Page 1

Ecological Applications, 20(4), 2010, pp. 1173–1182

? 2010 by the Ecological Society of America

Simultaneous modeling of habitat suitability, occupancy,

and relative abundance: African elephants in Zimbabwe

JULIEN MARTIN,1,2,7SIMON CHAMAILLE´-JAMMES,3JAMES D. NICHOLS,2HERVE´ FRITZ,3JAMES E. HINES,2

CHRISTOPHER J. FONNESBECK,4DARRYL I. MACKENZIE,5AND LARISSA L. BAILEY6

1Florida Cooperative Fish and Wildlife Research Unit, University of Florida, Gainesville, Florida 32611-0485 USA

2Patuxent Wildlife Research Center, United States Geological Survey, 12100 Beech Forest Road, Laurel, Maryland 20708 USA

3Universite´ de Lyon, Universite´ Lyon 1, CNRS, UMR 5558, Laboratoire de Biome´trie et Biologie Evolutive,

43 Boulevard du 11 Novembre 1918, Villeurbanne F-69622 France

4Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand

5Proteus Wildlife Research Consultants, P.O. Box 5193, Dunedin, New Zealand

6Department of Fish, Wildlife and Conservation Biology, 1474 Campus Delivery, Fort Collins, Colorado 80523 USA

Abstract.

models provides the opportunity to address fairly complex management and conservation

problems with relatively simple models. However, surprisingly few empirical studies have

simultaneously modeled habitat suitability and occupancy status of organisms over large

landscapes for management purposes. Joint modeling of these components is particularly

important in the context of management of wild populations, as it provides a more coherent

framework to investigate the population dynamics of organisms in space and time for the

application of management decision tools. We applied such an approach to the study of water

hole use by African elephants in Hwange National Park, Zimbabwe. Here we show how such

methodology may be implemented and derive estimates of annual transition probabilities

among three dry-season states for water holes: (1) unsuitable state (dry water holes with no

elephants); (2) suitable state (water hole with water) with low abundance of elephants; and (3)

suitable state with high abundance of elephants. We found that annual rainfall and the

number of neighboring water holes influenced the transition probabilities among these three

states. Because of an increase in elephant densities in the park during the study period, we also

found that transition probabilities from low abundance to high abundance states increased

over time. The application of the joint habitat–occupancy models provides a coherent

framework to examine how habitat suitability and factors that affect habitat suitability

influence the distribution and abundance of organisms. We discuss how these simple models

can further be used to apply structured decision-making tools in order to derive decisions that

are optimal relative to specified management objectives. The modeling framework presented in

this paper should be applicable to a wide range of existing data sets and should help to address

important ecological, conservation, and management problems that deal with occupancy,

relative abundance, and habitat suitability.

The recent development of statistical models such as dynamic site occupancy

Key words:

National Park, Zimbabwe; joint habitat occupancy modeling; Loxodonta africana; multistate site occupancy

models; structured decision making; surface water.

adaptive resource management; African elephants; detection probabilities; Hwange

INTRODUCTION

Conservation of natural resources often requires

managing abundance and spatial distribution of organ-

isms by acting on their habitat (Williams et al. 2002,

MacKenzie et al. 2006). One challenge is then to capture

the features of the system that are most relevant to the

management objectives while keeping the models as

simple as possible (Clark and Mangel 2001, Nichols

2001). The ability to simplify a problem to its most

critical components (i.e., develop a model) has often been

viewed as an art essential to the advancement of science

(Clark and Mangel 2001). In the context of management

there are at least two additional arguments in favor of

using simple models: (1) logistical difficulty of accumu-

lating detailed information over large spatiotemporal

scales; (2) computational limitations associated with

structured decision-making tools for deriving decisions

that are optimal relative to management objectives

(Conroy and Moore 2001). The recent development of

statistical models such as dynamic site occupancy models

provides the opportunity to resolve fairly complex

management and conservation problems with relatively

simplemodels (MacKenzieetal. 2006,2009).

Manuscript received 19 February 2009; revised 27 July 2009;

accepted 5 August 2009. Corresponding Editor: J. J.

Millspaugh.

7Present address: Fish and Wildlife Research Institute,

100 8th Avenue SE, St. Petersburg, Florida 33701 USA.

E-mail: julienm@ufl.edu

1173

Page 2

Surprisingly few empirical studies have modeled simul-

taneously the dynamics of habitat suitability, occupancy,

and abundances of organisms. Nevertheless, many

ecologists have recognized the importance of modeling

simultaneously occupancy and habitat suitability in the

context of metapopulation dynamics (Lande 1987,

Ovaskainen and Hanski 2003, MacKenzie et al. 2006).

In this way, the status of a species can be evaluated based

not only on occupancy, but also on suitability, of the

potential habitats (Lande 1987, Ovaskainen and Hanski

2003, MacKenzie et al. 2006). Joint modeling of these

components is therefore particularly important in the

context of management of populations (where manage-

ment may involve habitat modifications or manipula-

tions), as it provides a coherent framework for

investigating the population dynamics of organisms in

space and time for the application of management

decision tools (MacKenzie et al. 2006). Here we show

how such an approach may be implemented and provide

an example combining simultaneous modeling of habitat

suitability and occupancy states (i.e., low and high

abundances) in the context of the management of the

population of African elephants (Loxodonta africana)

(Blumenbach) of Hwange National Park, Zimbabwe.

