Evidence for a freezing tolerance growth rate trade-off in the live oaks (Quercus series Virentes) across the tropical temperate divide

Size: px
Start display at page:

Download "Evidence for a freezing tolerance growth rate trade-off in the live oaks (Quercus series Virentes) across the tropical temperate divide"

Transcription

1 Reserh Evidene for freezing tolerne growth rte trde-off in the live oks (Querus series Virentes) ross the tropil temperte divide Kri Koehler, lyson Center nd Jennine Cvender-res Deprtment of Eology, Evolution nd ehvior, University of Minnesot, 987 Upper uford Cirle, Sint Pul, MN 558, US uthor for orrespondene: Jennine Cvender-res Tel: Emil: vender@umn.edu Reeived: 2 ugust 2 epted: 26 Otoer 2 doi:./j x Key words: freezing tolerne, growth rte, live oks, Querus series Virentes, trde-off, tropil temperte divide. Summry It hs long een hypothesized tht speies re limited to the north y minimum temperture nd to the south y ompetition, resulting in trde-off etween freezing tolerne nd growth rte. We investigted the extent to whih the limti origins of popultions from four live ok speies (Querus series Virentes) were ssoited with freezing tolerne nd growth rte, nd whether speies fitted model of lolly dpted popultions, eh with nrrow limti tolernes, or of rodly dpted popultions with wide limti tolernes. orns from popultions of four speies ross tropil temperte grdient were grown under ommon tropil nd temperte onditions. Growth rte, seed mss, nd lef nd stem freezing trits were ompred with soure minimum tempertures. Mximum growth rtes under tropil onditions were negtively orrelted with freezing tolerne under temperte onditions. The minimum soure temperture predited the freezing tolerne of popultions under temperte onditions. The tropil speies Q. oleoides ws differentited from the three temperte speies, nd vrition mong speies ws greter thn mong popultions. The trde-off etween freezing tolerne nd growth rte supports the rnge limit hypothesis. Limited vrition within speies indites tht the distriutions of speies my e driven more strongly y rod limti ftors thn y highly lol onditions. Introdution entrl issue in eology is to understnd the mehnisms tht underlie the distriutions of speies. Climte is known to e ritil ftor ontrolling the rod-sle distriution of orgnisms (Huthinson, 98; Mrthur, 972; Gre, 987; Iverson & Prsd, 998; Rehfeldt et l., 999, 26; Cvender-res, 25; Chuine, 2), ut often the physiologil sis for limti nihe onstrints is unknown. Linking the physiologil tolernes of speies to their limti distriutions is importnt in prediting future distriutions of speies under hnging limti onditions (Morin et l., 27). In prtiulr, the freezing tolerne of speies often orresponds to the minimum tempertures in their limte of origin (Ski & Weiser, 973; Woodwrd, 99; izen & Woodok, 996), nd the ility of different speies to void or tolerte freezing stress through vrious mehnisms goes long wy to explin the geogrphi distriutions of speies (Prker, 963; George et l., 974; Lthm & Riklefs, 993). It hs long een hypothesized tht the distriutions of speies re limited y freezing tolerne in the north (in the Northern Hemisphere) nd y ompetition in the south (M- rthur, 972). potentil mehnism underlying this hypothesis is trde-off etween growth rte nd freezing tolerne (Woodwrd, 987; Shenk, 996; Loehle, 998; itken & Hnnerz, 2). In the north, the quisition of trits for old limtion nd freezing tolerne hs een hypothesized to impose ost in terms of resoure llotion tht results in lower growth rtes (Levitt, 98; ek, 988; Körner & Lrher, 988; Woodwrd, 99; Howe et l., 23); lk of freezing tolerne t the southern edge of the speies distriution thus permits higher growth rtes nd inresed ompetitive ility (Woodwrd & Pigott, 975; Woodwrd, 987). More generlly, inresed tolerne to ioti stress is elieved to trde off ginst growth nd ompetitive ilities in plnts (Tilmn, 988) s result of resoure limittions tht drive the evolution of llotion strtegies. In ddition to growth rte, seed mss is onsidered to e ritil life history ttriute ssoited with seson length tht my limit southern distriutions (Morin & Chuine, 26). Seed mss ontriutes diretly to solute growth rtes (Cvender- res et l., 24) nd is linked to inresed survivl nd ompetitive ility (Kitjim & Fenner, 2; Fenner & Thompson, 25; Turnull et l., 28). Towrds the tropis, higher seed mss my e fvored y longer seson length, whih llows longer time for ron umultion, nd my provide

2 2 Reserh New Phytologist ompetitive dvntge in highly diverse tropil ommunities in whih ompetitive intertions my dominte ssemly proesses. y ontrst, seed mss my e onstrined diretly y seson length t northern ltitudes (Moles & Westoy, 23; Chuine, 2), or my e limited y resoure investment in freezing tolerne, nd lrge seeds my e less dvntgeous t northern ltitudes where freezing stress is dominnt filter in ommunity ssemly. From historil iogeogrphi perspetive, if speies evolve in tropil regions with no freezing tolerne nd then expnd into the temperte zone, freezing tolerne my e quired simultneously with the evolution of slower growth during unfvorle periods, s oth re thought to e dvntgeous in sesonlly old limtes (Lrher & uer, 98; Körner & Lrher, 988; Kozlowski & Pllrdy, 997). Therefore, negtive reltionship etween freezing tolerne nd growth rte ould rise s result of differentil llotion of limited resoures or of orrelted evolution during rnge expnsion from the tropis to the temperte zone, or oth. For similr resons, negtive reltionship etween freezing tolerne nd seed size my lso e expeted. Vrition in freezing tolerne, s well s oth growth rtes nd seed size, mong speies ould ontriute to n explntion of rnge limits. Within speies, evidene of deline in growth rte t more northern ltitudes nd older tempertures is onsistent ross studies oth in situ (Roerds et l., 99; Mtys & Yetmn, 992; Rehfeldt et l., 999, 2) nd in ommon grdens (Smitherg & Weiser, 968; Li et l., 998; Oleksyn et l., 998). In ddition, severl studies hve shown similr reltionship ross speies (Rehfeldt, 997; Ymhir & Conover, 22; Green, 27; Svge, 2). ross speies, seed size in forest speies hs een shown to inrese towrds the tropis nd derese t high ltitudes (Moles & Westoy, 23; Morin & Chuine, 26). still deted question is whether popultions within speies show onservtism in their limti tolernes, perspetive used to defend limti nihe modeling pprohes (Wiens & Grhm, 25; Permn et l., 28). For exmple, freezing tolerne my hve evolved onservtively, suh tht ll popultions within speies (or linege) hve the sme resistne to freezing. Under this view, rodly distriuted speies exposed to rnge of tempertures my e dpted to tolerte wide rnge of limti onditions with little lol dpttion (Lrher, 25). Mny tree speies n survive muh older freezing tempertures thn our in their urrent rnge (Fuhigmi et l., 97; Ski & Weiser, 973; itken & dms, 996), suggesting tht freezing tolerne my not e ostly to mintin in speies with rod distriutions. Woody speies re known to hve rod eologil distriutions in omprison with hereous speies, whih hve more speilized nihes (Riklefs & Lthm, 992). If speies hve rod nd onserved limti tolernes, little vrition in limti tolernes would e expeted mong popultions. Within speies rnges, however, there is evidene tht the distriutions of plnt speies onsist of popultions genetilly suited to lol limtes (Morgenstern, 996; itken & Hnnerz, 2; Rehfeldt et l., 2; Lrher, 25; Cvender-res, 27), nd often show linl vrition in the limti tolernes of speies s result of dptive differentition (Endler, 977; Dvis & Shw, 2; Rehfeldt et l., 2; Howe et l., 23). Clinl vrition in freezing tolerne hs een demonstrted in severl tree speies, suggesting high levels of lol dpttion (Rehfeldt et l., 2; Li et l., 22; rnd et l., 25; Morin et l., 27; Friedmn et l., 28). In this study, we exmine growth, old limtion nd freezing tolerne within nd etween four speies in the live ok group (Querus setion Virentes) Q. virginin, Q. oleoides, Q. fusiformis nd Q. gemint in ommon grden experiment. The live oks re smll monophyleti linege ontining speies in the southern US nd Centrl meri. They re useful group in whih to exmine the mehnisms underlying geogrphi distriutions, euse they spn the tropil temperte divide, with severl speies overing lrge ltitudinl grdients. Previous studies hve estlished geneti nd morphologil differentition etween Q. gemint nd Q. virginin (Cvender-res & Phlih, 29) nd Q. virginin nd Q. oleoides (Cvender-res, 27; Cvender-res et l., 2), nd there is evidene tht the group originted in the tropis of Centrl meri nd susequently expnded into the temperte zone (Cvender-res et l., 2). Our gols were to estlish the extent to whih the distriutions of live ok speies rnges were ssoited with old limtion, freezing tolerne nd growth, onsistent with the hypothesis tht they re limited t the northern rnge y minimum temperture nd t the southern rnge y ompetitive ility (growth rte), nd whether live ok popultions fit model of lol dpttion with nrrow limti tolernes, or of rod limti tolernes with little vrition mong popultions. We speifilly tested, first, whether there ws popultion- nd or speies-level vrition in the ility to old limte. If more northern popultions nd or speies inresed their freezing tolerne signifintly under temperte onditions, ut more southern popultions did not, this provides evidene for the evolution of old hrdening in response to old temperture ues. Seond, we tested whether there ws trde-off etween freezing tolerne nd growth rte (oth solute nd reltive growth rtes). negtive reltionship, suh tht mternl lines with slower growth rtes exhiit greter freezing tolerne, would provide evidene for this trde-off. We lso exmined the reltionship etween freezing tolerne nd seed mss, euse seed mss n influene ompetitive ility nd hs een predited to vry with limti distriution (Morin & Chuine, 26). We note tht shde tolerne n drive ompetitive outomes in lte suessionl forests (zzz, 979; Grime, 979), ut we did not exmine it here, euse ll of the live oks n e hrterized s midsuessionl svnnh speies tht regenerte under similr (modertely high) light regimes (Kurz & Godfrey, 962; Spetor & Putz, 26; Klemens et l., 2). Finlly, we tested the extent to whih minimum tempertures t the popultion soure predited freezing tolerne nd growth rte. Clinl vrition in old limtion, freezing tolerne nd growth rtes mong popultions within speies would provide evidene for lol dpttion. lterntively, lrge differenes in freezing tolerne, growth rtes nd or limtion potentil etween speies, ut limited

