Dalmatians have a well-described change in purine metabolism

Transcription

1 J Vet Intern Med 2004;18: Inheritnce of Urinry Clculi in the Dlmtin D.L. Bnnsch, G.V. Ling, J. Be, nd T.R. Fmul Dlmtins re unique mong dogs in tht they excrete uric cid in their urine s the end product of purine metbolism rther thn llntoin s do other breeds of dogs. Urinry clculi form from urte (slts of uric cid) nd cn cuse urethrl obstruction in mle Dlmtins. Although ll Dlmtins hve the primry defect, only subset develops clinicl disese. We postulted tht clculi formtion might hve genetic component tht segregtes within the breed, cusing some nimls to form clculi nd others to never form clculi despite excreting uric cid in their urine. We used survey to scertin the urinry clculi sttus bsed on clinicl signs of dult Dlmtins ged 6 yers or older, nd we used pedigrees from these sme nimls to estimte the heritbility of the clinicl mnifesttion of urte clculi within the breed to be.87 (.75.96). The prevlence of the disese ws 34% ( %) mong mle Dlmtins in our survey. The high heritbility of the disese mkes it possible for breeders to effectively select ginst the disese. Key words: Cnine; Dog; Genetic; Heritbility; Inherited. Dlmtins hve well-described chnge in purine metbolism tht leds to the excretion of urte (slts of uric cid) in the urine rther thn the excretion of llntoin like most other breeds of dogs. 1 This reltive hyperuricosuri is lso seen in humns nd some gret pes who lck the enzyme uricse. The moleculr nture of the defect tht cuses hyperuricosuri in Dlmtins hs not been determined, but experiments hve shown tht Dlmtins hve uricse enzyme ctivity present in their livers. 2 The mode of inheritnce of the hyperuricosuri ws nlyzed by crossing Dlmtins to other cnine breeds. 3,4 The puppies produced in these crosses hd norml uric cid excretion in their urine consistent with recessively inherited disorder. The trit is fixed within the breed becuse ll purebred Dlmtins tht re tested excrete higher mounts of urte in their urine thn do norml dogs. Uric cid is poorly soluble in urine, nd the clinicl consequence of excreting lrge mounts of urte in the urine is higher incidence of urte clculi (stones) thn found in other breeds. 5 Clculi composed of urte cn cuse urethrl blockge in mle Dlmtins. The verge ge of onset of clinicl signs cused by stone formtion, including hemturi, strnguri, nd pollkiuri, is 4.5 yers. 5 7 Two remrkble observtions on clculi formtion in Dlmtins re tht not ll Dlmtins form clculi nd tht 97% of Dlmtins with stones composed of slts of uric cid re mle. 5 This result is surprising becuse ll Dlmtins tested hve the hyperuricosuri defect. One explntion for the reson why not ll Dlmtins show clinicl signs of the disese is tht n inherited fctor segregtes within the breed nd cuses subset of the dogs to form clculi. If this genetic fctor were X-linked, it could explin the higher numbers of ffected mles thn femles. Alter- From the Deprtments of Popultion Helth nd Reproduction (Bnnsch, Be) nd Medicine nd Epidemiology (Ling), School of Veterinry Medicine, nd the Deprtment of Animl Science (Fmul), College of Agriculturl nd Environmentl Sciences, University of Cliforni, Dvis, CA. Reprint requests: Dnik Bnnsch, DVM, PhD, VM:PHR School of Veterinry Medicine, One Shields Avenue, University of Cliforni, Dvis, Dvis, CA 95616; e-mil: dlbnnsch@ucdvis.edu. Submitted August 5, 2003; Revised October 21, 2003, nd Jnury 1, 2003; Accepted Mrch 29, Copyright 2004 by the Americn College of Veterinry Internl Medicine /04/ /$3.00/0 ntively, the predominnce of ffected mles could be cused by difference in the size of the urethr between mles nd femles. In prticulr, the os penis of the mle dog limits the size of the mle urethr. However, femles of other breeds show clinicl signs when they hve urinry clculi; therefore, the presence of stones in femle Dlmtins my occur but go unnoticed. An lterntive explntion is tht clculi formtion within the breed is cused by differences in husbndry or other environmentl fctors. The objective of the present study ws to confirm nd chrcterize genetic component to urinry clculi in the Dlmtin breed bsed on the clinicl signs of this disese. This disese would be difficult to study with controlled breeding experiments becuse it hs lte ge of onset (verge ge 4.69 yers 5 ) nd there my be strong environmentl component to disese mnifesttion. Rther, we chose to tke dvntge of the Dlmtins lredy produced by breeders to investigte genetic component of the disese. To do so, we solicited pedigrees nd disese sttus from the owners of Dlmtins by n online survey. Specificlly, we hoped to quntify the inheritnce of this disorder by the estimtion of heritbility with threshold model. Heritbility is mesure of the genetic similrity between prents nd offspring for the trit under investigtion, which, in this cse, ws clinicl signs of urte clculi. 