Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 oubnaesocp bu wc h adae e aiao xsigrsdns If residents. existing of capita per area land the twice about occupy areas urban to motn o hoeia,patcladeprclivsiain fubnfr n fhow for of and hold the form rule of urban are Zipf’s predictor of here important of investigations presented an empirical version time. Results is and over generalised expand emissions. LPD practical areas the vehicle urban theoretical, density. to motor for population similar for important and areas. relationship LPD rules urban among emissions-to-inhalation area, and have rank–size within land form results themselves UAs, urban population, arrange These the of people time-scales. US corroborate how multidecadal attributes to over but data For other pattern constant 2, International any, underlying roughly show of time-period. an if are factor suggest 2000, half-century Few, distributions a 1950–2000 LPD cent. this to than that per during during 1950 more finding 10 constant by from UAs than so changed example, less density remained US changed For population than, among LPD and differently time-scales. area average somewhat metre- values multidecade land behaves a over population, in and LPD people average from, variability of of distinct number little is the Distributions surprisingly LPD is area. metre) density. urban per people population an (units: across LPD strip time. wide over constant be would xcl qa o2 hnteprmtrgroup parameter parameter the the then for 2, Values to population. equal of in exactly value increase tendency cent central per a 10 with than UAs, among greater vary a with (UAs) areas oacmoaeicesn ouainsz.Ti ril rvdsasml e powerful yet simple a provides relationship article scaling following ( the This i.e. area Specifically, land increasing expansion. size. proposed: is urban is area this population land of urbanised description globe, increasing the mathematical throughout accommodate regions metropolitan most to In Summary. 2006] November form, final in 2005; December received, first [Paper Marshall D. Julian Expansion New Metropolitan A for Growth: Relationship Population Scaling and Area Land Urban udn rmteBig rga tUiest fBiihClmi,adsatu ud rmUiest fMneoa r gratefully suggestions. are Minnesota, and of comments University Print helpful from funds 0042-0980 for start-up Skaburskis and topics Columbia, Andrejs the British MN on editor of Minneapolis, discussions journal University fruitful S.E., at the for acknowledged. Drive Program Toffel and Pillsbury Bridge Mike reviewers the 500 thanks from anonymous Minnesota, author Funding The of three [email protected]. University also E-mail: Engineering, here, 7750. Civil 626 contained of 612 Fax: Department USA. the in 55455–0116, is Marshall D. to Julian are double populations urban 2000b). to urban in Nations, decades, expected (United live coming in areas In will time rural people first than the more for history, In 2007, rapidly. increasing approximately are populations Urban Introduction O:10.1080 DOI: ra tde,Vl 4 o 0 8910,Spebr2007 September 1889–1904, 10, No. 44, Vol. Studies, Urban A / / P 00420980701471943 / n 3003 Online 1360-063X uig15–00 hsrltosi sfudt odwl o SCnu urban Census US for well hold to found is relationship this 1950–2000, During . A nrae rprinlyt ouainsz ( size population to proportionally increases ) /  07 ilo nthe in billion 6 / 101889–16 # 07TeEioso ra Studies Urban of Editors The 2007 P = p e atrso oilitrcin and interactions social of to impacts, require- patterns environmental infrastructure in new their and from areas ments populations urban ways, affects rural many growth while Population (at years, constant remain 50 next A ffiffiffi  cle lna ouaindniy,o LPD) or density’, population ‘linear (called ,sgetn ht naeae newcomers average, on that, suggesting 2, P  asdt oe ( power a to raised ) ilo)o decline. or billion) 3 n were n )— n Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 fayseicubnae ( area urban population specific the any of that distri- address hypothesised the (1949) areas. rules urban Zipf on among scaling sizes focuses population of rule two bution One far, form. Thus factor urban a a 8. by of volume radius of its the increase doubling would size: sphere the to) linear proportional of an is cube (i.e. of with a volume scales As object the related. are example, attributes straightforward more or two how terms general in describe relationships Scaling Background Rule Scaling or are research. can trends future extant to planners these left modify to whether seek should discussing patterns elucidating and these as underlying such mechanisms Topics causal growth. urban patterns docu- in spatial vehicle article unobserved This health previously motor areas. ments urban of environmental in inhalation specific emissions human a find- issue: these for of implications ings discuss rules. for I rank–size Finally, evidence LPD over and present constant density population and relatively decades is for multiple areas values (LPD), LPD urban of density’ US distribution metric the form population that urban show ‘linear new a 1950–2000. called introduce during areas I panel urban Next, comprehensive US the for test using data I to validity size. area population land rule’s scaling urban urban a in in propose changes changes I relating First, rule sections. three comprised and is of theoretical paper The in of importance. growth topic practical to a response population, in urban time a over expands to leading density. population urban size, average in population decline faster global urban expanding is the area than as land urban rapidly are and as its areas rates) not urban predicting (albeit US, to growing the In and under- influences. growth to broad important this is standing occurs growth urban (Bettencourt economy al et regional the in changes 1890 hsatceepoe o ra adarea land urban how explores article This ,20;Rse,18) h su fwhere of issue The 1980). Rosser, 2007; ., P i clswt the with scales ) UIND MARSHALL D. JULIAN eteand centre sacntn ls nvleto value in close constant a is D fubnaes(Edmonston areas hundreds urban in of equation this applied has research P ( rank population h ouaino h ags ra t.Zipf’s as etc. generalised