Evolutionary responses of invasive grass species to variation in precipitation and soil nitrogen

Size: px
Start display at page:

Download "Evolutionary responses of invasive grass species to variation in precipitation and soil nitrogen"

Transcription

1 Journl of Ecology 216, 4, doi:.1111/ Evolutionry responses of invsive grss species to vrition in precipittion nd soil nitrogen Monic A. Nguyen 1 *, Amy E. Orteg 1, Kurt Q. Nguyen 1, Srh Kimll 2, Michel L. Goulden 3 nd Jennifer L. Funk 1 1 Schmid College of Science nd Technology, Chpmn University, Ornge, CA, USA; 2 Center for Environmentl Biology, University of Cliforni, Irvine, CA, USA; nd 3 Deprtment of Erth System Science, University of Cliforni, Irvine, CA, USA Summry 1. Glol climte models suggest tht mny ecosystems will experience reduced precipittion over the next century nd the consequences for invsive plnt performnce re lrgely unknown. Annul invsive species my e le to quickly evolve trits ssocited with drought escpe or tolernce through rpid genetic chnges. 2. We investigted the influence of 5 yers of wter nd nitrogen mnipultions on trit vlues in southern Cliforni grsslnd system. Seeds from two nnul grss species (Aven rt nd Bromus mdritensis) were collected from experimentl plots nd grown in common environment over two genertions. We mesured 14 physiologicl, morphologicl, phenologicl nd reproductive trits. 3. Both species displyed phenotypic differences depending on the wter tretment from which they were collected, ut not depending on the nitrogen tretment. Both species displyed trit vlues chrcteristic of drought escpe (e.g. erlier flowering in A. rt nd B. mdritensis, lower wter-use efficiency in B. mdritensis) when grown from the seeds collected from plots tht experienced five yers of reduced precipittion. Furthermore, A. rt individuls grown from the seeds collected from drought plots hd higher reproductive output nd higher photosynthetic performnce thn individuls grown from wter ddition plots, with individuls grown from mient plots displying intermedite trit vlues. Notly, we found no phenotypic vrition mong tretments for six root trits. 4. Synthesis. Trit differences were oserved following two genertions in common grden, suggesting tht tretment differences were geneticlly sed. This suggests tht popultions were responding to selection over the 5 yers of wter mnipultions, remrkly short time period. The rpid evolutionry responses oserved here my help these two widespred invsive grss species thrive under reduced precipittion scenrios, which could hve importnt implictions for fire dynmics, invsive species mngement nd ntive plnt restortion in communities invded y nnul grsses. Key-words: nnul species, Aven rt, Bromus mdritensis, drought escpe invsion ecology, invsive species, phenology, photosynthesis, root trits, wter-use efficiency Introduction Glol chnge, including increses in temperture, tmospheric CO 2 concentrtion nd nitrogen (N) input from nthropogenic ctivities, is one of the most significnt threts to nturl ecosystems. Further, glol climte models hve predicted the ltertions in inter- nd intr-nnul precipittion in mny regions (Melillo, Richmond & Yohe 214). *Correspondence uthor: E-mil: nguyen.n.monic@gmil.com Biologicl invsion is nother importnt gent of glol chnge with significnt effects on glol iodiversity (Millennium Ecosystem Assessment, 25). A met-nlysis of 41 cses of invsion found tht lien invsive plnts decrese the undnce nd diversity of ntive resident plnt species y 43.5% nd 5.7%, respectively (Vil et l. 2). Significnt impcts on ntive resident species undnce nd diversity re more likely to occur if the invding species is n nnul grss (Pysek et l. 212). Refining our understnding of how invsive plnts respond to environmentl vrition will 216 The Authors. Journl of Ecology 216 British Ecologicl Society

2 98 M. A. Nguyen et l. improve our ility to predict their effects on nturl plnt communities in the fce of glol chnge. In this study, we explore the dptive responses of two nnul invsive grss species to declines in precipittion nd incresed N deposition in southern Cliforni grsslnd. There re two mjor strtegies plnt cn employ to cope with reduced wter vilility: drought tolernce nd drought escpe. Drought tolernce, chrcterized y low photosynthetic ctivity, high wter-use efficiency (WUE, the rte of cron ssimiltion reltive to trnspirtion) nd slow growth, llows n individul to conserve resources while continuing to e ctive during the drought period (Sherrrd & Mherli 26; Frnks 211). Conversely, drought escpe involves the completion of n individul s life cycle efore the drought reches its most extreme stte. Drought escpe is chrcterized y high photosynthetic rtes, low WUE nd erly flowering (Sherrrd & Mherli 26; Frnks 211). An increse in N lloction to photosynthetic enzymes nd chlorophyll content in leves my ct to increse light hrvesting (Tershim & Evns 1988; Evns 1989) nd, consequently, cron fixtion over shorter period of time. Thus, incresed N vilility resulting from humn ctivities my enhnce the growth in species displying drought escpe strtegy. Will invsive species enefit from projected rid, N-rich conditions? High soil N concentrtions cn increse invsive species performnce (Huenneke et l. 199; Dvis, Grime & Thompson 2; Ostertg & Verville 22; Gross, Mittelch & Reynolds 25); however, the effects of N ddition re complex nd will depend on soil wter vilility, competition nd the form of ville N (Everrd et l. 2; Ross, Ehrenfeld & Ptel 211; Eskelinen & Hrrison 214). Furthermore, n nlysis of severl U.S. dt ses suggests tht invsive species tend to initite leves nd flower erlier in the growing seson compred to ntive species (Wolkovich & Clelnd 211). This phenologicl pttern, consistent with drought escpe, suggests tht mny nnul invsive species my e well suited to incresingly rid conditions. Mny studies hve shown tht invsive species cn e phenotypiclly plstic in response to chnges in wter, light nd nutrient vilility (e.g. Funk 28; Dvidson, Jennions & Nicotr 211); however, fewer studies hve exmined the potentil for invsive species to dpt to environmentl vrition through genetic chnges. In study compring flowering times of nnul Brssic rp efore nd fter four-yer drought in southern Cliforni, Frnks, Sim & Weiss (27) found tht seeds collected from wet nd dry environments post-drought flowered significntly erlier thn those collected efore the drought, which is chrcteristic of drought escpe response. Further, Frnks (211) suggested tht popultions of B. rp escpe drought through reduced WUE, which llows for rpid development nd erlier flowering. A study of the nnul invsive grss Aven rt grown in wet nd dry environments lso found strong evidence tht erlier flowering ws dptive under drought (Sherrrd & Mherli 26). Despite evidence of rpid evolution in the flowering times of B. rp nd A. rt, dptive responses to climte chnge my e slower or lcking in other trits nd for other species (Frnks, Sim & Weiss 27). Antomicl nd physiologicl chrcteristics of roots will influence oth wter nd N cquisition, yet few studies hve exmined root dpttion long precipittion grdient. Studies using congeneric nd conspecific pirs occurring in high nd low rinfll sites suggest tht low specific root length (SRL, m g 1 ), lrge root dimeter or slow root elongtion rtes my e fvoured under drier conditions, reflecting n investment in thick, longer-lived roots tht more efficiently trnsport wter (Wright & Westoy 1999; Nicotr, Bick & Westoy 22; Heschel et l. 24). We serched for evolutionry responses to N nd wter mnipultions in two invsive grss species (A. rt nd Bromus mdritensis) tht re widespred throughout much of the west cost of North Americ. We sujected popultions of oth species to ltered precipittion nd N vilility for 5 yers, collected seeds from multiple mternl plnts nd grew them in common environment over two genertions. We mesured suite of ove- nd elow-ground trits tht re ssocited with wter nd N use to ddress this question: Did invsive species exhiit trit differences in response to the 5-yer environmentl mnipultions tht persisted fter two genertions in common environment? If so, our results would suggest tht the trit differences were genetic nd, thus, the result of rpid evolution in response to environmentl chnge. Answering this question is criticl first step in understnding how invsive species my respond to future climte chnge. Mterils nd methods STUDY SITE AND SEED SOURCE The study site ws locted in grsslnd community within the Irvine Rnch Conservncy in Ornge County, Cliforni (Potts et l. 212; Allison et l. 213; Kimll et l. 214). Ornge County hs Mediterrnen climte chrcterized y hot, dry summers nd cool, wet winters. We focused on two invsive grss species, A. rt nd B. mdritensis, which were undnt t our site. These species re ntive to the Mediterrnen Bsin nd, due to repeted introductions, hve widespred glol distriutions. In Cliforni, where our study ws conducted, A. rt nd B. mdritensis hve overlpping ut slightly different geogrphic distriutions, with B. mdritensis occurring in more rid environments including the Mojve Desert (DeFlco et l. 23; Steers, Funk & Allen 211). Twenty-four experimentl plots (6.7 m m) extending over n re roughly one cre in size were imposed on existing vegettion, with ech plot rndomly exposed to one of three precipittion tretments (mient, wter ddition or wter reduction, n = 8 per tretment, Fig. 1). Ech plot ws divided lengthwise with ech hlf receiving one of two N tretments (mient or N ddition). The wter reduction tretment received pproximtely 51% less wter thn the mient wter tretment, while the wter ddition tretment received pproximtely 33% more over the five-yer mnipultion period (Mrch 27 My 212) (Kimll et l. 214). Cler, retrctle roofs were deployed during suset of winter storms to control wter input into the reduction plots. Rinfll collected from reduction plots ws stored in opque polyethylene tnks nd used to supplement

