Cov(b1i, b2i)	283.01	–	–
Var(e)	0.83	0.01	–

The polynomial model was defined as, $DF{I}_{i,t}=b_0+b_1{t}_1+b_2{t}_2+b_3{t}_3$, where $t_1,t_2,$and $t_3$ are the first-, second-, and third-degree orthogonal polynomial transformations of lactation day. Therefore, the regression coefficients correspond to orthogonal polynomial bases and do not directly represent effects of lactation day.

^a b ₀ is the intercept; b₁, b₂, and b₃ are the regression coefficients; e represents residual error .

^bRSD, residual standard deviation.

^cAIC, Akaike’s information criterion.

GMM models were fitted using Bayesian inference implemented in the brms R package (version 2.22.0; Bürkner 2017) with four Markov chains, 4000 iterations per chain, and 1000 warmup iterations. Default No-U-Turn Sampler settings were used. Polynomial models were fitted using the lmer function in the lme4 R package (Bates et al. 2015).

To account for the different statistical foundations of each framework, model performance was evaluated using the Watanabe-Akaike Information Criterion (WAIC; Watanabe 2010) for the Bayesian GMM models, while the Akaike Information Criterion (AIC; Akaike 1974) was used for polynomial models. Both frameworks were further assessed based on R² and residual standard deviation (RSD). Because WAIC and AIC are derived under different statistical paradigms, cross-framework comparisons were limited to R² and RSD. Statistical significance was declared at P-value < 0.05.

Parity effects

After selecting the best-fitting trajectory model (polynomial or GMM), parity effects were evaluated within that model framework. Parity was tested as a fixed effect, and parity × lactation day interactions were tested to determine whether FI trajectories differed among parity groups in both overall level and trajectory shape across lactation. Lactation day was represented using the same time structure specified in the selected trajectory model.

Incorporation of environmental covariates

After accounting for parity effects, environmental covariates (MT, MD and DGH24) were incorporated into the best-fitting parity-adjusted trajectory model. Three approaches were evaluated (Models 1–3). In Model 1, covariates were included as fixed linear effects; In Model 2, as interactions with lactation day polynomial terms (t₁–t₃; first- through third-degree orthogonal polynomials); while in Model  3, as proportional modifiers of predicted FI, structured as: predicted FI × (1 + β × Covariate), where β represents the proportional effect of the covariate on predicted FI. Improvement in model fit due to inclusion of environmental covariates was assessed by comparing models with and without covariates using AIC, RSD, and likelihood-ratio tests (LRT).

Scenario simulation and bootstrap inference

To quantify the different influence of MT and MD on daily FI, predicted FI was calculated from the third-order polynomial model including both MT and MD as covariates under four alternative environmental scenarios: (i) “Baseline” (MT = 0, MD = 0), representing population averages; (ii) “MT + 1 SD,” where MT increased by one SD while MD was held at 0; (iii) “MD + 1 SD,” where MD increased by one SD while MT was held at 0; and (iv) “Both + 1 SD,” simultaneous one SD increases in MT and MD. Predictions were averaged over the random-effects distribution to reflect population-level responses. Parametric bootstrap sampling (n = 300) was used to quantify uncertainty in the average marginal effects, with 95% confidence intervals calculated as the 2.5th and 97.5th percentiles of the bootstrap distribution. Scenario simulations were conducted only for the third-order polynomial model including MT and MD because this model provided the best fit in the model comparison stage.

Results

Model comparison

Nine alternative models were evaluated in total with different random-effect structures tested for both GMM and third-order polynomial as described in Tables 2 and 3, respectively. For both functional forms, inclusion of sow-specific random effects substantially improved model fit relative to fixed-effect models, as indicated by increased conditional R² values (Polynomial: 0.54–0.85, GMM: 0.54–0.82) and reduced RSD (Polynomial: 1.58–0.91 kg/d, GMM: 1.58–0.98 kg/d). Estimated random-effect variances for b₀, b₁, and b₂, together with non-zero covariances and residual variance components, confirmed considerable between-sow variability in both intake level and lactation curve shape.

