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Estimating Site Occupancy Rates When Detection Probabilities Are Less Than One

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Nondetection of a species at a site does not imply that the species is absent unless the probability of detection is 1. We propose a model and likelihood-based method for estimating site occupancy rates when detection probabilities are 1. The model provides a flexible framework enabling covariate information to be included and allowing for missing observations. Via computer simulation, we found that the model provides good estimates of the occupancy rates, generally unbiased for moderate detection probabilities (0.3). We estimated site occupancy rates for two anuran species at 32 wetland sites in Maryland, USA, from data collected during 2000 as part of an amphibian monitoring program, Frog-watch USA. Site occupancy rates were estimated as 0.49 for American toads (Bufo amer-icanus), a 44% increase over the proportion of sites at which they were actually observed, and as 0.85 for spring peepers (Pseudacris crucifer), slightly above the observed proportion of 0.83.
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83(8), 2002, pp. 2248–2255
2002 by the Ecological Society of America
I. M
D. N
B. L
J. A
A. L
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203 USA
U.S. Geological Survey, Patuxent Wildlife Research Center, 11510 American Holly Drive,
Laurel, Maryland 20708-4017 USA
U.S. Fish and Wildlife Service, Patuxent Wildlife Research Center, 11510 American Holly Drive,
Laurel, Maryland 20708-4017 USA
U.S. Geological Survey, Florida Caribbean Science Center, Southeastern Amphibian Research and Monitoring Initiative,
7920 NW 71st Street, Gainesville, Florida 32653 USA
Nondetection of a species at a site does not imply that the species is absent
unless the probability of detection is 1. We propose a model and likelihood-based method
for estimating site occupancy rates when detection probabilities are
1. The model provides
a flexible framework enabling covariate information to be included and allowing for missing
observations. Via computer simulation, we found that the model provides good estimates
of the occupancy rates, generally unbiased for moderate detection probabilities (
0.3). We
estimated site occupancy rates for two anuran species at 32 wetland sites in Maryland,
USA, from data collected during 2000 as part of an amphibian monitoring program, Frog-
watch USA. Site occupancy rates were estimated as 0.49 for American toads (
Bufo amer-
), a 44% increase over the proportion of sites at which they were actually observed,
and as 0.85 for spring peepers (
Pseudacris crucifer
), slightly above the observed proportion
of 0.83.
Key words: anurans; bootstrap;
Bufo americanus;
detection probability; maximum likelihood;
metapopulation; monitoring; patch occupancy;
Pseudacris crucifer;
site occupancy.
We describe an approach to estimating the proportion
of sites occupied by a species of interest. We envision
a sampling method that involves multiple visits to sites
during an appropriate season during which a species
may be detectable. However, a species may go unde-
tected at these sites even when present. Sites may rep-
resent discrete habitat patches in a metapopulation dy-
namics context or sampling units (e.g., quadrats) reg-
ularly visited as part of a large-scale monitoring pro-
gram. The patterns of detection and nondetection over
the multiple visits for each site permit estimation of
detection probabilities and the parameter of interest,
proportion of sites occupied.
Our motivation for considering this problem in-
volves potential applications in (1) large-scale moni-
toring programs and (2) investigations of metapopu-
lation dynamics. Monitoring programs for animal pop-
ulations and communities have been established
throughout the world in order to meet a variety of ob-
jectives. Most programs face two important sources of
Manuscript received 29 May 2001; revised 11 October 2001;
accepted 22 October 2001.
Present address: Proteus Research and Consulting Ltd.,
P.O. Box 5193, Dunedin, New Zealand.
Present address: International Association of Fish and
Wildlife Agencies, 444 N. Capitol Street NW, Suite 544,
Washington, D.C., 20001 USA.
variation that must be incorporated into the design
(e.g., see Thompson 1992, Lancia et al. 1994, Thomp-
son et al. 1998, Yoccoz et al. 2001, Pollock et al. 2002).
