Patterns of Fuel Use and Storage in Migrating Passerines

Size: px
Start display at page:

Download "Patterns of Fuel Use and Storage in Migrating Passerines"

Transcription

1 The Auk 127(1): , 2010 The Amerin Ornithologists Union, Printe in USA. Ptterns of Fuel Use n Storge in Migrting Psserines in Reltion to Fruit Resoures t Autumn Stopover Sites Su s n B. Sm i t h 1 n S o t t R. MWilli ms Deprtment of Nturl Resoures Siene, University of Rhoe Isln, Kingston, Rhoe Isln 02881, USA Astrt. Fuel eposition rtes of migrting irs my inite the qulity of hitt t stopover sites, yet little is known out how iet hits n foo vilility ffet ft n protein metolism in free-living songirs t stopover sites. We ompre plsm initors of ft eposition (triglyerie), ft tolism (B-hyroxyutyrte), n protein tolism (uri i) mong psserine speies tht re frugivorous to vrile egree uring utumn stopover on Blok Isln, Rhoe Isln. We lso ompre plsm lipi metolites from 3 of these speies tht were pture t 2 stopover sites with ifferent fruit unne. The more frugivorous Hermit Thrushes (Cthrus gutttus) h the highest plsm triglyerie, n uri i ws highest in the lest frugivorous speies smple on Blok Isln, ut other ifferenes mong speies were not lerly relte to iet. B-hyroxyutyrte ws more vrile mong the speies smple on Blok Isln. Plsm triglyerie ws signifintly higher in Hermit Thrushes pture on Blok Isln, where fruit resoures were unnt, thn in Hermit Thrushes pture t minln site in southern Rhoe Isln, where less fruit ws ville. Our results suggest tht iet hits my influene ft n protein metolism in migrting psserines, ut reful stuy esign n sttistil nlyses re neessry to ontrol for or minimize the effets of the mny influentil ftors tht ffet plsm metolites so they n e use to ssess fuel eposition in free-living irs n to ompre the qulity of migrtion stopover sites. Reeive 6 June 2008, epte 27 My Key wors: migrtion, plsm metolites, sesonl frugivory, songirs, stopover. Ptrones e Uso y Almenmiento e Comustile en Pseriformes Migrtorios on Relión Reursos e Frut en Sitios e Prs Migrtoris e Otoño Resumen. L ts e umulión e reursos energétios por prte e ls ves que se enuentrn en migrión puee inir l li el háitt en los sitios e prs migrtoris. Sin emrgo, se se poo sore er e ómo los háitos e limentión y l isponiili e limentos fetn el metolismo e ls grss y proteíns e ves silvestres en los sitios e pr. Comprmos iniores plsmátios e l umulión e grss (trigliérios), el tolismo e ls grss (B-hiroxiutirto) y el tolismo e proteíns (áio úrio) entre espeies e ves pseriformes on epeneni vrile e un iet frugívor urnte ls prs migrtoris e otoño en Blok Isln, Rhoe Isln. Tmién omprmos metolitos lipíios plsmátios e otrs tres espeies que fueron pturs en os sitios e pr migrtori que iferín en l unni e frutos. L espeie más frugívor, Cthrus gutttus, tuvo l myor nti e trigliérios plsmátios, y el áio úrio fue más lto en l espeie menos frugívor que fue muestre en Blok Isln. Sin emrgo, otrs iferenis entre espeies no se relionron lrmente on l iet. El B-hiroxiutirto fue el inior plsmátio más vrile entre ls ves muestres en Blok Isln. Los trigliérios plsmátios fueron signifitivmente más ltos en iniviuos e C. gutttus pturos en Blok Isln, one los frutos ern un reurso unnte, que en los iniviuos e l mism espeie pturos en un sitio ontinentl en el sur e Rhoe Isln, one hí menos frutos isponiles. Nuestros resultos sugieren que los háitos limentiios pueen influenir el metolismo e ls grss y proteíns en pseriformes migrtorios. Sin emrgo, es neesrio eliner iseños experimentles uiosos y nálisis e tos euos pr ontrolr o minimizr los efetos e otros ftores que tmién influenin los metolitos plsmátios, e moo e que éstos puen ser usos pr eterminr l umulión e energí en ves silvestres y pr omprr l li e los iferentes sitios e prs migrtoris. Annul migrtions of irs etween reeing n wintering grouns involve energetilly emning noturnl flights fuele primrily y store ft (Blem 1980). Smll songirs must regulrly stop etween flights to umulte energy stores to ontinue migrtion. Foo unne is importnt for effiient refueling n n influene the time spent t stopover sites (Biy n Green 1981; Shu n Jenni 2000, 2001). In ition, the qulity of foo resoures n ffet the rte t whih energy stores 1 Present ress: Deprtment of Biology, Villnov University, Villnov, Pennsylvni 19085, USA. E-mil: susn.smith@villnov.eu The Auk, Vol. 127, Numer 1, pges ISSN , eletroni ISSN y The Amerin Ornithologists Union. All rights reserve. Plese iret ll requests for permission to photoopy or reproue rtile ontent through the University of Cliforni Press s Rights n Permissions wesite, om/reprintinfo.sp. DOI: /uk

2 J n u ry 2010 Fu e l Use n St o r g e in Mi g r t i n g P s s e r i n e s 109 re reple (Birlein n Gwinner 1994, Birlein 2002). Thus, migrtion suess epens on the vilility of high-qulity hitts tht provie equte foo resoures, prtiulrly in res long migrtion orriors tht support lrge numers of irs uring migrtions. Beuse mny migrnts use stopover sites to inrese their energy stores, mesuring fuel eposition rtes of irs uring stopovers n provie informtion out the qulity n use of speifi sites. Fuel eposition rtes re typilly ssesse y mesuring mss hnge of irs repture uring stopovers or y ompring oy mss of irs pture t ifferent times of y to infer rte of mss gin s ily forging progresses (Winker et l. 1992; Winker 1995; Dunn 2000, 2002). The first pproh is limite y smll smple sizes euse few irs re repture uring short stopovers, wheres the seon pproh ssumes tht rrivl times n rtes of mss gin re similr mong ll iniviuls (Dunn 2000, 2002), n the results of these two types of nlyses re sometimes inonsistent (Winker et l. 1992, Bonter et l. 2007). Plsm metolite profiling vois these limittions n provies informtion out fuel use n eposition over the pst severl hours in iniviul irs pture one. For exmple, plsm onentrtions of lipi metolites inrese uring ft eposition (triglyerie) n tolism (B-hyroxyutyrte, nonesterifie ftty is, glyerol), n plsm uri i inreses uring protein tolism (Stevens 1996). Aoringly, plsm triglyeries n B-hyroxyutyrte were iretly relte to mss hnges of ptive irs over perio of severl hours (Jenni-Eiermnn n Jenni 1994, Jenni n Shwilh 2001) to severl ys (Willims et l. 1999, Semn et l. 2005). Plsm metolite profiling hs een use to etet ifferenes in fuel eposition rtes of migrting irs n hitt qulity t stopover sites (Shu n Jenni 2001; Guglielmo et l. 2002, 2005; Yenerg et l. 2002; Aeveo Semn et l. 2006; Willims et l. 2007). Here, we use plsm metolite profiling to ompre fuel eposition rtes mong vriety of songirs throughout utumn migrtion t stopover site n mong selete songirs with ifferent forging strtegies t 2 stopover sites with ifferent fruit unne. Mny psserine speies in estern North Ameri swith from primrily insetivorous iet on their reeing grouns to primrily frugivorous iet uring utumn migrtion (Prrish 1997). This ietry plstiity llows irs to utilize fruit resoures tht re often superunnt uring utumn n tht re presumly less energetilly expensive to fin n et thn inset prey (Prrish 2000). In ition, mny temperte fruits re high in ft or sugr (Thompson n Willson 1979, White 1989, Smith et l. 2007), whih my filitte migrtory fttening (Birlein n Simons 1995, Stevens 1996). We hypothesize tht higher fruit onsumption n enhne fuel eposition rtes of irs uring migrtory stopovers. We teste this hypothesis in two wys: (1) we ompre plsm metolites from vriety of songirs tht iffere in egree of frugivory while they inhite stopover site with unnt fruit, n (2) we ompre fuel eposition rtes of 3 songir speies with ifferent forging strtegies while they inhite 2 stopover sites tht iffere in fruit unne. Beuse we re involve in long-term (>40 yers) ir-ning progrms t oth the southern New Engln stopover sites use in the present stuy, our ojetives lso inlue etermining the reltive importne of environmentl n methoologil vriles tht my influene plsm lipi n protein metolite onentrtions n their interprettion s initors of physiologil n nutritionl stte of migrting songirs. Met h o s Stuy res. We onute our stuy t 2 lotions in southern Rhoe Isln. Blok Isln, whih is lote ~19 km off the southern ost of Rhoe Isln (41 12 N, W), is ielly lote to reeive lrge numers of migrting irs tht frequently rift offshore when they enounter the strong northwesterly wins typil uring utumn in southern New Engln s ostl res. These migrnts reorient themselves n onentrte t the north en of the isln efore flying k to the minln to ontinue migrtion (Ale 1977). The Cly He Preserve omprises lrge re of mritime shruln hitt t the north en of the isln (~77 h) tht serves s stopover site for mny of these psserine speies uring utumn migrtions (Bir n Niset 1960, Reinert et l. 2002). This re is hrterize uring utumn y superunnt wil fruits tht provie foo resoure for psserine migrnts uring utumn stopover (Prrish 1997, Smith et l. 2007). The shruln ommunity is ominte y wooy fruit-ering shrus, suh s Arrowwoo Viurnum (Viurnum enttum), Northern Byerry (Myri pensylvni), Blk Chokeerry (Aroni melnorp), n Common Wintererry (Ilex vertiillt). The ense unerstory lso ontins fruiting plnt speies suh s Amerin Pokewee (Phytol merin), Virgini Creeper (Prthenoissus quinquefoli), n Northern Dewerry (Ruus flgellris). Highly invsive speies, nmely Orientl Bittersweet (Celstrus oriultus), Multiflor Rose (Ros multiflor), n Autumn Olive (Elegnus umellt) re lso present within Cly He Preserve. The Kingston Willife Reserh Sttion (KWRS) is lote in southern Rhoe Isln in South Kingstown (41 27 N, W). The lnspe of this re is primrily eiuous forest pthes frgmente y evelope ln n griulturl fiels. Bning of songirs hs ourre eh fll sine 1956 long set of estlishe net lnes within eiuous wooln n erlysuessionl hitts in the nopy openings. The forest nopy is ominte y White Ash (Frxinus merin), Re Mple (Aer rurum), n oks (Querus spp.). Dominnt fruiting speies in the unerstory n nopy openings inlue Common Greenrier (Smilx rotunifoli), Orientl Bittersweet, Europen Privet (Ligustrum vulgre), n Fox Grpe (Vitis lrus). Arrowwoo Viurnum, Amerin Pokewee, Virgini Creeper, n Common Wintererry re rre n our in isolte pthes in the unerstory n nopy openings. Within-site omprisons. We smple loo from 8 speies of migrtory psserines tht ommonly our on Blok Isln. These speies were selete euse they were pture in suffiient numers (n 10) n iffer in level of frugivory while on Blok Isln uring utumn migrtion. Hermit Thrush (Cthrus gutttus), Yellow-rumpe Wrler (Denroi oront), Gry Ctir (Dumetell rolinensis), n Re-eye Vireo (Vireo oliveus) re highly frugivorous uring utumn migrtion on Blok Isln ( 74% fruit in fel smples; Prrish 1997). White-throte Sprrow (Zonotrihi liollis), Drk-eye Juno (Juno hyemlis), n Blue-hee Vireo (V. solitrius) onsume onsierly