3 New Phytologist Reserh 3 vrition mong popultions within rodly distriuted speies, would indite tht speies hve onserved limti nihes nd rod limti tolernes. Mterils nd Methods Study speies nd experimentl design The live oks (Querus series Virentes Nixon) onsist of seven speies of interfertile ostl oks tht spn the tropil temperte divide through the southern US, Mexio nd Centrl meri (Muller, 96; Nixon, 985; Nixon & Muller, 997). Live oks re evergreen to revi-deiduous (mintin leves in mild tempertures, ut my drop leves in response to old stress) trees hrterized y rhizomtous lonl growth, nd often our in shru form in the juvenile stge in response to low-nutrient soil onditions nd sesonl drought. We exmined four live ok speies (Fig. ): Querus virginin Miller (southern live ok), evergreen to revi-deiduous, ours in xeri snds to mesi sites from ostl est Texs to Virgini; Q. gemint Smll, evergreen to revi-deiduous (snd live ok), ours in xeri snds to mesi sites from Louisin to North Crolin; Q. fusiformis Smll (Texs live ok), evergreen to revi-deiduous, ours in xeri sites nd open woodlnds from Texs to Oklhom (Nixon & Muller, 997); nd Q. oleoides Shltdl. & Chm., tropil evergreen shru, ours in tropil dry forest from the north Pifi ost of Cost Ri to northern Mexio (ouher, 983; Nixon, 985). orns were olleted from one to five popultions within eh of four live ok speies: Q. virginin (North Crolin, northern Florid, southern Florid, Louisin nd Texs); Q. gemint (northern Florid nd North Crolin); Q. fusiformis (Texs); nd Q. oleoides (Mexio, elize nd Cost Ri) (Fig., Supporting Informtion Tle S). Coordintes for eh tree were reorded (Tle S) nd olletion permits, export import permits nd phytosnitry ertifites were otined (ville on request). Eh geogrphilly determined popultion inluded five to nine mternl fmilies nd. 5 individuls in eh fmily. Seeds were olleted from rndom trees within eh popultion; however, the numer of mternl fmilies per popultion ws reltively low nd these fmilies my not dequtely represent the entire popultion. Moreover, germintion mong fmilies ws unequl, nd some fmilies hd low numers. The length nd width of eh orn were mesured nd the orns were stored t 4 C until synhronous plnting in glsshouse filities t the University of Minnesot in Novemer 25. fter yr of growth in onstnt temperture nd wtering regime (tropil onditions), two replited limte tretments were implemented during the winter months of 26 (mid- Novemer to Mrh): tropil tretment, in whih dytime temperture ws mintined etween 3 nd 35 C, nd nighttime tempertures were etween 22 nd 26 C; nd temperte tretment, in whih winter growth tempertures rehed minimum night-time temperture of 4 C with dytime temperture of 5 C, simulting the monthly verge tempertures in Lieri, Cost Ri (southern rnge limit) nd Wilmington, North Crolin (northern rnge limit). Eh limte regime ws replited in two independently ontrolled glsshouse rooms. The photoperiod ws extended to 2 h during the winter, similr to Cost Ri (southern rnge limit). Summer photoperiods were left t nturl levels with mximum of 5.5 h, whih ws up to h longer thn in North Crolin (northern rnge limit) nd 3 h longer thn in Cost Ri. The photoperiod ws not limiting ftor in this experiment; however, the derese from 5.5 to 2 h my hve provided some ues for dormny. These limte tretments were repeted every yer for three susequent yers. Growth rte nd seed mss We ompred oth the solute growth rte (GR) nd reltive growth rte (RGR) in the growth rte freezing tolerne trdeoff. GR is the mount of iomss tht umultes in yer nd RGR is the mximum intrinsi growth rte. Plnts t () () Querus virginin Querus gemint Querus fusiformis Querus oleoides Fig. () Rnge mps for the four live ok speies: Querus virginin, Q. gemint, Q. fusiformis nd Q. oleoides, showing herrium reords nd olletion sites from Cvender-res et l. (2). () Lotion of seed soures (lrge shpes) for eh popultion, using the sme symols s in ().

4 4 Reserh New Phytologist northern ltitudes my grow more rpidly in erly spring, nd thus hve higher RGR, ut, y the end of the yer, my hve umulted less totl iomss (GR) euse of shorter growing seson. Therefore, in studies with sesonl vrition in growth, the GR of speies under ommon onditions is the ritil ftor to ompre mong popultions. eginning in erly Mrh 27, 3 months fter the strt of the winter limte tretment, ll individuls were monitored for mximum height (root ollr to pex of tllest stem), numer of leves (totl leves on ll stems) nd stem dimeter (mesured t the root ollr). llometri equtions used to estimte the iomss for eh speies were developed from dt in previous experiments (Cvender-res et l., 24). ove-ground iomss ws estimted using the mximum height, totl numer of leves nd stem dimeter. The sme eqution ws used for Q. virginin nd Q. fusiformis, euse of lk of iomss dt for Q. fusiformis. orn mss ws estimted using the orn volume. GR (g yr ) ) ws lulted s GR = (M finl ) M initil ) (T finl ) T initil ), where M finl is the iomss estimte from growth mesurements mde in Mrh 27, M initil is the estimted orn mss, T finl is the pproximte dte on whih plnts were mesured in Mrh 27 nd T initil is the dte of seedling emergene. RGR (g g ) yr ) ) ws lulted s RGR = log e (M finl ) ) log e (M initil ) (T finl ) T initil ). Seed mss ws mesured s the seed volume (V) t the time of plnting sed on the height (h) nd dimeter (d) of eh orn, ssuming n ellipsoid: V =4 3 (d 2) 2 (h 2). Fresh seed mss ws lulted on the sis of the empiril reltionship etween volume nd fresh mss with the seed ot removed sed on seed vrition for 48 orns for 6 speies of ok: M = 363V ).23 (R 2 =.97; Cvender-res et l., 24). Lef freezing tolerne In Ferury 29, freezing mnipultions were onduted to determine differenes in lef freezing sensitivity within nd etween the four speies grown in oth temperture tretments. Drk-limted hlorophyll fluoresene (F v F m ) ws mesured in situ to determine the mximum photosyntheti quntum yield for one lef. rnhlets with t lest five leves, inluding the mesured lef, were susequently ut under wter, pled in wter-filled rose tues in the drk nd frozen in tempertureontrolled freezer ox overnight t minimum temperture of ) C. Overnight freezing events were simulted using ustom-designed freezer ox (Perivl LT-5HID; Perivl Sientifi, In., Perry, Iow, US) following previously desried methods (Cvender-res & Holrook, 2; Cvender-res et l., 25; Cvender-res, 27) (Methods S). To llow reovery, frozen smples were pled in drk hmer t room temperture (25 C) efore the re-mesurement of drk-dpted F v F m following oorse et l. (998). Smples were mesured.5, 6, 2, 24 nd 48 h fter the freezing yle hd ended. pproximtely nine individuls were mesured in eh popultion nd limte tretment. The rnk order of vlues for speies remined onstnt ross these time points (Fig. S2); for revity, only vlues 6 h fter freezing re reported further. The deline in F v F m ws lulted s F v F m efore freezing minus F v F m fter freezing. Lef freezing tolerne ws lulted s one minus the deline in F v F m. Lef old limtion ility ws lulted s the differene etween the tropil nd temperte tretment divided y the tropil tretment for deline in F v F m fter freezing t ) C. Lef loss Lef loss or the development of winter deiduous strtegy is one dpttion to old tempertures y whih some speies void freezing dmge. lthough live oks often mintin their leves during the winter months, oth field nd experimentl dt indite tht senesene is indued y hilling nd vries mong popultions (Cvender-res & Holrook, 2; Cvender- res, 27). In Mrh 29, 4 months fter the strt of the winter limte tretment, lef loss ws quntified. The perentge of lef loss for eh plnt ws estimted on the sis of fllen leves in the pot nd lef srs, nd ws otined t the end of the tretment yle to pture ll sesonl loss. Stem freezing tolerne In Ferury 2, eletrolyte lekge ws mesured to determine stem freezing sensitivity. The eletrolyte lekge method uses hnges in eletril ondutivity to predit ell lysis in response to freezing (Flint et l., 967; Friedmn et l., 28). Stem segments (. 2.2 mm in dimeter) were exised from eh seedling, the leves were removed, stems were ut into five -m piees nd eh piee ws pled in seprte test-tue with ml of deionized wter. One tue ws stored t 4 C s nonfrozen ontrol nd the other tues were susequently frozen t four freezing tempertures () 5, ), ) 5 nd ) 2 C) in progrmmle freezing hmer (Cole-Prmer Instrument Co., Vernon Hills, IL, US) following the methods of Friedmn et l. (28) (Methods S). n verge of 2 individuls per popultion in eh limte tretment ws mesured. The index of injury t eh temperture (I t ) ws lulted s the perentge of ell lysis t eh freezing temperture (Flint et l., 967). The index of injury dt were rsin trnsformed for sttistil nlyses. Stem old limtion ility ws lulted s the differene etween the tropil nd temperte tretments divided y the tropil tretment for index of injury fter freezing t ) 5 C. Stem freezing tolerne ws lulted s minus the index of injury t eh freezing temperture. lthough the rnk order of vlues for stem freezing injury remined reltively onstnt t the speies level t ), ) 5 nd ) 2 C, vlues t ) 5 C showed slightly higher differentition mong speies (Fig. S2); for revity, only this mesurement is reported further. Dt nlysis Climte dt were ompiled from WorldClim (Hijmns et l., 25), using herrium speimen ourrene lolities (GIF Dt Portl, to determine limte rnges for ll four speies. The 9 ioclim limti prmeters nd ourrene lolities were used in the MXENT modeling

