landscape ecology land use structure & population density

8/17/2019 Landscape Ecology Land Use Structure & Population Density

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Landscape and Urban Planning 105 (2012) 74–85

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Landscape and Urban Planning

journal homepage: www.elsevier .com/ locate / landurbplan

Landscape ecology, land-use structure, and population density: Case study of theColumbus Metropolitan Area

Jia Lu a,∗, Jean-Michel Guldmann b

a Geosciences Program, Valdosta State University, 1500 N. PattersonSt,Valdosta, GA 31698, USAb City andRegional Planning, Ohio State University, 275West Woodruff Ave, Columbus,OH 43210, USA

a r t i c l e i n f o

Article history:

Received 17 February 2011Received in revised form

21 November 2011

Accepted 30 November 2011

Available online 3 February 2012

Keywords:

Population density

Urban modeling

Landscape ecology

Land use

GIS

Quantitative analysis

a b s t r a c t

Traditional population density models based on the distance to the major Central Business District (mono-

centric) or on distances to multiple employment centers (polycentric) are extended to include land-use

structure variables derived from landscape ecology theory. A comprehensive database is developed for

the Columbus Metropolitan Area (CMA) at the Traffic Analysis Zone (TAZ) level, using remotely sensed

land-use data, Census socio-economic data, and other local data. Fifteen landscape indices, organized into

four groups – size, complexity, diversity, neighborhood – are computed for each of the 1763 CMA TAZs,

using Fragstats. Models are estimated for each of the 7 CMA counties separately, yielding homogeneous

and consistent results. These county models are then pooled into a comprehensive CMA model, with

dummy variables and second-order terms. Overall, the results provide evidence of a polycentric struc-

ture, with both downtown Columbus and county CBDs acting as strong population attractors, and of the

importance of land-use structure in the determination of population density. Spatial indices representing

neighborhood and diversity factors significantly impact population density in most counties.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

The spatial distribution of a city’s population reflects economic,

social, technological, and market conditions, as well as planning

policies (e.g., infrastructure expansion), withsignificant impacts on

its social and environmental functionalities. Models of population

distribution and density are therefore central to forecasting urban

futures, andof great significanceto planners andpolicy makers. Not

surprisingly, population density patterns have been studied exten-

sively. Early research has focused on monocentric models, with

distance to the Central Business District (CBD) as the major deter-

minant of population density. The negative exponential model

with a constant gradient, as pioneered by Clark (1951), became the

“standard theory” (McDonald, 1989), under the assumption of a

long-run equilibrium between utility-maximizing consumers and

profit-maximizing suppliers of housing, with all jobs located in

the CBD. Newling (1969) proposed an alternative model by adding

a quadratic term in the exponential equation, and addressed the

existence of a density peak away from the city center. A review of

these monocentric population models is reported in Smith (1997).

Starting in the 1980s, this model gradually evolved into a polycen-

tric one to account for increasing suburbanization, the decline of

∗ Corresponding author. Tel.: +1 229 333 5752; fax: +1 229 219 1201.

E-mail addresses: [email protected] (J. Lu), [email protected]

(J.-M. Guldmann).

the historical CBD, and the emergence of new employment centers(Gordon, Richardson, & Wong, 1986; Griffith, 1981). The decline in

the CBD-related density gradient has been viewed as proof of the

shift from a centralized to a more dispersedurbanform after World

War II. The assumption of the polycentric model is that both work-

ers and employers value access to all employment centers in their

location decisions. At any location, density is taken as a function

of the distances or travel times to multiple employment centers.

Other variables (e.g., racial factors, metropolitan size, trans-

portation cost, and city age) and functional forms have been

used to explain population density (Alperovich, 1983). In addi-

tion, researchers have experimented with models better suited to

multiform density patterns. For instance, McDonald and Bowman

(1976) testten functional forms with 1960 census data on 16 urban

areas, including the negative exponential, binomial, gamma, lin-

ear, and quadratic forms. The exponential model with a quadratic

term provides the best fit. Models such as cubic spline (Anderson,

1982) and cubic polynomials (Bunting, Filion, & Priston, 2002) rec-

ognize the existence of more than one density peak and account

for both central city and suburban density inflections. Combin-

ing the use of GIS, 3-dimensional models and cartographic display

of population, Millward and Bunting (2008) have produced new

volcano-type density analyses based on local indicators of spatial

autocorrelation, capturing directional and sectoral density varia-

tions, and identifying inner-city and peripheral re-densifications.

Thus, from monocentric to multicentric modeling, from simple

exponential functional forms to a variety of other forms, from a

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J. Lu, J.-M. Guldmann / Landscape and Urban Planning 105 (2012) 74–85 75

simple distance variable to a variety of explanatory variables, and

from 2-dimensional to 3-dimensional models, urban population

density models have been expanded to better represent more

decentralized urban systems.

However, specialized land uses and a variety of social and

economic factors that drive development, make cities difficult to

analyze. Distances to major centers alone may not be sufficient

to explain density patterns. Urban development and the conver-

sion of rural, agricultural, and forested lands to mostly residential

uses, are major sources of site-dependent landscape changes, and

these changes may provide insights into population density pat-

terns. However, there has been no research as to whether spatial

landscape indices, as measures of land-use structure, may help fur-

ther explain population density. Research has shown that these

indices areable tocapture thedegree of human manipulation of the

landscape and to predict various ecological processes (O’Neill et al.,

1988). This paper introduces spatial indices, derived from land-

scapeecology, intopopulation density models. The overall research

hypothesis is that land-use structure, as measured by theseindices,

together with location characteristics and distances to major cen-

ters, has a significant impact on population density.

Research shows that surrounding land use types can affect the

development of the land itself, and neighborhood conditions offer

substantial predictive power (Zhou & Kockelman, 2008). This isalso a basic assumption in cellular automata models. Our gen-

eral hypothesis is that more complex and diverse patterns of land

use/land cover, less dominance by anyspecific land use, and higher

edge contrasts and inter-mixing of land uses, all of which create

more restrictions on land development, because of a likely com-

plex pattern of land ownership, more competing demands of land,

and the difficulty of assembling parcels of land into larger tracts

suitable for residential subdivisions and other large-scale develop-

ments. These restrictions are then expressed in the form of zoning

constraints, which preclude achieving economies of scale and lead

to higher costs of land development. Higher development den-

sity is then necessary to offset these higher costs. In contrast, it

is reasonable to assume that less complex and diverse patterns

imply fewer zoning restrictions on land development, less com-peting demands for land, and therefore lower development costs.

As a result, low-density developments become feasible, resulting

in lower population density. These hypotheses are examined by

analyzing the statistical relationships between (1) fifteen spatial

indices, eight locational characteristics, and distances to several

centers, and (2) population density in the case of the Columbus

(Ohio) Metropolitan Area (CMA). The results provide evidence that

several landscape indices have significant impacts on population

density.

The remainder of the paper is organized as follows. Landscape

ecology indicesand their applicationsare reviewedin Section 2. The

methodology is presented in Section 3. An overview of the CMA is

offered in Section 4, and the data sources aredescribed in Section 5.

