RESEARCH ARTICLE

Modeling habitat dynamics accounting for possiblemisclassification

Sophie Veran • Kevin J. Kleiner •

Remi Choquet • Jaime A. Collazo •

James D. Nichols

Received: 6 July 2011 / Accepted: 17 April 2012 / Published online: 24 May 2012

� Springer Science+Business Media B.V. (outside the USA) 2012

Abstract Land cover data are widely used in

ecology as land cover change is a major component

of changes affecting ecological systems. Landscape

change estimates are characterized by classification

errors. Researchers have used error matrices to adjust

estimates of areal extent, but estimation of land cover

change is more difficult and more challenging, with

error in classification being confused with change. We

modeled land cover dynamics for a discrete set of

habitat states. The approach accounts for state uncer-

tainty to produce unbiased estimates of habitat tran-

sition probabilities using ground information to inform

error rates. We consider the case when true and

observed habitat states are available for the same

geographic unit (pixel) and when true and observed

states are obtained at one level of resolution, but

transition probabilities estimated at a different level of

resolution (aggregations of pixels). Simulation results

showed a strong bias when estimating transition

probabilities if misclassification was not accounted

for. Scaling-up does not necessarily decrease the bias

and can even increase it. Analyses of land cover data in

the Southeast region of the USA showed that land

change patterns appeared distorted if misclassification

was not accounted for: rate of habitat turnover

was artificially increased and habitat composition

appeared more homogeneous. Not properly account-

ing for land cover misclassification can produce

misleading inferences about habitat state and dynam-

ics and also misleading predictions about species

distributions based on habitat. Our models that

explicitly account for state uncertainty should be

useful in obtaining more accurate inferences about

change from data that include errors.

Keywords Habitat dynamics � Land cover � Habitat

misclassification � Accuracy � Hidden Markov chain �Multi-event model

Electronic supplementary material The online version ofthis article (doi:10.1007/s10980-012-9746-z) containssupplementary material, which is available to authorized users.

S. Veran (&) � J. D. Nichols

USGS Patuxent Wildlife Research Center, 12100 Beech

Forest Road, Laurel, MD 20708, USA

e-mail: sophie.veran@supagro.inra.fr

S. Veran � J. A. Collazo

Department of Zoology and U.S. Geological Survey,

North Carolina Cooperative Fish and Wildlife Research

Unit, North Carolina State University, Campus Box 7617,

Raleigh, NC 27695, USA

K. J. Kleiner

School of Forestry and Wildlife Sciences, Forestry and

Wildlife Bldg., 602 Duncan Drive, Auburn, AL 36849,

USA

R. Choquet

Centre d’Ecologie Fonctionnelle et Evolutive, CNRS,

UMR 5175, 1919 Route de Mende, 34293 Montpellier

Cedex 5, France

123

Landscape Ecol (2012) 27:943–956

DOI 10.1007/s10980-012-9746-z

Introduction

Land cover data are widely used in ecology, as land

cover change, whether due to land use change or other

factors, is a major component of changes in ecological

systems (Vitousek 1994; Feddema et al. 2005). Land

cover data used as a proxy for habitat have proven

especially valuable for predicting the occurrence of

species (Mladenoff et al. 1995; Hirzel et al. 2004) and,

by extension, species distributions (Cowley et al.

2000; Luoto et al. 2002). With the increasing threat to

biodiversity induced by habitat loss and degradation

(Benıtez-Malvido and Martınez-Ramos 2003; Ferraz

et al. 2003), quantifying and modeling land cover

change and land cover dynamics at a large extent are

essential to efforts to detect and predict changes in the

natural environment and to better understand the

factors limiting the distribution of species.

Advances in geographic information systems (GIS)

have led to the availability of data on land cover at a

large extent. Such data have been widely used in

ecology to develop state transition models of land

cover dynamics (Jenerette and Wu 2001; Pastor et al.

2005). Indeed remote sensing offers a fast process to

obtain land cover images at a large extent. Map-like

representations of the earth’s surface are obtained

from remotely sensed data based on image classifica-

tion. But resulting maps and inferences represent final

products produced by a complicated process that can

introduce error at many points (Hess 1994; Foody

2002). As a result, most land cover data obtained using

remote sensing are characterized by classification

error. This classification error is often reported,

usually in the form of an error matrix or a confusion

matrix based on an accuracy assessment of the

classified data (Gallego 2004; Pontius and Millones

2011). Researchers have used error matrices to adjust

estimates of areal extent (Czaplewski 1992; Stehman

2009), but estimation of land cover change is more

difficult and more challenging, with error in classifi-

cation being confused with change (Pontius and Li

2010).

Absence of an approach for adequately dealing with

classification error ultimately limits the ability to

draw statistically valid conclusions about land cover

dynamics and their importance as drivers of ecolog-

ical processes (Hess 1994; Wickham et al. 1997).

Although awareness of this error issue is common in

the remote sensing community (Shao et al. 2001;

Powell 2004; Langford et al. 2006), its implications

have yet to be fully addressed. The objective of this

study is threefold: (1) to simulate land cover data with

and without error in habitat classification and compare

analyses of habitat dynamics based on observed data

(i.e., with classification errors) and true data (i.e.,

without classification errors); (2) to present a model-

ing approach that properly deals with habitat state

uncertainty, producing unbiased estimates of habitat

transition probabilities; (3) to illustrate our modeling

approach with a case study on the dynamics of forest

cover between 1970 and 2000 in the southeast region

of the USA.

Methods

We derived our modeling framework from methods

widely used in investigations of animal populations to

estimate probabilities of survival, transition and

recapture of marked individuals within a population

(Lebreton et al. 2009). To explain how we can adapt

this modeling framework to land cover dynamics

modeling, we will start with the simplest case where

land cover is assumed to be known without error.