5 New Phytologist Reserh 5 progrm to predit speies rnges nd to determine whih limte prmeters hd the gretest preditive vlue. The Mxent limte model predited speies distriutions very lose to tul distriutions (Fig. S); of the 9 ioclim vriles, the minimum temperture of the oldest month ontriuted the most to rnge preditions for ll four speies. Therefore, the minimum temperture of the oldest month is used s the limti vrile in ll susequent nlyses. Physiologil nd growth dt for individuls were verged ross mternl fmilies, nd mternl fmilies were grouped into popultions on the sis of lotion nd speies. NOVs for ll physiologil, growth rte nd minimum temperture dt were onduted with popultion nested within speies to determine speies- nd popultion-level differentition nd intertions with limte tretment. Student s t-test differentition ws used to determine speies nd popultion differenes within eh tretment. Liner regressions were used to test trde-offs etween growth rte, freezing tolerne, orn mss, old limtion nd minimum temperture of the oldest month ross mternl fmilies. We lso used NCOV to test whether growth rte nd minimum temperture, treted s ovrites, predited stem nd lef freezing tolerne when speies, popultion nd limte tretment were inluded in the model s fixed ftors. We otined restrited mximum likelihood (REML) vrine omponent estimtes to determine the perentge of totl vrition tht ould e ttriuted to speies nd to popultions. ll nlyses were onduted in JMP 7. (SS, Cry, NC, US). Results Climti distriutions The rnge of minimum tempertures for the three temperte speies (Q. virginin, Q. gemint nd Q. fusiformis) overlpped, ut ws distint for Q. oleoides (Fig. 2). The minimum tempertures of the oldest month t the highest proility of presene were s follows: Q. virginin (5 C), Q. gemint (8 C), Q. fusiformis (7 C) nd Q. oleoides (6 C). oth Q. virginin nd Q. fusiformis were distriuted ross rod rnge of minimum tempertures, wheres Q. gemint hd nrrower limti rnge (Fig. 2). hierrhil NOV, with popultion nested within speies, showed signifint vrition in the minimum temperture of the oldest month (P <.;Tle)etweenpopultionlotions. The northern popultions of North Crolin (Q. virginin) nd Texs (Q. fusiformis) experiened lower minimum tempertures (Fig. 2). However, Louisin, Texs nd northern Florid popultions were not signifintly different with regrd to the minimum temperture of the oldest month (Fig. 2). In North Crolin nd northern Florid, Q. gemint nd Q. virginin o-ourred nd were exposed to similr minimum tempertures. y ontrst, Q. virginin nd Q. fusiformis in Texs experiened signifintly different minimum tempertures (Fig. 2). Querus oleoides popultions ourred in lotions with higher minimum tempertures thn ll popultions of Q. virginin, Q. fusiformis nd Q. gemint (Fig. 2). () () Lef loss Cost Ri elize Mexio S Florid N Florid Louisin Texs N Crolin (Q. gemint) Texs (Q. fusiformis) Fig. 2 () Climti distriutions for four live ok speies sed on the perentges of herrium reord ourrenes for the minimum temperture in the oldest month ( C). The rnge of minimum tempertures for the three temperte speies (Querus virginin (VI); Q. gemint (GE); Q. fusiformis (FUS)) is overlpping, ut is distint for the tropil speies Q. oleoides (OL). () Minimum monthly tempertures for popultions within speies verged ross mternl fmily soure lotions (dt from WorldClim; Hijmns et l., 25): Q. virginin, squres; Q. gemint, rosses; Q. fusiformis, irles; Q. oleoides, tringles. For the North Crolin nd northern Florid popultions of Q. virginin nd Q. geminte, the lines re nerly identil nd only one is shown. Popultions nested within speies re signifintly differentited (). There ws lmost no lef loss under tropil onditions for popultions or speies (Fig. 3). However, Q. virginin nd Q. fusiformis exhiited signifint lef loss under temperte onditions (P <.; Tle ; Fig. 3). Within Q. virginin, Louisin nd Texs popultions exhiited greter lef loss thn southern Florid popultions (Fig. 3). Interestingly, Q. gemint ourred in the sme region s Q. virginin in North Crolin nd northern Florid, ut did not drop its leves in response to old tempertures (Fig. 3). There ws lrge mount of vrition within Q. fusiformis, used y individuls tht either lost very few or lmost ll of their leves. Under temperte onditions, 55% of vrition ws ttriuted to speies-level differenes nd 2% to popultion-level differenes (Tle S2). Cold limtion hierrhil NOV showed signifint vrition mong speies for oth lef nd stem old limtion ility (P =.2;

6 6 Reserh New Phytologist Tle NOV for lef nd stem freezing tolerne, perent lef loss, solute growth rte (GR), reltive growth rte (RGR), minimum temperture of the oldest month from popultion soures, lef nd stem freezing limtion Effet DF SS F rtio P vlue Lef freezing tolerne Speies <. Popultion (Speies) Growth temperture <. tretment Speies tretment <. Popultion (Speies) tretment Stem freezing tolerne Speies <. Popultion (Speies) Growth temperture <. tretment Speies tretment <. Popultion (Speies) tretment Lef loss Speies <. Popultion (Speies) Growth temperture <. tretment Speies tretment <. Popultion (Speies) tretment GR (g yr ) ) Speies <. Popultion (Speies) <. Growth temperture <. tretment Speies tretment Popultion (Speies) tretment RGR (g g ) yr ) ) Speies <. Popultion (Speies) <. Growth temperture tretment Speies tretment Popultion (Speies) tretment Minimum temperture C Speies <. Popultion (Speies) <. Lef freezing limtion Speies Popultion (Speies) Stem freezing limtion Speies Popultion (Speies) Signifint vlues (P <.5) re shown in old nd mrginlly signifint vlues (P <.) re shown in itlis. SS, sum of squres. P =.75), ut popultions nested within speies were not differentited signifintly (Tle ). For lef old limtion, 35% of the vrition ws found t the speies level nd % t the popultion level. For stem old limtion, 5% of vrition ws ttriuted to speies-level differenes nd 3% to popultion-level differenes (Tle S2). Lef freezing tolerne hierrhil NOV showed signifint intertion with limte tretment for oth speies (P <.) nd popultion nested within speies (P =.493; Tle ). Plnts grown under tropil onditions ll showed less lef freezing tolerne thn plnts limted to old tempertures, nd showed no signifint differentition in response to freezing t either the popultion or speies level (Fig. 3,d). Cold-limted plnts showed differentition in lef-level freezing tolerne t the speies level: the temperte speies Q. gemint, Q. virginn nd Q. fusiformis ll showed greter freezing tolerne thn the tropil speies Q. oleoides (Fig. 3). Under temperte onditions, within Q. virginin, the North Crolin popultion showed greter freezing tolerne thn the northern nd southern Florid popultions, exhiiting some popultion-level vrition (Fig. 3d). However, there were no differenes etween the northern Florid nd North Crolin popultions of Q. gemint with regrd to lef freezing tolerne. Querus oleoides showed the lowest stem freezing tolerne. Under temperte onditions, 69% of the vrition ws ttriuted to speies-level differenes nd 5% to popultion-level differenes (Tle S2). Stem freezing tolerne hierrhil NOV showed signifint intertion with limte tretment for speies (P <.), nd popultion nested within speies ws mrginlly signifint (P =.594, Tle ). Cold-limted plnts showed speies-level vrition fter freezing t ) 5 C (Fig. 3e). Querus oleoides showed the lowest freezing tolerne ross oth limte tretments (Fig. 3e). In the temperte tretment, Q. gemint showed less freezing tolerne thn Q. virginin or Q. fusiformis. Within Q. oleoides, there ws limited popultion-level differenes. However, the Mexin popultion exhiited greter stem freezing tolerne thn the Cost Rin or elizen popultions (Fig. 3f), orresponding to lower minimum temperture in Mexio (Fig. 2); the sme pttern ws not seen in lef freezing tolerne, however (Fig. 3d). Under temperte onditions, within Q. virginin, the North Crolin popultion showed less stem freezing dmge thn the northern nd southern Florid popultions, exhiiting some popultion-level vrition orresponding to ltitude (Fig. 3f). However, there were no differenes etween the northern Florid nd North Crolin popultions of Q. gemint. Under temperte onditions, 82% of the vrition in stem freezing tolerne ws ttriuted to speies nd 5% to popultion differenes(tle S2). Growth rte hierrhil NOV showed signifint vrition etween speies (P <.) nd popultion nested within speies (P <.; Tle ). However, intertions with limte tretment were not signifintly different. In generl, GR nd RGR showed similr ptterns in speies-level response (Fig. 3g,i). Growth rtes were redued in response to the temperte tretment

7 New Phytologist Reserh 7 () () de e de de d () (d) d d d d d d C C C C C C C C C Fig. 3 Speies (left olumn) nd popultion (right olumn) mens (± SE) under ontrolled tropil (gry) nd temperte (lk) limti onditions for lef loss (,), lef ( ) deline in F v F m fter freezing t ) C) (,d) nd stem ( ) index of injury fter freezing t ) 5 C) (e,f) freezing tolerne nd solute (GR) (g,h) nd reltive (RGR) (i,j) growth rtes. Speies: Querus virginin, VI, squres; Q. gemint, GE, rosses; Q. fusiformis, FUS, irles; Q. oleoides, OL, tringles. Popultions: Querus oleoides, CR_OL, Cost Ri; Z_OL, elize; MX_OL, Mexio; Q. virginn, FLS_VI, southern Florid; FLN_VI, northern Florid; L_VI, Louisin; TX_VI, Texs; NC_VI, North Crolin; Q. gemint, FLN_GE, northern Florid; NC_GE, North Crolin; Q. fusiformis, TX_FUS, Texs. Different letters indite signifint Student s t-test speies- nd popultion-level differentition (P <.5) within the tropil nd temperte tretments. (e) (g) (i) C C d C C (f) de e de d e d C E E E DE E CDE DE CD (h) C C CD CD DE E E E d de de de e de e (j) C C C CD CD DE F F d d EF de def ef f ef reltive to the tropil tretment for ll speies (Fig. 3g,i). Cold-limted plnts showed speies-level vrition (Fig. 3g,i). Querus oleoides showed redued GR in the temperte tretment, ut mintined higher growth rte thn ny of the temperte speies (Fig. 3d). In ddition, Q. fusiformis nd Q. gemint hd lower growth rtes thn Q. virginin. Within Q. virginin, old-limted plnts in the Louisin popultion hd higher growth rte (GR nd RGR) thn other Q. virginin popultions, similr to some popultions of Q. oleoides (Fig. 3h,i). For GR, 7% of the vrition ws ttriuted to speies-level differenes nd 3% to popultion-level differenes. For RGR, 54% of the vrition ws ttriuted to speies-level differenes nd 7% to popultion-level differenes (Tle S2). Seed mss differed signifintly mong speies, ut not mong popultions within speies (Fig. S2). Seed mss ws wekly orrelted with GR (R 2 =.92, P =.9, Fig. 5f), reltionship driven lrgely y speies; reltively little of the vrition in GR mong fmilies ws explined y seed mss. Seed mss ws not orrelted with RGR (Fig. S4). Trde-offs etween freezing tolerne, growth nd seed mss ross the tropil temperte grdient We found evidene for trde-off etween growth nd freezing tolerne ross four live ok speies (Fig. 4 ). The most pproprite test for trde-off etween growth nd freezing tolerne is etween growth rtes under nonstressed (tropil) onditions nd freezing tolerne under old-limted (temperte) onditions. This omprison ws possile, given tht seeds from the sme mother tree were plnted in oth tretments nd fmily men vlues for nonstressed growth nd old-limted freezing ould e ompred diretly. Fmilies with higher GRs hd lower freezing tolerne in oth stems nd leves (Fig. 4,). The sme ws true for RGR nd stem freezing tolerne, ut there ws no reltionship etween RGR nd lef freezing tolerne. oth lef nd stem freezing tolerne were negtively orrelted with seed mss (Fig. 4e,f), lthough the reltionship with stem freezing tolerne ws stronger. Cold limtion ility in oth leves (Fig. 4g) nd stems (Fig. 4h) ws negtively

