Evaluation of designs for reference families for livestock linkage mapping experiments

Abstract

The development of dense linkage maps consisting of highly polymorphic loci for livestock species is technically feasible. However, linkage mapping experiments are expensive as they involve many animals and marker typings per animal. To minimize costs of developing linkage maps for livestock species, optimizing designs for mapping studies is necessary. This study provides a general framework for evaluating the efficiency of designs for reference families consisting of two‐ or three‐ generation full‐sib or half‐sib families selected from a segregating population. The influence of number of families, number of offspring per family, family structure (either half‐sib or full‐sib) and marker polymorphism is determined. Evaluation is done for two markers with a recombination rate of .20 and for a marker and a dominant single gene with a recombination rate of .20. Two evaluation criteria are used: expected maximum lod score for detection of linkage and accuracy of an estimated recombination rate defined as probability that the true recombination rate is in an interval around the estimated recombination rate. First, for several designs the contribution of reference families to expected maximum lod score and accuracy is given. Second, the required number of families in a design to obtain a certain value for the evaluation criteria is calculated when number of offspring per family, family structure and marker polymorphism are specified. The required numbers increase when designs are optimized not only for expected maximum lod score but also for accuracy. The required number of animals to map a dominant single gene is very large. Therefore, a set of reference families should be designed for strictly mapping marker loci. Examples illustrate how tabulated results can be generalized to determine the values for a wide range of designs containing two‐ or three‐generation full‐sib or half‐sib families.     

Alström syndrome: further evidence for linkage to human chromosome 2p13

Alstr?m syndrome is a rare autosomal recessive disorder characterized by retinal degeneration, sensorineural hearing loss, early-onset obesity, and non-insulin-dependent diabetes mellitus. The gene for Alstr?m syndrome (ALMS1) has been previously localized to human chromosome 2p13 by homozygosity mapping in two distinct isolated populations - French Acadian and North African. Pair-wise analyses resulted in maximum lod (logarithm of the odds ratio) scores of 3.84 and 2.9, respectively. To confirm these findings, a large linkage study was performed in twelve additional families segregating for Alstr?m syndrome. A maximum two-point lod score of 7.13 (theta = 0.00) for marker D2S2110 and a maximum cumulative multipoint lod score of 9.16 for marker D2S2110 were observed, further supporting linkage to chromosome 2p13. No evidence of genetic heterogeneity was observed in these families. Meiotic recombination events have localized the critical region containing ALMS1 to a 6.1-cM interval flanked by markers D2S327 and D2S286. A fine resolution radiation hybrid map of 31 genes and markers has been constructed.     

An AFLP linkage map for Douglas-fir based upon multiple full-sib families

An amplified fragment length polymorphism (AFLP) linkage map for coastal Douglas-fir (Pseudotsuga menziesii) was constructed from eight full-sib families each consisting of 40 progeny. These families were part of the British Columbia Ministry of Forests second-generation progeny test program and represent typical family sizes used in progeny trials. For map construction, ten primer pairs using EcoRI+3 and MseI+4 were employed to identify and assay AFLP loci that segregated in backcross configurations. A new technique was used to obtain a single recombination rate for each pair of marker loci: for each locus pair, a recombination rate and log-odd value were estimated across all segregating families using a joint maximum likelihood function that considered the full dataset of segregating genotypes. The resulting matrix of recombination rates between all pairs of loci was used to construct an integrated linkage map using JoinMap. The final map consisted of 19 linkage groups spanning 938.6 cM at an average distance of 9.3 cM between markers. The simultaneous integration of data from multiple families may provide an effective way to construct a linkage map, using the genetic resources inherent in most tree improvement programs, where progeny tests of small size are conducted. The statistical property of number of families used is briefly discussed. For our data, at least three to four families greatly increased the chance of obtaining an informative locus in at least one family. Families as small as ten are adequate for closely linked loci (<10 cM), while the size used in our study (40) is adequate for loci within 30 cM.     

Segregation and linkage studies of plasma dopamine-beta-hydroxylase (DBH), erythrocyte catechol-O-methyltransferase (COMT), and platelet monoamine oxidase (MAO): possible linkage between the ABO locus and a gene controlling DBH activity.