Modeling land cover dynamics when land cover

is known without errors

By analogy with population studies, the map of the

region of interest is divided into a number of pixels,

with pixels representing the equivalent of individuals

in a population. At discrete occasions (or time points)

pixels are surveyed. Each pixel is linked to a

categorical covariate that can change over time; in

this study this covariate can take three possible values

defining the land cover type of the pixel (or state of the

pixel): Forest (F), Urban (U) for urbanized areas and

Managed (M), if the pixel is neither forest nor urban

(corresponding most of the time to agricultural areas).

Hence, in the same way that we can follow the fate of

each marked and recaptured individual of a population

over time (called a capture history), we can follow the

fate of each surveyed pixel over time. For example,

consider the history: F F F M M. This represents a

pixel assessed at five different times and classified as

forest during each of the first three time points and as

managed during the last two time points.

944 Landscape Ecol (2012) 27:943–956

123

Define pRt as the probability that a randomly

selected pixel at time t is in land type R. pRt can also

be viewed as the expected proportion of pixels in land

type R at time t.

Define NF, NU, and NM as the number of pixels from

a landscape of interest in forest, urban and managed

land cover types, respectively. Habitat dynamics can

produce changes in these numbers over time and can

be modeled as a first order Markov process governed

by a matrix of transition probabilities, wRSt , represent-

ing the probability that a pixel in state R at time t will

be in state S at time t ? 1 (e.g., see Breininger et al.

2010).

ENF

NM

NU

24

35

tþ1

0@

1A ¼ wt

NF

NM

NU

24

35

t

where wt ¼wFF

t wMFt wUF

t

wFMt wMM

t wUMt

wFUt wMU

t wUUt

24

35

ð1Þ

Note that the matrix is stochastic in that the

elements of each column sum to 1. Data required for

inference about NRt; pRt and wRS

t are the habitat

histories associated with each pixel in the area of

interest. For example if we assume the data were

known to represent truth (no misclassification of land

cover type) we could model the history F F F M M as:

Pr F F F M Mð Þ ¼ pFwFF1 wFF

2 wFM3 wMM

4 ð2Þ

More specifically, the above expression represents the

probability that a randomly selected pixel at some

initial time shows this sequence of land cover states.

Given such habitat history data for a set of pixels, and

this basic approach to modeling, we could estimate the

initial state and transition probability parameters

using, for example, maximum likelihood approaches

(Breininger et al. 2010).

Modeling land cover dynamics when data on land

cover types can have errors

We now consider the possibility that the land cover

type of a pixel in a map at any time point is not always

correctly determined by remote sensing. Thus in

absence of any further information, the actual land

cover on the ground (in contrast with the land cover on

the map) is not known. To follow the notation of

hidden Markov chains, we will say that the land cover

on the ground represents the true (but unknown) state,

as opposed to the land cover on the map that represents

the observable category, but with possible errors. State

uncertainty models were introduced to capture–

recapture modeling as a way of dealing with possible

misclassification by Kendall et al. (2003), and a

comprehensive general framework (multi-event mod-

els) was developed by Pradel (2005). The general

multi-event framework provides a natural approach to

handle state uncertainty and model land cover dynam-

ics accounting for misclassification (Fig. 1).

Fig. 1 Diagram illustrating the difference in modeling

approaches that do and do not incorporate accuracy in land

cover classification (et). Under approaches that ignore mis-

classification (a), pixels on the maps (Uo for pixel of Urban area

and Fo for pixel of Forest observed on the map) are assigned a

land cover type assuming no misclassification, and land cover

transition probabilities (wt) are directly estimated using these

observations on the map. Under approaches that deal with

misclassification errors (b), land cover of pixels on the ground (F

for pixels of Forest) is not known. Instead, land cover of pixels

on the maps is recognized to be a function of land cover on the

ground and probabilities of accuracy, et. Land cover transition

probabilities (wt) are then based on these hidden (but estimated)

land covers of pixels on the ground rather than on maps

observations

Landscape Ecol (2012) 27:943–956 945

123

For pixels at which we know both the land cover

type on the ground and on the map, we denote the

complete information about system state at one point

in time by the pair of values (RSo), indicating true state

R (land cover on the ground) and observed state So

(where the o subscript indicates ‘‘observable’’ for land

cover on the map). For example, a pixel might be

composed of forest on the ground but incorrectly

mapped, via remote sensing, as managed. Such pixel

will be coded as FMo.

In order to properly deal with misclassification

during inference, we consider a matrix of accuracy

probabilities eRSot (‘‘producer’s accuracy probabilities’’

in the terminology of Pontius and Lippitt 2006),

representing the probability that a pixel belonging to a

land cover type R on the ground at time t is classified in

type S in the map (in our notation So):

et ¼eFFo

t eMFot eUFo

t

eFMot eMMo

t eUMot

eFUot eMUo

t eUUot

24

35

We adopted the matrix notation used in Pontius and

Lippitt (2006): land cover types on the ground are

written in columns whereas land cover types on

the maps are in rows, with columns again summing

to 1.