Densities of African elephants have increased signif-

icantly in southern Africa, reaching very high densities

in some protected areas (Blanc et al. 2007). In such

places, concerns emerge that high elephant abundance

may be detrimental to biodiversity, particularly through

the impact of elephants on vegetation (O’Connor et al.

2007). Culling has been proposed as a possible

management action, but this option is ethically debat-

able and remains politically unattractive to many park

managers and other stakeholders (Owen-Smith et al.

2006). Studies conducted in Hwange National Park

suggest that managing surface water may offer an

alternative, more appealing, management strategy in

some places (Owen-Smith et al. 2006, Chamaille ´ -

Jammes et al. 2007b, c, Smit et al. 2007). By acting on

the number and distribution of suitable water holes (i.e.,

retaining water during the dry season) through changes

in artificial water supply, managers may be able to

influence the abundance and distribution of elephants

within parks. This, however, requires developing an

understanding of the dynamics of elephant distribution

across water holes.

We had two primary objectives related to conserva-

tion and management of elephants. Our first objective

was to better understand factors that govern site

occupancy dynamics of elephants in Hwange National

Park. Our second objective was to provide estimates of

transition probabilities to parameterize mechanistic

models that can be used as the basis for management

purposes (e.g., to identify decisions that are optimal

relative to specified management objectives; or to

simulate abundance and distribution of elephants under

a variety of management scenarios). Our models were

based on several a priori hypotheses and predictions.

We used likelihood-based dynamic multistate site

occupancy models (MacKenzie et al. 2009) to estimate

annual transition probabilities among three dry-season

states (m) of sites: unsuitable sites (denoted U, hence m¼

U), suitable sites with low abundance of elephants (0–50

counted over 24-h surveys, m ¼ L), and suitable sites

with high abundance of elephants (51–1600, m ¼ H). In

the context of our study, the sites were water holes.

Water holes were considered suitable habitats whenever

at least some water was present, and were considered

unsuitable otherwise.

For our purposes, we used the conditional binomial

parameterization of the dynamic multistate model,

wm

tþ1(as denoted by MacKenzie et al. 2009), where

wm

year tþ1 (i.e., contains water), given that the water hole

was in state m in year t (with m being state U, L, or H);

and Rm

tþ1is the probability that a suitable water hole

contains a high abundance of elephants (state H) in year

tþ1, given that it was in state m in year t. For example,

wU

year t þ 1, given that the water hole was unsuitable in

year t (i.e., was in state U). The parameterization just

described (hereafter referred to as wm

conditional binomial parameterization) provides a

natural description of the process we are trying to

model. Indeed, water holes are suitable or not (described

by parameter wm

occupied either by a low or high number of elephants

(described by parameter Rm

tþ1). In order to evaluate the

effect of several covariates (e.g., precipitation) on

transition probabilities wm

models that explicitly included these factors. For each of

the hypotheses, we made specific predictions about the

influence of our selected covariates on parameters wm

and Rm

tþ1.

First, we evaluated the hypothesis that rainfall

influences habitat suitability. Because the probability

that water holes retain water increases with increasing

rainfall (Chamaille ´ -Jammes et al. 2007a), we predicted a

positive relationship between rainfall and the probability

of transitioning from any state m at time t to a suitable

state at time tþ1 (i.e., wm

obtain reliable estimates of the magnitude of the rainfall

effect on habitat (water hole) transition probabilities.

Because this information may ultimately be incorporat-

ed into models that project the dynamics of elephants at

water holes, it was necessary for us to evaluate this

prediction, even though it may appear rather simple and

obvious.

Second, we evaluated the hypothesis that the total

number of water holes within a 10 km radius of a focal

water hole would influence the number of elephants

present at that water hole site. We chose 10 km because

most family herds typically do not travel .10 km from

water during the peak of the dry season (Stokke and du

Toit 2002). More specifically, we predicted a positive

relationship between the number of neighboring water

½ ?

½ ?

tþ1is the probability that a water hole is suitable in

tþ1Rm

½ ?

½ ?

½ ?

tþ1is the probability of a water hole being suitable in

½ ?

tþ1Rm

½ ?

tþ1, or the

½ ?

tþ1), and if they are suitable they are

½ ?

½ ?

tþ1and Rm

½ ?

tþ1, we developed

½ ?

tþ1

½ ?

½ ?

tþ1). Our primary interest was to

JULIEN MARTIN ET AL.1174

Ecological Applications

Vol. 20, No. 4

Page 3

holes associated with a site and the probability that a site

would transition to a high elephant abundance state at

time t þ 1, given that the site was suitable in t þ 1 (i.e.,

Rm

tþ1is influenced by the number of neighboring water

holes). Elephants may select sites with higher densities of

water holes to reduce their chance of being located far

away from any suitable sites if one or more neighboring

sites become unsuitable.

