Determination of methionine requirement for Pekin ducks: an integrated linear broken line and quadratic polynomial regression approach

This study evaluated the effects of dietary methionine (Met) levels on the growth performance of Pekin ducks and estimated their Met requirements during the starter (1 to 14 days; Exp. 1) and grower (15 to 35 days; Exp. 2) phases. In Exp. 1, 288 one-day-old male ducklings were randomly assigned to six diets containing analyzed Met levels of 0.291%, 0.343%, 0.392%, 0.438%, 0.483%, and 0.521% (six replicates; eight birds each). In Exp. 2, 150 ducks at 15 days of age were allocated to five diets with analyzed Met levels of 0.271%, 0.342%, 0.421%, 0.501%, and 0.566% (six replicates; five birds each). Growth performance was recorded in both experiments, and Met requirements were estimated using linear broken-line and quadratic polynomial models. During the starter phase, increasing Met intake resulted in linear and quadratic improvements in weight gain and a linear reduction in feed/gain (F/G). For the grower phase, weight gain showed a quadratic response, with the highest gain at 0.421% Met, while F/G decreased linearly and quadratically. Estimated Met requirements for the starter phase were 0.404% (linear broken-line) and 0.532% (quadratic polynomial), and for the grower phase were 0.371% and 0.473%, respectively. Using the intercept of the two models, recommended Met levels were 0.455% for starter ducks and 0.411% for growing ducks. These integrative values likely provide more practical and economically relevant recommendations than relying on a single model, as broken-line analysis may underestimate and quadratic models may overestimate actual nutrient requirements.

1 Introduction

Global duck meat demand continues to rise, with the duck population reaching about 6 billion worldwide (Hou and Liu, 2023). Modern meat-type ducks grow faster and convert feed more efficiently than earlier strains, resulting in potentially higher amino acid requirements. In current duck production, feed formulation aims to optimize growth and carcass yield (Han et al., 2025) by precisely meeting nutrient needs—insufficiency hinders performance, whereas excess increases cost and environmental nitrogen output. Amino acids, as essential nutrients, are therefore central to diet optimization. Accurate determination of their requirements is critical for improving efficiency, reducing waste, and minimizing environmental impact. Several regression approaches, including quadratic polynomial and linear broken-line models, have been used to estimate amino acid needs in ducks (Jiang et al., 2017; Ruan et al., 2018; Wu et al., 2019). However, each model has inherent advantages and limitations (Wu et al., 2021), making appropriate experimental design and model selection essential for reliable requirement estimates.

Methionine (Met), widely recognized as the first limiting amino acid for poultry, plays essential roles in protein accretion, transmethylation reactions, and the maintenance of cellular redox balance through the synthesis of antioxidant molecules such as glutathione (Liu et al., 2010; Wen et al., 2014; Babazadeh and Ahmadi Simab, 2022). Given these critical biological functions, extensive research has been devoted over recent decades to defining the Met requirements of ducks and elucidating its influence on growth performance, carcass development, and metabolic health (Xie et al., 2006; Ruan et al., 2018; Wu et al., 2019, 2022). Historically, a range of statistical models has been employed to estimate Met requirements in Pekin ducks, with the linear broken-line model (Wu et al., 2019, 2021) and the quadratic polynomial regression model (Xie et al., 2006; Ruan et al., 2018) being the most commonly used. Each model possesses inherent limitations: the broken-line model tends to generate more conservative estimates by identifying the minimal intake needed to prevent performance decline, whereas the quadratic model often predicts higher values because it incorporates diminishing returns beyond the point of maximal response. As a result, the true nutritional requirement likely lies between these two estimates. The intersection or convergence point of the linear broken-line and quadratic regression curves has therefore been proposed as a more biologically meaningful and practically applicable indicator of amino acid requirements (Baker et al., 2002; Spangler et al., 2019). In light of these considerations, the present study aimed to determine the dietary Met requirements of starter and growing Pekin ducks using an integrated analytical approach that combines the strengths of both the linear broken-line and quadratic polynomial regression models. This dual-model framework was expected to yield more robust and realistic requirement estimates, thus supporting more precise feed formulation for modern commercial duck production.