8 8 Reserh New Phytologist () Stem freezing tolerne (Temperte) () Lef freezing tolerne (Temperte) (e) Lef freezing tolerne (Temperte) (g) Lef old limtion (i) Lef old limtion R 2 = GR (g yr ) (Tropil) R 2 =.95 P = GR (g yr ) (Tropil) R 2 =.23 P = orn mss (g) R 2 =.62 P = GR (g yr ) (Tropil) R 2 =.9 P = RGR (g g yr ) (Tropil) () Stem freezing tolerne (Temperte) (d) Lef freezing tolerne (Temperte) (f) Stem freezing tolerne (Temperte) (h) Stem old limtion (j) Stem old limtion R 2 =.96 P = RGR (g g yr ) (Tropil) R 2 =.6 P = RGR (g g yr ) (Tropil) R 2 = orn mss (g) R 2 = GR (g yr ) (Tropil) R 2 = RGR (g g yr ) (Tropil) Fig. 4 Trde-offs etween growth rte in nonstressed tropil onditions nd freezing tolerne fter old limtion in temperte onditions ross mternl fmilies from four live ok speies: Querus virginin (squres), Q. gemint (rosses), Q. fusiformis (irles) nd Q. oleoides (tringles). Points represent fmily mens. Reltionships re shown for: temperte stem freezing tolerne ( ) index of injury fter freezing t ) 5 C) nd tropil solute growth rte (GR) (); temperte stem freezing tolerne nd tropil reltive growth rte (RGR) (); temperte lef freezing tolerne ( ) deline in F v F m fter freezing t ) C) nd tropil GR (); temperte lef freezing tolerne nd tropil RGR (d); temperte lef freezing tolerne nd orn mss (e); temperte stem freezing tolerne nd orn mss (f); lef old limtion ility ((tropil ) temperte) tropil for deline in F v F m fter freezing t ) C) nd GR under tropil onditions (g); stem old limtion ility ((tropil ) temperte) tropil for index of injury fter freezing t ) 5 C) nd GR under tropil onditions (h); lef old limtion ility nd RGR under tropil onditions (i); nd stem old limtion ility nd RGR under tropil onditions (j). Lest squres fitted lines re shown for signifint reltionships (P <.5); the dshed line (g) indites mrginl signifine. Corretions re not mde for multiple tests. orrelted with GR. Cold limtion ility of stems (Fig. 4j), ut not leves (Fig. 4i), ws negtively orrelted with RGR. The minimum temperture of the oldest month of the soure popultions predited freezing tolerne, growth nd old limtion (Fig. 5 h). In NCOV, GR signifintly predited stem freezing tolerne (P =.2,Tle2)whentkingintoount popultion- nd speies-level vritions, nd minimum temperture signifintly predited lef freezing tolerne when tking into ount speies- nd popultion-level vritions (P =.36, Tle 2). Minimum tempertures in the oldest month lso predited seed mss (Fig. 5e), reltionship driven lrgely y the ft tht the tropil speies, Q. oleoides, hd lrger seeds thn the speies tht ourred in temperte regions. Given tht seeds were olleted in the field, we nnot eliminte n environmentl influene on seed mss. However, vrition in seed mss ws greter etween thn within speies, despite steep environmentl grdients within speies rnges, suggesting tht seed mss my e genetilly onstrined t the speies level, s onluded in erlier studies (skin et l., 998; Morin & Chuine, 26). Disussion We provide evidene for trde-off etween growth rte nd freezing tolerne ross mternl fmilies from four speies of live ok (Querus series Virentes) tht spn the tropil temperte divide ross North nd Centrl meri. Mternl fmilies with

9 New Phytologist Reserh 9 Fig. 5 Minimum temperture of the oldest month in the limte of origin predits lef () nd stem () freezing tolerne nd reltive growth rte (RGR) () nd solute growth rte (d) under oth tropil (gry) nd temperte (lk) growth onditions in mternl fmilies from four live ok speies. Minimum temperture of the oldest month lso predits orn mss (e), nd orn mss is orrelted with GR under tropil (nonstressed) onditions (f). Minimum temperture of the oldest month further predits lef old limtion ility ((tropil ) temperte) tropil for deline in F v F m fter freezing t ) C) (g) nd stem old limtion ility ((tropil ) temperte) tropil for index of injury fter freezing t ) 5 C) (h). Points represent fmily mens. Querus virginin, squres; Q. gemint, rosses; Q. fusiformis, irles; Q. oleoides, tringles. Lest squres fitted lines re shown for tropil (lk) nd temperte (gry) tretments. The dshed gry line () indites mrginl signifine. Corretions re not mde for multiple tests. () Lef freezing tolerne () 6 RGR (g g yr ) (e) orn mss (g) (g).2 Lef old limtion Minimum temperture of oldest month ( C) Minimum temperture of oldest month ( C) Minimum temperture of oldest month ( C) R 2 =.37 R 2 =.568 R 2 =.36 R 2 =.26 R 2 =.6 P =.64 R 2 = Minimum temperture of oldest month ( C) () (d) (f) (h) Stem freezingtolerne GR (g yr ) GR (g yr ) (Tropil) Stem old limtion Minimum temperture of oldest month ( C) R 2 =.58 R 2 =.54 R 2 = 7 R 2 = Minimum temperture of oldest month ( C) R 2 =.92 P = orn mss (g) R 2 = Minimum temperture of oldest month ( C) higher freezing tolerne under temperte (old-limting) onditions hd slower growth rtes under tropil (nonstressed) onditions. These reltionships were strongest etween stem freezing tolerne () 5 C) nd oth GR nd RGR, ut were lso supported for lef freezing tolerne () C) nd GR (Fig. 4 d). Unlike mternl fmilies from Q. oleoides, fmilies from temperte ltitudes (from Q. virginin, Q. gemint nd Q. fusiformis) demonstrted the ility to inrese freezing tolerne in response to hilling growth tempertures. The ility to old limte nd express higher freezing tolerne under temperte onditions thn under tropil onditions ws ssoited with less ompetitive growth rtes under tropil (nonstressed) growth onditions (Figs 4g j, S3). Lower GRs in live oks from more northern ltitudes were driven y oth lower RGR (Fig. S4) nd redued seed mss (Fig. 5f). Seed mss delined with lower minimum tempertures (Fig. 5e) nd my e limited y the length of the growing seson euse of energy onstrints (Morin et l., 27; Chuine, 2). Our results indite tht, t more northern ltitudes, live oks hve een seleted to invest in freezing tolerne nd old limtion ility, rther thn higher growth rtes nd lrger seed sizes, whih my enfore speies oundries ross the tropil temperte divide. This trde-off supports the lssi hypothesis tht the distriutions of speies re limited y freezing tolerne in the north nd y ompetition in the south (Mrthur, 972; Woodwrd, 987; Shenk, 996; Gross & Prie, 2). Climte of origin predits growth rtes, seed mss, freezing tolerne nd old limtion ility Live ok speies showed signifint differentition in their sensitivity to freezing, s expeted from their limti distriutions (Fig. 2,). Under oth tropil nd temperte growth onditions, minimum tempertures in the limte of origin strongly predited freezing tolerne, growth rtes, seed mss nd old limtion ility of mternl fmilies (Fig. 5). Mternl fmilies from limtes with older winters hd slower growth rtes nd greter freezing tolerne thn those from milder limtes. Minimum temperture ws signifint ovrite prediting lef freezing tolerne when speies, popultion nd tretment were

10 Reserh New Phytologist Tle 2 NCOV inditing tht the solute growth rte (GR), reltive growth rte (RGR) nd minimum temperture re importnt ftors prediting lef nd stem freezing tolerne within nd mong four live ok (Querus series Virentes) speies Lef freezing tolerne Stem freezing tolerne Soure df SS F rtio P vlue df SS F rtio P vlue Speies < <. Popultion (speies) Growth temperture tretment < <. Speies tretment < Popultion (speies) tretment GR (g yr ) ) Speies < <. Popultion (speies) Growth temperture tretment < <. Speies tretment < <. Popultion (speies) tretment RGR (g g ) yr ) ) Speies <. Popultion (speies) Growth temperture tretment < <. Speies tretment < <. Popultion (speies) tretment Minimum temperture Signifint vlues (P <.5) re shown in old nd mrginlly signifint vlues (P <.) re shown in itli. SS, sum of squres. inluded in the model (Tle 2). Within Q. virginin, the speies with the gretest minimum temperture rnge, signifint vrition mong popultions ws deteted in stem nd lef freezing tolerne, s well s in GR nd RGR (Fig. 3 j), suggesting the lol dpttion of popultions to ltitudinl vrition in limte. Within Q. oleoides, the Mexin popultion lso showed greter freezing tolerne nd ility to old limte thn popultions from elize or Cost Ri (Fig. 3f). The Mexin soure popultions enounter mild freezing tempertures in the winter months, wheres the rest of the rnge of Q. oleoides does not. Fewer olletion sites for Q. gemint nd Q. fusiformis limited our ility to detet popultion-level vrition in these speies. The minimum temperture of the soure popultion lso strongly predited old limtion ility ross mternl fmilies in linl pttern (Fig. 5e,f). Under tropil growth onditions with no old limtion, there ws lower tolerne of stem nd lef freezing ross ll speies nd popultions, lthough it ws lowest in the tropil speies Q. oleoides (Fig. 3 f). The most northern fmilies (from North Crolin) showed the highest old tolerne nd old limtion ility. n inrese in old limtion ility t more northern ltitudes (Fig. 5e,f) provides evidene for dptive plstiity in response to the onset of winter tempertures. However, the vrition in freezing tolerne nd old limtion within speies ws low reltive to the vrition mong speies, suggesting tht the distriutions of speies my e more strongly driven y rod limti tolernes thn y lol dpttion. Seed mss lso inresed with minimum temperture of the oldest month (Fig. 5e). Minimum temperture is strongly ssoited with seson length nd the totl energy ville for photosynthesis during the growing seson. oth reprodutive output nd seed mss hve een predited to inrese with seson length (Chuine, 2), nd empiril evidene in forest trees indites tht seed mss dereses with ltitude (Morin et l., 27). Seed mss ws positively ssoited with GRs (Fig. 5f) nd proly ontriutes to ompetitive ility. Previous studies hve shown similr pttern of old nd freezing tolerne vrying with ltitude. Liner regressions for freezing nd minimum temperture for popultions of three ok speies, Q. ilex, Q. rour nd Q. puesens, were signifint t oth the inter- nd intrspeifi levels (Morin et l., 27). In etul pendul, the northern-most eotype ws more responsive thn the southern eotype to old limtion nd freezing tolerne (Li et l., 22). In Cornus stolonifer, more northern popultions showed greter limtion ility nd old resistne (Smitherg & Weiser, 968). Tmrix nd Populus popultions showed ltitudinl vrition for old hrdiness nd survivl (Friedmn et l., 28). Hereous speies, suh s ridopsis, lso exhiit linl vrition in freezing tolerne (Zhen & Ungerer, 28). Previous studies hve lso shown tht minimum temperture predits growth rte (Li et l., 998, 22; Rehfeldt et l., 2; Green, 27; Gimeno et l., 29; Svge, 2). In Mediterrnen evergreen ok speies, Q. ilex, grown under ommon onditions, individuls from more northern ltitudes hd lower growth rtes, nd linl vrition ourred etween popultions (Gimeno et l., 29). Contrsting freezing tolerne strtegies We sw severl different freezing tolerne strtegies in the temperte speies, whih hve overlpping limte distriutions (Fig. 2). In rod-lef evergreen trees tht reple leves on n nnul sis (lef exhngers, sensu Givnish, 22), erly

