BACKGROUND
walnut  is an economically important tree crop whose kernels very high nutritional values and is widely grown in many countries  <cit> .
walnut anthracnose, caused by colletotrichum gloeosporioides, is one of the most serious walnut diseases, which leads to sharp reductions in production  <cit> .
to date, chemical control has been the main measure for disease control; however, its use is restricted because of environmental problems and drug resistance in the pathogens .
therefore, resistance breeding is required.
genetic markers linked to resistance genes can improve the efficiency of breeding  <cit> .
with the development of genetic markers, resistance gene analogs  have been isolated from walnut, which indicated that anthracnose resistance in walnut was controlled by resistance genes   <cit> .
a high-density genetic linkage map represents an important tool for quantitative trait locus  mapping, and qtls for resistance to disease have been studied in many plants  <cit> .
several genetic linkage maps have been constructed for walnut; however, qtls associated with anthracnose resistance have not been reported.
in the past two decades, different molecular markers, including restriction fragment length polymorphisms   <cit> , random amplified polymorphic dna   <cit> , simple sequence repeat   <cit>  and inter-simple sequence repeat   <cit> , have been developed and used to evaluate genetic diversity of walnut.
rflp and rapd have been used to construct walnut genetic maps.
fjellstrom et al.
<cit>  first constructed a walnut genetic map using  <dig> rflp markers covering  <dig>  cm with an average marker spacing of  <dig>  cm.
woeste et al.
<cit>  obtained a walnut genetic map using  <dig> rflp and  <dig> rapd markers, based on a backcross  population with  <dig> individuals.
the total marker number on these maps is generally limited and some of the mapped markers have no sequence information.
therefore, a high-density genetic linkage map for walnut is required that comprises a large number of markers with sufficient sequence information.
in recent years, a bacterial artificial chromosome  library was used to develop single nucleotide polymorphism  markers in walnut  <cit> .
this approach is efficient to obtain more markers to increase the density of walnut maps.
the advent of next-generation sequencing , combined with the use of restriction enzymes, has proved valuable for the discovery, validation and assessment of a large number of genetic markers, which are essential to construct highly dense linkage maps, and to identify recombination breakpoints for qtl positions .
ngs led to the development of new methods, including reduced-representation sequencing using reduced-representation libraries  or complexity reduction of polymorphic sequences   <cit> , genotyping by sequencing   <cit>  and restriction-site associated dna sequencing   <cit> .
rad-seq is widely used for creating genetic linkage maps and snp discovery in large plant species  <cit> .
recently, the high-resolution method of specific length amplified fragment sequencing , which is based on rrls and high-throughput sequencing for large-scale genotyping and de novo snp discovery, was reported  <cit> .
slaf-seq technology has been used to construct high-density genetic maps for several plant species .
in this study, we constructed a high-density genetic linkage map containing a number of walnut snp markers using the slaf-seq approach, which was based on an f <dig> population with  <dig> individuals and two parental individuals.
subsequently, a qtl associated with anthracnose resistance was located and analyzed.
the results presented here will aid molecular marker-assisted breeding and walnut resistance genes identification.
RESULTS
analysis of slaf-seq data and slaf markers
<dig>  m pair-end reads were generated.
the q <dig>  was  <dig> % and guanine-cytosine  content was  <dig>  %.
the read numbers for slafs in the female and male parents were  <dig> , <dig> and  <dig> , <dig>  respectively.
the numbers of slafs in the female and male parents were  <dig>  and  <dig> , respectively.
the average coverage for each marker was  <dig> -fold and  <dig> -fold in the female and male parents, respectively.
in the f <dig> population, the read numbers of slafs in each individual ranged from  <dig>  to  <dig> , <dig>  with an average of  <dig> , <dig>  the numbers of slafs ranged from  <dig>  to  <dig> , with an average of  <dig>  in each individual.
the coverage ranged from  <dig> -fold to  <dig> -fold, with an average of  <dig> -fold .
the average sequence depths of these slafs were  <dig>  in the female parent,  <dig>  in the male parent and  <dig>  in the progeny.
<dig>  slaf markers were obtained, among which  <dig>   were polymorphic .
all polymorphic slafs were then genotyped separately for both parents and all individuals.
after discarding slaf markers that lacked parent information and contained many repeat sequences,  <dig>  markers were genotyped successfully and were classified into eight segregation types .
after filtering low-quality slaf markers, segregation distortion markers and other markers that were not suitable for map construction,  <dig>  polymorphic markers were obtained and were sorted to five segregation types .fig.