The empirical results are presented in Section 6. Section 7 presentsa summary of the results and a discussion of caveats. Section 8

concludes and outlines areas for further research.

2. Landscape ecology indices

2.1. Overview and definitions

Landscape ecology is based on the idea that there is a

link between spatial ecological pattern and processes. Spatial

indices or metrics have been developed by community and

population ecologists to study this link, using theoretical con-

cepts of disturbance, island biogeography, and information theory

(Gustafson, 1998; O’Neill et al., 1988; Tilman & Kareiva, 1997;

Turner, Gardner, & O’Neill, 2001). These indices are commonly

related to patch size, complexity, diversity, and neighborhood

structure. Size-related indices measure patch size characteris-

tics. Complexity-related indices measure how complicated patch

shapes are. Diversity-related indices measure how diversified

patches are. Neighborhood-related indices measure the rela-

tionship of a patch with its neighbors. Detailed mathematical

descriptions of these indices are available in McGarigal, Cushman,

Neel, and Ene (2002).

Because the Traffic Analysis Zone (TAZ) is the basic spatial unit

forthe empiricalanalysis reported in this paper,it is used in the fol-

lowing discussion. TAZs are made of blocks and block groups, and

are generallysmaller thantracts. Theyare defined by thedelineated

by state and/or local transportation agencies, such as Metropoli-

tan Planning Organization(MPOs).The U.S.Census Bureau provides

data forTAZs in conjunction with thecensus.All indices aredefined

foreachTAZ separately.EachTAZ is made ofa small orlargenumber

of patches, and each such patch represents a homogenous land-use

polygon. There may be, of course, several patches of the same land

use within a given TAZ, as long as they are not adjacent.

2.1.1. Size indices

The mean patch size (MPS) represents the average size of all

land-use polygons. The median patch size (MEDPS) representsthe median area of all land-use polygons. MEDPS complements

MPS when the distribution of patch sizes is skewed. The differ-

ence between the largest and smallest patch size is represented by

DMMA.The larger DMMA, the morepatch sizevariations. The patch

size standard deviation (PSSD) measures the distribution spread of

patch sizes.

The assumption of this study is that the higher MPSand MEDPS,

and the lower DMMA and PSSD, the less urbanization and the

more agricultural or forest land, hence fewer restrictions on future

land development. This implies less competing demands for land,

lowerdevelopmentcost, and,therefore, a higher likelihood of lower

development density.

2.1.2. Complexity indicesThe shape complexity index (SC) is calculated as the average

of the perimeter-to-area ratios of all land-use polygons. A high

value of SC indicates greater shape complexity. The circle has the

least perimeter-to-area ratio. The mean polygon fractal dimension

(MPFD) is an index of the complexity of the shapes of all polygons,

ranging between 1 and 2. MPFD approaches 1 for polygons with

very simple forms, such as circles or squares, and 2 for polygons

with highly convoluted perimeters. The mean shape index (MSI)

equals 1 when all patches are circular (vector) or square (raster),

and increases without limitas patch shapes become moreirregular.

The assumption of this study is that the higher SC, MPFD, and

MSI, probably the more mixing of land uses, the more compet-

ing demands for land, and therefore, the more restrictions on land

development. Suchrestrictionsimply a higher costof development,requiring higher development densities to offset these costs.

2.1.3. Diversity indices

Originally measures of diversity of species, these indices take

into account the relative abundance of different species. The num-

ber of polygons (NP) is the total number of different polygons

across all land uses. The relative patch richness (RPR), also called

evenness, represents the maximum diversity possible for land-use

types, and is calculated by dividing the number of patch types in a

TAZ by the maximum number of patch types in the whole region.

The larger RPR, the more diverse the TAZ. The Shannon’s Diversity

Index (SHDI) accounts for both the abundance and the evenness

of the land uses present in an area. SHDI increases as the num-

ber of different patch types increases, and/or the distribution of


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76 J. Lu, J.-M. Guldmann / LandscapeandUrban Planning 105 (2012) 74–85

the area among patch types becomes more even. For a given num-

ber of land-use types, SHDI is maximized when all land uses have

the same area. The Shannon’s evenness index (SHEI) is equal to

SHDI divided by logarithm of the number of land-use types. SHEI

ranges between 0 and1. SHEI = 0 when the landscape contains only

1 patch (no diversity) and approaches 1 as the distribution of the

area among different patch types becomes increasingly even. The

Dominance Index (DO) measures the magnitude of the dominance

of one or a few landuses over the others ina given area. This index

has been developed by O’Neill et al. (1988), based on information

theory. Large values of DO indicate that the area is dominated by

very few land-uses, whereas small values suggest a relatively even

distribution of land-uses.

The assumption of this study is that the higher NP, RPR, SHDI,

and SHEI,and thelower DO, the more land-use mixing, probablythe

more competition forland,and hence themore restrictionson land

development. These restrictions imply a higher development cost,

and,therefore, a higher development density to offsetdevelopment

costs.

2.1.4. Neighborhood indices

The Mean Edge Contrast Index (MECI) represents the mean

contrast between a given polygon and all polygons within a user-

specified neighborhood, based on contrast weights assigned to theedge lines between polygons. The average of all contrast values of

all edge lines is MECI. MECI= 0 if the landscape consists of only 1

polygon or the boundary contains no edge. In addition, MECI= 0

when all polygon perimeter segments involve polygon adjacencies

that have been given a zero-contrast weight. MECI= 100 when the

entire polygon perimeter is the maximum-contrast edge (w=1).

The MeanNearest-Neighbor Distance(MNN) refers to the distances

between polygons with the same land-use type. MNN equals the

average distance to the nearest neighboring polygon of the same

type, based on shortest edge-to-edge distance. MNN can be 0 if

there is no nearest neighbor. Polygons must be non-adjacent to be

included in the search for the nearest neighbor.

The Interspersion and Juxtaposition Index (IJI) is the only mea-

sure that explicitly accounts for the spatial configuration of patchtypes. Each patch is analyzed for adjacency with all other patch

types, and IJI measures the extent to which patch types are inter-

spersed, that is, equally bordering other patch types. IJI represents

the ratio of observed interspersion over maximum possible inter-

spersion for a given number of land-use types, andranges between

0 and 100. IJI approaches 0 when the distribution of adjacen-

cies among unique land-use types becomes increasingly uneven.

IJI= 100 when all land-use types are equally adjacent to all other

land-use types (that is, maximum interspersion and juxtaposition).

The assumption of this study is that the higher MECI, MNN,

and IJI, the more fragmented and complex the area in terms of

land-use mix, probably more competingdemands for land, andthe

more restrictions on land development. Such restrictions imply a

higher cost of development, and, therefore, a higher probability fora higher development density to offset higher development costs.

2.2. Applications of landscape indices

2.2.1. Natural environment

Kareiva (1990) shows thattheoretical ecological models (island,

stepping-stone, continuum) make it clear that the spatial subdivi-

sion of habitat can alter the stability of species interactions and

opportunities for coexistence, but suggests that the empirical chal-

lenge is to investigatemore rigorously therole of spatial subdivision

and dispersal in animal and vegetal communities. The following is

a short overview of such empirical studies.

