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we simulated data with alf ( dalquen et al . 2012 ) using the same basic setup as in a previous simulation - based benchmarking study of orthology prediction ( dalquen et al .
2013 ) : we used a topology with 30 species sampled from the tree of 224 -proteobacteria as estimated by the oma project ( altenhoff et al .
the ancestral genome consisted of 1,000 amino acid sequences sampled from the stationary distribution of the wag substitution model ( whelan and goldman 2001 ) , which was also used to simulate substitutions .
sequence length was sampled from a gamma distribution fitted on gene lengths of bacterial genomes .
rates for insertions and deletions were   per pam per site , and the length of each insertion and deletion was sampled from a zipfian distribution with exponent parameter 1.821 ( benner and cohen 1993 ) .
we created five scenarios with different rates of gene duplications , based on the resulting proportion of genes with a duplication background .
apart from a baseline with no duplications or losses , we chose four proportions that lie within the range believed to be present in real species ( zhang 2003 ) , between 10% and 40% .
the gene loss rate was kept constant , coinciding with the duplication rate of the data set with 10% duplications ( 0.003 per gene per pam unit ) .
all simulations were repeated five times to get an estimate of the sampling variance ( given fixed parameters ) .
table 2key statistics for simulated data sets% duplications010203040parameters values  no . of sequences1,000  distr . of seq .
sequence length50  substitution modelwag  insertion and deletion rate0.000125  gene duplication rate00.0030.00560.0090.0125  gene loss rate00.003  no . of species30key statistics  seq .
% gap chars in msa24.2723.2524.6426.2328.65  variance of % gap chars58.062.866.472.480.5  total species tree length763.6  minimum species tree height31.70  maximum species tree height77.80  average species tree height41.36  average distance between species pairs72.60 key statistics for simulated data sets in addition , we created eight scenarios where we varied also the loss rate . in four scenarios , duplication and loss rates
of the remaining scenarios , one had a proportion of genes with a duplication background of 10% and a loss rate that was three times the duplication rate .
two had a proportion of 30% of genes with a duplication background and a loss rate of either one - third of or three times the duplication rate .
for the last scenario , we set the loss rate to zero and the proportion of genes with a duplication background to 40% .
finally , we repeated all simulations on a smaller set of 20 genomes , using as underlying species tree a random subsample of the tree of 37 mammalian species from the oma project ( altenhoff et al .
we assembled six data sets , covering all kingdoms of the tree of life . with two exceptions
, we used the trees of different classes as inferred by the oma project and pruned them to 20 leaves by repeatedly identifying the most closely related pair of species and removing one of them . for the fungi data
set , we used all 23 fungi species available in oma , and for the data set of viridiplantae , we used all 12 species that are part of oma ( see supplementary tables s1s6 , supplementary material online , for the list of species in each data set ) .
we did not assume any species tree , as the methods tested do not require one as input .
for the computation of bbh , we followed the methodology described by wolf and koonin ( 2012 ) . for each data
set , we performed pairwise all - against - all protein sequence alignments of all genomes , using blast with an e - value of 0.01 .
blast hits were considered bbh if they scored   of the top - scoring hit . alongside bbh , we also ran inparanoid 4.1 ( ostlund et al .
2010 ) and gethogs ( altenhoff et al . 2013 ) on the data sets . for the latter method , we used the option of inferring the species tree from the data and derived the set of induced orthologous gene pairs from the hierarchical groupings . on the simulated data sets , we compared the set of inferred pairwise orthologs of all three methods with the set of true orthologs given by the simulation . to assess the performance of bbh on real data , we compared its output with the union and intersection sets of orthologous pairs from inparanoid and gethogs , which we considered bona fide orthologs
we simulated data with alf ( dalquen et al . 2012 ) using the same basic setup as in a previous simulation - based benchmarking study of orthology prediction ( dalquen et al .