<dig> valid read numbers and coverage for each of the f <dig> individuals.
the x-axes indicate the plant accession including each of the f <dig> individuals; the y-axis indicates read number and the secondary y-axis indicates cluster coverage
notes: polymorphic slaf marker indicates that the marker has two to four alleles; non-polymorphic slaf marker indicates that the marker has only one allele
fig.
<dig> number of polymorphic slaf markers for eight segregation patterns.
the x-axis indicates eight segregation patterns of polymorphic slaf markers; the y-axis indicates the number of markers
the basic characteristics of the genetic maps
after linkage analysis,  <dig>   of the  <dig>  markers were used to construct genetic linkage maps, while the other  <dig>  markers failed to be mapped onto the genetic map.
<dig> markers on the map showed significant  segregation distortion.
the average integrity of mapping markers was 100 %.
the average depth of the markers was  <dig>  in the female parent,  <dig>  in the male parent, and  <dig>  in the offspring.
among the  <dig>  markers,  <dig>  of these fell into  <dig> linkage groups  for the female map,  <dig> markers for the male map, and  <dig>  markers for the integrated map .
taking into account the size of all lgs, marker coverage amounted to  <dig> .36 cm for the female map,  <dig> .58 cm for the male map, and  <dig> .82 cm for the integrated map.
the average intervals between two adjacent mapped markers were  <dig>  cm,  <dig>  cm and  <dig>  cm for female maps, male maps, and integrated maps, respectively.fig.
<dig> integrated linkage map for groups  <dig> to  <dig> of walnut.
the map includes linkage groups  <dig> to  <dig> of walnut; the slaf markers and their locations are shown on the right and left side, respectively
fig.
<dig> integrated linkage map for groups  <dig> to  <dig> for walnut.
the map includes linkage groups  <dig> to  <dig> of walnut; the slaf markers and their locations are shown on the right and left side, respectively
fig.
<dig> integrated linkage map for groups  <dig> to  <dig> of walnut.
the map includes linkage groups  <dig> to  <dig> of walnut; the slaf markers and their locations are shown on the right and left side, respectively.
markers associated with resistance to anthracnose are labeled with green on lg14
all lgs are shown in table 2: lg <dig> contained the most markers for the female map , lg <dig> for the male map  and lg <dig> for the integrated map .
lg <dig> contained the fewest markers for the female map , lg <dig> and lg <dig> for the male map  and lg <dig> for the integrated map .
the longest lgs were lg <dig> for the female map , lg <dig> for the male map  and lg <dig> for the integrated map .
the shortest were lg <dig> for the female map and the integrated map, and lg <dig> and lg <dig> for the male map, with  <dig>  cm,  <dig>  cm and  <dig>  cm, respectively.table  <dig> basic characteristics of the  <dig> walnut linkage groups
distribution of marker types on the genetic map
the integrated map had three types of markers:  <dig> ‘snp_only,’  <dig> ‘indel_only,’ and  <dig> ‘snp&indel’.
‘snp_only’ was the main type, accounting for  <dig>  % of the markers on the integrated map.
the marker types in each of  <dig> lgs are shown in fig.
<dig>  lg <dig> and lg <dig> contained the highest percentage of ‘indel_only’ markers at  <dig>  %.
lg <dig> contained the highest percentage of ‘snp&indel’ markers and the lowest percentage of ‘snp_only’ markers, at  <dig>  % and  <dig>  %, respectively.
lg <dig> contained the highest percentage of ‘snp_only’ markers at  <dig>  %.fig.
<dig> percentages of diverse types of markers on each linkage group.
the x-axis indicates the  <dig> linkage groups of the integrated map, the y-axis indicates the percentages of three types of markers: ‘snp_only,’ ‘indel_only,’ and snp & indel on each linkage group
<dig>  snp loci were detected among the  <dig>  markers on the genetic maps, which correlated with two snp loci per slaf marker, and percentages of different snp types were investigated .
most of the snps were transition-type snps, containing r  and y  types, accounting for  <dig>  % and  <dig>  % of all snps, respectively.
the other snps were transversion-type snps  containing s , m , k , and w , with the percentages ranging from  <dig>  to  <dig>  %.table  <dig> statistics of snp types on the map
notes: number indicates the number of each snp type: r  and y  are transition-type snps, and s, m, k and w are transversion-type snps
visualization and evaluation of the genetic map
the quality of the integrated map was evaluated by haplotype mapping.
the population of double exchange and the genotyping errors were reflected in the haplotype map.
haplotype maps were produced for each of the  <dig> offspring and for the parental controls, using  <dig>  slaf markers, as described by west et al.