be area, can largest rule the of population one-third the equals area third-largest popu- the the of area; lation urban largest the of the population half equals area urban second-largest the of population the example, For area. urban largest miia ofcet.I theory, In coefficients. empirical aindniyvre ihna ra area. equation urban decay expo- nential monocentric an the proposed within (1951) and Clark varies density Ioannides lation 2003; 2000). Black Urzua, 2003; Henderson, 1999; Overman, (Gabaix, rule’ and of version ‘rank–size generalised this the supports research au ls to close value eemndvle for empirically than values less determined is density population residential where at districts, commercial (i.e. or park centre city the r at density population pcfi distance, specific xlrdcue n osqecso density (Anas of gradients consequences and, and 1991); causes Zheng, explored 1989; Skaburskis, 1985; (Anderson, cubic-spline a and 1966) Newling, al. 1992; (Anas et relationships Kim, exponential and 1993), Stern, (Batty relationships polycentric, power poly- (Bunting including often nomials equations, gradient density alternative, proposed estimating seilygvnteepce rwhin growth literature, expected the in the populations. urban gap given significant urban of especially a expansion current for is The rule areas scaling time. a over of and lack areas within urban locate populations among where of descrip- tion pre- mathematical a Findings provide time. how below sented over regarding expand rule, areas scaling urban new a proposes i ¼ ( eodsaigrl oue nhwpopu- how on focuses rule scaling second A uligo h w ue bv,ti article this above, rules two the on Building r ¼ stepplto est (km density population the is ) ) npatc,ct ete r often are centres city practice, In 0). P 00 Murakami 2000; , 1 / i ,where l D u not but 0 tal. et (km 2 i r P fta ra codn to according area, that of ) Pmi,20) Most 2003). (Pumain, 1 1 k) wyfo h city the from away (km), D tal. et 2 stepplto fthe of population the is 1998). , 0 2 D and ) MlsadTn 1980); Tan, and (Mills ( r ) P 02,inverse 2002), , tal. et ¼ i D ¼ 0 P tal. et D l Subsequent . 1 Ki 0 95,often 1985), , and , e (km a 2 D where , l 2 2005; , 0 r 2 a 2 where , 1 )ata sthe is are ) a a has K Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 ra.Euto 1 a qiaetybe equivalently urban can a among (1) as for not written Equation and time area areas. over urban is specific (scaling) portionality hr,fragvnubnarea, urban given a for where, ‘ where etices npplto ilsa yields population in increase cent o xml,i iywith city a in example, For where raadpplto epciey h par- The respectively. ameter population and area o ie ra ra adae cuid( occupied km area land units: area, urban given a for relates, here proposed relationship scaling and The Area Land Size between Population Time over Scaling qain()idctsthat indicates (1) equation rvdo ipoe:a siaefor estimate be an cannot disproved: (2) or and proved (1) Equations then large). constant), for very magnitude nearly popu- estimated (or while the constant varies essential area is land lation the if inherent is an one-par- limitation but captures described, This being respectively. relationship equation 2 and ameter 1 times h adaesa ie n respectively, 2 and 1 times and at areas land the nrae npplto ieacrigto according size accommodate (1) population equation to in expands increases area that posited vrg,nwoest h ra area on urban case, this the In to area. newcomers in average, increase cent ino h hnmn en investigated. being phenomena the consider population of a tion we offers and equation Instead, this population non-zero. whether are area, long growth known so land area, with and area as population urban final and any initial for derived be / A A dA A If en i rprinlt’ ee h pro- the Here, to’. proportional ‘is means ’ A 1 2 / P ¼ ¼ n 1 dA P n n  n and n eecntn,tedrvtv of derivative the constant, were P P 2 dP and stepplto–raelasticity. population–area the is P n ouainsz ( size population and ) 1 2 sa miia osatand constant empirical an is P n 2 dP r h ouainszsat sizes population the are ersn ml hne in changes small represent ADAE N OUAINGROWTH POPULATION AND AREA LAND n n useful A sifiie(or infinite is ¼ 1 ,a2per 2 a 3, and P descrip- .I is It ).  A n per 6 2 can are (2) (1) (3) A ; essbok en rae hn50mile 500 surrounding than of greater being density blocks population census the and est facnu lc rbokgroup block mile or 1000 block than census greater population being a the on of based density areas’ delin- Census ‘urban US the eates areas: urban US avail- for are able data political panel than Appropriate rather con- boundaries. example, growth) and of must (for density areas tinuous data population areas boundaries by The land urban determined and time). on populations urban based single multiple urban a for provide at values (i.e. areas cross-sec- over multiple than data rather for area tional time) values urban over (i.e. areas one data urban panel for or values time) (i.e. data e eti 00(NTT 04 Mulry, 2004; (CNSTAT, Robinson 2000 1 than 2006; in less to cent 1950 in per cent per 4 roughly 2004). from declined rates undercount Census Census, una- US are vailable. data UA the (US for estimates is Uncertainty elsewhere UAs of on start information available the Further at decade. delineated 000 each 50 are of UAs size greater. population or a have must (UAs) h raa nubnae.Gop1contains 1 Group area. urban an as classified first area Census the the when decade the were on areas and two 1980 analysis.) These in my 1990. from IL, UAs excluded not Danville, census but and US 2000, NC, were excep- two Concord, which (The are such. stays tions an it becomes population area’, area of ‘urban an once because Typically, time growth. over UAs of increases number The 1992). Census, US (US minor been have modifications the cen- subsequent changed 1950 but and suses, area because 1940 urban the between an analysis significantly of this definition Census for point rural than 2000). Robinson, urban and in (Hogan lower areas typically are rates 13km (193 siaigvle for values Estimating ‘n’ Parameter the of Estimates Empirical land residents. capita current per do as the area times three about occupy ra ra r