Among GMM models, the best fit was achieved by including random effects for both DFI_A and DFI₀ and modeling the curvature parameter C as a linear function of the random DFI_A (R² = 0.82; RSD = 0.98 kg/d; WAIC = 49,748; Table 2). For polynomial models, progressive addition of random intercept (b₀), linear (b₁), and quadratic (b₂) components resulted in sequential improvements in model fit. Therefore, the three-random-effect polynomial model yielded the highest conditional R² (0.85), the lowest RSD (0.91 kg/d), and the lowest AIC (50,671) (Table 3). To aid biological interpretation, the coefficients b₀, b₁, and b₂ represent distinct features of the lactation trajectory: b₀ shifts the baseline intake level vertically, b₁ dictates the linear acceleration (slope) during early lactation, b₂ governs the quadratic curvature (the openness of the arch around peak intake), and b₃ modulates the cubic trajectory, fine-tuning the inflection and stabilization of the descending phase during late lactation. The successive model improvements demonstrate that sows vary significantly not only in how much they eat overall, but also in their early-lactation escalation rates and the turning sharpness of their peak trajectories. When comparing the best-performing models from each model class, the polynomial model showed a higher R² and lower RSD than the GMM model, indicating a better overall fit. Therefore, the polynomial model was retained for subsequent analyses.

Parity-specific patterns in lactation feed intake

Predicted FI trajectories exhibited distinct, parity-dependent variations in overall magnitude, initial acceleration, and curvature, while all parity groups began lactation at similar levels (Fig. 1, Table 4). The baseline main effects of parity confirmed that overall FI capacity increased significantly with advanced maturity, shifting the entire curve upward for older sows; P2 and P3 + sows maintained a significantly higher average FI level compared to P1 sows (P2 = +1.24, P3+ = +1.91; both P-values < 0.001). The dynamic shape of the trajectories over time was dictated by highly significant parity by time interaction terms. During the initial phase of lactation, higher-parity sows demonstrated a substantially accelerated rate of FI commitment. This steep ascending slope was verified by the significantly positive linear interaction coefficients (P2:t₁ = +30.69, P3+:t₁ = +55.17; both P-value < 0.001), which visually manifest as a much sharper early-lactation climb in the P2 and P3 + curves relative to the gradual rise observed in P1. Driven by this rapid incline, peak predicted FI scaled upward with parity, reaching 7.77 kg/d for P1 (at day 19), 9.05 kg/d for P2 (at day 18), and 9.93 kg/d for P3+ (at day 19).

Figure 1.

Fixed-effect model-based predicted daily feed intake trajectories across parity groups over lactation days.

Table 4.

Fixed effects coefficients of the parity related term.

Term	Estimate	SE	t Value	P-value	Significance
b 0 (P1)	5.88	0.004	165.49	< 0.001	***
P2	1.24	0.01	16.16	< 0.001	***
P3+	1.91	0.01	31.25	< 0.001	***
b1	198.20	2.84	69.83	< 0.001	***
b2	−27.27	2.21	−12.35	< 0.001	***
b3	−21.09	1.29	−16.35	< 0.001	***
P2:t1	30.69	6.11	5.02	< 0.001	***
P3+:t1	55.17	4.87	11.34	< 0.001	***
P2:t2	−39.63	4.75	−8.34	< 0.001	***
P3+:t2	−44.32	3.78	−11.74	< 0.001	***
P2:t3	7.10	2.79	2.54	0.011	*
P3+:t3	15.80	2.21	7.15	< 0.001	***

P1, P2, P3 + represent parity 1, parity2 and parity 3 and plus, respectively; $t_1, t_2,$and $t_3$ are the first-, second-, and third-degree orthogonal polynomial transformations of lactation day.

Concurrently, the trajectories of multi-parous sows displayed a more pronounced transitional arc as they approached and passed these peak intakes. This greater structural curvature was driven by the significantly more negative quadratic interaction coefficients (P2:t_2 =−39.62, P3+:t_2 =−44.32; both P-value < 0.001). Visually, these negative coefficients bend the P2 and P3 + curves into more prominent, well-defined arches compared to the flatter, more linear progression of the P1 profile. Finally, the post-peak descending phase was fine-tuned by significant cubic interaction terms (P2:t₃ = +7.10, P-value < 0.05; P3+:t₃ = +15.80, P-value < 0.001). These positive cubic adjustments counteracted the severe downward pull of the quadratic effect during late lactation, preventing an abrupt crash in FI. This mathematical correction is visualized in Fig. 1, where the P2 and P3 + curves taper off smoothly and sustain a stabilized plateau from day 19 through day 22, rather than exhibiting a precipitous decline. The model fitness also improved by adding parity effect (AIC = 49,918, RSD = 0.91 kg/d).