<cit> .
the recombination events of each individual were displayed in the haplotype maps visually .
a large proportion of the recombination blocks were distinctly defined.
less than  <dig>  % contained no heterozygous fragments, and less than  <dig>  % was missing.
except for those that contained a few heterozygosity sites, all lgs distributed uniformity.
therefore, the f <dig> population was suitable for genetic analysis.
the relationship of recombination between markers from each lg was reflected by a heat map.
pairwise recombination scores for  <dig>  markers were used to construct heat maps to evaluate the integrated map quality .
the accuracy of mapping was estimated using the rate of recombination and genetic distance between two markers.
the qtl analysis of walnut anthracnose resistance
based on statistics data about the relative resistance index  of  <dig> individuals comprising the paternal parent, maternal parent and f <dig> offspring .
the rri of the paternal parent was  <dig> , the maternal parent was  <dig> .
a frequency distribution graph of rri was constructed and shown in fig.
<dig>  further analysis using interval mapping  detected one qtl that was associated with resistance to anthracnose, which ranged from  <dig>  to  <dig>  cm on lg <dig>  ten markers  in this interval that were above the lod threshold value  were considered to be linked markers to the anthracnose resistance trait.
the phenotypic variance explained by each marker ranged from  <dig>  to  <dig>  %, with an average of  <dig>  %, and their lod scores varied from  <dig>  to  <dig> , with an average of  <dig>  .fig.
<dig> the frequency distribution of the relative resistance index  of walnut individuals.
the x-axis indicates the rri; the y-axis indicates frequency of the rri
fig.
<dig> logarithm of odds  and percent phenotypic variance explained  curves on lg <dig> for anthracnose resistance of walnut.
the blue curve indicates lod scores of slaf markers against their genetic position on lg <dig>  the red curve indicates the pve of slaf markers against their genetic position on lg <dig>  the gray line indicates the threshold lod score
discussion
mapping population
the selection of mapping parents is important for constructing high-density map.
establishing a suitable mapping population is the first step in constructing a map and determines its quality.
for many agricultural crops, segregating crosses initiated with two contrasting inbred lines, such as the bc, double haploid , recombination inbred lines  and f <dig>  have been used commonly for genetic/qtl linkage mapping  <cit> .
for many forest trees, whose biological properties prevent the generation of inbred lines, and therefore, of any advanced crosses.
however, because of their high heterozygosis, tree species are able to generate large progeny sets from full-sib or half-sib crosses, and the crosses among their f1s often display substantial segregation  <cit> .
grattapaglia and sederoff  <cit>  put forward a so-called pseudo-testcross strategy for linkage mapping in a controlled cross between two parents.
in that method, the pseudo-testcross mapping strategy is based on the selection of single dose markers present in one parent and absent in the other.
walnut is a monoecious plant that develops unisexual female and male flowers within separate inflorescences of the same individual.
to construct a genetic map and detect qtls for anthracnose resistance, the f <dig> population from a cross between walnut cultivar ‘yuan lin’  and ‘qing lin’  was created by controlled pollination, and resistance to walnut anthracnose caused by c. gloeosporioides of the individuals was evaluated by rri .
rris of the female and male parents were  <dig>  and  <dig> , respectively; rris of offspring ranged from  <dig>  to  <dig> , with an average of  <dig> .
the coefficient of variation  was  <dig>  %.
the results showed that the anthracnose resistance of the f <dig> population was continual and had quantitative character of inheritance that would be controlled by multiple genes.
the segregation of slaf markers
slaf-seq can generate large numbers of markers and provide a good platform for species without a reference genome sequence, such as walnut  <cit> .
in this study, slaf-seq was applied to determine the genome sequence of walnut and a total of  <dig>  m pair-end reads were generated.
among the  <dig>  slaf markers obtained,  <dig>  slafs were polymorphic .