rue nTbe1based 1 Table in grouped are areas Urban starting- the as chosen is 1950 year The 2 2 U ess 04.Ubnareas Urban 2004). Census, (US ) tal. et n 93.Undercount 1993). , eurstime-series requires 2 2 36km (386 1891 2 2 2 2 ) emti en(km mean Geometric ofceto aiblt (percentage) variability of Coefficient emti tnaddvain2017141414141.9 1.4 1.4 1.4 1.4 1.7 2.0 deviation standard Geometric ouainwihe en(m mean Population-weighted ein802020101010250 150 190 180 230 250 810 (km Mean density Population Median emti en(m mean Geometric ein3400100013008 0 4805 0 1 000 118 700 59 800 84 200 85 000 143 000 120 000 394 (km UA per area Land Median b a ein(m Median (percentage) variability of Coefficient (km Median emti tnaddvain1415141514151.5 1.5 1.4 1.5 1.4 1.5 1.4 (m Mean density population Linear deviation standard Geometric Mean ouainwihe en(km mean Population-weighted ubro A ngop125 46 29 453 70 92 – 72 3 1 63 3 2 34 – 2 3 50 2 2000 4 142 1990 4 1980 5 56 1970 6 1960 Mean UA per Population before (percentage) or group 1950 in population US of group Portion in 1950–2000 UAs during of (UA) data area Number with urban censuses census of US Number a became area Year Ma’rfr oaihei mean. arithmetic to refers ‘Mean’ ofceto aiblt steaihei tnaddvaindvddb h rtmtcmean. arithmetic the by divided deviation standard arithmetic the is variability of Coefficient a a 2 2 1 2 ) 2 2 a 1 ) 484886464547.8 5.4 6.4 6.4 8.8 8.4 14 ) a 2 4 4 4 1 3 3 490 430 430 410 540 540 540 ) 2 2 1 792886667599.2 5.9 6.7 6.6 8.8 9.2 17 ) 2 2 7 5 4 7 6 6 510 460 460 470 540 550 570 ) ) 2 2 1 Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 11 180868951 8.9 8.6 8.0 11 17 61 ) 2 7 3 0 2 9 4 810 540 490 520 600 730 870 ) al 1. Table b b er20 ausfrubnfr trbtsfrsxubnae U)groups (UA) area urban six for attributes form urban for values 2000 Year ru ru ru ru ru ru 6 Group 5 Group 4 Group 3 Group 2 Group 1 Group 8 0 1 0 6 0 0 0 1 0 21045000 425 100 92 000 114 000 104 000 165 000 213 000 080 1 403030202020640 200 260 240 320 350 1470 1 0 8 0 9 0 550 500 490 500 580 600 610 76 73 54 120 12 48 6.4 42 35 7.0 37 43 6.9 39 37 9.3 44 63 11 38 97 22 42 40 l i groups six All

combined

1892 UIND MARSHALL D. JULIAN Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 ragop ihtoo oecnue.Teln o ru nbl eas h oa ouainfrthis for population total the because bold in 1 Group for line The censuses. more or two with groups area rwh hs mn h 6 A (see UAs 361 the among population Thus, rapid or growth. modest 2000 for pro- apply only and to is posed (1) 1960 Equation etc.). between for considered, are considered; changes are 2, 2000 par- Group and the 1950 estimate between to (2) equation ameter in used is groups. remaining the for than are 1 Group area size population land Mean urban 1960.) and for in values UA median an and as which classified Nevada, first Vegas, was year Las people. is the million exception where 1 (The UAs exceeded 37 population the 2000 of 36 Group groups. contains popu- remaining 1 US the the of of each cent com- in per lation 1, Group 2–4 only in US with live of pared cent) majority per groups A (56 other residents reasons. the following from the apart for Each stands 1 2000. Group in UAs. of census set unique recent a UAs represents most group as 6, classified the Group first through in areas on so contains and which 1960, in classified UAs first 1950 areas as the contains in 2 UAs Group as census; classified were that areas iue1. Figure h aiu uaino aafrec UA each for data of duration maximum The but other, each from differ groups six All n freape o ru ,changes 1, Group for example, (for itiuino ausetmtdfrteparameter the for estimated values of Distribution ru fUsi infiatylre hnfrteohrgroups. other the for than larger significantly is UAs of group  –0tmslre for larger times 3–10 ADAE N OUAINGROWTH POPULATION AND AREA LAND ossec mn h itiuin in distributions respectively.) the are cent per increases among 130 and size Consistency cent population per increase median 70 (Median mean cent respectively. and 3.3 per and and mean 3.7 are 10–50 size), values one-third a population roughly with in the UAs (i.e. remaining 1 the of Figure for population in respectively; for UAs in 2.0 values median increase and more and 2.1 cent mean experienced per the that size, 50 figure a of this than two-thirds in roughly UAs the mean for For overall The values respectively. median 1.3–3.7. range percentiles) and the 75th in and 25th are values interquartile the and spanning 1, (i.e. are 1.8–3.0 range Figure medians) the and in UA). in (means distributions an tendencies five became central territory the the the Among on depending year (i.e. groups census UA presents the of 1 of distribution each Figure the UAs, separately 310 For UA). remaining each for for the the data employing cent) of (again duration per declined than maximum or less (14 cent per increased UAs 10 either 51 population censuses, the which more or removed two for I data with 1) Table n neuto 1,frec ftefieurban five the of each for (1), equation in n r . n 2.3 and 2.7 are n ausfor values n 1893 are n Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 1894 aaee ausgvnb Edmonston Using by Appendix. given the values in parameter are equations evant r esnbyrbs osalcagsin changes application cases, small some (In to parameters. values input robust These reasonably areas. people, urban are 000 areas Canadian 000 urban 1 for and US and 000 for 250 2.1 between and with more 1.9 for with between values areas Estimated are people. urban million US estimated 1 for than yields 1.8 of 1951–1976 values for (1985) iue1sget htteapoc employed estimating approach of the that suggests 1 Figure sfldsrpino h aa ihdistri- with data, is the of butions of etc.) description 2, useful Group for years 40 for appropriate. years 50 1, (i.e. group Group each for duration ible einvlefor value median ainices,median increase, UAs and lation cent (for per growth 10–50 with population than significant growth population for modest for larger are rafrec Agop sbfr,the for before, values Resultant investigated As group. is each group. for duration UA possible land each maximum and the for population considers area cumulative) instead (i.e. investigating separately, total than rather UA but each data, same the lentv prahswr loue oesti- for to values used mate also to were approaches attributable alternative is consumption. half land capita per and popu- rising to growth area attributable land is lation UA’s time the over of expansion current half of about area land residents), the twice occupy comers ra ecmr eaiet xsigurban existing by For to occupied residents. relative area newcomers land typical urban elasticity the about population–area and the about infor- mation provide UAs, among vary which values,  tn ubn rm‘o ra’ h US The urban’. ‘not mile 1000 of separ- from value census density ‘urban’ population ating threshold by specify- the requires proposed ing analysis urban This gradient (1951). exponential Clark density second the The population 1.9. employs average and approach 2.3 to 1.6 from epciey.A niae above, indicated As respectively). 