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Acta Theriologica

, Volume 48, Issue 1, pp 25–34 | Cite as

Missing data in craniometrics: a simulation study

  • Olivier Gauthier
  • Pierre-Alexandre Landry
  • François-Joseph Lapointe
Article

Abstract

Craniometric measurements represent a useful tool for studying the differentiation of mammal populations. However, the fragility of skulls often leads to incomplete data matrices. Damaged specimens or incomplete sets of measurements are usually discarded prior to statistical analysis. We assessed the performance of two strategies that avoid elimination of observations: (1) pairwise deletion of missing cells, and (2) estimation of missing data using available measurements. The effect of these distinct approaches on the computation of inter-individual distances and population differentiation analyses were evaluated using craniometric measurements obtained from insular populations of deer micePeromyscus maniculatus (Wagner, 1845). In our simulations, Euclidean distances were greatly altered by pairwise deletion, whereas Gower’s distance coefficient corrected for missing data provided accurate results. Among the different estimation methods compared in this paper, the regression-based approximations weighted by coefficients of determination (r 2) outperformed the competing approaches. We further show that incomplete sets of craniometric measurements can be used to compute distance matrices, provided that an appropriate coefficient is selected. However, the application of estimation procedures provides a flexible approach that allows researchers to analyse incomplete data sets.

Key words

craniometry morphometry missing data estimation methods distance coefficients 

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References

  1. Genov P., Nikolov H., Massei G. and Gerasimov S. 1991. Craniometrical analysis of Bulgarian wild boar (Sus scrofa) populations. Journal of Zoology, London 225: 309–325.CrossRefGoogle Scholar
  2. Gower J. C. 1971. A general coefficient of similarity and some of its properties. Biometrics 27: 857–871.CrossRefGoogle Scholar
  3. Jolicoeur P. 1963. The multivariate generalization of the allometry equation. Biometrics 19: 497–499.CrossRefGoogle Scholar
  4. Koh H. S. and Peterson R. L. 1983. Systematics studies of deer mice,Peromyscus maniculatus Wagner (Cricetidae, Rodentia): analysis of age and secondary sexual variation in morphometric characters. Canadian Journal of Zoology 61: 2618–2628.CrossRefGoogle Scholar
  5. Landry P.-A. 2000. Effet de la configuration du paysage sur la variabilité génétique de populations de souris sylvestres (Peromyscus maniculatus: Rodentia, Muridae). PhD thesis, Université de Montréal, Montréal: 1–152.Google Scholar
  6. Landry P.-A. and Lapointe F.-J. 1999. The genetic heterogeneity of deer mouse (Peromyscus maniculatus) in an insular landscape. Researches on Population Ecology 41: 263–268.CrossRefGoogle Scholar
  7. Landry P.-A. and Lapointe F.-J. 2001. Within population craniometric variability of insular populations of deer mice,Peromyscus maniculatus, elucidated by landscape configuration. Oikos 95: 136–146.CrossRefGoogle Scholar
  8. Le Boulengé E., Legendre P., De Le Court C., Le Boulengé-Nguyen P. and Languy M. 1996. Microgeographic morphological differentiation in muskrats. Journal of Mammalogy 77: 684–701.CrossRefGoogle Scholar
  9. Legendre P. and Legendre L. 1998. Numerical ecology. Second ed. Elsevier Science B.V., Amsterdam: 1–853.Google Scholar
  10. Little R. J. A. 1988. A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association 83: 1198–1202.CrossRefGoogle Scholar
  11. Little R. J. A. and Rubin D. B. 1987. Statistical analysis with missing data. John Wiley & Sons, New York: 1–278.Google Scholar
  12. Lynch J. M. and Hayden T. J. 1995. Genetic influences on cranial form: variation among ranch and feral American minkMustela vison (Mammalia: Mustelidae). Biological Journal of the Linnean Society 55: 293–307.CrossRefGoogle Scholar
  13. Mahalanobis P. C. 1936. On the generalized distances in statistics. Proceeding of the National Institute of Science, India 2: 49–55.Google Scholar
  14. Mantel N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Research 27: 209–220.PubMedGoogle Scholar
  15. Okarma H. and Buchalczyk T. 1993. Craniometrical characteristics of wolvesCanis lupus from Poland. Acta Theriologica 38: 253–262.Google Scholar
  16. Rubin D. B. 1976. Inference with missing data. Biometrika 63: 581–592.CrossRefGoogle Scholar
  17. van Zyll de Jong C. G. and Kirkland G. L. Jr 1989. A morphometric analysis of theSorex cinereus group in central and eastern North America. Journal of Mammalogy 70: 110–122.CrossRefGoogle Scholar
  18. van Zyll de Jong C. G. and Nagorsen D. W. 1994. A review of the distribution and taxonomy ofMyotis keenii andMyotis evotis in British Columbia and the adjacent United States. Canadian Journal of Zoology 72: 1069–1078.CrossRefGoogle Scholar

Copyright information

© Mammal Research Institute, Bialowieza, Poland 2003

Authors and Affiliations

  • Olivier Gauthier
    • 1
  • Pierre-Alexandre Landry
    • 2
  • François-Joseph Lapointe
    • 1
  1. 1.Département de sciences biologiquesUniversité de Montréal C. P. 6128QuébecCanada
  2. 2.Metapopulation Research Group, Division of Population BiologyDepartment of Ecology and SystematicsFINFinland (P-AL)

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