3 Rpid evolution in two nnul exotic grsses 981 ddi on INITIAL POPULATION A. rt & B. mdritensis 8 plots 8 plots 8 plots mient reduc on 1-cre FIELD FIELD (5 yers) Tle 1. The numer of individuls of Aven rt nd Bromus mdritensis smpled for ech wter tretment. The numer of different plots tht mternl plnts originted from is given in prentheses. Becuse there ws no significnt effect of N on ny trit, individuls from the two N tretments were grouped within their respective wter tretments A. rt B. mdritensis Reduction 26 (7) 18 (8) Amient 21 (8) 15 (5) Addition 2 (8) 9 (3) F1 F2 F1 F2 COMMON GARDEN (2 yers) wter ddition plots through system of gsoline-powered pumps connected to drip tuing (Kimll et l. 214). Bseline N deposition t our study site is pproximtely 1.5 g m 2 yer 1 (Kimll et l. 214). Nitrogen ddition plots received 6 g N m 2 yer 1, vlue chosen to simulte site pproching N sturtion fter yers of continuous deposition (Kimll et l. 214). Supplementl N ws given in two pplictions: 2 g of quick-relese clcium nitrte following the first storm of the seson nd 4 g of slow-relese clcium nitrte following the first month of the growing seson (Kimll et l. 214). In My 212, the seeds were collected from rndomly selected mternl plnts of A. rt nd B. mdritensis nd trnsported to Chpmn University, which is locted 16 km from the field site nd hs similr wether conditions. To ensure the representtion of the entire popultion, nd minimize the effect of genetic drift, we tried to smple individuls from ll plots (n = 8) per wtering tretment. However, some plots did not contin individuls of oth species. When species ws present in given plot, we collected the seeds from one to eight mternl plnts in tht plot. Only seeds mture enough to e removed with gentle pull of the spikelet were collected. Seprte envelopes were used to ensure tht offspring from ech mother plnt remined isolted. On 3 Decemer 212, we germinted the seeds on moist filter pper t 4 C for 96 h. After germintion, only one seedling from ech mother plnt ws used; thus, ech replicte hd different mother. Becuse lter nlyses showed tht there ws no significnt effect of N on ny of the trits mesured, individuls from the two N tretments were grouped within ech wter tretment. We hd t lest nine replictes per wter tretment for B. mdritensis nd t lest 2 replictes per wter tretment for F1 F2 ABOVE & BELOWGROUND TRAIT SURVEY Fig. 1. Following 5 yers of wter mnipultions in the field (Irvine, CA), seeds were collected from experimentl plots nd grown in common environment over two genertions. Physiologicl, morphologicl nd phenologicl trits were mesured on the second genertion grown in common environment. A. rt (Tle 1). Following germintion, seedlings were trnsferred to 4.1-L pots filled with moistened potting soil (Sunshine Mix #1, Sun Gro Horticulture). Plnts were grown in full sun t Chpmn University nd wtered dily to sturtion. Becuse dpttion cnnot e ssumed sed on the phenotypes displyed in one genertion (Turner, Hufuer & Rieseerg 214), common grden experiments must occur over multiple genertions in order to differentite etween genetic nd epigenetic effects, including mternl effects (Morn & Alexnder 214). Mternl effects refer to sitution in which n individul s phenotype is determined not only y its genotype nd current environment, ut lso y the environment experienced y its mother (Lcey 1998). We controlled for mternl effects y growing seeds collected from the field (F1) nd their offspring (F2) in common environment (see Fig. 1). Any mternl effects present in the F1 genertion should hve een erdicted in the F2 genertion ecuse F1 plnts were grown under identicl environmentl conditions. Thus, tretment differences oserved in the F2 genertion should e the result of genetic differences rther thn mternl effects. We collected the seeds from ech F1 mother plnt nd germinted them s descried ove so tht ech F2 replicte hd different mother. Becuse of some mortlity during germintion nd estlishment, we hd slightly fewer replictes in the F2 genertion (n = 67 A. rt, n = 42 B. mdritensis) thn in the F1 genertion (n = 72 A. rt, n = 43 B. mdritensis) cross tretments. ABOVE-GROUND MEASUREMENTS Collection of physiologicl mesurements egn 7 dys fter germintion of the F2 genertion (Ferury 214). We conducted gsexchnge mesures with LI-64 portle photosynthesis system (LI-COR, Lincoln, NE, USA). We mintined constnt chmer conditions tht pproximted growing conditions, including CO 2 t 4 ll L 1, light t 18 lmol photon m 2 s 1, chmer temperture t 25 C nd reltive humidity t 52 62%. Mesures included photosynthetic rte, stomtl conductnce, trnspirtion rte nd instntneous WUE (photosynthetic rte/trnspirtion rte). When leves were too smll to fill the chmer, the lef re ws determined nd used to correct gs-exchnge dt. We mesured lef chlorophyll content with portle chlorophyll SPAD-52 meter (Spectrum Technologies, Plinfield, IL, USA). Three leves were hrvested following gs-exchnge nd chlorophyll mesures to determine lef dry mss per unit re (LMA) nd lef N concentrtion. The leves were scnned to determine totl lef re, dried t 6 C for 72 h nd weighed. The dried leves were then ground in Wiley mill with 4-mesh screen, nd lef N ws determined with n elementl nlyser (Costech 4, Pioltello, Itly). We ssessed the plnt size y mesuring cnopy cover prior to flowering, estimted s the product of plnt width long two