Comparative performance of polynomial models with environmental covariates

The incorporation of single environmental indicators (MT, DGH24, and MD) was evaluated using three model specifications (Table 5). Across all environmental indicators, Model 2, which incorporated the environmental covariate as an interaction with lactation day, consistently showed the best fit based on AIC and RSD. For MT, Model 2 reduced AIC from 49,918 (no environmental covariates) to 49,885 and slightly improved RSD from 0.9084 to 0.9076 kg/d. A similar pattern was observed for DGH24, where Model 2 produced the lowest AIC (49,915) compared with Model 1 (49,927) and Model 3 (49,938), although the improvement in RSD was minimal (0.9081 kg/d). Among the evaluated environmental indicators, MD provided the strongest improvement in model fit. Model 2 with MD achieved the lowest AIC (49,829) and the smallest RSD (0.9061 kg/d), outperforming the corresponding MT and DGH24 models. LRT indicated that MT and MD significantly improved model fit under all three specifications (P-value < 0.05), whereas DGH24 was significant only under Model 2 and 3 (P-value < 0.05) and showed no significant improvement under Model 1 (P-value = 0.45).

Table 5.

Comparison of different covariate inclusion strategies in daily feed intake prediction models.

Covariatea	Modelb	AICc	RSDd	P-valuee
MT	1	49,922	0.9084	<0.05
	2	49,885	0.9076	<0.001
	3	49,931	0.9083	<0.001
DGH24	1	49,927	0.9084	0.45
	2	49,915	0.9081	0.001
	3	49,938	0.9084	<0.05
MD	1	49,872	0.9075	<0.001
	2	49,829	0.9061	<0.001
	3	49,862	0.9068	<0.001

^aMT represents daily maximum air temperature; DGH24 represents degree-hours above 24°C; MD represents daily maximum dew point .

^bModel 1 represents environmental covariate added as a fixed linear effect; Model 2 represents environmental covariate added as an interaction with lactation day; Model 3 represents environmental covariate added as a proportional modifier of the predicted DFI.

^cAIC, Akaike’s information criterion.

^dRSD, residual SD.

^e P-value: Likelihood-ratio test comparing each candidate model to the base model without any environmental covariate, fitted using maximum likelihood.

Based on these results, MT and MD were retained for further modeling. A joint model including both MT and MD and their interactions with time components further improved model fit (Table 6), reducing AIC to 49,793 and RSD to 0.9043 kg/d (R² = 0.85). In this model, MD and its interactions with t₁ and t₂ were significant (P-value < 0.05), whereas MT showed significant interactions with t₂ and t₃ (P-value < 0.05). The negative interaction of MD:t₁ (−8.03) indicates that higher daily maximum dew points significantly decelerate and flatten the early-lactation slope, delaying the initial FI climb. Conversely, although MD:t₂ was negative (−3.65), since the baseline quadratic curvature is inherently negative (−27.35), this negative interaction further intensifies the downward bending of the curve, yielding a sharper, more restricted turning point around peak intake under high-humidity stress. In contrast, MT exhibited a different shaping dynamic. The positive quadratic interaction (+6.13) counteracts the negative baseline curvature, while the positive cubic interaction further fine-tunes the late-lactation phase and prevents an abrupt drop in FI during the final days.

Table 6.

Parameters for daily feed intake (kg/d) fitted to the polynomial function with covariate daily maximum air temperature (MT) and daily maximum dew point (MD).

