The Relative Contributions of the X Chromosome and Autosomes to Local Adaptation

Transcription

1 HIGHLIGHTED ARTICLE INVESTIGATION Te Relatve Contrbutons of te X Cromosome and Autosomes to Local Adaptaton Clémentne Lasne, Carla M. Sgrò, and Tm Connallon 1 Scool of Bologcal Scences, Monas Unversty, Clayton 3800, Australa ABSTRACT Models of sex cromosome and autosome evoluton yeld key predctons about te genomc bass of adaptve dvergence, and suc models ave been mportant n gudng emprcal researc n comparatve genomcs and studes of specaton. In addton to te adaptve dfferentaton tat occurs between speces over tme, selecton also favors genetc dvergence across geograpc space, wt subpopulatons of sngle speces evolvng conspcuous dfferences n trats nvolved n adaptaton to local envronmental condtons. Te potental contrbuton of sex cromosomes (te X or Z) to local adaptaton remans unclear, as we currently lack teory tat drectly lnks spatal varaton n selecton to local adaptaton of X-lnked and autosomal genes. Here, we develop populaton genetc models tat explctly consder te effects of genetc domnance, effectve populaton sze, and sex-specfc mgraton and selecton on te relatve contrbutons of X-lnked and autosomal genes to local adaptaton. We sow tat X-lnked genes sould nearly always dsproportonately contrbute to local adaptaton n te presence of gene flow. We also sow tat consderatons of domnance and effectve populaton sze wc play pvotal roles n te teory of faster-x adaptaton between speces ave surprsngly lttle nfluence on te relatve contrbuton of te X cromosome to local adaptaton. Instead, sex-based mgraton s te prmary medator of te strengt of spatal large-x effects. Our results yeld novel predctons about te role of sex cromosomes n local adaptaton. We outlne emprcal approaces n evolutonary quanttatve genetcs and genomcs tat could buld upon ts new teory. KEYWORDS clne; adaptaton; sex lnkage; domnance; effectve populaton sze THEORETICAL models of adaptaton ave expanded dramatcally durng te last two decades, and ave taken central roles n defnng many of te core conceptual questons tat currently drve emprcal researc n evolutonary genetcs and genomcs. Wat s te dstrbuton of penotypc effects among benefcal mutatons and fxed genetc varants (e.g., Orr 1998, 006; Martn and Lenormand 008)? Wat s te relatve mportance of new mutatons vs. standng genetc varaton durng te process of adaptaton (e.g., Hll198;OrrandBetancourt001;Hermsson and Pennngs 005)? Wat evolutonary rules, f any, govern te dynamcs of adaptaton n DNA sequence space (Smt 1970; Gllespe 1991; Orr 00)? How do populaton genetc parameters lke effectve populaton sze and te ftness effects of new mutatons nfluence genome-wde Copyrgt 017 by te Genetcs Socety of Amerca do /genetcs Manuscrpt receved August 8, 016; accepted for publcaton December 5, 016; publsed Early Onlne January 4, 017. Supplemental materal s avalable onlne at /genetcs /-/DC1. 1 Correspondng autor Scool of Bologcal Scences, Monas Unversty, Bldg. 18, Clayton, VIC 3800, Australa. E-mal tm.connallon@monas.edu patterns of adaptve genetc dvergence among speces (Gllespe 004; McCandls and Stoltzfus 014), and between dfferent regons of a genome (Carleswort 199; Orr 010; Glémn and Ronfort 013)? Tese teores ave also been nstrumental for nterpretng a wde array of emprcal patterns, rangng from mcrobal expermental evoluton (Martn and Lenormand 006) to genetc dssectons of quanttatve trats (Orr 005). Faster-X teory as been partcularly useful n drvng emprcal researc on te evolutonary genetcs of adaptaton (Mesel and Connallon 013) and te genetcs of reproductve solaton between speces (Presgraves 008). Ts teory focuses on te relatve rates of evoluton on sex cromosomes and autosomes, and te populaton genetc condtons tat lead to a dfferental accumulaton of adaptve substtutons at sex-lnked relatve to autosomal loc. We now know of several factors tat can nfluence te relatve rates of X vs. autosome substtuton, ncludng te genetc domnance of benefcal mutatons (Carleswort et al. 1987), sex dfferences n selecton (Carleswort et al. 1987), sex-based mutaton rates (Krkpatrck and Hall 004; Vcoso and Carleswort 009), mecansms of dosage compensaton Genetcs, Vol. 05, Marc

2 (Carleswort et al. 1987; Vcoso and Carleswort 009), adaptaton from new mutatons vs. standng genetc varaton (Orr and Betancourt 001; Connallon et al. 01), dstnct effectve populaton szes of dfferent cromosomes (Vcoso and Carleswort 009), and epstass (Connallon et al. 01). Faster-X researc as partcularly empaszed te nterplay between genetc domnance and adaptaton (e.g., Orr 010; Mesel and Connallon 013). Teory predcts tat X-lnked genes sould adapt more rapdly tan te autosomes wen benefcal mutatons are partally or completely recessve. Consequently, te frequent emprcal observatons of faster-x rates of adaptve substtuton could mply tat benefcal alleles are, on average, partally recessve (for dscusson, see Presgraves 008; Mank et al. 010; Orr 010; Mesel and Connallon 013). Te faster-x teory may also explan te dsproportonately large contrbuton of X-lnked genes to reproductve ncompatblty between speces (Coyne and Orr 1989; Masly and Presgraves 007). Faster-X teory as largely focused on long-term patterns of evolutonary cange and ter mplcatons for adaptve dfferentaton between speces. In contrast, ts teory s largely slent regardng te role of te X cromosome n adaptve dfferentaton between subpopulatons of sngle speces, n response to local envronmental condtons (for exceptons, see Owen 1986; Nagylak 1996; Parker and Hedrck 000). Te balance between mgraton and spatally varable selecton as been a major focus of classcal populaton genetcs teory, wc ncludes te mantenance of genetc dfferences between populatons excangng mgrants (Moran 1959, 196), te teory of clnes (Haldane 1948; Fser 1950), and te mantenance of genetc polymorpsm n spatally complex envronments (Levene 1953; Felsensten 1976; Hedrck et al. 1976; Hedrck 1986, 006). Recent teory as expanded upon ts classcal framework by consderng, for example, te evolutonary genetc bass of convergent adaptaton among subpopulatons of geograpcally wdespread speces (Ralp and Coop 010), and te populaton genetcs of adaptaton at speces range margns (Pescl et al. 013, 015). However, despte wdespread nterest n te genetcs of adaptaton across geograpc space (Hoban et al. 016), te potental contrbutons of X-lnked and autosomal genes to local adaptaton ave been largely overlooked. Teoretcally, we ave lttle to