Finally, we considered the potential influence, of a

general increase in elephant abundance in the park on

site-specific elephant abundance transition probabilities

Rm

tþ1. Regular culling of elephants was conducted in

Hwange National Park until 1986. To avoid the

disturbing effects of culling on elephant distribution

we used data collected afterward, when the population

first increased dramatically and then fluctuated at higher

abundance (Chamaille ´ -Jammes et al. 2008). Thus, we

predicted that transition probabilities Rm

creased during the second half of the study period

(1996–2005).

½ ?

½ ?

½ ?

tþ1have in-

METHODS

Study area

Hwange National Park covers ;15000 km2at the

northwest border of Zimbabwe (198000S, 268300E).

Vegetation is typical of southern African dystrophic

wooded savannas with patches of grassland. Surface

water becomes scarce during the dry season, as the river

network and most natural pans dry up. In addition to

the few natural water holes retaining water throughout

the dry season, artificial water holes can maintain water

availability year-round through ground water pumping

(Fig. 1). Due to increased surface water availability, the

elephant population has increased since the creation of

the park and has been controlled through culling up to

1986. The population has increased dramatically since

then and appears to have stabilized at .2 elephants/km2

(Chamaille ´ -Jammes et al. 2008). Heterogeneity across

space in elephant densities during the dry season is

linked to surface water availability (Chamaille ´ -Jammes

et al. 2007a).

Surveys

We used survey data that were collected between 1987

and 2005, after culling operations were stopped. Water

holes were surveyed annually during the dry season

(between September and October). Over a 24-h period at

full moon, all animals coming to drink were simulta-

neously recorded at the studied water holes from

observation platforms or cars located close to the water

hole (see Plate 1). Analyses of these census data in the

context of elephant management can be found in

Chamaille ´ -Jammes et al. (2007a, 2008) and Valeix et

al. (2008).

Statistical analysis

We used likelihood-based dynamic multistate site

occupancy models (MacKenzie et al. 2009) to estimate

annual transition probabilities (wm

earlier), the probability that a water hole was suitable at

time t (wt), and the probability that a water hole had a

high abundance of elephants at time t, given that the

water hole was suitable at time t (Rt). We followed the

notation of MacKenzie et al. (2009), according to which

transition probabilities (wm

script, whereas state variables (wtand Rt) do not. As

explained earlier, sites could be in one of three states

(m): unsuitable sites (denoted U, hence m¼U; i.e., water

holes with no water); suitable sites (i.e., water holes with

some water) with low abundance of elephants (0 to 50, m

¼L), and suitable sites with high abundance of elephants

(51–1600, m ¼ H). Initially we considered models that

included more states; unfortunately, sample sizes were

too small to produce reliable estimates and we had to

limit our analysis to the three states just described.

Beyond the obvious distinction between unsuitable and

suitable sites, the cutoff point between low and high

abundance had to distinguish an abundance category for

which the impact of elephants at the water hole was

deemed acceptable to park managers from a category

for which impact may be too high. There are few data in

the literature to link elephant impact to elephant

numbers, and we based our cutoff point on the

observation that at water holes where elephant abun-

dance was lower than 50, neighboring vegetation did not

suffer significant damage (S. Chamaille ´ -Jammes and H.

Fritz, personal observation). Thus, we believe that the

three states make sense from a management standpoint.

An additional benefit of using only three states is related

to computational limitations associated with decision-

½ ?

tþ1and Rm

½ ?

tþ1, described

½ ?

tþ1and Rm

½ ?

tþ1) carry a super-

FIG. 1.

entire Hwange National Park, Zimbabwe. Open squares

indicate the unmanaged water holes that were included in the

statistical analyses. Open circles indicate the unmanaged water

holes that were not included in the analyses. Solid circles

indicate the sites that could possibly be equipped with water

pumps.

Map of the study area, which encompasses the

June 20101175JOINT HABITAT OCCUPANCY OF ELEPHANTS

Page 4

making tools (e.g., stochastic dynamic programming)

for deriving optimal decisions with respect to specified

management objectives (Conroy and Moore 2001).

Although elephant census data were collected at 110

water holes, we only used natural water holes that were

not equipped with pumps, reducing our sample size to

47 sites. We focused on natural water holes because for

the other sites there was no good record of when pumps

were active or not. This uncertainty made it impossible

to separate influences of rain from those of pumping for

sites with pumps. The count of the number of

neighboring water holes (used as a covariate) included

all water holes (i.e., those with and without pumps, as

well ones for which count data were not available; this

total number was 163 water holes).

In our model notation, time dependency was denoted

as ‘‘t,’’ and no time variation was denoted ‘‘.’’. For

instance, fw[m](t)g indicates the habitat transition

probabilities, wm

indicates thatwm

developed several models that included the effect of

factors of particular interest on wm

rainfall (denoted RAIN) and the number of neighboring

water holes within a 10 km radius of each water hole site

(denoted NEI). Annual rainfall for year t was computed

as the cumulative rainfall from October in year t ? 1 to

September in year t (Chamaille ´ -Jammes et al. 2007a).