<dig>  polymorphic markers were successful genotyped and sorted into five segregation types .
ratios of segregation types were different in the populations, which indicated that the recombination frequency of different chromosomes was inconsistent during the period of meiosis  <cit> .
after linkage analysis,  <dig>  slaf markers were used to construct genetic maps.
‘snp_only’ markers were predominant  on the integrated map .
<dig>  snp loci were detected among the  <dig>  markers, corresponding to two snp loci per slaf markers .
you et al.
<cit>  identified  <dig>  genome-wide snps in walnut  using bacterial artificial chromosome end sequences .
our results indicated that slaf-seq is an effective method to develop snp markers for walnut.
segregation distortion is a widespread and common phenomenon in many plants, which deviates the frequency of alleles from representative mendelian ratio  <cit> .
the phenomenon may be related to the population type and environmental factor  <cit> .
seven hundred sixty one markers showed significant  segregation distortion, accounting for  <dig>  % of the markers on the integrated map.
bradshaw and stettler  <cit>  discovered that segregation distortion markers had almost the same mapping efficiency as segregation normal markers.
discarding segregation distortion markers would possibly cause the loss of massive amounts of information and decrease the coverage of the genome  <cit> .
zhang et al.
<cit>  and xu  <cit>  showed that segregation distortion markers did not have an effect on qtl mapping.
therefore, segregation distortion markers could be used to construct the genetic map.
linkage mapping
a high-density genetic linkage map aids qtl mapping for important economical traits.
genetic maps of walnut were reported by fjellstrom et al.
<cit>  and woeste et al.
<cit> .
however, because of the lack of a large number of molecular markers with sufficient sequence information, many qtls for target traits cannot be accurately detected.
here, among the  <dig>  markers,  <dig>  of these fell into  <dig> lgs for the female map,  <dig> markers for the male map, and  <dig>  markers for the integrated map, the average intervals between two adjacent mapped markers were  <dig>  cm,  <dig>  cm and  <dig>  cm for the female map, the male map, and the integrated map, respectively .
thus, the density of the map was higher than that of previous maps.
the  <dig> lgs corresponded to the haploid genome of walnut, which has  <dig> chromosomes  <cit> .
the quality of genetic map was evaluated by haplotype map , and the relationship of recombination between markers from each linkage group was reflected by heat map .
to avoid sequencing or mapping errors, high map strategy  <cit>  was used to order and correct slaf markers and for genotyping.
the results indicated the map is efficient, accurate and saturated.
li et al.
<cit>  and doerge  <cit>  considered that 10 cm marker density is sufficient to provide an accurate estimation of qtl positions for a population size between 100 ~  <dig>  consequently, we constructed the linkage map that met these requirements for qtl analysis.
qtl mapping for anthracnose resistance
qtl mapping for anthracnose resistance in other plants have been studied.
lee et al.
<cit>  obtained seven qtls for resistance to c. acutatum ‘ksca-1’ and c. capsici ‘thscc-1’ in pepper , two of which were major qtls.
petro et al.
<cit>  detected nine qtls associated with anthracnose resistance, which explained  <dig> – <dig>  % of the phenotypic variance in water yam .
woeste et al.
<cit>  obtained a rapd marker linked to hypersensitivity to the cherry leafroll virus from a walnut bc population using bulked segregant analysis .
in the present study, according to the high-density genetic map for walnut, one qtl for walnut anthracnose resistance was identified.
the interval of this qtl ranged from  <dig>  cm to  <dig>  cm on lg <dig>  and contained ten markers associated with anthracnose resistance , that the average intervals between two adjacent markers was  <dig>  cm.
the phenotypic variance explained by each marker ranged from  <dig>  to  <dig>  % .
a high lod threshold can decrease false positives effectively, and a lod threshold of 2–3 can control the value of α to within  <dig>   <cit> .
the  <dig> markers that were detected belonged to the segregation type hk × hk, which might indicate that the resistance to anthracnose was inherited from the parents.
in future experiments, we will use the qtl to develop efficient markers associated with walnut anthracnose resistance and to accelerate walnut breeding project.
CONCLUSIONS
high-density genetic linkage maps of walnut were constructed using the slaf-seq method.
the maps contained  <dig>  polymorphic markers, from which  <dig>  snp loci were detected.
one qtl was identified for resistance to anthracnose on lg <dig>  our results provide an important theoretical basis for walnut molecular assisted breeding and resistance gene identification.