Miller, Brooks, and Croonquist (1997) find that several indica-

tors of diversity and contagion are most effective in explaining the

levels of disturbance in bird and plant guilds in two watersheds.

Nott (2000) uses the mean patch size (MPS) to explain the popu-

lation of adult birds observed in deciduous woodlands and forests.

Tscharntke, Steffan-Dewenter, Kruess, and Thies (2002) show that

habitatsize andthe spatial arrangementof habitatfragments have a

significant impact on butterflies density. Perfecto and Vandermeer

(2002) use landscape metrics to analyze the decrease in the num-

ber of ant species away from a forest fragment. Steffan-Dewenter

(2003) investigates howthe densities of bees, wasps,and their nat-

ural enemies, vary with habitat area, diversity, and connectivity.

Theresults suggest that the structure of the surrounding landscape

is particularly important when species mainly prefer one habitat

type, but are also able to use different parts of the landscape (habi-

tat compensation). Finally, Castrejón, Pérez-Castañeda, and Defeo

(2005) use MPS to explain the spatial structure of shrimp popula-

tions.

Gibson, Pearce, Morris, Symondson, and Memmott (2007) use

MPS, the mean polygon fractal dimension (MPFD), the mean shape

index (MSI), and the dominance index (DO) to explain plant diver-

sityin bothorganic andconventional farms. Hurd, Wilson, Lammey,

andCivco (2001) use MPS, the patch size standarddeviation (PSSD),

and the shape complexity index (SC) to explain forest and non-

woody vegetated land cover dynamics. McGlynn and Okin (2006)

alsouse PSSD to analyze vegetation dynamics. Zeng andWu (2005),using data from China’s Wolong Natural Reserve, find that edge-

related indicators successfully measure landscape fragmentation.

Pfister (2004) uses MSI and MPFD to capture variations in for-

est fragmentation. Gustafson and Rasmussen (2002) use MPS to

determine the sensitivity of the landscape for forest management

purposes. Venema, Calamai, and Fieguth (2005) use the mean near-

est neighbordistance index (MNN) andother indicators to optimize

forest patch selection, applying a genetic algorithm. Finally, Lloret,

Calvo, Pons, and Díaz-Delgado (2002) use MPS and MNNto explain

wildfire patterns.

2.2.2. Built-up environment

Landscape metrics applied to urban land-use patches have been

used to analyze a variety of issues at the local and metropolitanscales.

Bockstael (1996)and Geoghegan, Wainger,and Bockstael(1997)

use spatial indices, such as the fractal dimension, the length of con-

flicting edges between residential and other developments,and the

percentage of preserved open space, in hedonic models of residen-

tial housing prices. Property values arefoundto increase with open

space and decrease with conflicting edges. Luck and Wu (2002)

compute several size and shape metrics along a 165km long and

15km wide transect of the Phoenix metropolitan area, and use

themto detect urbanizationgradients. Ji, Ma, Twibell,and Underhill

(2006) compute several landscape metrics for six different periods

(1972–2001)over the Kansas City metropolitanarea, anduse them

to identify regional patterns of urban sprawl. Munroe, Croissant,

and York (2005), using a sample of 251 parcels in Monroe County,Indiana, and the interspersion index, the largest patch index, and

other socioeconomic, biophysical and spatial variables, test the

hypothesis that the degree of landscape fragmentation varies with

zoning policies, even after accounting for topographical and socio-

economic differences. A contingency table analysis reveals that

the fragmentation of land uses is much higher at both the county

and parcel levels in places zoned for the highest housing density

and smallest lot sizes. Crews and Peralvo (2008) apply landscape

metrics to block group Census data to document changes in the

spatial configuration of race and class in South Carolina, and show

a strong connection between changes in these indices and changes

in median household income.

Batty and Kim (1992) argue that the power function is the

most appropriate form for population density, as it embodies the


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fractal property of self-similarity, a basic characteristic of urban

form. Schwarz (2010) uses landscape metrics and socio-economic

indicators to characterize and classify 231 European cities accord-

ing to their urban form (physical structure and population

characteristics). Using factor analysis, she identifies basic factors

leading to six clusters of cities. Huang, Lu, and Sellers (2007) con-

duct a similar analysis over 77cities located inAsia,theU.S.,Europe,

Latin America, and Australia. Jenerette and Potere (2010) com-

pute six metrics for 120 cities throughout the world, and associate

each city’s growth over 1990–2000 to changes in these metrics.

They use the results to project future urban landscapes in 2030.

Herold, Couclelis, and Clarke (2005) argue that land-use spatial

metrics deserve a place in the urban dynamics research agenda,

because their analysis over time can lead to specific hypotheses

about the processes at work (from structure to process), revers-

ing the deductive approach where urban structure is the spatial

outcome of pre-specified processes of urban change.

2.2.3. Limitations of landscape indices

The limitations of the applicability of landscape indices are

related to (1) their large number and the high correlations among

them, and(2) whether these pattern indicators are reflective of the

underlying processes they aim to explain.

Hargis, Bissonette, and David (1998) generate artificial land-scapes that mimic fragmentation processes while controlling for

the size and shape of patches, and find that several indices are

highly correlated, especially contagion, mean proximity, and edge

density. Several measures are linearly associated with landscape

disturbance,up to a 40%share of such landscapes, and non-linearly

beyond. The highest attainable value of each index is affected

by the average patch size or shape, and, in some cases, by both

attributes. Out of 26 spatial indices calculated over85 landuse/land

cover maps, Riitters et al. (1995) find that six indices – average

perimeter-area ratio, contagion, standardized patch shape, patch

perimeter-area scaling, number of attribute classes, and large-

patch density-area scaling – account for 87% of the variations of

all metrics.

Gustafson (1998) points to the need to examine the scalingof spatial indices, as the format and scale of the data can have

a profound impact on many indices. Rutledge (2003) argues that

landscape indices are not useful indicators of fragmentation effects,

and points to the need for models that incorporate fragmenta-

tion directly, providing a better understanding of when patterns

of fragmentation are important, and which processes operate at

which scales. Corry and Nassauer (2005) use landscape metrics to

assessthe implications of alternative plans for smallmammal habi-

tat quality,and compare the results with thoseof a spatiallyexplicit

habitat model. Theyfind thatno indexvalidlyassess habitatquality,

pointing to the need for more information about the relationship

between patterns and processes.

3. Methodology

The earlier population density models assumed a monocentric

urban structure, with distance to the traditional central business

district (DCBD) as the unique population density (DP) determinant,

with:

DP = F (DCBD) (1)

New variables were added later to improve the predictability of

the model, such as theovercrowdingin thecentralcity(Galle, Gove,

& McPherson, 1972), manufacturing employment,total population,

the percentage of non-white population, car ownership, substan-

dard housing in central cities, metropolitan size, median income,

a lagged value of the dependent variable (Mills, 1972), per capita

income, metropolitan size, transportation cost, city age, tightness

of the land market (Alperovich, 1983), tax, race, crime, amenities

(Mills, 1992), the urban historical context, changing transportation

technology, time of development, presence or absence of vacant

lots within the city, family size, type of housing, social class, eth-

nicity, method of measuring density, and the role of cumulative

urban development over time (Smith, 1997). These various factors

can be summarized by the vectorX = ( X 1, . . ., X n). Eq. (1) becomes:

DPP = F (DCBD,X ) (2)

Theeffectsof X havegenerally beenmeasuredby firstestimating

Eq. (1) over a cross-section of cities, and then by explaining the

variations of the estimated coefficients as functions of X .

