The Limousin breed, originated in France as a pure breed or in crossbreeding schemes^1,2 has productive, reproductive, and adaptive qualities that have allowed its distribution in a large number of countries and production systems^3,4,5; it has also been used in the development of synthetic breeds⁶. It arrived in Mexico through imports from Canada and the United States in the 1970s; the Mexican Association of Limousin Cattle Breeders (AMCGL, in Spanish) was established in 1989^7,8. It is currently distributed in 17 states, especially as a pure breed, although it is also used in open crossbreeding schemes and as a basis for the makeup of synthetic breeds, such as Limousan (5/8 Limousin and 3/8 Angus)⁹ and Brahmousin (5/8 Limousin and 3/8 Brahman)¹⁰.

The AMCGL coordinates the genealogical record of breed purity and purity degrees, as well as the production records that define the breed selection criteria and objectives⁷. Productive data associated with growth include live weight at birth and at 120, 210, and 365 d of age, with measurements at the plus or minus 45-d interval of the specified age. Live weight measurements generate a distribution of observations throughout the life of the animal, which together can be used to characterize and evaluate the growth curve. Non-linear models (NLM) characterize and analyze the animal growth curve based on the biological interpretation and applications of the regression coefficients, as well as growth parameters derived from the regression coefficients^11,12,13. Regression coefficients and growth parameters play an important role in decision making for management, nutrition, breeding, and genetic improvement programs^14,15,16,17. Based on the above, the objective of the present study was the selection and adjustment of a NLM to describe and evaluate the growth curve in Limousin cattle from Mexico.

The database consisted of live weight measurements in the weight interval from birth to 500 d of age in Limousin cattle (PB; purebred). In order to define the growth curve, four NLMs were evaluated: Brody (BRO), von Bertalanffy (BER), Gompertz (GOM), and logistic (LOG), all of which are made up of three regression coefficients (β1, β2, and β3)^12,13,18. In the NLM equations (Table 1), yi represents the live weight (kg) measured at time t ; β1, is the asymptotic value when t tends to infinity, interpreted as the adult weight parameter (AWP); β2, is an adjustment parameter when y ≠ 0 and t ≠ 0; and β3, is the growth rate (GR), expressing weight gain as a proportion of total weight. The BER, GOM, and LOG models are characterized by describing growth based on a sigmoid curve, for which age (AIP; months) and weight (WIP; kg) at the inflection point were calculated. The BRO model exhibits a growth curve with a constant GR and no inflection point. The regression coefficients were used to estimate the age at 50 % maturity (A50M), the degree maturity attained at 15 months (A15M) of age^19,20, as well as the correlation (r_ac) between GR and ADW.

Analyses were performed for each sex, using the Gauss-Newton method of the NLIN procedure of the SAS statistical analysis software²¹. The selection of the best-fitting model was based on^18,19: Akaike information criterion [AIC= n*nl(sse/n) + 2k]; Bayesian information criterion [BIC= n*nl(sse/n) + k*nl(n)]; coefficient of determination [R²= (1 - (sse/tss))]; and, overall standard error or model (OSE=ssen-p-1. Where: n = total number of data; sse= sum of squares of the error; tss = total sum of squares; k= number of parameters in the model; nl = natural logarithm. For AIC and BIC, the model with the lowest value was considered the best fit.

The AMCGL managed a herd register with various degrees of purity (DCB) for the purpose of increasing the Limousin cattle population through absorbing crossbreeding, based on crossbred cows and PB sires. With the model selected as the best fit in the PB population, the growth curve was characterized in populations defined by five DCB or generations: first (D1) with ½ Limousin; second (D2) with – Limousin; third (D3) with 7/8 Limousin; fourth (D4) with 15/16 Limousin; and, fifth (D5) with 31/32 Limousin. Table 2 describes the database analyzed in terms of BP and DCB.

In model selection, within sex with AIC and across sex with BIC, the best fitting model was BER, followed by BRO and GOM; in all models the R² was greater than 95 % (Table 3). Table 4 shows the results for the regression coefficients and product growth parameters of the evaluated NLMs. ADW estimation was higher for PB vs CB, in contrast, the GR was higher in CB. The genetic improvement scheme for Limousin cattle in Mexico includes weaning weights adjusted to 205 d⁷, with potential significance in the growth curves, given that the inflection point is located in the pre-weaning period. The BRO model was second in the model ranking; however, it exhibited outlier results for ADW, A50M and DM15. All models had a r_ac below -0.75 (Table 4), which indicates that high ADWs do not derive from high GRs. Figure 1 for males and Figure 2 for females depicts the growth based on the BER model for all genotypes evaluated.

