Analysis of lambing distribution in the Ripollesa sheep breed. II. Environmental and genetic sources of variation

Abstract

Seasonal reproduction patterns are typically observed in small ruminants and are a major limitation for production efficiency in most meat- and dairy-type production systems. Indeed, selection for reduced seasonality could be an appealing strategy for the small ruminant industry worldwide, although its genetic background has been poorly analyzed. One of the main limitations relied on the availability of appropriate analytical tools to cope with the circular (i.e. year-round) pattern of lambing and kidding data. The recent development of a heteroskedastic circular mixed model provided the statistical tool to go deeply into the knowledge of seasonality in small ruminants. In this study, 26 005 lambing distribution records from 4764 Ripollesa ewes collected in 20 purebred flocks were analyzed. The model accounted for systematic (lambing interval and ewe age), permanent environmental (flock-year-season and ewe) and additive genetic sources of variation influencing both mean and dispersion pattern (i.e. heteroskedasticity). Systematic effects suggested that first-lambing ewes and short lambing intervals delayed lambing date (~30 days) and increased dispersion of the lambing period. Nevertheless, this was partially compensated by ewe age, given that youngest females tended to concentrate the lambing peak. Flock-year-season, permanent ewe and additive genetic sources of variation reached moderate variance components for direct (and residual) effects on lambing distribution, they being 0.119 (0.156), 0.092 (0.132) and 0.195 (0.170) radians2, respectively. Moreover, all 95% credibility intervals were placed far from the null estimate. Covariances between direct and residual effects where high and positive for additive genetic (posterior mean, 0.814) and permanent ewe effects (posterior mean, 0.917), whereas it was not relevant for flock-year-season. Selection for direct additive genetic effects should be able to advance or delay the lambing peak, whereas selection applied on residual additive genetic effects should increase or reduce seasonality (i.e. concentrate or flatten the lambing peak). Moreover, the positive and relevant genetic covariance between direct and residual effects also suggested correlated genetic responses. As example, genetic selection for earlier lambing peaks must also reduce seasonality, whereas selection for narrower lambing seasons may originate a delay in the lambing peak. These results must be viewed as the first attempt to analyze systematic, environmental and genetic sources of variation of lambing distribution within the circular paradigm, they providing a reliable characterization of these effects within the context of an heteroskedastic model.

Analyses of lambing dates in sheep breeds using von Mises distribution

“…An additional model to analyse circular records in‐depth is the extended circular mixed model with heterogeneous variance (canalization circular model) developed by Casellas, Id‐Lahoucine, et al. (2019), Casellas, Martín de Hijas‐Villalba, et al. (2019).…”

“…Thus, this model assumes the presence of additive genetic effects (as fixed and other random effects) affecting the residual term (i.e., effects originated/controlling heterogeneous environmental variance; see Casellas, Id‐Lahoucine, et al. (2019), Casellas, Martín de Hijas‐Villalba, et al. (2019) for details).…”

“…In the context of canalization models, as seasonality is associated with a concentration of lambing in specific periods, the increase in the residual variance could be a hypothetical plausible strategy to reduce seasonality as proposed by Casellas, Id‐Lahoucine, et al. (2019). In contrast, selection for reducing the residual variance may potentially generate even more concentrated lambing peaks.…”

“…In contrast, selection for reducing the residual variance may potentially generate even more concentrated lambing peaks. Thus, the canalization circular model, with genetic sources of variation affecting the residual effects, offers opportunities for selection to increase residual variance and reduce seasonality (Casellas, Id‐Lahoucine, et al., 2019). However, the circular model has not been tested with simulated data or compared with traditional linear models yet.…”

“…In animal breeding, circular data have not received attention because of complicated statistical analysis and the general propensity of animal breeders to transform nonlinear to linear data (Erdem & Shi, 2011). Recently, Casellas, Id‐Lahoucine and Martín de Hijas‐Villalba (2019), Casellas, Martín de Hijas‐Villalba and Id‐Lahoucine (2019) derived the circular mixed model generalized from the Mulder and Klugkist (2017) circular model based on the von Mises distribution (Fisher, 1993). The circular model was adapted to include random sources of variations under the homogeneous variance model and also extended to account for partly genetic effects underlying the heterogeneity of environmental variance (i.e., canalization model) as proposed by SanCristobal‐Gaudy et al.…”