2 Materials and methods

2.1 Birds and experimental design

All experimental procedures were approved by the Animal Care and Use Committee of Chinese Academy of Agricultural Sciences (Approval number: IAS2018-15, IAS2018-16). Two experiments (Exp) were conducted using starter and growing Pekin ducks obtained from the Pekin Duck Breeding Center of the Chinese Academy of Agricultural Sciences. The birds were housed in plastic-floor pens (200 cm × 75 cm × 40 cm) with continuous lighting and had free access to water and feed throughout the trials. In Exp 1, a total of 288 one-day-old male Pekin ducklings with similar body weight (56.3 ± 0.2 g) were randomly assigned to 6 dietary treatments, each consisting of 6 replicates with 8 birds per replicate. In Exp 2, 180 one-day-old male Pekin ducklings were fed a common starter diet (ME: 12.1 MJ/kg, CP: 20%) for 14 days. On day 15, all ducks were individually weighed, and 150 birds (558.5 ± 4.4 g) were selected and randomly allocated to 5 dietary groups, each with 6 replicates containing 5 ducks. No medicines, antibiotics, growth promoters, or vaccines were used during the entire experiment. Before bird placement, all rooms and equipment were thoroughly cleaned, disinfected, and rested for 7 days. Strict biosecurity measures were maintained, including controlled access, dedicated clothing, and routine sanitation. The flock’s health was monitored daily, and no clinical signs requiring treatment were observed. These measures ensured that the study was conducted under strictly medication-free and vaccine-free conditions. The ambient temperature was maintained at 32 °C from days 1 to 3, gradually reduced to approximately 25 °C by day 14, and thereafter maintained between 18 °C and 22 °C for the remainder of the experimental period (Wu et al., 2022; Hao et al., 2021).

The corn-soybean meal basal diets used in both trials were formulated to meet the nutrient requirements for Pekin ducks as recommended by National Research Council (1994), with detailed compositions provided in Supplementary Table S1. To prepare the experimental diets, the basal diet without DL-Met supplementation was divided into several equal sublots. In Exp 1, birds in the six treatment groups received the basal starter diet supplemented with 0, 0.05%, 0.10%, 0.15%, 0.20%, or 0.25% crystalline DL-Met (purity ≥ 99%; Evonik Industries, Krefeld, Germany). In Exp 2, birds in the five groups were fed the basal grower diet supplemented with 0, 0.075%, 0.15%, 0.225%, or 0.30% crystalline DL-Met (purity ≥ 99%; Evonik Industries, Krefeld, Germany). The formulated mash diets were pelleted in both trials. The total Met and other amino acid content of two basal diets were analyzed (L-800, Hitachi, Tokyo, Japan) based on as-fed diets (Supplementary Table S1). The analyzed dietary Met levels in Exp 1 were 0.291%, 0.343%, 0.392%, 0.438%, 0.483%, and 0.521%, and those in Exp 2 were 0.271%, 0.342%, 0.421%, 0.501%, and 0.566%, respectively.

2.2 Data collection

At the end of each trial (14 d in Exp. 1 and 35 d in Exp. 2), birds were fasted overnight before body weight and residual feed per pen were measured. Weight gain, feed intake, and feed/gain ratio were calculated for the periods of 1 to 14 days (Exp. 1) and 15 to 35 days (Exp. 2). Both feed intake and feed/gain were adjusted to account for bird mortality.

2.3 Statistical analysis

Statistical analyses were performed using one-way ANOVA in SAS software (version 9.4; SAS Inst. Inc., Cary, NC), with the pen as the experimental unit. Linear and quadratic polynomial contrasts were applied to examine the effects of dietary Met levels on growth performance. Differences were considered statistically significant at P < 0.05, and variability was expressed as the pooled standard error of the mean (SEM). The Met requirements for Pekin ducks in both trials were estimated using linear broken-line (Robbins et al., 2006; Wu et al., 2019) and quadratic polynomial (Xie et al., 2006; Ruan et al., 2018) regression models. The broken-line model was defined as: y=L+U·(R−x), where y represents a growth performance variable (F/G), x is the dietary Met level (%), R is the estimated Met requirement, L is the response when x=R, and U is the slope of the line. In this model, y=L when x>R. The quadratic polynomial model was expressed as: y=A+Bx+Cx², where y is the growth performance variable, x is the dietary Met level, and A, B, and C are model parameters. The Met requirement was taken as the x value corresponding to the maximum (or minimum) y value in the quadratic polynomial model. To derive an objective estimate of the Met requirement, the intercept of the broken-line and quadratic polynomial regression models was used in the present study (Baker et al., 2002; Spangler et al., 2019).