The first source of variation is space. Many programs
seek to provide inferences about areas that are too large
to be completely surveyed. Thus, small areas must be
selected for surveying, with the selection being carried
out in a manner that permits inference to the entire area
of interest (Thompson 1992, Yoccoz et al. 2001, Pol-
lock et al. 2002).
The second source of variation important to moni-
toring program design is detectability. Few animals are
so conspicuous that they are always detected at each
survey. Instead, some sort of count statistic is obtained
(e.g., number of animals seen, heard, trapped, or oth-
erwise detected), and a method is devised to estimate
the detection probability associated with the count sta-
tistic. Virtually all of the abundance estimators de-
scribed in volumes such as Seber (1982) and Williams
et al. (
in press
) can be viewed as count statistics divided
by estimated detection probabilities. Not allowing for
detectability and solely using the count statistic as an
index to abundance is unwise. Changes in the count
may be a product of random variations or changes in
detectability, so it is impossible to make useful infer-
ence about the system under investigation.
The methods used to estimate detection probabilities
of individual animals (and hence abundance) at each
site are frequently expensive of time and effort. For
August 2002 2249
this reason, these estimation methods are often used in
detailed experiments or small-scale investigations, but
are not as widely used in large-scale monitoring pro-
grams. The methods proposed here to estimate the pro-
portion of sites (or more generally, the proportion of
sampled area) occupied by a species can be imple-
mented more easily and less expensively than the meth-
ods used for abundance estimation. For this reason, our
proposed method should be attractive as a basis for
large-scale monitoring programs, assuming that the
proportion of sites or area occupied is an adequate state
variable with respect to program objectives.
The second motivation for considering this estima-
tion problem involves the importance of patch occu-
pancy data to the study of metapopulation dynamics.
The proportion of patches occupied is viewed as a state
variable in various metapopulation models (e.g., Levins
1969, 1970, Lande 1987, 1988, Hanski 1992, 1994,
1997). So-called ‘‘incidence functions’’ (e.g., see Di-
amond 1975, Hanski 1992) depict the probability of
occurrence of a species in a patch, expressed as a func-
tion of patch characteristics such as area. Under the
assumption of a stationary Markov process, incidence
function data are sometimes used to estimate patch ex-
tinction and colonization probabilities (e.g., Hanski
1992, 1994, 1997, Moilanen 1999). Given the relevance
of patch occupancy data to metapopulation investiga-
tions and models, it seems important to estimate patch
occupancy probabilities properly. For most animal
sampling situations, detection of a species is indeed
indicative of ‘‘presence,’’ but nondetection of the spe-
cies is not equivalent to absence. Thus, we expect most
incidence function estimates of the proportion of patch-
es occupied to be negatively biased to some unknown
degree because species can go undetected when pre-
In this paper, we first present general sampling meth-
ods that permit estimation of the probability of site
occupancy when detection probabilities are
1 and
may vary as functions of site characteristics, time, or
environmental variables. We then present a statistical
model for site occupancy data and describe maximum
likelihood estimation under this model. We illustrate
use of the estimation approach with empirical data on
site occupancy by two anuran species at 32 wetland
sites in Maryland collected during 2000. Finally we
discuss extending this statistical framework to address
other issues such as colony extinction/colonization,
species co-occurrence, and allowing for heterogeneous
detection and occupancy probabilities
We use the following notation throughout this article:
, probability that a species is present at site
probability that a species will be detected at site
, given presence;
, total number of surveyed
, number of distinct sampling occasions;
ber of sites where the species was detected at time
, total number of sites at which the species was de-
tected at least once.
Our use of
, to signify detection probabilities, dif-
fers from its customary use in the metapopulation lit-
erature, where it is used to denote the probability of
species presence (our
). However, our notation is con-
sistent with the mark–recapture literature which pro-
vides the foundation of our approach.
