Anisotropic magnetofluid simulations are used to investigate the influence of several models of anisotropy reduction on the dynamic evolution of the magnetotail. Two distinct magnetotail dynamic models are studied: a nonresistive simulation driven by an external electric field as a representation of the substorm growth phase, and a resistive simulation with a uniform enhanced resistivity as a representation of the substorm expansive phase. The plasma models include one which is fully isotropic, the double adiabatic model in which pressures parallel and perpendicular to the background magnetic field are completely uncoupled, and a model in which small-scale instabilities impose an upper bound on the anisotropy. In this last model, anisotropies that exceed this bound are reduced on a short Alfvenic timescale. To investigate the transition to the fully isotropic model, a fourth plasma model is studied in which any anisotropy is reduced on the same short timescale. The growth phase magnetotail model is characterized by a localised increase in current density and by a reduction in the magnitude of B-z in the near-Earth neutral sheet; both of these effects are more pronounced for the more isotropic plasma models, For the expansive phase magnetotail model the development of a generalized tearing instability occurs faster and the substorm wedge currents grow stronger when the plasma model is closer to isotropy. In both magnetotail models the plasma anisotropy model strongly influences the spatial variation of B-z in the neutral sheet and hence the location where reconnection occurs and a neutral line forms. Both the driven and the unstable anisotropic models develop mirror-type anisotropies (p perpendicular to > p parallel to) in the (low beta or low current density) boundary regions of the plasma sheet and the adjacent lobes, while the (high beta or high current density) center region of the plasma/current sheet remains close to isotropy.