The key to inference in the case of state uncertainty

is to develop a model that deals not only with the

Fig. 2 Diagram illustrating the difference in modeling

approaches that do and do not incorporate accuracy in land

cover classification when scaling up from a pixel as a unit of

land cover to a cell being an aggregation of pixels (in this

example six pixels per cell). Under approaches that ignore

misclassification (a), cells on the maps are assigned a land cover

type according to their pixel composition (in this example a cell

with average Forest cover (Ao) has less than 50 % of pixels

Forest (Fo) whereas a cell with a Dominant forest cover (Do) has

more than 50 % of pixels Fo). Assuming no misclassification,

cell land cover transition probabilities (ct) are directly estimated

using these observations on the map. Under approaches that deal

with misclassification errors (b), land cover of pixels on the

ground (F for pixels of Forest and U for pixels of Urban area) is

not known. Instead, land cover of pixels on the maps is

recognized to be a function of land cover of pixels on the ground

and probabilities of pixel accuracy, et . Land cover of cells on the

maps is a function of land cover of cells on the ground and

probabilities of cell accuracy ht . Cell transition probabilities (ct)

are then based on these hidden (but estimated) land cover classes

of cells on the ground rather than on map observations

946 Landscape Ecol (2012) 27:943–956

123

underlying process of land cover dynamics but also

with the classification process. Consider the history

‘Fo Fo’ of a pixel analyzed by only remote-sensing (no

corresponding ground information) over two time

steps. This history depicts a pixel that was mapped as

Forest in the first occasion and as Forest in the second

occasion. This pixel could have been in the true

category Forest on the ground on both time points (i.e.,

the state classification could have been correct at both

time points). Another possibility is that this pixel was

‘‘Managed’’ or ‘‘Urban’’ on the ground at occasion 1

and ‘‘Forest’’ on the ground at occasion 2, indicating

that the pixel changed category between the two

periods. Similarly, the pixel’s land cover could have

been correctly classified as ‘‘Forest’’ at occasion 1 and

then misclassified at the second occasion (the pixel

was really ‘‘Managed’’ or ‘‘Urban’’ at occasion 2).

Finally, the pixel’s land cover type could have been

misclassified at both times. For sake of simplicity, we

assume that all of the parameters underlying our

probability model are constant over time and drop the t

subscript, but this equation could easily be adapted to

time-varying parameters as in Eq. 2. We write the

probability of this history (Fo Fo) as:

Pr FoFoð Þ¼pFeFFo wFFeFFoþwFUeUFoþwFMeMFo� �

þpMeMFo wMFeFFoþwMUeUFoþwMMeMFo� �

þpUeUFo wUFeFFoþwUUeUFoþwUMeMFo� �

ð3Þ

Because there are only three possible land cover types,

the sum of the pR parameters for all land cover types,

R, is one, so one of these parameters can be estimated

by subtraction, e.g.,P

RpR¼1;pM¼1�pF�pU . Sim-

ilarly,P

RwRS¼1 andP

S0eRSo¼1.

In the presence of misclassification, estimation of

the transition matrix w cannot be based solely on the

set of land cover histories obtained from maps, but

requires additional information. This information can

be of two types: (1) the matrix of accuracy probabil-

ities e, can be fixed (see Pontius and Millones (2011)

for one method to compute this matrix) and assumed to

be known, or (2) a sample of pixels having both land

cover type on the map and on the ground. This sample

of pixels is used to develop a likelihood component for

the classification process, thus providing the informa-

tion needed for inference about e. This component is

multiplied by the likelihood component for the data,

based only on information from the map, in order to

draw inference about w. If there is some uncertainty in

the accuracy matrix, the second method is recom-

mended when possible, since it will integrate this

uncertainty into the estimation process.

As an example of the modeling for pixels at

which ground information and observed (remotely

sensed) data are both available, consider the possible

history, FFo UFo. This history again pertains to two

points in time, but now contains information on both

true state (ground information) and observed state

(map) at each time. The pixel is characterized as

forest in time 1, is correctly classified as such in the

map, makes the transition to urban in time 2, and is

incorrectly classified as forest in the map. The

uncertainty associated with this history is reduced

relative to that for Fo Fo, leading to the following

probability model:

Pr FFo UFoð Þ ¼ pFeFFowFUeUFo ð4Þ

This simplified probability structure (compare Eqs. 3

and 4) permits direct estimation of all model param-

eters, which then resolves the uncertainty that charac-

terizes the modeling of remotely sensed data without

ground information (Eq. 3).

An important advantage of recognizing the analogy

between the modeling of animal state dynamics and

habitat dynamics is the ability to use existing software

to compute estimates (Breininger et al. 2010). Pro-

gram E-SURGE (Pradel 2005; Choquet et al. 2009)

has been developed to deal with general multistate

problems characterized by state uncertainty (also

called multi-event models in the capture recapture

literature, or hidden Markov chain models in other

areas), and we propose use of this software to deal with

this same problem in habitat dynamics (see for more

details in Supplementary Material 1). Armed with the

number of sample units exhibiting each habitat history

and the above probabilities associated with each

history (Eqs. 3, 4), maximum likelihood can be used

to compute estimates of parameters and associated

variances. In particular, estimates of accuracy param-

eters and land cover transition probabilities can be

separately estimated, avoiding the usual confounding

present in traditional approaches to analyzing such

data. Program ESURGE uses exactly this approach to

inference.

Landscape Ecol (2012) 27:943–956 947

123

Modeling land cover dynamics when land cover

types are defined by aggregating pixels

This direct modeling of classification and transition

parameters corresponds to the situation in which the

land cover categories are the same and defined at the

same resolution on the ground and in the maps. This

situation contrasts with that in which ground informa-

tion that informs accuracy parameters is used to make

inference on transition probabilities corresponding to

some different (typically coarser) level of resolution

that represents an aggregation of finer resolution data

(Fig. 2). We consider this latter situation below.

Satellite images provide a good illustration of the

problem posed by scaling-up. In the case of satellite

images, the elementary unit is the pixel. However, the

pixel level of resolution might not be relevant if we are

interested in modeling habitat dynamics for larger

spatial units. Instead it might be necessary to represent

cells as an aggregation of elementary pixels.

For example consider that we are interested in

modeling the forest dynamics of a region of 50 km by

500 km. Let’s assume for example a satellite image

resolution of 90 m by 90 m; hence this area is

composed of more than three million pixels, each

classified as Forest (F), Urban (U) or Managed (M).