Measurements of dopamine-beta-hydroxylase (DBH), catechol-O-methyltransferase (COMT), and monoamine oxidase (MAO) along with 27 polymorphic marker phenotypes were available for 162 patients with major affective disorders and 1,125 of their relatives. Levels of enzymes were previously found not to be associated with illness. Pedigree analysis methods for quantitative traits are used to test single-gene hypotheses for segregation of DBH in 32 families with 411 individuals. COMT in 30 families with 351 individuals, and MAO in 50 families with 309 individuals. The familial distribution of both DBH and COMT are consistent with two codominant alleles at the same locus that account for 56% and 59% of the total variance, respectively. MAO activity cannot be shown to be segregating as a single major gene, but a purely nongenetic hypothesis is also rejected. A possible linkage of a locus for DBH to the ABO locus is indicated by a maximum lod score of 1.82 at 0% and 10% recombination fractions for males and females, respectively. A lod score of 0.61 at 0% recombination for a similar analysis in a single large pedigree was reported by Elston et al., making the combined lod score for the two studies equal to 2.32 at 0% recombination.     

Genetic mapping of autosomal dominant Charcot-Marie-Tooth disease in a large French-Acadian kindred: identification of new linked markers on chromosome 17.

We have performed linkage analysis in a large French-Acadian kindred segregating one form of autosomal dominant Charcot-Marie-Tooth disease (CMTD) (type IA) using 17 polymorphic DNA markers spanning human chromosome 17 and demonstrate linkage to several markers in the pericentromeric region, including DNA probes pA10-41, EW301, S12-30, pTH17.19, c11-2B, and p11-2c11.5. Linkage of markers pA10-41 and EW301 to CMTD type IA has been reported elsewhere. Four new markers, 1516, 1517, 1541, and LL101, which map to chromosome 17 have been identified. The marker 1516 appears to be closely linked to the CMTD locus on chromosome 17 as demonstrated by a maximum lod score of 3.42 at theta (recombination fraction) = 0. This marker has been mapped to 17p11.2 using a somatic cell hybrid constructed from a patient with Smith-Magenis syndrome [46,XY, del(17)(p11.2p11.2)]. A lod score of 6.16 has been obtained by multipoint linkage analysis with 1516 and two markers from 17q11.2, pTH17.19, and c11-2B. The markers 1517 and 1541 have been mapped to 17p12-17q11.2 and demonstrate maximum lod scores of 2.35 and 0.63 at recombination values of .1 and .2, respectively. The marker LL101 has been mapped to 17p13.105-17p13.100 and demonstrates a maximum lod score of 1.56 at a recombination value of .1. Our study confirms the localization of CMTD type IA to the pericentromeric region of chromosome 17.     

Familial medullary thyroid carcinoma and multiple endocrine neoplasia type 2B map to the same region of chromosome 10 as multiple endocrine neoplasia type 2A.

Medullary thyroid carcinoma (MTC) occurs as a component of three well-described autosomal dominant familial cancer syndromes. Multiple endocrine neoplasia type 2A (MEN 2A) is characterized by MTC, pheochromocytomas, and parathyroid hyperplasia. Patients with the rarer multiple endocrine neoplasia type 2B (MEN 2B) syndrome develop MTC and pheochromocytomas, as well as mucosal neuromas, ganglioneuromatosis of the gastrointestinal tract, and a characteristic "marfanoid" habitus. Finally, MTC is transmitted in an autosomal dominant pattern in some families without associated pheochromocytomas or parathyroid hyperplasia (familial medullary thyroid carcinoma, MTC1(2). Sixty-one members of two well-characterized kindreds segregating MTC1 and 34 [corrected] members of six families segregating MEN2B were genotyped using a panel of RFLP probes from the pericentromeric region of chromosome 10 near a locus for MEN 2A. Statistically significant linkage was observed between the chromosome 10 centromere-specific marker D10Z1 and MTC1 (maximum pairwise lod score 5.88 with 0% recombination) and D10Z1 and MEN2B (maximum pairwise lod score 3.58 with 0% recombination). A maximum multipoint lod score of 4.08 was obtained for MEN2B at the position of D10Z1. In addition, 92 members of a previously unreported large MEN2A kindred were genotyped, and linkage to the pericentromeric region of chromosome 10 is reported (maximum pairwise lod score of 11.33 with 0% recombination between MEN2A and RBP3). These results demonstrate that both a locus for familial MTC and a locus for MEN 2B map to the pericentromeric region of chromosome 10, in the same region as a locus for MEN 2A. The finding that each of these three clinically distinct familial cancer syndromes maps to the same chromosomal region suggests that all are allelic mutations at the same locus or represent a cluster of genes involved in the regulation of neuroendocrine tissue development.     