Basic sampling situation
Here we consider situations in which surveys of spe-
cies at
specific sites are performed at
distinct oc-
casions in time. Sites are occupied by the species of
interest for the duration of the survey period, with no
new sites becoming occupied after surveying has be-
gun, and no sites abandoned before the cessation of
surveying (i.e., the sites are ‘‘closed’’ to changes in
occupancy). At each sampling occasion, investigators
use sampling methods designed to detect the species
of interest. Species are never falsely detected at a site
when absent, and a species may or may not be detected
at a site when present. Detection of the species at a
site is also assumed to be independent of detecting the
species at all other sites. The resulting data for each
site can be recorded as a vector of 1’s and 0’s denoting
detection and nondetection, respectively, for the oc-
casions on which the site was sampled. The set of such
detection histories is used to estimate the quantity of
interest, the proportion of sites occupied by the species.
General likelihood
We propose a method that parallels a closed-popu-
lation, mark–recapture model, with an additional pa-
rameter (
) that represents the probability of species
presence. In closed-population models, the focus is to
estimate the number of individuals never encountered
by using information garnered from those individuals
encountered at least once (e.g., see Otis et al. 1978,
Williams et al.,
in press
). In our application, sites are
analogous to individuals except that we observe the
number of sites with the history comprising
0’s (sites
at which the species is never detected over the
pling occasions); hence, the total population size of
sites is known, but the focus is to estimate the fraction
of those sites that the species actually occupies. One
could recast this problem into a more conventional
closed mark–recapture framework by only considering
those sites where the species was detected at least once.
Use of such data with closed-population, capture–re-
capture models (e.g., Otis et al. 1978) would yield es-
timates of population size that correspond to the num-
ber of sites where the species is present. However, the
following method enables additional modeling of
be investigated (such as including covariate informa-
A likelihood can be constructed using a series of
Ecology, Vol. 83, No. 8
probabilistic arguments similar to those used in mark–
recapture modeling (Lebreton et al. 1992). For sites
where the species was detected on at least one sampling
occasion, the species must be present and was either
detected or not detected at each sampling occasion. For
example, the likelihood for site
with history 01010
would be
However, nondetection of the species does not imply
absence. Either the species was present and was not
detected after
samples, or the species was not present.
For site
with history 00000, the likelihood is
Assuming independence of the sites, the product of all
terms (one for each site) constructed in this manner
creates the model likelihood for the observed set of
data, which can be maximized to obtain maximum like-
lihood estimates of the parameters.
Note that, at this stage, presence and detection prob-
abilities have been defined as site specific. In practice,
such a model could not be fit to the data because the
likelihood contains too many parameters: the model
likelihood is over-parameterized. However, the model
is presented in these general terms because, in some
cases, the probabilities may be modeled as a function
of site-specific covariates, to which we shall return.
When presence and detection probabilities are con-
stant across monitoring sites, the combined model like-
lihood can be written as
n. n n.
Using the likelihood in this form, our model could be
implemented with relative ease via spreadsheet soft-
ware with built-in function maximization routines, be-
cause only the summary statistics (
) and
are required. Detection probabilities could be time
specific, or reduced forms of the model could be in-
vestigated by constraining
to be constant across time
or a function of environmental covariates.
We suggest that the standard error of
be estimated
using a nonparametric bootstrap method (Buckland and
Garthwaite 1991), rather than the asymptotic (large-
sample) estimate involving the second partial deriva-
tives of the model likelihood (Lebreton et al. 1992).