There are many conservation questions for which

modeling habitat dynamics at a 90 m 9 90 m resolu-

tion is not relevant; that is, inferences at this level of

resolution might not correspond well to the level of

resolution at which ecological processes are thought to

occur. Instead assume that we divide the region into a

grid of 1,000 spatial cells of 25 km2 each. Each cell

will be composed of 3,086 pixels. Because in our

example analysis (see below) we are interested in the

forest dynamics of the whole region, we summarized

the pixel composition of each cell into one of three

possible states based on its proportion of forest pixels:

dominant forest (D) if more than 50 % of the pixels are

forest, average forest (A) if between 30 and 50 % of

the pixels are forest, and low forest (L) if fewer than

30 % of the pixels are forest. We are interested in

estimating the probabilities of transition of the cells

and not the pixels.

Hence the land cover type for a cell i at time t is

given by the vector of its pixel composition variables

[NF, NM, NU]i,t combined with the rule(s) for cell

category assignment:

Ti;t ¼ NFi;tþ NMi;t

þ NUi;tð5Þ

if NFi;t[ 0:5� Ti;t; cell is in category

dominant forest ðDÞif 0:3� Ti;t�NFi;t

� 0:5� Ti;t; cell i is

in category average forest ðAÞif NFi;t

\0:3� Ti;t; cell i is

in category low forest ðLÞ

8>>>>>>>>><>>>>>>>>>:

The dynamics of the whole set of cells can still

be modeled as a first order Markov process, but

governed by a different matrix of transition proba-

bilities ct (to differentiate from wt, the matrix of pixel

transition probabilities). We now follow the dynamics

of these larger cells, specifically the vector of number

of cells in state D (ND), in state A (NA) and in state L

(NL):

END

NA

NL

24

35

tþ1

0@

1A ¼ ct

ND

NA

NL

24

35

t

where ct ¼cDD

t cADt cLD

t

cDAt cAA

t cLAt

cDLt cAL

t cLLt

24

35

ð6Þ

with cRt , representing the probability that a cell in state

R at time t will be in state S at time t ? 1.

If there is no classification error, then the same

modeling approach described for pixels above under

‘‘modeling land cover dynamics when land cover is

known without error’’ can be used at the resolution of

the cell instead of the pixel, and the transition

probabilities at this level of resolution can be

estimated directly. However, misclassification of

pixels is likely to induce misclassification of cells.

For example a cell might be truly composed of a

majority of pixels in state F, but incorrectly observed

as composed of a majority of pixels in state M. In such

a case this cell will be assigned in the map to the land

cover type average forest cell (denoted Ao for observed

state Average forest) or marginal forest cell (denoted

Lo for observed state Low forest), despite being a

dominant forest cell (D) on the ground.

The land cover category for each cell i in the map at

time t is based on the number of pixels in the map in

this cell i NFo;NMo

;NUo½ �i;t such as:

TOi;t¼ NFoi;t

þ NMoi;tþ NUoi;t

ð7Þ

948 Landscape Ecol (2012) 27:943–956

123

if NFoi;t[ 0:5� TOi;t

; cell i is classified as

dominant forest in the map ðDOÞif 0:3� TOi;t

�NFoi;t� 0:5� TOi;t

; cell i

is classified as average forest in the map ðAOÞif NFoi;t

\0:3� TOi;t; cell i is

classified as low forest in the map ðLOÞ

8>>>>>>>>>><>>>>>>>>>>:

And the accuracy of the entire set of cells can as well

be modeled as a misclassification process governed by

a different matrix of accuracy probabilities, ht:

ht ¼hDDO

t hADOt hLDO

t

hDAOt hAAO

t hLAOt

hDLOt hALO

t hLLOt

24

35

This matrix, ht , establishes the relationship between

the vector of numbers of cells on the map (or observed)

being of land cover types D (NDo), A (NAo

) and L (NLo)

and the vector of numbers of cells on the ground in

each land cover type. The cell transition matrix ct can

be modeled using the same framework as previously

described, but with data of cell land cover histories

instead of pixel land cover histories. The same

additional information about the observation process

is required: either (1) a matrix of cell level accuracy

parameters, ht, or (2) at least some cells having

information on land cover on the ground and in the

map at the resolution of the cell.

However, often information on accuracy will only

be available at the pixel level of resolution and not at

the cell level. There is thus a mismatch between the

spatial resolution at which land cover type and

accuracy are being assessed. If ground information is

available for all pixels within a larger cell, then we

could simply use the modeling of Eqs. 3 and 4 above

at the resolution of the larger cell. However, this will

seldom be the case, as ground information will

typically come from a small subset of pixels within

any cell. In such a case, the vector describing ground

pixel composition of a cell i [NF, NM, NU]i,t cannot be

known, but can be approximated by its expectation

(constraining NF, NM and NU to be positive):

ENF

NM

NU

24

35

i;t

0@

1A ¼ e�1

t

NFo

NMo

NUo

24

35

i;t

ð8Þ

where e�1t is the inverse of the pixel matrix of

accuracy probabilities. Estimation of the classification

probabilities at the pixel level, et, can be accomplished

using the state uncertainty modeling described above.

Simulation study

We conducted a simulation study in order to: (1)

investigate the potential bias in estimates of transi-

tion probabilities when error in land cover classifi-

cation is not accounted for and (2) test the efficacy

of our approaches to modeling and inference. We

conducted the study at two levels of resolution, that

of the pixel and that of the cell comprised of many

pixels.

