  We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase
spaces can be used to treat a wide family of spin systems which exhibits
squeezing and entanglement effects. This algebraic framework is then applied to
the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time
evolution of certain special parameters related to the
Robertson-Schr\"{o}dinger (RS) uncertainty principle and some particular
proposals of entanglement measure based on collective angular-momentum
generators. Our results reinforce the connection between both the squeezing and
entanglement effects, as well as allow to investigate the basic role of spin
correlations through the discrete representatives of quasiprobability
distribution functions. Entropy functionals are also discussed in this context.
The main sequence correlations -> entanglement -> squeezing of quantum effects
embraces a new set of insights and interpretations in this framework, which
represents an effective gain for future researches in different spin systems.