The asymptotic estimate represents a lower bound on
the value of the standard error, and may be too small
when sample sizes are small. A random bootstrap sam-
ple of
sites is taken (with replacement) from the
monitored sites. The histories of the sites in the boot-
strap sample are used to obtain a bootstrap estimate of
. The bootstrap procedure is repeated a large number
of times, and the estimated standard error is the sample
standard deviation of the bootstrap estimates (Manly
Extensions to the model
.—It would be reasonable to expect that
may be some function of site characteristics such as
habitat type or patch size. Similarly,
may also vary
with certain measurable variables such as weather con-
ditions. This covariate information (X) can be easily
introduced to the model using a logistic model (Eq. 2)
(denote the parameter of interest as
and the vector of model parameters as B:
. (2)
1 + exp(XB)
does not change over time during the sam-
pling (the population is closed), appropriate covariates
would be time constant and site specific, whereas cov-
ariates for detection probabilities could be time varying
and site specific (such as air or water temperature).
This is in contrast to mark–recapture models in
which time-varying individual covariates cannot be
used. In mark–recapture, a time-varying individual
covariate can only be measured on those occasions
when the individual is captured; the covariate value is
unknown otherwise. Here, time-varying, site-specific
covariates can be collected and used regardless of
whether the species is detected. It would not be pos-
sible, however, to use covariates that change over time
and cannot be measured independent of the detection
is modeled as a function of covariates, the av-
erage species presence probability is
. (3)
Missing observations
.—In some circumstances, it
may not be possible to survey all sites at all sampling
occasions. Sites may not be surveyed for a number of
reasons, from logistic difficulties in getting field per-
sonnel to all sites, to the technician’s vehicle breaking
down en route. These sampling inconsistencies can be
easily accommodated using the proposed model like-
If sampling does not take place at site
at time
then that occasion contributes no information to the
model likelihood for that site. For example, consider
the history 10 11, where no sampling occurred at time
3. The likelihood for this site would be:
Missing observations can only be accounted for in this
manner when the model likelihood is evaluated sepa-
rately for each site, rather than using the combined form
of Eq. 1.
August 2002 2251
. 1. Results of the 500 simulated sets of data for
40, with no missing values. Indicated are the average value of
, ; the replication-based estimate of the true standard error of ,
( ); and the average estimate of the standard error
obtained from 200 nonparametric bootstrap samples, , for various levels of
, and
Simulation methods
A simulation study was undertaken to evaluate the
proposed method for estimating
. Data were generated
for situations in which all sites had the same probability
of species presence, and the detection probability was
constant across time and sites,
(·). The effects of
five factors were investigated: (1)
20, 40, or 60;
0.5, 0.7, or 0.9; (3)
0.1, 0.3, or 0.5; (4)
2, 5, or 10; (5) probability of a missing observation
0.0, 0.1, or 0.2.
For each of the 243 scenarios, 500 sets of data were
simulated. For each site, a uniformly distributed, pseu-
do-random number between 0 and 1 was generated (
and if
then the site was occupied. Further pseudo-
random numbers were generated and similarly com-
pared to
to determine whether the species was de-
tected at each time period, with additional random
numbers being used to establish missing observations.
(·) model was applied to each set of simulated
data. The resulting estimate of
was recorded and the
nonparametric bootstrap estimate of the standard error
was also obtained using 200 bootstrap samples.
Simulation results
Fig. 1 presents the simulation results for scenarios
40 with no missing values only, but these
are representative of the results in general. The full
simulation results are included in the Appendix.
Generally, this method provides reasonable estimates
of the proportion of sites occupied. When detection
probability is 0.3 or greater, the estimates of
reasonably unbiased in all scenarios considered for
5. When
2, only when detection probability is
at least 0.5 do the estimates of
appear to be reason-
able. For low detection probabilities, however,
to be overestimated when the true value is 0.5 or 0.7,
but underestimated when
equals 0.9. A closer ex-
amination of the results reveals that, in some situations
in which detection probability is low, tends to 1.
In most cases, the nonparametric bootstrap provides
a good estimate of the standard error for , the excep-
tion being for situations with low detection probabil-
Ecology, Vol. 83, No. 8
1. Relative difference in AIC (
AIC), AIC model
weights (
), overall estimate of the fraction of sites oc-
cupied by each species ( ), and associated standard error
( )).
