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We study the formation of auxin peaks in a generic class ofconcentration-based auxin transport models, posed on static plant tissues.Using standard asymptotic analysis we prove that, on bounded domains, auxinpeaks are not formed via a Turing instability in the active transportparameter, but via simple corrections to the homogeneous steady state. When theactive transport is small, the geometry of the tissue encodes the peaks'amplitude and location: peaks arise where cells have fewer neighbours, that is,at the boundary of the domain. We test our theory and perform numericalbifurcation analysis on two models which are known to generate auxin patternsfor biologically plausible parameter values. In the same parameter regimes, wefind that realistic tissues are capable of generating a multitude of stationarypatterns, with a variable number of auxin peaks, that can be selected bydifferent initial conditions or by quasi-static changes in the active transportparameter. The competition between active transport and production ratedetermines whether peaks remain localised or cover the entire domain. We relatethe occurrence of localised patterns to a snaking bifurcation structure, whichis known to arise in a wide variety of nonlinear media but has not yet beenreported in plant models.

Localised auxin peaks in concentration-based transport models of the shoot apical meristem