With increasing suburbanization, it became necessary to treat

metropolitan areas as polycentric, with multiple employment cen-

ters. Let D be the vector of distances to these centers. The general

polycentric model is then:

DP = F (D,X ) (3)

As discussedin Section 2.1, land-use structure,measured by spa-

tial indices, is likely to have an impact on population density. Let I

be the vector representing these indices. A generalized population

density function is then:

DP = F (D,X , I) (4)

The following sections describe the regional context, the data

sources and processing, and the procedure for estimating Eq. (4).

4. The ColumbusMetropolitan Area (CMA)

The Columbus Metropolitan Area (CMA) has been selected for

an empirical test of the ideas presented earlier. It is characterized

by a strong population growth, diverse land uses and activities, a

racial mix, a wide range of incomes, and a mix of urban, suburban,

and rural areas. It is located in relatively flat lands, with no bar-

riers to development. The city of Columbus is the capital of Ohio

and the seat of Franklin County. The CMA consists of 7 counties

(Franklin, Delaware, Union, Licking, Madison, Fairfield, and Pick-away), as illustrated in Fig. 1. The National Land Cover Database

(NLCD– U.S.Geological Survey, 2000) indicates thatRow Crops rep-

resents thelargest landcover type(51.9%), followed by Pasture/Hay

(20.1%), and deciduous forests (17.1%). Low-intensity residential

landrepresents about 4.0%and high-intensity residential land1.0%,

mostly located in Franklin County. Most low-intensity residential

land is concentrated in suburban subdivisions.

The CMA population, according to the U.S. Census, is concen-

trated in Franklin County (67.6%). Licking has the second highest

population share (9.2%), followed by Fairfield, Delaware, Pick-

away, and Union. Madison has the smallest population share

(2.5%). Delaware has the highest median income ($67,258), and

Franklin the lowest ($42,734). The distribution of the popula-

tion is not homogenous, as illustrated in Fig. 1. Most of thepopulation is located inthe majorcityof each county and surround-

ing edge cities, including Columbus (Franklin), Newark (Licking),

Delaware (Delaware), Marysville (Union), Lancaster (Fairfield),

London (Madison), and Circleville (Pickaway). Franklin county has

the highest population density, while the surrounding six counties

are more rural and with lower population density. This diversity,

combined with strong recent growth and easy access to local data,

makes the CMA an interesting case study for land-use and popula-

tion density analysis and modeling.

5. Data sources and processing

Land cover and land use information is derived from the

NLCD file downloaded from the U.S. Geological Survey (USGS)


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Fig. 1. Population density in the Columbus Metropolitan Area (person/millionft2; 1 f t2 = 0.09290304m2).

Source: CTPP (1990).

website. The source is leaves-off Landsat TM data, nominal-

1992 acquisitions, with a 30-m precision. The NLCD includes

22 land-use types, 14 of which actually exist in the CMA, as

illustrated in Fig. 2. All of the 15 spatial indices described

in Section 2, except the Dominance Index DO, have been

calculated using Fragstats (McGarigal et al., 2002), for each

of the 1763 TAZs of the CMA. The mean, median, and max-

imum TAZ sizes are 5.29, 0.99, and 73.8 km2, respectively.

DO was calculated with the SAS software. MECI was calcu-

lated with the contrast weights presented in Table 1. These

Fig. 2. Land use in theColumbus MetropolitanArea (NLCD) (1 mile =1.609344km).

Source: NLCD (1992).


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T a b l e

1

W e i g h t s f o r t h e c o m p u t a t i o n o f M E C I .

L a n d u s e

O p e n

w a t e r

L o w i n t e n s i t y

r e s i d e n t i a l

H i g h i n t e n s i t y


C o m m e r c i a l / i n d u s t r i a l /

t r a n s p o r t a t i o n

Q u a r r i e d / s t r i p

m i n e s /

g r a v e

l p i t s

B a r e r o c k

T r a n s i t i o n a l D e c i d u o u s /

e v e r g r e e n /

m i x e d f o r e s t

S h r u b

l a n d

O r c h a r d s /

v i n e y a r d

G r a s s l a n d /

h e r b a c e o

u s

C u l t i v a t e d W e t l a n d

O p e n w a t e r

0

L o w i n t e n s i t y r e s i d e n t i a l 3

0

H i g h i n t e n s i t y


4

2

0

C o m m e r c i a l / i n d u s t r i a l /

t r a n s p o r t a t i o n

5

3

2

0

Q u a r r i e d / s t r i p

m i n e s / g r a v e l p i t s

5

4

4

4

0

B a r e r o c k

1

3

3

4

1

0

T r a n s i t i o n a l

2

2

2

3

2

2

0

D e c i d u o u s / e v e r g r e e n /

m i x e d f o r e s t

2

2

3

3

2

4

1

0

S h r u b l a n d

2

2

3

3

2

3

1

2

0

O r c h a r d s / v i n e y a r d

3

2

3

3

2

4

1

2

1

0

G r a s s l a n d / h e r b a c e o u s

2

2

3

3

2

3

1

1

2

2

0

C u l t i v a t e d

3

2

3

3

2

4

1

2

2

1

1

0

W e t l a n d

1

3

4

4

4

5

2

1

1

3

1

1

0

calculations represented a major undertaking, requiring the

continuous use of all the computers in a GIS laboratory for over

2 months.

The other major data set is drawn from the 1990 Census Trans-

portation Planning Package (CTPP). The CTPP, sponsored by the

Department of Transportation and designed to meet the needs of

transportation planners, makes use of data gathered in the long

form of the decennial census. Data are available at the Traffic Anal-

ysis Zone (TAZ) level.

Finally, several datasets were provided by the Mid-Ohio

Regional Planning Commission (MORPC – www.morpc.org),

including GIS data for the street system, shopping centers, indus-

trial centers, hospitals, nursing homes, rivers and lakes, as well as

parks and golf courses. The approximate time frame for these data

is around 1995. They have been used to compute the distances to

the nearest land use or activity such as (1) major street, (2) shop-

ping center, (3)industrialcenter, (4)hospital, (5)nursing home, (6)

park, and(7)river. While these data arenot a perfect time matchfor

theCTPP (1990), they representthe most complete cross-section of

such data, and differences with the year 1990 are likely be small or

non-existentin most case. These data are thus deemedappropriate

for use in this research.