Model, by species
American toad
Spring peeper
ities. Again, this is caused by
estimates close to 1;
in such situations, the bootstrap estimate of the stan-
dard error is very small, which overstates the precision
of .
In general, increasing the number of sampling oc-
casions improves both the accuracy and precision of
, although in some instances there is little gain in
using 10 occasions rather than five. If only two occa-
sions are used, however, accuracy tends to be poor
unless detection probabilities are high, and even then
the standard error of is approximately double that of
using five sampling occasions.
Similarly, increasing the number of sites sampled,
also improves both the accuracy and precision of .
Not presented here are the simulation results for sce-
narios with missing observations. The proposed meth-
od appears to be robust to missing data, with the only
noticeable effect being (unsurprisingly) a loss of pre-
cision. In this study, on average, the standard error of
increased by 5% with 10% missing observations, and
by 11% with 20% missing observations. The bootstrap
standard error estimates also increased by a similar
amount, accounting well for the loss of information.
Field methods and data collection
We illustrate our method by considering monitoring
data collected on American toads (
Bufo americanus
and spring peepers (
Pseudacris crucifer
) at 32 wetland
sites located in the Piedmont and Upper Coastal Plain
physiographic provinces surrounding Washington,
D.C., and Baltimore, Maryland, USA. Volunteers en-
rolled in the National Wildlife Federation/U.S. Geo-
logical Survey’s amphibian monitoring program,
FrogwatchUSA, visited monitoring sites between 19
February 2000 and 12 October 2000. Sites were chosen
nonrandomly by volunteers and were monitored at their
convenience. Observers collected information on the
species of frogs and toads heard calling during a 3-min
counting period taken sometime after sundown. Each
species of calling frog and toad was assigned a three-
level calling index, which, for this study, was truncated
to reflect either detection (1) or nondetection (0).
The data set was reduced by considering only the
portion of data for each species between the dates of
first and last detection exclusive. Truncating the data
in this manner ensures that species were available to
be detected throughout that portion of the monitoring
period, thus satisfying our closure assumption. Includ-
ing the dates of first and last detection in the analysis
would bias parameter estimates because the data set
was defined using these points; hence, they were ex-
Three sites were removed after the truncation be-
cause they were never monitored during the redefined
period. Fewer than eight of the 29 sites were monitored
on any given day and the number of visits per site
varied tremendously, with a very large number of miss-
ing observations (
90%). Note that in the context of
this sampling, the entire sampling period included the
interval between the date at which the first wetland was
sampled and the date at which all sampling ended. A
missing observation was thus any date during this in-
terval on which a wetland was not sampled. Each time
a site was visited, air temperature was recorded. Sites
were defined as being either a distinct body of water
(pond, lake) or other habitat (swamp, marsh, wet mead-
ow). These variables were considered as potential cov-
ariates for detection and presence probabilities, re-
spectively. The data used in this analysis have been
included in the Supplement.
Results of field study
American toad
.—Daily records for the 29 sites, mon-
itored between 9 March 2000 and 30 May 2000, were
included for analysis. Sites were visited 8.9 times on
average (minimum
2, maximum
58 times), with
American toads being detected at least once at 10 lo-
cations (0.34). Three models with covariates and one
without were fit to the data (Table 1) and ranked ac-
cording to AIC (Burnham and Anderson 1998). The
four models considered have virtually identical weight,
suggesting that all models provide a similar description
of the data, despite the different structural forms.
Therefore we cannot make any conclusive statement
regarding the importance of the covariates, but there
is some suggestion that detection probabilities may in-
crease with increasing temperature and occupancy rates
may be lower for habitats consisting of a distinct body
of water. However, all models provide very similar es-
timates of the overall occupancy rate (
0.49), which
is 44% larger than the proportion of sites where toads
were detected at least once. The standard error for the
estimate is reasonably large and corresponds to a co-
efficient of variation of 27%.