Annual rainfall for the period 1987–2005 ranged from

289 mm to 850 mm. Finally, we considered models that

incorporated the increase in elephant abundance in the

park. In order to account for this effect, we considered a

‘‘before vs. after effect 1996’’ (denoted BA; the ‘‘before’’

time period corresponded to the first half of the study

period, 1987–1996). With these models, we predicted

that transition probabilities toward high-abundance

states would increase during the second half of the

study period, due to the global population increase over

the study period. By dividing the study period into two

periods of ;10 years each, we were able to compute

estimates that were relatively precise, yet reflected this

change in abundance. Note that we only modeled Rm

a function of NEI and BA. Although we had a priori

reasons to model wm

probability of a site being suitable depends on rainfall),

we did not have a priori reasons to believe that the

number of neighboring water holes or the study period

(BA effect) had an effect on water hole suitability (i.e.,

w1, wm

that transition probabilities to suitable states L or H

(indicated by Rm

t ) depended on NEI and BA.

To illustrate how our a priori expectations are

integrated into the models, we present the following

example. Model fw[m](RAIN)R[m](RAINþNEIþBA)g

assumed that transitions wU

affected by rainfall. The second term in the model

indicates that RU

rainfall, the number of neighboring water holes and a

‘‘before vs. after 1996’’ effect. No interactions among

½ ?

½ ?

tþ1, varied over time, whereas fw[m](.)g,

tþ1remained constant over time. We also

½ ?

tþ1and Rm

½ ?

tþ1: annual

½ ?

tþ1as

½ ?

tþ1as a function of rainfall (i.e., the

½ ?

tþ1). In contrast, we had a priori reasons to expect

½ ?

½ ?

tþ1, wL ½ ?

tþ1, and wH

½ ?

tþ1were all

½ ?

tþ1, RL ½ ?

tþ1, and RH

½ ?

tþ1were influenced by

these three predictor variables were considered; hence,

the effect of the variables are additive (on the logistic

scale) as denoted by the ‘‘þ’’ symbol. All models were

fitted in program PRESENCE 2.2 (Hines 2008).

Although the models and software that we used can

estimate detection probabilities, in our application the

‘‘robust design survey data’’ (i.e., repeat surveys within

each year over several years; for details, see MacKenzie

et al. 2006) necessary to estimate detection were not

available. However, elephants in non-forested habitat

provide a sampling situation in which detection prob-

abilities are expected to be extremely high. In the context

of this application, ‘‘perfect detection’’ equates to

correctly identifying water holes as having either low

or high elephant abundance. Given the abundance

categories used here, we believe this assumption is

reasonable and therefore we fixed detection probability

parameters to 1 in program PRESENCE 2.2 (Hines

2008).

We also could have used an alternative formulation to

directly model transition probabilities among states (U,

L, and H) instead of using the wm

binomial parameterization. In a typical multistate

model, /qs

t

can be defined as the probability that a site

in state q at time t is in state s at time t þ 1. In this

example, q and s are states (i.e., L, H, or U defined

earlier). For instance, /UH

t

that is unsuitable (i.e., in state U) at time t is suitable

and is occupied by more than 50 elephants (i.e., is in

state H) at time tþ1. As explained by MacKenzie et al.

(2009), there is a straightforward correspondence

between these two parameterizations:

2

½ ?

tþ1Rm

½ ?

tþ1conditional

½ ?

½?

is the probability that a site

1 ? wU

wU

wU

2

½ ?

tþ1

1 ? wL ½ ?

wL ½ ?

wL ½ ?

tþ1

1 ? wH

wH

wH

½ ?

tþ1

½ ?

tþ1ð1 ? RU

½ ?

½ ?

tþ1Þ

tþ1ð1 ? RL ½ ?

tþ1RL ½ ?

3

tþ1Þ

½ ?

tþ1ð1 ? RH

½ ?

½ ?

tþ1Þ

tþ1RU

½ ?

tþ1

tþ1

tþ1RH

½ ?

tþ1

64

3

75

¼

/UU

t

/UL

t

/UH

t

/LU

t

/LL

t

/LH

t

/HU

t

/HL

t

/HH

t

6475:

ð1Þ

½ ?

t

Therefore, one can derive estimates for the /qs

parameterization from estimates obtained from the

wm

latter parameterization is that both parameters are

modeled as binomial random variables. Thus, one does

not have to constrain the transition probabilities out of a

particular state to sum to 1, making the wm

parameterization more stable computationally. In addi-

tion, with our covariate modeling, it was natural to

focus separately on habitat transitions (wm

elephant abundance transitions conditional on habitat

suitability (Rm

tþ1). Therefore, we first estimated parame-

ters wm

insights, we used these estimates to derive unconditional

½ ?

tþ1Rm

½ ?

tþ1parameterization. One advantage of using the

½ ?

tþ1Rm

½ ?

tþ1

½ ?

tþ1) and

½ ?

½ ?

tþ1and Rm

½ ?

tþ1and then, to gain complementary

JULIEN MARTIN ET AL.1176

Ecological Applications

Vol. 20, No. 4

Page 5

transition probability (/qs

L, and H.

Regardless of the parameterization, a typical encoun-

ter history at water hole j (noted hj) would look like: hj¼

HLUL; that is, the site contained water and over 50

elephants (state H) during the first season, it contained

water but ,50 elephants were counted (state L) during

the second and fourth seasons and the site was dry (state

U) in the third season. The probability statement for this

encounter history under model fw[m](t)R[m](t)g based

on the wm

tþ1

w1R1wH

w1R1corresponds to the probability of the water hole

being suitable and being in state H during the first

occasion. The terms wH

probability of the water hole remaining suitable but

moving to state L between time periods 1 and 2.

