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Characterization of Surface Modifications by White Light Interferometry: Applications in Ion Sputtering, Laser Ablation, and Tribology Experiments
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LEFKOVITCH'S ERROR.

James S Farris1, Mari Källersjö1

  • 1Molekylärsystematiska laboratoriet, Naturhistoriska riksmuseet, Box 50007 S-104 05 Stockholm, Sweden.

Cladistics : the International Journal of the Willi Hennig Society
|December 18, 2021
PubMed
Summary

Lefkovitch's formula for binary character incompatibility may be inaccurate. This occurs because it can overcount compatibilities when characters share the same number of apomorphic states, affecting phylogenetic analyses.

Area of Science:

  • Evolutionary Biology
  • Phylogenetics
  • Systematics

Background:

  • Assessing character compatibility is crucial in phylogenetic inference.
  • Lefkovitch's formula is a method used to calculate the probability of incompatibility between binary characters.

Purpose of the Study:

  • To identify and explain the source of inaccuracy in Lefkovitch's formula for binary character incompatibility.
  • To highlight the conditions under which the formula yields incorrect results.

Main Methods:

  • Analysis of Lefkovitch's formula for probability calculations.
  • Identification of redundant counting in compatibility assessments.
  • Examination of specific conditions leading to formula inaccuracy.

Main Results:

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  • Lefkovitch's formula can produce incorrect probabilities of incompatibility.
  • The inaccuracy arises from redundantly counting compatible character states.
  • This issue is specifically observed when characters exhibit an equal number of terminals in the apomorphic state.

Conclusions:

  • Lefkovitch's formula requires careful application due to potential inaccuracies.
  • Researchers should be aware of the conditions that lead to overcounting compatibilities.
  • Alternative or corrected methods may be needed for precise phylogenetic analyses involving binary characters.