3 110 Sm i t h n MWilli m s Au k, Vo l. 127 less fruit n more insets thn these other speies uring utumn migrtion ( 62% fruit in fel smples; Prrish 1997). Bloo smples from 2 White-rowne Sprrows (Z. leuophrys) were omine with those from the ongeneri White-throte Sprrow (herefter Zonotrihi ) for the nlyses. We esigne our loo-smpling protool so tht it oul fit within the typil ily sheule t ir-ning sttions. We pture irs using 30-mm nylon mist nets situte long estlishe trils within the shruln hitt in Cly He Preserve uring utumn Nets were opene t sunrise on eh morning of opertion, n irs were inlue in susequent nlyses if they were pture 1 6 h fter sunrise. This ensure tht irs h egun forging in the morning efore they were pture. Birs were extrte from nets t intervls of min n then rought to entrl lotion where they were hel in loth holing-gs until morphologil mesurements n loo smples were otine. We rew ~50 μl of loo from the rhil vein fter punture with 27-guge neele n ollete it in heprinize pillry tues. After loo ws rwn, we mesure wing hor n oy mss n then relese the irs. We reore the time of y s net hek time when irs were extrte from nets n then onverte the time of y to numer of full hours plus frtions of hours fter sunrise (herefter hours fter sunrise ). This ontrolle for hnges in time of sunrise s the seson progresse. Blee time ws reore s the time elpse etween the net hek n loo smpling. Only irs for whih lee time ws 30 min were inlue in susequent nlyses. Bloo smples were entrifuge t 8,000 rpm for 10 min to seprte plsm from re loo ells, n plsm ws then store t 80 C until nlysis. Between-site omprisons. We pture n le Hermit Thrushes, Yellow-rumpe Wrlers, n White-throte Sprrows t KWRS n on Blok Isln. We selete these speies euse they re ommonly pture t oth sites n re sesonlly frugivorous uring utumn migrtion (Prrish 1997). We onute loo smpling, proesse loo, n mesure irs using the sme proeures esrie ove. Birs were then ne with serilly numere feerl luminum leg ns n relese. Nets were operte t oth sites on 4 ys in 2004 (21, 23, 26, n 28 Otoer) n 4 ys in 2005 (16, 18, 20, n 27 Otoer). The simultneous pture of irs t oth sites minimizes ifferenes in wether or migrtion ptterns mong smpling ys t the 2 sites. We lso minimize temporl vrition in ily forging y inluing only irs pture within the sme 2.5-h perio in the morning t eh site on eh smpling y. We ssesse frequeny of ourrene of 10 plnt speies tht proue fruits n the presene of ripe fruit t eh site in 2005 to ompre the vilility of fruit resoures etween sites for the following speies: Arrowwoo Viurnum, Northern Byerry, Amerin Pokewee, Virgini Creeper, Blk Chokeerry, Ros spp., Orientl Bittersweet, Common Wintererry, Common Greenrier, n Europen Privet. Smpling ws onute within twenty-four 4-m 2 plots lote 1 m into the vegettion long the estlishe net lnes or trils. We reore the presene of plnt speies tht proue fruits n the presene of ripe fruit on these plnts in eh plot on Blok Isln n t KWRS on 6 n 7 Otoer 2005, respetively. We reognize tht there my e nnul vrition in fruit proution n tht fruit vilility my hve een ifferent in 2004 n However, suh vrition is likely to ffet these 2 sites similrly eh yer given their reltive proximity. Mesurement of plsm metolites. We mesure onentrtions of triglyerie (TRIG), B-hyroxyutyrte (BUTY), n uri i in plsm ollete for within-site omprisons mong speies pture on Blok Isln, n we mesure TRIG n BUTY in plsm ollete for etween-site omprisons (Blok Isln vs. KWRS). We mesure TRIG y sequentil enpoint ssy (Sigm, St. Louis, Missouri; 5 μl plsm, 240 μl regent A, 60 μl regent B) y first mesuring free glyerol n then sutrting free glyerol onentrtion from mesure totl triglyerie onentrtion. We mesure BUTY y kineti ssy (R-Biophrm, Mrshll, Mihign; 5 μl smple, 150 μl working solution, 3 μl BUTY ehyrogense, re kinetilly for 30 min) using metho similr to tht of Guglielmo et l. (2005). We mesure uri i y enpoint ssy (TECO Dignostis, Anheim, Cliforni; 5 μl smple, 300 μl regent). Smples with smll plsm volumes were ilute 2-fol to 3-fol with 0.9% NCl efore ll ssys, n we repete mesurements until the oeffiient of vrition etween replites ws <10%. Sttistil nlyses. The ir speies tht we use vry onsierly in overll oy size, n these struturl ifferenes in oy size will influene oy mss (Connell et l. 1960). Thus, we juste oy mss for mesure of oy size y using the resiuls from liner regression of oy mss n wing length in ll susequent nlyses. We use n informtion-theoreti pproh to investigte the importne of 5 vriles for explining vrition in TRIG, BUTY, n uri i onentrtions of irs uring utumn stopover on Blok Isln. We evlute moel set ontining ll possile omintions of speies, hours fter sunrise, te, size-orrete oy mss, n lee time. We lulte Akike s informtion riterion juste for smll smple sizes (AIC ) n use ifferenes in AIC (Δ i = AIC i AIC min ) to rnk nite moels (Burnhm n Anerson 2002). We onsiere nite moels with Δ i < 2 sustntilly supporte (Burnhm n Anerson 2002). We use Akike weights (w i ) to lulte eviene rtios (w 1 /w j ; Burnhm n Anerson 2002) to etermine the reltive likelihoo of eh nite moel (w j ) ompre with the highestrnke moel (w 1 ). We then lulte the reltive importne (w + (j)) of eh explntory vrile y summing the w i ross ll nite moels in whih tht vrile ourre (Burnhm n Anerson 2002). We use Person s orreltion oeffiients to lrify the iretion of the reltionship etween the highest-rnke ontinuous vriles n metolite onentrtions. We then use nlysis of ovrine (ANCOVA) with post ho Tukey s HSD tests to test for expliit ifferenes in metolite onentrtions mong the speies pture on Blok Isln in utumn We use reltive importne vlues s guie to etermine whih vriles (hours fter sunrise, te, lee time, n oy mss juste for oy size) to inlue s ovrites in ANCOVA. We then eliminte ovrites tht i not ontriute signifintly to the moel. We onute preliminry nlyses to etermine whether metolite onentrtions iffere etween yers in ll irs exept Hermit Thrush euse of smll smple sizes in Twoftor nlysis of vrine (ANOVA) with yer n speies s fixe vriles revele no ifferenes etween yers; therefore, we omine yers for ll susequent nlyses. Blee time ws not reore for ll irs in 2004 t KWRS; therefore, we etermine