Heterogeneity in X-linked recessive Charcot-Marie-Tooth neuropathy.

Three families presenting with X-linked recessive Charcot-Marie-Tooth neuropathies (CMT) were studied both clinically and genetically. The disease phenotype in family 1 was typical of CMT type 1, except for an infantile onset; two of five affected individuals were mentally retarded, and obligate-carrier females were unaffected. Families 2 and 3 showed distal atrophy with weakness, juvenile onset, and normal intelligence. Motor-nerve conduction velocities were significantly slowed, and electromyography data were consistent with denervation in affected CMT males in all three families. Thirty X-linked RFLPs were tested for linkage studies against the CMT disease loci. Family 1 showed tight linkage (recombination fraction [theta] = 0) to Xp22.2 markers DXS16, DXS143, and DXS43, with peak lod scores of 1.75, 1.78, and 2.04, respectively. A maximum lod score of 3.48 at DXS16 (theta = 0) was obtained by multipoint linkage analysis of the map DXS143-DXS16-DXS43. In families 2 and 3 there was suggestion of tight linkage (theta = 0) to Xq26 markers DXS86, DXS144, and DXS105, with peak lod scores of 2.29, 1.33, and 2.32, respectively. The combined maximum multipoint lod score of 1.81 at DXS144 (theta = 0) for these two families occurred in the map DXS10-DXS144-DXS51-DXS105-DXS15-DXS52++ +. A joint homogeneity analysis including both regions (Xp22.2 and Xq26-28) provided evidence against homogeneity (chi 2 = 9.12, P less than .005). No linkage to Xp11.12-q22 markers was observed, as was reported for X-linked dominant CMT and the Cowchock CMT variant. Also, the chromosomes 1 and 17 CMT loci were excluded by pairwise linkage analysis in all three families.     

Genetic heterogeneity in X-linked amelogenesis imperfecta.

The AMELX gene located at Xp22.1-p22.3 encodes for the enamel protein amelogenin and has been implicated as the gene responsible for the inherited dental abnormality X-linked amelogenesis imperfecta (XAI). Three families with XAI have been investigated using polymorphic DNA markers flanking the position of AMELX. Using two-point linkage analysis, linkage was established between XAI and several of these markers in two families, with a combined lod score of 6.05 for DXS16 at theta = 0.04. This supports the involvement of AMELX, located close to DXS16, in the XAI disease process (AIH1) in those families. Using multipoint linkage analysis, the combined maximum lod score for these two families was 7.30 for a location of AIH1 at 2 cM distal to DXS16. The support interval around this location extended about 8 cM proximal to DXS92, and the AIH1 location could not be precisely defined by multipoint mapping. Study of recombination events indicated that AIH1 lies in the interval between DXS143 and DXS85. There was significant evidence against linkage to this region in the third family, indicating locus heterogeneity in XAI. Further analysis with markers on the long arm of the X chromosome showed evidence of linkage to DXS144E and F9 with no recombination with either of these markers. Two-point analysis gave a peak lod score at DXS144E with a maximum lod score of 2.83 at theta = 0, with a peak lod score in multipoint linkage analysis of 2.84 at theta = 0. The support interval extended 9 cM proximal to DXS144E and 14 cM distal to F9.(ABSTRACT TRUNCATED AT 250 WORDS)     

Autosomal dominant macrothrombocytopenia with leukocyte inclusions (May-Hegglin anomaly) is linked to chromosome 22q12-13