 walnut is an economically important tree crop whose kernels very high nutritional values and is widely grown in many countries. walnut anthracnose, caused by colletotrichum gloeosporioides, is one of the most serious walnut diseases, which leads to sharp reductions in production. to date, chemical control has been the main measure for disease control; however, its use is restricted because of environmental problems and drug resistance in the pathogens. therefore, resistance breeding is required. genetic markers linked to resistance genes can improve the efficiency of breeding. with the development of genetic markers, resistance gene analogs have been isolated from walnut, which indicated that anthracnose resistance in walnut was controlled by resistance genes. a high-density genetic linkage map represents an important tool for quantitative trait locus mapping, and qtls for resistance to disease have been studied in many plants. several genetic linkage maps have been constructed for walnut; however, qtls associated with anthracnose resistance have not been reported. in the past two decades, different molecular markers, including restriction fragment length polymorphisms, random amplified polymorphic dna, simple sequence repeat and inter-simple sequence repeat, have been developed and used to evaluate genetic diversity of walnut. rflp and rapd have been used to construct walnut genetic maps. fjellstrom et al. first constructed a walnut genetic map using rflp markers covering  cm with an average marker spacing of  cm. woeste et al. obtained a walnut genetic map using rflp and rapd markers, based on a backcross population with individuals. the total marker number on these maps is generally limited and some of the mapped markers have no sequence information. therefore, a high-density genetic linkage map for walnut is required that comprises a large number of markers with sufficient sequence information. in recent years, a bacterial artificial chromosome library was used to develop single nucleotide polymorphism markers in walnut. this approach is efficient to obtain more markers to increase the density of walnut maps. the advent of next-generation sequencing, combined with the use of restriction enzymes, has proved valuable for the discovery, validation and assessment of a large number of genetic markers, which are essential to construct highly dense linkage maps, and to identify recombination breakpoints for qtl positions. ngs led to the development of new methods, including reduced-representation sequencing using reduced-representation libraries or complexity reduction of polymorphic sequences, genotyping by sequencing and restriction-site associated dna sequencing. rad-seq is widely used for creating genetic linkage maps and snp discovery in large plant species. recently, the high-resolution method of specific length amplified fragment sequencing, which is based on rrls and high-throughput sequencing for large-scale genotyping and de novo snp discovery, was reported. slaf-seq technology has been used to construct high-density genetic maps for several plant species. in this study, we constructed a high-density genetic linkage map containing a number of walnut snp markers using the slaf-seq approach, which was based on an f population with individuals and two parental individuals. subsequently, a qtl associated with anthracnose resistance was located and analyzed. the results presented here will aid molecular marker-assisted breeding and walnut resistance genes identification.  analysis of slaf-seq data and slaf markers  m pair-end reads were generated. the q was % and guanine-cytosine content was %. the read numbers for slafs in the female and male parents were, and, respectively. the numbers of slafs in the female and male parents were and, respectively. the average coverage for each marker was -fold and -fold in the female and male parents, respectively. in the f population, the read numbers of slafs in each individual ranged from to, with an average of, the numbers of slafs ranged from to, with an average of in each individual. the coverage ranged from -fold to -fold, with an average of -fold. the average sequence depths of these slafs were in the female parent, in the male parent and in the progeny. slaf markers were obtained, among which were polymorphic. all polymorphic slafs were then genotyped separately for both parents and all individuals. after discarding slaf markers that lacked parent information and contained many repeat sequences, markers were genotyped successfully and were classified into eight segregation types. after filtering low-quality slaf markers, segregation distortion markers and other markers that were not suitable for map construction, polymorphic markers were obtained and were sorted to five segregation types.fig. valid read numbers and coverage for each of the f individuals. the x-axes indicate the plant accession including each of the f individuals; the y-axis indicates read number and the secondary y-axis indicates cluster coverage notes: polymorphic slaf marker indicates that the marker has two to four alleles; non-polymorphic slaf marker indicates that the marker has only one allele fig. number of polymorphic slaf markers for eight segregation patterns. the x-axis indicates eight segregation patterns of polymorphic slaf markers; the y-axis indicates the number of markers the basic characteristics of the genetic maps after linkage analysis, of the markers were used to construct genetic linkage maps, while the other markers failed to be mapped onto the genetic map. markers on the map showed significant segregation distortion. the average integrity of mapping markers was 100 %. the average depth of the markers was in the female parent, in the male parent, and in the offspring. among the markers, of these fell into linkage groups for the female map, markers for the male map, and markers for the integrated map. taking into account