Itema	Estimate	SE	P-value	R 2	RSDb	AICc
b0	5.89	0.004	<0.001	0.85	0.9043	49,793
Parity2	1.24	0.01	<0.001
Parity3+	1.90	0.01	<0.001
b1	200.50	2.82	<0.001
b2	−27.35	2.19	<0.001
b3	−22.20	1.31	<0.001
MD	−0.14	0.001	<0.001
MT	0.01	0.001	<0.001
Parity2:t1	29.24	6.06	<0.001
Parity3+:t1	53.73	4.83	<0.001
Parity2:t2	−39.08	4.70	<0.001
Parity3+:t2	−42.33	3.74	<0.001
Parity2:t3	8.50	2.78	<0.001
Parity3+:t3	18.08	2.21	<0.001
MD:t1	−8.03	1.73	<0.001
MD:t2	−3.65	1.78	<0.05
MD:t3	−0.04	1.76	0.82
MT:t1	3.06	1.79	0.09
MT:t2	6.13	1.87	0.001
MT:t3	6.47	1.86	<0.001
Var(b0i)	0.59	–	–
Var(b1i)	3,190.79	–	–
Var(b2i)	1,577.92	–	–
Cov(b0i, b1i)	15.62	–	–
Cov(b0i, b2i)	−15.25	–	–
Cov(b1i, b2i)	763.07	–	–
Var(e)	0.82	0.01	–

The model was defined as, $DF{I}_{i,t}=b_0+b_1{t}_1+b_2{t}_2+b_3{t}_3+MD·t_1+MD·t_2+MD·t_3+MT·t_1+MT·t_2+MT·t_3$, where $t_1, t_2,$and $t_3$ are the first-, second-, and third-degree orthogonal polynomial transformations of lactation day. Therefore, the regression coefficients correspond to orthogonal polynomial bases and do not directly represent effects of lactation day.

^a b ₀ is the intercept; b₁, b₂, and b₃ are the regression coefficients; e represents residual error.

^bRSD, residual SD .

^cAIC, Akaike’s information criterion.

To provide an actionable tool for farm managers, the final mixed-effects model was algebraically back-transformed into closed-form equations expressed in terms of original lactation day and observed weather conditions (Supplementary File S1, available as supplementary data at Translational Animal Science online).

Predicted Feed-Intake under environmental scenarios

Predicted daily FI was evaluated under four environmental scenarios using parametric bootstrap (n = 300) to assess the contribution of each covariate on FI (Table 7; Fig. 2). Relative to baseline conditions (ie population average values), MT + 1 SD resulted in an average marginal increase of 0.08 kg/d (+1.21%). MD + 1 SD resulted in an average marginal decrease of 0.14 kg/d (−2.11%). When both MT and MD were increased by 1 SD, the average marginal effect was −0.06 kg/d (−0.90%). All 95% confidence intervals did not include zero (Table 7).

Table 7.

Parametric bootstrap estimates of marginal effects of environmental scenarios on daily feed intake (kg/d).

Scenariosa	2.5%	50%	97.5%
Baseline	6.62	6.63	6.64
MT + 1 SD	0.06	0.08	0.11
MD + 1 SD	−0.17	−0.14	−0.11
Both + 1 SD	−0.07	−0.06	−0.04

^aMT represents daily maximum air temperature; MD represents daily maximum dew point .

Figure 2.

Predicted sow daily feed intake curves during lactation under four environmental scenarios: Baseline (both MT and MD at their means), MT + 1 SD (MD at its mean), MD + 1 SD (MT at its mean), and both + 1 SD (MT and MD each increased by one SD). MT represents daily maximum air temperature and MD represents daily maximum dew point.

Predicted FI curves under each scenario are illustrated in Fig. 2. The MD + 1 SD scenario consistently produced the lowest intake curve, particularly in late lactation, whereas the MT + 1 SD scenario yielded slightly higher intake relative to baseline. The combined scenario (Both + 1 SD) remained lower than baseline throughout lactation but did not decline as sharply as the MD-only scenario.