7 Rnging from 0 (no genetic resemblnce between prents nd offspring) to 1 (identicl resemblnce), heritbility lso provides mens of ssessing the likely success of breeding progrm intended to reduce the prevlence of clculi in Dlmtins. A threshold model is necessry element of this nlysis becuse of the binry nture of the phenotype of urinry clculi (ie, presence or bsence). As such, our nlysis must ddress nd ccommodte the obvious nonnormlity found in the distribution of phenotypes. The threshold model is the most commonly used nd most powerful pproch to ssessing inheritnce in binry chrcters. 7 After estimting the heritbility, we intended to serch for evidence of segregting locus of lrge effect on urinry clculi by mens of complex segregtion nlysis. 7 This technique hs long been used by geneticists to ssess lterntive modes of disese inheritnce in humns, nd we hoped to determine if the presence of urinry clculi could be explined by the ction of single locus. Mterils nd Methods Phenotypic informtion ws collected from Dlmtin owners by survey vilble on the World Wide Web. Prticipnts in the survey

2 484 Bnnsch et l were recruited by n rticle plced in the Dlmtin Club of Americ mgzine (The Spotter) nd by the uthors notifiction of the study to regionl Dlmtin clubs. Survey questions included bseline dt of dte of birth, gender, nd spy or neuter sttus, s well s the Americn Kennel Club (AKC) registrtion numbers nd prents registered nmes. The survey ws constructed to encourge n ccurte ssessment of urinry clculi sttus by sking series of questions bout the tretment nd outcome of the disese, including whether the stones were removed (either surgiclly or by other methods) or left in the bldder. Dogs were counted s ffected bsed on the owners responses to the questionnire. Informtion ws collected on dogs tht were older thn 6 yers of ge to llow expression of the phenotype. Owners were sked if their dogs hd crystls in their urine s seprte question from the question of urinry clculi becuse, in the uthor s experience (GVL), mny Dlmtin owners inccurtely equte crystlluri with urinry clculi. Prevlence of clculi in Dlmtin ptients of the Veterinry Medicl Teching Hospitl (VMTH), University of Cliforni Dvis, ws determined by reviewing records of ll Dlmtins seen t the hospitl from 1985 to Dogs were counted s ffected if they hd history of stone disese or if dignosis of stone disese ws mde t the VMTH. The estimtion of heritbility, s well s the subsequent complex segregtion nlysis, is bsed on set of Dlmtins with recorded urinry clculi phenotype. The form of this phenotype is binry (ie, ffected versus unffected). Owners of 179 dogs prticipted in the project by submitting completed online surveys. In ddition to the 179 dogs with known phenotype, 562 reltives of these dogs (without known dignosis of urinry clculi) were entered into the nlysis for totl of 741 dogs in the dt set. Pedigrees were purchsed online through the AKC to estblish reltionships mong the nimls for which we hd phenotypic dt. Along with the dignosis, vriety of dditionl informtion bout the mount of wter consumed dily by the dogs nd the time periods when the dogs were llowed ccess to wter nd urintion sites ws collected to identify environmentl fctors shred mong ffected dogs. Owners were sked if their dogs slept inside, hd free ccess to wter during the dy nd night, were llowed to urinte outside during the dy nd night, nd if the owners perceived tht their dogs drnk lot of wter. Estimtion of heritbility is conducted with threshold models, 8 n pproch typicl for binry nd ordered ctegoricl trits. The observtion of urinry clculi is considered s binry trit s y ij (y ij 0 when unffected; 1 when ffected) for the j-th dog (j 1, 2,..., 179) of the i-th sex (i 1 for mles; 2 for femles). The ssumption of threshold models is such tht this ctegoricl phenotype is ssumed to be relted to n underlying, unobservble continuous vrite through set of 3 fixed thresholds [ 0 ; 1 0; 2 ]. Note