the size of all lgs, marker coverage amounted to.36 cm for the female map,.58 cm for the male map, and.82 cm for the integrated map. the average intervals between two adjacent mapped markers were  cm,  cm and  cm for female maps, male maps, and integrated maps, respectively.fig. integrated linkage map for groups to of walnut. the map includes linkage groups to of walnut; the slaf markers and their locations are shown on the right and left side, respectively fig. integrated linkage map for groups to for walnut. the map includes linkage groups to of walnut; the slaf markers and their locations are shown on the right and left side, respectively fig. integrated linkage map for groups to of walnut. the map includes linkage groups to of walnut; the slaf markers and their locations are shown on the right and left side, respectively. markers associated with resistance to anthracnose are labeled with green on lg14 all lgs are shown in table 2: lg contained the most markers for the female map, lg for the male map and lg for the integrated map. lg contained the fewest markers for the female map, lg and lg for the male map and lg for the integrated map. the longest lgs were lg for the female map, lg for the male map and lg for the integrated map. the shortest were lg for the female map and the integrated map, and lg and lg for the male map, with  cm,  cm and  cm, respectively.table basic characteristics of the walnut linkage groups distribution of marker types on the genetic map the integrated map had three types of markers: ‘snp_only,’ ‘indel_only,’ and ‘snp&indel’. ‘snp_only’ was the main type, accounting for % of the markers on the integrated map. the marker types in each of lgs are shown in fig.  lg and lg contained the highest percentage of ‘indel_only’ markers at %. lg contained the highest percentage of ‘snp&indel’ markers and the lowest percentage of ‘snp_only’ markers, at  % and  %, respectively. lg contained the highest percentage of ‘snp_only’ markers at  %.fig. percentages of diverse types of markers on each linkage group. the x-axis indicates the linkage groups of the integrated map, the y-axis indicates the percentages of three types of markers: ‘snp_only,’ ‘indel_only,’ and snp & indel on each linkage group snp loci were detected among the markers on the genetic maps, which correlated with two snp loci per slaf marker, and percentages of different snp types were investigated. most of the snps were transition-type snps, containing r and y types, accounting for  % and  % of all snps, respectively. the other snps were transversion-type snps containing s, m, k, and w, with the percentages ranging from to  %.table statistics of snp types on the map notes: number indicates the number of each snp type: r and y are transition-type snps, and s, m, k and w are transversion-type snps visualization and evaluation of the genetic map the quality of the integrated map was evaluated by haplotype mapping. the population of double exchange and the genotyping errors were reflected in the haplotype map. haplotype maps were produced for each of the offspring and for the parental controls, using slaf markers, as described by west et al.. the recombination events of each individual were displayed in the haplotype maps visually. a large proportion of the recombination blocks were distinctly defined. less than  % contained no heterozygous fragments, and less than  % was missing. except for those that contained a few heterozygosity sites, all lgs distributed uniformity. therefore, the f population was suitable for genetic analysis. the relationship of recombination between markers from each lg was reflected by a heat map. pairwise recombination scores for markers were used to construct heat maps to evaluate the integrated map quality. the accuracy of mapping was estimated using the rate of recombination and genetic distance between two markers. the qtl analysis of walnut anthracnose resistance based on statistics data about the relative resistance index of individuals comprising the paternal parent, maternal parent and f offspring. the rri of the paternal parent was, the maternal parent was. a frequency distribution graph of rri was constructed and shown in fig.  further analysis using interval mapping detected one qtl that was associated with resistance to anthracnose, which ranged from to  cm on lg ten markers in this interval that were above the lod threshold value were considered to be linked markers to the anthracnose resistance trait. the phenotypic variance explained by each marker ranged from to  %, with an average of  %, and their lod scores varied from to, with an average of.fig. the frequency distribution of the relative resistance index of walnut individuals. the x-axis indicates the rri; the y-axis indicates frequency of the rri fig. logarithm of odds and percent phenotypic variance explained curves on lg for anthracnose resistance of walnut. the blue curve indicates lod scores of slaf markers against their genetic position on lg the red curve indicates the pve of slaf markers against their genetic position on lg the gray line indicates the threshold lod score discussion mapping population the selection of mapping parents is important for constructing high-density map. establishing a suitable mapping population is the first step in constructing a map and determines its quality. for many agricultural crops, segregating crosses initiated with two contrasting inbred lines, such as the bc, double haploid, recombination inbred lines and f have been used commonly for genetic/qtl linkage mapping. for many forest trees, whose biological properties prevent the generation of inbred lines, and therefore, of any advanced crosses. however, because of their high heterozygosis, tree species are able to generate large progeny sets from full-sib or half-sib crosses, and the crosses among their f1s often display substantial segregation. grattapaglia and sederoff put forward a so-called