Macrothrombocytopenia with leukocyte inclusions (May-Hegglin anomaly) is a rare autosomal dominant disorder characterized by thrombocytopenia, giant platelets, and D?hle body-like inclusions in leukocytes. To determine the genetic basis of this disorder, we performed a genome-wide screen for linkage in three families with May-Hegglin anomaly. For the pooled analysis of the three families, three markers on chromosome 22 had two-point logarithm-of-difference (lod) scores greater than 3, with a maximum lod score of 3.91 at a recombination fraction (theta) of 0.076 for marker D22S683. Within the largest family (MHA-1), the maximum lod score was 5.36 at theta=0 at marker D22S445. Fine mapping of recombination events using eight adjacent markers indicated that the minimal disease region of family MHA-1 alone is in the approximately 26 cM region from D22S683 to the telomere. The maximum lod score for the three families combined was 5.84 at theta=0 for marker IL2RB. With the assumption of locus homogeneity, haplotype analysis of family MHA-4 indicated the disease region is centromeric to marker D22S1045. These data best support a minimal disease region from D22S683 to D22S1045, a span of about 1 Mb of DNA that contains 17 known genes and 4 predicted genes. Further analysis of this region will identify the genetic basis of May-Hegglin anomaly, facilitating subsequent characterization of the biochemical role of the disease gene in platelet formation.     

Fragile X syndrome: diagnosis using highly polymorphic microsatellite markers.

We describe two highly polymorphic microsatellite AC repeat sequences, VK23AC and VK14AC, which are closely linked to the fragile X at Xq27.3. Both VK23AC (DXS297) and VK14AC (DXS292) are proximal to the fragile site. Two-point linkage analysis in 31 fragile X families gave (a) a recombination frequency of 1% (range 0.00%-4%) with a maximum lod score of 32.04 for DXS297 and (b) a recombination frequency of 7% (range of 3%-15%) with a maximum lod score of 12.87 for DXS292. Both of these polymorphisms are applicable to diagnosis by linkage in families with fragile X syndrome. A multipoint linkage map of genetic markers at Xq27.3 was constructed from genotyping these polymorphisms in the CEPH pedigrees. The DXS292 marker is in the DXS98-DXS297 interval and in 3 cM proximal to DXS297.     

A refined genetic map of the region of chromosome 17 surrounding the von recklinghausen neurofibromatosis (NF1) gene

The von Recklinghausen neurofibromatosis (NF1) gene has been mapped to the pericentromeric region of chromosome 17. We conducted linkage analyses of NF1 by using 10 polymorphic DNA markers from this chromosomal region. We ascertained 20 American Caucasian NF1 families (163 individuals, 98 NF1 affected) in Michigan and Ohio and also studied a large family ascertained primarily in North Carolina. The following markers were used in this study: HHH202, TH17.19, D17Z1, ERBA1, EW203, EW206, EW207, EW301, CRI-L581, and CRI-L946. NF1 did not recombine with either TH17.19 or HHH202 in any of the informative meioses surveyed (maximum lod scores of 17.04 and 7.21, respectively, at a recombination fraction of .00), indicating that these markers map very close to the NF1 gene. We also report evidence of three instances of recombination between NF1 and the centromeric marker D17Z1 (maximum lod score of 13.43 at a recombination fraction of .04), as well as two crossovers between pairs of marker loci. We find no evidence of locus heterogeneity, and our results support the localization of the NF1 gene to proximal chromosome 17q.     

Linkage of the gene for an X-linked mental retardation disorder to a hypervariable (AGAT)n repeat motif within the human hypoxanthine phosphoribosyltransferase (HPRT) locus (Xq26).

We recently reported a new X-linked mental retardation (XLMR) disorder in a four-generation family of Dutch descent. Features included Dandy-Walker malformation, basal ganglia disease, and seizures. Twenty-six family members, including two living affected males and two obligate carriers, were available for study. No evidence of linkage was observed between the disease locus and RFLPs from several X-chromosome regions, including Xp21-p22 (13 markers), proximal Xq (four markers), and Xq28 (three markers). However, a new hypervariable short tandem repeat (STR) within the HPRT gene at Xq26 showed positive linkage to the disease locus, with a maximum lod score of 2.19 at a recombination fraction of 0. A second hypervariable marker in Xq26, the dinucleotide repeat XL90A3 (DXS425), showed a lod score of .84 at a recombination fraction of .11. Both the HPRT and DXS425 markers were typed in 40 CEPH families, and subsequent multipoint linkage analysis showed the following order: Xcen-DXS425-(HPRT,XLMR)-F9-qter. HPRT and these flanking markers are therefore useful for carrier detection and prenatal diagnosis in this family. This study illustrates that hypervariable STRs will be powerful tools for linkage analysis and genetic diagnosis, particularly when relatively small families are involved.     