tht 1 is set to 0 for computtionl convenience, with no loss in generlity or ffect on subsequent dt nlysis. The model for is similr to ny we might use for continuous phenotypes. The lgebric form of the model is ijk sex i sleep j k e ijk (1) where ijk is n unobservble continuous vrite for the k-th (k 1, 2,..., 179) dog of the i-th sex (i 1 for mle; 2 for femle) in the j-th clss for sleeping in the house (j 1 for yes; 2 for no). The is n unknown constnt, sex i is the contribution of the i-th sex to the expression of urinry clculi, sleep j is the potentil effect of sleeping in the house on the expression of urinry clculi, k is the dditive genetic contribution of the k-th niml, nd e ijk is n unknown residul. Both k nd e ijk re ssumed to be rndom effects with 0 mens nd vrinces 2 (the dditive genetic vrince) nd e2 (the residul vrince), respectively. The rndom niml effect ccounts for the covrince in phenotype of reltives nd is ssumed to be multivritely normlly distributed, with covrince structure bsed upon the dditive reltionships mong ll dogs in the dt set. Becuse the underlying scle is unobservble, we ssume tht the totl vrince is P2 2 e2 where e2 1.0, with no loss of generlity Note tht the heritbility of urinry trct clculi, on the unobservble continuous scle, cn be estimted s h 2 2 /( 2 e2 ). Other questions from the survey lso re included in the threshold model nlysis, though terms for these questions re not included in model (Eqution 1) in the interest of brevity. These questions ddress drinking hbits during the dy nd night. Becuse the ssumed distribution of the unobservble vrite is norml, estimtes of the effects of the yes nd no replies to the questions lso re normlly distributed, fct tht cn be used in the ssessment of the significnce of these replies to the presence or bsence of urinry clculi. To rrive t estimtes of 2, e2, we used mixed model Byesin strtegy outlined by Sorensen et l. 11 Estimtion of the distribution of the unknown prmeters uses technique of numericl integrtion referred to s Gibbs smpling. 12 The lgorithm is bsed on the itertive genertion of sequence of rndom vribles from the known conditionl distributions of the prmeters given the likelihood function of the dt. Subsequent estimtes of the prmeters re found in the nlysis of this sequence of rndom numbers, clled the Gibbs smple. Here we generted totl of 250,000 smples of possible heritbility. Our estimte of heritbility is tken from the men of every 25th iterte, fter discrding the first 20,000 smples, for totl 9,200 smple observtions (ie, 9,200 [250,000 20,000]/25). The interested reder is directed to Sorensen et l 11 nd to Vn Tssell nd Vn Vleck, 13 the uthors of the public domin softwre by which this nlysis ws performed, for more complete description of the Gibbs smpling process nd its theoreticl justifiction. To evlute the possible segregtion of single locus with lrge effect on the urinry trct clculi phenotype, we turned to regressive logistic models developed for complex segregtion nlysis. 14 A logistic model ws used becuse the softwre for complex segregtion nlysis in threshold models does not exist. Commonly used in the nlysis of binry disese trits, such models re built round the nturl logrithm of the rtio of the mrginl probbilities ln{pr(ffected)/pr(unffected)} i for niml i. With some lgebric mnipultion, this leds to the expression Pr(ffected) e i /(1 e i ) where, for niml i, i sex i g i i e i (2) nd sex i is the contribution of gender to the probbility of being ffected, g i is the possible contribution to disese of mjor locus, i is polygenic contribution to disese, nd e i is the residul contribution to the probbility of being ffected. This prmeteriztion permits the fitting of descriptive, independent vribles (equivlent to tht in the nlysis of vrince) s well s terms for polygenic nd single gene contributions. A thorough discussion of complex segregtion nlysis is provided by Lynch nd Wlsh. 15 The technique is intended to integrte Mendelin trnsmission genetics, llele frequency, nd penetrnce with the ptterns of covrince mong reltives expected in polygenic models of inheritnce. Elston et l 16 outline criteri tht must be stisfied before cceptnce of the mjor gene model in order to reduce the incidence of flse positives. Fitting the vriety of models necessry for complex segregtion nlysis of urinry clculi ws conducted by Sttisticl Anlysis for Genetic Epidemiology (SAGE) softwre. Before