pseudo-testcross strategy for linkage mapping in a controlled cross between two parents. in that method, the pseudo-testcross mapping strategy is based on the selection of single dose markers present in one parent and absent in the other. walnut is a monoecious plant that develops unisexual female and male flowers within separate inflorescences of the same individual. to construct a genetic map and detect qtls for anthracnose resistance, the f population from a cross between walnut cultivar ‘yuan lin’ and ‘qing lin’ was created by controlled pollination, and resistance to walnut anthracnose caused by c. gloeosporioides of the individuals was evaluated by rri. rris of the female and male parents were and, respectively; rris of offspring ranged from to, with an average of. the coefficient of variation was  %. the results showed that the anthracnose resistance of the f population was continual and had quantitative character of inheritance that would be controlled by multiple genes. the segregation of slaf markers slaf-seq can generate large numbers of markers and provide a good platform for species without a reference genome sequence, such as walnut. in this study, slaf-seq was applied to determine the genome sequence of walnut and a total of  m pair-end reads were generated. among the slaf markers obtained, slafs were polymorphic. polymorphic markers were successful genotyped and sorted into five segregation types. ratios of segregation types were different in the populations, which indicated that the recombination frequency of different chromosomes was inconsistent during the period of meiosis. after linkage analysis, slaf markers were used to construct genetic maps. ‘snp_only’ markers were predominant on the integrated map. snp loci were detected among the markers, corresponding to two snp loci per slaf markers. you et al. identified genome-wide snps in walnut using bacterial artificial chromosome end sequences. our results indicated that slaf-seq is an effective method to develop snp markers for walnut. segregation distortion is a widespread and common phenomenon in many plants, which deviates the frequency of alleles from representative mendelian ratio. the phenomenon may be related to the population type and environmental factor. seven hundred sixty one markers showed significant segregation distortion, accounting for  % of the markers on the integrated map. bradshaw and stettler discovered that segregation distortion markers had almost the same mapping efficiency as segregation normal markers. discarding segregation distortion markers would possibly cause the loss of massive amounts of information and decrease the coverage of the genome. zhang et al. and xu showed that segregation distortion markers did not have an effect on qtl mapping. therefore, segregation distortion markers could be used to construct the genetic map. linkage mapping a high-density genetic linkage map aids qtl mapping for important economical traits. genetic maps of walnut were reported by fjellstrom et al. and woeste et al.. however, because of the lack of a large number of molecular markers with sufficient sequence information, many qtls for target traits cannot be accurately detected. here, among the markers, of these fell into lgs for the female map, markers for the male map, and markers for the integrated map, the average intervals between two adjacent mapped markers were  cm,  cm and  cm for the female map, the male map, and the integrated map, respectively. thus, the density of the map was higher than that of previous maps. the lgs corresponded to the haploid genome of walnut, which has chromosomes. the quality of genetic map was evaluated by haplotype map, and the relationship of recombination between markers from each linkage group was reflected by heat map. to avoid sequencing or mapping errors, high map strategy was used to order and correct slaf markers and for genotyping. the results indicated the map is efficient, accurate and saturated. li et al. and doerge considered that 10 cm marker density is sufficient to provide an accurate estimation of qtl positions for a population size between 100 ~  consequently, we constructed the linkage map that met these requirements for qtl analysis. qtl mapping for anthracnose resistance qtl mapping for anthracnose resistance in other plants have been studied. lee et al. obtained seven qtls for resistance to c. acutatum ‘ksca-1’ and c. capsici ‘thscc-1’ in pepper, two of which were major qtls. petro et al. detected nine qtls associated with anthracnose resistance, which explained –  % of the phenotypic variance in water yam. woeste et al. obtained a rapd marker linked to hypersensitivity to the cherry leafroll virus from a walnut bc population using bulked segregant analysis. in the present study, according to the high-density genetic map for walnut, one qtl for walnut anthracnose resistance was identified. the interval of this qtl ranged from  cm to  cm on lg and contained ten markers associated with anthracnose resistance, that the average intervals between two adjacent markers was  cm. the phenotypic variance explained by each marker ranged from to  %. a high lod threshold can decrease false positives effectively, and a lod threshold of 2–3 can control the value of α to within. the markers that were detected belonged to the segregation type hk × hk, which might indicate that the resistance to anthracnose was inherited from the parents. in future experiments, we will use the qtl to develop efficient markers associated with walnut anthracnose resistance and to accelerate walnut breeding project.  high-density genetic linkage maps of walnut were constructed using the slaf-seq method. the maps contained polymorphic markers, from which snp loci were detected. one qtl was identified for resistance to anthracnose on lg our results provide an important theoretical basis for walnut molecular assisted breeding and resistance gene identification. 