2 ncnlso,euto 1 rvdsa provides (1) equation conclusion, In sacmaio ihteersls two results, these with comparison a As n ausgvni iue1 The 1. Figure in given values n n n ae ntemxmmposs- maximum the on based ¼ h rtapoc employs approach first The . n o vrg,ubnnew- urban average, (on 2 is  n .Typical 2. 2 . ausare values 2 0prcn popu- cent per 50 sue ee Rel- here. used is n UIND MARSHALL D. JULIAN  n values and 3 range tal. et n n n o P.U onisso iia patterns: similar second show but counties US density, LPD. population is for California for LPD; for twelfth sixteenth population contrast, but for In and second density, both. ranked density is in Island last population Rhode ranks both Alaska in LPD; Jersey first lists; New both ranks significantly. in rank rank change similar others a LPD, by have ranking and states density some when population by example, states US For density. lation and people. density 50 population contains LPD. illustrates area land 2 of urban Figure strip an metre-wide example, a for across metre, that per mean meaning: people intuitive would 50 root an of square has value the LPD a be area. to a land here of take urban by the I divided of which width) area, population or (length urban measure linear the is area when forecasts. example, growth urban case, tool—for long-term making the an planning as were consideration urban that further merit If might approximately LPD time. fact, over in is, constant LPD investi- whether to remain worthwhile gate is would It time. LPD) over constant or density’, population ec au of value from dency data gradient Edmonston population and data census exponential US of analyses preceding The Density Population Linear earlier. the presented of tendencies central with or for factor-of-2 estimates yield ation, the can in changes values larger change input cent the yields per par- in 10 input a to data example, sensitive ameters—for highly exponential gradient are that to results density equations Appendix population the of ouainsz.I h aewhere group parameter equation the of case that implication is an (1) the 2, to in equal In increase) exactly cent size. per 50 population than (more changes approaches alternative value the both suggest Thus, robust.) P sntmrl ettmn fpopu- of restatement a merely not is LPD urban an of density population linear The tal. et n  18)sgetacnrlten- central a suggest (1985) for 2 n ol o econsidered be not would n ,epcal o large for especially 2, siae nti situ- this In estimate. n hc sconsistent is which , PA n distributions 2 0.5 (‘linear n is Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 00 ouaindniisfrteethree these ( for comparable are densities UAs Population 2000. n 9tmslre hnfrAe 8m (8 Ames for than larger times 19 and 1009000; ais P o e ok(5 m (151 York New for LPD varies: ntrso ouainadln area, land and population is of York New terms In iue2. Figure est os(..LDi rprinlto proportional is LPD LPD ( (i.e. A area straightforward: does on density is less depends density lation different significantly others. and for counties similar some are ranks for LPD and density population 90km 7930 ie agrta o e ren 3 m (35 Orleans New for than larger times edt aeasalrLDvle u not ( A but IA As Ames, value, density. consider size population LPD illustration, smaller smaller population a a smaller necessarily have a to with tend areas urban LD—h ubro epei ti fln xedn ul costeubnae ( area urban the across fully extending land of strip a in people of number (LPD)—the ouaindniy ahmtcly P sdsic rm n eae oehtdfeetythan, differently somewhat behaves and from, distinct is LPD Mathematically, density. population ( ren and Orleans n setrto(..lnt iie by population and area divided area urban land an length spatially, Once defined area. is (i.e. urban shape an ratio of the width) to aspect relates LPD and popu- and between density lation difference potential another s4. km 40.9 is P 2 ¼ h anrao P ifr rmpopu- from differs LPD reason main The lhuhnticroae nti analysis, this in incorporated not Although ¼ 0.5 09km 40.9 1780000; est spootoa to proportional is density ; 2 1 2 uln a o nilsrtv ra ra ms oa(population, Iowa Ames, area: urban illustrative an for map Outline A hl ouaindniyadLDaesmlr P sntmrl ettmn of restatement a merely not is LPD similar, are LPD and density population While . .Aeaepplto est ( density population Average ). ¼  2 ,NwOlas A( LA Orleans, New ), 4 ie agrta Ames. than larger times 346 2 km 825  7tmslre hnNew than larger times 17 A ¼ 2  390km 970 13 ,adNwYr,NY York, New and ), 20km 1250 A hnpopulation than ) ADAE N OUAINGROWTH POPULATION AND AREA LAND ouaindniy(e iue 3–6). Figures (see density population 2 P 2 A ,i year in ), 2 ¼ u LPD but ) 2 1 2 0700; 50 .Thus, ). 