We generated a data set of 1,000 initial cells, each

cell being composed of 3,000 pixels, with overall

probabilities of dominant forest (D) of 0.65, average

forest (A) of 0.22 and low forest (L) of 0.13. Based on

the land cover category of each cell, we randomly

generated the pixel composition for the initial time

within each cell: a dominant forest cell having a

random percentage of forest pixels (F) distributed

uniformly and ranging between 50 and 100 %, an

average forest cell with a percentage of forest pixels

between 30 and 50 % and a low forest cell with fewer

than 30 % of forest pixels. A random percentage

(distributed as U[0,1]) of the remaining pixels was

then assigned to urbanized areas (U) and its comple-

mentary percentage to managed areas (M) We

assumed a constant pixel transition matrix w and used

it to stochastically generate the sequence of true

habitats over four time steps for each pixel. At each

time step we also generated the land cover type on the

map of each pixel, using an assumed pixel matrix

of producer’s accuracy parameters, e. For sake of

simplicity, we assumed in the simulation a constant

matrix of accuracy, but this method can easily be

extended to accuracy parameters varying over time,

which is likely to happen when using satellite images

at different times. Aggregations of the pixel data

provided the land cover category on the ground for

each cell, and aggregations of pixel data with errors of

classification provided the land cover type on the map

for each cell.

We conducted both pixel-level and cell-level

analyses of these simulated data. For both pixel-

level and cell-level analyses, we first estimated the

transition matrix based only on land cover on the

map, hence implicitly assuming these to represent

data without error, or in terms of modeling

Landscape Ecol (2012) 27:943–956 949

123

assuming that the pixel matrix of accuracy was an

identity matrix. In a second step we estimated the

transition matrix of land cover on the ground. For

the pixel-scale analysis we analyzed nine million

pixel histories. Among these, 1,000 pixels were

randomly selected to represent the ground informa-

tion sample, for which we knew both information

on the ground and on the map for the last occasion.

We estimated the pixel habitat transition matrix w

and the pixel accuracy matrix e directly using

E-SURGE with some (1,000) pixels modeled directly

as in Eq. 4, and the remainder modeled using mixture

structures of the type specified in Eq. 3. For the cell-

scale analysis we approximated the land cover on the

ground of each cell by using its expected true pixel

composition as described in Eq. 8 and estimated both

the habitat transition matrix c and the cell accuracy

matrix h. All models were fit using program E-SURGE

(Choquet and Nogue 2010). Following Burnham and

Anderson (2002), we relied on AIC to select among

the models with constant or time varying habitat

transition and error probabilities. In the pixel-scale

analysis, the pixel accuracy matrix was estimated

directly from the pixel histories. In the cell-level

analysis, this matrix was considered to be known

(based on the estimates from the pixel-level analysis)

(see Supplementary Material 1 for the parameteriza-

tion used in E-SURGE).

We generated two data sets using two pairs of pixel

transition and accuracy matrices: a first pair of data

sets with a high accuracy rate (high accuracy proba-

bilities on the diagonal of the matrix e), but a high rate

of habitat turnover (relatively low transition probabil-

ities on the diagonal of the matrix w):

w ¼ Time t þ 1

Time tF M U

FO

MO

UO

0:80 0:05 0:15

0:10 0:90 0:05

0:10 0:05 0:80

24

35

and

e ¼ Map

Ground

F M UFO

MO

UO

0:90 0:05 0:10

0:05 0:90 0:00

0:05 0:05 0:90

24

35

A second pair of data sets was generated with a lower

habitat turnover but a lower accuracy rate:

w ¼ Time t þ 1

Time tF M U

FO

MO

UO

0:90 0:05 0:10

0:05 0:90 0:00

0:05 0:05 0:90

24

35

and

e ¼ Map

Ground

F M UFO

MO

UO

0:80 0:05 0:15

0:10 0:90 0:05

0:10 0:05 0:80

24

35

We note that time-invariant error matrices at the pixel

level are not expected to necessarily produce time-

invariant error matrices at the cell level. Error matrices

at the level of the cell will be a function of both pixel-

scale error matrices and the true distribution of state-

specific pixels (the number of pixels of each state within

each cell). Because correct classification probabilities

vary among pixel states, and because pixel states change

over time, error matrices associated with aggregations

of pixels can exhibit patterns of temporal variation that

differ from those of the pixels themselves.

Study area analyses

In addition to the simulation study, we analyzed actual

data for land cover dynamics from a part of the

southeastern region of the USA (85.5� West,

31.25� North). We divided the region into a grid of

8,304 spatial cells of 25 km2. The land cover on the

map was classified based on data using 60 m resolu-

tion satellite imagery from the Landsat Multi-spectral

Scanner available in 1973, 1986, 1991 and 2000. Each

cell was composed of 3,084 pixels classified as Urban

(U), Forest (F) or Managed (M) over these four times.

The pixel composition of each cell was summarized in

order to classify cells as dominant forest (D), average

forest (A), and low forest (L) using the same rules as

previously described.

The accuracy matrix for the land cover classifica-

tion e was estimated using data from 290 randomly

selected pixels from the 2001 satellite image with

digital orthographic quarter quads (DOQQs). The low

thematic resolution in the classified satellite imagery

(three classes) was easily interpretable within the

aerial photos to provide the assumed land cover on the

ground. With ground information available only for

2001, we had to assume a pixel accuracy matrix that

950 Landscape Ecol (2012) 27:943–956

123

was constant over time. We used this estimated pixel

matrix of accuracy to estimate the expected true pixel

composition of each cell following Eq. 8. In a first step

we estimated the cell-level habitat state transition

probabilities based on the cells on the map (implicitly

assuming these to represent truth) (model 1). In a

second step we estimated the corrected transition

matrix by approximating the land cover on the ground

of each cell using its expected true pixel composition

as described in Eq. 8 (model 2).