high-density genetic maps for walnut containing lgs were constructed using the slaf-seq method with an f population. the results will aid molecular marker-assisted breeding and walnut resistance genes identification. one qtl was detected for anthracnose resistance. the interval of this qtl ranged from  cm to  cm on lg and ten markers in this interval that were above the threshold value were considered to be linked markers to the anthracnose resistance trait. one qtl for walnut anthracnose resistance was identified based on the map. the recently developed specific length amplified fragment sequencing is an efficient strategy that can obtain large numbers of markers with sufficient sequence information to construct high-density genetic maps and permits detection of quantitative trait loci for molecular breeding. juglans regia lgenetic mapspecific length amplified fragment sequencingslaf-seqanthracnosecolletotrichum gloeosporioidesquantitative trait locusqtlissue-copyright-statement© the author 2015 polymorphic markers were sorted into five segregation types and markers of them were used to construct genetic linkage maps: of these fell into linkage groups for the female map, markers for the male map, and markers for the integrated map. taking into account the size of all lgs, the marker coverage was.36 cm for the female map,.58 cm for the male map, and.82 cm for the integrated map. slaf markers were obtained, of which were polymorphic. mapping markers contained single nucleotide polymorphisms loci, which corresponded to two snp loci per slaf marker. resistance to anthracnose, caused by colletotrichum gloeosporioides, is a major objective of walnut genetic improvement in china. walnut is an economically important tree crop. ‘snp_only’ markers accounted for  % of the markers on the integrated map. the phenotypic variance explained by each marker ranged from to  %, and their lod scores varied from to. the average intervals between two adjacent mapped markers were  cm,  cm and  cm for three maps, respectively.
 walnut is an economically important tree crop. resistance to anthracnose, caused by colletotrichum gloeosporioides, is a major objective of walnut genetic improvement in china. the recently developed specific length amplified fragment sequencing is an efficient strategy that can obtain large numbers of markers with sufficient sequence information to construct high-density genetic maps and permits detection of quantitative trait loci for molecular breeding.  slaf-seq generated  m paired-end reads. slaf markers were obtained, of which were polymorphic. polymorphic markers were sorted into five segregation types and markers of them were used to construct genetic linkage maps: of these fell into linkage groups for the female map, markers for the male map, and markers for the integrated map. taking into account the size of all lgs, the marker coverage was.36 cm for the female map,.58 cm for the male map, and.82 cm for the integrated map. the average intervals between two adjacent mapped markers were  cm,  cm and  cm for three maps, respectively. ‘snp_only’ markers accounted for  % of the markers on the integrated map. mapping markers contained single nucleotide polymorphisms loci, which corresponded to two snp loci per slaf marker. according to the integrated map, we used interval mapping to detect our quantitative trait. one qtl was detected for anthracnose resistance. the interval of this qtl ranged from  cm to  cm on lg and ten markers in this interval that were above the threshold value were considered to be linked markers to the anthracnose resistance trait. the phenotypic variance explained by each marker ranged from to  %, and their lod scores varied from to.  high-density genetic maps for walnut containing lgs were constructed using the slaf-seq method with an f population. one qtl for walnut anthracnose resistance was identified based on the map. the results will aid molecular marker-assisted breeding and walnut resistance genes identification. electronic supplementary material the online version of this article contains supplementary material, which is available to authorized users. keywords juglans regia lgenetic mapspecific length amplified fragment sequencingslaf-seqanthracnosecolletotrichum gloeosporioidesquantitative trait locusqtlissue-copyright-statement© the author 2015 