6. Empirical results

6.1. Density model exploratory analyses

Population density models are first estimated for the whole

CMA. Two measures of density are considered: total TAZ popula-

tion divided by (1) total TAZ area (gross density), and (2) total TAZ

residential area (net density). The distance from each TAZ centroid

to the Columbus CBD, DCOL, is first considered, together with both

the linear and exponential functional forms. The exponential form

ln(DP) = a+ b×DCOL (5)

yields by far the highest R2 (0.26) with gross density, which isretained in further analyses. The distance to Columbus CBD (DCOL)

is not significant when using netpopulation density (R2 = 0.02), but

it is so with gross density.

The next step expands Eq. (5) by including the distances to all

the 43 employment centers defined by the metropolitan planning

agency MORPC for the 1990 CTPP. The listing of the centers and

their precise TAZ compositions are available in the 1990 CTPP files

for the Columbusmetropolitanarea. Thisinformationcan be down-

loaded from www.bts.gov, or can be obtained from the authors

upon request.

Theresults produce 20 coefficients significant at the5% level (12

negativeand 8 positive), withR2 = 0.58. The 12 negativecoefficients

pertain to (1) the major CBD in each of the 6 peripheral counties,

and (2) 6 centers within Franklin. The 8 positive coefficients arerelated to 5 centers in Franklin, and 1 each in Licking, Fairfield, and

Delaware.

Since the 12 centers with the correct coefficients signs (nega-

tive coefficient) include the six peripheral county seat cities and

downtown Columbus (seat of Franklin county), and since the cen-

ters with correct coefficient signs are almost as numerous as the

those with wrongones,we conclude thatconsidering all these cen-

ters simultaneously may not lead to a satisfactory density model,

and instead opt for a more incremental approach, focusing first

on the individual counties separately. This approach may better

account for county heterogeneity, ranging from primarily rural

(Delaware, Fairfield, Pickaway, Madison, Union) to primarily urban

(Franklin and Licking). The focus is therefore set, in the next step,

on developing county-specific models, while, however, accounting

http://www.morpc.org/http://www.bts.gov/http://www.bts.gov/http://www.morpc.org/


7/12


for inter-county effects, and, in particular, the effect of the major

center of the CMA – Columbus downtown CBD.

6.2. Correlation analysis of landscape indices

Correlationsamong the15 indices are presentedin Table 2. Sev-

eral indices are strongly correlated with each other. For example,

the Mean Patch Size (MPS) is positively correlated with PSSD (0.78)

and DMMA (0.59). A possible reason is the larger the average size,

the more variations between patch sizes (PSSD), and the more the

difference between minimum and maximum sizes (DMMA). MPS

is also negatively correlated with MECI (−0.52), SHDI (−0.53), SHEI

(−0.52), IJI (−0.54), and DO (0.42). A possible reason is that places

with more diversified land uses tend to be in urbanized areas, with

smaller patch sizes. The number of patches (NP) is strongly cor-

related with RPR (0.57), DMMA (0.52), and DO (0.45), because the

more patches, themore land uses, andthe more variations in patch

size. Shannon’s Diversity Index (SHDI) is strongly correlated with

RPR (0.64) and SHEI (0.85). Thus, the more diversity, the more

land-usetypes. Likewise,the Dominance Index (DO) is stronglycor-

related with PSSD (0.63), MNN (0.44), RPR (0.53), SHEI (−0.52), IJI

(−0.73), and DMMA (0.61). The Mean Shape Index (MSI) is strongly

correlated with SC (0.56). The Mean Nearest Neighbor Distance

(MNN) is correlated with SHEI (−0.41) and DO (0.44). The MeanEdge Contrast Index (MECI) is correlated with MPS (−0.52), SHDI

(0.46), SHEI (0.49), PSSD (−0.44), IJI (0.49), and DMMA (−0.42).

The above results suggest that the higher the land-use contrast

(MECI), the higher the diversity of land-uses, the smaller each indi-

vidual patch, and the smaller the mean patch size and patch size

standard deviation. Therefore, MECI encompasses both diversity

and contrast factors, and could be a representative independent

variable in the density model. The results also show that the Dom-

inance Index (DO) is strongly correlated with NP, RPR, and DMMA.

Thus, DO encompasses both dominance and diversity, and could

also be a representative independent variable in the density model.

6.3. County-level population density models

In line with the results in Section 6.1, the exponential functional

form was selected for the county models. In a first step, the dis-

tances to themain county CBD, DCTY, andto downtown Columbus,

DCOL, were considered for each of the six counties surrounding

Franklin. The rationale for this selection is that the county CBD is

likely to exert a strong influence on the location of population in

the central areas of the county surrounding this CBD, while areas

closer to the border with Franklin are more likely to be influenced

by the metropolitan center (downtown Columbus). This prelimi-

nary estimation yielded significant and negative coefficients for all

these counties, with R2 equal to 0.28 for Delaware, 0.51 for Lick-

ing, 0.32 for Fairfield, 0.31 for Pickaway, 0.16 for Madison, and 0.23

for Union. In the case of Franklin, DCOL= DCTY, with R2 = 0.24. The

Franklin model was expanded by considering the distances to theCBDs of all six surrounding counties. All these additional distances

turned out to be insignificant, except for the distance to Delaware

CBD (Delaware city). This is not surprising in view of the strong

population growth in the northern parts of Franklin adjacent to

Delaware. Next,the sevencountymodelswere further expanded by

considering the other distance-to-amenity variablesand the spatial

indices variables.

The amenity distance variables were not significant and were

discarded from further modeling. Overall, in all counties, the R2

increased dramatically after adding the land-use structure vari-

ablesMECI (Mean EdgeContrast Index),and DO(DominanceIndex).

Both variables are significant and the signs of their coefficients are

the same in all models and consistent with the underlying features

they measure, as further discussed below. None of theother spatial

indices variablesturned out to be significant afterinclusion intothe

density model. The final seven county population density models

are presented in Table 3.

The R2 varies from 0.39 for Franklin to 0.84 for Fairfield. Note

that Franklin, with by far the largest numbers of observations

(1117), is much more complex to model than the other surround-

ing counties, each with a dominantcity surrounded by mostlyrural

areas. The coefficient of distance to downtownColumbus is always

negative, but insignificant for Delaware, Madison, and Union coun-

ties. This coefficient (gradient) is largest for Franklin (−0.00004),

followed by Licking (−0.000015), Pickaway (0.000011), and Fair-

field (−0.000007). Thus, population density declines most steeply

in Franklin, but the lesser effects of DCOL in the other counties

can be explained by the fact that this effect starts taking place

only at the border of the county with Franklin. The effect of the

metropolitan center is thus necessarily attenuated. The gradients

for the distances to county CBDs vary from −0.000025 for Licking

to−0.000007 for Fairfield. All coefficients are significant at least at

the 15% level, except for Union. The gradients for Delaware, Fair-

field, Pickaway, Madison, and Union are all close to each other,

pointing to a consistent pattern across these counties. The coef-

ficients for MECI are all significant at the 5% level, except Union

(10%), and always positive. They vary from a low 0.0374 in Union

to a high of 0.1110 in Fairfield. The coefficients for DO are all neg-ative and significant at the 5% level. They vary from −1.356 in

Franklin to −2.516 in Delaware. The results for MECI and DO are

consistent with the hypothesis that population density increases

with more mixed land uses with high edge contrasts (MECI), and

decreaseswith thedominance by a fewland uses(DO). For example,

areas suchas theCBDs, withhigh-edge contrastsbetweencommer-

cial and high-intensity residential, high-intensity residential and

industrial, and high-intensity residential and transportation land

uses, tend to have higher population density. On the other hand,

these CBD areas, with more mixed land-uses, are less dominated

by a few land uses only.

