Conservation Genetics

, Volume 8, Issue 2, pp 489–495 | Cite as

Evaluation of ancestral inbreeding coefficients: Ballou’s formula versus gene dropping

  • Surachai Suwanlee
  • Roswitha BaumungEmail author
  • Johann Sölkner
  • Ino Curik
Original Paper


Estimation of the purging of detrimental effects through inbreeding and selection is an important issue in conservation genetics opening new perspectives for the management of small populations. In 1997 Ballou proposed the ancestral inbreeding coefficient, which is calculated recursively via pedigree inbreeding coefficients, as a tool for evaluating the purging of deleterious alleles in zoo populations. The formula of Ballou assumes independence of inbreeding and ancestral inbreeding coefficients at any stage of the recursion. This study investigates the consequences of this inaccuracy on the estimation of true ancestral inbreeding, i.e. the proportion of alleles within a genome that has undergone inbreeding in the past. As an alternative we propose the estimation of ancestral inbreeding by the method of gene dropping. The methods are compared by stochastic simulation for various models with respect to mode of inheritance (neutral, detrimental and lethal alleles) and different settings for population size and initial allele frequencies. In all scenarios the proportion of alleles within a genome that has undergone inbreeding in the past was overestimated by Ballou’s formula. The overestimation was more pronounced in smaller populations but was not affected by genetic model or initial allele frequency. In contrast, the ancestral inbreeding coefficient calculated by gene dropping provided a robust estimate of ancestral inbreeding in most models and settings. A marginal overestimation was observed only in models with lethal alleles. Therefore, we recommend applying the gene dropping approach to estimate ancestral inbreeding coefficients.


Ancestral inbreeding Inbreeding depression Genetic load Purging Stochastic simulations 


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We are grateful to B. Tier for providing the algorithm to compute pedigree inbreeding coefficients and D. Tupajic for helping with the figure preparation. This research project was financial supported by the Royal Thai government.


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Surachai Suwanlee
    • 1
  • Roswitha Baumung
    • 1
    Email author
  • Johann Sölkner
    • 1
  • Ino Curik
    • 2
  1. 1.Division of Livestock SciencesUniversity of Natural Resources and Applied Life Sciences, Vienna (BOKU)ViennaAustria
  2. 2.Department of Animal Science, Faculty of AgricultureUniversity of ZagrebZagrebCroatia

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