4 J n u ry 2010 Fu e l Use n St o r g e in Mi g r t i n g P s s e r i n e s 111 whether lee time oul e exlue s n explntory vrile y lulting Person s orreltion oeffiients etween lee time n metolite onentrtions n ompring lee time mong sites n speies with two-wy ANOVA for ll other smples for whih lee time ws reore. Blee time ws not signifintly orrelte with TRIG (P = 0.81) or BUTY (P = 0.10) onentrtions, n verge lee time ws similr etween sites (F = 2.1, f = 1 n 58, P = 0.15) n mong speies (F = 0.1, f = 2 n 58, P = 0.91), presumly euse we limite our site-omprison t set y speies, time of y, n te. Our stuy esign for the etweensite omprison effetively ontrolle for te y limiting smpling to 4 ys eh yer. Thus, we eliminte lee time n te s potentil ovrites. We use n informtion-theoreti pproh (s esrie ove for within-site omprisons) to evlute the importne of site, speies, hours fter sunrise, n size-orrete oy mss for explining vrition in TRIG n BUTY onentrtions in irs pture t the 2 stopover sites. We then use two-wy ANOVA with site n speies s fixe ftors to test for expliit ifferenes in TRIG onentrtions etween sites. Heterogeneity of vrine of BUTY onentrtions etween sites for Hermit Thrush n etween speies t KWRS prelue the use of two-wy ANOVA to test for speifi site ifferenes. Thus, we use one-wy ANOVA to ompre BUTY onentrtions mong speies on BI n the Kruskl-Wllis test to ompre BUTY onentrtions mong speies t KWRS. We then use two-smple t-tests using the Stterthwite pproximtion for egrees of freeom when there ws unequl vrine etween speies or sites. Speies-speifi ifferenes in BUTY onentrtions etween sites were onsiere signifint t P = 0.017, tking into ount Bonferroni orretion for ompring 3 speies. We lulte perent presene (numer of plots present / totl plots 100) of eh fruiting plnt speies n presene of ripe fruit seprtely for eh site n yer for tulr representtion of plnt presene t. We use hi-squre tests (2 2 ontingeny tles) to ompre the frequeny of ourrene for eh fruiting plnt speies or ripe fruit etween sites. The TRIG, BUTY, n uri i onentrtions of irs pture on Blok Isln uring utumn 2005 evite from normlity. Therefore, we log (X + 1) trnsforme TRIG n BUTY, n we trnsforme uri i using the fourth root power trnsformtion, X (0.25), whih normlize the t. These trnsforme metolite onentrtions were use for ll within-site nlyses on Blok Isln. The BUTY onentrtions of irs pture t KWRS n on Blok Isln were log (X + 1) trnsforme n, onsequently, the t were normlly istriute for etween-site omprisons. All sttistil tests were lulte using SAS, version 9.1 (SAS Institute, Cry, North Crolin), with the signifine level set t P < Re s u lt s Vrition in plsm metolites of irs pture on Blok Isln. Speies, hours fter sunrise, n size-orrete oy mss were inlue in the highest-rnke moel explining vrition in plsm TRIG (see Tle 1 for rw metolite onentrtions use for within-site nlyses); however, 2 other moels lso h sustntil support, with Δ i < 2 (Tle 2). Reltive importne vlues suggeste tht speies n hours fter sunrise were more importnt thn te, lee time, n size-orrete oy mss for explining vrition in TRIG (Tle 3). Hours fter sunrise ws onsistently positively orrelte with TRIG ross speies (overll: r = 0.36, P < 0.001; Hermit Thrush: r = 0.47, P = 0.001; Yellow-rumpe Wrler: r = 0.43, P = 0.01; Gry Ctir: r = 0.39, P = 0.05; Re-eye Vireo: r = 0.21, P = 0.51; Zonotrihi: r = 0.60, P = 0.01; Drk-eye Juno: r = 0.38, P = 0.15; Blue-hee Vireo: r = 0.47, P = 0.12). The moel explining plsm BUTY onentrtions ws more omplex euse speies, hours fter sunrise, te, n lee time were inlue in the highest-rnke moel (Tle 2). In ition, there were 3 other moels with Δ i < 2, whih were only times less likely to explin more vrition thn the highest-rnke moel (Tle 2). Reltive importne vlues suggest tht speies, te, n lee time were more importnt thn hours fter sunrise n size-orrete oy mss (Tle 3). Dte ws negtively orrelte with BUTY, n orreltion oeffiients were vrile mong speies (overll: r = 0.17, P = 0.04; Hermit Thrush: r = 0.06, P = 0.69; Yellow-rumpe Wrler: r = 0.59, P < 0.001; Gry Ctir: r = 0.14, P = 0.50; Re-eye Vireo: r = 0.88, P < 0.001; Zonotrihi: r = 0.03, P = 0.90; Drk-eye Juno: r = 0.43, P = 0.10; Blue-hee Vireo: r = 0.18, P = 0.58). Blee time ws positively orrelte with BUTY, lthough the strength of this orreltion vrie onsierly mong speies (overll: r = 0.15, Tle 1. Cpture t n metolite onentrtions for migrtory irs smple on Blok Isln, Rhoe Isln, uring utumn Men (± SE) onentrtions of plsm triglyerie (TRIG), B-hyroxyutyrte (BUTY), n uri i (UA) re provie lthough trnsforme vlues were use in ll sttistil nlyses. Speies n Dte HAS Blee time Mss e TRIG (mm) BUTY (mm) UA (mm) Hermit Thrush ± ± ± ± ± ± 0.03 Gry Ctir ± ± ± ± ± ± 0.04 Yellow-rumpe Wrler ± ± ± ± ± ± 0.04 Re-eye Vireo ± ± ± ± ± ± 0.06 Zonotrihi ± ± ± ± ± ± 0.05 Drk-eye Juno ± ± ± ± ± ± 0.09 Blue-hee Vireo ± ± ± ± ± ± 0.09 Zonotrihi inlues White-throte Sprrow n White-rowne Sprrow. Rnge of ll pture tes for given speies. Dte = Julin te of pture, where 277 = 4 Otoer Men (± SE) hours fter sunrise t pture. Men (± SE) minutes etween net extrtion n loo smpling. e Men (± SE) oy mss (g) t loo smpling.

5 112 Sm i t h n MWilli m s Au k, Vo l. 127 Tle 2. Moel seletion results for the 5 highest-rnke nite moels tht explin vrition in plsm metolite onentrtions of irs smple on Blok Isln, Rhoe Isln, uring utumn Moels re rnke on the sis of Akike weights (w i ). Metolite n moel n K Mximize log e (L) AIC Δ i w i w 1 /w j Triglyerie Y = speies + HAS + mss Y = speies + HAS Y = speies + HAS + mss + te Y = speies + HAS + mss + t Y = speies + HAS + te B-hyroxyutyrte Y = speies + HAS + t + te Y = speies + HAS + mss + t + te Y = speies + t + te Y = speies + mss + t + te Y = speies + HAS + te Uri i Y = speies + te Y = speies + t + te Y = speies + mss + te Y = speies + HAS + te Y = speies + mss + t + te Prmeters: Y = trnsforme metolite onentrtions (see text), HAS = hours fter sunrise t pture, te = Julin te of pture, mss = resiuls from liner regression of oy mss n wing length, n t = time (min) etween net extrtion n loo smpling. Numer of estimle regression prmeters in moel inluing the interept n vrine. Clulte s: [ 0.5n*log e (RSS/n)], where RSS is the resiul sum of squres. Eviene rtio where w 1 = the highest-rnke moel. P = 0.06: Hermit Thrush: r = 0.29, P = 0.06; Yellow-rumpe Wrler: r = 0.03, P = 0.87; Gry Ctir: r = 0.40, P = 0.05; Re-eye Vireo: r = 0.01, P = 0.97; Zonotrihi: r = 0.55, P = 0.03; Drk-eye Juno: r = 0.12, P = 0.67; Blue-hee Vireo: r = 0.35, P = 0.27). Speies n te were inlue in the highest-rnke moel explining plsm uri i onentrtions (Tle 2). Moels tht inlue lee time or size-orrete oy mss lso h sustntil support. Reltive importne vlues lrifie tht speies n te were the most importnt vriles explining uri i onentrtions (Tle 3). However, we i not etet signifint orreltion etween te n uri i (overll: r = 0.09, P = 0.27; Hermit Thrush: r = 0.25, P = 0.12; Yellow-rumpe Wrler: r = 0.35, P = 0.10; Gry Ctir: r = 0.13, P = 0.59; Re-eye Vireo: r = 0.52, P = 0.08; Zonotrihi: r = 0.21, P = 0.43; Drk-eye Juno: r = 0.11, P = 0.67; Blue-hee Vireo: r = 0.40, P = 0.22). Tle 3. Reltive importne (w + (j)) of preitor vriles tht explin vrition in plsm metolite onentrtions of migrtory irs on Blok Isln, Rhoe Isln, uring utumn Moel set Speies HAS Dte Mss Blee time e Triglyerie B-hyroxyutyrte Uri i Trnsforme metolite onentrtions were use for nlyses (see text). Hours fter sunrise t pture. Julin te of pture. Resiuls from liner regression of oy mss n wing length. e Time (minutes) etween net extrtion n loo smpling. Hermit Thrush h higher TRIG onentrtions thn ll other speies fter ounting for hours fter sunrise (speies: F = 8.2, f = 6 n 157, P < 0.001; HAS: F = 35.8, f = 1 n 157, P < 0.001; Fig. 1). We etete signifint speies*te intertion for BUTY. If we restrite our t set to Otoer smples only when we pture 90% of iniviuls, this intertion ws no longer signifint. We foun signifint ifferenes in BUTY onentrtions mong speies pture uring Otoer while ontrolling for oth te n lee time (speies: F = 17.2, f = 6 n 140, P < 0.001; te: F = 14.0, f = 1 n 140, P < 0.001; lee time: F = 15.6, f = 1 n 140, P < 0.001). Yellow-rumpe Wrler h higher BUTY onentrtions thn ll other speies exept Zonotrihi spp. (Fig. 1), n Zonotrihi h higher BUTY onentrtions thn Hermit Thrush n Gry Ctir (Fig. 1). Zonotrihi, Drkeye Juno, n Blue-hee Vireo h higher onentrtions of uri i thn the other 4 speies fter orreting for te (speies: F = 25.0, f = 6 n 135, P < 0.001; te: F = 7.9, f = 1 n 135, P = 0.001; Fig. 1). Site ifferenes in plsm metolites. Site n speies were inlue in the highest-rnke moel explining vrition in plsm TRIG onentrtions (see Tle 4 for rw lipi metolite onentrtions use for etween-site nlyses); however, the moel tht inlue site, speies, n hours fter sunrise lso h sustntil support (Tle 5). Speies n site ifferenes were the most importnt vriles, n hours fter sunrise n oy mss were less importnt for explining vrition in TRIG onentrtions of irs pture t the 2 sites (Tle 6). Conentrtions of TRIG were higher in irs pture on Blok Isln thn in those from KWRS, n this ifferene n primrily e ttriute to higher TRIG onentrtions in Hermit Thrushes from Blok

