Current theories and models of the formation of phyllotactic patterns at plant apical meristems center on either transport of the growth hormone auxin or the mechanical buckling of the plant tunica. By deriving a continuum approximation of an existing discrete biochemical model and comparing it with a mechanical model, we show that the model partial differential equations are similar in form. The implications of this universality in the form of the equations on interpreting the results of simulations are discussed. We develop a combined model that incorporates the coupling of biochemistry and mechanics. The combined model is accessible to analysis by reduction to a set of ordinary differential equations for the amplitudes of shapes associated with both the auxin concentration field and plant surface deformation. Analysis of these amplitude equations reveals the parameter choices under which the two mechanisms may cooperate in determining the pattern, or under which one or the other mechanism may dominate.