Spring peeper
.—Daily records for the 29 sites, mon-
itored between 27 February 2000 and 30 May 2000,
were included for analysis. Sites were visited, on av-
August 2002 2253
erage, 9.6 times (minimum
2, maximum
66 visits),
with spring peepers being detected at least once at 24
locations (0.83). The same models as those for the
American toad were fit to the spring peeper data and
the results are also displayed in Table 1. Here the two
(·) models have virtually zero weight, indicating that
(Temperature) models provide a much better de-
scription of the data. We suspect that this effectis due,
partially, to a tapering off of the calling season as spring
progresses into summer. The
model clearly has greatest weight and suggests that
estimated occupancy rates are lower for distinct bodies
of water (0.77) than for other habitat types (1.00). This
is not unexpected, given spring peepers were actually
detected at all sites of the latter type. Regardless of
how the models ranked, however, all models provide
a similar estimate of the overall occupancy rate that is
only marginally greater than the number of sites where
spring peepers were detected at least once. This sug-
gests that detection probabilities were large enough that
spring peepers probably would be detected during the
monitoring if present.
The method proposed here to estimate site occupancy
rate uses a simple probabilistic argument to allow for
species detection probabilities of
1. As shown, it pro-
vides a flexible modeling framework for incorporating
both covariate information and missing observations.
It also lays the groundwork for some potentially ex-
citing extensions that would enable important ecolog-
ical questions to be addressed.
From the full simulation results for scenarios with
low detection probabilities, it is very easy to identify
circumstances in which one should doubt the estimates
. We advise caution if an estimate of
very close
to 1 is obtained when detection probabilities are low
0.15), particularly when the number of sampling oc-
casions is also small (
7). In such circumstances, the
level of information collected on species presence/ab-
sence is small, so it is difficult for the model to dis-
tinguish between a site where the species is genuinely
absent and a site where the species has merely not been
Our simulation results may also provide some guid-
ance on the number of visits to each site required in
order to obtain reasonable estimates of occupancy rate.
If one wishes to visit a site only twice, then it appears
that the true occupancy rate needs to be
0.7 and de-
tection probability (at each visit) should be
0.3. Even
then, however, precision of the estimate may be low.
Increasing the number of visits per site improves the
precision of the estimated occupancy rate, and the re-
sulting increase in information improves the accuracy
of the estimate when detection probabilities are low.
We stress that whenever a survey (of any type) is being
designed, some thought should be given to the likely
results and method of analysis, because these consid-
erations can provide valuable insight on the level of
sampling effort required to achieve ‘‘good’’ results.
Logistical considerations of multiple visits will prob-
ably result in some hesitancy to use this approach, but
we suggest that the expenditure of extra effort to obtain
unbiased estimates of parameters of interest generally
will be preferable to the expenditure of less effort to
obtain biased estimates. If travel time to sites is sub-
stantial, then multiple searches or samples may be con-
ducted by multiple observers, or even by a single ob-
server, at a single trip to a site, e.g., conduct two or
more 3-min amphibian calling surveys in a single night
at the same pond. If large numbers of patches must be
surveyed, then it may be reasonable to conduct multiple
visits at a subset of sites for the purpose of estimating
detection probability, and perhaps associated covariate
relationships. Then this information on detection prob-
ability, perhaps modeled as a function of site-specific
covariates, could be applied to sites visited only once.
Issues about optimal design require additional work,
but it is clear that a great deal of flexibility is possible
in approaches to sampling.