gude predctons about te relatve contrbutons of te X and autosomes to local adaptaton. Here, we address ts gap n teory by mergng classcal populaton genetc models of local adaptaton (e.g., Haldane 1948; Moran 1959, 196) and X-cromosome evoluton (e.g., Haldane 194; Avery 1984). We specfcally nvestgate te relatve contrbutons of X-lnked and autosomal loc to local adaptaton across abrupt and contnuous envronmental gradents (results can also be appled to Z-lnkage n speces wt female-eterogametc sex determnaton, e.g., brds and Lepdoptera). Our models jontly consder te effects of sexbased mgraton, sex dfferences n selecton, genetc domnance, and te effectve populaton szes of X-lnked and autosomal loc on te extent of spatal adaptve dfferentaton at X-lnked and autosomal loc. In contrast to te teory of faster-x dvergence between speces were domnance plays a major role n sapng te relatve rates of X vs. autosome substtuton we fnd tat te relatve contrbuton of te X to local adaptaton s largely determned by sex-specfc mgraton rates and s relatvely nsenstve to te domnance coeffcents of locally adapted alleles. Te models predct a spatal large-x effect over most of te parameter space of domnance and sex-specfc selecton, partcularly wen mgraton rates are male based. Model In contrastng te responses of autosomal and X-lnked loc to selecton for local adaptaton, we take tree complementary approaces. Frst, we bult upon Moran s nfluental model of dvergence between a par of dfferentally selected populatons (Moran 1959, 196; Carleswort and Carleswort 010, Capter 4; Felsensten 015) to quantfy equlbrum genetc dvergence under mgraton-selecton balance. Second, we extended classcal clne teory (Haldane 1948; Carleswort and Carleswort 010, Capter 4; Felsensten 015) to develop analytcal predctons for te slopes of X-lnked and autosomal clnes. Trd, we carred out stocastc forward smulatons of genetc clnes under mgraton, selecton, and genetc drft n a one-dmensonal steppng-stone model wt dscrete abtats dstrbuted along an envronmental gradent. For eac model, we follow te frequences of two alleles per locus. We arbtrarly label te alleles A and B, wt q referrng to te frequency of allele A, and1 q to te frequency of B. Eac allele s favored n te dfferent populatons, or n dfferent locatons across te envronmental gradent. Moran s two-populaton model Followng Moran (1959, 196), we consdered a symmetrcal, two-populaton model n wc te A allele s favored n one of te populatons and te B allele s favored n te oter (see Table 1 for te sex-specfc ftness parameterzaton for eac populaton and mode of nertance). Effects of drft are assumed to be neglgble. We also assume tree forms of symmetry n te model (1) equal mgraton rates between populatons 1 and, () equal selecton coeffcents aganst te nferor omozygote genotype wtn eac populaton, and (3) equal populaton szes. As n earler work (.e., usng autosomal models; see Carleswort and Carleswort 010, Capter 4) we assume tat te rate of mgraton (d) and strengt of selecton (s) are bot weak (d and s are bot small), and we can terefore approxmate te total rate of cange n allele frequences, per populaton, as te sum of te expected canges under mgraton and selecton, ndvdually. Specfcally, we model te total cange n frequency of an arbtrary, focal populaton as Dq ¼ Dq mg þ Dq sel ; (1a) were Dq mg and Dq sel represent te net cange n frequency wtn te focal populaton due to mgraton and to local 186 C. Lasne, C. M. Sgrò, and T. Connallon

3 Table 1 Ftness values by genotype, sex, and locaton for te abrupt envronmental cange model Sex Moran model Clne model Ftness value per genotypes AA, A AB BB, B Female Pop. 1 x, 0 1 s f 1 s f 1 1 Pop. x s f 1 s f Male (autosome) Pop. 1 x, 0 1 s m 1 s m 1 1 Pop. x s m 1 s m Male (X-lnked) Pop. 1 x, 0 1 s m 1 Pop. x s m Pop., populaton. selecton, respectvely. Expressons for Dq sel are presented furter below. Cange n populaton 1 due to mgraton s gven by Dq mg =(q q 1 )d, were q 1 and q represent te frequences of A n populaton 1 and, respectvely, and d refers to te fracton of gene copes tat mgrate between te populatons. Te frequency cange n populaton due to mgraton s Dq mg =(q 1 q )d. Followng pror teory (Berg et al. 1998; Laporte and Carleswort 00; Hedrck 007), te mgraton rate for an autosomal locus s d A =(d f + d m )/; te mgraton rate for an X-lnked locus s d X = (d f + d m )/3. Note tat d s rougly analogous to te mgraton parameter, m, tat we use n te subsequent clne models. We dstngus between m and d to avod confuson about te slgtly dfferent defntons of mgraton n Moran and clne models of local adaptaton. Clne model In our clne model, te populaton s spread wt unform densty across a contnuous, one-dmensonal envronmental gradent (wt locaton represented by x). Mgraton s symmetrcal n drecton, and te strengts of mgraton and selecton are assumed to be weak. Effects of drft are assumed to be neglgble. Under tese condtons, te equlbrum reactondffuson equaton descrbng allele frequency at locaton x s m d q dx þ Dq sel ¼ 0; (1b) were m refers to te mean-squared dspersal dstance of ndvduals relatve to ter locatons at brt (ncdentally, ts parameter s functonally equvalent to te mgraton rate between adjacent abtats n a steppng-stone model; see Felsensten 015), and Dq sel s te local response to selecton, n terms of te cange n frequency of te A allele. Te mgraton parameter m takes nto account dfferental mgraton rates between te sexes. Smlar to te two-populaton model from above, te net mgraton rate for an autosomal locus s m A =(m f + m m )/, were m f and m m are female and male mgraton rates, respectvely, and te net mgraton rate for an X-lnked locus s m X = (m f + m m )/3. We assume tat te envronment canges abruptly at locaton x =0alongtegradent(.e., tsmodelnvolves a step clne; Haldane 1948). Allele B s favored n one drecton away from te envronmental transton (wen x, 0), wle A s favored n te oter drecton (x. 0). In te step-clne model, te strengt of selecton for or aganst te A allele swtces abruptly at te envronmental transton, but ten remans constant furter away from te transton pont (see Fgure 1, left and mddle panels, and Table 1). We caracterze selecton n eac sex relatve to te fttest genotype, wt sex-specfc selecton coeffcents (s f, s m ) representng te strengt of selecton aganst te least-ft genotype, per locaton. Genetc domnance and local responses to selecton Parameters 1 and represent te domnance coeffcents for locally maladaptve alleles (Table 1) 1 refers