1 )is4 PA P 2 2 2 ¼ 1 1 1 ). s14 km 1240 is ) ) a eanda osatoe h aefive- same the period. over form decade author’s constant urban as the of remained To attribute has surprising. other over no is and knowledge, consistency LPD area of The population, time density. in groups, changes population UA significantly are than and cent) decades all per less six 10 multiple For than over the (less small 1. LPD for in Table attributes changes form in urban groups four is of groups density. population for UA than LPD among for greater variability general, 00vle o P n ouaindensity m population 51 and are LPD for values 2000 are year Population-weighted UAs 1. Table census in US presented for values LPD 2000 Year Linear for Density Values Population US Historical and Current urban temporally. an and spatially for vary may LPD area density, population results. different area. Like yield land may of approaches root measures. Other square other employs paper or This mean linear width, employed: maximum is which area width, on urban an depends of measure LPD contrast, concepts. In unambiguous relatively are density iue3peet omlsdma values mean normalised presents 3 Figure 2 2 2 1 n vrg ierpplto density population linear average and n 1 km 810 and P s5 0;ln area, land 700; 50 is , 2 2 epciey In respectively. PA 2 0.5 1895 )—is A , Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 1896 omlsdt h rtya fdt ie er15 o ru ,ya 90frGop2 t. n the all and For are etc.) order, density. 2, Values (in population represent Group and lines for 2–5. four (LPD) 1960 the Groups density plots, year population five for 1, linear all Group values population, For for line. area, show each 1950 bottom) for charts year to value (i.e. top 2000 four data year from remaining the of is the year label first numerical 1; the Group to normalised for values presents 3. Figure eae ssrrsn.Goercmeans Geometric five surprising. over consistency is magnitude. of decades and degree shape the Again, curve distri- retains LPD the bution popu- but time, declined Over has 1. 1950–2000 density Group lation in during UAs 142 LPD the for and density lation lt,pplto,ae n ouaindniycag infiaty u P ean eaieyconstant. relatively remains LPD but significantly, change density population and area population, plots, iue4peet itiuin fpopu- of distributions presents 4 Figure hne nma ra omatiue o Subnaes 9020.Telregraph large The 1950–2000. areas, urban US for attributes form urban mean in Changes UIND MARSHALL D. JULIAN rdcin P ausdrn h next the during following are values the changes LPD suggest but results prediction: increased, These has small. GSD declined has 1.8– and GM and time, Over 17–19 respectively. are 2.0 4 Figure LPD in distributions the for dimensionless) (GSD; deviations G;uis m units: (GM; 2 1 n emti standard geometric and ) Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 00a n15 ( 1950 in people in from of as con- number 2000 length same 1950–2000, the across during roughly in An km tained 28.2 land to increased residents. km of 16.0 which existing strip Akron, metre-wide than As times average land each 2.6 2.6. occupied time, average more is on over resident grew new 1950–2000, population Akron’s during Akron for 15–00 o ru ra ra.Wiepplto est itiuin aedcie vrtime, over declined have distributions density population While areas. urban 1 Group for (1950–2000) 4. Figure n t adae nrae yafco f3.1 km of 797 factor people) to a 000 by 255 570 increased (from to area land 000 55 its 370 1950– and by (from During increased cent Ohio. per population Akron, Akron’s density 1: 2000, Group population alphabetically UA in while first the consider time declines, over stant m respectively. 14–17 2.0–2.3 of GSD and and GM have to are expected 2030) and 2020 2010, (years censuses three . euto npplto est (from density km population 715 to in 1440 reduction 2.0 82k)adLDdcie yol 12 only to m by 16.0 20.2 to declined (from 23.0 (from LPD cent cent per and per km) 80 28.2 by increased ie ihru rdw.FrArn H the OH, Akron, For down. or up either time, population decreasing density. a at living were people silsrto fhwLDcnrmi con- remain can LPD how of illustration As o niiulUs P hne over changes LPD UAs, individual For n neuto 1,bsdo hs aafor data these on based (1), equation in itiuino ouaindniyadlna ouaindniy(P)frtesxcnu years census six the for (LPD) density population linear and density population of Distribution 2 2  .Sur oto adarea land of root Square ). 2pol) u hs 22 those but people), 22 2 ,yedn atrof factor a yielding ), h P itiuinhsntcagdsignificantly. changed not has distribution LPD the ADAE N OUAINGROWTH POPULATION AND AREA LAND 2 1 .Tevalue The ). 2 1 lsdrn–ierl o ouaindensity population for ( rule rank–size gener- the alised of example, For form rule. rank– generalised rank–size the Zipf’s to mimic that well population rules size LPD—conform area, and density investi- here—population, attributes form gated urban Area, main four Population, The for LPD and Density Population Rules Rank–Size long-term this of mobility. pre- straightforward description Results and novel mathematical in UAs. a mobility offer among distributions here population sented and LPD from within results both in 4 Consist- time Figure distribution. over the down ency UAs or individual up move while an unchanging, experiencing (nearly) UAs of decline cent a per experiencing increase. in UAs 30 with of change cent, and cent per median 30 per is the 70 1950–2000 Among UAs, during 29). 1 LPD to 60 of Group factor (from CA a the PA by Jose, Pittsburg, decreased San for and for 2 47) 3 to of 14 factor (from a by increased 9020.I h aepro,LD(m LPD period, same during the cent In per 12 1950–2000. minor—only was change r )is hs h vrl P itiuinis distribution LPD overall the Thus, r i ¼ Ki a where , r i stepopulation the is 1897 2 1 ) Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 il h aksz ueprmtr for The 2. parameters Table in rule provided shown), UAs (not rank–size 1 Group area the land figures yield and analogous for population and Best-fit for 5, rule. Figure rank-size for generalised lines confor- a perfect to indicate mity would in line figures straight a these UAs; 1 Group for values and LPD density population presents for 5 analo- Figure are gous. attributes rules form urban three other rank–size the Generalised constants. twl ognrlsdrn–ierls For data, rules. population 1950 rank–size year data generalised the the to that indicating well 1, fit to close are values population with area urban ranking density the for density 1898 03.Tedsrbtossonhr upr eeaie eso fZp’ uefrpplto density population for (Pumain, rule rule Zipf’s rank–size of version population generalised (1949) a Zipf’s 1950–2000. support investigate during censuses here to six shown used the distributions for plot areas, The similar urban 2003). a 1 Group mirrors for figure are plotted This Values (right). rank LPD