BACKGROUND
the last decade has seen the advances in the field of demographic history involving gene flow of domesticated species  <cit> , <cit> .
initially, the studies of demographic history involving gene flow were mainly focused on crop plants  <cit> .
the studies of domesticated animals, although they are crucial for human beings, are relatively lagged behind that of crop plants  <cit> .
until recently, some studies have investigated demography of domesticated animals, such as dog  <cit> , chicken  <cit>  and pig  <cit> .
when considerable attention has been focused on these species, the same as domesticated species, few similar evolutionary studies have involved the domesticated silkworm, bombyx mori.
the domesticated silkworm, b. mori, is an economically important insect, and widely distributed in many regions especially china, korea, japan and india  <cit> .
in addition to its economic importance for farmers in these countries, the domesticated silkworm is a model of lepidopteran insects in basic research because of its short life cycle, and adaptation to laboratory culture  <cit> .
the draft genome sequences of the domesticated silkworm were completed in  <dig>  <cit> , <cit>  and a new assembly of the genome sequence as well as the resequencing data were released in  <dig>  <cit>  and in  <dig>  <cit> .
these advances have also greatly promoted research on silkworm functional and evolutionary genomics.
with re-sequencing data of representative domesticated silkworm strains and wild silkworm samples from diverse geographic regions, the candidates of domestication genes were identified  <cit> .
however, one puzzling observation in this study is that, although domesticated strains are clearly genetically differentiated from the wild ones, they still harbor ~83% of the variation observed in wild silkworm  <cit> .
later, using genetic evidence and coalescent simulation method, we showed that the domesticated silkworm lost 33-49% of nucleotide diversity relative to wild silkworm, which may attribute to a historical bottleneck during its domestication  <cit> .
furthermore, we investigated the phylogeny and evolutionary history of silkworm based on both mitochondrial loci and nuclear loci sequences  <cit> .
however, some issues about inference of the demographic history involving gene flow of b. mori remain unresolved.
probably, the lack of sophisticated statistical methods limits the study of demographic history of silkworm.
fortunately, the latest approximate bayesian computation  method is suitable for assuming different demographic models in bayesican framework to infer evolutionary history of model species  <cit> – <cit> .
a growing number of studies have demonstrated that gene flow between wild and domesticated animal populations during domestication occurred frequently  <cit> .
typical evidence was found not only in pigs  <cit> , sheep and goats  <cit> , as well as bactrian camel  <cit>  but also in domesticated crop plants genus zea <cit>  and pearl millet  <cit> .
however, the demographic history of silkworm involving gene flow has not been investigated.
because gene flow likely occurred in different phases of the whole demographic history of silkworm, in this study we first referred the evolutionary models of the crop species mentioned above and hypothesized different evolutionary models to describe the demographic history of b. mori.
then, we evaluated the most possible demographic scenario using the coalescent simulation and abc method  <cit> , <cit>  by combining the available nuclear dna sequences and our newly sequenced data.
additionally, we also discussed the introgression pattern based on inferred evolutionary scenario with the goal of understanding the demographic history of silkworm.
RESULTS
the characteristics of data used in this study
to avoid the effect of artificial selection and natural selection on the inference of the demographic history of silkworm as well as the detection of gene flow, we chose  <dig> loci that show neutral evolution in our previous studies  <cit> , <cit> .
furthermore, tajima’s test  <cit>  on each of  <dig> newly sequenced loci is not significant , suggesting that these loci evolved in a neutral manner.
thus, all of  <dig> loci used in this study show a neutral evolution pattern.
demographic history of silkworm
to investigate the occurrence of gene flow between the domesticated and wild silkworms, the demographic history of silkworm domestication was estimated by using coalescent simulation and abc method.
four models  were assumed .
eight demographic parameters  were estimated.
the posterior density curve of each parameter for each model was also calculated .
these parameters can be converted into effective population size  and time in years using the formulation of θ = 4neμ and in units of 4 n <dig> generations, assuming the mutation rate μ =  <dig>  × 10−8/bp/generation  <cit> .
the values of these parameters are calculated .
we found that four models have very different parameter values.