Results

Simulated data

Pixel-level analysis

For both high and low levels of pixel accuracy, estimates

of transition probabilities that do not account for

misclassification are strongly biased (Table 1). For an

average accuracy of 90 %, when there is on average

16.8 % change on the ground, the maps show on average

a 32 % change. With a lower accuracy of 83 %, the maps

show 37 % change when the average change on the

ground is only 10 %. Specifically, values on the diagonal

of the transition matrix, which represent the probabilities

of remaining in the same habitat, are substantially

underestimated (respectively for high and low pixel

accuracy; wFF ¼ 0:709 (standard error 0.0002) instead

of 0.8, and wFF ¼ 0:676 0:0002ð Þ instead of 0.9;

wMM ¼ 0:606 0:0003ð Þ and, wMM ¼ 0:643 0:0003ð Þinstead of 0.9; wUU ¼ 0:629 0:0003ð Þ instead of 0.8

and wUU ¼ 0:551 0:0003ð Þ instead of 0.9 And values

above and below the diagonal, i.e., probabilities of

land cover change, tend to be overestimated (for

instance respectively for high and low pixel accu-

racy, wMF ¼ 0:160 0:0002ð Þ and wMF ¼ 0:229 0:003ð Þ

Table 1 Estimates of land cover transition matrix at the pixel level of resolution from simulated data

High accuracy Low accuracy

True values Model 1 Model 2 True values Model 1 Model 2

Probability of transition w (and standard errors)

wFF ¼ 0.80 0.709 (0.0002) 0.800 (0.0003) 0.90 0.676 (0.0002) 0.900 (0.0002)

wFM ¼ 0.10 0.156 (0.0002) 0.100 (0.0002) 0.05 0.155 (0.0002) 0.050 (0.0002)

wFU ¼ 0.10 0.135 (0.0002) 0.100 (0.0002) 0.05 0.169 (0.0002) 0.050 (0.0002)

wMF ¼ 0.05 0.160 (0.0002) 0.056 (0.0004) 0.05 0.229 (0.0003) 0.050 (0.0004)

wMM ¼ 0.90 0.688 (0.0003) 0.889 (0.0005) 0.90 0.643 (0.0003) 0.900 (0.0004)

wMU ¼ 0.05 0.152 (0.0002) 0.055 (0.0003) 0.05 0.128 (0.0002) 0.050 (0.0003)

wUF ¼ 0.15 0.202 (0.0003) 0.150 (0.0004) 0.00 0.278 (0.0003) 0.001 (0.0006)

wUM ¼ 0.05 0.169 (0.0003) 0.051 (0.0003) 0.10 0.171 (0.0002) 0.100 (0.0004)

wUU ¼ 0.80 0.629 (0.0003) 0.799 (0.0005) 0.90 0.551 (0.0003) 0.899 (0.0006)

Probability of pixel accuracy e (and standard errors)

eFFo ¼ 0.90 1 0.900 (0.0003) 0.80 1 0.800 (0.0002)

eFMo ¼ 0. 05 0 0.050 (0.0002) 0.10 0 0.100 (0.0001)

eFUo ¼ 0.05 0 0.050 (0.0002) 0.10 0 0.100 (0.0001)

eMFo ¼ 0.05 0 0.050 (0.0003) 0.05 0 0.056 (0.0002)

eMMo ¼ 0.90 1 0.900 (0.0004) 0.90 1 0.888 (0.0002)

eMUo ¼ 0.05 0 0.050 (0.0003) 0.05 0 0.056 (0.0002)

eUFo ¼ 0.00 0 0.000 (0.0001) 0.15 0 0.150 (0.0004)

eUMo ¼ 0.10 0 0.010 (0.0004) 0.05 0 0.005 (0.0002)

eUUo ¼ 0.90 1 0.900 (0.0004) 0.80 1 0.800 (0.0003)

Model 1 not accounting for error in the observation process (pixel matrix of accuracy fixed to an identity matrix), Model 2 use of

ground information sample to estimate the pixel matrix of accuracy

Landscape Ecol (2012) 27:943–956 951

123

instead of 0.05, or wUF ¼ 0:202 0:0003ð Þ instead of

0.150 and wUF ¼ 0:278 0:0003ð Þ instead of 0. Thus

relatively small misclassification probabilities for

habitat state can produce large bias in estimated

habitat transition probabilities. In contrast with model

1, where misclassification is not accounted for, the

models incorporating data from the ground informa-

tion sample (model 2) lead to approximately unbiased

estimates of transition probabilities (Table 1) for both

levels of accuracy.

Cell-level analysis

Although we generated data using a time-constant

pixel accuracy matrix, the model selected in the cell-

level analysis had time-varying probabilities of mis-

classification (respectively for low and high pixel

accuracy; DAIC = 55 for time-varying accuracy

matrix vs. constant accuracy matrix, and DAIC =

114).The probability of correctly classifying a dom-

inant forest cell (D) strongly decreased over time,

ranging from 0.927 (0.008) to 0.318 (0.016) for data

generated with the highest pixel accuracy, whereas it

only decreased from 0.849 (0.007) to 0.695 (0.011) for

data generated with the lowest pixel accuracy (Fig. 3

and Supplementary Material 2 for a detailed presen-

tation of all parameters estimated). In any case, using

expected ground pixel composition to estimate prob-

abilities of accuracy at the resolution of the cell

resulted in relatively accurate estimates (Fig. 3 and

Supplementary Material 2).

As in the pixel-level analysis, estimates of transi-

tion probabilities at the cell-level based on our

modeling approach accounting for misclassification

are approximately unbiased, whereas estimates that do

not account for misclassification are substantially

biased (Fig. 3). Specifically, failure to deal with

misclassification yields underestimates of probabili-

ties of remaining in the category of dominant forest

(D) (Fig. 3), with respectively for high and low pixel

accuracy, �cDD equal to 0.490 (0.012) instead of 0.714

(0.011), and �cDDequal to 0.834 (0.009) instead of

0.895 (0.006). Moreover, according to the most

supported model, transition probabilities at the cell

(a) (b)

(c) (d)

Fig. 3 Simulation results. Probabilities hDDo that a dominant

forest cell (D) is observed as dominant forest (Do) for high

(a) and low (b) matrices of pixel accuracy and probabilities, cDD

that dominant forest cell (D) at time t will remain as dominant

forest (D) at time t ? 1, for high (c) and low (d) pixel matrices

of accuracy. Dashed lines represent estimates based on true

habitat states (these are only known because we generated the

data), short dashed lines represent estimates from the model

accounting for pixel classification error and straight linesrepresent estimates of transitions from the model based only on

observed habitat states. For c and d, dashed lines are masked by

short dashed lines

952 Landscape Ecol (2012) 27:943–956

123

level did not vary over time for data generated

with low pixel accuracy and low pixel transition

probabilities (DAIC = 11 favoring a constant habitat

transition matrix over a time-varying habitat transition

matrix). However, transition probabilities estimated at

the cell-level without accounting for misclassification

show strong evidence of time variation (DAIC = 38 in

favor of a time-varying habitat transition matrix vs. a

constant habitat transition matrix).