Similarly, (1? wL ½ ?

site in state L at time 2 transitions to unsuitable in time

3. Finally, the terms wU

of the site becoming suitable between times 3 and 4 and

then being characterized by a low abundance of

elephants at time 4.

We used Akaike’s information criterion (AIC) for

model selection (Akaike 1973, Burnham and Anderson

2002). DAIC for the ith model was computed as AICi?

minimum AIC. AIC weight (w) was also used as a

measure of relative support for each model (w ranged

from 0 to 1, with 1 indicating maximum support;

Burnham and Anderson 2002).

½ ?

t ) estimates among states U,

½ ?

tþ1and Rm

2(1 ? RH

½ ?

parameterization would be:

2)(1 ? wL ½ ? ½ ?½ ?

3)wU

½ ?

4(1 ? RU

½ ?

4). The statement

½ ?

2(1 ?RH

½ ?

2) correspond to the

3) corresponds to the probability that a

½ ?

4(1? RU

½ ?

4) reflect the probability

Effect of covariates on transition probabilities

Parameters wm

logistic function of rainfall (RAIN), the number of

neighboring water holes (NEI), and the ‘‘before vs. after

1996’’ effect (BA).

For example, Rm

tþ1was modeled as

?

¼ bINTþ bRAIN3ðRAINÞ þ bBA3BA

where bINT is the intercept and bRAIN is the slope

parameter for the relationship between rainfall andRm

Although rainfall was measured in millimeters, it was

converted to meters in the analysis; hence bRAINshould

be interpreted in terms of meters of rainfall. bBAis the

parameter that accounts for the ‘‘before vs. after 1996’’

effect. BA ¼ 1 corresponds to the first half of the study

period (1987–1996) and BA ¼ 0 corresponds to the

second half of the study period (1997–2005).

½ ?

tþ1and Rm

½ ?

tþ1were modeled as a linear-

½ ?

logit Rm

½ ?

tþ1

?

¼ ln

Rm

tþ1

½ ?

1 ? Rm

½ ?

tþ1

!

ð2Þ

½ ?

tþ1.

RESULTS

AIC model weights (w) suggested that the model

fw[m](RAIN)R[m](RAIN þ NEI þ BA)g was best

supported by the data (w ¼ 0.93; Table 1). As expected,

the model revealed a positive relationship between

rainfall (RAIN) and the probability that a water hole

was suitable, wm

time t (Table 2, Fig. 2). The number of neighboring

water holes (NEI) was also included in the most

parsimonious model, indicating that this factor influ-

ences the distribution of elephants at the water holes,

Rm

tþ1. However, the predicted positive relationship

between the number of neighboring water holes and

Rm

tþ1was equivocal. For instance, the data suggested a

positive relationship for RH

(Table 2, Fig. 3). There was some evidence that

transition probabilities from any state at time t to high

abundance at time t þ 1, given that the water hole was

suitable at time t þ 1 (Rm

second half of the study period (Fig. 3). Indeed,

estimates of Rm

tþ1were greater during the second half

of the study period than during the first half (i.e.,ˆbBA

was negative for RU

corresponds to the first time period, 1987–1996; see

Table 2). However, the confidence intervals for the

estimated slope parameters overlapped zero for all

transition probabilities except RH

relationship between annual rainfall and RU

RH

tþ1, which would indicate that as precipitation increas-

es, elephants tend to disperse (ˆbRAINwas negative for

each of these parameters; Table 2).

Using Eq. 1 and the estimates presented in Table 2, we

derived estimates of /LH

t

and /HL

number of neighboring water holes, precipitation, and

the ‘‘before vs. after 1996’’ effect (Fig. 4). There was

some evidence that /LH

t

decreased during years of high

precipitation, but there was no evidence of a relationship

between the number of neighboring water holes and

/LH

t

(Fig. 4a). Conversely /HL

½ ?

tþ1, regardless of the occupancy state at

½ ?

½ ?

½ ?

tþ1, but not for RL ½ ?

tþ1and RU

½ ?

tþ1

½ ?

tþ1), were greater during the

½ ?

½ ?

tþ1, RL ½ ?

tþ1, and RH

½ ?

tþ1; BA ¼ 1

½ ?

tþ1. There was negative

½ ?

tþ1, RL ½ ?

tþ1, and

½ ?

½?½

t

?

as a function of the

½?

½?

½

t

?

increased during years

TABLE 1.

for elephants in Hwange National Park, Zimbabwe.

Model selection of joint habitat occupancy models

Model

DAICwK

w[m](RAIN) R[m](RAIN þ NEI þ BA)

w[m](RAIN) R[m](RAIN þ BA)

w[m](RAIN) R[m](RAIN þ NEI)

w[m](RAIN) R[m](RAIN)

w[m](RAIN) R[m](BA)

w[m](RAIN) R[m](.)

w[m](.) R[m](RAIN þ NEI þ BA)

w[m](.) R[m](NEI)

w[m](.) R[m](.)

