ARTICLES. A role for a neo-sex chromosome in stickleback speciation
|
|
- Norman Williamson
- 6 years ago
- Views:
Transcription
1 Vol Octoer 9 doi:1.138/nture8441 A role for neo-sex chromosome in stickleck specition Jun Kitno 1 {, Joseph A. Ross 1,2 {, Seiichi Mori 3, Mnu Kume 4, Felicity C. Jones 5, Yinggung F. Chn 5, Devin M. Asher 6 {, Jne Grimwood 6 {, Jeremy Schmutz 6 {, Richrd M. Myers 6 {, Dvid M. Kingsley 5 & Ctherine L. Peichel 1 Sexul ntgonism, or conflict etween the sexes, hs een proposed s driving force in oth sex-chromosome turnover nd specition. Although closely relted species often hve different sex-chromosome systems, it is unknown whether sex-chromosome turnover contriutes to the evolution of reproductive isoltion etween species. Here we show tht newly evolved sex chromosome contins genes tht contriute to specition in threespine stickleck fish (Gsterosteus culetus). We first identified neo-sex chromosome system found only in one memer of symptric species pir in Jpn. We then performed genetic linkge mpping of mle-specific trits importnt for reproductive isoltion etween the Jpnese species pir. The neo-x chromosome contins loci for mle courtship disply trits tht contriute to ehviourl isoltion, wheres the ncestrl X chromosome contins loci for oth ehviourl isoltion nd hyrid mle sterility. Our work not only provides strong evidence for lrge X-effect on reproductive isoltion in verterte system, ut lso provides direct evidence tht young neo-x chromosome contriutes to reproductive isoltion etween closely relted species. Our dt indicte tht sex-chromosome turnover might hve greter role in specition thn ws previously pprecited. Sexully ntgonistic selection hs een proposed s mjor driving force in the evolution of sex chromosomes. Specificlly, nturl selection is expected to fvour linkge etween genes with sexully ntgonistic effects (tht is, eneficil in one sex nd detrimentl in the other) nd the sex-determintion locus, resulting in reduction of recomintion etween sex chromosomes 1. In n XY sex-chromosome system, reduction in recomintion ultimtely leds to the degenertion of the Y chromosome, therey exposing lleles on the hemizygous X chromosome to selection in mles 2. Thus, mle-eneficil lleles, mnifested s sexully dimorphic nd/or sexully selected trits, re predicted to ccumulte on the X chromosome 3,4. When these mle-eneficil trits or lleles re importnt for reproductive isoltion etween species, the X chromosome is lso predicted to hve key role in specition. A disproportiontely lrge effect of the X chromosome hs een demonstrted for hyrid mle sterility 5,6, lthough the dt supporting lrge X-effect for other isolting rriers hs een less consistent 6. Sexully ntgonistic selection is lso predicted to drive the divergence of sex-chromosome systems etween closely relted species 7,8. Sex-chromosome turnover hs een oserved cross mny tx, ut it is prticulrly striking in fishes 9,1. Mny independent groups of fishes show evidence for the rpid evolution of sex chromosomes through severl different mechnisms, including the trnsposition of n existing mle-determintion locus to n utosome 11, the evolution of new mle-determintion locus on n utosome 12, nd fusions etween n utosome nd n existing Y chromosome 13,14. It hs een suggested tht the rpid turnover of sex chromosomes driven y sexul conflict might lso hve role in the high specition rtes seen in some groups of fishes However, direct role for sex-chromosome turnover in specition hs not een empiriclly investigted in ny system. Here we demonstrte tht there is newly formed sex-chromosome system in threespine stickleck popultion found in Jpn. This Jpn Se form diverged from the Pcific Ocen threespine stickleck during periods of geogrphicl isoltion etween the Se of Jpn nd the Pcific Ocen out million yers go,19. Becuse we cn cross the derived Jpn Se form to the ncestrl Pcific Ocen form, we hve een le to tke dvntge of the genetic tools ville for the threespine stickleck to investigte whether the evolution of neo-sex chromosome hs contriuted to the evolution of mle trits tht ct s isolting rriers etween the derived Jpn Se nd the ncestrl Pcific Ocen popultions. Jpn Se stickleck neo-sex chromosome In ll threespine stickleck popultions exmined previously, including the Pcific Ocen form, linkge group 19 (LG19) is the sex chromosome nd LG9 is n utosome 14,21,22. However, in the course of mking linkge mp from Jpn Se cross, we noticed tht severl LG9 mrkers co-segregted with LG19 mrkers previously found to e tightly linked to the sex-determintion locus in region of reduced recomintion nd rerrngements on the Y chromosome 21,22. This ssocition ws oserved when mle meioses, ut not femle meioses, were nlysed (Fig. 1). These dt indicted tht one copy of LG9 might e fused to one copy of LG19 (the Pcific Ocen Y chromosome), forming neo-y chromosome in Jpn Se sticklecks. Therefore, we performed fluorescence in situ hyridiztion (FISH) with LG19 nd LG9 proes on metphse chromosome spreds from two different popultions of the Jpn Se form. We found tht the Jpn Se mles (n 5 4) from two different popultions hve n odd numer of chromosomes (2n 5 41), with one lrge 1 Division of Humn Biology, Fred Hutchinson Cncer Reserch Center, 11 Firview Avenue North, Settle, Wshington 9819, USA. 2 Grdute Progrm in Moleculr nd Cellulr Biology, University of Wshington, Settle, Wshington 98195, USA. 3 Biologicl Lortory, Gifu-keizi University, Ogki, Gifu , Jpn. 4 Aqu Restortion Reserch Center, Pulic Works Reserch Institute, Kkmighr, Gifu , Jpn. 5 Deprtment of Developmentl Biology nd Howrd Hughes Medicl Institute, Stnford University, Stnford, Cliforni 9435, USA. 6 Deprtment of Genetics nd Stnford Humn Genome Center, Stnford University, Stnford, Cliforni 9434, USA. {Present ddresses: Deprtment of Ecology nd Evolutionry Biology, Grdute School of Life Sciences, Tohoku University, Sendi, Miygi , Jpn (J.K.); Deprtment of Biology, University of Mrylnd, College Prk, Mrylnd 742, USA (J.A.R.); HudsonAlph Institute for Biotechnology, Huntsville, Alm 3586, USA (D.M.A., J.G., J.S. nd R.M.M.) 9 Mcmilln Pulishers Limited. All rights reserved 179