2013 ) : we used a topology with 30 species sampled from the tree of 224 -proteobacteria as estimated by the oma project ( altenhoff et al .
the ancestral genome consisted of 1,000 amino acid sequences sampled from the stationary distribution of the wag substitution model ( whelan and goldman 2001 ) , which was also used to simulate substitutions .
sequence length was sampled from a gamma distribution fitted on gene lengths of bacterial genomes .
rates for insertions and deletions were   per pam per site , and the length of each insertion and deletion was sampled from a zipfian distribution with exponent parameter 1.821 ( benner and cohen 1993 ) .
we created five scenarios with different rates of gene duplications , based on the resulting proportion of genes with a duplication background .
apart from a baseline with no duplications or losses , we chose four proportions that lie within the range believed to be present in real species ( zhang 2003 ) , between 10% and 40% .
the gene loss rate was kept constant , coinciding with the duplication rate of the data set with 10% duplications ( 0.003 per gene per pam unit ) .
all simulations were repeated five times to get an estimate of the sampling variance ( given fixed parameters ) .
table 2key statistics for simulated data sets% duplications010203040parameters values  no . of sequences1,000  distr . of seq .
sequence length50  substitution modelwag  insertion and deletion rate0.000125  gene duplication rate00.0030.00560.0090.0125  gene loss rate00.003  no . of species30key statistics  seq .
% gap chars in msa24.2723.2524.6426.2328.65  variance of % gap chars58.062.866.472.480.5  total species tree length763.6  minimum species tree height31.70  maximum species tree height77.80  average species tree height41.36  average distance between species pairs72.60 key statistics for simulated data sets in addition , we created eight scenarios where we varied also the loss rate . in four scenarios , duplication and loss rates
of the remaining scenarios , one had a proportion of genes with a duplication background of 10% and a loss rate that was three times the duplication rate .
two had a proportion of 30% of genes with a duplication background and a loss rate of either one - third of or three times the duplication rate .
for the last scenario , we set the loss rate to zero and the proportion of genes with a duplication background to 40% .
finally , we repeated all simulations on a smaller set of 20 genomes , using as underlying species tree a random subsample of the tree of 37 mammalian species from the oma project ( altenhoff et al .
we assembled six data sets , covering all kingdoms of the tree of life . with two exceptions
, we used the trees of different classes as inferred by the oma project and pruned them to 20 leaves by repeatedly identifying the most closely related pair of species and removing one of them . for the fungi data set , we used all 23 fungi species available in oma , and for the data set of viridiplantae , we used all 12 species that are part of oma ( see supplementary tables s1s6 , supplementary material online , for the list of species in each data set ) .
we did not assume any species tree , as the methods tested do not require one as input .
for the computation of bbh , we followed the methodology described by wolf and koonin ( 2012 ) . for each data set , we performed pairwise all - against - all protein sequence alignments of all genomes , using blast with an e - value of 0.01 .
blast hits were considered bbh if they scored   of the top - scoring hit . alongside bbh , we also ran inparanoid 4.1 ( ostlund et al .
2010 ) and gethogs ( altenhoff et al . 2013 ) on the data sets . for the latter method
, we used the option of inferring the species tree from the data and derived the set of induced orthologous gene pairs from the hierarchical groupings . on the simulated data sets , we compared the set of inferred pairwise orthologs of all three methods with the set of true orthologs given by the simulation . to assess the performance of bbh on real data , we compared its output with the union and intersection sets of orthologous pairs from inparanoid and gethogs , which we considered bona fide orthologs
supplementary figures s1s8 and tables s1s6 are available at genome biology and evolution online ( http://www.gbe.oxfordjournals.org/ ) .
bidirectional best hits ( bbh ) , which entails identifying the pairs of genes in two different genomes that are more similar to each other than either is to any other gene in the other genome , is a simple and widely used method to infer orthology . 
 a recent study has analyzed the link between bbh and orthology in bacteria and archaea and concluded that , given the very high consistency in bbh they observed among triplets of neighboring genes , a high proportion of bbh are likely to be bona fide orthologs . 
 however , limited by their analysis setup , the previous study could not easily test the reverse question : which proportion of orthologs are bbh ? in this follow - up study 
 , we consider this question in theory and answer it based on conceptual arguments , simulated data , and real biological data from all three domains of life . 
 our analyses corroborate the findings of the previous study , but also show that because of the high rate of gene duplication in plants and animals , as much as 60% of orthologous relations are missed by the bbh criterion .