2014/06/05 by Cécile Ané, Ané, Cécile, Lam Tung Ho +3 · 1 citation
Environmental Science · #Animal Ecology and Behavior Studies #Computational Engineering #Ecology and Vegetation Dynamics Studies #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Finance #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Statistics Theory (math.ST) #Wildlife Ecology and Conservation #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1406.1568
openalex publication_date 2014/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Diffusion processes on trees are commonly used in evolutionary biology to\nmodel the joint distribution of continuous traits, such as body mass, across\nspecies. Estimating the parameters of such processes from tip values presents\nchallenges because of the intrinsic correlation between the observations\nproduced by the shared evolutionary history, thus violating the standard\nindependence assumption of large-sample theory. For instance Ho and An 'e\n citeHoAne13 recently proved that the mean (also known in this context as\nselection optimum) of an Ornstein-Uhlenbeck process on a tree cannot be\nestimated consistently from an increasing number of tip observations if the\ntree height is bounded. Here, using a fruitful connection to the so-called\nreconstruction problem in probability theory, we study the convergence rate of\nparameter estimation in the unbounded height case. For the mean of the process,\nwe provide a necessary and sufficient condition for the consistency of the\nmaximum likelihood estimator (MLE) and establish a phase transition on its\nconvergence rate in terms of the growth of the tree. In particular we show that\na loss of \√(n)-consistency (i.e., the variance of the MLE becomes\n\Ω(n-1), where n is the number of tips) occurs when the tree growth\nis larger than a threshold related to the phase transition of the\nreconstruction problem. For the covariance parameters, we give a novel,\nefficient estimation method which achieves \√(n)-consistency under natural\nassumptions on the tree.\n