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Statistical measures of uncertainty for branches in phylogenetic trees inferred from molecular sequences by using model-based methods

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Wrobel B.

Journal of Applied Genetics

2008

vol. 49

issue 1

49-67

In recent years, the emphasis of theoretical work on phylogenetic inference has shifted from the development of new tree inference methods to the development of methods to measure the statistical support for the topologies. This paper reviews 3 approaches to assign support values to branches in trees obtained in the analysis of molecular sequences: the bootstrap, the Bayesian posterior probabilities for clades, and the interior branch tests. In some circumstances, these methods give different answers. It should not be surprising: their assumptions are different. Thus the interior branch tests assume that a given topology is true and only consider if a particular branch length is longer than zero. If a tree is incorrect, a wrong branch (a low bootstrap or Bayesian support may be an indication) may have a non-zero length. If the substitution model is oversimplified, the length of a branch may be overestimated, and the Bayesian support for the branch may be inflated. The bootstrap, on the other hand, approximates the variance of the data under the real model of sequence evolution, because it involves direct resampling from this data. Thus the discrepancy between the Bayesian support and the bootstrap support may signal model inaccuracy. In practical application, use of all 3 methods is recommended, and if discrepancies are observed, then a careful analysis of their potential origins should be made.

National evaluation for calving ease, gestation length and birth weight by linear and threshold model methodologies

100%

Lee D., Misztal I., Bertrand J. K., Rekaya R.

Data included 393 097 calving ease, 129 520 gestation length, and 412 484 birth weight records on 412 484 Gelbvieh cattle. Additionally, pedigrees were available on 72 123 animals. Included in the models were effects of sex and age of dam, treated as fixed, as well as direct, maternal genetic and permanent environmental effects and effects of contemporary group (herd-year-season), treated as random. In all analyses, birth weight and gestation length were treated as continuous traits. Calving ease (CE) was treated either as a continuous trait in a mixed linear model (LM), or as a categorical trait in linear-threshold models (LTM). Solutions in TM obtained by empirical Bayes (TMEB) and Monte Carlo (TMMC) methodologies were compared with those by LM. Due to the computational cost, only 10 000 samples were obtained for TMMC. For calving ease, correlations between LM and TMEB were 0.86 and 0.78 for direct and maternal genetic effects, respectively. The same correlations but between TMEB and TMMC were 1.00 and 0.98, respectively. The correlations between LM and TMMC were 0.85 and 0.75, respectively. The correlations for the linear traits were above .97 between LM and TMEB but as low as 0.91 between LM and TMMC, suggesting insufficient convergence of TMMC. Computing time required was about 2 hrs, 5 hrs, and 6 days for LM, TMEB and TMMC, respectively, and memory requirements were 169, 171, and 445 megabytes, respectively. Bayesian implementation of threshold model is simple, can be extended to multiple categorical traits, and allows easy calculation of accuracies; however, computing time is prohibitively long for large models.

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2 Journal of Applied Genetics

1 2008

1 2002

1 Bertrand J. K.

1 Lee D.

1 Misztal I.

1 Rekaya R.

1 Wrobel B.

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Statistical measures of uncertainty for branches in phylogenetic trees inferred from molecular sequences by using model-based methods

National evaluation for calving ease, gestation length and birth weight by linear and threshold model methodologies