In summary, population density is highest around downtown

Columbus in primarily urban Franklin, and also highest around

the downtowns of the primarily rural counties. Population den-sity declines away from the county CBDs into the remainder of

the county, but then increases again towards the county border

with Franklin, due to urban sprawl produced by the central city of

Columbus, except in Delaware and Madison (where the distance

to Columbus CBD does not impact population density). Delaware

is a unique case, because of its very high rate of new housing and

business development within the CMA. The case of Madison sug-

gests that there is not much urban sprawl from Columbus towards

southwestern rural counties. Indeed, the southwestern part of the

CMA is not developing as fast as its northern part. The distance

to Union county CBD (Marysville) has a weak effect on population

density. This suggests a greater spread of the population in Union,

unlike other counties, which is consistent with the fact that Union

is primarily a rural county, andthe farming community tends to bespread out.

6.4. Metropolitan-level population density models

Because the county models presented in the previous section

display so much similarity, the data for the seven counties were

pooled to estimate expanded single population density models for

the whole metropolitan area.This expansion includes dummy vari-

ables to account for intercept variations across counties, as well

as second-order and interaction terms. Four models of increasing

complexity have been estimated. The quadratic form can capture

non-linear effects. More generally, the unknown density function

can be formulated as an infinite Taylor polynomials series. Retain-

ing the linear terms represents the simplest approximation of


8/12


Table 2

Pearson correlation coefficients of spatial indices.

MPS MEDPS DMMA PSSD SC MPFD MSI NP RPR SHDI SHEI DO MECI MNN IJI

MPS 1.00 0.41 0.59 0.78 −0.23 −0.15 −0.07 0.14 −0.08 −0.53 −0.62 0.42 −0.52 0.39 −0.54

MEDPS 0.41 1.00 −0.06 −0.07 −0.26 0.03 −0.18 −0.10 −0.32 −0.33 −0.36 −0.27 −0.36 −0.12 0.02

DMMA 0.59 −0.06 1.00 0.92 −0.19 −0.21 −0.12 0.52 0.26 −0.27 −0.40 0.61 −0.42 0.25 −0.54

PSSD 0.78 −0.07 0.92 1.00 −0.16 −0.22 −0.07 0.34 0.18 −0.34 −0.46 0.63 −0.44 0.34 −0.56

SC −0.23 −0.26 −0.19 −0.16 1.00 0.00 0.56 −0.30 −0.23 −0.06 0.14 −0.08 0.13 0.05 0.16

MPFD −0.15 0.03 −0.21 −0.22 0.00 1.00 0.04 −0.12 −0.16 −0.01 0.06 −0.18 0.18 −0.09 0.10

MSI −0.07 −0.18 −0.12 −0.07 0.56 0.04 1.00 −0.25 −0.25 −0.07 0.15 −0.09 0.08 0.07 −0.01NP 0.14 −0.10 0.52 0.34 −0.30 −0.12 −0.25 1.00 0.57 0.16 −0.09 0.45 −0.27 0.05 −0.39

RPR −0.08 −0.32 0.26 0.18 −0.23 −0.16 −0.25 0.57 1.00 0.64 0.22 0.53 0.14 0.12 −0.16

SHDI −0.53 −0.33 −0.27 −0.34 −0.06 −0.01 −0.07 0.16 0.64 1.00 0.85 −0.23 0.46 −0.28 0.54

SHEI −0.62 −0.36 −0.40 −0.46 0.14 0.06 0.15 −0.09 0.22 0.85 1.00 −0.52 0.49 −0.41 0.71

DO 0.42 −0.27 0.61 0.63 −0.08 −0.18 −0.09 0.45 0.53 −0.23 −0.52 1.00 −0.12 0.44 −0.73

MECI −0.52 −0.36 −0.42 −0.44 0.13 0.18 0.08 −0.27 0.14 0.46 0.49 −0.12 1.00 −0.24 0.49

MNN 0.39 −0.12 0.25 0.34 0.05 −0.09 0.07 0.05 0.12 −0.28 −0.41 0.44 −0.24 1.00 −0.23

IJI −0.54 0.02 −0.54 −0.56 0.16 0.10 −0.01 −0.39 −0.16 0.54 0.71 −0.73 0.49 −0.23 1.00

this series. Expanding to the second order improves the approx-

imation of the true functional form. The results are presented

in Table 4.

Model 1 includes only the four independent variables used in

the separate county analyses: DCOL, DCTY, MECI, and DO. DCTY is

thedistance from each TAZcentroid to the CBD/center ofthe countywhere it is located and to Delaware city in the case of Franklin, and

DCOL is the distance from that TAZ centroid to the Columbus CBD.

All the estimated coefficients are significant at the 5% level, and

with negative signs consistent with the previous results, except

for MECI. Model 2 expands Model 1 by adding county dummy

variables:

IC045= 1 if the TAZ is in Fairfield, =0 otherwise; IC049= 1 if the

T AZ is in Franklin, =0 otherwise; IC089= 1 if the TAZ is in Lick-

ing, =0 otherwise; IC097 = 1 if the TAZ is in Madison, =0 otherwise;

IC129= 1 if the TAZ is in Pickaway, =0 otherwise; IC159=1 if the

TAZ is in Union, =0 otherwise.

Model 3 expands Model 2 by adding the squares of the vari-

ables DCTY, DCOL, MECI, and DO. Model 4 expands Model 3 by

adding the following interaction terms: MECI×DO, DCTY ×MECI,

DCOL ×MECI, DCTY ×DO, andDCOL ×DO. DCOL ×DCTY turnedout

to be insignificant, and is not included. The formulation of Model 4

is:

ln(DP) = exp(a0 +

i=1→6

˛iICi + a1DCTY + a2DCTY 2+ a3DCOL

+a4DCOL 2+ a5MECI+ a6DO+ a7MECI

2+ a8DO

2

+a9MECI×DO+ a10DCTY ×MECI+ a11DCTY ×DO

+a12DCOL ×MECI+ a13DCOL ×DO) (6)

where ICi isthe dummy variable for county i. The R2 increases from

0.600 for Model 1 to0.630for Model 2,0.654for Model 3,and 0.659for Model 4. In the following analyses, the focus is on Model 4.

All the variables in Model 4 are significant at the 10% level,

except DO2, DCOL ×MECI, and IC129. The dummy variables help

differentiate the intercepts of the density curves, and thus the

CBD densities, among the seven counties. The regression intercept

(−6.824) characterizes Delaware county (all the dummy vari-

ables =0), and, in exponential form, is equal to e−6.824 = 0.001087.