4 982 M. A. Nguyen et l. perpendiculr xes. We checked plnts dily nd recorded dte of flowering, defined s the first ppernce of florets. While oth species lrgely reproduce y selfing in nturl popultions (Johnsen- Morris & Ltt 26; Grossmn & Rice 214), outcrossing does occur; thus, plnts from different tretments were grown in the sme re ut with physicl rriers etween them to void cross-fertiliztion. Though sptilly seprted, ll tretments received similr light nd wter levels dily. From Mrch to June 214, mture seeds were collected, ir-dried nd weighed to determine totl seed iomss s metric of reproductive fitness. ROOT MEASUREMENTS To otin root mesures for the F2 genertion, seeds from suset of F1 plnts from the ove-ground trit survey were germinted using the procedure descried ove nd trnsferred to 4.1-L pots filled with moistened snd perlite vermiculite (1:1:1) mixture. Plnts were rndomly selected within plots nd, s with ove-ground mesures, we smpled from ll plots (n = 8) per wtering tretment where possile. We hd eight replictes per wtering tretment for ech species. Seedlings were grown for 5 weeks, receiving totl of.5 g N,.5 g P nd.5 g K (Mircle-Gro) over the first 2 weeks. The plnts were wtered dily to sturtion except on dys when pots received fertilizer. After 5 weeks, the plnts were hrvested nd the roots were wshed nd scnned using the WinRHIZO imge nlysis system (Regent Instruments Inc., Queec, QC, Cnd) to determine totl root length. Root growth rte (cm per dy), root length density (root length per volume of soil) nd fine root rtio [the rtio of fine root length (dimeter <.5 mm) to totl root length] were clculted. We seprted elow- nd ove-ground iomss, dried them t 6 C for 72 h nd weighed them to determine root-to-shoot iomss rtio (R: S) nd specific root length (SRL, m g 1 ). Biomss ws comined, ground nd nlysed for N concentrtion s descried ove. Plnt N uptke rte (g N per dy) ws clculted s [(plnt iomss 9 plnt N)/growing dy numer]. STATISTICAL ANALYSES Box Cox trnsformtions of the dt were used where necessry to meet the ssumptions of normlity for sttisticl nlyses. We performed nlysis of vrince (ANOVA) with wter nd N tretment s fixed effects nd plot s rndom effect to compre trit vlues etween tretments within ech species. The significnce of fixed effects ws ssessed using Stterthwite pproximted degrees of freedom. We used type III sums of squres ANOVA for mixed-effects model in the LME4 pckge in R ( v.3.2.). Following Morn (23), ll P-vlues re reported nd sequentil Bonferroni corrections for multiple sttisticl tests were not conducted. Post hoc nlyses were performed using Tukey s honestly significnt difference. Results There ws no significnt effect of N on ny trit; thus, dt from the two N tretments were grouped within wter tretment nd N s min effect ws excluded from ll susequent nlyses. vilility ffected severl ove-ground trits in A. rt s well s first flowering dte nd wter-use efficiency in B. mdritensis (Tle 2). With respect to Tle 2. F-vlues clculted from one-wy nov for second-genertion (F2) plnts of two invsive grss species with wter tretment s fixed fctor nd plot s rndom fctor. Numertor nd denomintor degrees of freedom for F-vlues re presented in prentheses. Significnt effects (P <.5) re in oldfce type Aven rt Bromus mdritensis F P F P Aove-ground trits Photosynthetic rte 3.82 (2,18) (2,4).645 Lef chlorophyll 5.9 (2,67) (2,41).84 WUE.18 (2,24) (2,4).8 Lef N content 2.62 (2,64) (2,41).224 LMA.23 (2,66) (2,42).36 Cnopy cover 3.32 (2,67) (2,42).235 Flowering dte 8.4 (2,67) < (2,41) <.1 Seed iomss 8.92 (2,67) < (2,42).7 Below-ground trits Root growth rte.49 (2,24) (2,42).586 R:S.3 (2,24) (2,24).339 Root length density.47 (2,24) (2,24).527 Fine root rtio.93 (2,12) (2,24).575 Specific root length.57 (2,17) (2,24).748 N uptke rte.62 (2,24) (2,24).583 WUE, -use efficiency; LMA, lef mss per re; R:S, root-to-shoot iomss rtio. physiologicl trits, photosynthetic rte nd lef chlorophyll content in A. rt differed cross wter tretments with trend towrds higher trit vlues in the wter reduction tretment reltive to the mient nd dded precipittion tretments (Tle 2, Fig. 2). Photosynthetic rte nd chlorophyll content did not differ cross tretments in B. mdritensis (Tle 2, Fig. 3). -use efficiency ws lower in plnts from the reduced precipittion plots in B. mdritensis compred to the mient nd wter ddition tretments (Tle 2, Fig. 3). There ws no difference in WUE cross the tretments in A. rt (Fig. 2). The pttern oserved in B. mdritensis ws driven y higher trnspirtion rtes in plnts from reduced precipittion plots (dt not shown). hd no significnt effect on lef N content in either species (Tle 2, Fig. 2). With respect to growth nd reproductive trits, flowering dte ws erlier in the wter reduction nd mient wter tretments reltive to the wter ddition tretment in oth A. rt nd B. mdritensis (Figs 2 nd 3; Tle 2). Plnts from the wter reduction plots in A. rt lso produced greter seed iomss reltive to the ddition plots, with plnts from the mient plots displying intermedite seed iomss (Fig. 2). There ws significnt effect of wter on cnopy cover in A. rt with higher cnopy cover in wter reduction plots reltive to wter ddition plots (Tle 2, Fig. 2). However, there ws no difference in seed iomss or cnopy cover cross wtering tretments in B. mdritensis (Fig. 3). LMA did not differ mong tretments for either species (Figs 2 nd 3). There ws no significnt effect of wter on root trits of either species in the F2 genertion (Tle 2, Fig. S1 in Supporting Informtion).

5 Rpid evolution in two nnul exotic grsses 983 Photosynthetic rte (µmol CO 2 per m 2 per s) 15 5 () () WUE (µmol C per mmol H 2 O) Lef N content (%) (c) (d) Lef chlorophyll content (SPAD units) (e) (f) First flowering dte (dy of yer) LMA (g per m 2 ) Fig. 2. Photosynthetic rte (), wter-use efficiency (), lef nitrogen content (c), lef chlorophyll content (d), first flowering dte (e), lef mss per re (f), seed iomss (g) nd cnopy cover (h) for Aven rt from three wtering tretments grown in common environment (F2 genertion). Mens nd stndrd errors of wter ddition, mient nd reduction tretments re shown. Different letters denote significnt differences mong mens s determined through post hoc Tukey s HSD tests. Where pplicle, significnt effects of wter re noted. Seed iomss (g per plnt) (g) Addition Amient Reduction (h) Addition Amient Reduction Cnopy cover (cm 2 per plnt) Discussion Our results suggest tht invsive species my exhiit rpid evolutionry chnge following 5 yers of glol chnge mnipultions. Trit differences occurred in response to ltered wter vilility, ut not in response to the chnges in ville N. Erlier flowering (A. rt nd B. mdritensis) nd lower WUE (B. mdritensis) in the reduced wter tretment re in line with drought escpe response s found in previous work (Sherrrd & Mherli 26; Frnks, Sim & Weiss 27; Frnks 211). Aven rt from wter reduction plots lso hd significntly higher totl reproductive iomss thn individuls from wter ddition plots, nd photosynthetic rte nd lef chlorophyll content showed trends towrds higher vlues in wter reduction plots thn in mient wter plots, suggesting tht these physiologicl responses my e dvntgeous in drought-prone regions. High lef chlorophyll content my llow for incresed light hrvesting over shorter periods of time, s evidenced y higher photosynthetic rtes, nd thus enle n incresed reproductive output. Higher reproductive output my lso hve resulted from n erlier flowering time or shift in lloction from vegettive to reproductive structures (Wolfe & Tonsor 214) nd could increse the numer of successful offspring in rid environments, where estlishment is difficult. Notly, we found tht field mnipultions did not lter root trits, which is lrgely unstudied outside of model orgnisms (reviewed in Coms et l. 213). Previous studies of root dpttion in nturl systems hve focused on conspecific or congeneric comprisons of species from different rinfll environments, which reflect evolution over potentilly long time-scles (Wright & Westoy 1999; Nicotr, Bick & Westoy 22; Heschel et l. 24). It is possile tht our