complex segregtion nlysis, SAGE requires fmily structure without loops (ie, pedigree free of inbreeding). This limittion is computtionl, not genetic or sttisticl. The 741 individul dogs were ctegorized into 30 distinct fmilies of Dlmtins. However, 1 fmily contined 347 dogs, including severl loops of inbreeding. SAGE is incpble of performing complex segregtion nlysis in such lrge, complex pedigree. Accordingly, this 1 ctul fmily ws ressigned into 6 seprte fmilies by removing the ncestors responsible for the inbreeding, followed by duplicting this ncestor s new niml to crete independent fmilies. At the end of this process were 36 fmilies tht included ll 179 recorded dogs, but severl dogs were represented in more thn 1 of the 6 creted fmilies. The impct on the finl complex segregtion nlysis is expected to

3 Urinry Clculi in Dlmtions 485 Tble 1. s of genetic vrince, heritbility, nd contrsts mong independent vribles long with their stndrd errors nd empiricl 95% confidence intervls for urinry trct clculi in Dlmtins in threshold model. 95% Empiricl Confidence Intervl Question Prmeter Men Stndrd Error Sleep in house? Out t night? Wter t night? Out in dy? Wter in dy? Drink? Additive vrince Heritbility Mles Femles mke the detection of mjor locus more difficult, becuse reltionships tht we know exist will be lost in the nlysis. Results Our survey provided 179 dogs (99 mles, 80 femles) of known disese phenotypes, 144 dogs ( %; percentge stndrd error) were unffected, nd 35 ( %) were ffected. Of the 35 dogs ffected, 34 were mles. We wished to determine if the prevlence of the disese in our survey popultion ws similr to the disese prevlence in Dlmtins. To do this, we lso estimted the disese prevlence in our hospitl popultion from 1985 to There were 565 Dlmtins seen t the VMTH; 294 were mles, of which 66 were dignosed with urinry clculi nd 12 hd history of urinry clculi. Among ll observed Dlmtins, 78 of 565 ( %) were ffected, nd ccordingly this 95% confidence intervl (CI) overlps with tht found in our survey. Among mles exclusively, our survey hd 34 ffected dogs from totl of 99 mles (ie, %), where the lso overlps the hospitl smple (ie, %). A summry of the results from the nlysis of the threshold model, including n estimte of the heritbility of urinry trct clculi on the underlying, unobservble scle for ech of the phenotypic clssifiction schemes, is presented in Tbles 1 nd 2. As shown, the men heritbility of the Gibbs smple is.87, with 95% of the vlues rnging from.75 to.96. Evidence for the difference in the prevlence of urinry trct clculi cross genders is shown in Tble 1. The men difference in genders, on the underlying scle, ws estimted s 7.06 with n empiricl from 2.6 to An intervl tht does not spn zero (0.0) is evidence tht gender differences re in the expression of urinry clculi. Conversely, s the men estimtes of the survey question effects in Tble 1 indicte, ll these hve CIs tht overlp 0.0 nd cn therefore be considered to not hve significnt contribution to urinry clculi. The generl results of the complex segregtion nlysis re presented in Tble 2. When interpreting the results of this nlysis, the form of the model is bsed on the cumultive logistic function. Accordingly, the prmeter estimtes of Tble 2 would be used to compute the vrite i of Eqution 2, which could, if desired, be trnsformed to Pr(ffected). 14 Although the threshold nlysis considered vriety of explntory vribles, the results presented in Tble 1 indicte tht only gender ws significnt contributor to the incidence of urinry clculi. Accordingly, the complex segregtion nlysis included only n effect for gender, ignoring the dditionl explntory vribles. Given the strong gender differences presented in Tble 1, we lso considered 2nd nlysis of our dt restricted only to mles (ie, ll femle phenotypes were recoded s unknown). It hs been suggested tht differences in the femle urethr llow for the pssge of stones, nd we wnted Tble 2. Prmeter estimtes ( ) for complex segregtion nlysis in logistic model of urinry trct clculi in Dlmtins in both no mjor locus model nd generl mjor locus model with Mendelin trnsmission. No Mjor Generl Mjor Pooled susceptibility Covrite: Sex AA susceptibility AB susceptibility BB susceptibility Prent offspring covrince b Frequency (A) Ln (likelihood) , stndrd error; CI, confidence intervl;, not pplicble. b Prent offspring covrince is term to ccommodte residul polygenic vrition.