11 New Phytologist Reserh senesene nd lef sission in response to hilling represent strtegy to void freezing dmge. lterntively, leves n e mintined for longer, ut hve higher freezing tolerne. We found evidene of evolution towrds erly lef sission in oth Q. virginn nd Q. fusiformis, with elerted lef loss fter old exposure in temperte onditions reltive to lef loss in tropil onditions. y ontrst, Q. gemint mintined its leves throughout the durtion of the winter period under temperte onditions (Fig. 3), ut hd higher lef freezing tolerne (Fig. 3). Querus gemint nd Q. virginin o-our from North Crolin to entrl Florid, where they experiene similr winter tempertures in their lol environments. Querus virginin pprently shows greter investment thn Q. gemint in proteting its stem tissue from freezing dmge, wheres the ltter mintins its leves under old onditions nd shows greter investment in proteting them from freezing dmge. The vrition in response to freezing my e explined y the eologil nihe differentition oserved in Q. virginin nd Q. gemint (Nixon, 985; Cvender-res & Phlih, 29). These symptri speies show nihe differentition ross soil types, with Q. virginn found in moister, nutrient-rih soils nd Q. gemint found in drier, nutrient-poor sites (Cvender-res et l., 24). Morphologil dt support the differentition etween the speies, s Q. virginin llotes greter proportion of its resoures to shoots nd hs lrger nd thinner leves, wheres Q. gemint invests less in shoots nd hs smller nd denser leves (Cvender-res & Phlih, 29). lthough denser leves my hve dpted in response to dry hitt onditions, dense leves re lso n importnt ttriute in old-tolernt plnts (Loehle, 998). Explining trde-offs etween growth nd freezing tolerne In order for trde-off to e iologilly importnt, fitness dvntge in one environment would result in lower fitness in ontrsting environment, nd vie vers. Greter stem nd lef freezing tolerne fter old limtion presumly provides fitness dvntge in sesonl limtes tht inur winter freezing. Greter umulted iomss under yer-round wrm onditions presumly provides fitness dvntge in the tropis. There is no seletive dvntge to investing in high freezing tolerne in the sene of freezing stress, nd tively growing tissues re inherently vulnerle to freezing (Howe et l., 23; Li et l., 23). s freezing tempertures eome more severe nd the durtion of winter inreses t higher ltitudes, nturl seletion would e expeted to use n inrese in freezing tolerne in plnts nd the ility to old limte. Explining the redued growth in older limtes is somewht more omplited, nd there re likely to e multiple ontriuting ftors. In prtiulr, two explntions re supported y the urrent study. The first is tht resoure llotion to freezing tolerne limits llotion to growth. numer of iohemil hnges our during old limtion tht onfer freezing tolerne, inluding n inrese in sturted lipids, the umultion of wter-solule solutes nd onformtionl hnges in ell memrnes (Levitt, 98; ek, 988). In ddition, struturl investments, suh s the development of thiker leves, re importnt for old limtion (Chot & Hiks, 982; Körner & Lrher, 988). Resoure investment in physiologil nd struturl trits for old nd freezing tolerne is thus hypothesized to use more onservtive growth. The lower growth rtes (RGR nd GR) in soure lotions with older winters, even under nonstressed, tropil onditions (Fig. 5,d), nd in mternl fmilies with higher freezing tolerne nd old limtion ility, support this explntion. seond potentil ontriuting ftor to slower growth is tht shorter seson length t northern ltitudes limits reprodutive output nd seed size s there is less time for ron umultion (Morin & Chuine, 26; Chuine, 2). Redued seed size my then drive lower GRs. Consistent with this explntion, seed mss is redued in limtes with older winters (Fig. 5e), where the growing seson is presumly shorter, nd seed size is orrelted with GR (Fig. 5f). The ltter reltionship is signifint, lthough the vrition explined is low: R 2 =.92, P =.9. Therefore, seed mss my e ontriuting diretly to the trdeoff etween GR nd freezing tolerne. However, redued seed mss nnot explin the negtive reltionship etween stem freezing tolerne nd RGR (R 2 =.29,, Fig. 4j), euse seed mss is not orrelted with RGR (Fig. S4). The strongest reltionships etween freezing tolerne nd growth re found when GR is the mesure of growth (Fig. 4; Tle 2). However, RGR nd GR re strongly positively orrelted (R 2 = 9, P =., Fig. S4). oth RGR nd seed mss, whih re oth positively orrelted with GR nd minimum tempertures, ut negtively orrelted with stem freezing tolerne, thus ontriute to the trde-off etween freezing tolerne nd GR. It is interesting to note tht lef freezing tolerne is negtively ssoited with seed mss nd GR, ut not with RGR (Fig. 4 e). RGR my e less likely thn GR to trde off with freezing tolerne, euse rpid growth rtes my e required in short growing sesons. lterntively, slower growth in old limtes my e dptive, if more onservtive growth strtegy limits the risk of tissue dmge (Guy, 99). Given the limits to ron umultion with shorter seson length, seson length my drive seletion for oth lower seed mss nd lower GR; however, the smller seed, slower growth strtegy my lso e onsequene of resoure llotion to old tolerne (Lmers et l., 28). Life history strtegies nd limits to rnge expnsion Low tempertures re mjor limittion to northern rnge expnsion in mny speies tht lk freezing tolerne (Ski & Weiser, 973; Riklefs et l., 999). The lk of old limtion ility nd freezing tolerne exhiited y Q. oleoides indites physiologil rrier tht proly prevents expnsion eyond its northern rnge limit. The extremely limited migrtion of Q. oleoides northwrds over the lst 2 million yr is supported y moleulr evidene (Cvender-res et l., 2). If growth rte is n inditor of reltive fitness nd ompetitive ility (Lmers et l., 28; Moles et l., 29), the growth rte freezing tolerne trde-off lso implies tht southern expnsion of the

12 2 Reserh New Phytologist temperte speies, Q. virginin, Q. gemint nd Q. fusiformis, my e limited y their inferior ompetitive ility reltive to the tropil speies, Q. oleoides, or reltive to other speies t or elow their southern rnge limits. Speies generlly hve mximum growth rtes t their southern rnge limit, ut do not inrese their growth rtes when grown further south or under optiml onditions (Lnglet, 97; Ski & Lrher, 987; Roerds et l., 99; Loehle, 998). This is true for the temperte speies Q. fusiformis nd Q. gemint, ut ws more vrile for Q. virginin. Under yer-round tropil onditions, popultions of the temperte speies Q. gemint nd Q. fusiformis mintined lower growth rtes nd were unle to inrese growth rtes to level omprle with tht of tropil Q. oleoides (Fig. 3g,i). However, some mternl fmilies nd one popultion of Q. virginn (Louisin) hd GRs similr to tht of Q. oleoides under tropil onditions (Fig. 3h,j). This suggests tht, lthough Q. gemint nd Q. fusiformis my hve limited ility to inrese their growth rtes under tropil onditions, some Q. virginin popultions my hieve ompetitive growth rtes. There ws muh greter overlp in RGR thn in GR vlues, suh tht regressions with RGR s the preditor of freezing tolerne were less signifint (Fig. 4 d). The totl iomss hieved y plnt within given period of time (GR) my ultimtely e the est preditor of fitness nd or ompetitive ility. Seed mss is lso ssoited with ompetitive ility nd ontriutes diretly to GR. However, other ftors not investigted, inluding suseptiility to ioti pthogens nd pests (Reder, 992; lexnder & Holt, 998; Meiners & Hndel, 2; Fine et l., 24), re thought to ply n importnt role in mediting ompetition nd limiting speies rnges. Sesonl drought tht ours throughout the rnge of Q. oleoides in Centrl meri my lso intert with temperture to medite speies rnges. symmetril gene flow etween Q. oleoides nd Q. virginin, with higher rtes southwrds thn northwrds (Cvender-res et l., 2), suggests tht lk of freezing tolerne my present more formidle rrier to northwrd expnsion thn does the lk of ompetitive ility to southwrd expnsion. Lol dpttion or rod limti tolernes? ross the ltitudinl grdient of the live ok group, we found limited vrition mong popultions, suggesting onserved speies-level limti tolernes. In Q. virginin, the northern-most popultion of North Crolin exhiited greter lef nd stem freezing tolerne thn the Florid popultions, nd men vlues of the popultions suggested linl vrition long the ltitudinl grdient (Fig. 3d,f). previous ut more limited study with Q. virginin found similr differentition etween the North Crolin nd Florid popultions for lef freezing tolerne, inditing tht the popultion-level differenes re repetle, even ross different experimentl onditions nd olletion lotions (Cvender-res, 27). Minimum temperture is good preditor for freezing tolerne ross mternl fmilies (Fig. 4e,f), reltionship driven y oth the vrition mong speies nd within Q. virginin nd, to lesser extent, within Q. oleoides. Within the rodly distriuted speies, Q. virginin nd Q. oleoides, vrition mong mternl fmilies followed ltitudinl trjetory, showing deresed freezing tolerne with inresed growth rte (Fig. 3d,f,h,j). These results suggest some degree of lol dpttion to freezing, prtiulrly within Q. virginin. Lol dpttion within Q. virginin must hve ourred sine the Pleistoene, when Q. virginin nd Q. oleoides re thought to hve diverged from ommon nestor (Cvender-res et l., 2). study with Querus suer found popultion-level differentition under winter onditions sed on the nnul temperture of the popultion soure (rnd et l., 25). Other studies support the lol dpttion hypothesis nd show popultion-level vrition in old sensitivity orresponding to hitt of origin (Rehfeldt et l., 22). Clinl vrition in freezing tolerne hs een demonstrted in severl tree speies, inditing lol dpttion (Duousso et l., 996; Rehfeldt et l., 2; rnd et l., 25; Cvender-res, 27; Morin et l., 27). Nevertheless, the trde-off ourred lrgely ross speies (Fig. 4 d; Tle ), suh tht temperte speies exhiited slower growth rtes nd higher levels of freezing tolerne, wheres the tropil speies mintined higher growth rtes nd exhiited greter lef nd stem dmge in response to freezing. The limited vrition mong popultions, ompred with the vrition mong speies, in freezing tolerne (Tle ) indites onservtism in the limti nihes of speies. This finding is onsistent with limited lol dpttion in popultions of Mediterrnen holm ok (Gimeno et l., 29). Conserved limti nihes nd rod limti tolernes my thus e more importnt thn the lol dpttion of popultions in determining speies rnges. ross the temperte nd tropil divide, we see distint rek, s evidened y the redued ility of Q. oleoides to old limte nd void freezing dmge. This orresponds with the nrrow rnge of minimum tempertures of Q. oleoides when ompred with the three more temperte speies exhiiting overlpping temperture rnges (Fig. 2). oth Q. virginin nd Q. fusiformis hve firly rod rnge of minimum temperture limti tolernes (Fig. 2). Temperte speies tht enounter high limti vriility throughout the yer my e dpted to tolerte wide rnge of limti onditions nd thus oupy rod ltitudinl nd limti distriutions with limited lol dpttion (Jnzen, 967; Lrher, 25; Morin & Chuine, 26). Conlusions The trde-off etween freezing tolerne nd growth rte supports the lssi rnge limit hypothesis, whih posits tht the distriutions of speies re limited y freezing tolerne in the north nd y ompetition in the south (Mrthur, 972; Woodwrd, 987; 988; Shenk, 996; Gross & Prie, 2). Speies nd popultions from older limtes hve greter ility to enhne their freezing tolerne fter exposure to old tempertures thn those from more tropil ltitudes, providing evidene for dptive plstiity. Freezing tolerne, old limtion ility nd diminution of growth rtes hve proly

