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\section{Root development}  The formation of LRs is a complex and highly coordinated process that depends on the interplay of hormones, where auxin acts as a central component. Indeed, the deficiency of many nutrients has been reported to affect the levels of one or more hormones in plants (for review, see Rubio et al., 2009).\cite{Giehl2014}.The response is conditionated by both the perception of the nutrient status by the plant and locally by the root(see {\cite{Forde2001}.for a review). root {\cite{Forde2001}  \subsection{Root changes to localized nutrient patches}  There is considerable literature concerning the localized responses of root systems to nutrient patches. \cite{Drew1975} reported an increase in lateral root initiation in response to phosphate, nitrate or ammonium patches.