to te relatve domnance of te A allele n populaton 1 (n te Moran model) and n regons were x, 0(nteclnemodel); refers to te domnance of B n populaton (Moran) and n regons were x. 0(clnemodel).Allelesavecodomnant,or addtve, ftness effects wen 1 = =1/.Followngteprevous teory on opposng selecton between envronments (see Curtsnger et al. 1994; Prout 000; Fry 010), we consder two dealzed models of allelc domnance across te speces range. Frst, we consder a benefcal reversal of domnance model (ereafter domnance reversal ; see Curtsnger et al. 1994), were = 1 =, 1/. In ts nstance, allele A s domnant to B n locatons were A s favored, and allele B s domnant to A n locatons were B s favored (see Fgure 1, mddle and rgt panels, and Table1).Tspartcularparameterzaton emerges n scenaros were ftness landscapes are concave around local ftness optma (see Fry 010; Manna et al. 011; Martn and Lenormand 015). Second, we consder a model of parallel domnance (Curtsnger et al. 1994; also see Kdwell et al. 1977), were = 1 =1 ; refers to te domnance of A relatve to B (.e., A s recessve wen, 1/, wereas A s domnant wen. 1/; Fgure 1, left panel). In ts case, te domnance relaton between A and B s constant across te entre speces range a scenaro tat apples wen tere s a monotonc relaton between locaton n te speces range and selecton on a penotype for wc alleles exbt consstent levels of domnance (e.g.,temelansm penotype, wt dfferent populatons favorng/dsfavorng melanc forms). Under weak, sex-specfc selecton (0, s m, s f 1), and benefcal reversal of domnance ( = 1 = ), te cange n frequency of te A allele at an autosomal locus can be descrbed by te followng equatons. In regons of te speces range were allele A s favored (populaton of te Moran Local Adaptaton on X and Autosomes 187

4 Under te parallel domnance scenaro ( = 1 =1 ), te local response to selecton remans te same n populaton 1 and x, 0. For populaton and x. 0, te response to selecton on an autosome and X, respectvely, s Dq sel ¼ Dq f þ Dq m ðs f þ s m Þqð1 qþ þ qð1 Þ (4a) Fgure 1 Spatal varaton n relatve ftness for eac of te tree genotypes (AA, BB, and AB). Examples of te domnance reversal scenaro ( = 1 = = 0.3; see Table 1) are sown n te center and rgt panels. An example of parallel domnance [ = 1 =(1 ) = 0.3; see Table 1] s sown n te left panel. Two scenaros of envronmental cange n ftness are sown te frst two panels depct a step clne n ftness tat abruptly transtons at te center of te range (locaton x = 0); te trd panel sows a ramp clne, wt a gradual ncrease n te strengt of selecton away from te center of te range. Analytcal results descrbe evoluton under te abrupt cange model and for eac form of domnance (te frst two panels). Smulatons caracterze evoluton under all four scenaros of selecton and domnance te tree scenaros depcted n te tree panels, above, as well as te gradual cange scenaro wt a domnance reversal (not depcted n fgure). model; x. 0 n te clne model), te local response to selecton s gven by Dq sel ¼ Dq f þ Dq m ðs f þ s m Þqð1 qþ 1 qð1 Þ (a) Oterwse (Moran populaton 1; clne locaton x, 0), te local response to selecton s Dq sel ¼ Dq f þ Dq m ðs f þ s m Þqð1 qþ þ qð1 Þ (b) For eac expresson, Dq f and Dq m refer to te frequency canges due to selecton n females and males, respectvely; te total frequency due to local selecton s smply te average of sex-specfc canges. For te X cromosome, local responses to selecton are descrbed by Dq sel ¼ Dq f þ Dq m 3 for populaton or x. 0, and Dq sel ¼ Dq f þ Dq m 3 s f 1 qð1 Þ þ s m qð1 qþ 3 (3a) s f þ qð1 Þ þ s m qð1 qþ 3 (3b) for populaton 1 or x, 0. Te factor of two n Dq f reflects te twofold ger rate of X cromosome transmsson troug moters compared to faters. and Dq sel ¼ Dq f þ Dq m 3 Analyss of te models s f þ qð1 Þ qð1 qþ 3 þ s m (4b) We quantfed equlbrum patterns of allele frequency dfferentaton among populatons by analyzng Equaton 1, a and b, usng relevant expressons for m, d and Dq sel for eac model and mode of nertance. Detals of te Moran model analyss are presented n Appendx A. Detals of te clne model analyss, wc follows te approac outlned n Felsensten (015), are presented n Appendx B. Moran model analyss For te Moran model, we focused on two classes of results. Frst, assumng addtve ftness effects ð 1 ¼ ¼ 1=Þ; te equlbrum frequency of A across te populatons s ^q ¼ð^q 1 þ ^q Þ= ¼ 1= For an autosomal locus, te allele frequency dfference between populatons s vffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff " # u 4ðd m þ d d A ¼ ^q ^q 1 ¼ t 1 þ f Þ 4ðd m þ d f Þ (5a) s m þ s f s m þ s f For an X-lnked locus, te allele frequency dfference between populatons s vffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff " # u ðd d X ¼ ^q ^q 1 ¼ t 1 þ f þ d m Þ ðd f þ d m Þ s m þ s f s m þ s f (5b) Second, for cases were ftness effects are nonaddtve, we obtaned approxmatons for equlbrum allele frequences, assumng tat mgraton s g relatve to selecton (e.g., d s). For te domnance reversal model ð ¼ 1 ¼ Þ; te overall allele frequency for eac locus remans at ^q ¼ð^q 1 þ ^q Þ= ¼ 1= Te allele frequency dfference between populatons s well approxmated (n te lmt of g mgraton relatve to selecton) by d A ¼ ^q ^q 1 for an autosomal locus, and s m þ s f 8ðd f þ d m Þ ; (6a) 188 C. Lasne, C. M. Sgrò, and T. Connallon

5 d X ¼ ^q ^q 1 s m þ s f 4ðd f þ d m Þ (6b) rffffffffffffffffffffffffffffffffffffffffffffffffffffffff s y X ¼ f þ s m (9b) 3ðm f þ m m Þ for an X-lnked locus. Under parallel domnance and autosomal lnkage (and agan, assumng d s), te equlbrum frequency of A s p ð1 3Þþ ffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1 3ð1 Þ ^q A ¼ ; (7a) 3ð1 Þ and te frequency dfferentaton between populatons s ^q A ð1 ^q A Þ þ ^q A ð1 Þ ðs m þ s f Þ d A (7b) d m þ d f Wt parallel domnance and X-lnkage, we get qffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ^q X ¼ ½s fð1 3Þ s m Šþ ½s f ð13þs m Š þ 6ðs f þ s m Þs f ð1 Þ ; 6s f ð1 Þ (7c) and d X ^q X ð1 ^q X Þ s f ð þ ^q X ð1 ÞÞ þ s m (7d) d m þ d f Clne model analyss For te clne model, approxmatons are based on te assumpton tat range boundares are suffcently far from te envronmental transton pont (at x =0)tatA eventually approaces fxaton on one sde of te transton pont (q / 1asx / N), and B approaces fxaton on te oter sde (q / 0 as x / N). Valdty of ts assumpton does not necessarly requre te speces range to be nfnte; rater, selecton must be suffcently strong relatve to te dstance to eac range boundary. Under domnance reversal