Review Topic 14: Relationships between two numerical variables

Review Topic 14: Relationships between two numerical variables Review Topi 14: Reltionships etween two numeril vriles Multiple hoie 1. Whih of the following stterplots est demonstrtes line of est fit? A B C D E 2. The regression line eqution for the following grph

More information

THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL

THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL THE INFLUENCE OF MODEL RESOLUTION ON AN EXPRESSION OF THE ATMOSPHERIC BOUNDARY LAYER IN A SINGLE-COLUMN MODEL P3.1 Kot Iwmur*, Hiroto Kitgw Jpn Meteorologil Ageny 1. INTRODUCTION Jpn Meteorologil Ageny

More information

Effects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue

Effects of Drought on the Performance of Two Hybrid Bluegrasses, Kentucky Bluegrass and Tall Fescue TITLE: OBJECTIVE: AUTHOR: SPONSORS: Effets of Drought on the Performne of Two Hyrid Bluegrsses, Kentuky Bluegrss nd Tll Fesue Evlute the effets of drought on the visul qulity nd photosynthesis in two hyrid

More information

ANALYSIS AND MODELLING OF RAINFALL EVENTS

ANALYSIS AND MODELLING OF RAINFALL EVENTS Proeedings of the 14 th Interntionl Conferene on Environmentl Siene nd Tehnology Athens, Greee, 3-5 Septemer 215 ANALYSIS AND MODELLING OF RAINFALL EVENTS IOANNIDIS K., KARAGRIGORIOU A. nd LEKKAS D.F.

More information

Project 6: Minigoals Towards Simplifying and Rewriting Expressions

Project 6: Minigoals Towards Simplifying and Rewriting Expressions MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy

More information

Generalization of 2-Corner Frequency Source Models Used in SMSIM

Generalization of 2-Corner Frequency Source Models Used in SMSIM Generliztion o 2-Corner Frequeny Soure Models Used in SMSIM Dvid M. Boore 26 Mrh 213, orreted Figure 1 nd 2 legends on 5 April 213, dditionl smll orretions on 29 My 213 Mny o the soure spetr models ville

More information

Lecture Notes No. 10

Lecture Notes No. 10 2.6 System Identifition, Estimtion, nd Lerning Leture otes o. Mrh 3, 26 6 Model Struture of Liner ime Invrint Systems 6. Model Struture In representing dynmil system, the first step is to find n pproprite

More information

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35.

First compression (0-6.3 GPa) First decompression ( GPa) Second compression ( GPa) Second decompression (35. 0.9 First ompression (0-6.3 GP) First deompression (6.3-2.7 GP) Seond ompression (2.7-35.5 GP) Seond deompression (35.5-0 GP) V/V 0 0.7 0.5 0 5 10 15 20 25 30 35 P (GP) Supplementry Figure 1 Compression

More information

1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the

More information

Comparing the Pre-image and Image of a Dilation

Comparing the Pre-image and Image of a Dilation hpter Summry Key Terms Postultes nd Theorems similr tringles (.1) inluded ngle (.2) inluded side (.2) geometri men (.) indiret mesurement (.6) ngle-ngle Similrity Theorem (.2) Side-Side-Side Similrity

More information

Iowa Training Systems Trial Snus Hill Winery Madrid, IA

Iowa Training Systems Trial Snus Hill Winery Madrid, IA Iow Trining Systems Tril Snus Hill Winery Mdrid, IA Din R. Cohrn nd Gil R. Nonneke Deprtment of Hortiulture, Iow Stte University Bkground nd Rtionle: Over the lst severl yers, five sttes hve een evluting

More information

Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions

Activities. 4.1 Pythagoras' Theorem 4.2 Spirals 4.3 Clinometers 4.4 Radar 4.5 Posting Parcels 4.6 Interlocking Pipes 4.7 Sine Rule Notes and Solutions MEP: Demonstrtion Projet UNIT 4: Trigonometry UNIT 4 Trigonometry tivities tivities 4. Pythgors' Theorem 4.2 Spirls 4.3 linometers 4.4 Rdr 4.5 Posting Prels 4.6 Interloking Pipes 4.7 Sine Rule Notes nd

More information

An Experimental Evolutionary Study on Adaptation to Temporally Fluctuating ph in Escherichia coli

An Experimental Evolutionary Study on Adaptation to Temporally Fluctuating ph in Escherichia coli 406 An Experimentl Evolutionry Study on Adpttion to Temporlly Flututing ph in Esherihi oli Brdley S. Hughes* Alistir J. Cullum Alert F. Bennett Deprtment of Eology nd Evolutionry Biology, University of

More information

University of Sioux Falls. MAT204/205 Calculus I/II

University of Sioux Falls. MAT204/205 Calculus I/II University of Sioux Flls MAT204/205 Clulus I/II Conepts ddressed: Clulus Textook: Thoms Clulus, 11 th ed., Weir, Hss, Giordno 1. Use stndrd differentition nd integrtion tehniques. Differentition tehniques

More information

1B40 Practical Skills

1B40 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 information

Probability. b a b. a b 32.

Probability. b a b. a b 32. Proility If n event n hppen in '' wys nd fil in '' wys, nd eh of these wys is eqully likely, then proility or the hne, or its hppening is, nd tht of its filing is eg, If in lottery there re prizes nd lnks,

More information

Introduction to Olympiad Inequalities

Introduction to Olympiad Inequalities Introdution to Olympid Inequlities Edutionl Studies Progrm HSSP Msshusetts Institute of Tehnology Snj Simonovikj Spring 207 Contents Wrm up nd Am-Gm inequlity 2. Elementry inequlities......................

More information

Arrow s Impossibility Theorem

Arrow s Impossibility Theorem Rep Voting Prdoxes Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Voting Prdoxes Properties Arrow s Theorem Leture Overview 1 Rep

More information

A Study on the Properties of Rational Triangles

A Study on the Properties of Rational Triangles Interntionl Journl of Mthemtis Reserh. ISSN 0976-5840 Volume 6, Numer (04), pp. 8-9 Interntionl Reserh Pulition House http://www.irphouse.om Study on the Properties of Rtionl Tringles M. Q. lm, M.R. Hssn

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Nme Dte hpter 9 Mintining Mthemtil Profiieny Simplify the epression. 1. 500. 189 3. 5 4. 4 3 5. 11 5 6. 8 Solve the proportion. 9 3 14 7. = 8. = 9. 1 7 5 4 = 4 10. 0 6 = 11. 7 4 10 = 1. 5 9 15 3 = 5 +

More information

Intermediate Math Circles Wednesday 17 October 2012 Geometry II: Side Lengths

Intermediate Math Circles Wednesday 17 October 2012 Geometry II: Side Lengths Intermedite Mth Cirles Wednesdy 17 Otoer 01 Geometry II: Side Lengths Lst week we disussed vrious ngle properties. As we progressed through the evening, we proved mny results. This week, we will look t

More information

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES PAIR OF LINEAR EQUATIONS IN TWO VARIABLES. Two liner equtions in the sme two vriles re lled pir of liner equtions in two vriles. The most generl form of pir of liner equtions is x + y + 0 x + y + 0 where,,,,,,

More information

THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL

THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL THE ASYMMETRY OF COASTAL WATER LEVEL RESPONSE TO LANDFALLING HURRICANES SIMULATED BY A THREE-DIMENSIONAL STORM SURGE MODEL Mhun Peng *, Lin Xie nd Leonrd J. Pietrfes Deprtment of Mrine, Erth nd Atmospheri

More information

For a, b, c, d positive if a b and. ac bd. Reciprocal relations for a and b positive. If a > b then a ab > b. then

For a, b, c, d positive if a b and. ac bd. Reciprocal relations for a and b positive. If a > b then a ab > b. then Slrs-7.2-ADV-.7 Improper Definite Integrls 27.. D.dox Pge of Improper Definite Integrls Before we strt the min topi we present relevnt lger nd it review. See Appendix J for more lger review. Inequlities:

More information

Modeling of Catastrophic Failures in Power Systems

Modeling of Catastrophic Failures in Power Systems Modeling of tstrophi Filures in Power Systems hnn Singh nd lex Sprintson Deprtment of Eletril nd omputer Engineering Texs &M hnn Singh nd lex Sprintson Modeling of tstrophi Filures Motivtion Reent events

More information

Lecture 6: Coding theory

Lecture 6: Coding theory Leture 6: Coing theory Biology 429 Crl Bergstrom Ferury 4, 2008 Soures: This leture loosely follows Cover n Thoms Chpter 5 n Yeung Chpter 3. As usul, some of the text n equtions re tken iretly from those

More information

Appendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities

Appendix C Partial discharges. 1. Relationship Between Measured and Actual Discharge Quantities Appendi Prtil dishrges. Reltionship Between Mesured nd Atul Dishrge Quntities A dishrging smple my e simply represented y the euilent iruit in Figure. The pplied lternting oltge V is inresed until the

More information

DETERMINING SIGNIFICANT FACTORS AND THEIR EFFECTS ON SOFTWARE ENGINEERING PROCESS QUALITY

DETERMINING SIGNIFICANT FACTORS AND THEIR EFFECTS ON SOFTWARE ENGINEERING PROCESS QUALITY DETERMINING SIGNIFINT FTORS ND THEIR EFFETS ON SOFTWRE ENGINEERING PROESS QULITY R. Rdhrmnn Jeng-Nn Jung Mil to: rdhrmn_r@merer.edu jung_jn@merer.edu Shool of Engineering, Merer Universit, Mon, G 37 US

More information

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models

Estimation of Global Solar Radiation in Onitsha and Calabar Using Empirical Models Communitions in Applied Sienes ISS 0-77 Volume, umer, 0, 5-7 Estimtion of Glol Solr dition in Onitsh nd Clr Using Empiril Models M.. nuhi, J. E. Ekpe nd G. F Ieh Deprtment of Industril Physis, Eonyi Stte