2 NATURE Vol Octoer 9 unpired chromosome tht hyridized to the LG19 nd LG9 proes, providing evidence for the LG9 Y chromosome fusion (Fig. 1 nd Supplementry Fig. 1). In contrst, the Jpn Se femles (n 5 4) from oth popultions hve n even numer of chromosomes (2n 5 42), nd the LG9 nd LG19 proes hyridize to seprte chromosome pirs (Fig. 1 nd Supplementry Fig. 1). Becuse the fused copy of LG9 segregtes with the Y chromosome in Jpn Se mles, the other copy segregtes s n X chromosome; this neo-sex chromosome system is defined s n X 1 X 2 Y system 13, in which X 1 is the ncestrl X chromosome (LG19) nd X 2 is the neo-x chromosome (LG9). Thus, the Jpn Se form hs unique neo-sex chromosome system, which hs proly evolved within the pst million yers of isoltion etween the Pcific Ocen nd Jpn Se sticklecks,19. Components of reproductive isoltion We hve the opportunity to test the role of this neo-sex chromosome in reproductive isoltion etween the Jpn Se nd the Pcific Ocen forms ecuse oth re ndromous nd migrte into Lke Akkeshi nd the Bekneushi mrsh during the reeding seson. In this loction, they co-occur, long with hyrid dults nd juveniles, within hyrid zone in the Bekneushi River (Mid2 in Fig. 2, nd Supplementry Fig. 2). We found tht temporl isoltion, ehviourl isoltion nd hyrid mle sterility contriute to reproductive isoltion etween the forms in the hyrid zone (Supplementry Fig. 3 nd Supplementry Discussion). We previously demonstrted tht ehviourl isoltion nd hyrid mle sterility re symmetric, ut ct in complementry directions 19. Pcific Ocen femles mte exclusively with Pcific Ocen mles, wheres the Jpn Se femles mte with oth types of mles in lortory mte-choice trils 19. Although Jpn Se femles do mte with Pcific Ocen mles, hyrid mles resulting from this cross hve severely reduced fertility, wheres reciprocl hyrid mles nd ll hyrid femles re fertile 19. To test whether reproductive isoltion is linked to sex-chromosome divergence, we first investigted which mle mting trits contriute to symmetric ehviourl isoltion. First, we nlysed the reltionship etween finl femle choice nd differences in mle ody size nd found tht oth types of femles tend to choose lrger mles (Fig. 3; Pcific Ocen femles, n 5 3, coefficient estimte 5.254, Z , P 5.228, logistic regression; Jpn Se femles, n 5 29, coefficient estimte 5.122, Z , P 5.8, logistic regression). Becuse Jpn Se mles (stndrd length mm (men 6 s.e.m.), n 5 59) re smller thn Pcific Ocen mles (stndrd length mm, n 5 45; nlysis of vrince (ANOVA), F 1, , P, ), divergence in ody size is one of the fctors tht contriutes to symmetric ehviourl isoltion. However, even in the sence of ody size divergence, Pcific Ocen femles still hve 93.5% proility (95% confidence intervl ) of choosing conspecific mle (Fig. 3), suggesting tht other fctors re involved in Pcific Ocen femle choice. We found tht difference in mle dorsl ehviour lso contriutes to symmetric ehviourl isoltion. Dorsl is component of mle mting ehviour specific to threespine sticklecks in which the mle rises his dorsl spines nd pricks the femle. This ehviour might help the mle ssess the femle, provide tctile stimultion to induce femle spwning, or ct s wy for the mle to disply his dorsl spines to the femle 23,24. In Jpn Se mles, the Femle meiosis LG19 (X 1 ) LG19 FISH proe Stn33 Stn6 Stn7 Stn274 Stn284 Stn256 Stn Mp LG9 (X 2 ) Stn15 Stn17 X 1 X 1 X 2 X 2 X 1 X 2 LG19 FISH proe Mle meiosis LG9-LG19 Stn6 Stn8 Stn225 Stn113 Stn114 Stn115 neo-y Jpn Se femle (2n = 42) Jpn Se mle (2n = 41) LG9 FISH proe Stn256 Stn284 Cyp Mp Sex Stn12 (mle) Stn15 Stn17 Stn 1º E N 4º N 3º N N Akkeshi By 13º E Se of Jpn 14º E Pcific Ocen Jpnese rchipelgo Mid2 Upstrem Mid1 Bekneushi River Lke Lke Akkeshi Akkeshi 6 dults 6 juveniles 7 dults 7 juveniles Pro of ssignment Jpn Se form Pro of ssignment Pro of ssignment Lke () Pro of ssignment Lke (84) Mid1 (1) Pcific Ocen form Mid2 (122) Mid2 (7) (46) (37) (22) (138) Upstrem (13) Upstrem (77) (11) (24) LG9 FISH proe Stn113 Stn225 Stn116 1 cm Figure 1 Genetic nd cytogenetic evidence of fusion etween one copy of LG9 nd the Y chromosome in Jpn Se mles., A cross etween Jpn Se individuls ws used to crete linkge mp. The femle meiotic mps (X X recomintion) of LG19 (X 1 ) nd LG9 (X 2 ) re to the left, nd the mle meiotic mp (X Y recomintion) of LG9/19 (neo-y) is to the right. LG19 (X 1 ) is in green nd LG9 (X 2 ) is in mgent. Genetic distnces etween the mrkers re drwn to scle. Scle r, 1 centimorgns (cm). Severl LG9 nd LG19 mrkers do not recomine with ech other or with the sexdetermintion locus (Sex) in mles. The coloured rs to the left of the mp indicte the reltive position of the FISH proes., The X 1 nd X 2 chromosomes from representtive Akkeshi Jpn Se femle metphse spred nd the X 1,X 2 nd neo-y chromosomes from representtive Akkeshi Jpn Se mle metphse spred re shown. A LG9 BAC (mgent) nd LG19 BAC (green) were used s proes for FISH. 9 Mcmilln Pulishers Limited. All rights reserved Figure 2 Distriution of the Jpnese threespine stickleck species pir in region of symptry., The top pnel shows mp of the Jpnese rchipelgo, indicting the loction of Akkeshi in estern Hokkido, Jpn. The ottom pnel shows mp of our four collection sites (Lke, Mid1, Mid2 nd Upstrem) in Lke Akkeshi nd the Bekneushi mrsh. Scle r, 2 km., The top pnels show representtive photos of Jpn Se mle nd Pcific Ocen mle. Scle r, 1 mm. Genetic nlysis of fish collected in 6 (n 5 61) nd 7 (n 5 368) ws performed using STRUCTURE. There re two genetic clusters in Akkeshi (Supplementry Fig. 2), with the Jpn Se cluster shown in red, nd the Pcific Ocen cluster shown in green. In the STRUCTURE plots, ech individul is indicted y single verticl line. The proility of ssignment to the Jpn Se cluster or the Pcific Ocen cluster is indicted y the extent of the coloured r. Fish collected from the sme loction re grouped together, with loctions seprted y thick lck lines. The numer of individuls per loction is indicted in prenthesis. The Jpn Se form is mostly found in the lke, wheres the Pcific Ocen form is mostly found in the upstrem region of the Bekneushi River. The midstrem region (Mid2) is hyrid zone tht contins oth prentl forms nd hyrids.