condtons, te autosome and X- lnked clne maxma (respectvely) are and sffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff ð5 þ 6Þðs y A ¼ f þ s m Þ 48ðm f þ m m Þ (8a) sffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff y X ¼ s f ð5 þ 6Þþ8s m 4ðm f þ m m Þ (8b) In bot cases, te equlbrum allele frequency at te correspondng mdpont of te speces range s ^q x¼0 ¼ 05 Under parallel domnance, te clne maxma for autosomal and X-lnked loc, respectvely, are and rffffffffffffffffffffffffffffffffffffffffffffffffff s y A ¼ f þ s m 6ðm f þ m m Þ (9a) Te equlbrum allele frequences at te range center (under autosomal and X-lnked nertance, respectvely) are and ^q A; x¼0 1 þ 1 8 ^q X; x¼0 1 þ s fð1 Þ 8ðs f þ s m Þ Smulatons of te steppng-stone model (10a) (10b) We expanded upon te analytcal results by mplementng a one-dmensonal steppng-stone model tat ncludes H dscrete abtat patces (or demes ) (we assume H s an even nteger), and dscrete generatons. Populaton sze s constant over tme and unform across te demes. As before, we follow te frequences of alleles A and B per locus. We consdered two patterns of selecton across te envronmental gradent. To facltate comparsons wt te analytcal results, we frst consdered te case were ftness values per genotype sft abruptly at te range center (.e., between deme H/ and deme 1 + H/). In ts step-clne scenaro, te A allele s favored n demes 1 + H/ troug H, and te B allele s favored n demes 1 troug H/. Te relatve ftnesses of te tree possble genotypes are equvalent to tose depcted n Table 1. Second, we consdered a model of gradually cangng selecton across demes. Selecton agan favors te B allele n demes 1 troug H/; A s favored n te remanng demes. Te strengt of selecton for A or B ncreases away from te mdpont of te speces range, and eventually reaces a maxmum at te endponts of te envronmental gradent (see Fgure 1 and Table ). We consdered te same forms of domnance as n te analytcal models (.e., domnance reversal and parallel domnance). Te lfe cycle of te speces follows te order of brt, mgraton, local selecton wtn demes, and random matng among te adults of eac deme (.e., after selecton). For an arbtrary deme between = and = H 1, eac female and male as a probablty m f and m m, respectvely, of mgratng to an adjacent deme, and a probablty of 1 m f and 1 m m of remanng n te deme of brt. Mgratng ndvduals are equally lkely to mgrate to eac of te two adjacent demes (.e., ndvduals mgratng from te t deme are equally lkely to land n deme 1 or n deme + 1). Demes at te edge of te speces range (demes 1 and H) excange mgrants wt one negborng deme. We assume tat range boundares are reflectng (see e.g., Garca-Ramos and Krkpatrck 1997), wt eac female and male from deme 1 or deme H mgratng to te adjacent deme (deme or deme H 1) wt probabltes m f / and m m /, respectvely. Female and male ndvduals tat are born n deme 1 or deme H reman wt probablty 1 m f / and 1 m m /. We also Local Adaptaton on X and Autosomes 189

6 Table Ftness values by genotype, sex, and locaton for te gradual envronmental cange model Sex Locaton Ftness value per genotypes AA, A AB BB, B Female # H/ 1 + s(, f) s(, f) 1. H/ 1 1 s(, f) 1 s(, f) Male (autosome) # H/ 1 + s(, m) s(, m) 1. H/ 1 1 s(, m) 1 s(, m) Male (X-lnked) # H/ 1 + s(, m) 1. H/ 1 1 s(, m) Te above apples n a steppng-stone model wt H demes, were H s an even nteger, s j s a constant tat represents te selecton for te jt sex at eac of te boundary demes, and s(, j) s a functon representng te selecton coeffcent for te jt sex n te t deme s(, j) =s j [ (1 + H)]/(H 1). consdered a model were local selecton occurs before mgraton and random matng, and found smlar results. For smplcty, we present te results and recursons for models were mgraton occurs before selecton (see Supplemental Materal, Fle S1, for furter detals). For pont of comparson wt te analytcal results, we frst carred out determnstc smulatons for te abrupt and gradual envronmental cange models. Eac smulaton run was ntated wt equal frequences of te two alleles n eac deme. Determnstc smulatons were terated for a mnmum of 10,000 generatons, wc was suffcent to reac equlbrum. Clne slopes were calculated as te allele frequency dfference between a gven par of adjacent demes. Ts approac to quantfyng clne slope yelds comparable results to te analytcal clne model wen allele frequency cange s rougly lnear across te speces range center; oterwse, estmates of te maxmum clne slope are downwardly based n te steppng-stone model (for dscusson, see Capter 4 of Felsensten 015). To ease comparson, we focused on parameter space leadng to lnear cange near te center of te speces range (as wen s/m, 1). Genetc drft was ncorporated by way of multnomal samplng of adult genotypes (see, e.g., Carleswort and Carleswort 010, pp. 9 30). We assumed tat eac deme produces N f and N m adult females and males tat randomly mate (wtn demes) to produce offsprng of te next generaton. Followng te standard Wrgt Fser model of drft (Carleswort and Carleswort 010), we sampled genotypes for N m males and N f females from a multnomal dstrbuton, wt probabltes of eac genotype based on te expected (determnstc) genotype frequences for adults of te deme. Genotype frequences of breedng adults (after samplng) were ten used to calculate expected frequences of adult genotypes n te next generaton. Assumng tat ndvduals of eac sex produce a Possondstrbuted number of offsprng n eac generaton, ten te autosomal and X-lnked effectve populaton szes are smple functons of N f and N m (see Avery 1984; Hartl and Clark 007, p. 14). Te effectve populaton sze for an autosomal locus s N ea =4N f N m /(N f + N m ), and te effectve sze for an X-lnked locus s N ex =9N f N m /(4N m +N f ). We note tat tere are more complex models for X-lnked and autosome effectve szes tat take nto account dfferent forms of reproductve success varance among breedng males and females (see Laporte and Carleswort 00; Vcoso and Carleswort 009). Our approac represents te smplest route to ncorporate drft and dfferent relatve effectve szes of X-lnked and autosomal genes. We specfcally consdered te effect of tree dfferent ratos of X-to-autosome effectve populaton szes on te evoluton of clne slopes (1) te null X/autosome rato of N ex /N ea = 0.75, () a dampened X/autosome rato of N ex /N ea = 0.6, and (3) an elevated X/autosome rato of N ex /N ea = 1. For eac set of selecton, mgraton, and effectve populaton sze parameters we carred out 1000 replcate smulaton runs. Eac run