6 984 M. A. Nguyen et l. Photosynthetic rte (µmol CO 2 per m 2 per s) 15 5 () () WUE (µmol C per mmol H 2 O) Lef N content (%) (c) (d) Lef chlorophyll content (SPAD units) First flowering dte (dy of yer) (e) (f) LMA (g per m 2 ) Seed iomss (g per plnt) 15 5 (g) Addition Amient Reduction (h) Addition Amient Reduction Cnopy cover (cm 2 per plnt) Fig. 3. Photosynthetic rte (), wter-use efficiency (), lef nitrogen content (c), lef chlorophyll content (d), first flowering dte (e), lef mss per re (f), seed iomss (g) nd cnopy cover (h) for Bromus mdritensis from three wtering tretments grown in common environment (F2 genertion). Mens nd stndrd errors of wter ddition, mient nd reduction tretments re shown. Different letters denote significnt differences mong mens s determined through post hoc Tukey s HSD tests. Where pplicle, significnt effects of wter re noted. five-yer experiment ws too short to oserve the differences in root trits. In the sence of rpid genetic responses, plsticity in root trits my e n importnt mechnism for responding to environmentl chnges on short time-scles. In response to the reductions in wter vilility, individul plnts cn increse root iomss, root elongtion rte nd SRL to mximize wter cquisition (e.g. Willims & Blck 1994; Pdill et l. 29; Drenovsky, Khsnov & Jmes 212; Lrson & Funk 216). Severl of these responses (rpid elongtion, high SRL) re contrry to strtegies found in species dpted to low rinfll environments (Wright & Westoy 1999; Nicotr, Bick & Westoy 22). More dt re needed to understnd the reltive role of plsticity nd genetic dpttion in elow-ground trit responses to the vrition in wter vilility. In contrst to wter mnipultion, nitrogen ddition over five-yer period did not result in detectle trit differences. Previous work from these field plots suggested tht N ddition only incresed grsslnd productivity when comined with wter ddition, nd only in some yers (M. L. Goulden, unpul. dt). It is possile tht the proximity of the suplots (mient nd N ddition within single plot) my explin why N ddition filed to lter trits in either species. Crosspollintion or seed dispersl my hve contriuted to gene flow mong suplots. While mny studies hve found tht exotic nnul grsses respond positively to N ddition (e.g. Huenneke et l. 199; Dvis, Grime & Thompson 2; Gross, Mittelch & Reynolds 25), growth rtes my sturte or decline t high soil N (e.g. Pdgett & Allen 1999; Mttingly & Reynolds 214). Our site is reltively fertile (.19% N nd mg P kg 1 ; J. L. Funk, unpul. dt), likely resulting from historic cttle grzing nd N deposition in the Ornge County re. Thus, N mnipultions my yield different results if conducted in more N-limited environments.

7 Rpid evolution in two nnul exotic grsses 985 One novel impliction of our study is tht it my e possile for invsive plnt species to dpt to environmentl chnge over just 5 yers or five genertions. Although there re exmples of rpid evolution in other weed species (Frnks, Sim & Weiss 27; Frenck et l. 213; Sultn et l. 213; Grossmn & Rice 214), 5 yers is remrkly short time period sed on dt from other studies. In review of evolutionry responses of invsive species to novel environmentl conditions, Morn & Alexnder (214) suggested tht significnt evolutionry chnges in relevnt trits re not likely to e oserved in <25 genertions. For exmple, Turner, Hufuer & Rieseerg (214) confirmed tht rpid evolution in growth nd reproductive output hs occurred in popultions of Centure diffus in the invded rnge, which were seprted from ntive popultions y yers, or pproximtely 5 genertions. Similrly, Dlugosh & Prker (28) found evidence for rpid evolution of growth rte, dte of first flowering nd size of Hypericum cnriense in wht they predicted to e 25 genertions following introduction. Our results suggest tht popultions of nnul invsive grsses cn show significnt chnges in response to environmentl conditions in s little s five genertions. Higher rtes of cron ssimiltion, erlier phenology nd higher reproductive output in weedy species under conditions of reduced precipittion could hve importnt implictions t the community level. In Mediterrnen climte ecosystems, such s our southern Cliforni site, rinfll occurs lmost exclusively during the winter months (Novemer to My) nd drought often rings reduced rinfll nd/or shorter rinfll period. Invsive species tht re le to complete their life cycle during shorter wet seson while mintining or, in our cse, enhncing reproductive output (A. rt) will hve n dvntge over species tht hve longer life cycles nd re dversely ffected y drought. Although A. rt my e more evolutionrily responsive to wter mnipultion thn B. mdritensis (displyed more phenotypic responses), the differences in solute trit vlues suggest tht B. mdritensis ws etter t executing drought escpe strtegy thn A. rt (lower LMA nd WUE, higher totl reproductive iomss nd lef N content compred to A. rt; Figs 2 nd 3). Consequently, B. mdritensis ws one of the most common species in reduced precipittion plots fter 5 yers (Goulden et l., unpul. dt). While we did not mesure trit vlues in co-occurring ntive species, the plot-level community composition dt suggest tht ntive grsslnd species my hve limited potentil to respond to drought on short time-scles. Future reserch should test for dptive evolution in co-occurring ntive nd invsive species to ssess the potentil impct tht rpid evolution my hve on community-level processes nd ecosystem function. Acknowledgements We thnk Julie Lrson nd Dine Cmpell for comments on the mnuscript. Plots were estlished with funding from the U.S. Deprtment of Energy Progrm in Ecosystem Reserch. Additionl support ws provided y Chpmn University nd the Center for Environmentl Biology t the University of Cliforni Irvine. Dt ccessiility F2 genertion root trits figure: see Figure S1, Supporting Informtion. F2 ove- nd elow-ground trit dt: Zenodo doi:.5281/zenodo.4649 (Funk 216). References Allison, S.D., Lu, Y., Weihe, C., Goulden, M.L., Mrtiny, A.C., Treseder, K.K. & Mrtiny, J.B.H. (213) Microil undnce nd composition influence litter decomposition response to environmentl chnge. Ecology, 94, Coms, L.H., Becker, S.R., Cruz, V.M.V., Byrne, P.F. & Dierig, D.A. (213) Root trits contriuting to plnt productivity under drought. Frontiers in Plnt Science, 4, 442. Dvidson, A.M., Jennions, M. & Nicotr, A.B. (211) Do invsive species show higher phenotypic plsticity thn ntive species nd if so, is it dptive? A met-nlysis. Ecology Letters, 14, Dvis, M.A., Grime, J.P. & Thompson, K. (2) Fluctuting resources in plnt communities: generl theory of invsiility. Journl of Ecology, 88, DeFlco, L.A., Bryl, D.R., Smith-Longozo, V. & Nowk, R.S. (23) Are Mojve Desert nnul species equl? Resource cquisition nd lloction for the invsive grss Bromus mdritensis susp. ruens (Pocee) nd two ntive species. Americn Journl of Botny, 9, Dlugosh, K.M. & Prker, I.M. (28) Invding popultions of n ornmentl shru show rpid life history evolution despite genetic ottlenecks. Ecology Letters, 11, Drenovsky, R.E., Khsnov, A. & Jmes, J.J. (212) Trit convergence nd plsticity mong ntive nd invsive species in resource-poor environments. Americn Journl of Botny, 99, Eskelinen, A. & Hrrison, S. (214) Exotic plnt invsions under enhnced rinfll re constrined y soil nutrients nd competition. Ecology, 95, Evns, J.R. (1989) Photosynthesis nd nitrogen reltionships in leves of C3 plnts. Oecologi, 78, Everrd, K., Seloom, E.W., Hrpole, W.S. & de Mzncourt, C. (2) Plnt wter use ffects competition for nitrogen: why drought fvors invsive species in Cliforni. The Americn Nturlist, 175, Frnks, S.J. (211) Plsticity nd evolution in drought voidnce nd escpe in the nnul plnt Brssic rp. New Phytologist, 19, Frnks, S.J., Sim, S. & Weiss, A.E. (27) Rpid evolution of flowering time y n nnul plnt in response to climte fluctution. Proceedings of the Ntionl Acdemy of Sciences of the United Sttes of Americ, 4, Frenck, G., vn der Linden, L., Mikkelsen, T.N., Brix, H. & Jørgensen, R.B. (213) Response to multi-genertionl selection under elevted [CO 2 ] in two temperture regimes suggests enhnced cron ssimiltion nd incresed reproductive output in Brssic npus L. Ecology nd Evolution, 3, Funk, J.L. (216) Dt from Evolutionry responses of invsive grss species to vrition in precipittion nd soil nitrogen, Zenodo, DOI:.5281/zenodo.4649, Funk, J.L. (28) Differences in plsticity etween invsive nd ntive plnts from low resource environment. Journl of Ecology, 96, Gross, K.L., Mittelch, G.G. & Reynolds, H.L. (25) Grsslnd invsiility nd diversity: responses to nutrients, seed input, nd disturnce. Ecology, 86, Grossmn, J.D. & Rice, K.J. (214) Contemporry evolution of n invsive grss in response to elevted tmospheric CO 2 t Mojve Desert FACE site. Ecology Letters, 17, Heschel, M.S., Sultn, S.E., Glover, S. & Slon, D. (24) Popultion differentition nd plstic responses to drought stress in the generlist nnul Polygonum persicri. Interntionl Journl of Plnt Sciences, 165, Huenneke, L.F., Hmurg, S.P., Koide, R., Mooney, H.A. & Vitousek, P.M. (199) Effects of soil resources on plnt invsion nd community structure in Cliforni serpentine grsslnd. Ecology, 71, Johnsen-Morris, A.D. & Ltt, R.G. (26) Fitness consequences of hyridiztion etween ecotypes of Aven rt: hyrid rekdown, hyrid vigor, nd trnsgressive segregtion. Evolution, 6, Kimll, S., Goulden, M., Suding, K. & Prker, S. (214) Altered wter nd nitrogen input shifts succession in Southern Cliforni costl sge community. Ecologicl Applictions, 24,