3 NATURE Vol Octoer 9 dorsl disply is gretly exggerted, nd the mle pushes the femle upwrds during dorsl (Fig. 3) 19. Furthermore, dorsl spine length is sexully dimorphic (mles hve longer spines thn femles) in the Jpn Se form 25. In contrst, in the Pcific Ocen form, the dorsl disply is wek (Fig. 3), nd dorsl spine length is not sexully dimorphic 19,25. We found tht the Pcific Ocen femles frequently escped nd did not resume mting fter they encountered the ggressive dorsl of Jpn Se mles, wheres the Jpn Se femles did not escpe from mles fter dorsl (Fig. 3). Genetic mpping of isolting rriers To investigte the chromosoml loctions of the isolting rriers etween the two forms, we ckcrossed F 1 hyrid (Jpn Se femle 3 Pcific Ocen mle) femles to Pcific Ocen mles nd conducted quntittive trit locus (QTL) mpping of mle dorsl, mle dorsl spine length, mle ody size, nd hyrid mle sterility. Individuls were genotyped with 9 single nucleotide polymorphism (SNP) mrkers nd 13 other microstellite mrkers tht together spn the stickleck genome. Hyrid mle sterility nd mle ody size mpped to LG19 (Fig. 4, Supplementry Fig. 4 nd Supplementry Tle 1), which is the ncestrl X chromosome shred y the Jpn Se form nd Pcific Ocen form. Dorsl nd first dorsl spine length mpped to distinct loctions on LG9 (Fig. 4, Supplementry Fig. 4 nd Supplementry Tle 1), which is the neo-x chromosome in the Jpn Se form. A genome-wide scn for episttic interctions identified significnt conspecific interction etween loci on LG19 for hyrid mle sterility (log likelihood rtio of linkge (LOD) compring the full model with interction to the dditive model 5 5.8; genome-wide significnce threshold ( 5.5); Supplementry Fig. 5). No significnt episttic interctions were found for ny other trits or loci exmined. Our dt demonstrte tht loci importnt for oth prezygotic nd postzygotic isoltion mp to the X chromosomes in this nturl verterte system. This lrge X-effect is unlikely to result from n overrepresenttion of these chromosomes in the stickleck genome, s LG9 nd LG19 comprise just 9.% of the stickleck genome (.2 megses (M) ech of M totl 4.5% for ech linkge group in the stickleck genome ssemly; BROAD S1, Fe 6). Becuse mpping in ckcross proly overestimtes the effects of the hemizygous X chromosome 26, we lso performed QTL mpping of the sme trits in n independent F 2 intercross to ensure tht the oserved lrge X-effect ws not simply the result of our ckcross mpping strtegy. We still detect QTL for dorsl nd first dorsl spine length on LG9 nd QTL for mle sterility nd ody size on LG19, with the ddition of single QTL for testis size on LG1 (Supplementry Fig. 6 nd Supplementry Tle 2). Proility of choosing conspecific mle Proility of choosing conspecific mle Pcific Ocen femle choice 1 1 Mle ody size difference (mm) (Pcific Ocen mle Jpn Se mle) Jpn Se femle choice Mle swim-up distnce during dorsl (mm) Percentge of femle escpe 1 1 Mle ody size difference (mm) (Jpn Se mle Pcific Ocen mle) PO mle PO mle 8 JS mle Pcific Ocen femle 8 JS mle Pcific Ocen femle Grvid femle Dorsl disply (swim-up) Courting mle 16 PO mle 16 PO mle JS mle Jpn Se femle JS mle Jpn Se femle Figure 3 Behviourl isoltion results from divergence in mle ody size nd mle dorsl ehviour., The top pnel indictes the preferences of Pcific Ocen femles (n 5 3), nd the ottom pnel indictes the preferences of Jpn Se femles (n 5 29) s function of mle ody size divergence. The horizontl xes indicte the ody size difference in mm etween mles (conspecific mle stndrd length minus heterospecific mle stndrd length). Ech symol indictes mte choice tril, in which 1 indictes the femle chose conspecific mle, nd indictes the femle chose heterospecific mle. Trils were conducted with lortory-rered Pcific Ocen mles (solid circles), resident freshwter Pcific mles (solid tringles), or without size mnipultion (open circles). The logistic regression curves indicte the proility of femle choosing conspecific mle for given difference in mle ody size., The top pnel shows the distnce Pcific Ocen (PO) or Jpn Se (JS) mle moved upwrds during dorsl with Pcific Ocen or Jpn Se femles. The ottom pnel shows the percentge of trils in which femle escped fter dorsl y either Pcific Ocen or Jpn Se mle. The smple size for ech mting pir is shown ove ech column. Lower cse letters ove the rs represent pirs tht re significntly different from ech other (pirwise Mnn Whitney U-test, P,.5 fter Bonferroni correction). FISH proe FISH proe 9 Mcmilln Pulishers Limited. All rights reserved LG19 (X 1 ) Sperm numer Body length c ss ss Stn7 LG19 LG19 37 Stn274.5 Stn235* 31 Idh P X P Y J X1 P Y Stn256 ss ss Stn192 Cyp19* Mp 8 8 P X P Y J X1 P Y LG9 (X 2 ) Dorsl Dorsl spine length 15 ss ss Stn1 LG9 LG Stn99 P 9 P 9 J X2 P 9 ss ss Stn* 1.5 ss Stn Stn11.5 ss Stn113 ss * P Stn P 9 J X2 P 9 1 cm Dorsl Body length Sperm numer Adjusted dorsl spine length Figure 4 Genetic mpping of isolting rriers., Genetic linkge mps of LG19 (X 1 ; green) nd LG9 (X 2 ; mgent) in the ckcross. The loctions of FISH proes re indicted to the left of the mp, wheres the nmes of genetic mrkers re indicted to the right. The sterisk indictes the mrker closest to the QTL pek., For ech QTL, the LOD score is indicted cross the top nd is plotted reltive to the positions of the mrkers indicted in, with distnce in cm indicted. The hyrid mle sterility QTL is represented y sperm numer, the ody size QTL is represented y ody length, nd the dorsl QTL is represented y men dorsl. The dorsl spine length QTL is represented y first dorsl spine length, which ws nlysed with ody length s n intercting covrite. Dshed lines indicte the genome-wide significnce thresholds determined y permuttion tests ( 5.5). c, For ech trit, the phenotypic vlues (men 6 s.e.m.) re indicted for genotypes t the mrker closest to the QTL pek; tht is, Cyp19 for sperm numer, Stn235 for ody length, SNP ss for men dorsl, nd Stn for dorsl spine length. Smple sizes for ech genotypic clss re shown in the grph. These were the only genomic regions with significnt phenotype-genotype ssocitions fter Bonferroni correction (P,.1), detected either y Kruskl Wllis test (sperm numer, ody length, nd dorsl ) or y nlysis of covrince (ANCOVA) (dorsl spine length). 1
4 NATURE Vol Octoer 9 Discussion Mpping of hyrid mle sterility to the ncestrl X chromosome (LG19) is consistent with previous studies on hyrid mle sterility in other systems 5,6, suggesting tht the lrge X-effect on hyrid mle sterility is common cross diverse tx. Although the resons for the lrge X-effect on hyrid sterility re deted 5, in some cses it results from genetic conflict in the form of sex rtio meiotic drive 27,28. However, we find no evidence for sex rtio distortion in the wekly fertile F 1 hyrid mles resulting from cross etween Jpn Se femles nd Pcific Ocen mles (Supplementry Tle 3). We do, however, find evidence for conspecific epistsis etween X-linked loci, which is commonly oserved for hyrid mle sterility in Drosophil 29,3. Despite this finding of common lrge X-effect cross widely seprted tx, we found no evidence for ny effect of the neo-x chromosome on hyrid mle sterility. It my e tht the reltive ge nd/or levels of degenertion of sex chromosomes re importnt fctors in determining whether the X chromosome contriutes to the evolution of hyrid mle sterility. Unlike mle sterility, mle courtship disply trits conferring ehviourl isoltion etween the Jpn Se nd Pcific Ocen forms mp to oth the ncestrl X chromosome nd the neo-x