Samples of phylogenetic trees arise in a variety of evolutionary and biomedical applications, and the Fréchet mean in Billera-Holmes-Vogtmann tree space is a summary tree shown to have advantages over other mean or consensus trees. However, use of the Fréchet mean raises computational and statistical issues which we explore in this paper. The Fréchet sample mean is known often to contain fewer internal edges than the trees in the sample, and in this circumstance calculating the mean by iterative schemes can be problematic due to slow convergence. We present new methods for identifying edges which must lie in the Fréchet sample
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