8 986 M. A. Nguyen et l. Lcey, E.P. (1998) Wht is n dptive environmentlly induced prentl effect? Mternl Effects s Adpttions (eds T. Mousseu & C. Fox), pp Oxford University Press, Oxford, UK. Lrson, J.E. & Funk, J.L. (216) Seedling root responses to soil moisture nd the identifiction of elowground trit spectrum cross three growth forms. New Phytologist, 2, Mttingly, W.B. & Reynolds, H.L. (214) Soil fertility lters the nture of plnt resource interctions in invded grsslnd communities. Biologicl Invsions, 16, Melillo, J.M., Richmond, T.C. & Yohe, G.W. (214) Climte Chnge Impcts in the United Sttes: The Third Ntionl Climte Assessment. pp U.S. Glol Chnge Reserch Progrm, doi:.793/jz31wj2. Millennium Ecosystem Assessment (25) Ecosystems nd Humn Well-Being: Biodiversity Synthesis. World Resources Institute, Wshington, DC, USA. Morn, M.D. (23) Arguments for rejecting the sequentil Bonferroni in ecologicl studies. Oikos,, Morn, E.V. & Alexnder, J.M. (214) Evolutionry responses to glol chnge: lessons from invsive species. Ecology Letters, 17, Nicotr, A.B., Bick, N. & Westoy, M. (22) Seedling root ntomy nd morphology: n exmintion of ecologicl differentition with rinfll using phylogeneticlly independent contrsts. Oecologi, 13, Ostertg, R. & Verville, J.H. (22) Fertiliztion with nitrogen nd phosphorus increses undnce of non-ntive species in Hwiin montne forests. Plnt Ecology, 162, Pdgett, P.E. & Allen, E.B. (1999) Differentil responses to nitrogen fertiliztion in ntive shrus nd exotic nnuls common to mediterrnen costl sge scru of Cliforni. Plnt Ecology, 144, Pdill, F.M., Mirnd, J.D., Jorquer, M.J. & Pugnire, F.I. (29) Vriility in mount nd frequency of wter supply ffects roots ut not growth of rid shrus. Plnt Ecology, 24, Potts, D.L., Suding, K.N., Winston, G.C., Roch, A.V. & Goulden, M.L. (212) Ecologicl effects of experimentl drought nd prescried fire in southern Cliforni costl grsslnd. Journl of Arid Environments, 81, Pysek, P., Jrosik, V., Hulme, P.E., Pergl, J., Hejd, M., Schffner, U. & Vil, M. (212) A glol ssessment of invsive plnt impcts on resident species, communities nd ecosystems: the interction of impct mesures, invding species trits nd environment. Glol Chnge Biology, 18, Ross, K.A., Ehrenfeld, J.G. & Ptel, M.V. (211) The effects of nitrogen ddition on the growth of two exotic nd two ntive forest understory plnts. Biologicl Invsions, 13, Sherrrd, M.E. & Mherli, H. (26) The dptive significnce of drought escpe in Aven rt, n nnul grss. Evolution, 6, Steers, R.J., Funk, J.L. & Allen, E.B. (211) Cn resource-use trits predict ntive vs. exotic plnt success in cron mended soils? Ecologicl Applictions, 21, Sultn, S.E., Horgn-Koelski, T., Nichols, L.M., Riggs, C.E. & Wples, R.K. (213) A resurrection study revels rpid dptive evolution within popultions of n invsive plnt. Evolutionry Applictions, 6, Tershim, I. & Evns, J.R. (1988) Effects of light nd nitrogen nutrition on the orgniztion of the photosynthetic pprtus in spinch. Plnt nd Cell Physiology, 29, Turner, K.G., Hufuer, R.A. & Rieseerg, L.H. (214) Rpid evolution of n invsive weed. New Phytologist, 22, Vil, M., Bsnou, C., Pysek, P., Josefsson, M., Genovesi, P., Gollsch, S., Nentwig, W., Olenin, S., Roques, A., Roy, D., Hulme, P.E. & Prtners, A.D. (2) How well do we understnd the impcts of lien species on ecosystem services? A pn-europen, cross-tx ssessment Frontiers in Ecology nd the Environment, 8, Willims, D.G. & Blck, R.A. (1994) Drought response of ntive nd introduced Hwiin grss. Oecologi, 97, Wolfe, M.D. & Tonsor, S.J. (214) Adpttion to spring het nd drought in northestern Spnish Aridopsis thlin. New Phytologist, 21, Wolkovich, E.M. & Clelnd, E.E. (211) The phenology of plnt invsions: community ecology perspective. Frontiers in Ecology nd the Environment, 9, Wright, I.J. & Westoy, M. (1999) Differences in seedling growth ehviour mong species: trit correltions cross species, nd trit shifts long nutrient compred to rinfll grdients. Journl of Ecology, 87, Received 8 Septemer 215; ccepted 31 Mrch 216 Hndling Editor: Jennifer Lu Supporting Informtion Additionl Supporting Informtion my e found in the online version of this rticle: Figure S1. Effects of wter vilility on root trits.

Supplementary material

Supplementary material 10.1071/FP11237_AC CSIRO 2012 Accessory Puliction: Functionl Plnt Biology 2012, 39(5), 379 393. Supplementry mteril Tle S1. Effect of wter regime nd genotype on different growth prmeters: spike dry mtter

More information

Tests for the Ratio of Two Poisson Rates

Tests for the Ratio of Two Poisson Rates Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson

More 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

Reducing Nonpoint Source Pollution through Effective Ditch Management

Reducing Nonpoint Source Pollution through Effective Ditch Management Reducing Nonpoint Source Pollution through Effective Ditch Mngement Meliss Huert DNREC Division of Wtershed Stewrdship Dringe Progrm University of Delwre Artificil Dringe in Delwre Engineered system to

More information

Simulated climate vegetation interaction in semi-arid regions affected by plant diversity

Simulated climate vegetation interaction in semi-arid regions affected by plant diversity SULMNTARY INFORMATION DOI: 0.038/NGO96 Simulted climte vegettion interction in semi-rid regions ffected y plnt diversity M. Clussen,,*, S. Bthiny, V. Brovkin nd T. Kleinen []{Mx lnck Institute for Meteorology,

More information

UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2007

UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2007 EXAMINATIONS: SUBJECT, COURSE AND CODE: HYDROLOGY 20 DURATION: HOURS TOTAL MARKS: 00 Internl Exminer : Ms ML Wrburton : Prof RE Schulze : Ms KT Chetty : Mr MJC Horn Externl Exminer : Prof PJT Roberts STUDENTS

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

The steps of the hypothesis test

The steps of the hypothesis test ttisticl Methods I (EXT 7005) Pge 78 Mosquito species Time of dy A B C Mid morning 0.0088 5.4900 5.5000 Mid Afternoon.3400 0.0300 0.8700 Dusk 0.600 5.400 3.000 The Chi squre test sttistic is the sum of

More 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

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

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of

More information

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses

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

3.94 ± 0.50 (95% CI) Correlative inhibition index (slope)

3.94 ± 0.50 (95% CI) Correlative inhibition index (slope) Supplementl Tle S. Selected rchitecturl prmeters of phy nd phyphy grown under. Vlues re mens ± SE, except for predicted primry rosette rnches where the vlues re the men with the ssocited 9% confidence

More information

Physics 1402: Lecture 7 Today s Agenda

Physics 1402: Lecture 7 Today s Agenda 1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls:

More information

0.1 THE REAL NUMBER LINE AND ORDER

0.1 THE REAL NUMBER LINE AND ORDER 6000_000.qd //0 :6 AM Pge 0-0- CHAPTER 0 A Preclculus Review 0. THE REAL NUMBER LINE AND ORDER Represent, clssify, nd order rel numers. Use inequlities to represent sets of rel numers. Solve inequlities.