chromosome. Interestingly, mle ody size is sexully dimorphic in oth the Jpn Se nd Pcific Ocen forms 25 nd mps to the ncestrl X chromosome. In contrst, first dorsl spine length is only sexully dimorphic in the Jpn Se form 25, nd the dorsl disply is exggerted in the Jpn Se mles; these trits oth mp to the neo-x chromosome. Thus, these disply trits might hve evolved s result of differentil fitness effects etween mles nd femles specificlly in the Jpn Se linege. Although our cross design did not llow us to directly test whether these trits mpped to the neo-y chromosome s predicted y theory 7,8, it is possile tht selection for linkge etween mle eneficil trits, such s dorsl nd dorsl spine length, nd the sex-determintion locus ctully promoted the spred of the fusion etween LG9 nd the Y chromosome in the Jpn Se popultion 7. Alterntively, these mle eneficil trits my hve ccumulted on the neo-x chromosome 3 fter the formtion of the neo-y chromosome in the lst million yers. In either cse, our dt provide direct empiricl evidence linking sex chromosome turnover nd reproductive isoltion etween closely relted species. The turnover of sex chromosomes etween species is common in mny groups of nimls, where closely relted species often differ in sex-determintion nd sex-chromosome systems 9,1. Although it hs een suggested tht sex-chromosome turnover might drive rpid specition in cichlid fishes in which femle colour trit is linked to n invding ZW sex-chromosome system 15 17, this hypothesis hs not een directly tested. Given the potentil role of sexul ntgonism in driving oth sex-chromosome evolution 1,3,7,8 nd specition 31,32, we suggest tht sex-chromosome divergence etween closely relted species should e given further considertion s n importnt mechnism contriuting to the evolution of reproductive isoltion. METHODS SUMMARY Threespine sticklecks of the Pcific Ocen nd the Jpn Se form were collected with seine nets nd minnow trps in Lke Akkeshi nd the Beukneushi River in My July of 3 8. Jpn Se fish were lso collected from n lloptric site (Cpe of Benkei) on the west cost of Hokkido in 8. For cytogenetic nd ehviourl studies, live fish were trnsported to the Fred Hutchinson Cncer Reserch Center; ll experimentl procedures were pproved y the Institutionl Animl Cre nd Use Committee (IACUC numer 1575). Cytogenetics nd FISH were performed on Jpn Se mles (n 5 2) nd femle (n 5 1) from Akkeshi, s well s Jpn Se mles (n 5 2) nd femles (n 5 3) from the lloptric site, using fluorescently lelled cteril rtificil chromosome (BAC) clones s previously descried 22. For popultion genetic nlysis, 969 fish were genotyped with 12 neutrl microstellite mrkers (Supplementry Tle 4). Mte-choice experiments were conducted s previously descried 19. For QTL mpping, Jpn Se femle nd Pcific Ocen 2 mle were crossed to otin n F 1 hyrid fmily (J 1 3 P 1 ). These F 1 femles were crossed with mles resulting from cross etween Pcific Ocen femle nd nother Pcific Ocen mle (P 2 3 P 3 ) to generte ckcross progeny. At mturity, 76 ckcross mles were phenotyped for trits relted to ody size, fertility nd dorsl ehviour. These mles were genotyped with LG9 nd LG19 microstellites, s well s pnel of SNP mrkers distriuted cross the stickleck genome (Supplementry Tle 5). All DNA isoltion nd microstellite genotyping were conducted s previously descried 19 ; SNP genotyping ws performed using Illumin Golden Gte rrys. The genotypes of 9 SNPs nd 14 microstellites were used to crete linkge mp in JoinMp 3. (ref. 33), nd QTL nlyses were performed in MpQTL 4. (ref. 34) nd R/qtl 35. Received 4 My; ccepted August 9. Pulished online 27 Septemer 9. 9 Mcmilln Pulishers Limited. All rights reserved 1. Rice, W. R. The ccumultion of sexully ntgonistic genes s selective gent promoting the evolution of reduced recomintion etween primitive sex chromosomes. Evolution 41, (1987). 2. Rice, W. R. Genetic hitchhiking nd the evolution of reduced genetic ctivity of the Y sex chromosome. Genetics 116, (1987). 3. Rice, W. R. Sex chromosomes nd the evolution of sexul dimorphism. Evolution 38, (1984). 4. Chrlesworth, B., Coyne, J. A. & Brton, N. H. The reltive rtes of evolution of sex chromosomes nd utosomes. Am. Nt. 13, (1987). 5. Presgrves, D. C. Sex chromosomes nd specition in Drosophil. Trends Genet. 24, (8). 6. Qvrnström, A. & Biley, R. I. Specition through evolution of sex-linked genes. Heredity 12, 4 15 (9). 7. Chrlesworth, D. & Chrlesworth, B. Sex differences in fitness nd selection for centric fusions etween sex-chromosomes nd utosomes. Genet. Res. 35, (198). 8. vn Doorn, G. S. & Kirkptrick, M. Turnover of sex chromosomes induced y sexul conflict. Nture 449, (7). 9. Ezz, T., Stiglec, R., Veyrunes, F. & Grves, J. A. M. Reltionships etween verterte ZW nd XY sex chromosome systems. Curr. Biol. 16, R736 R743 (6). 1. Mnk, J. E., Promislow, D. E. L. & Avise, J. C. Evolution of lterntive sexdetermining mechnisms in teleost fishes. Biol. J. Linn. Soc. 87, (6). 11. Worm, R. A. et l. Comprtive genome nlysis of the primry sex-determining locus in slmonid fishes. Genome Res. 13, (3). 12. Tnk, K., Tkehn, Y., Nruse, K., Hmguchi, S. & Skizumi, M. Evidence for different origins of sex chromosomes in closely relted Oryzis fishes: sustitution of the mster sex-determining gene. Genetics 177, (7). 13. White, M. J. D. Animl Cytology nd Evolution (Univ. Press, 1973). 14. Ross, J. A. et l. Turnover of sex chromosomes in the stickleck fishes (Gsterosteide). PLoS Genet. 5, e1391 (9). 15. Seehusen, O., vn Alphen, J. J. M. & Lnde, R. Color polymorphism nd sex rtio distortion in cichlid fish s n incipient stge in symptric specition y sexul selection. Ecol. Lett. 2, (1999). 16. Lnde, R., Seehusen, O. & vn Alphen, J. J. M. Mechnisms of rpid symptric specition y sex reversl nd sexul selection in cichlid fish. Genetic , (1). 17. Kocher, T. D. Adptive evolution nd explosive specition: the cichlid fish model. Nture Rev. Genet. 5, (4).. Higuchi, M. & Goto, A. Genetic evidence supporting the existence of two distinct species in the genus Gsterosteus round Jpn. Environ. Biol. Fishes 47, 1 16 (1996). 19. Kitno, J., Mori, S. & Peichel, C. L. Phenotypic divergence nd reproductive isoltion etween symptric popultions of ndromous threespine sticklecks. Biol. J. Linn. Soc. 91, (7).. Kingsley, D. M. & Peichel, C. L. in Biology of the Three-Spined Stickleck (eds Östlund-Nilsson, S., Myer, I. & Huntingford, F.) (CRC Press, 7). 21. Peichel, C. L. et l. The mster sex-determintion locus in threespine sticklecks is on nscent Y chromosome. Curr. Biol. 14, (4). 22. Ross, J. A. & Peichel, C. L. Moleculr cytogenetic evidence of rerrngements on the Y chromosome of the threespine stickleck fish. Genetics 179, (8). 23. Foster, S. A. in The Evolutionry Biology of the Threespine Stickleck (eds Bell, M. A. & Foster, S. A.) (Oxford Univ. Press, 1994). 24. Wootton, R. J. A Functionl Biology of Sticklecks (Croom Helm, 1984). 25. Kitno, J., Mori, S. & Peichel, C. L. Sexul dimorphism in the externl morphology of the threespine stickleck (Gsterosteus culetus). Copei 7, (7). 26. Wu, C.-I. & Dvis, A. W. Evolution of postmting reproductive isoltion: the composite nture of Hldne s rule nd its genetic ses. Am. Nt. 142, (1993). 27. To, Y., Hrtl, D. L. & Lurie, C. C. Sex-rtio segregtion distortion ssocited with reproductive isoltion in Drosophil. Proc. Ntl Acd. Sci. USA 98, (1). 28. Phdnis, N. & Orr, H. A. A single gene cuses oth mle sterility nd segregtion distortion in Drosophil hyrids. Science 323, (9).