0

5.6

9.2

10.9

21.4

27.1

37.5

62.1

63.9

0.93

0.06

0.01

0

0

0

0

0

0

20

17

17

14

14

11

17

11

8

Notes: The parameter w[m]corresponds to the component of

the model that pertains to transition probability wm

probability that a water hole is suitable in year tþ1, given that

the water hole was in state m in year t (with m being state:

unsuitable [U], low abundance [L], or high abundance [H]). R[m]

corresponds to the component of the model that pertains to trans-

ition probability Rm

tþ1; the probability that a suitable water hole

contains a high abundance of elephants (state H) in year t þ 1,

given that it was in state m in year t. BA is the before–after

effect; NEI is the number of neighboring water holes; RAIN is

rainfall at time t. AIC is the Akaike information criterion;

DAIC for the ith model is computed as AICi? minimum AIC;

w is the AIC weight; K is the number of parameters.

½ ?

tþ1, the

½ ?

June 20101177 JOINT HABITAT OCCUPANCY OF ELEPHANTS

Page 6

of high precipitation and there was some evidence of a

negative relationship between the number of neighbor-

ing water holes and /HL

t

(Fig. 4b). In addition, /LH

greater during the second half of the study period,

whereas the opposite was observed for /HL

Based on the most parsimonious model, the estimate of

the probability of a water hole being suitable in 1987,

ˆw87, was 0.31 (SE ¼ 0.08) and the probability that a

suitable water hole contained a high abundance of

elephants (state H) in 1987, given that it was suitable in

1987,ˆR87, was 0.78 (SE ¼ 0.14). The remaining models

received very little support from the data, based on w (w

? 0.06; Table 1). Model w[m](t)R[m](t) did not reach

numerical convergence and therefore was not included

in our evaluation of competing models.

½?½

t

?

was

½

t

?

(Fig. 4).

DISCUSSION

Despite the importance of modeling occupancy and

habitat suitability simultaneously, examples of such

studies are scarce (Lande 1987, Ovaskainen and

Hanski 2003, MacKenzie et al. 2006). Here we have

modeled the habitat at a site as either unsuitable (i.e.,

with no water and therefore no chance of any elephants

being present) or suitable. Suitable sites are then further

categorized into one of two possible states. In our case,

the occupancy states were two classes of abundance (low

or high), although in other applications other categories

could be used (e.g., presence or absence of the target

species). In fact, a greater number of categories could be

used if conducive with the objective of the study and if

adequate data are available. Here we have also assumed

that these categories are observed without error, but the

modeling framework presented by MacKenzie et al.

(2009) is flexible enough to relax this assumption. This

modeling framework is implemented in easy-to-use

software PRESENCE 2.2, which should make this

approach all the more useful to ecologists, conservation

biologists, and managers.

The results regarding our specific case study provide

useful insights into the dynamics of elephants at water

holes, which can be used to better manage elephant

populations in Hwange National Park. As expected

from previous studies of this system (Chamaille ´ -Jammes

et al. 2007a, 2008), rainfall appears to be critical in

influencing the distribution and abundance of elephants

in the park (Fig. 2, Table 2). All supported models

suggest a strong positive relationship between rainfall

and the transition probabilities from unsuitable to

suitable states. As explained earlier, our goal was not

so much to further test the hypothesis that rainfall

influences water hole suitability (which is self evident

and was shown by Chamaille ´ -Jammes et al. 2007a), but

rather to estimate parameters of this relationship for the

purpose of modeling the effect of rainfall on water hole

suitability (Fig. 2).

Models that included the effects of the number of

neighboring water holes (within 10 km) received some

support. However, support for the prediction of a

positive relationship between the number of neighboring

water holes and Rm

tþ1was inconsistent. For instance,

there was a positive relationship for RH

RL ½ ?

tþ1(Table 2, Fig. 3). In addition, when

looking at the derived parameters, we found no

relationship between the number of neighboring water

holes and transition probabilities from low to high

abundance (/LH

t

; Fig. 4a). Under our a priori hypoth-

½ ?

½ ?

tþ1, but not for

tþ1and RU

½ ?

½?

TABLE 2.Parameter estimates for the most parsimonious model, with standard errors and upper and lower 95% confidence limits.

w[m](RAIN) R[m](RAIN þ NEI þ BA)

logit(wU

b

EstimateSE Lower 95% CI Upper 95% CI

½ ?

tþ1) ¼ bINTþ bRAIN3 RAIN

bINT

bRAIN

bINT

bRAIN

bINT

bRAIN

bINT

bRAIN

bNEI

bBA

bINT

bRAIN

bNEI

bBA

bINT

bRAIN

bNEI

bBA

?4.667

5.773

0.688

1.056

?6.042

3.660

?3.292

7.885

logit(wL ½ ?

tþ1) ¼ bINTþ bRAIN3 RAIN

?1.257

3.282

1.347

2.455

?3.950

?1.627

?1.611

?0.076

2.243

?15.252

?0.666

?3.184

?0.451

?11.571

?0.273

?2.414

1.474

?10.107

0.011

?3.283

1.436

8.192

logit(wH

½ ?

tþ1) ¼ bINTþ bRAIN3 RAIN

?0.197

2.612

0.707

1.344

1.217

5.300

logit(RU

þ bNEI3 NEI þ bBA3 BA

½ ?

tþ1) ¼ bINTþ bRAIN3 RAIN8.199

?8.525

?0.371

?1.439

3.548

?4.996

0.007

?0.660

4.446

?5.953

0.233

?1.817

2.978

3.363

0.147

0.872

14.154

?1.799

?0.076

0.306

logit(RL ½ ?