was carred out for N ea generatons to elmnate effects of ntal allele frequency condtons. All smulatons were carred out n R verson 3.1. (R Core Team 014). A full descrpton of te smulaton algortm can be found n Fle S1; correspondng R code as been deposted n GtHub (ttps//gst.gtub. com/clemlasne). Data avalablty Te autors state tat all data necessary for confrmng te conclusons presented n te artcle are represented fully wtn te artcle. Results In te followng results, we focus on te amount of genetc dvergence at X-lnked relatve to autosomal loc wen eac evolves n response to spatally varyng selecton. Frst, we present results for a two-populaton model of mgratonselecton balance (as n Moran 1959, 196; Carleswort and Carleswort 010, Capter 4). Second, we present analytcal results for allele frequency clnes n a speces tat s contnuously dstrbuted across an abrupt envronmental transton. Trd, we present smulaton results from a steppngstone model of populaton subdvson, wc expand upon te analytcal predctons by consderng bot gradual and abrupt cange n selecton across space and genetc drft. Fourt, we quantfy te relatve contrbutons of te X and autosomes to te ftness load of mgrant relatve to natve ndvduals n a focal envronment. Fnally, we close by bencmarkng adaptve dfferentaton of X-lnked and autosomal genes relatve to dfferentaton of neutrally evolvng loc. Adaptve dfferentaton n te two-populaton model To quantfy adaptve dfferentaton between te two populatons of te Moran model (Moran 1959, 196), we used te fxaton ndex F ST ¼ d 4^q ð1 ^q Þ ; (11) were d s te equlbrum allele frequency dfference between populatons, ^q s te overall equlbrum allele 190 C. Lasne, C. M. Sgrò, and T. Connallon

7 frequency for te A allele (.e., averaged between populatons), and refers to te nertance mode ( ={A, X}). Equaton 11 was evaluated usng relevant expressons from Equatons 5 7. In te followng results, we present te rato of F ST at X-lnked relatve to autosomal loc, denoted FST X =FA ST Consder te smplest scenaro were adaptve alleles ave addtve ftness effects. In ts case, dfferental contrbutons of te X and autosomes to local adaptaton are mnmzed wen mgraton s weak relatve to te strengt of selecton for populaton dfferentaton (see Fgure, left panel). Under weak mgraton (.e., d / 0), eac allele approaces fxaton were t s favored (F ST / 1), and FST X =FA ST approaces one. As te rate of mgraton ncreases, dfferentaton between populatons becomes more pronounced on te X relatve to te autosomes, provded tere s some mgraton troug males ðfst X =FA ST. 1 wen d m. 0; see Fgure, left panel); te dscrepancy between te X and autosomes becomes amplfed wt ger mgraton n males tan females (d m. d f ). Te extent of populaton dvergence on te X and autosomes, wle dependent on te sex-averaged strengt of selecton, s unaffected by sex dfferences n selecton. To explore te mpact of domnance on genetc dfferentaton at X-lnked and autosomal genes, we developed extended results for eac model of domnance descrbed above (domnance reversal and parallel domnance), assumng g mgraton relatve to selecton (d s; FST X =FA ST agan converges to one under weak mgraton). Overall, domnance as a relatvely mnor nfluence on te relatve contrbuton of te X and autosomes to dvergence. For te domnance reversal scenaro, as no effect at all, and n ts case te addtve results reman applcable (see Fgure and Fgure S1). Smlar results emerge from te parallel domnance model, toug n ts case te magntude of large-x effects are somewat dampened by devatons from addtvty ½FST X =FA ST declnes as (1 ) / 0], partcularly so wen selecton s stronger n males tan females (see Fgure S1). Ts latter result emerges from te effect of parallel domnance on te denomnator of te F ST equaton [4q (1 q ) n Equaton 11]. Parallel domnance leads to unequal equlbrum frequences of te par ofalleles,wcdecreases q (1 q ) and nflates F ST. Ts effect s dampened under X-lnked nertance, because selecton n males promotes relatvely equal equlbrum frequences of A and B alleles [from Equaton 7, a and c, q X (1 q X ). q A (1 q A ) wen s m. 0; oterwse, q X = q A = 1/]. X-lnked and autosomal allele frequency clnes In keepng wt teoretcal and emprcal tradtons n clne researc, we consder te relatve responses of X-lnked vs. autosomal loc to local selecton by calculatng clne slopes of X-lnked relatve to autosomal genes across te envronmental transton (.e., te rato of maxmum clne slopes, y X /y A ). For bot domnance scenaros, te X responds more effcently tan te autosomes to spatally varable selecton over most of te parameter space of domnance, sex-specfc selecton, and mgraton (Fgure 3). In te smplest case of Fgure Adaptve dvergence under mgraton-selecton balance n te Moran, two-populaton model. Te left panel (based on Equatons 5, a and b, and 11) sows ow te strengt of mgraton relatve to selecton nfluences te rato of dfferentaton at X-lnked vs. autosomal loc. Te x-axs sows te sex-averaged mgraton rate relatve to te sexaveraged strengt of selecton d=s ¼ðdf þ d m Þ=ðs f þ s m Þ Te rgt panel (based on Equatons 6, 7, and 11) sows te effects of domnance on te rato of dfferentaton at X-lnked vs. autosomal loc, wt equal selecton n females and males (s f = s m ; for te cases of male-lmted and female-lmted selecton, see Fgure S1). For pont of reference, te dased, gray lne sows te relatve rate of adaptve substtuton on te X compared to te autosomes, as predcted by Carleswort et al. [1987; from ter equaton a, te rato of adaptve substtutons on te X relatve to autosomes s R =(1+)/(4), dased black lne]. Te domnance coeffcent () sdefned as = 1 = n te domnance reversal case, = 1 =1 under parallel domnance (see Table 1), and as te domnance of benefcal mutatons n te Carleswort et al. (1987) model. addtve ftness effects ( = 1/), te rato of clne slopes reduces to y X y A ¼ rffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff m m 1 þ (1) m f þ m m As n te two-populaton context, te relatve contrbuton of te X to local adaptaton n a clne becomes p maxmzed under male-lmted mgraton ðy X =y A ¼ ffffff 1414 wen m f /m m = 0), and mnmzed under female-lmted mgraton (y X /y A = 1 wen p m m /m f = 0). Wt equal mgraton of eac sex, y X =y A ¼ ffffffffffffffffffffffff ð4=3þ 115 Ts set of results remans applcable under parallel domnance condtons (Fgure 3). For te domnance reversal case, te rato of clne slopes becomes margnally dependent on sex-specfc selecton and domnance condtons. Neverteless, sex-specfc mgraton patterns reman te domnant drver of dfferences between te X and autosomes (see Fgure 3). Clnal dvergence of allele frequences can also be expressed usng F ST metrcs between populatons tat are located on opposte sdes of te envronmental transton (.e., betweenpopulatonsatlocatonsx and x, werex =0s Local Adaptaton on X and Autosomes 191