4 486 Bnnsch et l Tble 3. s of genetic vrince, heritbility, nd contrsts mong independent vribles long with their stndrd errors nd empiricl 95% confidence intervls for urinry trct clculi in Dlmtins in threshold model where ll femles re recorded with phenotype of unknown. Sleep in house? Out t night? Wter t night? Out in dy? Wter in dy? Drink? Question Prmeter Men Additive vrince Heritbility Stndrd Error % Empiricl Confidence Intervl to ddress the possibility tht the contribution of ny mjor gene my be more clerly expressed in mles thn in femles. Tbles 3 nd 4 re vrition of the results first considered in Tbles 1 nd 2. However, the conclusions to be drwn from Tbles 3 nd 4 re no different from those to be drwn from Tbles 1 nd 2, specificlly tht the presence of urinry clculi ppers to hve strong hereditry component, but there is no evidence of segregting mjor locus with n ffect on this binry chrcter. Discussion Reports on the inheritnce of disese typiclly ddress the nture of the smpling process, usully evluting the degree to which the smple t hnd cn be considered rndom smple of the popultion of inference. Although we re concerned with the potentil impct nonrndom smpling cn hve on the interprettion of results, we re encourged by the similrity in the prevlence of urinry clculi mong the Dlmtins in our survey nd the prevlence mong Dlmtin ptients of the VMTH. The similrity in prevlence lso lends strength to the ccurcy of the phenotype dt provided by owners. Although wry of the impct of scertinment bis in our nlyses, we believe our smple of dogs to be representtive of the Dlmtin breed. Regrdless, the impct of such smpling on the estimtion of heritbility is likely to be smll not lrge enough to lter our conclusion tht the incidence of urinry clculi in Dlmtins is trit with strong hereditry component. In fct, heritbility of this order is suggestive, by itself, of the segregtion of single locus of lrge effect. Morton nd McLen 17 demonstrted tht mjor loci tend to increse the heritbility of trit in given popultion, nd vlue greter thn.70 is comprtively lrge for mny polygenic trits. How these 179 dogs entered our smple is criticl to the evlution of inheritnce. Most dt sets in disese genetics re constructed round ffected nimls (ie, probnds), nd this set of dt is no exception. However, rther thn using ffected dogs from the hospitl popultion, we tried to obtin rndom smple of Dlmtins by sking for informtion on ll Dlmtins nd not just Dlmtins with clinicl signs of urinry clculi. Our survey ws clled the Dlmtin Survey rther thn stone survey to ttrct more rndom smple of prticipnts. One cvet of the survey pproch for phenotype dt is tht it is possible tht Dlmtins cn hve urinry clculi without displying clinicl signs. If this is the cse, then our nlysis hs identified the genetic influence on the mnifesttion of the disese rther thn clculi formtion. This smpling strtegy mkes correction for scertinment bis problemtic. In the estimtion of heritbility, it is importnt to note tht mixed liner models re cpble of ccommodting nonrndomly smpled dt. 18 Accordingly, the estimtion of the heritbility of urinry trct clculi should not be bised by fmily selection, provided the dogs t the bse of the pedigree (dogs with no prents identified) cn be considered rndom smple of Dlmtins. There is no obvious test for this ssumption becuse the dogs t the bse of the pedigree hve no recorded urinry clculi phenotype. As our threshold nlysis indictes, we lso cn confirm the well-known observtion of strong gender effect. No evidence of mjor locus ws identified when only mles were given recorded phenotype, indicting tht n X- linked mode of inheritnce is n unlikely explntion for the gender effect. It is difficult to imgine environmentl fctors tht would produce the strong gender effect, nd, consequently, we re left with the conclusion tht mles show clinicl signs bsed on their urethrl ntomy. Surprisingly, none of the questions sked regrding the husbndry of nimls in their home provided significnt explntion for the production of urinry clculi. Our hope hd been tht knowledge of such environmentl fctors thought to contribute to the production of urinry clculi would help us uncover the contributions of segregting mjor locus. However, complex segregtion nlysis filed to provide sttisticl evidence of mjor locus, just s the environmentl fctors included in our survey filed to explin vrition in observtions of urinry clculi. An importnt environmentl fctor tht we did not ddress in this nlysis is the effect of diet on urinry clculi formtion. Our estimtes of the prevlence of clinicl disese in mle Dlmtins rnge from to 34.34%. The importnce of this disese to the helth of Dlmtins should not be underestimted. As result of this initil evlution of the inheritnce of the clinicl signs of urinry clculi in Dlmtins, we conclude tht, given the mgnitude of the heritbility estimte, selection ginst this trit should be highly successful.