5 NATURE Vol Octoer Orr, H. A. & Irving, S. Complex epistsis nd the genetic sis of hyrid sterility in the Drosophil pseudooscur Bogot-USA hyridiztion. Genetics 158, 9 11 (1). 3. Swmur, K., Roote, J., Wu, C.-I. & Ymmoto, M. T. Genetic complexity underlying hyrid mle sterility in Drosophil. Genetics 166, (4). 31. Gvrilets, S. Fitness Lndscpesnd theoriginof Species (Princeton Univ. Press, 4). 32. Arnqvist, G. & Rowe, L. Sexul Conflict (Princeton Univ. Press, 5). 33. Vn Ooijen, J. W. & Voorrips, R. E. JoinMp 3., Softwre for the Clcultion of Genetic Linkge Mps (Plnt Reserch Interntionl, 1). 34. Vn Ooijen, J. W., Boer, M. P., Jnsen, R. C. & Mlieprd, C. MpQTL 4., Softwre for the Clcultion of QTL Positions on Genetic Mps (Plnt Reserch Interntionl, 2). 35. Bromn, K. W., Wu, H., Sen, S. & Churchill, G. A. R/qtl: QTL mpping in experimentl crosses. Bioinformtics 19, (3). Supplementry Informtion is linked to the online version of the pper t Acknowledgements We thnk M. Nishitni, J. Kitjim, M. Nishid, S. Tkeym, T. Andoh, T. Kuwhr, C. Torii, Akkeshi Fisheries Coopertive Assocition, Akkeshi Wterfowl Center, S. Brdy, A. Southwick, ll memers of the Peichel lortory, nd mny field ssistnts for technicl help nd discussion. We thnk J. Boughmn, T. Brdshw, H. Mlik, J. McKinnon, N. Phdnis nd D. Schluter for comments on the mnuscript. We lso thnk the Brod Institute for the pulic relese of n initil stickleck genome ssemly. This reserch ws supported y the Uehr Memoril Foundtion (J.K.), Grnt-in-Aid for Scientific Reserch from the Ministry of Eduction, Culture, Sports, Science, nd Technology of Jpn, nd Wter nd People Project of Reserch Institute for Humnity nd Nture (S.M.), Akkeshi Town Grnts-in-Aid for Scientific Reserch in the Lke Akkeshi-Bekneushi Wetlnd (M.K.), Burroughs Wellcome Fund Creer Awrd in the Biomedicl Sciences (C.L.P.), nd Ntionl Institutes of Helth grnts T32 GM727 (J.A.R.), R1 GM754 (C.L.P.) nd P5 HG2568 (R.M.M., D.M.K. nd C.L.P.). Author Contriutions J.K., S.M. nd C.L.P. conceived nd designed the study. F.C.J., Y.F.C., D.M.A., J.G., J.S., R.M.M. nd D.M.K. contriuted new regents nd crried out the SNP genotyping experiments for genome-wide linkge mpping. J.K., J.A.R., S.M., M.K. nd C.L.P. performed ll other experiments nd nlysed the dt. J.K. nd C.L.P. wrote the mnuscript. Author Informtion All SNP informtion hs een deposited t Reprints nd permissions informtion is ville t Correspondence nd requests for mterils should e ddressed to C.L.P. (cpeichel@fhcrc.org). 9 Mcmilln Pulishers Limited. All rights reserved 3
Genetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary
Outline Genetic Progrmming Evolutionry strtegies Genetic progrmming Summry Bsed on the mteril provided y Professor Michel Negnevitsky Evolutionry Strtegies An pproch simulting nturl evolution ws proposed
More informationMidterm#1 comments. Overview- chapter 6. Recombination. Recombination 1 st sense
Midterm#1 comments So fr, ~ 10% of exms grded, wide rnge of results: 1 perfect score, 1 score < 100pts rtil credit is given if you get prt of the nswer right Tests will e returned next Thursdy Some of
More informationCourse Information. Computational Genetics Lecture 1. Course Prerequisites. Course Goals
Course Informtion. Computtionl Genetics Lecture 1 ckground Redings: Chpter 2&3 of n introduction to Genetics, Griffiths et l. 2000, Seventh Edition (CS/Fishch/Other lirries). This clss hs een edited from
More informationSupplementary material
10.1071/FP11237_AC CSIRO 2012 Accessory Puliction: Functionl Plnt Biology 2012, 39(5), 379 393. Supplementry mteril Tle S1. Effect of wter regime nd genotype on different growth prmeters: spike dry mtter
More informationLAMEPS Limited area ensemble forecasting in Norway, using targeted EPS
Limited re ensemle forecsting in Norwy, using trgeted Mrit H. Jensen, Inger-Lise Frogner* nd Ole Vignes, Norwegin Meteorologicl Institute, (*held the presenttion) At the Norwegin Meteorologicl Institute
More informationTests for the Ratio of Two Poisson Rates
Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson
More informationHETEROSIS, a term to describe the superiority of
Copyright Ó 2008 y the Genetics Society of Americ DOI: 10.1534/genetics.108.091942 Dominnce, Overdominnce nd Epistsis Condition the Heterosis in Two Heterotic Rice Hyrids Lnzhi Li,* Kiyng Lu, Zhoming Chen,*
More informationDOI:.8/nc5 Cpilities of MCAK Sidesliding, endctching on microtuules MCAKdecorted ed Functions in mitotic spindle Prometphse Slides on the microtuule surfce + Redily slides long the microtuule surfce Strongly
More informationHaplotype Frequencies and Linkage Disequilibrium. Biostatistics 666
Hlotye Frequencies nd Linkge isequilirium iosttistics 666 Lst Lecture Genotye Frequencies llele Frequencies Phenotyes nd Penetrnces Hrdy-Weinerg Equilirium Simle demonstrtion Exercise: NO2 nd owel isese
More informationSexual selection enables long-term coexistence despite ecological equivalence. Local carrying capacity. Effective density of competitors
LETTER doi:.38/nture97 Sexul selection enles long-term coexistence despite ecologicl equivlence Leithen K. M Gonigle {, Rupert Mzzucco 2, Srh P. Otto & Ulf Dieckmnn 2 Empiricl dt indicte tht sexul preferences
More informationLect 11: Inbreeding, evolution at multiple loci. Exam 1, Monday, 2 October. Consequences of Inbreeding: Genotype frequencies
Lect 11: Inreeding, evolution t multiple loci Exm 1, Mondy, 2 Octoer Non-rndom mting-- Inreeding evolutionry consequences Synthesis: drift-migrtion: popultion structure Popultion genetics of pririe chickens
More informationList all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.