þ bNEI3 NEI þ bBA3 BA

tþ1Þ ¼ biNTþ bRAIN3 RAIN2.000

3.288

0.140

0.877

7.547

1.580

0.287

1.095

logit(RH

þ bNEI3 NEI þ bBA3 BA

½ ?

tþ1) ¼ bINTþ bRAIN3 RAIN 1.486

2.077

0.111

0.733

7.417

?1.799

0.456

?0.350

Notes: BA is the before–after effect (BA¼1 corresponds to the first half of the study period [1987–1996]; BA¼0 corresponds to

the second half of the study period [1997–2005]). NEI is the number of neighboring water holes; RAIN is rainfall at time t; bINTis

the intercept, and bRAINis the slope parameter for the relationship between rainfall andRm

the ‘‘before vs. after 1996’’ effect; and bNEIis the slope parameter for the relationship between the number of neighboring water

holes and Rm

½ ?

tþ1; bBAis the parameter that accounts for

½ ?

tþ1.

JULIEN MARTIN ET AL. 1178

Ecological Applications

Vol. 20, No. 4

Page 7

esis that elephants tend to concentrate preferentially in

areas with higher densities of water holes, we would

have expected a positive relationship. An a posteriori

hypothesis for the observed patterns is related to the

competition for food resources, which should push

elephants to avoid areas with high abundance of

elephants. When the surface water is low elephants have

no choice but to concentrate in areas with high water

hole densities, but as the number of suitable water holes

increases (with rainfall), elephants may disperse into less

utilized areas, exploiting increased food production.

This again might explain the lack of relationship

between the number of neighboring water holes and

/LH

t

(Fig. 4a) and the stronger negative relationship

between the number of neighboring water holes and

/HL

t

when precipitation is high (Fig. 4b). This a

posteriori hypothesis is also supported by the fact that

there was a negative relationship between rainfall and

RU

would indicate that as precipitation increases, elephants

tend to disperse. Finally, models that included a ‘‘before

vs. after 1996’’ effect were supported by the data and

indicated that transition probabilities Rm

during the second half of the study period.

In addition to being a valuable tool for investigating

the spatiotemporal dynamics of animal populations, the

type of model presented here can be used to parameter-

ize management models or simulate how changes in

environmental conditions may affect the distribution of

elephants in the park. For instance, the dynamic model

underlying our estimation is a Markov chain model (see

also Martin et al. 2009a) of the type

½?

½?

½ ?

tþ1, RL ½ ?

tþ1, and RH

½ ?

tþ1(ˆbRAINwas negative; Table 2), which

½ ?

tþ1increased

ntþ1¼ Hnt

ð3Þ

where ntis a column vector,

nU

t

nL

nH

t

t

2

4

3

5

that specifies the number of sites in each state at time t.

For instance, nU

tcorresponds to the number of sites in

state U, and H is a transition matrix that includes the

transition probabilities among states U, L, and H:

2

H ¼

/UU

t

/UL

t

/UH

t

/LU

t

/LL

t

/LH

t

/HU

t

/HL

t

/HH

t

64

3

75:

Estimates of some of these probabilities are presented

in Fig. 4 and can be derived from estimates presented in

Table 2 (by using Eq. 1). Based on Eq. 3, it would be

possible to project the consequences of future changes in

rainfall patterns (e.g., associated with global climate

change) on elephant distribution and abundance cate-

gories in the park. However, we believe that this

approach may be most useful in the context of

structured decision making (e.g., Williams et al. 2002,

Martin et al. 2009b). For instance, the managers’

objective may be to achieve distribution and abundance

categories of elephants that appear compatible with the

socioeconomic and ecological needs of the park (e.g.,

that could be based on historical levels). In this case, the

next step would be to develop a management model that

links management actions to elephant distribution and

abundance category. One potential action, in this

specific case study, is to activate or deactivate artificial

water pumps at water holes equipped with such devices.

Once a management model has been developed,

optimization methods such as stochastic dynamic

programming (Lubow 1999, 2001) or reinforcement

FIG. 2.

tion probabilities (wm

hole being suitable in year t þ 1, given that it was in state m in

year t (with m¼U [unsuitable], L [suitable with low abundance

of elephants], or H [suitable with high abundance]). The thick

black lines correspond to the estimates of transition probabil-

ities, and the thin black lines correspond to the 95% CI.

Relationships between annual rainfall and transi-

½ ?

tþ1is the probability of a water

tþ1), where wm

½ ?