Site occupancy may well change over years or be-
tween seasons as populations change; new colonies
could be formed or colonies could become locally ex-
tinct. When sites are surveyed on more than one oc-
casion between these periods of change, for multiple
periods, the approach described here could be com-
bined with the robust design mark–recapture approach
(Pollock et al. 1990). For example, suppose that the
anuran sampling described in our examples is contin-
ued in the future, such that the same wetland sites are
surveyed multiple times each summer, for multiple
years. During the periods when sites are closed to
changes in occupancy, our approach could be used to
estimate the occupancy rate as in our example. The
change in occupancy rates over years could then be
modeled as functions of site colonization and extinction
rates, analogous with the birth and death rates in an
open-population mark–recapture study. Such Markov
models of patch occupancy dynamics will permit time-
specific estimation and modeling of patch extinction
and colonization rates that do not require the assump-
tions of
1 or process stationarity invoked in pre-
vious modeling efforts (e.g., Erwin et al. [1998] re-
1; Hanski [1992, 1994] and Clark and Ro-
senzweig [1994] required both assumptions).
Often monitoring programs collect information on
the presence/absence of multiple species at the same
sites. An important biological question is whether spe-
cies co-occur independently. Does the presence/ab-
sence of species A depend upon the occupancy state
of species B? Our method of modeling species presence
could be extended in this direction, enabling such im-
portant ecological questions to be addressed. The mod-
el could be parameterized in terms of
(in addition
): the probability that both species A and
species B are present at a site. However, the number
Ecology, Vol. 83, No. 8
of parameters in the model would increase exponen-
tially with the number of species, so reasonably good
data sets might be required. For example, four addi-
tional parameters would be required to model co-oc-
currences between species A, B, and C (
), but if six species were being modeled, 57 extra
parameters would need to be estimated.
Not addressed are situations in which presence and
detection probabilities are heterogeneous, varying
across sites. Some forms of heterogeneity may be ac-
counted for with covariate information such as site
characteristics or environmental conditions at the time
of sampling. On other occasions, however, the source
of heterogeneity may be unknown. We foresee that
combining our method with the mixture model ap-
proach to closed-population, mark–recapture models of
Pledger (2000) would be one solution, which enables
the problem to be contained within a likelihood frame-
work. It may also be possible to combine our method
with other closed-population, mark–recapture methods
such as the jackknife (Burnham and Overton 1978) or
coverage estimators (Chao et al. 1992). For different
sampling frameworks, where monitoring is performed
on a continuous or incidental basis rather than at dis-
crete sampling occasions, combining our methods with
the Poisson family of models (Boyce et al. 2001,
MacKenzie and Boyce 2001) may also be feasible, par-
ticularly for multiple years of data.
The three extensions to the proposed methods are
currently the focus of ongoing research on this general
topic of estimating site occupancy rates.
Software to perform the above modeling has been
included in the Supplement.
We would like to thank ChristopheBarbraud, Mike Conroy,
Ullas Karanth, Bill Kendall, Ken Pollock, John Sauer, and
Rob Swihart for useful discussions of this general estimation
problem and members of the USGS Southeastern Amphibian
Research and Monitoring Initiative for discussions on am-
phibian monitoring. Atte Moilanen provided a constructive
review of the manuscript, as did a second anonymous re-
viewer. Our thanks also go to the Frogwatch USAvolunteers
directed by Sue Muller at Howard County Department of
Parks and Recreation for collection of the data.
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Full results of the simulation study are available in ESA’s Electronic Data Archive:
Ecological Archives
Software, source code, and the sample data sets are available in ESA’s Electronic DataArchive:
Ecological Archives
... Occupancy models (MacKenzie et al. 2002;Kéry and Royle 2016) were fit to the presence-absence data in the database compiled for this study and the values of the selected environmental predictors at the sample locations. The estimated relationships between occurrence and the predictors from the fitted models were then used to predict the probability of occurrence at each grid cell across the entire study area, including unsampled areas. ...
... One does not have to assume that every sampled absence is a true absence. However, occupancy models have several important assumptions (MacKenzie et al. 2002;Kéry and Royle 2016). ...