More information

(h+ ) = 0, (3.1) s = s 0, (3.2)

(h+ ) = 0, (3.1) s = s 0, (3.2) Chpter 3 Nozzle Flow Qusistedy idel gs flow in pipes For the lrge vlues of the Reynolds number typilly found in nozzles, the flow is idel. For stedy opertion with negligible body fores the energy nd momentum

More information

PLANT POPULATION INFLUENCES ON MAIZE PHYSIOLOGICAL RESPONSES TO NITROGEN APPLICATION

PLANT POPULATION INFLUENCES ON MAIZE PHYSIOLOGICAL RESPONSES TO NITROGEN APPLICATION PLANT POPULATION INFLUENCES ON MAIZE PHYSIOLOGICAL RESPONSES TO NITROGEN APPLICATION C.R. Boomsm nd T.J. Vyn Purdue University, West Lfyette, Indin Astrt Pst geneti improvements in mize (Ze mys L.) hve

More information

QUADRATIC EQUATION. Contents

QUADRATIC EQUATION. Contents QUADRATIC EQUATION Contents Topi Pge No. Theory 0-04 Exerise - 05-09 Exerise - 09-3 Exerise - 3 4-5 Exerise - 4 6 Answer Key 7-8 Syllus Qudrti equtions with rel oeffiients, reltions etween roots nd oeffiients,

More information

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications

AP CALCULUS Test #6: Unit #6 Basic Integration and Applications AP CALCULUS Test #6: Unit #6 Bsi Integrtion nd Applitions A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS IN THIS PART OF THE EXAMINATION. () The ext numeril vlue of the orret

More information

On the Scale factor of the Universe and Redshift.

On the Scale factor of the Universe and Redshift. On the Sle ftor of the Universe nd Redshift. J. M. unter. john@grvity.uk.om ABSTRACT It is proposed tht there hs been longstnding misunderstnding of the reltionship between sle ftor of the universe nd

More information

a) Read over steps (1)- (4) below and sketch the path of the cycle on a P V plot on the graph below. Label all appropriate points.

a) Read over steps (1)- (4) below and sketch the path of the cycle on a P V plot on the graph below. Label all appropriate points. Prole 3: Crnot Cyle of n Idel Gs In this prole, the strting pressure P nd volue of n idel gs in stte, re given he rtio R = / > of the volues of the sttes nd is given Finlly onstnt γ = 5/3 is given You

More information

A Non-parametric Approach in Testing Higher Order Interactions

A Non-parametric Approach in Testing Higher Order Interactions A Non-prmetri Approh in Testing igher Order Intertions G. Bkeerthn Deprtment of Mthemtis, Fulty of Siene Estern University, Chenkldy, Sri Lnk nd S. Smit Deprtment of Crop Siene, Fulty of Agriulture University

More information

Thermodynamics. Question 1. Question 2. Question 3 3/10/2010. Practice Questions PV TR PV T R

Thermodynamics. Question 1. Question 2. Question 3 3/10/2010. Practice Questions PV TR PV T R /10/010 Question 1 1 mole of idel gs is rought to finl stte F y one of three proesses tht hve different initil sttes s shown in the figure. Wht is true for the temperture hnge etween initil nd finl sttes?

More information

System Validation (IN4387) November 2, 2012, 14:00-17:00

System Validation (IN4387) November 2, 2012, 14:00-17:00 System Vlidtion (IN4387) Novemer 2, 2012, 14:00-17:00 Importnt Notes. The exmintion omprises 5 question in 4 pges. Give omplete explntion nd do not onfine yourself to giving the finl nswer. Good luk! Exerise

More information

Arrow s Impossibility Theorem

Arrow s Impossibility Theorem Rep Fun Gme Properties Arrow s Theorem Arrow s Impossiility Theorem Leture 12 Arrow s Impossiility Theorem Leture 12, Slide 1 Rep Fun Gme Properties Arrow s Theorem Leture Overview 1 Rep 2 Fun Gme 3 Properties

More information

Linear Algebra Introduction

Linear Algebra Introduction Introdution Wht is Liner Alger out? Liner Alger is rnh of mthemtis whih emerged yers k nd ws one of the pioneer rnhes of mthemtis Though, initilly it strted with solving of the simple liner eqution x +

More information

Lecture 18: Species, Hybrids, and QTL. Oct 23, 2006

Lecture 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 information

Discrete Mathematics and Probability Theory Spring 2013 Anant Sahai Lecture 17

Discrete 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 information

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3

I1 = 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 information

Discrete Mathematics and Probability Theory Summer 2014 James Cook Note 17

Discrete 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 information

THE PYTHAGOREAN THEOREM

THE PYTHAGOREAN THEOREM THE PYTHAGOREAN THEOREM The Pythgoren Theorem is one of the most well-known nd widely used theorems in mthemtis. We will first look t n informl investigtion of the Pythgoren Theorem, nd then pply this

More information

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem.

Lesson 2: The Pythagorean Theorem and Similar Triangles. A Brief Review of the Pythagorean Theorem. 27 Lesson 2: The Pythgoren Theorem nd Similr Tringles A Brief Review of the Pythgoren Theorem. Rell tht n ngle whih mesures 90º is lled right ngle. If one of the ngles of tringle is right ngle, then we

More information

Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point

Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply

More information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 H 3 CH3 C. NMR spectroscopy. Different types of NMR 6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht

More information

p-adic Egyptian Fractions

p-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 information

Continuous Random Variables

Continuous 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 information

TOPIC: LINEAR ALGEBRA MATRICES

TOPIC: LINEAR ALGEBRA MATRICES Interntionl Blurete LECTUE NOTES for FUTHE MATHEMATICS Dr TOPIC: LINEA ALGEBA MATICES. DEFINITION OF A MATIX MATIX OPEATIONS.. THE DETEMINANT deta THE INVESE A -... SYSTEMS OF LINEA EQUATIONS. 8. THE AUGMENTED

More information

Genetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary

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 information

Section 6: Area, Volume, and Average Value

Section 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 information

Spacetime and the Quantum World Questions Fall 2010

Spacetime and the Quantum World Questions Fall 2010 Spetime nd the Quntum World Questions Fll 2010 1. Cliker Questions from Clss: (1) In toss of two die, wht is the proility tht the sum of the outomes is 6? () P (x 1 + x 2 = 6) = 1 36 - out 3% () P (x 1

More information

Section 4.4. Green s Theorem

Section 4.4. Green s Theorem The Clulus of Funtions of Severl Vriles Setion 4.4 Green s Theorem Green s theorem is n exmple from fmily of theorems whih onnet line integrls (nd their higher-dimensionl nlogues) with the definite integrls

More information

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique? XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk out solving systems of liner equtions. These re prolems tht give couple of equtions with couple of unknowns, like: 6= x + x 7=

More information

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR

6.3.2 Spectroscopy. N Goalby chemrevise.org 1 NO 2 CH 3. CH 3 C a. NMR spectroscopy. Different types of NMR 6.. Spetrosopy NMR spetrosopy Different types of NMR NMR spetrosopy involves intertion of mterils with the lowenergy rdiowve region of the eletromgneti spetrum NMR spetrosopy is the sme tehnology s tht

More information

VIBRATION ANALYSIS OF AN ISOLATED MASS WITH SIX DEGREES OF FREEDOM Revision G

VIBRATION ANALYSIS OF AN ISOLATED MASS WITH SIX DEGREES OF FREEDOM Revision G B Tom Irvine Emil: tom@virtiondt.om Jnur 8, 3 VIBRATION ANALYSIS OF AN ISOLATED MASS WITH SIX DEGREES OF FREEDOM Revision G Introdution An vionis omponent m e mounted with isoltor grommets, whih t s soft

More information

Centre de Referència en Economia Analítica

Centre de Referència en Economia Analítica Centre de Referèni en Eonomi Anlíti Brelon Eonomis Working Pper Series Working Pper nº 69 Regions of Rtionlity: Mps for ounded gents Roin M. Hogrth nd Ntli Kreli Otoer, 005 Regions of rtionlity: Mps for

More information

12.4 Similarity in Right Triangles

12.4 Similarity in Right Triangles Nme lss Dte 12.4 Similrit in Right Tringles Essentil Question: How does the ltitude to the hpotenuse of right tringle help ou use similr right tringles to solve prolems? Eplore Identifing Similrit in Right

More information

Review of Gaussian Quadrature method

Review 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 information

NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE

NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE NEW CIRCUITS OF HIGH-VOLTAGE PULSE GENERATORS WITH INDUCTIVE-CAPACITIVE ENERGY STORAGE V.S. Gordeev, G.A. Myskov Russin Federl Nuler Center All-Russi Sientifi Reserh Institute of Experimentl Physis (RFNC-VNIIEF)

More information

CS 573 Automata Theory and Formal Languages

CS 573 Automata Theory and Formal Languages Non-determinism Automt Theory nd Forml Lnguges Professor Leslie Lnder Leture # 3 Septemer 6, 2 To hieve our gol, we need the onept of Non-deterministi Finite Automton with -moves (NFA) An NFA is tuple

More information

Effects of Applying Accumulator Straw in Soil on Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris under Cadmium Stress

Effects of Applying Accumulator Straw in Soil on Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris under Cadmium Stress Interntionl Conferene on Mnufturing Siene nd Engineering (ICMSE 2015) Effets of Applying Aumultor Strw in Soil on Nutrient Uptke nd Soil Enzyme Ativity of Cpsell burs-pstoris under Cdmium Stress Jin Wng1,,

More information

8 THREE PHASE A.C. CIRCUITS

8 THREE PHASE A.C. CIRCUITS 8 THREE PHSE.. IRUITS The signls in hpter 7 were sinusoidl lternting voltges nd urrents of the so-lled single se type. n emf of suh type n e esily generted y rotting single loop of ondutor (or single winding),

More information

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and

Lecture 27: Diffusion of Ions: Part 2: coupled diffusion of cations and Leture 7: iffusion of Ions: Prt : oupled diffusion of tions nd nions s desried y Nernst-Plnk Eqution Tody s topis Continue to understnd the fundmentl kinetis prmeters of diffusion of ions within n eletrilly

More information

A Mathematical Model for Unemployment-Taking an Action without Delay

A Mathematical Model for Unemployment-Taking an Action without Delay Advnes in Dynmil Systems nd Applitions. ISSN 973-53 Volume Number (7) pp. -8 Reserh Indi Publitions http://www.ripublition.om A Mthemtil Model for Unemployment-Tking n Ation without Dely Gulbnu Pthn Diretorte

More information

Electromagnetism Notes, NYU Spring 2018

Electromagnetism Notes, NYU Spring 2018 Eletromgnetism Notes, NYU Spring 208 April 2, 208 Ation formultion of EM. Free field desription Let us first onsider the free EM field, i.e. in the bsene of ny hrges or urrents. To tret this s mehnil system

More information

April 8, 2017 Math 9. Geometry. Solving vector problems. Problem. Prove that if vectors and satisfy, then.