6 J n u ry 2010 Fu e l Use n St o r g e in Mi g r t i n g P s s e r i n e s 113 Isln thn in those from KWRS (site: F = 6.7, f = 1 n 71, P = 0.01; speies: F = 3.3, f = 2 n 71, P = 0.04; site*speies: F = 3.1, f = 2 n 71, P = 0.05; Fig. 2). Speies n hours fter sunrise were inlue in the highestrnke moel explining vrition in plsm BUTY onentrtions, ut 2 other moels h sustntil support (Tle 5). Interspeifi ifferenes n hours fter sunrise h the highest reltive importne vlues, wheres site n oy mss were less importnt for explining vrition in plsm BUTY onentrtions of irs t the 2 stopover sites (Tle 6). Overll, BUTY onentrtions were similr etween sites (t = 1.0, f = 70, P = 0.33; Fig. 2). Hermit Thrushes h the lowest BUTY onentrtions of the 3 speies on Blok Isln (F = 13.6, f = 2 n 39, P < 0.001), ut there were no interspeifi ifferenes in BUTY onentrtions t KWRS (χ 2 = 0.4, f = 2, P = 0.84; Fig. 2). Site ifferenes in fruit vilility. In 2005, the following plnt speies tht proue fruits were more ommon on Blok Isln thn t KWRS: Arrowwoo Viurnum, Northern Byerry, Virgini Creeper, Blk Chokeerry, n Ros spp. (Tle 7). By ontrst, Common Greenrier n Europen Privet were less ommon on Blok Isln thn t KWRS (Tle 7). The following plnt speies more ommonly h ripe fruit on Blok Isln thn t KWRS: Arrowwoo Viurnum, Virgini Creeper, Blk Chokeerry, n Ros spp. (Tle 7). There were signifintly more fruits present on Common Greenrier n Europen Privet t KWRS thn on Blok Isln (Tle 7). Di s u s s i o n Fig. 1. Lest-squres (LS) mens (± SE) of plsm triglyerie (log [TRIG + 1]), B-hyroxyutyrte (log [BUTY + 1]), n uri i (UA 0.25 ) onentrtions fter orreting for signifint ovrites (see text) for migrtory psserine speies pture on Blok Isln, Rhoe Isln, in utumn Arevitions: HETH = Hermit Thrush, GRCA = Gry Ctir, YRWA = Yellow-rumpe Wrler, REVI = Re-eye Vireo, DEJU = Drk-eye Juno, n BHVI = Blue-hee Vireo. Zonotrihi inlues White-throte n White-rowne sprrows. Brs with ifferent letters within eh grph re signifintly ifferent. Our results emonstrte tht plsm lipi n protein metolites iffer mong speies of migrting songirs uring utumn migrtion, whih my e ttriutle, in prt, to interspeifi ifferenes in iet hits n fruit vilility t stopover sites. In ition, ftors suh s time of pture, time tken to lee the ir, n te my ffet iniviul plsm lipi n protein metolite onentrtions in ifferent wys. However, stnrize protools tht limit loo smpling to portion of the y or tht restrit smpling to ertin speies or perios of the migrtion seson will further minimize the influene of these potentilly onfouning vriles on plsm metolite onentrtions in free-living irs. Plsm triglyerie s n initor of fttening. Our results suggest tht plsm TRIG is likely the single most useful lipi metolite for ssessing fttening n fuel eposition in free-living migrtory irs. Plsm TRIG ws reltively unffete y most potentilly onfouning ftors ommon in fiel stuies, suh s time lg etween net extrtion n loo smpling or te of pture. Plsm TRIG vlues onsistently inrese with hours fter sunrise when irs were pture, n this positive reltionship etween time of y n TRIG hs een shown in mny speies of free-living psserines (Jenni n Jenni-Eiermnn 1996, Jenni- Eiermnn n Jenni 1997, Guglielmo et l. 2005). Conentrtions of TRIG inrese rpily in response to the onset of feeing fter sunrise n my eventully plteu (Jenni-Eiermnn n Jenni 1996, 1997). We i not etet suh plteu, lthough we only smple irs 6 h fter sunrise. Plsm TRIG onentrtions in our stuy inite tht fttening rtes of migrting songirs iffer mong speies n

7 114 Sm i t h n MWilli m s Au k, Vo l. 127 Tle 4. Cpture t n plsm metolite onentrtions for 3 migrtory speies pture on Blok Isln (BI) n t Kingston Willife Reserh Sttion (KWRS), Rhoe Isln, uring utumn 2004 n Speies Site n HAS Mss TRIG BUTY Hermit Thrush KWRS ± ± ± ± 0.59 BI ± ± ± ± 0.14 Yellow-rumpe Wrler KWRS ± ± ± ± 0.29 BI ± ± ± ± 0.21 White-throte Sprrow KWRS ± ± ± ± 0.30 BI ± ± ± ± 0.38 Men (± SE) hours fter sunrise t pture. Men (± SE) oy mss (grms) t loo smpling. Men (± SE) onentrtions (mm) of plsm triglyerie. Men (± SE) onentrtions (mm) of plsm B-hyroxyutyrte. Trnsforme vlues were use in ll nlyses (see text). Tle 5. Moel seletion results for the 5 highest-rnke nite moels tht explin vrition in plsm metolite onentrtions of irs smple on Blok Isln n t Kingston Willife Reserh Sttion, Rhoe Isln, uring utumn 2004 n Moels re rnke on the sis of Akike weights (w i ). Metolite n moel n K Mximize log e (L) AIC Δ i w i w 1 /w j Triglyerie Y = site + speies Y = site + speies + HAS Y = site + speies + mss Y = site + speies + HAS + mss Y = site B-hyroxyutyrte Y = speies + HAS Y = speies Y = site + speies + HAS Y = speies + HAS + mss Y = site + speies Prmeters: Y = metolite onentrtion (log [X + 1] trnsforme vlues were use for B-hyroxyutyrte nlyses), HAS = hours fter sunrise t pture, n mss = resiuls from liner regression of oy mss n wing length. Numer of estimtle regression prmeters in moel inluing the interept n vrine. Clulte s [ 0.5n*log e (RSS/n)], where RSS is the resiul sum of squres. Eviene rtio where w 1 = the highest-rnke moel. stopover sites, n these ifferenes my e relte to iet n qulity of foo resoures t stopover sites in ition to other speiesspeifi trits. For exmple, Hermit Thrush h the highest plsm TRIG onentrtions, n it is lso one the most frugivorous of the speies tht we stuie. However, Hermit Thrush is lso one of the heviest speies smple, n some previous stuies of songirs Tle 6. Reltive importne (w + (j)) of preitor vriles tht explin vrition in plsm metolite onentrtions of migrtory psserines pture on Blok Isln n t Kingston Willife Reserh Sttion, Rhoe Isln, in utumn 2004 n Moel set Site Speies HAS Mss Triglyerie B-hyroxyutyrte Hours fter sunrise t pture. Resiuls from liner regression of oy mss n wing length. Log (X + 1) onentrtions were use in nlyses. hve emonstrte positive reltionship etween plsm TRIG n oy mss (Guglielmo et l. 2005, Cersle n Guglielmo 2006) or ft mss (Smith n MWillims 2009). We foun tht oy mss ws only moertely relte to plsm TRIG ross speies even fter orreting for overll oy size, n visul estimtes of suutneous ft revele tht Hermit Thrush h verge ft sores ompre with other speies. Therefore, the higher TRIG onentrtions of Hermit Thrush in the present stuy re not likely ttriutle simply to the lrger overll oy size of this speies ompre with other, smller-oie speies. If the egree of sesonl frugivory is positively relte to plsm TRIG, Hermit Thrush shoul hve the highest TRIG, long with other primrily frugivorous speies (Yellow-rumpe Wrler, Re-eye Vireo, n Gry Ctir). However, these other speies i not hve TRIG levels s high s those in Hermit Thrush, whih suggests tht interspeifi ifferenes within site nnot e fully expline y iet hits. Further support for the importne of iet hits on plsm TRIG onentrtions is provie y our fining tht plsm TRIG ws higher in Hermit