for example, nb <dig> is equal to ~ <dig>  individuals :  <dig>  –  <dig> ) in the ‘no gene flow’ model, ~ <dig>  individuals  in the ‘continuous gene flow’ model, ~ <dig>  individuals  in the ‘gene flow at bottleneck’ model, and ~ <dig>  individuals  in the ‘gene flow after bottleneck’ model; td is equal to ~ <dig>  years  in the ‘no gene flow’ model, ~ <dig>  years  in the ‘continuous gene flow’ model, ~ <dig>  years  in the ‘gene flow at bottleneck’ model, and ~ <dig>  years  in the ‘gene flow after bottleneck’ model.
to determine which model is the most likely scenario for silkworm domestication, the value of bayes factor  was calculated.
the results showed that the maximum value of k was produced by ‘gene flow at bottleneck’ model .
according to this model, the scenario for silkworm domestication was as follows.
the effective population sizes of the domesticated silkworm population at the modern and bottleneck stages are  <dig>  :  <dig>  –  <dig> ) and  <dig>  , respectively.
additionally, we also estimated the divergence time: the starting time of the domestication is ~ <dig>  years ago ; the time of bottleneck ended in the domesticated silkworm is ~ <dig>  years ago  .
this model showed that gene flow occurred at the bottleneck stage during silkworm domestication.
however, the direction of gene flow between the domesticated silkworm and wild silkworm is still unknown.
k: bayes factor; πsilent-d: πsilent values for b. mori; ssilent-d: ssilent values for b. mori.
parameters of the preferred model were estimated.
θ and τ are converted to n and t  respectively.
conversion procedure is based on the equation θ = 4n1μ, neutral mutation rate μ =  <dig>  × 10− <dig> per site per generation was used.
detection of gene flow direction
to determine the direction of gene flow between the two populations, three models were assumed .
based on these models, simulations were performed by using the software of migrate  <dig> .
<dig>  the results showed that the model probabilities of model a, model b and model c are  <dig> ,  <dig>  and  <dig> , respectively .
this indicates that model a with the bidirectional gene flow during bottleneck is the most likely scenario.
accordingly, we estimated the migration rates.
the migration rate from wild to domesticated silkworms is  <dig>    while the migration rate from domesticated to wild silkworms is  <dig>  .
to further confirm bidirectional gene flow occurred during silkworm domestication, the ima program was used to perform simulation analysis  <cit> , <cit> .
likelihood-ratio test on bidirectional migration between ancestral sub-populations is significant .
the maximum likelihood estimates of the bidirectional migration rate from wild to domesticated silkworm population  and from domesticated to wild silkworm population  are  <dig>   and  <dig>   , respectively .
this further suggests that the bidirectional migration might occur during silkworm domestication.
furthermore, the results of both approaches suggested that the migration rate from domesticated to wild silkworms is larger than that from wild to domesticated silkworms.
d: b. mori; w: b. mandarina; lbf: log bayes factor.
discussion
since the genome sequence of the domesticated silkworm was completed, many studies have used the genome-wide nuclear data and the classic sequencing data of individual nuclear loci to infer the demography and domestication of silkworm  <cit> – <cit> , <cit> , <cit> .
although these studies provide a lot of useful information for understanding the origin and domestication of the domesticated silkworm, they appear to ignore detection of gene flow between the domesticated and wild populations.
previous studies based on the nuclear genome data suggested that the domesticated silkworm lost only approximately 17% of nucleotide diversity measured by θ relative to wild silkworm  <cit> .
however, our previous studies revealed that the domesticated silkworm lost 33-49% of nucleotide diversity measured by θ relative to wild silkworm and experienced a severe bottleneck during domestication  <cit> , <cit> , <cit> .
as indicated previously, the main reason leading to this big difference is that studies based on solexa sequencing data might have underestimated the level of nucleotide diversity in wild silkworm  <cit> .
the nucleotide diversity in the domesticated silkworm was found to be at a very similar level measured as θ between the classic sequencing data and solexa resequencing data, however, the nucleotide diversity in wild silkworm was greatly underestimated when the solexa resequencing data were used  <cit> .
the possible reason is that the genome sequence of wild silkworm, b. mandarina, has not been available to date, thus, the genome sequence of the domesticated silkworm was used as a reference for calling snps in both the domesticated and wild silkworms.
because resequencing reads are usually short , some mapping algorithms cannot map sequence reads with more than one or two differences from a reference genome sequence  <cit> .
thus, we decided to reconsider the demographic history of the domesticated silkworm using a combined data set of nuclear loci by classic sequencing rather than the whole genome resequencing data by solexa.
it will be good time to better infer the demographic history of the domesticated silkworm using the whole genome resequencing data only when the genome sequence of wild silkworm, b. mandarina, is available in future.