April 8, 2017 Math 9. Geometry. Solving vector problems. Problem. Prove that if vectors and satisfy, then. pril 8, 2017 Mth 9 Geometry Solving vetor prolems Prolem Prove tht if vetors nd stisfy, then Solution 1 onsider the vetor ddition prllelogrm shown in the Figure Sine its digonls hve equl length,, the prllelogrm

More information

Section 1.3 Triangles

Section 1.3 Triangles Se 1.3 Tringles 21 Setion 1.3 Tringles LELING TRINGLE The line segments tht form tringle re lled the sides of the tringle. Eh pir of sides forms n ngle, lled n interior ngle, nd eh tringle hs three interior

More information

PYTHAGORAS THEOREM WHAT S IN CHAPTER 1? IN THIS CHAPTER YOU WILL:

PYTHAGORAS THEOREM WHAT S IN CHAPTER 1? IN THIS CHAPTER YOU WILL: PYTHAGORAS THEOREM 1 WHAT S IN CHAPTER 1? 1 01 Squres, squre roots nd surds 1 02 Pythgors theorem 1 03 Finding the hypotenuse 1 04 Finding shorter side 1 05 Mixed prolems 1 06 Testing for right-ngled tringles

More information

Applying Hyperaccumulator Straw in Cd-Contaminated Soil Enhances Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris

Applying Hyperaccumulator Straw in Cd-Contaminated Soil Enhances Nutrient Uptake and Soil Enzyme Activity of Capsella bursa-pastoris Interntionl Conferene on Mnufturing Siene nd Engineering (ICMSE 2015) Applying Hyperumultor Strw in Cd-Contminted Soil Enhnes Nutrient Uptke nd Soil Enzyme Ativity of Cpsell burs-pstoris Jin Wng1,, Keng

More information

6.5 Improper integrals

6.5 Improper integrals Eerpt from "Clulus" 3 AoPS In. www.rtofprolemsolving.om 6.5. IMPROPER INTEGRALS 6.5 Improper integrls As we ve seen, we use the definite integrl R f to ompute the re of the region under the grph of y =

More information

Green s Theorem. (2x e y ) da. (2x e y ) dx dy. x 2 xe y. (1 e y ) dy. y=1. = y e y. y=0. = 2 e

Green s Theorem. (2x e y ) da. (2x e y ) dx dy. x 2 xe y. (1 e y ) dy. y=1. = y e y. y=0. = 2 e Green s Theorem. Let be the boundry of the unit squre, y, oriented ounterlokwise, nd let F be the vetor field F, y e y +, 2 y. Find F d r. Solution. Let s write P, y e y + nd Q, y 2 y, so tht F P, Q. Let

More information

Learning Partially Observable Markov Models from First Passage Times

Learning Partially Observable Markov Models from First Passage Times Lerning Prtilly Oservle Mrkov s from First Pssge s Jérôme Cllut nd Pierre Dupont Europen Conferene on Mhine Lerning (ECML) 8 Septemer 7 Outline. FPT in models nd sequenes. Prtilly Oservle Mrkov s (POMMs).

More information

22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of:

22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of: 22: Union Fin CS 473u - Algorithms - Spring 2005 April 14, 2005 1 Union-Fin We wnt to mintin olletion of sets, uner the opertions of: 1. MkeSet(x) - rete set tht ontins the single element x. 2. Fin(x)

More information

Defining Areas with Nil Landslide Hazard is a step toward a Comprehensive Landslide Loss Model

Defining Areas with Nil Landslide Hazard is a step toward a Comprehensive Landslide Loss Model is step towrd Comprehensive Lndslide Loss Model F.ASCE, F.GSA, Ame Foster Wheeler, Los Angeles, CA, USA, jeff.keton@mefw.om Consulting Insurne Atury, Huntington Beh, CA, USA, rjrothjr@verizon.net Astrt

More information

TIME AND STATE IN DISTRIBUTED SYSTEMS

TIME AND STATE IN DISTRIBUTED SYSTEMS Distriuted Systems Fö 5-1 Distriuted Systems Fö 5-2 TIME ND STTE IN DISTRIUTED SYSTEMS 1. Time in Distriuted Systems Time in Distriuted Systems euse eh mhine in distriuted system hs its own lok there is

More information

Algorithm Design and Analysis

Algorithm Design and Analysis Algorithm Design nd Anlysis LECTURE 5 Supplement Greedy Algorithms Cont d Minimizing lteness Ching (NOT overed in leture) Adm Smith 9/8/10 A. Smith; sed on slides y E. Demine, C. Leiserson, S. Rskhodnikov,

More information

Factorising FACTORISING.

Factorising FACTORISING. Ftorising FACTORISING www.mthletis.om.u Ftorising FACTORISING Ftorising is the opposite of expning. It is the proess of putting expressions into rkets rther thn expning them out. In this setion you will

More information

Matrices SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics (c) 1. Definition of a Matrix

Matrices SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics (c) 1. Definition of a Matrix tries Definition of tri mtri is regulr rry of numers enlosed inside rkets SCHOOL OF ENGINEERING & UIL ENVIRONEN Emple he following re ll mtries: ), ) 9, themtis ), d) tries Definition of tri Size of tri

More information

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report

Thermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block

More information

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive

More information

Proving the Pythagorean Theorem

Proving the Pythagorean Theorem Proving the Pythgoren Theorem W. Bline Dowler June 30, 2010 Astrt Most people re fmilir with the formul 2 + 2 = 2. However, in most ses, this ws presented in lssroom s n solute with no ttempt t proof or

More information

Behavior Composition in the Presence of Failure

Behavior Composition in the Presence of Failure Behvior Composition in the Presene of Filure Sestin Srdin RMIT University, Melourne, Austrli Fio Ptrizi & Giuseppe De Giomo Spienz Univ. Rom, Itly KR 08, Sept. 2008, Sydney Austrli Introdution There re

More information

Global alignment. Genome Rearrangements Finding preserved genes. Lecture 18

Global alignment. Genome Rearrangements Finding preserved genes. Lecture 18 Computt onl Biology Leture 18 Genome Rerrngements Finding preserved genes We hve seen before how to rerrnge genome to obtin nother one bsed on: Reversls Knowledge of preserved bloks (or genes) Now we re

More information

Algorithm Design and Analysis

Algorithm Design and Analysis Algorithm Design nd Anlysis LECTURE 8 Mx. lteness ont d Optiml Ching Adm Smith 9/12/2008 A. Smith; sed on slides y E. Demine, C. Leiserson, S. Rskhodnikov, K. Wyne Sheduling to Minimizing Lteness Minimizing

More information

CS 491G Combinatorial Optimization Lecture Notes

CS 491G Combinatorial Optimization Lecture Notes CS 491G Comintoril Optimiztion Leture Notes Dvi Owen July 30, August 1 1 Mthings Figure 1: two possile mthings in simple grph. Definition 1 Given grph G = V, E, mthing is olletion of eges M suh tht e i,

More information

SECTION A STUDENT MATERIAL. Part 1. What and Why.?

SECTION A STUDENT MATERIAL. Part 1. What and Why.? SECTION A STUDENT MATERIAL Prt Wht nd Wh.? Student Mteril Prt Prolem n > 0 n > 0 Is the onverse true? Prolem If n is even then n is even. If n is even then n is even. Wht nd Wh? Eploring Pure Mths Are

More information

Technische Universität München Winter term 2009/10 I7 Prof. J. Esparza / J. Křetínský / M. Luttenberger 11. Februar Solution

Technische Universität München Winter term 2009/10 I7 Prof. J. Esparza / J. Křetínský / M. Luttenberger 11. Februar Solution Tehnishe Universität Münhen Winter term 29/ I7 Prof. J. Esprz / J. Křetínský / M. Luttenerger. Ferur 2 Solution Automt nd Forml Lnguges Homework 2 Due 5..29. Exerise 2. Let A e the following finite utomton:

More information

The University of Nottingham SCHOOL OF COMPUTER SCIENCE A LEVEL 2 MODULE, SPRING SEMESTER MACHINES AND THEIR LANGUAGES ANSWERS

The University of Nottingham SCHOOL OF COMPUTER SCIENCE A LEVEL 2 MODULE, SPRING SEMESTER MACHINES AND THEIR LANGUAGES ANSWERS The University of ottinghm SCHOOL OF COMPUTR SCIC A LVL 2 MODUL, SPRIG SMSTR 2015 2016 MACHIS AD THIR LAGUAGS ASWRS Time llowed TWO hours Cndidtes my omplete the front over of their nswer ook nd sign their

More information

NON-DETERMINISTIC FSA

NON-DETERMINISTIC FSA Tw o types of non-determinism: NON-DETERMINISTIC FS () Multiple strt-sttes; strt-sttes S Q. The lnguge L(M) ={x:x tkes M from some strt-stte to some finl-stte nd ll of x is proessed}. The string x = is

More information

Student Activity 3: Single Factor ANOVA

Student 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 information

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0) 1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this

More information

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.

1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light. 1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the

More information

3 Angle Geometry. 3.1 Measuring Angles. 1. Using a protractor, measure the marked angles.

3 Angle Geometry. 3.1 Measuring Angles. 1. Using a protractor, measure the marked angles. 3 ngle Geometry MEP Prtie ook S3 3.1 Mesuring ngles 1. Using protrtor, mesure the mrked ngles. () () (d) (e) (f) 2. Drw ngles with the following sizes. () 22 () 75 120 (d) 90 (e) 153 (f) 45 (g) 180 (h)

More information

A Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version

A Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version A Lower Bound for the Length of Prtil Trnsversl in Ltin Squre, Revised Version Pooy Htmi nd Peter W. Shor Deprtment of Mthemtil Sienes, Shrif University of Tehnology, P.O.Bo 11365-9415, Tehrn, Irn Deprtment

More information

CS 2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014

CS 2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014 S 224 DIGITAL LOGI & STATE MAHINE DESIGN SPRING 214 DUE : Mrh 27, 214 HOMEWORK III READ : Relte portions of hpters VII n VIII ASSIGNMENT : There re three questions. Solve ll homework n exm prolems s shown

More information

Chlorophyll fluorescence measures of seagrasses Halophila ovalis and Zostera capricorni reveal differences in response to experimental shading

Chlorophyll fluorescence measures of seagrasses Halophila ovalis and Zostera capricorni reveal differences in response to experimental shading Mr Biol (7) 152:45 414 DOI 1.17/s227-7-7-6 RESEARCH ARTICLE Chlorophyll fluoresene mesures of segrsses Hlophil ovlis nd Zoster priorni revel differenes in response to experimentl shding Junit S. Bité Æ

More information

Symmetrical Components 1

Symmetrical Components 1 Symmetril Components. Introdution These notes should e red together with Setion. of your text. When performing stedy-stte nlysis of high voltge trnsmission systems, we mke use of the per-phse equivlent

More information