IC049 (Franklin) hasthe largest value (1.611), andthus an intercept

of (−0.824+ 1.611). Fairfield, Licking, and Madison have relatively

close values (0.760, 0.819, 0.613), followed by the cluster of Pick-

away and Union (0.242 and 0.380). If there were only one CBD, and

the distance to this CBD (DCTY) was the only independent vari-

able, then this intercept would measure the density at the CBD

(distance =0). This, however, is not the case because of the otherdistance to the alternative CBD (DCOL) and variables MECI and DO.

Nevertheless, the ranking is not unexpected, and reflects differ-

ences among counties in terms of their urban/rural characters.

The effects on density of other variables (DCTY, DCOL, MECI,

DO) cannot be captured by simple visual inspection, as would

be the case in a linear functional form, because of the squared

and interaction terms. To measure these effects, the elasticities of

the dependent variable (DP) are computed with respect to all the

Table 3

Population density modelsfor thesevencounties of theCMA (dependent variable: logarithmof population density).

Variable Franklin Delaware Licking Fairfield Pickaway Madison Union

Intercept −7.170 −11.360 −8.880 −11.790 −10.050 −11.100 −10.200

(−15.10)* , a (−11.43)* (−10.90)* (−17.25)* (−7.63)* (−11.45)* (−9.66)*DCTY b −0.00002 −0.000009 −0.000025 −0.000007 −0.000013 −0.000008 −0.000009

(−8.58)* (−1.77)** (−6.41)* (−2.06)* (−2.00)* (−1.43)*** (−1.27)

DCOL c −0.00004 0.000001 −0.000015 −0.000007 −0.000011 −0.000006 0.000001

(−12.04)* (−0.27) (−5.34)* (−2.53)* (−2.37)* (−1.30) (−0.18)

MECI 0.042 0.080 0.083 0.111 0.078 0.093 0.037

(5.41)* (4.48)* (6.77)* (9.74)* (2.94)* (5.10)* (1.67)**

DO −1.356 −2.516 −1.650 −1.688 −2.026 −2.053 −2.495

(−8.62)* (−6.32)* (−5.26)* (−7.46)* (−3.74)* (−6.33)* (−5.76)*

Number of observations 1117 105 208 86 67 103 77

R2 0.39 0.63 0.67 0.84 0.61 0.59 0.58

* p< = 5 %.** p< = 10% .

*** p< = 15% .a Numbers in parentheses denote t-values for each variables.b DCTY denotes thedistance tothe centerof themajor city ofeachof theperipheralcounties.In thecaseof Franklin,it denotes thedistance toDelawarecity(1 ft= 0.3048m).c

DCOL denotes distance to Columbus CBD (1ft = 0.3048m). Theoriginal datasets from various sources were mostly measured in ft; thus, ft was used in this analysis.


9/12


Table 4

Pooled metropolitan-level population density models (dependent variable: logarithm of population density).

Variable Model 1 Model 2 Model 3 Model 4

Intercept −9.556 −9.929 −9.313 −6.824

(−32.62)* (−32.58)* (−15.67)* (−5.47)*

DCTY a −2.10E−05 −2.41E−05 −7.32E−05 −9.62E−05

(−11.6)* (−13.58)* (−13.63)* (−8.47)*

DCTY 2 5.41E−10 5.09E−10

(9.31)* (7.42)*

DCOL b

−9.96E−06 −1.14E−05 −3.02E−05 −4.01E−05(−8.62)* (−9.06)* (−4.13)* (−3.44)*

DCOL 2 7.43E−11 5.53E−11

(−2.67)* (1.81)**

MECI 0.083 0.060 0.137 0.105

(18.44)* (−12.22)* (−7.2)* (3.38)*

MECI2 −1.35E−03 −1.74E−03

(−4.52)* (−5.24)*

DO −2.004 −1.584 −1.171 −3.440

(−18.52)* (−14.15)* (−2.79)* (−4.45)*

DO2 −0.152 −0.267

(−0.67) (−1.07)

MECI×DO 0.029

(2.72)*

DCTY ×MECI 3.93E−07

(1.86)**

DCTY ×DO 1.48E−05

(3.03)*

DCOL ×MECI 2.01E−07

(1.21)

DCOL ×DO 8.97E−06

(2.29)*

IC045 0.757 0.736 0.760

(3.84)* (3.86)* (4.00)*

IC049 1.397 1.673 1.611

(9.57)* (11.56)* (11.02)*

IC089 1.093 0.835 0.819

(6.38)* (4.91)* (4.80)*

IC097 0.412 0.454 0.613

(2.11)* (2.35)* (3.13)*

IC129 0.229 0.178 0.242

(1.08) (0.86) (1.17)

IC159 0.400 0.312 0.380

(1.93)* (1.52)*** (1.85)**

R2 0.597 0.630 0.654 0.659

* p< = 5 %.** p< = 10% .

*** p< = 15% .a DCTY: distance to countyCBD.b DCOL: distance to alternative CBD (Delaware city forFranklin county, and Columbus CBD Forthe surrounding six counties).

independent variables. If X is an independent variable,the elasticity

of DP is computed as:

ε X =∂DP

∂X

DP

X (7)

ε X measures the percentage changes in DP resulting from a 1%

change in X . The four elasticities can be derived from Eq. (6), with:

εDCTY = (a1 + 2a2DCTY + a10MECI+ a11DO)×DCTY (8)

εDCOL = (a3 + 2a4DCOL + a12MECI+ a13DO)×DCOL (9)

εMECI = (a5 + 2a7MECI+ a9DO+ a10DCTY + a12DCOL)×MECI (10)

εDO = (a6 + 2a8DO+ a9MECI+ a11DCTY + a13DCOL) ×DO (11)

Descriptive statistics for DCTY, DCOL, MECI, and DO for the

whole CMA andfor each county separately arepresented in Table 5.

Their mean values have been used to compute the four elasticities

for each county and the CMA. The results are reported in Table 6.

While it is important to remember that the samplemeans donot

represent actual TAZs, but rather composite TAZs, some interesting

patterns emerge in Table 6. εDCTY , εDCOL , and εDO are always neg-

ative, while εMECI is always positive. εDCTY varies within relatively

narrow ranges across county: (0.94–1.21). Franklin has the highest

elasticities (1.21). εDCOL varies in the range (1.13–1.49). Franklin

has the highest elasticity (1.49). The values of εMECI v ary in the

range (1.27–2.45). Finally, the values of εDO vary within the range

(0.92–2.23). Franklin and Licking have the lowest values for both

εMECI andεDO, while higher values characterizethe other morerural

counties.Thus, landuse dominance effects on densitiesare stronger

in rural than in urban counties.

In order to further assess the variations of the four elasticities,

they have been computed with the actual value of (DCTY, DCOL,MECI, DO) across thesample used to estimate thepooled models in

Table 4. The calculations have been carried out for the whole CMA

and for each county separately. The elasticities means, minima,

maxima, and standard deviations are reported in Table 7.