Habitat dynamics of the Southeast region of the USA

The pixel accuracy matrix e based on 290 observed

and ground information pixels was estimated to be

e¼

F M UF0

M0

U0

0:772ð0:028Þ 0:082ð0:011Þ 0:145ð0:024Þ0:089ð0:019Þ 0:918ð0:011Þ 0:000ð0:001Þ0:139ð0:025Þ 0:000ð0:001Þ 0:845ð0:024Þ

24

35

This pixel accuracy matrix was then used to

calculate the expected true pixel composition of cells

of 25 km2. At the cell level, probabilities of correctly

assigning habitats remained high and remarkably

stable over time for average and low forest cells,

whereas they ranged between 0.737 (0.007) and 0.870

(0.005) for dominant forest cells (Table 2). Accord-

ingly, estimates of habitat transition probabilities were

different between models accounting or not for such

classification error: the probability of a cell remaining

in the category of dominant forest (D) was underes-

timated in models assuming no error of classification

(the average transition probability �cDD over a period of

10 years equals 0.808 (0.010) vs. 0.861 (0.010) when

accounting for misclassification) whereas the proba-

bility of an average forest cell (A) remaining in the

same land cover type was overestimated (the average

transition probability �cAA over a period of 10 years

equals 0.385 (0.002) vs. 0.257 (0.004) when account-

ing for misclassification).

The consequence of such a bias in the estimation of

land cover transitions when classification error is not

accounted for will be a distorted view of the dynamics

of the system: in our examples, the land cover

composition seems more homogeneous than it really

is and the proportion of dominant forest cells is

increasingly underestimated over time (Fig. 4), which

can be interpreted as a larger decline in forest cover of

the entire area than actually occurs.

Discussion

In this study we described the problem resulting from

possible habitat classification errors when modeling

habitat dynamics based on land cover data assessed,

for example, by remote sensing. Data generated by

simulation confirm the potential impact of habitat

misclassification on estimates of habitat transition

parameters (Pontius and Lippitt 2006). Indeed, for

both simulated data sets and both levels of integration

(pixels or aggregations of pixels), not taking into

account the possible misclassification always leads to

biased estimates of habitat transition probabilities.

In the first level of integration, illustrated with the

example of pixels from satellite images, we found that

if land cover pixels are falsely considered as observed

without errors, probabilities of remaining in the same

land cover category are underestimated, and proba-

bilities of land cover change are overestimated. Thus

the dynamics of such habitats are seen as having a

higher turnover than in reality. But the reverse

situation, where the system would be perceived as

more static than in reality could as well occur if errors

result in overestimation of the land cover type

exhibiting the greatest change over time.

In the case where data informing classification

probabilities are obtained at one level of resolution

(e.g., pixel level), but land cover types are defined at a

different level (e.g., cells composed of an aggregation

of pixels), this scaling-up makes it difficult to predict

the impact of such classification errors on transition

probability estimates. Indeed, although we generated

data with constant probabilities of pixel misclassifi-

cation over time, the probabilities of land cover

misclassification at the level of the cell were varying

over time as a function of variation in pixel compo-

sition of each cell over time. Thus, when sampling

land cover for ground information in order to estimate

classification errors, there are some advantages to

sampling at the resolution of the pixel, estimating a

pixel accuracy matrix and scaling-up rather than

sampling directly at the resolution of the cell, espe-

cially if misclassification data are available from only

one point in time, but are to be applied to data from

multiple sampling times. On the other hand, by using

expected values of the pixel composition on the

ground to estimate the state of the cell on the ground

(Eq. 8), the variance associated with estimation of the

error parameters cannot be integrated in the analysis of

Landscape Ecol (2012) 27:943–956 953

123

habitat dynamics. An unexpected effect of scaling-up

is the fact that good pixel classification accuracy does

not necessarily translate into good cell accuracy: cells

generated with good pixel accuracy but high habitat

transition rates had an average probability of cell

misclassification higher than cells generated with

lower pixel accuracy and lower habitat transition

rates. As a consequence, the greatest bias in habitat

transition probability estimates did occur with the data

generated with the highest pixel accuracy. This finding

emphasizes the difficulties of extrapolation of infor-

mation about pixel accuracy to inferences about

habitat misclassification at a different level of

resolution.

The approach to modeling and inference that we

presented to deal with habitat state uncertainty

produces approximately unbiased estimates of state

transition probabilities at both resolutions, the pixel

and the cell. The basic approach can be implemented

in existing software such as E-SURGE (Choquet et al.