Mth Anlysis CP WS 4.X- Section 4.-4.4 Review Complete ech question without the use of grphing clcultor.. Compre the mening of the words: roots, zeros nd fctors.. Determine whether - is root of 0. Show
More informationMatching patterns of line segments by eigenvector decomposition
Title Mtching ptterns of line segments y eigenvector decomposition Author(s) Chn, BHB; Hung, YS Cittion The 5th IEEE Southwest Symposium on Imge Anlysis nd Interprettion Proceedings, Snte Fe, NM., 7-9
More informationTransient Stimulation of Distinct Subpopulations of Striatal Neurons Mimics Changes in the Value of Competing Actions
Supplementl mterils for: Trnsient Stimultion of Distinct Supopultions of Stritl Neurons Mimics Chnges in the Vlue of Competing Actions Lung-Ho Ti, A. Moses Lee,2, Nor Benvidez 3, Antonello Bonci 4,,6,
More informationStudent Activity 3: Single Factor ANOVA
MATH 40 Student Activity 3: Single Fctor ANOVA Some Bsic Concepts In designed experiment, two or more tretments, or combintions of tretments, is pplied to experimentl units The number of tretments, whether
More informationA Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE
Southwestern U.S. Ground Motion Chrcteriztion Senior Seismic Hzrd Anlysis Committee Level 3 Workshop #2 October 22-24, 2013 A Brief Review on Akkr, Sndikky nd Bommer (ASB13 GMPE Sinn Akkr Deprtment of
More informationHamiltonian Cycle in Complete Multipartite Graphs
Annls of Pure nd Applied Mthemtics Vol 13, No 2, 2017, 223-228 ISSN: 2279-087X (P), 2279-0888(online) Pulished on 18 April 2017 wwwreserchmthsciorg DOI: http://dxdoiorg/1022457/pmv13n28 Annls of Hmiltonin
More informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
More informationQuantitative Genetics and Twin Studies
Count Count Count Count Quntittive Genetics nd Twin Studies n Introduction! co de Geus -Dept. Biologicl Psychology -Netherlnds Twin Register msterdm, the Netherlnds 600 N = 6602 M = 48,27 SD = 25,0 75
More information0.1 THE REAL NUMBER LINE AND ORDER
6000_000.qd //0 :6 AM Pge 0-0- CHAPTER 0 A Preclculus Review 0. THE REAL NUMBER LINE AND ORDER Represent, clssify, nd order rel numers. Use inequlities to represent sets of rel numers. Solve inequlities.
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationChapter 9 Definite Integrals
Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished
More informationLecture 18: Species, Hybrids, and QTL. Oct 23, 2006
Leture 18: Speies, Hyrids, nd QTL Ot 23, 2006 ourse Logistis Reminder: Guest leture Fridy, Novemer 3 Reding posted on wesite 2 nd Reminder: no lss on Wednesdy, Novemer 1 nother 2 nd Reminder: Everyone
More information2.4 Linear Inequalities and Interval Notation
.4 Liner Inequlities nd Intervl Nottion We wnt to solve equtions tht hve n inequlity symol insted of n equl sign. There re four inequlity symols tht we will look t: Less thn , Less thn or
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More information8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8. re nd volume scle fctors 8. Review U N O R R E TE D P G E PR O O FS 8.1 Kick off with S Plese refer to the Resources t in the Prelims
More informationMath 31S. Rumbos Fall Solutions to Assignment #16
Mth 31S. Rumbos Fll 2016 1 Solutions to Assignment #16 1. Logistic Growth 1. Suppose tht the growth of certin niml popultion is governed by the differentil eqution 1000 dn N dt = 100 N, (1) where N(t)
More informationSupplementary Information to The role of endogenous and exogenous mechanisms in the formation of R&D networks
Supplementry Informtion to The role of endogenous nd exogenous mechnisms in the formtion of R&D networks Mrio V. Tomsello 1, Nicol Perr 2, Cludio J. Tessone 1, Márton Krsi 3, nd Frnk Schweitzer 1 1 Chir
More informationSUPPLEMENTARY INFORMATION
VOLUME: ARTICLE NUMBER: 3 In the formt provided y the uthors nd unedited. Developmentl constrints shpe the evolution of the nemtode mid-developmentl trnsition Hrel Zlts nd Iti Yni,3 Fculty of Biology,
More informationDiscrete Mathematics and Probability Theory Spring 2013 Anant Sahai Lecture 17
EECS 70 Discrete Mthemtics nd Proility Theory Spring 2013 Annt Shi Lecture 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion,
More information4.1. Probability Density Functions
STT 1 4.1-4. 4.1. Proility Density Functions Ojectives. Continuous rndom vrile - vers - discrete rndom vrile. Proility density function. Uniform distriution nd its properties. Expected vlue nd vrince of
More informationNon-Linear & Logistic Regression
Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find
More informationNew data structures to reduce data size and search time
New dt structures to reduce dt size nd serch time Tsuneo Kuwbr Deprtment of Informtion Sciences, Fculty of Science, Kngw University, Hirtsuk-shi, Jpn FIT2018 1D-1, No2, pp1-4 Copyright (c)2018 by The Institute
More informationEnergy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene
Force (kcl mol -1 Å -1 ) Energy (kcl mol -1 ) 3 1-1 - -3 Mixed Mo-only S-only Grphene 6 5 3 1 Mixed Mo-only S-only Grphene - -1-1 1 Pore xis (Å) -1 1 Pore xis (Å) Supplementry Figure 1 Energy Brriers.