Discussion

Model selection and structural considerations

Accurate characterization of lactation FI trajectories is essential for interpreting how environmental conditions relate to FI across time. In the present study, both GMM and polynomial mixed-effects models were evaluated. Although GMM functions are widely used to describe monotonic increases toward an asymptote (Schinckel et al. 2010; Cabezón et al. 2016), the FI patterns observed in the current dataset exhibited a modest decline during late lactation. Importantly, this population-level decline should not be interpreted as evidence that all sows followed the same pattern. Rather, the average trajectory reflects the aggregation of sows with heterogeneous FI dynamics, including individuals whose FI continued to increase, plateaued, or declined near weaning. Similar variation has been reported previously, where approximately 14% of sows with a 28-d lactation exhibited decreased FI between day 19 of lactation and 28-d weaning (Cabezón et al. 2017). Furthermore, substantial between-sow variation in relative FI was observed during both mid- and late-lactation periods in that study, consistent with the heterogeneity observed in the present dataset. The inclusion of sow-specific random effects for the quadratic term of lactation day allowed the polynomial mixed model to account for these individual differences in FI trajectory shape.

Such biological complexity is difficult to capture using asymptotic growth functions such as the GMM, which inherently constrain trajectories to approach a plateau without accommodating subsequent declines. In contrast, the cubic polynomial model provided sufficient flexibility to represent both the increase toward peak FI and the modest decline observed at the population level. Moreover, the polynomial mixed-effects framework supported a more comprehensive random-effects structure, allowing between-sow variation to be modeled not only in baseline FI but also in the rate and curvature of FI change across lactation. Collectively, these findings support the use of flexible mixed-effects functions when lactation FI trajectories deviate from strictly monotonic patterns and suggest that such approaches may be particularly advantageous in populations managed under extended lactation systems (Cabezón et al. 2017).

Parity-specific intake dynamics

Lactation FI trajectories showed parity-related differences, characterized primarily by suppressed consumption and a more gradual maternal adaptation in primiparous sows compared to their multiparous counterparts (Fig. 1). The fundamental divergence lies in the velocity of early-lactation intake escalation and the absolute magnitude of the peak. This pattern likely reflects differences in physiological maturity and nutrient partitioning, and is consistent with previous reports (Cabezón et al. 2016, 2017). From a biological standpoint, younger sows face constraints associated with smaller body size, gastrointestinal capacity, and concurrent nutrient demands for continued growth alongside milk production (Auldist and King 1995; Revell et al. 1998; Cabezón et al. 2016), which altogether explains the differences encountered in consumption. Conversely, multiparous sows manifested an aggressive “high-width, sharp-climb” FI strategy (Fig. 1).

From a practical management perspective, these findings strongly advocate for the implementation of parity-specific phase-feeding strategies in commercial hog farms. Because the consumption trajectories begin to diverge dramatically within the first week of farrowing, precision nutritional interventions—such as tailoring dietary energy density or feed delivery schedules—should be deployed early in lactation to accommodate the rapid volumetric surge required by older sows while avoiding metabolic or gastrointestinal overload in primiparous females.

Environmental covariates and lactation-day dependence

Environmental effects on FI were most effectively represented when environmental covariates were fitted as interactions with lactation-day components rather than as fixed linear effects or proportional effects (Table 5). This result suggests that environmental associations with FI are day-dependent, varying according to the lactation progress rather than acting uniformly. Such day-dependence is biologically plausible, given that metabolic heat production increases throughout lactation as milk synthesis and FI rise (NRC 2012; Cabezón et al. 2017). As internal heat load intensifies, the capacity of sows to dissipate heat may become increasingly constrained. Therefore, allowing environmental covariates to interact with lactation-day terms provides a better representation of the dynamic physiological progression of lactation.

Among the environmental indicators evaluated (MT, MD and DGH24), MD was the most informative single predictor of FI variation. Previous studies reported limited effects of humidity indicators, including relative humidity and dew point, on lactation FI in sows (Cabezón et al. 2016). In contrast, the significant effect observed in the present study likely reflects the broader variation in atmospheric moisture conditions in our dataset (MD range: 12.03–26.85°C). Dew point represents the absolute moisture content of the air and influences both the thermal environment and the effectiveness of evaporative heat-loss mechanisms. Present study found that evaporative cooling systems may reduce dry-bulb temperature while simultaneously increasing air moisture, potentially intensifying the thermal load even when ambient temperature appears moderate (Huynh et al. 2007; Wiegert et al. 2022). In addition, its cooling efficiency declines as atmospheric moisture increases (Bjerg et al. 2019). Consequently, ambient dew point may influence sow FI not only through direct effects of environmental moisture load but also indirectly through reduced cooling effectiveness during periods of elevated humidity. Therefore, rather than representing only a relative humidity metric, ambient dew point may serve as an integrated indicator of environmental conditions associated with thermal stress under commercial production settings. The improved performance of models incorporating MD highlights the importance of considering humidity-related indicators rather than relying solely on temperature to characterize environmental effects on lactation FI.