since previous studies have ignored the detection of gene flow between the domesticated and wild silkworms  <cit> – <cit> , <cit> , this study intended to detect possible introgression pattern of the domesticated and wild populations.
currently, very few studies had investigated the evolutionary pattern of the domesticated silkworm, b. mori.
therefore, quite limited available model information could be used when we started to investigate the demographic history of the domesticated silkworm.
using previous studies on historical divergence and gene flow of genus zea and pearl millet as references  <cit> , <cit> , therefore, we hypothesized four evolutionary scenarios by adding gene flow to reconsider the silkworm’s domestication.
we found that the ‘gene flow at bottleneck’ model is the most likely scenario.
according to this model, the starting time of the silkworm domestication is ~ <dig>  years ago ; the time of bottleneck ended in the domesticated silkworm is ~ <dig>  years ago .
these results are consistent with our previous results based on the phylogenetic analyses in which the domestication of silkworm was estimated to occur about  <dig>  years ago  <cit> .
in addition, the estimate of the silkworm domestication time is also well consistent with the domestication time estimates of rice  as well as maize   <cit> , <cit> .
these results are nearly consistent with the evidence from fossils  <cit> .
in addition, the domestication time of most livestock can be traced back to  <dig> - <dig>  years ago  <cit> .
our divergence timing estimation is also within the timeframe.
therefore, our results are reasonable.
coalescent simulation indicated that the gene flow might occur during the period of bottleneck.
three possible reasons may explain this.
first, the overlapping geographic regions between the domesticated and wild silkworm populations might facilitate the gene flow  <cit> .
wild silkworm is not only widely distributed in the regions of jiangsu and zhejiang provinces, but also can be found in anhui and shandong provinces in china.
interestingly, these areas are also the main regions of sericulture  <cit> .
second, the lack of the absolute reproductive isolation is likely to be another important factor that leads to gene flow between the populations.
in fact, the domesticated and wild silkworms have not formed the completely reproductive isolation up to now.
they are able to interbreed with each other.
this may provide some convenience for gene exchanging between these two species.
third, the environmental factors may also provide opportunities for gene flow between the populations during silkworm domestication.
the initial rearing conditions of the domesticated silkworm may be very simple and open compared with present-day’s rearing environments  <cit> .
this may also increase the opportunities of contact and hybridization between the domesticated and wild silkworms.
besides these factors, economic expansion and urbanization might also affect gene flow.
rapid economic expansion and intensive urbanization may be common causes of the habitat fragmentation and may eventually reduce the gene flow on wildlife populations between different fragmented landscapes  <cit> , <cit> .
thus economic expansion and urbanization could be the reasons of why gene flow occurred at the period of bottleneck rather than at the recent.
to determine the direction of gene flow during bottleneck, simulations were performed by using the software of migrate  <dig> .
<dig>  the results indicated that bidirectional gene flow during the bottleneck period between the populations is the most likely scenario .
in addition, the im simulation results also supported the bidirectional gene migration between the domesticated and wild silkworm populations rather than the unidirectional gene flow model .
the gene flow direction from the domesticated silkworm to wild silkworm might be caused by the situation that the domesticated silkworms were discarded together with their excrement into natural environment  <cit> .
the gene flow from wild silkworm to the domesticated silkworm might be because of that wild silkworm was introduced by breeders, as an important genetic source, to hybrid with the domesticated silkworm to produce desirable strains  <cit> , <cit> .
in this study, we revealed that there was gene flow between the domesticated and wild silkworms.
our finding is consistent with the observations in maize  <cit> , pig  <cit> , <cit> , chicken  <cit> , cattle  <cit> , <cit> , cats  <cit> , horses  <cit> , and honeybee  <cit> .
it appears that gene flow is ubiquitous between domesticated species and their wild relatives.
our results may add a dimension to highlight the important role of gene flow in domestication of crops and animals.
furthermore, as more and more population genomics data become available and new statistical methods are developed, we believe that long-standing questions about the role of gene flow in species formation will be resolved soon  <cit> .
CONCLUSIONS
in this study, we hypothesized different models to describe the demographic history and the gene flow between b. mori and its wild relative, b. mandarina.
the starting time of silkworm domestication was estimated to be approximate  <dig>  years ago; the time of domestication termination was  <dig>  years ago.
bi-directional gene flow might occur during silkworm domestication.
our findings add a dimension to highlight the important role of gene flow in domestication of crops and animals.

