Does Horton's law of branch length apply to open branching systems?

Abstract

Horton analysis has been applied to colonies of mycelial fungi and the mean branch lengths of branches per branch order tend to form a direct arithmetical, not geometric, series with branch order. Data for two botanical trees also show the arithmetical relationship. It is argued, from simulation models, that for branching systems showing outward unconstrained growth an arithmetical relationship results when linear growth rate of the elements is constant, but that a geometric relationship may result when linear growth rate shows a progressive decline.