2009) using frequentist statistics, or it can also be

easily implemented under a Bayesian approach, using

hierarchical modeling with MCMC (Royle and Dor-

azio 2008). The method presented in this study

assumes that land cover dynamics can be usefully

modeled as a first order Markov chain, and that pixels

are independent for both transition and misclassifi-

cation probabilities. Models relaxing the assumption

Table 2 Dynamics of forest cover in the Southeast Region of the USA area: estimation of transition and accuracy matrices c and h

for three habitat states (dominant forest cells (D), average forest cells (A) and low forest cells (L)) over time

Model 1: no accounting for error in the observation

process

Model 2: accounting for error (computing expected true habitat

states)

1973–1986 1986–1991 1991–2000 1973–1986 1986–1991 1991–2000

Probability of cell transition c (and standard errors)

cDD ¼ 0.720 (0.009) 0.760 (0.008) 0.966 (0.003) 0.809 (0.008) 0.803 (0.007) 0.982 (0.002)

cDA ¼ 0.233 (0.009) 0.211 (0.008) 0.032 (0.003) 0.142 (0.007) 0.157 (0.006) 0.017 (0.002)

cDL ¼ 0.047 (0.004) 0.029 (0.003 0.001 (0.001) 0.049 (0.004) 0.039 (0.003) 0.002 (0.001)

cAD ¼ 0.396 (0.010) 0.269 (0.008) 0.763 (0.008) 0.516 (0.011) 0.336 (0.011) 0.864 (0.008)

cAA ¼ 0.474 (0.010) 0.526 (0.010) 0.229 (0.009) 0.336 (0.011) 0.404 (0.011) 0.125 (0.008)

cAL ¼ 0.130 (0.007) 0.205 (0.008) 0.008 (0.002) 0.148 (0.009) 0.260 (0.010) 0.012 (0.002)

cLD ¼ 0.033 (0.003) 0.030 (0.003) 0.166 (0.006) 0.083 (0.004) 0.059 (0.004) 0.270 (0.008)

cLA ¼ 0.267 (0.007) 0.142 (0.006) 0.394 (0.009) 0.213 (0.006) 0.112 (0.005) 0.291 (0.008)

cLL ¼ 0.700 (0.007) 0.828 (0.006) 0.440 (0.009) 0.704 (0.007) 0.829 (0.007) 0.439 (0.008)

Model 1: no accounting for error

in the observation process

(identity matrix)

Model 2: accounting for error (computing expected true habitat states)

1973 1986 1991 2000

Probability of cell accuracy h (and standard errors)

hDDo ¼ 1 0.746 (0.008) 0.737 (0.007) 0.770 (0.007) 0.870 (0.005)

hDAo ¼ 0 0.254 (0.008) 0.263 (0.007) 0.230 (0.007) 0.130 (0.005)

hDLo ¼ 0 0 0 0 0

hADo ¼ 0 0 0 0 0

hAAo ¼ 1 0.937 (0.007) 0.964 (0.004) 0.961 (0.005) 0.968 (0.005)

hALo ¼ 0 0.063 (0.007) 0.036 (0.004) 0.039 (0.005) 0.032 (0.005)

hLDo ¼ 0 0 0 0 0

hLAo ¼ 0 0.001 (0.001) 0.001 (0.001) 0.002 (0.001) 0.007 (0.002)

hLLo ¼ 1 0.999 (0.001) 0.999 (0.001) 0.998 (0.001) 0.993 (0.002)

Values without standard errors indicate estimates at the boundaries

954 Landscape Ecol (2012) 27:943–956

123

of a first order Markov chain have been developed

in the framework of animal monitoring and capture–

recapture models. Such models, called memory

models (Hestbeck et al. 1991; Brownie et al. 1993;

Lebreton et al. 2009; Rouan et al. 2009) allow

dependence of transition probabilities not only on

the state of the system at time t but also on the states at

previous time steps. Hence, in our framework, land

cover transition can easily be modeled as a function of

previous land cover categories that have characterized

a pixel.

The assumption of independence of pixels can also

be relaxed for both transition and misclassification

probabilities. Indeed spatial correlation for both pixel

dynamics and pixel misclassification is likely (Weaver

and Perera 2004). Incorporating autologistic functions

to model spatial autocorrelation is now achievable

using Bayesian methods, pseudo-likelihood and like-

lihood approaches (Lichstein et al. 2002; Dormann

et al. 2007; Royle and Dorazio 2008; Bled et al. 2011;

Yackulic et al. 2012). However, being able to incor-

porate spatial autocorrelation of misclassification

probabilities requires a specific sample strategy for

ground pixels. For example if we assume that pixel

misclassification is correlated to the land cover type of

immediate neighbors, it is then necessary to have the

land cover type on the ground and on the maps of a

random sample of pixels and of their neighbors. Thus

even with more complex modeling, sampling ground

information remains very important in order to

estimate accuracy matrices. Our approach also

assumes that while habitat state at time t is Markovian,

the classification probability at time t is not. Thus, we

assume that we are equally likely to misclassify forest

as agriculture regardless of whether the true state in the

previous time was agriculture or forest. This assump-

tion could also be relaxed, with efficient estimation

aided by specific sampling designs (assessing true

state for the same set of pixels in at least two

successive time periods).

The consequences of not accounting for habitat

misclassification go beyond biased estimates of land

cover transition probabilities. For example in our

analysis of the southeast region of the USA, the

distribution of land cover type appears more homoge-

neous than in reality because of an underestimated

proportion of dominant forest cells and an overesti-

mated proportion of average forest cells, which in turn

can be interpreted as a lower forest cover of the entire

area than in reality. Methods currently exist to correct

estimates of land cover extents (Czaplewski 1992;

Gallego 2004; Stehman 2009), but they have not been

generalized yet, especially when studying species–

environment relationships. The approach that we used

for the pixel-level analysis not only yields approxi-

mately unbiased estimates of habitat state and change

but also associated estimates of sampling variance that

properly include misclassification and its estimation.

The approach that we used for aggregations of pixels

into cells assumed that the error matrix was known,

and did not include variation associated with the fact

that these classification probabilities were estimated.

However, for subsequent uses at the cell level, we plan

to develop a bootstrap approach that incorporates all

relevant variance components. Not properly account-

ing for land cover misclassification can not only

produce misleading inferences about habitat state and

dynamics, but also about species distribution patterns

based on these covariates (Lavorel et al. 2004).

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