More information3.94 ± 0.50 (95% CI) Correlative inhibition index (slope)
Supplementl Tle S. Selected rchitecturl prmeters of phy nd phyphy grown under. Vlues re mens ± SE, except for predicted primry rosette rnches where the vlues re the men with the ssocited 9% confidence
More information( ) 1. Algebra 2: Final Exam Review. y e + e e ) 4 x 10 = 10,000 = 9) Name
Algebr : Finl Exm Review Nme Chpter 6 Grph ech function. Determine if the function represents exponentil growth or decy. Determine the eqution of the symptote, the domin nd the rnge of the function. )
More informationExploring parametric representation with the TI-84 Plus CE graphing calculator
Exploring prmetric representtion with the TI-84 Plus CE grphing clcultor Richrd Prr Executive Director Rice University School Mthemtics Project rprr@rice.edu Alice Fisher Director of Director of Technology
More informationParse trees, ambiguity, and Chomsky normal form
Prse trees, miguity, nd Chomsky norml form In this lecture we will discuss few importnt notions connected with contextfree grmmrs, including prse trees, miguity, nd specil form for context-free grmmrs
More informationReview of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
More informationDiscrete Mathematics and Probability Theory Summer 2014 James Cook Note 17
CS 70 Discrete Mthemtics nd Proility Theory Summer 2014 Jmes Cook Note 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion, y tking
More informationThe Properties of Stars
10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product
More informationCHAPTER 9 LECTURE NOTES: CHROMOSOME MUTATION II: CHANGES IN NUMBERS
CHPTER 9 LECTURE NOTES: CHROMOSOME MUTTION II: CHNGES IN NUMBERS I. berrnt euploidy. Generl info. Euploidy refers to the sitution in which n orgnism hs one complete set of chromosomes or n integer multiple
More informationChapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses
Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of
More informationSupplementary Figure 1
Supplementry Figure (nesthetized) (wke) Normlized mplitude.5 Pek width (ms).6.4.2 4 2 2 x 3 Wveform slope Normlized mplitude.5 Pek width (ms).6.4.2 x 3 3 2 Wveform slope c (nesthetized) d (wke) Normlized
More information1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
More informationFormal Languages and Automata
Moile Computing nd Softwre Engineering p. 1/5 Forml Lnguges nd Automt Chpter 2 Finite Automt Chun-Ming Liu cmliu@csie.ntut.edu.tw Deprtment of Computer Science nd Informtion Engineering Ntionl Tipei University
More informationCM10196 Topic 4: Functions and Relations
CM096 Topic 4: Functions nd Reltions Guy McCusker W. Functions nd reltions Perhps the most widely used notion in ll of mthemtics is tht of function. Informlly, function is n opertion which tkes n input
More information1 ELEMENTARY ALGEBRA and GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE
ELEMENTARY ALGEBRA nd GEOMETRY READINESS DIAGNOSTIC TEST PRACTICE Directions: Study the exmples, work the prolems, then check your nswers t the end of ech topic. If you don t get the nswer given, check
More informationFarey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University
U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions
More informationContinuous Random Variable X:
Continuous Rndom Vrile : The continuous rndom vrile hs its vlues in n intervl, nd it hs proility distriution unction or proility density unction p.d. stisies:, 0 & d Which does men tht the totl re under
More informationThe steps of the hypothesis test
ttisticl Methods I (EXT 7005) Pge 78 Mosquito species Time of dy A B C Mid morning 0.0088 5.4900 5.5000 Mid Afternoon.3400 0.0300 0.8700 Dusk 0.600 5.400 3.000 The Chi squre test sttistic is the sum of
More informationCoimisiún na Scrúduithe Stáit State Examinations Commission
M 30 Coimisiún n Scrúduithe Stáit Stte Exmintions Commission LEAVING CERTIFICATE EXAMINATION, 005 MATHEMATICS HIGHER LEVEL PAPER ( 300 mrks ) MONDAY, 3 JUNE MORNING, 9:30 to :00 Attempt FIVE questions
More informationLinear Inequalities. Work Sheet 1
Work Sheet 1 Liner Inequlities Rent--Hep, cr rentl compny,chrges $ 15 per week plus $ 0.0 per mile to rent one of their crs. Suppose you re limited y how much money you cn spend for the week : You cn spend
More informationTitle of file for HTML: Supplementary Information Description: Supplementary Figures. Title of file for HTML: Peer Review File Description:
Title of file for HTML: Supplementry Informtion Description: Supplementry Figures Title of file for HTML: Peer Review File Description: WTP SST IPO PDO WTP leds IPO PDO Supplementry Figure 1 IPO (or PDO)
More informationTorsion in Groups of Integral Triangles
Advnces in Pure Mthemtics, 01,, 116-10 http://dxdoiorg/1046/pm011015 Pulished Online Jnury 01 (http://wwwscirporg/journl/pm) Torsion in Groups of Integrl Tringles Will Murry Deprtment of Mthemtics nd Sttistics,
More information4.4 Areas, Integrals and Antiderivatives
. res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order
More informationLecture 08: Feb. 08, 2019
4CS4-6:Theory of Computtion(Closure on Reg. Lngs., regex to NDFA, DFA to regex) Prof. K.R. Chowdhry Lecture 08: Fe. 08, 2019 : Professor of CS Disclimer: These notes hve not een sujected to the usul scrutiny
More informationSUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION doi: 1.138/nnno.29.451 Aove-ndgp voltges from ferroelectric photovoltic devices S. Y. Yng, 1 J. Seidel 2,3, S. J. Byrnes, 2,3 P. Shfer, 1 C.-H. Yng, 3 M. D. Rossell, 4 P. Yu,
More informationDate Lesson Text TOPIC Homework. Solving for Obtuse Angles QUIZ ( ) More Trig Word Problems QUIZ ( )
UNIT 5 TRIGONOMETRI RTIOS Dte Lesson Text TOPI Homework pr. 4 5.1 (48) Trigonometry Review WS 5.1 # 3 5, 9 11, (1, 13)doso pr. 6 5. (49) Relted ngles omplete lesson shell & WS 5. pr. 30 5.3 (50) 5.3 5.4
More informationPlane Surveying Levelling
Deprtment of Civil Engineering, UC Introduction: Levelling is mens y which surveyors cn determine the elevtion of points, using other known points s references. Levelling is perhps the most sic of surveying
More informationContinuous Random Variables
CPSC 53 Systems Modeling nd Simultion Continuous Rndom Vriles Dr. Anirn Mhnti Deprtment of Computer Science University of Clgry mhnti@cpsc.uclgry.c Definitions A rndom vrile is sid to e continuous if there
More informationANALYSIS OF FAST REACTORS SYSTEMS
ANALYSIS OF FAST REACTORS SYSTEMS M. Rghe 4/7/006 INTRODUCTION Fst rectors differ from therml rectors in severl spects nd require specil tretment. The prsitic cpture cross sections in the fuel, coolnt
More informationa * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2
18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions
More informationThe Influence of Interface and Semiconductor Bulk Traps Generated Under HEFS on MOSFET`s Electrical Characteristics
Proceedings of the 5th Smll Systems Simultion Symposium 2014, Niš, Seri, 12th-14th Ferury 2014 The Influence of Interfce nd Semiconductor Bulk Trps Generted Under HEFS on MOSFET`s Electricl Chrcteristics
More informationMath 42 Chapter 7 Practice Problems Set B
Mth 42 Chpter 7 Prctice Problems Set B 1. Which of the following functions is solution of the differentil eqution dy dx = 4xy? () y = e 4x (c) y = e 2x2 (e) y = e 2x (g) y = 4e2x2 (b) y = 4x (d) y = 4x
More informationAS a powerful design in the case of quantitative traits the ESP method remains powerful when used with caution.
Copyright 2002 by the Genetics Society of Americ Considertions on Study Designs Using the Extreme Sibpirs Methods Under Multilocus Oligogenic Models Chi Gu*,1 nd D. C. Ro*, *Division of Biosttistics nd
More informationCreating A New Planck s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram
nd Jogj Interntionl Physics Conference Enhncing Network nd Collortion Developing Reserch nd Eduction in Physics nd Nucler Energy Septemer 6-9, 007, Yogykrt-Indonesi Creting A New Plnck s Formul of Spectrl
More informationMA 15910, Lessons 2a and 2b Introduction to Functions Algebra: Sections 3.5 and 7.4 Calculus: Sections 1.2 and 2.1
MA 15910, Lessons nd Introduction to Functions Alger: Sections 3.5 nd 7.4 Clculus: Sections 1. nd.1 Representing n Intervl Set of Numers Inequlity Symol Numer Line Grph Intervl Nottion ) (, ) ( (, ) ]
More information3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.