Figure 1 Growth curves for Limousin males. Purity, purebred animals; D1, 1/2 Limousin; D2, 3/4 Limousin; D3, 7/8 Limousin; D4, 15/16 Limousin; D5, 31/32 Limousin 

Figure 2 Growth curves for Limousin females. Purity, purebred animals; D1, 1/2 Limousin; D2, 3/4 Limousin; D3, 7/8 Limousin; D4, 15/16 Limousin; D5, 31/32 Limousin 

In purebred Limousin cattle with three different production systems, Igarzabal et al³ reported GOM as the best fitting model. In crossbreeding schemes of Limousin with Angus, Hereford, and MARC III, Zimmermann et al¹⁷ used the BRO model to characterize the growth curve and evaluate live weight at maturity; in Limousin x Friesian cattle, they represented growth based on the GOM model²². In the Madrasin breed, product of the crossbreeding of Limousin with Madura, the growth described a sigmoid type curve, characterized with the LOG model²³. Growth curves evaluated with the BER model were reported in Holstein²⁴, Pyrenean, and Blonde cattle³.

In Mexico, several studies have discussed contrasts in the type of growth curve across breeds. For growth curves without an inflection point, in five zebu breeds in tropical cattle ranching, Domínguez-Viveros et al²⁵ reported that the best fitting NLMs were Brody, Meloum III and Mitscherlich; the BRO model in particular was selected as the one with the best fit in Romosinuano cows²⁰, as well as in Tropicarne¹⁹ and Salers cattle²⁶. For sigmoid growth curves, Contreras et al²⁷ in Jersey, Holstein, and Jersey-Holstein crossbred cows, the selected MNLs were GOM, LOG, and BER, respectively; the BER model has been reported for Hereford cattle²⁶.

The incorporation of replacement heifers at the reproductive phase is of transcendence for the genetic progress and profitability of the herd. This procedure is carried out in three stages²⁸: at the onset of pituitary maturation, triggered at a certain age and weight; followed by the development of the ovaries and body growth; maturation of the uterus as a consequence of pituitary development and its hormonal influence on body growth and ovarian activity, allowing the heifer to mate and develop gestation. Several studies have analyzed the influence of growth parameters on reproductive variables^20,24,29; Thus, the inflection point has been associated^13,30,31 with the onset of the reproductive phase. Age at first calving is an indicator of the time it takes for an animal to reach sexual maturity and reproduce for the first time, and mating at approximately 15 mo, with age at first calving of approximately 24 mo, has positive effects on cow longevity and productivity^32,33. Based on the BER model, differences are observed in CB vs PB females for the components of the growth curve (Table 4), which can be attributed to genetic differences across breeds and heterosis effects resulting from the crossing scheme. In PB heifers, AIP was estimated at 3.7 mo with a WIP of 131.2 kg; in CB, AIP and WIP were in the ranges of 2.9 to 3.7 mo and 110.9 to 124.4 kg, with average values of 3.3 and 116.4, respectively. A50M in females, was estimated to be at 10.6 mo in PB, and within the range of 8.9 to 10.5 mo for CB, with an average value of 9.5 months. For DM15 in females, the average value was 90.5 % for CB, while the estimate for PB was 87.9 %. In contrast, among females from other populations and based on the BER model: Contreras et al²⁷ for Holstein, Jersey and crossbreds estimated AIP (months) and WIP (kg) in the ranges of 7.4 to 9.8 and 115.0 to 151.7, respectively; in five zebu breeds, Domínguez-Viveros et al²⁵ reported AIP and WIP estimates in the ranges of 3.9 to 11.7 and 107.2 to 230.9, respectively; in Romosinuano²⁰, Tropicarne¹⁹, and Siboney²⁹. AIP - WIP results were 15.5 - 132.5, 7.7 - 180.5 and 5.9 - 152.4, respectively.

As for the males, the selection of stallions is carried out among PB, and they are incorporated for reproduction from one year of age; however, lowering the age of entry into reproduction reduces the generation gap and has an impact on genetic progress³⁴. The growth curve can influence the development of the reproductive phase; in Bos taurus breeds, the physiological events associated with reproduction begin at six to eight months; maturity and reproductive capacity are determined by the quality of the semen, with variations due to the effects of live weight, growth rate, scrotal circumference, among other factors³⁵. The results indicate that PB males reach 50 % maturity at 13 mo of age, with values above 80 % at 15 mo of age (Table 4). In contrast²⁶, Hereford and Salers cattle reported maturity levels of 68.2 % and 76.6 % at one year, respectively. On the other hand, growth curve indicators are associated with profitability in production; the GR has an effect on age and slaughter weight; degree of maturity is important for efficiency and carcass composition^16,22. Various authors^15,36,37 have assessed the differences and derivations of the growth curve in relation to production for purebred males and various crosses.

The best fitting model was von Bertalanffy, which described a sigmoid growth curve, with differences in growth parameters across the evaluated genotypes. Tipping point estimates are within the context of pre-weaning growth.