ABSTRACT
The general aim of this thesis has been to analyse sources of variation for some of the most important components of fertile artificial insemination (AI) dose production in order to explore the interest and limitations of different strategies for their genetic improvement in a paternal line of rabbits selected for growth rate. These components refer to seminal production and quality traits, being considered the male reproductive performance as the final expression of the effect of the seminal characteristics and the effect of the interaction among them and with the female.
Threshold and linear mixed models have been used in all the studies included in this thesis under a Bayesian approach. 
In chapter 1, genetic parameters of male libido and characteristics involved in the ejaculate rejection criteria and semen production traits have been estimated as well as the genetic relationship between all of these traits with average daily gain (ADG). A linear tri-trait model was used to analyse sperm concentration, ejaculate volume and ADG. Threshold and linear two-trait models were used for the analyses of the remaining traits with ADG. The amount of ejaculates rejected for AI was high (38 %), primarily due to low individual sperm motility scores. Male libido and variables related to the quality of the ejaculate such as presence of urine and calcium carbonates in the ejaculate, individual sperm motility, semen pH and suitability for AI of the ejaculate (which involves the subjective combination of several semen quality traits) were found to be lowly heritable, but repeatable. This indicates performance of bucks for seminal quality traits and libido in AI centres would be more strongly affected by management practices rather than genetic selection. Semen production traits (sperm concentration, ejaculate volume and total number of sperm) exhibited moderate values of heritability (h2) suggesting the possibility of effective selection for these traits. A moderate to high negative genetic correlation (rg) was estimated between sperm concentration and ejaculate volume suggesting that total number of sperm would be of most interest to select for. The ADG was estimated to have a moderate to low h2, to have a low, positive rg with sperm concentration, to have a low, negative rg with ejaculate volume, and to be genetically uncorrelated with all remaining traits analysed. Therefore, it is concluded that selection for increasing ADG in paternal lines is expected to have no detrimental effects on male libido and traits involved in semen quality and little to no effect on semen production traits.
The aim of chapter 2 was to explore the feasibility of indirect selection of male contribution to fertility through the use of semen pH because it is an immediate, not expensive and easy to measure global marker of the expression of some seminal quality traits. Different methods were used to model the relationship between pH of the pool of ejaculates of each male in the day and male fertility (defined as the failure or the success to AI): 1) ignoring genetic and environmental correlations and including pH either as a covariate or as a cross-classified effect on fertility, 2) a two-trait mixed model, and 3) recursive two-trait mixed models. Crossbreed does from 2 maternal lines were artificially inseminated with buck semen from a paternal line in a commercial farm environment. A negative, and almost linear, effect of pH on fertility was detected. The semen pH and male fertility h2 were approximately 0.18 and approximately 0.10 across all the models, respectively. Genetic correlations between traits were negative, but the highest posterior density interval at 95% included zero in all the model were it was estimated. All models predicted fertility data reasonably well and the correlation between EBV (estimated breeding values) in all models was close to 1. Thus, no differences in results were obtained considering, or not considering, genetic and environmental correlations between pH and male fertility and assuming, or not assuming, recursiveness between each trait. This is because the magnitude of the effect of pH on fertility was not large enough and the low precission obtained for the parameter estimates. Therefore, the same results were obtained even though the models were of different complexity. From this chapter, it can be concluded that semen pH could be an interesting trait to be used to select qualitatively better ejaculates for AI to increase fertility. However, it does not seem to be advisable to use semen pH as a selection criterion to improve male fertility by indirect selection.
In Chapter 3, male and female contributions to fertility were jointly analysed using two different models: the additive threshold model and the product threshold model, both adequate for the analysis of binary AI results. The additive threshold model proposes that the underlying variable of fertility is the result of the sum of genetic and environmental effects of the two individuals involved in the mating whereas the product threshold model assumes that an observed AI outcome is the result of the product of two unobserved variables corresponding to the fertility of the two individuals involved in the mating. Both, the product and additive threshold models showed similar ability to predict an independent set of fertility data. For example, the percentage of wrong predictions was 38% in both models and they also did not differ in the mean square error of the prediction, the sensitivity and specificity of the prediction and in the positive and negative predicted values obtained. The product threshold model allows calculating the probabilities of fertility success for each sex as well as evaluating which sex is responsible for an AI failure. Male and female probabilities of a fertility success were similar and high (87% and 83%, respectively) and the percentages of AI failure specifically due to male and female fertility problems were 39% and 54%, respectively. Although estimates of the genetic correlation between male and female contributions to fertility were imprecise, both models showed similar values: 0.21 and 0.31 for the product and the additive model, respectively. However, interpretation of some of the parameter estimates obtained with the product threshold model (e.g. h2 and variance components) is not straightforward and cannot be compared with the corresponding figures obtained with the additive threshold model. The h2 for the male contribution to fertility was 0.17 and 0.04 in the product and additive threshold model, respectively. The correlation between the EBV for male and female contributions to fertility obtained in each model were close to 1 and the percentage of animals in common in the top 10% best/worst animals was high (more than 76%) in both models. Hence, from the point of view of selection in rabbits, irrespective of the model of choice, small changes in the evaluation of the individuals for fertility would be encountered.  