3 Results

3.1 Growth performance

As presented in Table 1, weight gain exhibited both linear (P = 0.0034) and quadratic (P = 0.0366) responses to increasing Met levels, while feed/gain showed a linear decreased (P = 0.0006) of Pekin ducks from 1 to 14 days of age. No significant difference was observed in the feed intake of Pekin ducks in response to increasing dietary Met levels (P = 0.3349). Similarly, for Pekin ducks from 15 to 35 days of age (Table 2), increasing dietary Met levels significantly improved weight gain (P = 0.0397) and markedly reduced the feed/gain ratio (P < 0.0001). Weight gain responded quadratically (P = 0.0215) to dietary Met supplementation, peaking at the dietary 0.421% level. While the feed/gain showed significant linear and quadratic decrease (P < 0.0001). Although feed intake was not significantly affected overall (P = 0.2048), a linear decreasing trend was observed (P = 0.0394).

Table 1

Table 1. Effects of dietary methionine on growth performance of Pekin ducks from hatch to 14 days of age (Exp. 1).¹

Table 2

Table 2. Effects of dietary methionine on growth performance of Pekin ducks from 15 to 35 days of age (Exp. 2).¹

3.2 Estimation of Met requirement

In both Exp. 1 (Table 1) and Exp. 2 (Table 2), the feed/gain responded significantly (P = 0.0172; P < 0.0001) to dietary Met levels, with the relationship being well fitted by linear broken-line (P = 0.0315; P = 0.0195) and quadratic polynomial (P = 0.0414; P = 0.0167) regression models. In Exp.1, linear broken line regression analysis for feed/gain during 1 to 14 days yielded a Met requirement of 0.404%, whereas the quadratic polynomial minimum regression analysis estimated a higher Met requirement of 0.532% (Table 3, Figure 1A). The intercept of the linear broken line and quadratic polynomial methods yielded an intermediate Met requirement of 0.455% (Table 3, Figure 1A). In Exp.2, linear broken line and quadratic polynomial minimum regression analysis yielded a Met requirement of 0.371% and 0.473% for feed/gain, respectively, for growing Pekin ducks from 15 to 35 days of age, and the intercept of the broken line and quadratic polynomial methods determined 0.411% as the Met requirement (Table 3, Figure 1B).

Table 3

Table 3. Summary of Met requirements of Pekin ducks estimated using the different regression methods.

Figure 1

Figure 1. Determination of methionine requirements for starter (A) and growing (B) Pekin ducks. Requirement estimated for feed/gain by linear broken line (a), quadratic polynomial (b), and the intercept of the broken line and quadratic polynomial (c).

4 Discussion

In both studies, Met-deficient basal diets were formulated using corn and soybean meal without crystalline DL-Met supplementation. As expected, the analyzed total Met levels in the starter (0.291%) and grower (0.261%) diets were both below the National Research Council (1994) recommendations (0.40% for 0 to 2 week and 0.3% for 2 to 7 week), which confirmed that the basal diets were Met-deficient as intended. Feeding the Met-deficient basal diets resulted in significant growth depression of poultry. However, consistent with previous studies in broilers (Wen et al., 2014; Peng et al., 2018), ducks (Xie et al., 2006; Wu et al., 2019, 2021), and geese (Yang et al., 2018), dietary Met supplementation significantly enhanced growth performance in both experiments with starter and growing Pekin ducks, as reflected by increased ADG and decreased F/G. In the present study, dietary Met supplementation resulted in a substantial reduction in F/G from 1.98 to 1.76 (0.22 units, 11% decrease) during 15 to 35 days of age. Independent studies have reported comparable reductions in F/G when Met levels were increased, including decreases of 0.23 (from 2.30 to 2.07, 10% decrease) and 0.21 units (from 2.05 to 1.84, 10.2% decrease) in Pekin ducks from 14 to 42 days of age (Wu et al., 2019), 0.23 units (from 3.27 to 3.04, 7% decrease) in growing Pekin ducks from 21 to 49 days of age (Xie et al., 2006), and 0.14 units (from 1.76 to 1.62, 7% decrease) in Pekin ducks from 21 to 49 days of age fed the diet containing bakery meal and wheat middling (Zeng et al., 2015). However, high-quality feed ingredients (only corn and soybean meal) without unconventional protein sources were utilized in our study, thereby minimizing potential nutritional confounders. It is well established that 4^th to 5^th weeks represent the period of most rapid growth in Pekin ducks, after which feed conversion efficiency generally declines. During this critical phase, dietary Met level, the first limiting amino acid, serves as a key and highly sensitive determinant of growth performance. Consequently, the observed magnitude of improvement in F/G, which slightly exceeds that reported in other studies, may be explained by differences in the ducks’ rearing phase and the formulation of the experimental diets.