 the last decade has seen the advances in the field of demographic history involving gene flow of domesticated species,. initially, the studies of demographic history involving gene flow were mainly focused on crop plants. the studies of domesticated animals, although they are crucial for human beings, are relatively lagged behind that of crop plants. until recently, some studies have investigated demography of domesticated animals, such as dog, chicken and pig. when considerable attention has been focused on these species, the same as domesticated species, few similar evolutionary studies have involved the domesticated silkworm, bombyx mori. the domesticated silkworm, b. mori, is an economically important insect, and widely distributed in many regions especially china, korea, japan and india. in addition to its economic importance for farmers in these countries, the domesticated silkworm is a model of lepidopteran insects in basic research because of its short life cycle, and adaptation to laboratory culture. the draft genome sequences of the domesticated silkworm were completed in, and a new assembly of the genome sequence as well as the resequencing data were released in and in. these advances have also greatly promoted research on silkworm functional and evolutionary genomics. with re-sequencing data of representative domesticated silkworm strains and wild silkworm samples from diverse geographic regions, the candidates of domestication genes were identified. however, one puzzling observation in this study is that, although domesticated strains are clearly genetically differentiated from the wild ones, they still harbor ~83% of the variation observed in wild silkworm. later, using genetic evidence and coalescent simulation method, we showed that the domesticated silkworm lost 33-49% of nucleotide diversity relative to wild silkworm, which may attribute to a historical bottleneck during its domestication. furthermore, we investigated the phylogeny and evolutionary history of silkworm based on both mitochondrial loci and nuclear loci sequences. however, some issues about inference of the demographic history involving gene flow of b. mori remain unresolved. probably, the lack of sophisticated statistical methods limits the study of demographic history of silkworm. fortunately, the latest approximate bayesian computation method is suitable for assuming different demographic models in bayesican framework to infer evolutionary history of model species –. a growing number of studies have demonstrated that gene flow between wild and domesticated animal populations during domestication occurred frequently. typical evidence was found not only in pigs, sheep and goats, as well as bactrian camel but also in domesticated crop plants genus zea and pearl millet. however, the demographic history of silkworm involving gene flow has not been investigated. because gene flow likely occurred in different phases of the whole demographic history of silkworm, in this study we first referred the evolutionary models of the crop species mentioned above and hypothesized different evolutionary models to describe the demographic history of b. mori. then, we evaluated the most possible demographic scenario using the coalescent simulation and abc method, by combining the available nuclear dna sequences and our newly sequenced data. additionally, we also discussed the introgression pattern based on inferred evolutionary scenario with the goal of understanding the demographic history of silkworm.  the characteristics of data used in this study to avoid the effect of artificial selection and natural selection on the inference of the demographic history of silkworm as well as the detection of gene flow, we chose loci that show neutral evolution in our previous studies,. furthermore, tajima’s test on each of newly sequenced loci is not significant, suggesting that these loci evolved in a neutral manner. thus, all of loci used in this study show a neutral evolution pattern. demographic history of silkworm to investigate the occurrence of gene flow between the domesticated and wild silkworms, the demographic history of silkworm domestication was estimated by using coalescent simulation and abc method. four models were assumed. eight demographic parameters were estimated. the posterior density curve of each parameter for each model was also calculated. these parameters can be converted into effective population size and time in years using the formulation of θ = 4neμ and in units of 4 n generations, assuming the mutation rate μ =   × 10−8/bp/generation. the values of these parameters are calculated. we found that four models have very different parameter values. for example, nb is equal to ~ individuals: – ) in the ‘no gene flow’ model, ~ individuals in the ‘continuous gene flow’ model, ~ individuals in the ‘gene flow at bottleneck’ model, and ~ individuals in the ‘gene flow after bottleneck’ model; td is equal to ~  years in the ‘no gene flow’ model, ~  years in the ‘continuous gene flow’ model, ~  years in the ‘gene flow at bottleneck’ model, and ~  years in the ‘gene flow after bottleneck’ model. to determine which model is the most likely scenario for silkworm domestication, the value of bayes factor was calculated. the results showed that the maximum value of k was produced by ‘gene flow at bottleneck’ model. according to this model, the scenario for silkworm domestication was as follows. the effective population sizes of the domesticated silkworm population at the modern and bottleneck stages are: – ) and, respectively. additionally, we also estimated the divergence time: the starting time of the domestication is ~  years ago; the time of bottleneck ended in the domesticated silkworm is ~  years ago. this model showed that gene flow occurred