Previous studies concerning reproductive performance after natural mating in rabbits and in other livestock species reported an almost null male contribution. Chapter 4, aimed to explore if individual variation in the male contribution to fertility and prolificacy could be better observed under limited conditions of AI, such as decreased sperm concentration, small or null preselection of ejaculates for any semen quality trait, or a long storage period of the AI doses. Therefore, it was determined if an interaction existed between male genotype and the AI conditions for male effects on fertility and prolificacy after AI performed under different conditions. Fertility (success or failure to AI) and prolificacy (total number of kits born per litter) were analyzed in 2 sets of independent analyses and the existence of interaction was assessed in each set using the Character State model in which the phenotype measurements in the different environments were analysed as different traits. In the first step, the different AI conditions were determined uniquely by the sperm dosage (10 and 40 ×106 spermatozoa/mL). In the second step, the different conditions were determined by all the factors involved in the AI process as a whole (conditions and duration of the storage period of the dose, female genotype, and environmental conditions on the farm). Threshold and linear two-trait models were assumed for fertility and prolificacy, respectively. The sperm dosage had a clear effect on fertility and prolificacy, which favoured the greater dosage (+0.13% and +1.25 kits born, respectively). Prolificacy was more sensitive to sperm reduction than was fertility. Male h2 for fertility were 0.09 for both sperm dosages, and were 0.08 and 0.06 for male prolificacy with a smaller and larger sperm dosage, respectively. No genotype × sperm dosage interaction was found. Therefore, the same response to selection to improve male reproductive performance could be achieved at any sperm concentration. On the other hand, an interaction could exist between the male genotype and AI conditions for male effect on fertility and prolificacy, such as the time and storage conditions of the AI doses, the female genotype, or the environment. There could be a scale effect because of differences in the magnitude of the additive variances for male fertility and prolificacy after AI in the two AI conditions. Moreover, rankings of male EBV for those traits could differ depending on AI conditions because genetic correlations of fertility and prolificacy after AI at different conditions could be said to be different from 1 (the probability of a genetic correlation of being less than 0.75 was 83% for male fertility and 100% for male prolificacy). The existence of this interaction also implies that conditions that give the maximum genetic progress could be chosen to optimize the breeding program for male reproductive performance under given conditions of semen utilization. 
Last chapter of this thesis has aimed to determine the critical periods around the AI time in which the environmental temperature has a major effect on male and female contributions to fertility. To achieve that, we have used the product threshold model as it allows providing specific estimates of the effects affecting each one of the members involved in an AI outcome. Data of AI and records of indoor daily temperature were used. The average maximum daily temperature and the proportion of days of the period in which the maximum temperature was above 25ēC were used as temperature descriptors. These descriptors were calculated for several periods around the AI day. In the case of the males, four periods of time covered different stages of the spermatogenesis, the transit through the epididymus of the sperm and the AI day and fertilization. For the females, five periods of time covered the phases of pre-ovulatory follicular maturation, the AI day and ovulation, fertilization and peri-implantational stage of the embryos, the embryonic and early fetal periods of gestation and finally the late gestation until birth. The effect of the different temperature descriptors was estimated in the corresponding male and female liabilities in a set of threshold product models. The environmental temperature of the AI day seems to be the most relevant temperature descriptor affecting male fertility, since high temperature records in the AI day caused a decrease in male fertility (representing a loss of 6 % in male fertility with respect to thermo-neutrality). Departures from the thermo-neutral zone in temperature descriptors covering several periods before AI until early gestation had a negative effect on female fertility, being especially sensitive the peri-implantational period of the embryos (representing a loss of 5-6 % in male fertility with respect to thermo-neutrality). The latest period of gestation was unaffected by the temperature. We can conclude that the product threshold model allowed us to estimate that male and female fertility are specifically affected by temperature in different periods around the insemination time. However, the magnitude and the persistency of the temperatures reached in the commercial conditions of this study do not seem to be high enough to lead to a large effect on male and female rabbit fertility.