The objective of this work was to present a reparametrization of a means deviation model from contemporary groups up to an unrestricted animal model (Lush's mixed model equations - LMME). Applying restrictions on the LMME, the animal model was obtained in accordance with Henderson (Henderson's mixed model equations - HMME). To obtain the HMME, restrictions of the type <img border=0 width=32 height=32 id="_x0000_i1028" src="../../../../img/revistas/rbz/v28n3/a07fr1.gif">were imposed and these demanded the necessity of unrealistic assumptions, as the absence of selection, so that the HMME properties could be proved. For the different examined situations, the restrictions were confirmed. The summation of these restrictions can be incorrectly understood as property of the solutions of an animal model in that the animals-base have the summation of their genetic values equal to zero.
mixed model under selection; genetic property; reparameterization; restriction
