All the statistical analyses were conducted using R statistical software (Version 4.0.4 R Core Team 2021 R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; https://www.R-project.org/ accessed on 16 March 2021). To compare the fertility rate amongst each group of every trial, a Chi-square test was used. To evaluate the association between the variables of the first trial (melatonin treatment and BCS) and either DRIL or litter size, a two-way ANOVA and the following linear model was performed:

where yijk is the trait measured for each animal (DRIL or litter size), Ti is the fixed effect of the treatment (2 levels, j = treated and untreated), Bj is the fixed effect of BCS (2 levels, j = >2.5 and <2.5), TiBj is the interaction between treatment and BCS, Sk is the random effect of the ram (k = 8 rams) and eijk is the random residual effect of each observation.

To estimate the association between the variables of the second trial (melatonin treatment and the period of treatment) and either DRIL or litter size, a two-way ANOVA and the following linear model was performed:

where yijk is the trait measured for each animal (DRIL or litter size), Ti is the fixed effect of the treatment (2 levels, j = treated and untreated), Pj is the fixed effect of the period of treatment (3 levels, j = 15 March, 15 April and 15 May), TiPj is the interaction between treatment and the period of treatment, Sk is the random effect of the ram (k = 12 rams) and eijk is the random residual effect of each observation.

To analyse the association between the variables of the third trial (melatonin treatment and the period of previous lambing) and either DRIL or litter size, a two-way ANOVA and the following linear model was performed:

where yijk is the trait measured for each animal (DRIL or litter size), Ti is the fixed effect of the treatment (2 levels, j = treated and untreated), Lj is the fixed effect of the period of the previous lambing (3 levels, j = November, December and January), TiLj is the interaction between treatment and the period of treatment, Sk is the random effect of the ram (k = 12 rams) and eijk is the random residual effect of each observation.

Data regarding the DRIL and litter size were expressed as least square means ± SEM. Multiple comparisons of the least square means were performed using Tukey’s method (library Agricolae, R package version 1.3-1. Statistical Procedures for Agricultural Research. https://CRAN.R-project.org/package=agricolae, accessed on 25 March 2021). p ≤ 0.05 was considered statistically significant.

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