8 J n u ry 2010 Fu e l Use n St o r g e in Mi g r t i n g P s s e r i n e s 115 Tle 7. Presene of 10 plnt speies (perent ourrene in twenty-four 4-m 2 plots) on Blok Isln (BI) n t Kingston Willife Reserh Sttion (KWRS), Rhoe Isln, n presene of ripe fruits (perent ourrene in the sme plots) of eh plnt speies uring Plnt presene (%) Fruit presene (%) Speies BI KWRS χ 2 BI KWRS χ 2 Arrowwoo Viurnum ** ** Northern Byerry ** Virgini Creeper ** ** Amerin Pokewee Blk Chokeerry * * Common Wintererry Orientl Bittersweet Common Greenrier *** * Ros spp *** *** Europen Privet *** *** *P < 0.05, **P < 0.01, ***P < 0.001; f = 0.05 n 1. Fig. 2. Men (± SE) plsm triglyerie (TRIG) n B-hyroxyutyrte (log [BUTY + 1]) onentrtions in Hermit Thrushes (HETH), Yellowrumpe Wrlers (YRWA), n White-throte Sprrows (WTSP) pture t Kingston Willife Reserh Sttion (soli rs) or on Blok Isln (hthe rs), Rhoe Isln, uring utumn migrtion, 2004 n Thrushes pture on Blok Isln, where high-qulity ntive fruits re unnt, thn in Hermit Thrushes pture t KWRS, where fruit vilility n qulity were muh lower. In ition, Hermit Thrushes pture on Blok Isln h higher plsm TRIG thn Yellow-rumpe Wrlers n White-throte Sprrows, n these interspeifi ifferenes were sent in irs pture t KWRS, where fruit ws less unnt. We reognize tht there re mny other ifferenes etween speies n our stuy sites, in ition to fruit resoures, tht my ontriute to vrition in plsm TRIG onentrtions. For exmple, Hermit Thrushes, White-throte Sprrows, Drk-eye Junos, n Yellow-rumpe Wrlers ll winter on Blok Isln to some extent (S. Comings pers. omm.); however, speies tht re stritly migrnts uring utumn on Blok Isln (Blue-hee Vireo n Re-eye Vireo) showe no extrorinry pttern of ft eposition. Gry Ctir is the only speies smple in our stuy tht is known to ree on Blok Isln (S. Comings pers. omm.), n plsm TRIG ws lowest in this speies, perhps euse some irs were not yet in migrtory stte. It is lso possile tht the fuel eposition rte ws influene y ge or sex (Woorey n Moore 1997, Yong et l. 1998, Jones et l. 2002, Heise n Moore 2003). Age is not likely n importnt ftor explining interspeifi vrition in fuel eposition rtes on Blok Isln, euse nerly ll irs pture were hth-yer. In generl, more oler irs re pture t KWRS thn on Blok Isln, ut this is not likely signifint ftor for Hermit Thrushes, most of whih pture t KWRS were hth-yer. Further, Drk-eye Juno ws the only speies in whih more mles thn femles were pture (mong iniviuls tht oul e relily sexe). Molt is proly irrelevnt to the interspeifi ifferenes in plsm metolites reporte here, euse most of the irs smple were just ompleting their presi molt n so were t reltively similr molt stges. In ition, plsm lipi metolites o not orrelte strongly with intensity of molt throughout the presi molting perio in migrtory songirs (Jenni-Eiermnn n Jenni 1996). Given tht iet n other interspeifi ifferenes my ontriute to vrition in plsm metolite onentrtion, suh interspeifi omprisons shoul e unertken with ution or limite to speies with very similr life histories, iet hits, n migrtion strtegies. Plsm B-hyroxyutyrte s n initor of ft tolism. The most vrile of the 3 metolites mesure in this stuy ws BUTY, n the most plusile explntory AIC moels inlue ovrites suh s lee time. The positive reltionship etween lee time n plsm BUTY onentrtions in irs pture in our stuy hs previously een esrie in free-living irs, though not onsistently ross ll stuies or speies (Jenni- Eiermnn n Jenni 1996; Guglielmo et l. 2002, 2005; Aeveo Semn et l. 2006). Given tht BUTY inreses rpily uring trnsitions etween physiologil sttes n short-term fsts uring the y (Jenni-Eiermnn n Jenni 1991, 1997; Jenni n Jenni- Eiermnn 1992), lee time is n importnt ovrite to mesure in stuies of free-living irs so tht its influene on metolite onentrtions n e resse. Plsm BUTY ws lso negtively relte to te of pture, lthough this reltionship ppere to e importnt in only few speies, like the Yellow-rumpe

9 116 Sm i t h n MWilli m s Au k, Vo l. 127 Wrler n the Re-eye Vireo. The effet of te on BUTY onentrtions in our stuy is iffiult to interpret euse smpling of given ir speies vrie through time. Our results suggest tht te will likely lwys e n importnt onfouning ftor in suh nlyses, euse mny ifferent speies migrte t ifferent times within given seson. Plsm BUTY ws ifferent mong ir speies pture on Blok Isln, even fter ontrolling for te n lee time, whih suggests tht itionl ftors influene BUTY onentrtions. Hermit Thrush n Gry Ctir re highly frugivorous, n they h the lowest BUTY onentrtions uring utumn migrtion on Blok Isln, where fruit ws unnt. However, other ifferenes etween speies were not lerly relte to iet. If BUTY is negtively ffete y fruit vilility, we woul expet plsm onentrtions to e higher t KWRS, where vilility of highenergy fruits, suh s Arrowwoo Viurnum, is lower thn on Blok Isln. However, site ws of reltively low importne for explining BUTY onentrtions, n the interspeifi ifferenes in BUTY mong irs pture on Blok Isln were not pprent t KWRS. We onlue tht BUTY is less onsistent initor of fuel eposition rtes thn TRIG in migrtory psserines euse of the mny itionl potentil soures of vrition. Plsm uri i s n initor of protein tolism. Plsm uri i onentrtions iffere sustntilly etween ir speies pture on Blok Isln. In generl, less frugivorous speies h higher onentrtions thn more frugivorous speies. Given tht plsm uri i ws positively relte to protein intke in previous stuies of ptive irs (Golstein et l. 2001, Smith et l. 2007), the lower onentrtions in free-living frugivorous irs my our euse most fruits hve less protein thn other ville foos (Smith et l. 2007). Plsm uri i ws lso influene, to lesser egree, y te of pture, lthough the ft tht there ws not signifint orreltion etween uri i n te of pture for ny of the speies suggests tht the reltionship etween these 2 vriles my e nonliner. If plsm uri i is relte to onsumption of high-protein inset resoures, this oul explin the eline in plsm uri i s utumn progresse n inset resoures eline. The effet of te is not strightforwr, euse most of our irs were pture lter in the seson, primrily euse of verse wether tht prelue mist netting on erlier tes. Uri i my e useful for stuies of free-living irs, euse it seems to relily inite ietry protein intke in ptive stuies n euse it ws less sensitive to other ftors like lee time, time of y, n oy mss. Implitions for hitt qulity n migrtion monitoring t stopover sites. Fruit vilility n influene the unne of frugivorous lnir speies n their use of speifi hitts uring utumn migrtion (Blke n Hoppes 1986, Mrtin n Krr 1986, Prrish 2000, Suthers et l. 2000, Roewl n Brittinghm 2004). Our t suggest tht highly frugivorous migrtory speies n refuel t fster rte when fruit iversity, qulity, n vilility re high, s emonstrte y higher plsm TRIG in irs pture on Blok Isln. The fruit resoures present t KWRS re ominte y few speies tht hve low energy ensity (e.g., Orientl Bittersweet) or tht re voie y migrting irs n persist into the winter (e.g., Europen Privet) more thn the ommon high-energy fruits (e.g., Arrowwoo Viurnum) foun in the mritime shruln hitt on Blok Isln. Therefore, these high-qulity fruit resoures my e useful initor of hitt qulity t stopover sites. However, stopover hitts must provie suffiient mounts of other foos, suh s insets, tht n e utilize y less frugivorous speies tht re unle to rely primrily on fruits uring utumn stopover. Plsm metolites n provie useful informtion out fuel eposition n resoure use of irs t migrtion stopover sites, provie tht severl importnt vriles re onsiere. Although plsm TRIG n BUTY n urtely inite ifferenes in mss hnge etween sites in fiel-pture irs (Guglielmo et l. 2005), we suggest tht plsm TRIG n uri i, ut not BUTY, re the est nites for use t ning n monitoring sttions. Within given stopover site, plsm TRIG n provie informtion out short-term fuel eposition in iniviuls, n uri i my provie informtion out reltive mounts of ietry protein in irs pture one. Further, we foun tht plsm TRIG n uri i were less sensitive to vrition in lee time thn BUTY. This is prtiulrly importnt when it is unfesile to ontinuously monitor nets to reor the ext time of pture. However, we stress tht minimizing the time etween net pture n lee time is ritil to ensuring tht plsm TRIG represents the feeing stte of iniviul irs. Plsm lipi metolites my relily inite fttening rtes of irs, lthough omprisons mong speies shoul e limite to speies with similr iet hits n to sesons when irs et similr foos, euse lrge ifferenes in ietry mronutrient omposition, prtiulrly sugr n protein ontent, my influene lipi metolite onentrtions (Smith et l. 2007, Smith n MWillims 2009). Given these potentil iet effets, plsm lipi metolites re likely to e most useful for proviing qulittive estimtes of the trjetory of ft eposition in iniviul free-living irs. Using suh metolites to quntittively estimte mount of ft eposition in free-living irs will require itionl stuies tht iretly mesure oth metolite onentrtions n tul ft eposition rtes in onjuntion with mesurements of ietry mronutrient intke. A k n o w l e g m e n t s We thnk S. Comings n the Nture Conservny for fiel support on Blok Isln. We re grteful to P. Pton, L. Du, D. Cooper, M. MEnroe, n A. Alreht for oopertion n ssistne with loo smpling n ning t Kingston Willife Reserh Sttion. Use of wil irs ws pprove uner University of Rhoe Isln Institutionl Animl Cre n Use Committee protool no. AN Funing ws provie y the Rhoe Isln Agriulturl Experiment Sttion, Sigm-Xi Grnts-in-Ai of Reserh to S.B.S., n Ntionl Siene Fountion grnt (IBN ) to S.R.M. This is ontriution 5213 of the University of Rhoe Isln Agriulturl Experiment Sttion. Literture Cite Ale, K. P The orienttion of psserine noturnl migrnts following offshore rift. Auk 94: Aeveo Semn, D. A., C. G. Guglielmo, R. W. Elner, n T. D. Willims Lnspe-sle physiology: Site ifferenes in