More information

Enhancing Botanical Composition and Wildlife Habitat of Pastures in South Central Iowa through Soil Disturbance by Mob-grazing of Beef Cattle

Enhancing Botanical Composition and Wildlife Habitat of Pastures in South Central Iowa through Soil Disturbance by Mob-grazing of Beef Cattle Animl Industry Report AS 66 ASL R2888 214 Enhncing Botnicl Composition nd Wildlife Hitt of Pstures in South Centrl Iow through Soil Disturnce y Mo-grzing of Beef Cttle Justin J. Bisinger Iow Stte University,

More information

Diverse modes of eco-evolutionary dynamics in communities of antibiotic-producing microorganisms

Diverse modes of eco-evolutionary dynamics in communities of antibiotic-producing microorganisms In the formt provided y the uthors nd unedited. ULEMENTAY INFOMATION VOLUME: 1 ATICLE NUMBE: 0189 iverse modes of eco-evolutionry dynmics in communities of ntiiotic-producing microorgnisms Klin Vetsigin

More information

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

Fully Kinetic Simulations of Ion Beam Neutralization

Fully Kinetic Simulations of Ion Beam Neutralization Fully Kinetic Simultions of Ion Bem Neutrliztion Joseph Wng University of Southern Cliforni Hideyuki Usui Kyoto University E-mil: josephjw@usc.edu; usui@rish.kyoto-u.c.jp 1. Introduction Ion em emission/neutrliztion

More information

SUMMER KNOWHOW STUDY AND LEARNING CENTRE

SUMMER KNOWHOW STUDY AND LEARNING CENTRE SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18

More information

Non-Linear & Logistic Regression

Non-Linear & Logistic Regression Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find

More information

Assessing the speed and predictability of local adaptation in invasive California poppies (Eschscholzia californica)

Assessing the speed and predictability of local adaptation in invasive California poppies (Eschscholzia californica) doi:./j.4-9.6.9.x Assessing the speed nd predictbility of locl dpttion in invsive Cliforni poppies (Eschscholzi clifornic) E. A. LEGER* & K. J. RICE *Deprtment of Nturl Resources nd Environmentl Science,

More information

The 1 th International and The 4 th National Congress on Recycling of Organic Waste in Agriculture April 2012 in Isfahan, Iran

The 1 th International and The 4 th National Congress on Recycling of Organic Waste in Agriculture April 2012 in Isfahan, Iran The 1 th Interntionl nd The 4 th Ntionl Congress on The Effect of Prticle Size nd Composting Period on (C/N) Rtio of Dte- Plm Wste Min Mortzvi 1, Ahmd Mohmmdi Ghehsreh 2 nd Mhmoud Klsi 3 1. M.Sc. Student,

More information

AB Calculus Review Sheet

AB Calculus Review Sheet AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is

More 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

dy ky, dt where proportionality constant k may be positive or negative

dy ky, dt where proportionality constant k may be positive or negative Section 1.2 Autonomous DEs of the form 0 The DE y is mthemticl model for wide vriety of pplictions. Some of the pplictions re descried y sying the rte of chnge of y(t) is proportionl to the mount present.

More information

( ) as a fraction. Determine location of the highest

( ) as a fraction. Determine location of the highest AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if

More information

MIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model:

MIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model: 1 2 MIXED MODELS (Sections 17.7 17.8) Exmple: Suppose tht in the fiber breking strength exmple, the four mchines used were the only ones of interest, but the interest ws over wide rnge of opertors, nd

More information

LAMEPS Limited area ensemble forecasting in Norway, using targeted EPS

LAMEPS Limited area ensemble forecasting in Norway, using targeted EPS Limited re ensemle forecsting in Norwy, using trgeted Mrit H. Jensen, Inger-Lise Frogner* nd Ole Vignes, Norwegin Meteorologicl Institute, (*held the presenttion) At the Norwegin Meteorologicl Institute

More information

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 20: Second Law of Thermodynamics CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het

More information

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x). AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f

More information

Designing Information Devices and Systems I Spring 2018 Homework 7

Designing Information Devices and Systems I Spring 2018 Homework 7 EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should

More information

Population bottleneck : dramatic reduction of population size followed by rapid expansion,

Population bottleneck : dramatic reduction of population size followed by rapid expansion, Selection We hve defined nucleotide diversity denoted by π s the proportion of nucleotides tht differ between two rndomly chosen sequences. We hve shown tht E[π] = θ = 4 e µ where µ cn be estimted directly.

More information

Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis

Chapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source

More information

3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.

3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression. SECTION. Eponents nd Rdicls 7 B 7 7 7 7 7 7 7 NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd

More information

Temperature influence compensation in microbolometer detector for image quality enhancement

Temperature influence compensation in microbolometer detector for image quality enhancement .26/qirt.26.68 Temperture influence compenstion in microolometer detector for imge qulity enhncement More info out this rticle: http://www.ndt.net/?id=2647 Astrct y M. Krupiński*, T. Sosnowski*, H. Mdur*

More information

List all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.

List all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1. Mth Anlysis CP WS 4.X- Section 4.-4.4 Review Complete ech question without the use of grphing clcultor.. Compre the mening of the words: roots, zeros nd fctors.. Determine whether - is root of 0. Show

More information

Interpreting Integrals and the Fundamental Theorem

Interpreting Integrals and the Fundamental Theorem Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of

More information

QUADRATURE is an old-fashioned word that refers to

QUADRATURE is an old-fashioned word that refers to World Acdemy of Science Engineering nd Technology Interntionl Journl of Mthemticl nd Computtionl Sciences Vol:5 No:7 011 A New Qudrture Rule Derived from Spline Interpoltion with Error Anlysis Hdi Tghvfrd

More information

Classification: Rules. Prof. Pier Luca Lanzi Laurea in Ingegneria Informatica Politecnico di Milano Polo regionale di Como

Classification: Rules. Prof. Pier Luca Lanzi Laurea in Ingegneria Informatica Politecnico di Milano Polo regionale di Como Metodologie per Sistemi Intelligenti Clssifiction: Prof. Pier Luc Lnzi Lure in Ingegneri Informtic Politecnico di Milno Polo regionle di Como Rules Lecture outline Why rules? Wht re clssifiction rules?