Various regression models, including the quadratic polynomial, linear, and quadratic broken-line models, have been employed in previous studies to estimate Met requirements in ducks (Xie et al., 2006; Ruan et al., 2018; Wu et al., 2019). However, each of these modeling approaches has its own advantages and limitations (Wu et al., 2021). In the present study, the quadratic polynomial and linear broken-line models were employed to evaluate Met requirements in Pekin ducks. When using the feed/gain as the response variable, the linear broken-line regression estimated Met requirements at 0.404% and 0.371% for starter and growing Pekin ducks, respectively. In contrast, higher values of 0.532% and 0.473% were obtained using quadratic polynomial regression under the same performance criterion. These differences were largely consistent with previous observations that quadratic polynomial regression tends to overestimate the requirement, whereas linear broken-line regression often yields underestimates (Baker et al., 2002; Spangler et al., 2019). Furthermore, the Met requirements for starter and growing Pekin ducks were determined to be 0.455% and 0.411%, respectively, using the intercept of the broken line and quadratic polynomial method. The comparison of regression methodologies demonstrated a clear pattern that linear broken-line regression generated the most conservative Met requirement estimates, quadratic polynomial regression produced the most liberal estimates, and their intersection provided intermediate values. This pattern confirms earlier findings that the broken-line and quadratic polynomial methods tend to underestimate and overestimate requirements, respectively, while their intersection offers a practical compromise, as established by Baker et al. (2002) and recently validated by Spangler et al. (2019). The Met requirements for feed/gain estimated by the intercept of the linear broken line and quadratic polynomial regression (0.455% and 0.411% for the starter and growing periods, respectively) were substantially higher than the National Research Council (1994) recommendations of 0.40% and 0.30%, which were derived from a single study on Muscovy ducks (Leclerq and de Carvile, 1977). The recently established Chinese standard, National Standardization Administration of the People’s Republic of China (2024) recommends total dietary Met requirements of 0.45% and 0.40% for starter (1 to 2 weeks) and growing (3 to 5 weeks) Pekin ducks, respectively. These values are closely aligned with the requirements derived from the intercept of the linear broken-line and quadratic polynomial models in the current study. These consistencies further support the notion that modern, fast-growing Pekin ducks exhibit greater Met needs than those reported in earlier literature (Xie et al., 2006). The discrepancies between historical recommendations and contemporary estimates likely reflect genetic improvements, enhanced growth rates, and changes in commercial production systems over the past decades. Moreover, variation in experimental design, response criteria, and statistical models contributes to differences among published nutrient requirement values (Hasanvand et al., 2017; Ghorab et al., 2025). In this study, the convergence of estimates obtained from both the linear broken-line and quadratic polynomial models strengthens the reliability of the current findings. Collectively, the results underscore the importance of periodically reevaluating amino acid requirements to ensure that feeding standards remain aligned with ongoing genetic and management advancements in the duck industry. Future studies incorporating integrated modeling approaches and larger datasets may further refine Met requirement estimates and improve precision in diet formulation.

5 Conclusion

Taken together, multiple regression methods can be applied to determine Met requirements in Pekin ducks. This study demonstrated that the intercept of broken-line and quadratic polynomial models yielded Met requirements of 0.455% and 0.411% for starter and growing Pekin ducks, respectively, based on feed/gain responses. These values likely represent more economically viable recommendations than those derived from either method alone, since the individual models may underestimate (linear broken-line) or overestimate (quadratic polynomial) the actual requirements. The integrated application of both regression models will be considered for evaluating the nutritional requirements of ducks in future studies.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.

Ethics statement

The animal study was approved by Animal Care and Use Committee of Chinese Academy of Agricultural Sciences. The study was conducted in accordance with the local legislation and institutional requirements.

Author contributions

YW: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Writing – original draft, Writing – review & editing. JC: Data curation, Formal analysis, Methodology, Writing – original draft. JT: Data curation, Formal analysis, Methodology, Writing – original draft. YY: Data curation, Formal analysis, Methodology, Writing – review & editing. SH: Conceptualization, Investigation, Supervision, Writing – review & editing. ZW: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Writing – review & editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the National Key R&D Program of China (2022YFD1301800), National Natural Science Foundation of China (32402790), China Agriculture Research System of MOF and MARA (CARS-42-10), Science and Technology Innovation 2030-Major Project (2023ZD0406307), Agricultural Science and Technology Innovation Program of Chinese Academy of Agricultural Sciences (CAAS-ASTIP-2023-IFR-13; CAAS-IFR-ZDRW202301).

Acknowledgments

The authors gratefully thank all members who have contribution to this project in our department.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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The author(s) declared that generative AI was not used in the creation of this manuscript.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fanim.2025.1727330/full#supplementary-material

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