June 20101179 JOINT HABITAT OCCUPANCY OF ELEPHANTS

Page 8

learning (Fonnesbeck 2005) can then be applied to

identify optimal decisions relative to specified objectives

(e.g., Martin et al. 2009b). In our application, we believe

that switching pumps on or off is more likely to lead to a

behavioral response (i.e., movement) than a numerical

response (i.e., mortality). However, these issues should

probably be considered when developing the manage-

ment models. In any cases, our statistical analyses

provide baseline estimates to parameterize such man-

agement models. It is also worth noting that one can

think of several similar management problems. For

example, for amphibians that breed in vernal pools,

habitat (i.e., the vernal pool) may be considered as

unsuitable if it is dry (MacKenzie et al. 2006); the

management goal could then be to maintain a desired

number of vernal pools occupied by amphibians while

minimizing the cost associated with vernal pool man-

agement (e.g., mechanically manipulating pool size or

depth; D. I. MacKenzie, J. D. Nichols, L. L. Bailey, and

J. E. Hines, unpublished manuscript).

Ideally, one should account for detection probabilities

when estimating transition probabilities among occu-

pancy or abundance states (Yoccoz et al. 2001, Williams

et al. 2002). Unfortunately, the design of many historical

FIG. 4.

number of neighboring water holes, and transition probabilities

(/). Transition probabilities are between suitable sites (with

high [H] and low [L] abundance of elephants). The gray surface

corresponds to the pre-1996 period, and the white surface to the

post-1996 period.

Relationships between annual rainfall (mm), the

FIG. 3.

of neighboring water holes (‘‘neighbors’’), and transition

probabilities (Rm

tþ1is the probability of the water hole

being in state H in year tþ1 given that it is suitable in tþ1 and

was in state m in year t. The gray surface corresponds to the

pre-1996 period, and the white surface to the post-1996 period.

Relationships between annual rainfall, the number

½ ?

tþ1). Rm

½ ?

JULIEN MARTIN ET AL. 1180

Ecological Applications

Vol. 20, No. 4

Page 9

large-scale monitoring programs does not allow for the

estimation of detectability. In these instances the types

of models presented here can be helpful to reduce errors

associated with detectability by assigning individuals to

broad classes of abundances instead of modeling

uncorrected count data directly. Assigning observations

to broad categories reduces the possibility of a

misclassification error, which is a manifestation of

imperfect detection (e.g., false absences). However, we

agree with Yoccoz et al. (2001) and strongly encourage

biologists to design monitoring programs that will

explicitly consider both detection and sampling varia-

tion to avoid errors associated with these two sources of

variations (otherwise, if detection probability is less than

1, resulting inference might be unreliable). In fact, in

situations where repeated observations of each site have

been conducted within a relatively short time frame each

year, it is then possible to simultaneously estimate

detection probabilities and transition probabilities with

dynamic multistate site occupancy models (MacKenzie

et al. 2009; D. I. MacKenzie, J. D. Nichols, L. L. Bailey,

and J. E. Hines, unpublished manuscript). This is made

particularly easy with the recent implementation of this

model into the user-friendly software PRESENCE 2.2.

To conclude, we see several advantages of our

approach in wildlife habitat management and other

ecological applications. First, the type of joint habitat–

occupancy models that we applied provides a coherent

framework to examine how habitat suitability (and

factors that affect habitat suitability) influences the

distribution and abundance of organisms. Because of

their simplicity, these models can also be used to apply

structured decision-making tools in order to derive

decisions that are optimal relative to specified objectives

(e.g., Martin et al. 2009b). Indeed, this use was a

motivation for this work. If detection probabilities

cannot be estimated from existing data sets, pooling

counts into large categories of abundance may be a

reasonable approach to minimize state misclassification.

Then, when better designs are implemented in order to

collect the information needed to deal directly with

detection probabilities, the same models can readily be

framed to deal with such data (e.g., MacKenzie et al.

2009).

In fact this similarity of models that do or do not

make assumptions about perfect detection probability

emphasizes a point that is not well understood by

population index proponents. If one does have the

fortunate situation in which detection probabilities are

not an important issue (e.g., perhaps elephants in open

landscapes), detection parameters may simply be con-

strained to equal 1 in the same software (e.g.,

PRESENCE) that has been developed to incorporate

possible nondetection. This software still fits dynamic

models and still presents parameter estimates and

associated variance estimates that deal with estimation

PLATE 1.Elephant water hole survey from an observation platform. Photo credit: S. Chamaille ´ -Jammes.

June 20101181 JOINT HABITAT OCCUPANCY OF ELEPHANTS

Page 10

of multinomial parameters from samples of sites or

individual animals. The central point is that claims of

perfect detection do not absolve one from consideration

of the other components of variation in dynamic

modeling and estimation, and indeed such components

are dealt with in the same software used to deal with the

more general problems that include nondetection. Thus,

the modeling framework presented in this paper should

be applicable to a wide range of existing data sets, and

should help to address important ecological, conserva-

tion, and management problems that deal with occu-

pancy, abundance, and habitat suitability.

ACKNOWLEDGMENTS

This work was partially funded by the CNRS program

‘‘Inge ´ nierie E´cologique’’ and the BioFUN grant of the French

‘‘Agence Nationale de la Recherche’’ (ANR-05-BDIV-013-01).

We are indebted to Wildlife Environment Zimbabwe, which

provided the census data.

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