10 J n u ry 2010 Fu e l Use n St o r g e in Mi g r t i n g P s s e r i n e s 117 refueling rtes inite y plsm metolite nlysis in freeliving migrtory snpipers. Auk 123: Bir, J., n I. C. T. Niset Northwr fll migrtion on the Atlnti ost n its reltion to offshore rift. Auk 77: Birlein, F How to get ft: Nutritionl mehnisms of sesonl ft umultion in migrtory songirs. Nturwissenshften 89:1 10. Birlein, F., n E. Gwinner Nutritionl mehnisms n temporl ontrol of migrtory energy umultion in irs. Annul Review of Nutrition 14: Birlein, F., n D. Simons Nutritionl pttions in migrting irs. Isrel Journl of Zoology 41: Biy, C. J., n R. E. Green Autumn migrtion strtegies of Ree n Sege wrlers. Ornis Sninvi 12:1 12. Blke, J. G., n W. G. Hoppes Influene of resoure unne on use of tree-fll gps y irs in n isolte woolot. Auk 103: Blem, C. R The energetis of migrtion. Pges in Animl Migrtion, Orienttion, n Nvigtion (S. A. Guthreux, Jr., E.). Aemi Press, New York. Bonter, D. N., T. M. Donovn, n E. W. Brooks Dily mss hnges in lnirs uring migrtion stopover on the south shore of Lke Ontrio. Auk 124: Burnhm, K. P., n D. R. Anerson Moel Seletion n Multimoel Inferene: A Prtil Informtion-Theoreti Approh, 2n e. Springer-Verlg, New York. Cersle, D. J., n C. G. Guglielmo Dietry effets on preition of oy mss hnges in irs y plsm metolites. Auk 123: Connell, C. E., E. P. Oum, n H. Kle Ft-free weights of irs. Auk 77:1 9. Dunn, E. H Temporl n sptil ptterns in ily mss gin of Mgnoli Wrlers uring migrtory stopover. Auk 117: Dunn, E. H A ross-cn omprison of mss hnge in irs uring migrtion stopover. Wilson Bulletin 114: Golstein, D. L., L. Guntle, n C. Flugher Renl response to ietry protein in the House Sprrow Psser omestius. Physiologil n Biohemil Zoology 74: Guglielmo, C. G., D. J. Cersle, n C. Elermire A fiel vlition of plsm metolite profiling to ssess refueling performne of migrtory irs. Physiologil n Biohemil Zoology 78: Guglielmo, C. G., P. D. O Hr, n T. D. Willims Extrinsi n intrinsi soures of vrition in plsm lipi metolites of free-living Western Snpipers (Cliris muri). Auk 119: Heise, C. D., n F. R. Moore Age-relte ifferenes in forging effiieny, molt, n ft eposition of Gry Ctirs prior to utumn migrtion. Conor 105: Jenni, L., n S. Jenni-Eiermnn Metoli ptterns of feeing, overnight fste n flying night migrnts uring utumn migrtion. Ornis Sninvi 23: Jenni, L., n S. Jenni-Eiermnn Metoli responses to iurnl feeing ptterns uring the postreeing, moulting n migrtory perios in psserine irs. Funtionl Eology 10: Jenni, L., n R. Shwilh Plsm metolite levels inite hnge in oy mss in Ree Wrlers Aroephlus sirpeus. Avin Siene 1: Jenni-Eiermnn, S., n L. Jenni Metoli responses to flight n fsting in night-migrting psserines. Journl of Comprtive Physiology B 161: Jenni-Eiermnn, S., n L. Jenni Plsm metolite levels preit iniviul oy-mss hnges in smll long-istne migrnt, the Gren Wrler. Auk 111: Jenni-Eiermnn, S., n L. Jenni Metoli ifferenes etween the postreeing, moulting n migrtory perios in feeing n fsting psserine irs. Funtionl Eology 10: Jenni-Eiermnn, S., n L. Jenni Diurnl vrition of metoli responses to short-term fsting in psserine irs uring the postreeing, molting n migrtory perio. Conor 99: Jones, J., C. M. Frnis, M. Drew, S. Fuller, n M. W. S. Ng Age-relte ifferenes in oy mss n rtes of mss gin of psserines uring utumn migrtory stopover. Conor 104: Mrtin, T. E., n J. R. Krr Pth-utiliztion y migrting irs: Resoure oriente? Ornis Sninvi 17: Prrish, J. D Ptterns of frugivory n energeti onition in Nerti lnirs uring utumn migrtion. Conor 99: Prrish, J. D Behviorl, energeti, n onservtion implitions of forging plstiity uring migrtion. Pges in Stopover Eology of Nerti Neotropil Lnir Migrnts: Hitt Reltions n Conservtion Implitions (F. R. Moore, E.). Stuies in Avin Biology, no. 20. Reinert, S. E., E. Lphm, n K. Gffett Lnir migrtion on Blok Isln: Community omposition n onservtion implitions for n isln stopover hitt. Pges in The Eology of Blok Isln: Proeeings of the Rhoe Isln Nturl History Survey Conferene, Otoer 28, 2000 (P. W. Pton, L. L. Goul, P. V. August, n A. O. Frost, Es.). Rhoe Isln Nturl History Survey, Kingston. Roewl, P. G., n M. C. Brittinghm Stopover hitts of lnirs uring fll: Use of ege-ominte n erlysuessionl forests. Auk 121: Shu, M., n L. Jenni Fuel eposition of three psserine ir speies long the migrtion route. Oeologi 122: Shu, M., n L. Jenni Stopover urtions of three wrler speies long their utumn migrtion route. Oeologi 128: Shu, M., n L. Jenni Vrition of fuelling rtes mong sites, ys n iniviuls in migrting psserine irs. Funtionl Eology 15: Semn, D. A., C. G. Guglielmo, n T. D. Willims Effets of physiologil stte, mss hnge n iet on plsm metolite profiles in the Western Snpiper Cliris muri. Journl of Experimentl Biology 208: Smith, S. B., K. H. MPherson, J. M. Bker, B. J. Piere, D. W. Polesk, n S. R. MWillims Fruit qulity n onsumption y songirs uring utumn migrtion. Wilson Journl of Ornithology 119: Smith, S. B., n S. R. MWillims Dietry mronutrients ffet lipi metolites n oy omposition of migrtory psserine, the White-throte Sprrow (Zonotrihi liollis). Physiologil n Biohemil Zoology 82:

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

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

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

Appendix A: HVAC Equipment Efficiency Tables

Appendix A: HVAC Equipment Efficiency Tables Appenix A: HVAC Equipment Effiieny Tles Figure A.1 Resientil Centrl Air Conitioner FEMP Effiieny Reommention Prout Type Reommene Level Best Aville 11.0 or more EER 14.6 EER Split Systems 13.0 or more SEER

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

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

Counting Paths Between Vertices. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs

Counting Paths Between Vertices. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs Isomorphism of Grphs Definition The simple grphs G 1 = (V 1, E 1 ) n G = (V, E ) re isomorphi if there is ijetion (n oneto-one n onto funtion) f from V 1 to V with the property tht n re jent in G 1 if

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

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

Statistics in medicine

Statistics in medicine Sttistis in meiine Workshop 1: Sreening n ignosti test evlution Septemer 22, 2016 10:00 AM to 11:50 AM Hope 110 Ftm Shel, MD, MS, MPH, PhD Assistnt Professor Chroni Epiemiology Deprtment Yle Shool of Puli

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

Surds and Indices. Surds and Indices. Curriculum Ready ACMNA: 233,

Surds and Indices. Surds and Indices. Curriculum Ready ACMNA: 233, Surs n Inies Surs n Inies Curriulum Rey ACMNA:, 6 www.mthletis.om Surs SURDS & & Inies INDICES Inies n surs re very losely relte. A numer uner (squre root sign) is lle sur if the squre root n t e simplifie.

More information

Now we must transform the original model so we can use the new parameters. = S max. Recruits

Now we must transform the original model so we can use the new parameters. = S max. Recruits MODEL FOR VARIABLE RECRUITMENT (ontinue) Alterntive Prmeteriztions of the pwner-reruit Moels We n write ny moel in numerous ifferent ut equivlent forms. Uner ertin irumstnes it is onvenient to work with

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

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

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

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

Weed Management in Strawberry

Weed Management in Strawberry Wee Siene Wee Mngement in Strwerry Prinipl Investigtor Dr. Steven Fennimore Coopertive Extension Wee Speilist Dept. of Plnt Sienes University of Cliforni, Dvis USDA Agriulturl Reserh Sttion 1636 Est Alisl

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

Algebra 2 Semester 1 Practice Final

Algebra 2 Semester 1 Practice Final Alger 2 Semester Prtie Finl Multiple Choie Ientify the hoie tht est ompletes the sttement or nswers the question. To whih set of numers oes the numer elong?. 2 5 integers rtionl numers irrtionl numers

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

MCH T 111 Handout Triangle Review Page 1 of 3

MCH T 111 Handout Triangle Review Page 1 of 3 Hnout Tringle Review Pge of 3 In the stuy of sttis, it is importnt tht you e le to solve lgeri equtions n tringle prolems using trigonometry. The following is review of trigonometry sis. Right Tringle:

More information

18.06 Problem Set 4 Due Wednesday, Oct. 11, 2006 at 4:00 p.m. in 2-106

18.06 Problem Set 4 Due Wednesday, Oct. 11, 2006 at 4:00 p.m. in 2-106 8. Problem Set Due Wenesy, Ot., t : p.m. in - Problem Mony / Consier the eight vetors 5, 5, 5,..., () List ll of the one-element, linerly epenent sets forme from these. (b) Wht re the two-element, linerly

More information

Eigenvectors and Eigenvalues

Eigenvectors and Eigenvalues MTB 050 1 ORIGIN 1 Eigenvets n Eigenvlues This wksheet esries the lger use to lulte "prinipl" "hrteristi" iretions lle Eigenvets n the "prinipl" "hrteristi" vlues lle Eigenvlues ssoite with these iretions.