at the bottleneck stage during silkworm domestication. however, the direction of gene flow between the domesticated silkworm and wild silkworm is still unknown. k: bayes factor; πsilent-d: πsilent values for b. mori; ssilent-d: ssilent values for b. mori. parameters of the preferred model were estimated. θ and τ are converted to n and t respectively. conversion procedure is based on the equation θ = 4n1μ, neutral mutation rate μ =   × 10− per site per generation was used. detection of gene flow direction to determine the direction of gene flow between the two populations, three models were assumed. based on these models, simulations were performed by using the software of migrate. the results showed that the model probabilities of model a, model b and model c are, and, respectively. this indicates that model a with the bidirectional gene flow during bottleneck is the most likely scenario. accordingly, we estimated the migration rates. the migration rate from wild to domesticated silkworms is while the migration rate from domesticated to wild silkworms is. to further confirm bidirectional gene flow occurred during silkworm domestication, the ima program was used to perform simulation analysis,. likelihood-ratio test on bidirectional migration between ancestral sub-populations is significant. the maximum likelihood estimates of the bidirectional migration rate from wild to domesticated silkworm population and from domesticated to wild silkworm population are and, respectively. this further suggests that the bidirectional migration might occur during silkworm domestication. furthermore, the results of both approaches suggested that the migration rate from domesticated to wild silkworms is larger than that from wild to domesticated silkworms. d: b. mori; w: b. mandarina; lbf: log bayes factor. discussion since the genome sequence of the domesticated silkworm was completed, many studies have used the genome-wide nuclear data and the classic sequencing data of individual nuclear loci to infer the demography and domestication of silkworm –,,. although these studies provide a lot of useful information for understanding the origin and domestication of the domesticated silkworm, they appear to ignore detection of gene flow between the domesticated and wild populations. previous studies based on the nuclear genome data suggested that the domesticated silkworm lost only approximately 17% of nucleotide diversity measured by θ relative to wild silkworm. however, our previous studies revealed that the domesticated silkworm lost 33-49% of nucleotide diversity measured by θ relative to wild silkworm and experienced a severe bottleneck during domestication,,. as indicated previously, the main reason leading to this big difference is that studies based on solexa sequencing data might have underestimated the level of nucleotide diversity in wild silkworm. the nucleotide diversity in the domesticated silkworm was found to be at a very similar level measured as θ between the classic sequencing data and solexa resequencing data, however, the nucleotide diversity in wild silkworm was greatly underestimated when the solexa resequencing data were used. the possible reason is that the genome sequence of wild silkworm, b. mandarina, has not been available to date, thus, the genome sequence of the domesticated silkworm was used as a reference for calling snps in both the domesticated and wild silkworms. because resequencing reads are usually short, some mapping algorithms cannot map sequence reads with more than one or two differences from a reference genome sequence. thus, we decided to reconsider the demographic history of the domesticated silkworm using a combined data set of nuclear loci by classic sequencing rather than the whole genome resequencing data by solexa. it will be good time to better infer the demographic history of the domesticated silkworm using the whole genome resequencing data only when the genome sequence of wild silkworm, b. mandarina, is available in future. since previous studies have ignored the detection of gene flow between the domesticated and wild silkworms –,, this study intended to detect possible introgression pattern of the domesticated and wild populations. currently, very few studies had investigated the evolutionary pattern of the domesticated silkworm, b. mori. therefore, quite limited available model information could be used when we started to investigate the demographic history of the domesticated silkworm. using previous studies on historical divergence and gene flow of genus zea and pearl millet as references,, therefore, we hypothesized four evolutionary scenarios by adding gene flow to reconsider the silkworm’s domestication. we found that the ‘gene flow at bottleneck’ model is the most likely scenario. according to this model, the starting time of the silkworm domestication is ~  years ago; the time of bottleneck ended in the domesticated silkworm is ~  years ago. these results are consistent with our previous results based on the phylogenetic analyses in which the domestication of silkworm was estimated to occur about  years ago. in addition, the estimate of the silkworm domestication time is also well consistent with the domestication time estimates of rice as well as maize,. these results are nearly consistent with the evidence from fossils. in addition, the domestication time of most livestock can be traced back to -  years ago. our divergence timing estimation is also within the timeframe. therefore, our results are reasonable. coalescent simulation indicated that the gene flow might occur during the period of bottleneck. three possible reasons may explain this. first, the overlapping geographic regions between the domesticated and wild silkworm populations might facilitate the gene flow. wild