When temperature and dew point were included jointly, model performance improved further (Table 6), indicating that temperature contributed information beyond moisture content alone. The combined environmental effects were consistent with reduced FI under higher overall thermal load. From a practical perspective, these findings suggest that monitoring ambient dew point in addition to temperature may improve heat-stress management decisions. Elevated dew point conditions may indicate periods during which evaporative cooling systems provide reduced thermal relief, potentially requiring additional mitigation strategies such as increased air velocity, conductive cooling approaches, cooled drinking water, or modified feeding schedules (Bjerg et al. 2019). Together, these findings support the use of multidimensional environmental indicators when evaluating lactation FI dynamics under commercial production conditions.

Limitations and future directions

Some limitations must be acknowledged. Environmental data were obtained from an external climatic database and therefore represent ambient conditions rather than precise in-barn microclimates. Although internal and external environmental conditions are not identical, the use of external weather data to evaluate heat stress responses in commercial swine populations is well established in the literature, particularly in retrospective studies where continuous in-barn environmental monitoring is unavailable (Bloemhof et al. 2013; Sevillano et al. 2016; Tiezzi et al. 2020; Freitas et al. 2021). Indeed, substantial correlations between weather station and in-barn dry bulb temperature (r = 0.81–0.85) and relative humidity (r = 0.48–0.79) have been reported in lactating sow facilities during summer conditions (Johnson et al. 2023), supporting the biological relevance of external weather variables as indicators of the thermal environment experienced by sows. Nevertheless, the environmental coefficients reported here should be interpreted as associations with external ambient conditions rather than direct estimates of sow-level thermal exposure, and future studies incorporating continuous in-barn monitoring would help clarify the relationships among ambient weather conditions, barn microclimate, and sow FI. Additionally, the dataset was restricted to late spring and summer months (May–July), and extension of this modeling framework to year-round data would be valuable to evaluate FI dynamics under a broader range of thermal and management conditions (Cecil et al. 2025). Finally, due to limited records beyond day 22 of lactation, later-lactation FI trajectories were not captured, and future studies with longer observation windows would help characterize post-peak dynamics more completely.

Conclusions

A cubic polynomial mixed-effects model outperformed GMM models when used to characterize lactation FI in a commercial sow population. The most reasonable reason is that the first can better accommodate both peak intake and subsequent decline in FI. Parity was a major determinant of FI trajectory shape and magnitude, underscoring the importance of parity-aware interpretation and management. Environmental effects were best represented as lactation-day-dependent interactions, rather than constant reductions. Dew point was the most informative single environmental indicator, with maximum accuracy of FI prediction being reached when dew point was combined with temperature. When analyzed together, our results indicate that incorporating multidimensional environmental covariates into flexible FI models may enhance precision feeding and climate-adaptive management strategies in modern sow production systems.

Glossary

List of abbreviations

AIC

Akaike Information Criterion

DGH24

degree-hours above 24°C

FI

feed intake

GMM

generalized Michaelis–Menten

MD

daily maximum dew point

MT

daily maximum air temperature

P1

parity 1

P2

parity 2

P3+

parity 3 and higher

RMSE

root mean square error

RSD

residual standard deviation

WAIC

Watanabe-Akaike Information Criterion

Supplementary data

Supplementary data is available at Translational Animal Science online.

Funding

None declared.

Conflicts of interest

HF is an employee of Jyga Technologies Inc—GESTAL, which provided the data used in this study.

Data availability

The daily maximum temperature and dew point data used in this study were obtained from the publicly available NASA POWER database (https://power.larc.nasa.gov/). The sow feed intake data that support the findings of this study are available from the corresponding author upon reasonable request, pending permission from the farm that provided the data.