While the mean values of the elasticities have the same signs

as those in Table 6, it is clear that they vary across ranges of neg-

ative and positive values. For instance, in the case of the whole

CMA, εDCTY varies from−1.90 to 5.53, with a mean of −0.67, which

clearly points to a skewed distribution. Similarly, εDCOL varies

between −3.61 and 0.95, with a mean of −1.30. Thus, there are

circumstances, characterized by specific combinations of values

for DCTY, DCOL, MECI, and DO (see Eqs. (8) and (9)) where den-

sity increases with distance, similar to the pattern of volcanoes and

craters identified by Millward and Bunting (2008). Likewise, εMECI


10/12


Table 5

Basic statistics for model variables (1ft = 0.3048m).

County Variable Mean Minimum Maximum Standard deviation

CMA DCTY (ft) 36,354 0 11,1631 22,480

DCOL (ft) 125,110 59,231 235,065 32,660

MECI 33.80 0.00 58.26 9.37

DO 0.89 0.00 1.89 0.37

Delaware DCTY (ft) 42,458 1755 98,679 23,975

DCOL (ft) 109,471 65,110 175,109 28,803

MECI 28.57 10.84 50.99 6.86

DO 1.08 0.32 1.77 0.30

Fairfield DCTY (ft) 42,251 432 93,476 25,030

DCOL (ft) 129,349 59,805 197,781 32,314

MECI 27.37 9.64 43.77 7.10

DO 1.02 0.24 1.57 0.33

Franklin DCTY (ft) 34,448 1037 81,154 18,617

DCOL (ft) 117,824 59,231 193,514 26,924

MECI 37.50 0.00 55.70 7.96

DO 0.77 0.00 1.83 0.31

Licking DCTY (ft) 32,382 90 111,631 29,759

DCOL (ft) 159,183 68,047 235,065 31,946

MECI 33.10 0.00 58.26 7.82

DO 0.93 0.00 1.81 0.29

Madison DCTY (ft) 44,991 0 110,020 24,563

DCOL (ft) 118,972 69,113 195,609 29,217

MECI 22.47 0.00 44.12 7.86

DO 1.28 0.13 1.89 0.43

Pickaway DCTY (ft) 46,374 0 102,749 26,123

DCOL (ft) 121,611 65,027 178,231 31,477

MECI 24.59 8.94 40.17 6.53

DO 1.29 0.32 1.75 0.34

Union DCTY (ft) 37,451 884 92,544 25,726

DCOL (ft) 151,537 74,119 230,054 36,247

MECI 24.75 0.00 44.30 8.64

DO 1.21 0.07 1.84 0.44

varies between−1.56 and 3.68, with a meanof 1.39, and εDO varies

between −4.76 and 0.04, with a mean of −1.20. Again, there are

combinations of the independent variables that will produce signsfor εMECI and εDO that are different from the central tendencies.

However, such deviations are very limited in thecase of εDO, witha

maximum value of 0.04. Similar “across-sign” patterns emerge for

some counties, but not all. This is the case of Franklin, which is not

surprising, as it dominates the CMA sample; εDCTY changes signs in

all counties, but εDCOL remains always negative in Delaware, Fair-

field, and Pickaway counties; εMECI is always positive in Madison

and Pickaway counties; and εDO is always negative in Delaware,

Fairfield, Madison, and Pickaway counties.

7. Discussion

The goal of this research was to expand empirical population

density models, by incorporating, within a polycentric frame-work, land-use structure variables. The CMA andits seven counties

have been used as a test bed for this empirical investigation.

Table 6

Elasticitiesfor each countyand theCMA at thesample means.

County εDCTY εDCOL εMECI εDO

CMA −1.19 −1.43 1.78 −1.14

Delaware −1.09 −1.37 2.16 −1.71

Fairfield −1.16 −1.44 2.24 −1.43

Franklin −1.21 −1.49 1.27 −0.92

Licking −1.18 −1.19 2.04 −1.00

Madison −1.02 −1.30 2.37 −2.23

Pickaway −0.94 −1.23 2.45 −2.11

Union −1.14 −1.13 2.11 −1.76

Table 7

Basic statistics for population density elasticities.

County Variable Mean Minimum Maximum Standard deviation

CMA εDCTY −0.67 −1.90 5.53 0.73

εDCOL −1.30 −3.61 0.95 0.45

εMECI 1.39 −1.56 3.68 0.96

εDO −1.20 −4.76 0.04 0.77

Delaware εDCTY −0.52 −1.50 3.25 0.81

εDCOL −1.26 −2.39 −0.13 0.32

εMECI 1.94 −0.87 3.01 0.76

εDO −1.74 −3.61 −0.49 0.70

Fairfield εDCTY −0.53 −1.76 2.04 0.76

εDCOL −1.31 −2.54 −0.34 0.38

εMECI 2.00 −0.46 2.92 0.67

εDO −1.49 −3.02 −0.23 0.70

Franklin εDCTY −0.85 −1.84 1.02 0.39

εDCOL −1.41 −3.28 0.01 0.40

εMECI 1.03 −1.48 3.03 0.88

εDO −0.94 −3.98 0.02 0.54

Licking εDCTY −0.27 −1.36 5.53 1.16

εDCOL −1.07 −3.61 0.95 0.52

εMECI 1.74 −1.56 3.48 0.92

εDO −1.02 −2.14 0.00 0.48

Madison εDCTY −0.41 −1.74 2.93 0.93

εDCOL −1.18 −2.26 0.58 0.48

εMECI 2.10 0.00 3.45 0.57

εDO −2.31 −4.76 −0.10 1.05

Pickaway εDCTY −0.22 −1.38 4.52 1.13

εDCOL −1.12 −2.05 −0.44 0.37

εMECI 2.24 0.64 3.23 0.60

εDO −2.15 −3.69 −0.27 0.79

Union εDCTY −0.45 −1.90 2.60 0.91

εDCOL −0.96 −2.80 0.63 0.70

εMECI 2.08 −0.32 3.68 0.81

εDO −1.81 −3.93 0.04 0.99


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Jia Lu is an assistantprofessor at Valdosta StateUniversity. Shereceived herPh.D. incity and regional planning from The Ohio State University. She also holds a masterdegree in Community Planning from University of Cincinnati. Her research inter-ests focuses on urban modeling, urban planning, GIS, environmental studies, andgeography.She haspublisheda bookand a fewbook chaptersregardingtheseissues.

Jean-MichelGuldmann isa professorofcityand regionalplanningat TheOhioStateUniversity. He holds a Ph.D. in urban andregionalplanning from theIsrael Instituteof Technology, Haifa, Israel, and a masters in industrial engineering from the Ecoledes Mines,Nancy, France.His researchfocuseson thequantitativemodeling ofurbanstructure,energyand telecommunicationsinfrastructures,and environmentalplan-

ning, particularlyair quality andwater issues. He haspublisheda book and over60articles and book chapters on these issues.
https://www.denix.osd.mil/denix/Public/ES-Programs/Conservation/Legacy/Neo-Tropical/neotropical.htmlhttps://www.denix.osd.mil/denix/Public/ES-Programs/Conservation/Legacy/Neo-Tropical/neotropical.htmlhttps://www.denix.osd.mil/denix/Public/ES-Programs/Conservation/Legacy/Neo-Tropical/neotropical.html

landscape ecology land use structure & population density

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