silkworm is not only widely distributed in the regions of jiangsu and zhejiang provinces, but also can be found in anhui and shandong provinces in china. interestingly, these areas are also the main regions of sericulture. second, the lack of the absolute reproductive isolation is likely to be another important factor that leads to gene flow between the populations. in fact, the domesticated and wild silkworms have not formed the completely reproductive isolation up to now. they are able to interbreed with each other. this may provide some convenience for gene exchanging between these two species. third, the environmental factors may also provide opportunities for gene flow between the populations during silkworm domestication. the initial rearing conditions of the domesticated silkworm may be very simple and open compared with present-day’s rearing environments. this may also increase the opportunities of contact and hybridization between the domesticated and wild silkworms. besides these factors, economic expansion and urbanization might also affect gene flow. rapid economic expansion and intensive urbanization may be common causes of the habitat fragmentation and may eventually reduce the gene flow on wildlife populations between different fragmented landscapes,. thus economic expansion and urbanization could be the reasons of why gene flow occurred at the period of bottleneck rather than at the recent. to determine the direction of gene flow during bottleneck, simulations were performed by using the software of migrate. the results indicated that bidirectional gene flow during the bottleneck period between the populations is the most likely scenario. in addition, the im simulation results also supported the bidirectional gene migration between the domesticated and wild silkworm populations rather than the unidirectional gene flow model. the gene flow direction from the domesticated silkworm to wild silkworm might be caused by the situation that the domesticated silkworms were discarded together with their excrement into natural environment. the gene flow from wild silkworm to the domesticated silkworm might be because of that wild silkworm was introduced by breeders, as an important genetic source, to hybrid with the domesticated silkworm to produce desirable strains,. in this study, we revealed that there was gene flow between the domesticated and wild silkworms. our finding is consistent with the observations in maize, pig,, chicken, cattle,, cats, horses, and honeybee. it appears that gene flow is ubiquitous between domesticated species and their wild relatives. our results may add a dimension to highlight the important role of gene flow in domestication of crops and animals. furthermore, as more and more population genomics data become available and new statistical methods are developed, we believe that long-standing questions about the role of gene flow in species formation will be resolved soon.  in this study, we hypothesized different models to describe the demographic history and the gene flow between b. mori and its wild relative, b. mandarina. the starting time of silkworm domestication was estimated to be approximate  years ago; the time of domestication termination was  years ago. bi-directional gene flow might occur during silkworm domestication. our findings add a dimension to highlight the important role of gene flow in domestication of crops and animals. 
gene flow plays an important role in domestication history of domesticated species. our findings add a dimension to highlight the important role of gene flow in domestication of crops and animals. in this study, four model-based evolutionary scenarios to describe the demographic history of b. mori were hypothesized. estimates of silkworm domestication time are nearly consistent with the archeological evidence and our previous results. however, little is known about the demographic history of domesticated silkworm involving gene flow with its wild relative. using approximate bayesian computation method and dna sequence data from nuclear loci, we found that the gene flow at bottleneck model is the most likely scenario for silkworm domestication. using coalescent simulation analysis, we also found that bi-directional gene flow occurred during silkworm domestication. importantly, we found that the bi-directional gene flow might occur during silkworm domestication. coalescent simulationapproximate bayesian computationgene flowbombyx mori the starting time of silkworm domestication was estimated to be approximate  years ago; the time of domestication termination was  years ago.
 gene flow plays an important role in domestication history of domesticated species. however, little is known about the demographic history of domesticated silkworm involving gene flow with its wild relative.  in this study, four model-based evolutionary scenarios to describe the demographic history of b. mori were hypothesized. using approximate bayesian computation method and dna sequence data from nuclear loci, we found that the gene flow at bottleneck model is the most likely scenario for silkworm domestication. the starting time of silkworm domestication was estimated to be approximate  years ago; the time of domestication termination was  years ago. using coalescent simulation analysis, we also found that bi-directional gene flow occurred during silkworm domestication.  estimates of silkworm domestication time are nearly consistent with the archeological evidence and our previous results. importantly, we found that the bi-directional gene flow might occur during silkworm domestication. our findings add a dimension to highlight the important role of gene flow in domestication of crops and animals. coalescent simulationapproximate bayesian computationgene flowbombyx mori 