Autosomal recessive nonsyndromic deafness locus DFNB63 at chromosome 11q13.2–q13.3

A genome wide linkage analysis of nonsyndromic deafness segregating in a consanguineous Pakistani family (PKDF537) was used to identify DFNB63, a new locus for congenital profound sensorineural hearing loss. A maximum two-point lod score of 6.98 at θ = 0 was obtained for marker D11S1337 (68.55 cM). Genotyping of 550 families revealed three additional families (PKDF295, PKDF702 and PKDF817) segregating hearing loss linked to chromosome 11q13.2-q13.3. Meiotic recombination events in these four families define a critical interval of 4.81 cM bounded by markers D11S4113 (68.01 cM) and D11S4162 (72.82 cM), and SHANK2, FGF-3, TPCN2 and CTTN are among the candidate genes in this interval. Positional identification of this deafness gene should reveal a protein necessary for normal development and/or function of the auditory system.     

Detection of linkage for heterogeneous disorders by using multipoint linkage analysis.

We have compared the efficiency of the lod score test which assumes heterogeneity (lod2) to the standard lod score test which assumes homogeneity (lod1) when three-point linkage analysis is used in successive map intervals. If it is assumed that a gene located midway between two linked marker loci is responsible for a proportion of disease cases, then the lod1 test loses power relative to the lod2 test, as the proportion of linked families decreases, as the flanking markers are more closely linked, and as more map intervals are tested. Moreover, when multipoint analysis is used, linkage for a disease gene is more likely to be incorrectly excluded from a complete and dense linkage map if true genetic heterogeneity is ignored. We thus conclude that, in general, the lod2 linkage test is more efficient for detecting a true linkage when a complete genetic marker map is screened for a heterogeneous disorder.     

Two families with familial amyotrophic lateral sclerosis are linked to a novel locus on chromosome 16q

Amyotrophic lateral sclerosis (ALS) is a fatal adult-onset disease in which motor neurons in the brain and spinal cord degenerate by largely unknown mechanisms. ALS is familial (FALS) in 10% of cases, and the inheritance is usually dominant, with variable penetrance. Mutations in copper/zinc super oxide dismutase (SOD1) are found in 20% of familial and 3% of sporadic ALS cases. Five families with ALS and frontotemporal dementia (ALS-FTD) are linked to 9q21, whereas one family with pure ALS is linked to 18q21. We identified two large European families with ALS without SOD1 mutations or linkage to known FALS loci and conducted a genomewide linkage screen using 400 microsatellite markers. In both families, two-point LOD scores >1 and a haplotype segregating with disease were demonstrated only across regions of chromosome 16. Subsequent fine mapping in family 1 gave a maximum two-point LOD score of 3.62 at D16S3137 and a three-point LOD score of 3.85 for markers D16S415 and D16S3137. Haplotype analysis revealed no recombination > approximately 30 cM, (flanking markers at D16S3075 and D16S3112). The maximum two-point LOD score for family 2 was 1.84 at D16S415, and the three-point LOD score was 2.10 for markers D16S419 and D16S415. Definite recombination occurred in several individuals, which narrowed the shared haplotype in affected individuals to a 10.1-cM region (flanking markers: D16S3396 and D16S3112). The region shared by both families on chromosome 16q12 corresponds to approximately 4.5 Mb on the Marshfield map. Bioinformatic analysis of the region has identified 18 known genes and 70 predicted genes in this region, and sequencing of candidate genes has now begun.     

Mapping of facioscapulohumeral muscular dystrophy gene to chromosome 4q35-qter by multipoint linkage analysis and in situ hybridization

We have recently assigned the facioscapulohumeral muscular dystrophy (FSHD) gene to chromome 4 by linkage to the microsatellite marker Mfd 22 (locus D4S171). We now report that D4S139, a VNTR locus, is much more closely linked to FSHD. Two-point linkage analysis between FSHD and D4S139 in nine informative families showed a maximum combined lod score (Zmax) of 17.28 at a recombination fraction theta of 0.027. Multipoint linkage analysis between FSHD and the loci D4S139 and D4S171 resulted in a peak lod score of 20.21 at 2.7 cM from D4S139. Due to the small number of recombinants found with D4S139, the position of the FSHD gene relative to that of D4S139 could not be established with certainty. D4S139 was mapped to chromosome 4q35-qter by in situ hybridization, thus firmly establishing the location of the FSHD gene in the subtelomeric region of chromosome 4q. One small family yielded a negative lod score for D4S139. In the other families no significant evidence for genetic heterogeneity was obtained. Studies of additional markers and new families will improve the map of the FSHD region, reveal possible genetic heterogeneity, and allow better diagnostic reliability.     