8 Fgure 3 Te effects of sex-specfc selecton, sex-based mgraton, and domnance on te relatve rates of clnal dvergence at X-lnked and autosomal loc. Sold curves are based on te analytcal results from Equatons 8 and 9. Te frst and second panels sow te effects of sexspecfc mgraton (m f and m m n females and males, respectvely; selecton s equal between te sexes) on te evoluton of X-lnked and autosomal clnes. Te trd panel sows te effects of sex-specfc selecton(s f and s m n females and males; mgraton s equal between te sexes). For pont of reference, te dased lne sows te relatve rate of adaptve substtuton on te X compared to te autosomes, as predcted by Carleswort et al. [1987; from ter equaton a, te rato of adaptve substtutons on te X relatve to autosomes s R =(1+)/ (4), dased black lne]. Te domnance coeffcent () s defned as = 1 = n te domnance reversal case, = 1 =1 under parallel domnance (see Table 1), and as te domnance of benefcal mutatons n te Carleswort et al. (1987) model. te pont of transton). For populatons far removed from te envronmental transton (.e., far enoug tat te locally maladapted allele s elmnated, or nearly so), F ST for te X, te autosomes, and ter rato approaces one. For subpopulatons close to te envronmental transton, we can revst te addtve effects model from above ( = 1/) and quantfy dvergence between nearby subpopulatons (at postons x and x, were x approaces te envronmental transton pont) usng te expressons for an autosomal locus, and F A ST ðxþ s m þ s f 6ðm f þ m m Þ F X ST ðxþ s m þ s f 3ðm f þ m m Þ (13a) (13a) for an X-lnked locus (see Appendx B). Te rato of F ST for X-lnked and autosomal loc smplfes to te square of te rato of clne slopes, F X ST =FA ST ¼ðy X=y A Þ ; wc reaces a maxmum of two under male-lmted mgraton. Steppng-stone clnes under gradual envronmental cange and genetc drft Te analytcal models provde a baselne set of expectatons regardng te relatve role of te X cromosome n local adaptaton along a clne. On te oter and, ter results are restrctve by relyng on two crtcal assumptons. Frst, tey assume tat te envronmental transton s abrupt, wc excludes te lkely possblty of gradual envronmental cange across te speces range. Second, te results gnore mpacts of populaton sze, wc are known to affect te relatve rates of X-to-autosome adaptve substtuton between speces (Vcoso and Carleswort 009). To relax bot assumptons, we carred out smulatons usng a steppngstone model wt H demes along a one-dmensonal geograpc axs. Wen possble, we ave cosen parameter values of mgraton and selecton to facltate drect comparsons between smulated and analytcal results (e.g., m. s; seeaboveforcommentsregardngcomparsons between models). Abrupt vs. gradual envronmental cange We compared smulated outcomes from two dstnct selecton models (1) an abrupt cange model, wc corresponds to te scenaro used n te analytcal results; and () a gradual cange model, n wc te ntensty of selecton gradually ncreases wt dstance from te range center (see Fgure 1, mddle and rgt panels, Table 1, and Table ; te gradual cange model corresponds to te rampng scenaro descrbed n Felsensten 015). Altoug tere are some quanttatve dfferences n te equlbrum clnes of te two models wt large-x effects dampened under te rampng scenaro n general, we observed smlar patterns of spatal dvergence at X-lnked and autosomal loc for te two forms of envronmental cange (Fgure 4). Effectve populaton sze and te rato of X and autosome adaptve dvergence To nvestgate te senstvty of te determnstc results to genetc drft, we carred out stocastc (Wrgt Fser) smulatons tat nclude selecton, mgraton, and multnomal samplng of genotypes among te breedng adults n eac subpopulaton (see Model secton above). Tese stocastc results devated from determnstc predctons wen te strengt of selecton was effectvely weak (.e., wen N e s was small, were N e s te local effectve populaton sze and s s te sex-averaged strengt of selecton; see Fgure 5). Under neutralty (N e s = 0), te amount of spatal dvergence was smlar for te X and autosomes wen eac ad a smlar effectve populaton sze (e.g., N ex /N ea = 1). A lower X-lnked effectve populaton sze (N ex /N ea, 1) amplfed te effects of genetc drft at X-lnked loc, resultng n excess neutral dvergence on te X and ger X-toautosome dvergence ratos tan expected under determnstc selecton wtout drft. Dspartes between te stocastc and determnstc predctons declned rapdly wt ncreasng 19 C. Lasne, C. M. Sgrò, and T. Connallon

9 Fgure 4 Relatve rates of local adaptaton on te X and autosomes comparson between analytcal and steppng-stone models under abrupt and gradual envronmental cange. Analytcal results (sold curves) are based on Equatons 7 and 10. s and 4 sow te results of determnstc forward smulatons of te steppng-stone model, under an abrupt (s; Table 1) or gradual (4; Table ) envronmental transton. Results are presented for tree mgraton scenaros male-lmted mgraton (blue), female-lmted mgraton (red), and equal mgraton between te sexes (black). Parameters were m =(m m + m f )/ = 0.1, s =(s m + s f )/ = 0.00, and H = 100 abtats n te steppng-stone model. effectve strengt of selecton (ncreasng N e s; Fgure 5). Wen selecton s effectvely strong (N e s. 10), predctons from te determnstc models are robust to dfferences n te relatve populaton szes of X-lnked and autosomal loc. Relatve contrbuton of te X and autosomes to te ftness load of mgrants Te results above can be used to quantfy te relatve contrbutons of X-lnked and autosomal loc to te ftness load of mgrant relatve to natve ndvduals of a populaton. For smplcty, we focus on te addtve case ( = 1/) and quantfy te ftness load (ftness of mgrants relatve to natves) as L ¼ w N w M w N ; (14) were w N and w M represent te mean ftness of natve and mgrant ndvduals, respectvely, wtn a focal abtat. From Equaton 14, we can quantfy te relatve contrbuton of an X-lnked and autosomal locus to te mgrant ftness load; assumng tat eac locus as a ftness effect of s j n te jt sex (see Appendx C). In te two-populaton model, te relatve qffffffffffffffffffffffffffffff load on te X and autosomes smplfes to L X =L A ¼ FST X =FA ST; wc (gven te results presented