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

Analysis of Temporal Interactions with Link Streams and Stream Graphs

Analysis of Temporal Interactions with Link Streams and Stream Graphs Anlysis of Temporl Intertions with n Strem Grphs, Tiphine Vir, Clémene Mgnien http:// ltpy@ LIP6 CNRS n Soronne Université Pris, Frne 1/23 intertions over time 0 2 4 6 8,,, n for 10 time units time 2/23

More information

Momentum and Energy Review

Momentum and Energy Review Momentum n Energy Review Nme: Dte: 1. A 0.0600-kilogrm ll trveling t 60.0 meters per seon hits onrete wll. Wht spee must 0.0100-kilogrm ullet hve in orer to hit the wll with the sme mgnitue of momentum

More information

Necessary and sucient conditions for some two. Abstract. Further we show that the necessary conditions for the existence of an OD(44 s 1 s 2 )

Necessary and sucient conditions for some two. Abstract. Further we show that the necessary conditions for the existence of an OD(44 s 1 s 2 ) Neessry n suient onitions for some two vrile orthogonl esigns in orer 44 C. Koukouvinos, M. Mitrouli y, n Jennifer Seerry z Deite to Professor Anne Penfol Street Astrt We give new lgorithm whih llows us

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

for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx

for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx Applitions of Integrtion Are of Region Between Two Curves Ojetive: Fin the re of region etween two urves using integrtion. Fin the re of region etween interseting urves using integrtion. Desrie integrtion

More information

ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY

ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY ER 316: REIO EGIEERIG HER 3 RE LWS & SOIHIOMERY 1 OULIE R 1: Rte Lws Reltive Rtes of Retion Retion Orer & Rte Lw Retion Rte onstnt, k R 2: Stoihiometry th System Stoihiometri le low System Stoihiometri

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

CARLETON UNIVERSITY. 1.0 Problems and Most Solutions, Sect B, 2005

CARLETON UNIVERSITY. 1.0 Problems and Most Solutions, Sect B, 2005 RLETON UNIVERSIT eprtment of Eletronis ELE 2607 Swithing iruits erury 28, 05; 0 pm.0 Prolems n Most Solutions, Set, 2005 Jn. 2, #8 n #0; Simplify, Prove Prolem. #8 Simplify + + + Reue to four letters (literls).

More information

Lesson 2.1 Inductive Reasoning

Lesson 2.1 Inductive Reasoning Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, 2. 400, 200, 100, 50, 25,, 3. 1 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2,

More information

Lecture 2: Cayley Graphs

Lecture 2: Cayley Graphs Mth 137B Professor: Pri Brtlett Leture 2: Cyley Grphs Week 3 UCSB 2014 (Relevnt soure mteril: Setion VIII.1 of Bollos s Moern Grph Theory; 3.7 of Gosil n Royle s Algeri Grph Theory; vrious ppers I ve re

More information

Solutions for HW9. Bipartite: put the red vertices in V 1 and the black in V 2. Not bipartite!

Solutions for HW9. Bipartite: put the red vertices in V 1 and the black in V 2. Not bipartite! Solutions for HW9 Exerise 28. () Drw C 6, W 6 K 6, n K 5,3. C 6 : W 6 : K 6 : K 5,3 : () Whih of the following re iprtite? Justify your nswer. Biprtite: put the re verties in V 1 n the lk in V 2. Biprtite:

More information

Lesson 2.1 Inductive Reasoning

Lesson 2.1 Inductive Reasoning Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, 2. 400, 200, 100, 50, 25,, 3. 1 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2,

More information

Technology Mapping Method for Low Power Consumption and High Performance in General-Synchronous Framework

Technology Mapping Method for Low Power Consumption and High Performance in General-Synchronous Framework R-17 SASIMI 015 Proeeings Tehnology Mpping Metho for Low Power Consumption n High Performne in Generl-Synhronous Frmework Junki Kwguhi Yukihie Kohir Shool of Computer Siene, the University of Aizu Aizu-Wkmtsu

More information

2.4 Theoretical Foundations

2.4 Theoretical Foundations 2 Progrmming Lnguge Syntx 2.4 Theoretil Fountions As note in the min text, snners n prsers re se on the finite utomt n pushown utomt tht form the ottom two levels of the Chomsky lnguge hierrhy. At eh level

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

H SERIES. Algebra Basics. Algebra Basics. Solutions. Curriculum Ready.

H SERIES. Algebra Basics. Algebra Basics. Solutions. Curriculum Ready. Alger Bsis H SERIES Alger Bsis Curriulum Rey www.mthletis.om Copyright 009 P Lerning. All rights reserve. First eition printe 009 in Austrli. A tlogue reor for this ook is ville from P Lerning Lt. ISBN

More information

I 3 2 = I I 4 = 2A

I 3 2 = I I 4 = 2A ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents

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

The Stirling Engine: The Heat Engine

The Stirling Engine: The Heat Engine Memoril University of Newfounln Deprtment of Physis n Physil Oenogrphy Physis 2053 Lortory he Stirling Engine: he Het Engine Do not ttempt to operte the engine without supervision. Introution Het engines

More information

10.7 Assessment criteria for the individual investigation

10.7 Assessment criteria for the individual investigation Unit 6 Prtil Biology n Investigtive Skills 10.7 for the iniviul investigtion Reserh n rtionle There is some ttempt to provie rtionle for the hoie of investigtion in terms of its sope n its reltion to iologil

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

The DOACROSS statement

The DOACROSS statement The DOACROSS sttement Is prllel loop similr to DOALL, ut it llows prouer-onsumer type of synhroniztion. Synhroniztion is llowe from lower to higher itertions sine it is ssume tht lower itertions re selete

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

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

J. Environ. Sci. & Natural Resources, 4(2): 83-87, 2011 ISSN

J. Environ. Sci. & Natural Resources, 4(2): 83-87, 2011 ISSN J. Environ. Si. & Nturl Resoures, 4(2): 83-87, 2011 ISSN 1999-7361 Totl Nutrient Uptke y Grin plus Strw n Eonomi of Fertilizer Use of Rie Muttion STL-655 Grown uner Boro Seson in Sline Are M. H. Kir, N.

More information

Probability The Language of Chance P(A) Mathletics Instant Workbooks. Copyright

Probability The Language of Chance P(A) Mathletics Instant Workbooks. Copyright Proility The Lnguge of Chne Stuent Book - Series L-1 P(A) Mthletis Instnt Workooks Copyright Proility The Lnguge of Chne Stuent Book - Series L Contents Topis Topi 1 - Lnguge of proility Topi 2 - Smple

More information

MATH 122, Final Exam

MATH 122, Final Exam MATH, Finl Exm Winter Nme: Setion: You must show ll of your work on the exm pper, legily n in etil, to reeive reit. A formul sheet is tthe.. (7 pts eh) Evlute the following integrls. () 3x + x x Solution.

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

Section 2.1 Special Right Triangles

Section 2.1 Special Right Triangles Se..1 Speil Rigt Tringles 49 Te --90 Tringle Setion.1 Speil Rigt Tringles Te --90 tringle (or just 0-60-90) is so nme euse of its ngle mesures. Te lengts of te sies, toug, ve very speifi pttern to tem

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

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

SIMPLE NONLINEAR GRAPHS

SIMPLE NONLINEAR GRAPHS S i m p l e N o n l i n e r G r p h s SIMPLE NONLINEAR GRAPHS www.mthletis.om.u Simple SIMPLE Nonliner NONLINEAR Grphs GRAPHS Liner equtions hve the form = m+ where the power of (n ) is lws. The re lle

More information

UNCORRECTED SAMPLE PAGES. surds NUMBER AND ALGEBRA

UNCORRECTED SAMPLE PAGES. surds NUMBER AND ALGEBRA Chpter Wht you will lern A Irrtionl numers n surs (0A) B Aing n sutrting surs (0A) C Multiplying n iviing surs (0A) D Binomil prouts (0A) E Rtionlising the enomintor (0A) F Review of inex lws (Consoliting)

More information

Let s divide up the interval [ ab, ] into n subintervals with the same length, so we have

Let s divide up the interval [ ab, ] into n subintervals with the same length, so we have III. INTEGRATION Eonomists seem muh more intereste in mrginl effets n ifferentition thn in integrtion. Integrtion is importnt for fining the epete vlue n vrine of rnom vriles, whih is use in eonometris

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

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

CSE 332. Sorting. Data Abstractions. CSE 332: Data Abstractions. QuickSort Cutoff 1. Where We Are 2. Bounding The MAXIMUM Problem 4

CSE 332. Sorting. Data Abstractions. CSE 332: Data Abstractions. QuickSort Cutoff 1. Where We Are 2. Bounding The MAXIMUM Problem 4 Am Blnk Leture 13 Winter 2016 CSE 332 CSE 332: Dt Astrtions Sorting Dt Astrtions QuikSort Cutoff 1 Where We Are 2 For smll n, the reursion is wste. The onstnts on quik/merge sort re higher thn the ones

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

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 BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals

AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals AP Clulus BC Chpter 8: Integrtion Tehniques, L Hopitl s Rule nd Improper Integrls 8. Bsi Integrtion Rules In this setion we will review vrious integrtion strtegies. Strtegies: I. Seprte the integrnd into

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

5. Every rational number have either terminating or repeating (recurring) decimal representation.

5. Every rational number have either terminating or repeating (recurring) decimal representation. CHAPTER NUMBER SYSTEMS Points to Rememer :. Numer used for ounting,,,,... re known s Nturl numers.. All nturl numers together with zero i.e. 0,,,,,... re known s whole numers.. All nturl numers, zero nd

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

Applied. Grade 9 Assessment of Mathematics. Multiple-Choice Items. Winter 2005

Applied. Grade 9 Assessment of Mathematics. Multiple-Choice Items. Winter 2005 Applie Gre 9 Assessment of Mthemtis Multiple-Choie Items Winter 2005 Plese note: The formt of these ooklets is slightly ifferent from tht use for the ssessment. The items themselves remin the sme. . Multiple-Choie

More information

Particle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 3 : Interaction by Particle Exchange and QED. Recap

Particle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 3 : Interaction by Particle Exchange and QED. Recap Prtile Physis Mihelms Term 2011 Prof Mrk Thomson g X g X g g Hnout 3 : Intertion y Prtile Exhnge n QED Prof. M.A. Thomson Mihelms 2011 101 Rep Working towrs proper lultion of ey n sttering proesses lnitilly

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

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx Clulus Chet Sheet Integrls Definitions Definite Integrl: Suppose f ( ) is ontinuous Anti-Derivtive : An nti-derivtive of f ( ) on [, ]. Divide [, ] into n suintervls of is funtion, F( ), suh tht F = f.