Linkage of cystic fibrosis locus and polymorphic DNA markers in 14 families

Linkage relationships between the cystic fibrosis (CF) locus and three polymorphic DNA markers were examined in 14 families, five of which were of Hispanic origin. Tight linkage was found between the CF locus and MET (maximum lod score = 7.16 at theta = .001), and between CF and pJ3.11 (maximum lod score = 3.87 at theta = .001). We observed two recombinations between CF and collagen, yielding a maximum lod score of 0.359 at theta = .125, and one recombination in the cluster CF-MET-pJ3.11. Analysis by the seriation method indicates the order COL-pJ3.11-CF-MET.     

Identification of a closely linked DNA marker, DXS178, to further refine the X-linked agammaglobulinemia locus

X-linked agammaglobulinemia (XLA) is an inherited recessive disorder in which the primary defect is not known and the gene product has yet to be identified. Utilizing genetic linkage analysis, we previously localized the XLA gene to the map region of Xq21.3-Xq22 with DNA markers DXS3 and DXS17. In this study, further mapping was performed with two additional DNA probes, DXS94 and DXS178, by means of multipoint analysis of 20 families in which XLA is segregating. Thirteen of these families had been previously analyzed with DXS3 and DXS17. Three crossovers were detected with DXS94 and no recombinations were found between DXS178 and the XLA locus in 9 informative families. Our results show that XLA is closely linked to DXS178 with a two-point lod score of 4.82 and a multipoint lod score of 10.24. Thus, the most likely gene order is DXS3-(XLA,DXS178)-DXS94-DXS17, with the confidence interval for location of XLA lying entirely between DXS3 and DXS94. In 2 of these families, we identified recombinants with DXS17, a locus with which recombination had not previously been detected by others in as many as 40 meiotic events. Furthermore, DXS178 is informative in both of these families and does not show recombination with the disease locus. Therefore, our results indicate that DXS178 is linked tightly to the XLA gene.     

Optimal sampling of a population to determine QTL location, variance, and allelic number

In a population intended for breeding and selection, questions of interest relative to a specific segregating QTL are the variance it generates in the population, and the number and effects of its alleles. One approach to address these questions is to extract several inbreds from the population and use them to generate multiple mapping families. Given random sampling of parents, sampling strategy may be an important factor determining the power of the analysis and its accuracy in estimating QTL variance and allelic number. We describe appropriate multiple-family QTL mapping methodology and apply it to simulated data sets to determine optimal sampling strategies in terms of family number versus family size. Genomes were simulated with seven chromosomes, on which 107 markers and six QTL were distributed. The total heritability was 0.60. Two to ten alleles were segregating at each QTL. Sampling strategies ranged from sampling two inbreds and generating a single family of 600 progeny to sampling 40 inbreds and generating 40 families of 15 progeny each. Strategies involving only one to five families were subject to variation due to the sampling of inbred parents. For QTL where more than two alleles were segregating, these strategies did not sample QTL alleles representative of the original population. Conversely, strategies involving 30 or more parents were subject to variation due to sampling of QTL genotypes within the small families obtained. Given these constraints, greatest QTL detection power was obtained for strategies involving five to ten mapping families. The most accurate estimation of the variance generated by the QTL, however, was obtained with strategies involving 20 or more families. Finally, strategies with an intermediate number of families best estimated the number of QTL alleles. We conclude that no overall optimal sampling strategy exists but that the strategy adopted must depend on the objective.Communicated by P. Langridge     

Amplification of the COL2A1 3′ variable region used for segregation analysis in a family with the Stickler syndrome

Summary Amplification of a variable region 3 to the human type II collagen gene (COL2A1) has permitted segregation analysis in a three generation Stickler syndrome pedigree. This family had previously proved uninformative for the known restriction fragment length dimorphisms. Amplification of the variable region revealed five distinguishable alleles, of which three were segregating in this family. The lod score in favour of linkage was 2.86 at zero recombination.