SECTION. Eponents nd Rdicls 7 B 7 7 7 7 7 7 7 NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd
More informationSUPPLEMENTARY INFORMATION
doi:.38/nture8499 doi:.38/nture8499 5 6 5 4.5 Firing rte (Hz) -67-65 -66-6 -58 V m (mv) -7-67 -68-66 -64 c Thet power (mv ) -73-69 -7-7 -7.5.8 3....9.9.4.6.6. 9 8 9 8 9 8 9 8 9 8 Supplementry Figure Firing
More informationp-adic Egyptian Fractions
p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction
More informationMCB : Homologous Recombination
MC 421-2006: Homologous Recomintion Prt I. Definitions Chnges in DN re clled muttions. Muttions cn e chnges in one se, in severl ses, in mny ses. Recomintion is lso chnge is DN. How is it different from
More informationsupplementary information
DOI: 1.138/nc8 Top-GFP!-ctenin GFP Intensity 3 1 1 3 5 6 7 8 Nucler Bet-Ctenin c MUC FABP KRT 8 5 3 6 15 1 5 LGR5 ASCL AXIN 15 5 15 5 Figure S1 TOP-GFP expression nd reltion with nucler β-ctenin, wnt trgets
More informationLecture 3: Equivalence Relations
Mthcmp Crsh Course Instructor: Pdric Brtlett Lecture 3: Equivlence Reltions Week 1 Mthcmp 2014 In our lst three tlks of this clss, we shift the focus of our tlks from proof techniques to proof concepts
More information8Similarity ONLINE PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8.4 re nd volume scle fctors 8. Review Plese refer to the Resources t in the Prelims section of your eookplus for comprehensive step-y-step
More informationDiverse modes of eco-evolutionary dynamics in communities of antibiotic-producing microorganisms
In the formt provided y the uthors nd unedited. ULEMENTAY INFOMATION VOLUME: 1 ATICLE NUMBE: 0189 iverse modes of eco-evolutionry dynmics in communities of ntiiotic-producing microorgnisms Klin Vetsigin
More informationUNIT 3 Indices and Standard Form Activities
UNIT 3 Indices nd Stndrd Form Activities Activities 3.1 Towers 3.2 Bode's Lw 3.3 Mesuring nd Stndrd Form 3.4 Stndrd Inde Form Notes nd Solutions (1 pge) ACTIVITY 3.1 Towers How mny cubes re needed to build
More informationState space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies
Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response
More information( ) as a fraction. Determine location of the highest
AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if
More informationAB Calculus Review Sheet
AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is
More informationMinimal DFA. minimal DFA for L starting from any other
Miniml DFA Among the mny DFAs ccepting the sme regulr lnguge L, there is exctly one (up to renming of sttes) which hs the smllest possile numer of sttes. Moreover, it is possile to otin tht miniml DFA
More information1) Genetic Architecture and (Number of loci, no. of alleles per locus, Mechanisms of gametic production Genetic system, Mendel s rules, etc)
HARDY-WEINBERG LECTURE, 997 POP GEN, BIO 48 Introduction When studying popultion genetics nd evolution, we must look t how genetic vrition (moleculr level impcts the gene pool/deme (popultion level. Consider
More informationexpression simply by forming an OR of the ANDs of all input variables for which the output is
2.4 Logic Minimiztion nd Krnugh Mps As we found ove, given truth tle, it is lwys possile to write down correct logic expression simply y forming n OR of the ANDs of ll input vriles for which the output
More informationIntermediate Math Circles Wednesday, November 14, 2018 Finite Automata II. Nickolas Rollick a b b. a b 4
Intermedite Mth Circles Wednesdy, Novemer 14, 2018 Finite Automt II Nickols Rollick nrollick@uwterloo.c Regulr Lnguges Lst time, we were introduced to the ide of DFA (deterministic finite utomton), one
More information378 Relations Solutions for Chapter 16. Section 16.1 Exercises. 3. Let A = {0,1,2,3,4,5}. Write out the relation R that expresses on A.
378 Reltions 16.7 Solutions for Chpter 16 Section 16.1 Exercises 1. Let A = {0,1,2,3,4,5}. Write out the reltion R tht expresses > on A. Then illustrte it with digrm. 2 1 R = { (5,4),(5,3),(5,2),(5,1),(5,0),(4,3),(4,2),(4,1),
More informationExponents and Logarithms Exam Questions
Eponents nd Logrithms Em Questions Nme: ANSWERS Multiple Choice 1. If 4, then is equl to:. 5 b. 8 c. 16 d.. Identify the vlue of the -intercept of the function ln y.. -1 b. 0 c. d.. Which eqution is represented
More informationSOME INTEGRAL INEQUALITIES OF GRÜSS TYPE
RGMIA Reserch Report Collection, Vol., No., 998 http://sci.vut.edu.u/ rgmi SOME INTEGRAL INEQUALITIES OF GRÜSS TYPE S.S. DRAGOMIR Astrct. Some clssicl nd new integrl inequlities of Grüss type re presented.
More information( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).
AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f
More information2 Calculate the size of each angle marked by a letter in these triangles.
Cmridge Essentils Mthemtics Support 8 GM1.1 GM1.1 1 Clculte the size of ech ngle mrked y letter. c 2 Clculte the size of ech ngle mrked y letter in these tringles. c d 3 Clculte the size of ech ngle mrked
More informationLinear Systems with Constant Coefficients
Liner Systems with Constnt Coefficients 4-3-05 Here is system of n differentil equtions in n unknowns: x x + + n x n, x x + + n x n, x n n x + + nn x n This is constnt coefficient liner homogeneous system
More informationNew Expansion and Infinite Series
Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University
More informationPopulation bottleneck : dramatic reduction of population size followed by rapid expansion,
Selection We hve defined nucleotide diversity denoted by π s the proportion of nucleotides tht differ between two rndomly chosen sequences. We hve shown tht E[π] = θ = 4 e µ where µ cn be estimted directly.
More informationPrerequisites CHAPTER P
CHAPTER P Prerequisites P. Rel Numers P.2 Crtesin Coordinte System P.3 Liner Equtions nd Inequlities P.4 Lines in the Plne P.5 Solving Equtions Grphiclly, Numericlly, nd Algericlly P.6 Comple Numers P.7
More informationComparison Procedures
Comprison Procedures Single Fctor, Between-Subects Cse /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects Two Comprison Strtegies post hoc (fter-the-fct) pproch You re interested in discovering
More informationChapters Five Notes SN AA U1C5
Chpters Five Notes SN AA U1C5 Nme Period Section 5-: Fctoring Qudrtic Epressions When you took lger, you lerned tht the first thing involved in fctoring is to mke sure to fctor out ny numers or vriles
More informationFault Modeling. EE5375 ADD II Prof. MacDonald
Fult Modeling EE5375 ADD II Prof. McDonld Stuck At Fult Models l Modeling of physicl defects (fults) simplify to logicl fult l stuck high or low represents mny physicl defects esy to simulte technology
More informationROB EBY Blinn College Mathematics Department
ROB EBY Blinn College Mthemtics Deprtment Mthemtics Deprtment 5.1, 5.2 Are, Definite Integrls MATH 2413 Rob Eby-Fll 26 Weknowthtwhengiventhedistncefunction, wecnfindthevelocitytnypointbyfindingthederivtiveorinstntneous
More informationCryptanalysis of Substitution-Permutation Networks Using Key-Dependent Degeneracy *
Cryptnlysis of Substitution-Permuttion Networks Using Key-Dependent Degenercy * Howrd M. Heys Electricl Engineering, Fculty of Engineering nd Applied Science Memoril University of Newfoundlnd St. John
More informationA signalling model of school grades: centralized versus decentralized examinations
A signlling model of school grdes: centrlized versus decentrlized exmintions Mri De Pol nd Vincenzo Scopp Diprtimento di Economi e Sttistic, Università dell Clbri m.depol@unicl.it; v.scopp@unicl.it 1 The
More informationChapter 6 Continuous Random Variables and Distributions
Chpter 6 Continuous Rndom Vriles nd Distriutions Mny economic nd usiness mesures such s sles investment consumption nd cost cn hve the continuous numericl vlues so tht they cn not e represented y discrete
More information