More information

Automata and Regular Languages

Automata and Regular Languages Chpter 9 Automt n Regulr Lnguges 9. Introution This hpter looks t mthemtil moels of omputtion n lnguges tht esrie them. The moel-lnguge reltionship hs multiple levels. We shll explore the simplest level,

More information

Calibrating In-field Diagnostic Tools to Improve Nitrogen Management for High Yield and High Protein Wheat in the Sacramento Valley

Calibrating In-field Diagnostic Tools to Improve Nitrogen Management for High Yield and High Protein Wheat in the Sacramento Valley 2013-2014 Reserh Report to the Cliforni Whet Commission Clirting In-fiel Dignosti Tools to Improve Nitrogen Mngement for High Yiel n High Protein Whet in the Srmento Vlley PI: Mrk Luny, UC Coopertive Extension

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

Bivariate drought analysis using entropy theory

Bivariate drought analysis using entropy theory Purue University Purue e-pus Symposium on Dt-Driven Approhes to Droughts Drought Reserh Inititive Network -3- Bivrite rought nlysis using entropy theory Zengho Ho exs A & M University - College Sttion,

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

Chapter 8 Roots and Radicals

Chapter 8 Roots and Radicals Chpter 8 Roots nd Rdils 7 ROOTS AND RADICALS 8 Figure 8. Grphene is n inredily strong nd flexile mteril mde from ron. It n lso ondut eletriity. Notie the hexgonl grid pttern. (redit: AlexnderAIUS / Wikimedi

More information

Chem Homework 11 due Monday, Apr. 28, 2014, 2 PM

Chem Homework 11 due Monday, Apr. 28, 2014, 2 PM Chem 44 - Homework due ondy, pr. 8, 4, P.. . Put this in eq 8.4 terms: E m = m h /m e L for L=d The degenery in the ring system nd the inresed sping per level (4x bigger) mkes the sping between the HOO

More information

Phylogenies via Quartets

Phylogenies via Quartets Phylogenies vi Qurtets Dvi Brynt rynt@mth.mgill. LIRMM, Frne CRM, U. e M. U. Cnterury MGill University Bite-size trees There is only one unroote tree for one, two or three tx... But there re four unroote

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

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

Engr354: Digital Logic Circuits

Engr354: Digital Logic Circuits Engr354: Digitl Logi Ciruits Chpter 4: Logi Optimiztion Curtis Nelson Logi Optimiztion In hpter 4 you will lern out: Synthesis of logi funtions; Anlysis of logi iruits; Tehniques for deriving minimum-ost

More information

Note 12. Introduction to Digital Control Systems

Note 12. Introduction to Digital Control Systems Note Introduction to Digitl Control Systems Deprtment of Mechnicl Engineering, University Of Ssktchewn, 57 Cmpus Drive, Ssktoon, SK S7N 5A9, Cnd . Introduction A digitl control system is one in which the

More information

APPROXIMATION AND ESTIMATION MATHEMATICAL LANGUAGE THE FUNDAMENTAL THEOREM OF ARITHMETIC LAWS OF ALGEBRA ORDER OF OPERATIONS

APPROXIMATION AND ESTIMATION MATHEMATICAL LANGUAGE THE FUNDAMENTAL THEOREM OF ARITHMETIC LAWS OF ALGEBRA ORDER OF OPERATIONS TOPIC 2: MATHEMATICAL LANGUAGE NUMBER AND ALGEBRA You shoul unerstn these mthemtil terms, n e le to use them ppropritely: ² ition, sutrtion, multiplition, ivision ² sum, ifferene, prout, quotient ² inex

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

Conservation Law. Chapter Goal. 6.2 Theory

Conservation Law. Chapter Goal. 6.2 Theory Chpter 6 Conservtion Lw 6.1 Gol Our long term gol is to unerstn how mthemticl moels re erive. Here, we will stuy how certin quntity chnges with time in given region (sptil omin). We then first erive the

More information

Decision-making with multiple alternatives

Decision-making with multiple alternatives Deision-mking with multiple lterntives Anne K Churhln, Roozeh Kini & Mihel N Shlen 28 Nture Pulishing Group http://www.nture.om/ntureneurosiene Simple pereptul tsks hve li the grounwork for unerstning

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

A Primer on Continuous-time Economic Dynamics

A Primer on Continuous-time Economic Dynamics Eonomis 205A Fll 2008 K Kletzer A Primer on Continuous-time Eonomi Dnmis A Liner Differentil Eqution Sstems (i) Simplest se We egin with the simple liner first-orer ifferentil eqution The generl solution

More information

Mid-Term Examination - Spring 2014 Mathematical Programming with Applications to Economics Total Score: 45; Time: 3 hours

Mid-Term Examination - Spring 2014 Mathematical Programming with Applications to Economics Total Score: 45; Time: 3 hours Mi-Term Exmintion - Spring 0 Mthemtil Progrmming with Applitions to Eonomis Totl Sore: 5; Time: hours. Let G = (N, E) e irete grph. Define the inegree of vertex i N s the numer of eges tht re oming into

More information

b a wt ccd8 dad2 Secondary branches 15 e cd normal low b 2

b a wt ccd8 dad2 Secondary branches 15 e cd normal low b 2 A 3 1 Shoot mss (g) B Root mss (g) C 8 Primry rnhes D 8 Seonry rnhes 1 e E 8 Shoot mss/rnhes norml low 1 F 8 8 Shoot mss/root mss 8 8 Supplementl Figure 1 Aitionl phenotypi t reore from the plnts esrie

More information

TIME-VARYING AND NON-LINEAR DYNAMICAL SYSTEM IDENTIFICATION USING THE HILBERT TRANSFORM

TIME-VARYING AND NON-LINEAR DYNAMICAL SYSTEM IDENTIFICATION USING THE HILBERT TRANSFORM Proeeings of ASME VIB 5: th Biennil Conferene on Mehnil Virtion n Noise Septemer 4-8, 5 Long Beh, CA, USA DETC5-84644 TIME-VARYING AND NON-LINEAR DYNAMICAL SYSTEM IDENTIFICATION USING THE HILBERT TRANSFORM

More information

Trigonometry Revision Sheet Q5 of Paper 2

Trigonometry Revision Sheet Q5 of Paper 2 Trigonometry Revision Sheet Q of Pper The Bsis - The Trigonometry setion is ll out tringles. We will normlly e given some of the sides or ngles of tringle nd we use formule nd rules to find the others.

More information

Grade 6. Mathematics. Student Booklet SPRING 2008 RELEASED ASSESSMENT QUESTIONS. Assessment of Reading,Writing and Mathematics, Junior Division

Grade 6. Mathematics. Student Booklet SPRING 2008 RELEASED ASSESSMENT QUESTIONS. Assessment of Reading,Writing and Mathematics, Junior Division Gre 6 Assessment of Reing,Writing n Mthemtis, Junior Division Stuent Booklet Mthemtis SPRING 2008 RELEASED ASSESSMENT QUESTIONS Plese note: The formt of these ooklets is slightly ifferent from tht use

More information

Lecture 8: Abstract Algebra

Lecture 8: Abstract Algebra Mth 94 Professor: Pri Brtlett Leture 8: Astrt Alger Week 8 UCSB 2015 This is the eighth week of the Mthemtis Sujet Test GRE prep ourse; here, we run very rough-n-tumle review of strt lger! As lwys, this

More information

The GATE frame. GATE Graphic Approach To Epidemiology. GATE study design (PECOT) GATE study application. GATE study appraisal (RAMMbo)

The GATE frame. GATE Graphic Approach To Epidemiology. GATE study design (PECOT) GATE study application. GATE study appraisal (RAMMbo) GA Grphi Approh o piemiology he GA frme Grphi Apprisl ool for piemiology Grphi Arhiteturl ool for piemiology the shpe of every epiemiologil stuy GA stuy esign () GA stuy nlyses (G & G) G G GA stuy pprisl

More information

F / x everywhere in some domain containing R. Then, + ). (10.4.1)

F / x everywhere in some domain containing R. Then, + ). (10.4.1) 0.4 Green's theorem in the plne Double integrls over plne region my be trnsforme into line integrls over the bounry of the region n onversely. This is of prtil interest beuse it my simplify the evlution

More information

Electronic Circuits I Revision after midterm

Electronic Circuits I Revision after midterm Eletroni Ciruits I Revision fter miterm Dr. Ahme ElShfee, ACU : Fll 2018, Eletroni Ciruits I -1 / 14 - MCQ1 # Question If the frequeny of the input voltge in Figure 2 36 is inrese, the output voltge will

More information

CH 17: Flexible Mechanical Elements

CH 17: Flexible Mechanical Elements CH 17: lexible Mehnil Elements lexible mehnil elements (belts, hins, ropes re use in onveying systems n to trnsmit power over long istnes (inste of using shfts n gers. The use of flexible elements simplifies

More information