title: Algorithmic approaches to aid species' delimitation in multidimensional morphospace.
abstract: BACKGROUND
  The species is a fundamental unit of biological pattern and process, but its delimitation has proven a ready source of argument and disagreement. Here, we discuss four key steps that utilize statistical thresholds to describe the morphological variability within a sample and hence assess whether there is evidence for one or multiple species. Once the initial set of biologically relevant traits on comparable individuals has been identified, there is no need for the investigator to hypothesise how specimens might be divided among groups, nor the traits on which groups might be separated.
  
  
  RESULTS
  Principal components are obtained using robust covariance estimates and retained only if they exceed threshold amounts of explanatory power, before model-based clustering is performed on the dimension-reduced space. We apply these steps in an attempt to resolve ongoing debates among taxonomists working on the extinct Eocene planktonic foraminifera Turborotalia, providing statistical evidence for two species shortly before the lineage's extinction near the Eocene/Oligocene boundary.
  
  
  CONCLUSIONS
  By estimating variance robustly (samples containing incipient species are unlikely to be scaled optimally by means and standard deviations) and identifying thresholds relevant to a particular system rather than universal standards, the steps of the framework aim to optimize the chances of delineation without imposing pre-conceived patterns onto estimates of species limits.
authors.affiliation: Imperial College London, Silwood Park Campus, Ascot, Berkshire, UK. thomas.ezard@imperial.ac.uk
authors.forename: Thomas H G
authors.initials: TH
authors.lastname: Ezard
authors.forename: Paul N
authors.initials: PN
authors.lastname: Pearson
authors.forename: Andy
authors.initials: A
authors.lastname: Purvis
mesh_terms: D000465:Algorithms; D000818:Animals; D016000:Cluster Analysis; D056908:Foraminifera / Q000145:classification* / Q000235:genetics; D049810:Genetic Speciation; D008954:Models, Biological; D015233:Models, Statistical; D025341:Principal Component Analysis; D013045:Species Specificity