above, e.g., Fgure ) falls wtn te range 1, L X /L A,. Usng a smlar approac to te clne context, we can quantfy te load of ndvduals born slgtly above te envronmental transton (from locaton x; 1 x. 0) tat mgrate to just below te transton (to locaton x). In ts case, te relatve load on te X and autosomes smplfes to L X /L A = y X /y A. From above (e.g., Fgure3),tsfallswtnterange1, L X / L A, O. Fgure 5 Influence of effectve populaton sze on genetc dvergence between adjacent demes n te steppng-stone model. Results sow te maxmum values of F X ST and F A ST between pars of adjacent demes along te gradent (.e., te maxmum of H 1 parwse F ST values). Results tat track F ST at te center of te speces range (.e., across te envronmental transton) are ndstngusable. Eac panel compares determnstc forward smulatons (gray lne) aganst stocastc smulatons for dfferent ratos of X-lnked to autosome effectve populaton sze (N ex /N ea ). Te effectve strengt of selecton (N e s)referstoteproduct of local populaton sze [N =N ea = 4N f N m /(N f +N m )] and te selecton coeffcent (s = s f = s m = 0.05). Parameters were set to = 0.5, m =(m m + m f )/ = 0.1, and H = 30 abtats n te steppng-stone model. Populaton dfferentaton at selected relatve to neutral loc Te teory presented above predcts tat te X wll contrbute dsproportonately to local adaptaton under a broad set of bologcal condtons (.e., wen tere s apprecable mgraton of te eterogametc sex). On te oter and, genetc drft accounts for populaton dfferentaton at most loc wtn a genome, and dentfyng dfferentally selected loc aganst ts genomc background of neutral dvergence represents a major callenge n populaton genomcs (Hoban et al. 016). One approac for dentfyng canddate loc under local selecton s to establs a neutral dstrbuton of F ST (e.g., based on genome-wde polymorpsm data) and subsequently target outler loc tat fall outsde te neutral range; outler loc represent canddate genes respondng to local selecton (Lewontn and Krakauer 1973). Ts approac poses a callenge n te context of X vs. autosome comparsons, because te dstrbuton of neutral F ST can systematcally dffer between cromosomes (e.g., Laporteand Carleswort 00; Hedrck 007), leadng to dfferent opportuntes to dentfy canddate loc respondng to local selecton. Because te breadt of te dstrbuton of neutral F ST wll often be greater on te X tan te autosomes (e.g., due to Local Adaptaton on X and Autosomes 193

10 reduced N e for X-lnked genes and/or male-based mgraton), t may be more dffcult to relably dentfy outler F ST loc on te X despte elevated contrbutons of X-lnked genes to local adaptaton. We can apply te teory of neutral F ST to establs a teoretcal baselne of neutral populaton dfferentaton on te X and te autosomes, and classfy scenaros n wc outler F ST analyss wll dentfy X-lnked and autosomal canddate loc for local adaptaton. We focus our attenton on F ST between a par of populatons wt g levels of mgraton and low neutral F ST, leadng to relatvely promsng condtons for dentfyng selected loc wt F ST above te neutral range. Followng standard teory (e.g., Slatkn 1991; Laporte and Carleswort 00) and assumng effectvely strong mgraton on bot te X and autosomes (specfcally, N e m 1 m,weren e and m represent te effectve populaton sze and effectve mgraton rate for nertance system ={A, X}), te expected F ST on te X relatve to te autosomes s EðF ST X Þ EðF ST A Þ N eam A N ex m X ¼ 3N ea 4N ex ðm f þ m m Þ ðm f þ m m Þ (15) Based on Equaton 15, mean neutral dvergence on te X exceeds tat of te autosomes under broad condtons of effectve populaton sze (e.g., N ex /N ea, 1) and sex-based mgraton (e.g., m m /m f. 0) (see Fgure S). Neverteless, te excess adaptve dfferentaton on te X relatve to autosomes (descrbed above) s often ger tan te Xvs.autosome dfferences at neutral loc. For example, n te two-populaton model wt addtve ftness effects and strong mgraton relatve to selecton, te X-to-autosome F ST rato at selected loc wll be greater tan te rato of mean neutral F ST (Equaton 15) as long as te followng condton s true N ex. 3ðm f þ m m Þ N ea 8ðm f þ m m Þ (16a) Te condton s always met wen N ex /N ea. 0.75, and te crteron for excess dvergence at selected loc becomes more permssve wt ger male tan female mgraton (.e., m m /m f. 1). In te clne models at te speces range center (and under te same assumptons as above,.e. =1/;m s), te crteron for a ger X-to-autosome F ST rato at selected relatve to neutral loc s N ex N ea. 3 4 (16b) To quantfy opportuntes for selected loc on te X and autosomes to reac outler status, we smulated te dstrbuton of neutral F ST for X-lnked and autosomal loc (eac based on 10,000 smulated neutral loc) n te two-populaton model of populaton subdvson. We ten calculated te fracton of nonneutral loc at wc selecton s suffcently strong to drve F ST beyond te 95t percentle tal of te neutral F ST dstrbuton, per cromosome. We assumed an exponental dstrbuton of selecton coeffcents at selected loc, wt dentcal ftness effect dstrbutons among loc on te X and autosomes. Tese smulatons sow tat Equaton 16a provdes a useful bencmark for te relatve fracton of selected loc tat reac outler status on te X and autosomes (Fgure 6; were te X as a ger fracton of outler loc tan te autosomes wen Equaton 16a s true). In general, te X exbts an excess of outlers relatve to te autosomes, despte ts tendency for ger neutral F ST (Fgure 6). Te dscrepancy n te number of outler loc on te X and autosomes s senstve to te average ftness effect of selected loc, E(s). As E(s) decreases n magntude, a smaller fracton of selected loc reac outler status on bot cromosome types, but te relatve fracton reacng outler status becomes more asymmetrcal between cromosomes (e.g., to te left of eac x-axs of Fgure 6). Dscusson Te teory presented ere predcts tat te X cromosome (as well as te Z n speces wt female-eterogametc sex determnaton) wll make a dsproportonately large contrbuton to adaptve genetc dfferentaton between populatons tat are connected troug gene flow. In contrast to teores of faster-x dvergence between speces (see Vcoso and Carleswort 006; Mesel and Connallon 013), te outszed contrbuton of te X to local adaptaton s relatvely nsenstve to sex-based natural selecton, genetc domnance, or effectve populaton sze. Instead, te magntude of te large- X effect n local adaptaton nges upon te relatve rate of mgraton n females and males. Hg rates of mgraton wtn te eterogametc sex (.e., males n speces wt an X; females n speces wt Z