More information

Predict Global Earth Temperature using Linier Regression

Predict Global Earth Temperature using Linier Regression Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id

More information

Hamiltonian Cycle in Complete Multipartite Graphs

Hamiltonian Cycle in Complete Multipartite Graphs Annls of Pure nd Applied Mthemtics Vol 13, No 2, 2017, 223-228 ISSN: 2279-087X (P), 2279-0888(online) Pulished on 18 April 2017 wwwreserchmthsciorg DOI: http://dxdoiorg/1022457/pmv13n28 Annls of Hmiltonin

More information

Roadmap. Tropical seagrasses: natural & anthropogenic impacts 5/15/2015

Roadmap. Tropical seagrasses: natural & anthropogenic impacts 5/15/2015 Rodmp Tropicl segrsses: nturl & nthropogenic impcts Mrine Botny 5.14.15 Angel L Quiros Introduction to tropicl segrsses Threts to segrsses My thesis: Lnd to se impcts on segrsses The Mechnism : A field

More information

6. Photoionization of acridine through singlet and triplet channels

6. Photoionization of acridine through singlet and triplet channels Chpter 6: Photoioniztion of cridine through singlet nd triplet chnnels 59 6. Photoioniztion of cridine through singlet nd triplet chnnels Photoioinztion of cridine (Ac) in queous micelles hs not yet een

More information

New data structures to reduce data size and search time

New data structures to reduce data size and search time New dt structures to reduce dt size nd serch time Tsuneo Kuwbr Deprtment of Informtion Sciences, Fculty of Science, Kngw University, Hirtsuk-shi, Jpn FIT2018 1D-1, No2, pp1-4 Copyright (c)2018 by The Institute

More information

Linear Inequalities. Work Sheet 1

Linear Inequalities. Work Sheet 1 Work Sheet 1 Liner Inequlities Rent--Hep, cr rentl compny,chrges $ 15 per week plus $ 0.0 per mile to rent one of their crs. Suppose you re limited y how much money you cn spend for the week : You cn spend

More information

Linear Systems with Constant Coefficients

Linear Systems with Constant Coefficients Liner Systems with Constnt Coefficients 4-3-05 Here is system of n differentil equtions in n unknowns: x x + + n x n, x x + + n x n, x n n x + + nn x n This is constnt coefficient liner homogeneous system

More information

Psychrometric Applications

Psychrometric Applications Psychrometric Applictions The reminder of this presenttion centers on systems involving moist ir. A condensed wter phse my lso be present in such systems. The term moist irrefers to mixture of dry ir nd

More information

STRAND J: TRANSFORMATIONS, VECTORS and MATRICES

STRAND J: TRANSFORMATIONS, VECTORS and MATRICES Mthemtics SKE: STRN J STRN J: TRNSFORMTIONS, VETORS nd MTRIES J3 Vectors Text ontents Section J3.1 Vectors nd Sclrs * J3. Vectors nd Geometry Mthemtics SKE: STRN J J3 Vectors J3.1 Vectors nd Sclrs Vectors

More information

Derivations for maximum likelihood estimation of particle size distribution using in situ video imaging

Derivations for maximum likelihood estimation of particle size distribution using in situ video imaging 2 TWMCC Texs-Wisconsin Modeling nd Control Consortium 1 Technicl report numer 27-1 Derivtions for mximum likelihood estimtion of prticle size distriution using in situ video imging Pul A. Lrsen nd Jmes

More information

Math 42 Chapter 7 Practice Problems Set B

Math 42 Chapter 7 Practice Problems Set B Mth 42 Chpter 7 Prctice Problems Set B 1. Which of the following functions is solution of the differentil eqution dy dx = 4xy? () y = e 4x (c) y = e 2x2 (e) y = e 2x (g) y = 4e2x2 (b) y = 4x (d) y = 4x

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

Comparison Procedures

Comparison Procedures Comprison Procedures Single Fctor, Between-Subects Cse /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects Two Comprison Strtegies post hoc (fter-the-fct) pproch You re interested in discovering

More information

Role of Endophytic Fungi in Forage Production of Tall Fescue, Festuca arundinacea

Role of Endophytic Fungi in Forage Production of Tall Fescue, Festuca arundinacea Proceedings of The Fourth Interntionl Irn & Russi Conference 327 Role of Endophytic Fungi in Forge Production of Tll Fescue, Festuc rundince 1 2 Mohmmd Rez Szlin, Rez Mohmmdi nd AghFkhr Mirlohi 1, 2, 3-Deprtment

More information

The role of ammonia in plant physiology

The role of ammonia in plant physiology The role of mmoni in plnt physiology Ineke Stulen, An Cstro, nd Luit J. De Kok Lortory of Plnt Physiology University of Groningen The Netherlnds N is essentil mino cids nd proteins N uptke nd ssimiltion

More information

SOME INTEGRAL INEQUALITIES OF GRÜSS TYPE

SOME INTEGRAL INEQUALITIES OF GRÜSS TYPE RGMIA Reserch Report Collection, Vol., No., 998 http://sci.vut.edu.u/ rgmi SOME INTEGRAL INEQUALITIES OF GRÜSS TYPE S.S. DRAGOMIR Astrct. Some clssicl nd new integrl inequlities of Grüss type re presented.

More information

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

Chapter 9 Definite Integrals

Chapter 9 Definite Integrals Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished

More information

4.1. Probability Density Functions

4.1. Probability Density Functions STT 1 4.1-4. 4.1. Proility Density Functions Ojectives. Continuous rndom vrile - vers - discrete rndom vrile. Proility density function. Uniform distriution nd its properties. Expected vlue nd vrince of

More information

Acceptance Sampling by Attributes

Acceptance Sampling by Attributes Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire

More information

Haplotype Frequencies and Linkage Disequilibrium. Biostatistics 666

Haplotype Frequencies and Linkage Disequilibrium. Biostatistics 666 Hlotye Frequencies nd Linkge isequilirium iosttistics 666 Lst Lecture Genotye Frequencies llele Frequencies Phenotyes nd Penetrnces Hrdy-Weinerg Equilirium Simle demonstrtion Exercise: NO2 nd owel isese

More information

CBE 291b - Computation And Optimization For Engineers

CBE 291b - Computation And Optimization For Engineers The University of Western Ontrio Fculty of Engineering Science Deprtment of Chemicl nd Biochemicl Engineering CBE 9b - Computtion And Optimiztion For Engineers Mtlb Project Introduction Prof. A. Jutn Jn

More information

AQA Chemistry Paper 2

AQA Chemistry Paper 2 AQA hemistry Pper 2 1.1 A student is plnning n investigtion into how the concentrtion of hydrochloric cid ffects the rte of the rection with mrle chips. Wht is the independent vrile? Tick one ox. (1 mrk)

More information

TImath.com Algebra 2. Constructing an Ellipse

TImath.com Algebra 2. Constructing an Ellipse TImth.com Algebr Constructing n Ellipse ID: 9980 Time required 60 minutes Activity Overview This ctivity introduces ellipses from geometric perspective. Two different methods for constructing n ellipse

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

Factors affecting the phonation threshold pressure and frequency

Factors affecting the phonation threshold pressure and frequency 3SC Fctors ffecting the phontion threshold pressure nd frequency Zhoyn Zhng School of Medicine, University of Cliforni Los Angeles, CA, USA My, 9 57 th ASA Meeting, Portlnd, Oregon Acknowledgment: Reserch

More information

Lecture INF4350 October 12008

Lecture INF4350 October 12008 Biosttistics ti ti Lecture INF4350 October 12008 Anj Bråthen Kristoffersen Biomedicl Reserch Group Deprtment of informtics, UiO Gol Presenttion of dt descriptive tbles nd grphs Sensitivity, specificity,

More information

Larval dispersal. Settlement. Larval production Post-settlement. Sources of spatial and temporal variation in recruitment

Larval dispersal. Settlement. Larval production Post-settlement. Sources of spatial and temporal variation in recruitment Sources of sptil nd temporl vrition in recruitment Lrvl dispersl Sources of sptil nd temporl vrition in recruitment Processes ffecting SETTLEMENT of lrve 1) Physicl processes Settlement Lrvl production

More information

CS103B Handout 18 Winter 2007 February 28, 2007 Finite Automata

CS103B Handout 18 Winter 2007 February 28, 2007 Finite Automata CS103B ndout 18 Winter 2007 Ferury 28, 2007 Finite Automt Initil text y Mggie Johnson. Introduction Severl childrens gmes fit the following description: Pieces re set up on plying ord; dice re thrown or

More information

Farey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University

Farey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions

More information

3.1 Exponential Functions and Their Graphs

3.1 Exponential Functions and Their Graphs . Eponentil Functions nd Their Grphs Sllbus Objective: 9. The student will sketch the grph of eponentil, logistic, or logrithmic function. 9. The student will evlute eponentil or logrithmic epressions.