and 5. Figure rt h lblRrlUbnMapping Rural–Urban Global The evaluated. the are databases first, This the Three throughout areas. globe. areas urban urban considers Canadian) section in analysis, (and, US one only consider above analyses The Internationally LPD and n for Values original the the rule. not to but rule well and rank–size conform generalised LPD data contrast, density In population rule. rank–size (non-gener- million), alised) original 12 the for versus support million indicating (15 value largest K sapoiaeyeult h dataset the to equal approximately is eainhpbtenpplto est n ouaindniyrn lf)adbtenLPD between and (left) rank density population and density population between Relationship i and , K and a r empirical are a UIND MARSHALL D. JULIAN 2 and 1 n o LPD. for and R 2 con o 7prcn fcte nthe are in 6 cities Figure of countries of cent three attributes per these Two 77 database). US; for the account and (Thailand, presented Nations, in India countries and three density United for 17 similarities population LPD in general in in trends shows cities between 6 8 394 Figure for 2000a). (Table area land countries and lation LPD. mean lation-weighted ra ra,GUPdt r iia for similar US are and with data LPD GRUMP median Compared areas, areas. urban are urban GRUMP Census in values  density population areas urban all average country. for the each area within on land based and LPD population estimate to para- here the time-series, for or estimates meter generate panel cross- cannot are than they data rather GRUMP sectional the prelimi- Because considered values nary. be should thus, next 218 in 2004); presented still in (CIESIN, version—i.e. ‘alpha’ development values areas an GRUMP urban currently are 2004). 55384 (CIESIN, for countries area and size land population of dataset comprehensive cross-sectional a provides (GRUMP), Project 0prcn ihrta ausfrUS for values than higher cent per 50 h eoddtbs rvdsubnpopu- urban provides database second The einadpplto-egtdmean population-weighted and Median n ahr h RM aaaeused are data GRUMP the Rather, .  ie oe o popu- for lower times 3 Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 P 2 m 220 km 3,800 density Population LPD ra adae ,0 km 3,200 area land Urban itro P hno ouaindniy(i.e. density in population of R than than LPD pre- LPD of better dictor a is in areas population urban first, variability density): urban greater among yields variability population ra ouainteei arwrrange given narrower a a for is lines, there comparing population best-fit when urban three or the country among one and for data comparing within-country points when (i.e. for density less than population LPD popu- for is variability urban between-country specific there plot); any left lation, the in in secondly, than plot and, right the in greater en eaieymr eedn npopu- (i.e. is density on density population LPD with dependent compared more lation of relatively results being necessary mathematically a hiad n h S ifrne mn h he onre r iia ntelf n ih plots. right and left (i.e. the density in population similar than are LPD countries of predictor three better the a among is Differences population US. Urban the and Thailand, 6. Figure ouain1 ilo 8mlin1 ilo 7million 57 million 15 million 18 million 12 Population ags aae ausaepeetdhr o oprsn hyaentaprmtri h oie aksz rule. rank–size modified the in parameter a not are they comparison; for here presented are values dataset Largest 2 ausfrtebs-trgeso ie are lines regression best-fit the for values ieaelre ntergtpo hni h etpo) aaaefo h ntdNtos(2000a). Nations United the from are Data plot). left the in than plot right the in larger are line eainhpo ra ouaint ouaindniy(et n oLD(ih)frIndia, for (right) LPD to and (left) density population to population urban of Relationship PA 2 al 2. Table 1 n P is LPD and ags au ndataset in value Largest 9020 9020 9020 902000 1950 2000 1950 2000 1950 2000 1950 oie aksz ueprmtr o ru ra areas urban 1 Group for parameters rule rank–size Modified 2 2 2 1 2 ADAE N OUAINGROWTH POPULATION AND AREA LAND ,0 km 1,700 400km 14,000 PA 5 m 150 2 0.5 thus, ; 2 2 a 2 1 2 ,0 km 6,200 ,0 km 5,900 3 m 230 essdtst n h er19 median km 1550 1990 US 1990 is year year density the the population and in dataset) million than census 2.5 larger the is times population (22 densities: median large 1990 population and year relatively Kenworthy and have the populations dataset 1960– in (2000) during areas Laube per population These 10 than in 1990. greater a increase with con- cent areas here 26 Analyses the areas. sider urban 1960– during 35 decade for by 1990 area land and popu- lation contains (2000), Laube and Kenworthy plot). left of ag si h S.Vle o h parameter the for Values US). the n in as large (mean h hr aaae ae aae by dataset panel a database, third The y 2 2 ai ausi h ih ltta nthe in than plot right the in values -axis 2 1 2 K ,0 km 2,300 000km 50,000 ¼ 8 m 280 .;median 1.7; 2 2 2 1 2 2 2 2 2 0.32 0.62 0.97 1.06 R ¼ 2 ausfrtebest-fit the for values a .;rne 0.6–3.9) range: 1.5; 2 2 2 2 .507 0.95 0.74 0.95 0.35 0.98 0.88 0.71 0.96 1.02 .009 0.93 0.99 1.20 2 2 tieas (twice R 1899 2 Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 aiblt netmtdvle for values estimated in variability nyi vrg P ssgetdb h value the by n suggested is conform consist- LPD though average to Even in rule. ency appears size–rank distri- a LPD to the well values. in of mainly stability bution long-term consideration of careful because worth is LPD Implications multiple over constant values, decades. median approximately distri- and LPD are mean the of including magnitude bution, that and data census shape US the corroborates the it from panel observation areas, the com- urban international contains large and paratively small other. this relatively each is to dataset although similar are in 1990 Thus, shown) in (not and distri- values Cumulative 1960 LPD cent. for per plots 20 butions than less are o28m 208 to during change cent m 62 per value: 5 the than 1960–1990; for than (less larger US significantly over Canada. are constant and and roughly and time are Kenworthy data US the (2000) for Laube the values LPD for Median values above than, smaller slightly reported or to, similar are uig16–90 u h hne (from changes the m but 82 increased 1960–1990, values during LPD popu- mean and Mean lation-weighted US). the for than higher times ayfcosiflec xaso fthe of expansion influence implications. their factors understand Many to and patterns, within-city form) mobility to as jobs (such them dynamics relate urban findings, these both migration. considering between-city and those within- growth especially urban models, calibrating and for useful corroborating be this may LPD on consistency, Based long-term half-century. UAs past consist- the such over shown the ency have attri- form average for urban other of any, butes decades if per Few, here. multiple 10 studied expected. than over less be changed cent might has LPD LPD Average average in varia- greater bility that groups area among and UAs 1900 ¼ diinlwr sncsayt explain to necessary is work Additional / o qain() hr ssufficient is there (1), equation for 2 2 osn aac,plcnrcurban polycentric balance, housing 1 o9 m 96 to 2 1 o ouainwihe mean) population-weighted for 2 1 o en rm15m 175 from mean; for 2 1 hc ssix is which , n UIND MARSHALL D. JULIAN among 2 1 ain nti okwt individuals’ interactions with environmental work (Anas and this decisions in vations of expansion by area. land influenced urban long is the similarly factors as A of such culture. list factors and social values and, norms, crime); and disamenities as and amenities (such restaurants) employment parks, of as prevalence (such housing, and education; supply quality for as such demand infrastruc- factors other economic and geogra- ture; systems physical transport including phy; area, land urban adta hi er,wientexceeding not while and peers, constraints income their than more land consume resi- to existing desire of people’s reflects area dents land capita per about the each occupies twice that average, on fact newcomer, the urban perhaps Or, popu- density. two- linear lation in the consistency fact long-term this of to and leads them, transport terms around along in space dimensional as than such rather manner, corridors, linear a environment in their form with interact to urban people leads vehicle-centric modern perhaps uha oo eilsi nubnae,can area, urban source, an in emission vehicles motor an as to such attributable health motor impact environmental of The effects emissions. health vehicle to relates here sented this if LPD widespread. more to becomes questions metric normative apply worthwhile be to influ- may to it how density, literature population and ence whether planning about in practice and debate Given significant pattern. this the shift to whether try discuss should not planners does article while the time, over example, consistent be to For observed are distributions normative. LPD than growth— urban rather about observations of series a and costs changes housing income, costs. multidecadal transport in cities reflect among pre- here results urban standpoint, the sented and at this curve land From area new bid-rent boundary. developing urban the of cost of an the slope of free- the size the reflects equilibrium that argue market Economists travagant. uuersac a onc h obser- the connect may research Future n rcia plcto ffidnspre- findings of application practical One empirical— are here presented analyses The tal. et 98.Freape ospeculate, to example, For 1998). , / rapaigoverex- appearing or Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 spootoa oLD o ouaindensity as population (Lai not LPD, to (such areas proportional urban is in benzene) emissions and monoxide carbon vehicle the non-reactive in atmospheric for pollutant fraction a Intake of environment. persistence people, and mixing and atmospheric to owing emissions of emissions rate dilution population, between exposed the proximity of size the including possible. when (reduced) avoided be that efficiently to lungs—something is more people’s are to indicate delivered emissions would A vehicle value emitted. that fraction kg collec- per intake inhaled residents larger are urban mg by 15 tively average, on that, urban US (Marshall in for areas emission value vehicle typical of a types is certain which million, fraction per intake 15 of an of example, efficiency’ For area. ‘exposure urban an the to zero quantifies from one, ranging number dimensionless eils n ol lone otakover track to of need also impacts would health one environmental vehicles, under- to the course, (Of stand constant. be emission also the vehicle would of then mass time, per impact over exposure constant were given area a in urban emissions vehicle of the fraction If intake emissions. vehicle motor urban forecast time-scales. multidecadal over constant urban approximately a remained of has to emissions fraction vehicle Thus, decline intake 1). approximation, cent Group first per for 25 are 1950–2000 a during LPD example, (for decades. population-weighted modest several in past changed as Changes the not areas, over has urban LPD, significantly US average by in between measured vehicles here proximity and presented well- average people Results that spatially mowers cleaners.) suggested lawn dry are gasoline and as that outdoor such example, distributed, sources’ vehicles—for ‘area similar motor sources for hold to to likely is same (The oiiy(elhipc e asinhaled) mass per impact (Bennett and (health emitted) intake three mass day), toxicity per of per inhaled (mass product (mass fraction rate the emission as terms: estimated be often naefato eed nsvrlfactors, several on depends fraction Intake ra lnigseaisaeotnue to used often are scenarios planning Urban tal. et tal. et 00 Marshall 2000; , 02.Itk rcin a fraction, Intake 2002). , tal. et 05) ol mean would 2005b), , ADAE N OUAINGROWTH POPULATION AND AREA LAND tal. et 2005b). , ie esrta h einU 10 versus km (1700 490 UA median the 3.5 than is denser Angeles times Los example, For does. density population than areas urban among more varies planners, urban assessors. risk and for exposure lution pol- air important and presented practitioners between health environmental Findings are (and areas). here rural areas and urban signifi- urban varies among emission impact vehicle cantly exposure of the mass between areas), per rural (and and areas urban urban