cromosomes) elevate te relatve contrbuton of sex-lnked genes to adaptve dfferentaton between subpopulatons of a speces. In te followng sectons, we address tree bologcal mplcatons of te new teory. We frst outlne te major ponts of dfference between spatal and temporal models of X and autosome evoluton; we dssect te dstnct bologcal condtons tat gve rse to large-x effects n adaptaton across spatal vs. temporal scales. Second, we outlne callenges and potental approaces for testng te teory. We empasze tat wle few studes to date ave examned te contrbutons of te X and autosomes to local adaptaton te teory presented ere provdes a useful roadmap for future emprcal researc n te arena of local adaptaton. Trd, we provde an overvew of lmtatons of our models, were eac justfes future teoretcal work on te populaton genetcs of X-lnked adaptaton wtn structured populatons. Contrbutons of te X to local adaptaton vs. long-term adaptve dvergence Evolutonary scenaros of spatal and temporal dvergence follow dstnct teoretcal tradtons, and use dstnct modelng approaces. Te teory of local adaptaton on te X and autosomes, presented ere, s most readly compared to a 194 C. Lasne, C. M. Sgrò, and T. Connallon

11 Fgure 6 Outler status of X-lnked and autosomal loc n te twopopulaton model. Te curves sow te relatve fracton of selected loc tat fall wtn te upper 95t percentle tal of te neutral dstrbuton of F ST.Treescenarosofmgratonaresownfemale-lmted mgraton (d f. 0; d m =0),equalmgraton(d f = d m. 0); and malelmted mgraton (d f =0;d m. 0). Neutral F ST dstrbutons, ncludng 95t percentle tresolds, were obtaned by smulatng 10,000 neutral loc for eac cromosome and eac scenaro of N ex /N ea.resultsare sown for te specfc caseofn ea =5000and(m f + m m )/ = 0.1. Addtonal results, usng larger effectve populaton szes and smaller mgraton rates, are presented n Fle S1. DetermnstcequatonsforF ST under selecton and addtve ftness effects were used to quantfy te fractons of selected loc tat reac te 95t percentle tresold of neutral loc, and assumng tat selecton coeffcents [.e., s =(s f + s m )/] are exponentally dstrbuted wt a mean of E(s) under eac mode of lnkage. well-developed teory on te relatve rate of adaptve substtutons at X-lnked and autosomal genes (faster-x teory). Below, we dscuss two promnent ponts of contrast between tese teores. In te faster-x teory, te X adapts more rapdly tan te autosomes wen benefcal mutatons are, on average, partally or completely recessve, wc reflects te nflated fxaton probabltes of rare benefcal mutatons on te X (e.g., Avery 1984; Carleswort et al. 1987; but see Vcoso and Carleswort 009). In contrast, te new teory reveals a modest effect of domnance n contexts of local adaptaton (e.g., Fgure and Fgure 3). Ts nsenstvty to domnance arses from a smple cause. Dvergence under gene flow depends prmarly on te rate of evolutonary response to selecton on ntermedate-frequency alleles, as opposed to fxaton probabltes of rare mutatons. Domnance as a reduced mpact on te response to selecton wen alternatve alleles at a locus are bot common wtn a populaton. And, n te absence of any major effects of domnance on X-lnked and autosome evolutonary dynamcs, te tendency of te X to dverge more extensvely tan autosomes reflects ts nerently greater responsveness to natural selecton (regardless of domnance) afeaturetat as long been recognzed by populaton genetcs teory (see Avery 1984). Te relatve rates of X-to-autosome adaptve substtuton are also senstve to te effectve populaton szes of X-lnked and autosomal genes (N ex and N ea, respectvely), wt large ratos of N ex /N ea enancng faster-x effects (.e., N ex /N ea. 0.75) and small ratos dampenng tem (.e., N ex /N ea, 0.75) (see Vcoso and Carleswort 009). In contrast, te contrbuton of te X to local adaptaton s relatvely nsenstve to effectve populaton sze, provded te overall effcacy of selecton s strong (e.g., N e s 10). Ts feature of local adaptaton models once agan reflects te mportance of selecton on common genetc varants. Effectve populaton sze plays a mnor role n te dynamcs of ntermedatefrequency alleles, because effectvely strong selecton (large N e s) gves rse to pseudodetermnstc evolutonary dynamcs of benefcal alleles (Barton 1998). Emprcal observatons of dstnct evolutonary dynamcs of X-lnked and autosomal genes potentally provde sgnals of sex-specfc evolutonary processes, and may reveal features of te genetc bass of adaptaton (Vcoso and Carleswort 006; Mesel and Connallon 013). Gven te fundamental dfferences between spatal and temporal scenaros of adaptaton, large-x effects n local adaptaton and faster- X patterns of adaptve substtuton reveal fundamentally dstnct features of te evolutonary genetcs of adaptaton. Wereas faster-x effects emerge from genetc constrants tat lmt rates of adaptaton (.e., Carleswort et al. 1987; Orr and Betancourt 001; Orr 010; Connallon et al. 01); large-x effects n local adaptaton arse from ntrnsc propertes of X-cromosome transmsson, and reflect adaptve constrants mposed by gene flow between dvergently selected populatons. Testng for a large-x effect n local adaptaton By generatng new predctons about te evolutonary genetc bass of local adaptaton, te new teory provdes a strong motvaton to emprcally quantfy te roles of X- and Z-lnked genes n local adaptaton. Below, we outlne two complementary approaces for testng te teory. Te most stragtforward approac s to drectly map te genetc bass of trats tat are known to ave dverged under selecton for local adaptaton. Ts approac sould be feasble n emprcal systems, were controlled crosses can be carred out wt relatve ease and were trats subject to local selecton may be measured wt g replcaton and under standardzed envronmental condtons (.e., n te laboratory or greenouse). Several crossng approaces can be taken to solate effects of te X from oter regons of te genome, and tese range from relatvely smple to complex (Renold 1998; Farbarn and Roff 006; Masly and Presgraves 007). One obvous system were ts drect mappng approac would apply s Drosopla, wc sows predctable patterns of spatal dvergence n response to envronmental varaton by lattude (Hoffmann and Weeks 007; Sgrò et al. 010). Geograpcally wdespread plant speces (wt sex cromosomes) may also prove useful, wt transplant experments allowng for drect estmaton of genotype-by-envronment effects on ftness. Wle drect mappng strateges for parttonng X-lnked effects on quanttatve trat varaton are wdely Local Adaptaton on X and Autosomes 195