Causal relationships between milk quality and coagulation properties in Italian Holstein-Friesian dairy cattle

Background: Recently, selection for milk technological traits was initiated in the Italian dairy cattle industry based on direct measures of milk coagulation properties (MCP) such as rennet coagulation time (RCT) and curd firmness 30 min after rennet addition (a30) and on some traditional milk quality traits that are used as predictors, such as somatic cell score (SCS) and casein percentage (CAS). The aim of this study was to shed light on the causal relationships between traditional milk quality traits and MCP. Different structural equation models that included causal effects of SCS and CAS on RCT and a30 and of RCT on a30 were implemented in a Bayesian framework. Results: Our results indicate a non-zero magnitude of the causal relationships between the traits studied. Causal effects of SCS and CAS on RCT and a30 were observed, which suggests that the relationship between milk coagulation ability and traditional milk quality traits depends more on phenotypic causal pathways than directly on common genetic influence. While RCT does not seem to be largely controlled by SCS and CAS, some of the variation in a30 depends on the phenotypes of these traits. However, a30 depends heavily on coagulation time. Our results also indicate that, when direct effects of SCS, CAS and RCT are considered simultaneously, most of the overall genetic variability of a30 is mediated by other traits. Conclusions: This study suggests that selection for RCT and a30 should not be performed on correlated traits such as SCS or CAS but on direct measures because the ability of milk to coagulate is improved through the causal effect that the former play on the latter, rather than from a common source of genetic variation. Breaking the causal link (e.g. standardizing SCS or CAS before the milk is processed into cheese) would reduce the impact of the improvement due to selective breeding. Since a30 depends heavily on RCT, the relative emphasis that is put on this trait should be reconsidered and weighted for the fact that the pure measure of a30 almost double-counts RCT

On the Primary Coverings of Finite Solvable and Symmetric Groups

A primary covering of a finite group $G$ is a family of proper subgroups of $G$ whose union contains the set of elements of $G$ having order a prime power. We denote with $\sigma_0(G)$ the smallest size of a primary covering of $G$, and call it the primary covering number of $G$. We study this number and compare it with its analogous $\sigma(G)$, the covering number, for the classes of groups $G$ that are solvable and symmetric

Improving social game engagement on Facebook through enhanced socio-contextual information

In this paper we describe the results of a controlled study of a social game, Magpies, which was built on the Facebook Online Social Network (OSN) and enhanced with contextual social information in the form of a variety of social network indices. Through comparison with a concurrent control trial using an identical game without the enhanced social information, it was shown that the additional contextual data increased the frequency of social activity between players engaged in the game. Despite this increase in activity, there was little increase in growth of the player-base when compared to the control condition. These findings corroborate previous work that showed how socio-contextual enhancement can increase performance on task-driven games, whilst also suggesting that it can increase activity and engagement when provided as context for non task-driven game environments