5 Urinry Clculi in Dlmtions 487 Tble 4. Prmeter estimtes ( ) for complex segregtion nlysis in logistic model of urinry trct clculi in Dlmtins in both no mjor locus model nd generl mjor locus model with Mendelin trnsmission where ll femles re recorded with phenotype of unknown. No Mjor Generl Mjor Pooled susceptibility AA susceptibility AB susceptibility BB susceptibility Prent offspring covrince b Frequency (A) Ln (likelihood) , stndrd error; CI, confidence intervl;, not pplicble. b Prent offspring covrince is term to ccommodte residul polygenic vrition. This dvice my be quite difficult to put into prctice becuse of the possibility of lte onset of clinicl signs secondry to urinry clculi, time tht my well come fter breeding decisions hve been mde. A screening test for urinry clculi would be very useful in this breed becuse it would be importnt to identify dogs t risk for obstruction s well s tool to id in breeding decisions. Footnotes SAGE softwre, Deprtment of Epidemiology nd Biosttistics, Rmmelkmp Center for Eduction nd Reserch, MetroHelth Cmpus, Cse Western Reserve University, Clevelnd, OH Acknowledgments This work ws supported by the AKC Cnine Helth foundtion nd the Center for Compnion Animl Helth, School of Veterinry Medicine, University of Cliforni Dvis, Dvis, CA. The uthors wish to thnk Cthy Rinldo nd Rob Tryon for their technicl ssistnce s well s the Dlmtin owners who prticipted. References 1. Sorenson JL, Ling GV. Metbolic nd genetic spects of urte urolithisis in Dlmtins. J Am Vet Med Assoc 1993;203: Giesecke D, Tiemeyer W. Defect of uric cid uptke in Dlmtin dog liver. Experienti 1984;40: Keeler CE. The inheritnce of predisposition to renl clculi in the Dlmtin. J Am Vet Med Assoc 1940;96: Schible RH. Genetic predisposition to purine uroliths in Dlmtin dogs. Vet Clin North Am Smll Anim Prct 1986;16: Ling GV, Frnti CE, Ruby AL, et l. Urolithisis in dogs. II: Breed prevlence, nd interreltions of breed, sex, ge, nd minerl composition. Am J Vet Res 1998;59: Sorenson JL, Ling GV. Dignosis, prevention, nd tretment of urte urolithisis in Dlmtins. J Am Vet Med Assoc 1993;203: Cse LC, Ling GV, Ruby AL, et l. Urolithisis in Dlmtions: 275 cses ( ). J Am Vet Med Assoc 1993;203: Flconer DS, Mcky TFC. Introduction to Quntittive Genetics, 4th ed. Essex, UK: Longmn Group LTD; 1996: Hrville DA, Mee RW. A mixed model procedure for nlyzing ordered ctegoricl dt. Biometrics 1984;40: Ginol D, Foulley JL. Sire evlution for ordered ctegoricl dt with threshold model. Genet Sel Evol 1983;15: Sorensen DA, Anderson S, Ginol D, et l. Byesin inference in threshold models using Gibbs smpling. Genet Sel Evol 1995;27: Gemn S, Gemn D. Stochstic relxtion, Gibbs distributions nd Byesin restortions of imges. IEEE Trns Pttern Anlysis Mchine Intell 1984;6: Vn Tssell CP, Vn Vleck LD. A set of Fortrn progrms to pply Gibbs smpling to niml models for vrince component estimtion. In: A Mnul for use of MTGSAM. US Dept of Agriculture, Agriculturl Reserch Service; Avilble t: gov/curtvt/mtgsm.html. Accessed June 1, Bonney GE. Regressive logistic models for fmilil disese nd other binry trits. Biometrics. Biometrics 1986;42: Lynch M, Wlsh B. Genetics nd Anlysis of Quntittive Trits. Sunderlnd, MA: Sinuer; 1998:xvi. 16. Elston RC, Nsmboodrii KK, Glueck CJ, et l. Studies of the genetic trnsmission of hypercholesterolemi nd hypertriglyceridemi in 195 member kindred. Ann Hum Genet 1975;39: Morton NE, Mclen CJ. Anlysis of fmily resemblnce. III Complex segregtion of quntittive trits. Am J Hum Genet 1974;26: Henderson CR. Applictions of liner models in niml breeding. Guelph, Ontrio, Cnd: University of Guelph; 1984.