sig- among varies fraction constant nificantly intake mean roughly Because US time. appear over but values area, results median given and any on increase in may Based decrease fraction or contrary.) intake here, evi- the of presented lack to a to part dence in owing time, con- For over assumed stant is toxicity toxicity. pollutants, all or and frac- most intake emissions besides terms tion—namely, other two the time elh(e Marshall public (see and health a pollution vehicle air of be consumption, standpoint LPD—may energy the small from goal popu- a planning large but a density has lation IA—which areas Ames, as urban such that high-density suggest would small-population, this LPD, to proportional Cervero, Holtzclaw and Frank (Ewing 2001; proportional density are population exercise to other and walking to wish controls. emission might stringent more values seek fraction intake higher 11vru . m 7.8 UA median versus the than (141 Angeles times Los for 18 greater fraction—is intake approximation, 00wr nlsdt netgt changes investigate to analysed 1950– during were (UAs) 2000 areas urban US for Data Conclusion via vehicle achievable choices. and be design urban neighbourhood-scale also people reduced emissions—may between and levels proximity exercise increased tion, consump- energy vehicle objectives—reduced h nig ugs htitk fraction intake that suggest findings The ial,i eil sg n eesof levels and usage vehicle if Finally, 2 2 ,btLDadhne oafirst a to hence, LPD—and but ), tal. et tal. et 02 u naefato is fraction intake but 2002) , 05 rmkn 2002; Frumpkin, 2005; , 2 1 tal. et .Ubnaeswith areas Urban ). 05) Similar 2005a). , 1901 Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 einvleof value median a A References implications. practical the and further explore underpinnings theoretical the investigate hs nig o te aaes(o example, (for Angel datasets other for findings these here. presented findings the of appli- practical cation of one is fraction emissions Intake vehicle urban consist- distributions. LPD multidecadal in ency reveals rapid or also moderate with growth), although areas dataset, urban panel (26 small The one data. and panel data with cross-sectional (1949) with investi- one Zipf’s were gated: datasets of international forms Two conform rule. generalised LPD to among and than well density averages more a Population varies for for LPD. density or (either population area areas), but, time urban density; over single population comparing than when more varies areas. mathematical urban among mobility and Results within population straightforward long-term time. of over description a consistent so provide urban of are attributes average form other fact, any, 1950–2000. if in during Few, are, investigated constant groups approximately UA the for distributions time. (LPD) density over population constant Linear approximately be would ainsz nrae ymr hn1 per group 10 than for more values by Typical cent. popu- increases when size well lation reasonably hold to appears A vrtm nubnln rasz ( size area land ( urban size population in time over 1902 A A NDERSON NAS NAS Literature structure, spatial Urban h aepnnilmncnrcmodel, monocentric Economics Urban of panexponential Journal The 5 p 413–425. pp. 25, iy eprlcagsi ui-pieurban cubic-spline in patterns, changes density temporal city: a diinlwr ol sflyconfirm usefully could work Additional LPD UAs, comparing when general, In / . A A., , A A., , tal et P PA n where , .E 18)Tecagn tutr of structure changing The (1985) E. J. , 2 ,20 n Robinson and 2005 ., RNOTT 6 p 1426–1464. pp. 36, , RNOTT 0.5 ‘ierpplto density’) population (‘linear P .J n S and J. 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US of urbanized 3 section characteristics, areas, population general 1.html). rnil fLatEffort Least Addison-Wiley. of Principle onaymvmn n htoshape, ghetto Studies and movement boundary W iiin(http: graphic Division book esn bevtosfo Shuttle-Mir from Sons. & Wiley John Observations Missions Sensing (Eds) essbsdo eorpi analysis, demographic States 1061–1071. United Association pp. on Statistical 88, American 1990 the of based the Journal in Census coverage lation o ifslaw, Zipf’s for 6 p 397–401. profile, pp. metro- density 26, Vancouver the area’s at politan look brief a gradients: ueuo h ess ahntn C(http: DC Washington, www.census.gov Census, the of Bureau classification rset:Te19 Revision 1999 org The Prospects: naso einlSine(Historical Science Regional gradient, of density Archive) population Annals urban the n t eemnns aesuyo Tokyo, of case-study a Studies Urban determinants: its and ot mrc unie yaayi of L P. analysis K. Shuttle- by in: and Skylab Mir, Apollo, quantified from photographs America North 257–260. urbanization.pdf). .K (1949) K. G. , OODROW ENSUS / ENSUS / .I 19)Hsoia ahdpnec of path-dependence Historical (1993) I. D. , esa .P 19)Mtooia pta structure spatial Metropolitan (1991) X.-P. , .M 20)Asml n fcettest efficient and simple A (2000) M. C. , e ok ntdNtosStatistics Nations United York: New . population .B 18)Tednmc fghetto of dynamics The (1980) B. J. , yai at niomns Remote Environments: Earth Dynamic N N 7 p 231–235. pp. 17, , / / .G,A G., J. , 7 p 259–283. pp. 27, , p 54,22 6–7.NwYork: New 269–270. 262, 25–41, pp. , ATIONS products ATIONS population .(99 nesosi ra density urban in Inversions (1989) A. , (2004) (1992) .A 19)Etmto fpopu- of Estimation (1993) A. K. , SDprmn fCommerce, of Department US . 8 p 87–104. pp. 28, , / / www / (2000b) geo ess20 ra n rural and urban 2000 Census (2000a) HMED // cnmc Letters Economics dyb ULLA 90Cnu fpopulation, of Census 1990 / ua eairadthe and Behavior Human unstats.un.org pubsarchive / / eot1990–CP–1–1C, Report www / dyb2000.htm). censusdata . G B., , n .V D V. L. and ol Urbanization World eorpi Year- Demographic abig,MA: Cambridge, . / ua UPTA / // ra Studies Urban ua_2k.html). / urbanization / (www.un , www.census. / unsd 90pubs .D and D. P. , 6 pp. 66, , ESSINOV / Urban demo- 1903 n / The cp- // in / / , , Downloaded By: [Marshall, Julian D.] At: 18:58 11 September 2007 h ete(at centre the Radius aaee o h ra raEquation 1951) (Clark, gradient density Population area urban the for Parameter A1. 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