More information

Validation of APHRODITE Precipitation Data for Humid and Sub Humid Regions of Pakistan

Validation of APHRODITE Precipitation Data for Humid and Sub Humid Regions of Pakistan Pkistn Journl of Meteorology Vol.9, Issue 17: July 2012 Vlidtion of APHRODITE Precipittion Dt for Humid nd Su Humid Regions of Pkistn Ali, G. 1, 2, G. Rsul 2, T. Mhmood 2, Q. Zmn 2, S. B. Cheem 2 Astrct

More information

Vadose Zone Hydrology

Vadose Zone Hydrology Objectives Vdose Zone Hydrology 1. Review bsic concepts nd terminology of soil physics. 2. Understnd the role of wter-tble dynmics in GW-SW interction. Drcy s lw is useful in region A. Some knowledge of

More information

Rates of chemical reactions

Rates of chemical reactions Rtes of chemicl rections Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) 2 5 2 2 n(1 α) 2αn

More information

Chapter 6 Techniques of Integration

Chapter 6 Techniques of Integration MA Techniques of Integrtion Asst.Prof.Dr.Suprnee Liswdi Chpter 6 Techniques of Integrtion Recll: Some importnt integrls tht we hve lernt so fr. Tle of Integrls n+ n d = + C n + e d = e + C ( n ) d = ln

More information

( ) where f ( x ) is a. AB/BC Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).

( ) where f ( x ) is a. AB/BC Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x). AB/ Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 Find the intersection of f ( x) nd g( x). A3 Show tht f ( x) is even. A4 Show tht

More information

Math 31S. Rumbos Fall Solutions to Assignment #16

Math 31S. Rumbos Fall Solutions to Assignment #16 Mth 31S. Rumbos Fll 2016 1 Solutions to Assignment #16 1. Logistic Growth 1. Suppose tht the growth of certin niml popultion is governed by the differentil eqution 1000 dn N dt = 100 N, (1) where N(t)

More information

ORDER REDUCTION USING POLE CLUSTERING AND FACTOR DIVISION METHOD

ORDER REDUCTION USING POLE CLUSTERING AND FACTOR DIVISION METHOD Author Nme et. l. / Interntionl Journl of New Technologies in Science nd Engineering Vol., Issue., 7, ISSN 9-78 ORDER REDUCTION USING POLE CLUSTERING AND FACTOR DIVISION METHOD A Chinn Nidu* G Dileep**

More information

The impact of wind on air temperature distribution in Athens and in Santorini

The impact of wind on air temperature distribution in Athens and in Santorini Interntionl Conference Pssive nd Low Energy Cooling 133 The impct of wind on ir temperture distribution in Athens nd in Sntorini I. Livd, K. Nichou nd M. Sntmouris Lbortory of Meteorology, Section of Applied

More information

Section 4: Integration ECO4112F 2011

Section 4: Integration ECO4112F 2011 Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic

More information

Energy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene

Energy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene Force (kcl mol -1 Å -1 ) Energy (kcl mol -1 ) 3 1-1 - -3 Mixed Mo-only S-only Grphene 6 5 3 1 Mixed Mo-only S-only Grphene - -1-1 1 Pore xis (Å) -1 1 Pore xis (Å) Supplementry Figure 1 Energy Brriers.

More information

13: Diffusion in 2 Energy Groups

13: Diffusion in 2 Energy Groups 3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups

More information

Torsion in Groups of Integral Triangles

Torsion in Groups of Integral Triangles Advnces in Pure Mthemtics, 01,, 116-10 http://dxdoiorg/1046/pm011015 Pulished Online Jnury 01 (http://wwwscirporg/journl/pm) Torsion in Groups of Integrl Tringles Will Murry Deprtment of Mthemtics nd Sttistics,

More information

Design and Analysis of Single-Factor Experiments: The Analysis of Variance

Design and Analysis of Single-Factor Experiments: The Analysis of Variance 13 CHAPTER OUTLINE Design nd Anlysis of Single-Fctor Experiments: The Anlysis of Vrince 13-1 DESIGNING ENGINEERING EXPERIMENTS 13-2 THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT 13-2.1 An Exmple 13-2.2

More information

Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Thoms Whithm Sith Form Pure Mthemtics Unit C Alger Trigonometry Geometry Clculus Vectors Trigonometry Compound ngle formule sin sin cos cos Pge A B sin Acos B cos Asin B A B sin Acos B cos Asin B A B cos

More information

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE Southwestern U.S. Ground Motion Chrcteriztion Senior Seismic Hzrd Anlysis Committee Level 3 Workshop #2 October 22-24, 2013 A Brief Review on Akkr, Sndikky nd Bommer (ASB13 GMPE Sinn Akkr Deprtment of

More information

ARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac

ARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac REVIEW OF ALGEBRA Here we review the bsic rules nd procedures of lgebr tht you need to know in order to be successful in clculus. ARITHMETIC OPERATIONS The rel numbers hve the following properties: b b

More information

Resources. Introduction: Binding. Resource Types. Resource Sharing. The type of a resource denotes its ability to perform different operations

Resources. Introduction: Binding. Resource Types. Resource Sharing. The type of a resource denotes its ability to perform different operations Introduction: Binding Prt of 4-lecture introduction Scheduling Resource inding Are nd performnce estimtion Control unit synthesis This lecture covers Resources nd resource types Resource shring nd inding

More information

a * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2

a * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2 18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions

More information

Midterm#1 comments. Overview- chapter 6. Recombination. Recombination 1 st sense

Midterm#1 comments. Overview- chapter 6. Recombination. Recombination 1 st sense Midterm#1 comments So fr, ~ 10% of exms grded, wide rnge of results: 1 perfect score, 1 score < 100pts rtil credit is given if you get prt of the nswer right Tests will e returned next Thursdy Some of

More information

STEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA. 0 if t < 0, 1 if t > 0.

STEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA. 0 if t < 0, 1 if t > 0. STEP FUNCTIONS, DELTA FUNCTIONS, AND THE VARIATION OF PARAMETERS FORMULA STEPHEN SCHECTER. The unit step function nd piecewise continuous functions The Heviside unit step function u(t) is given by if t

More information

Technical Note: Analytical sensitivity analysis of a two parameter recursive digital baseflow separation filter

Technical Note: Analytical sensitivity analysis of a two parameter recursive digital baseflow separation filter Hydrol. Erth Syst. Sci., 16, 451 455, 2012 www.hydrol-erth-syst-sci.net/16/451/2012/ doi:10.5194/hess-16-451-2012 Author(s) 2012. CC Attriution 3.0 License. Hydrology nd Erth System Sciences Technicl Note:

More information

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus 7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e

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 Variable X:

Continuous Random Variable X: Continuous Rndom Vrile : The continuous rndom vrile hs its vlues in n intervl, nd it hs proility distriution unction or proility density unction p.d. stisies:, 0 & d Which does men tht the totl re under

More information

The Influence of Interface and Semiconductor Bulk Traps Generated Under HEFS on MOSFET`s Electrical Characteristics

The Influence of Interface and Semiconductor Bulk Traps Generated Under HEFS on MOSFET`s Electrical Characteristics Proceedings of the 5th Smll Systems Simultion Symposium 2014, Niš, Seri, 12th-14th Ferury 2014 The Influence of Interfce nd Semiconductor Bulk Trps Generted Under HEFS on MOSFET`s Electricl Chrcteristics

More information

Parse trees, ambiguity, and Chomsky normal form

Parse trees, ambiguity, and Chomsky normal form Prse trees, miguity, nd Chomsky norml form In this lecture we will discuss few importnt notions connected with contextfree grmmrs, including prse trees, miguity, nd specil form for context-free grmmrs

More information

Physics 202H - Introductory Quantum Physics I Homework #08 - Solutions Fall 2004 Due 5:01 PM, Monday 2004/11/15

Physics 202H - Introductory Quantum Physics I Homework #08 - Solutions Fall 2004 Due 5:01 PM, Monday 2004/11/15 Physics H - Introductory Quntum Physics I Homework #8 - Solutions Fll 4 Due 5:1 PM, Mondy 4/11/15 [55 points totl] Journl questions. Briefly shre your thoughts on the following questions: Of the mteril

More information

Designing finite automata II

Designing finite automata II Designing finite utomt II Prolem: Design DFA A such tht L(A) consists of ll strings of nd which re of length 3n, for n = 0, 1, 2, (1) Determine wht to rememer out the input string Assign stte to ech of

More information