Technical Report
Full-text available
This report provides maps with information about the observed and predicted distributions of individual deep-sea coral taxa (primarily genera) and hardbottom habitats in U.S. waters off the Atlantic coasts of states from Virginia to Florida. For each taxon, the maps show the presence or absence of the taxon at sample locations in the presence-absence database compiled in this study and the predicted occurrence (posterior median occupancy probability) and variability in the predicted occurrence (posterior CV of the occupancy probability) across the study area on the 100 x 100 m resolution model grid. In addition, there are maps that show the predicted genus richness (i.e., the number of genera expected to occur at each grid cell) and variability in the predicted genus richness for the 23 genera included in the multi-taxon model.
... Montana each year from 2007 -2020 (Miller et al. 2011, 2013, Rich et al. 2013, Inman et al. 2019). Occupancy models use detection/non-detection data and environmental predictors to estimate probabilities of animal occurrence on the landscape while accounting for imperfect detection (MacKenzie et al. 2002). The approach has been used to monitor presence of many species, including wolves (Rich et al. 2013, Ausband et al. 2014, Bassing et al. 2019, Stauffer et al. 2021. ...
... Detection/non-detection data is used to generate encounter histories of the study species within a gridded study area (MacKenzie et al. 2002). In our case, encounter histories included observations where wolves were not detected ("0"), detected with uncertainty ("1"), and detected with certainty ("2"). ...
A clear connection between basic research and applied management is often missing or difficult to discern. We present a case study of integration of basic research with applied management for estimating abundance of gray wolves (Canis lupus) in Montana, USA. Estimating wolf abundance is a key component of wolf management but is costly and time intensive as wolf populations continue to grow. We developed a multi‐model approach using an occupancy model, mechanistic territory model, and empirical group size model to improve abundance estimates while reducing monitoring effort. Whereas field‐based wolf counts generally rely on costly, difficult‐to‐collect monitoring data, especially for larger areas or population sizes, our approach efficiently uses readily available wolf observation data and introduces models focused on biological mechanisms underlying territorial and social behavior. In a three‐part process, the occupancy model first estimates the extent of wolf distribution in Montana, based on environmental covariates and wolf observations. The spatially explicit mechanistic territory model predicts territory sizes using simple behavioral rules and data on prey resources, terrain ruggedness, and human density. Together, these models predict the number of packs. An empirical pack size model based on 14 years of data demonstrates that pack sizes are positively related to local densities of packs, and negatively related to terrain ruggedness, local mortalities, and intensity of harvest management. Total abundance estimates for given areas are derived by combining estimated numbers of packs and pack sizes. We estimated the Montana wolf population to be smallest in the first year of our study, with 91 packs and 654 wolves in 2007, followed by a population peak in 2011 with 1,252 wolves. The population declined approximately 6% thereafter, coincident with implementation of legal harvest in Montana. Recent numbers have largely stabilized at an average of 191 packs and 1,141 wolves from 2016 – 2020. This new approach accounts for biologically based, spatially explicit predictions of behavior to provide more accurate estimates of carnivore abundance at finer spatial scales. By integrating basic and applied research, our approach can therefore better inform decision‐making and meet management needs.
... And still other authors focus on trying to avoid the negative bias in the estimation of parameters derived from the fact that species can go unnoted even though they are present. For example, MacKenzie et al. [19] propose a likelihood-based method to estimate site occupancy rates when the probability of detection error is positive, which avoids bias in estimating the proportion of occupied patches when there is error detection. ...
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The detection of target species is of paramount importance in ecological studies, with implications for environmental management and natural resource conservation planning. This is usually done by sampling the area: the species is detected if the presence of at least one individual is detected in the samples. Green & Young (Green & Young 1993 Sampling to detectrare species. Ecol. Appl . 3 , 351–356. ( doi:10.2307/1941837 ) introduce two models to determine the minimum number of samples n to ensure that the probability of failing to detect the species from them, if the species is actually present in the area, does not exceed a fixed threshold: based on the Poisson and the Negative Binomial distributions. We generalize them to two scenarios, one considering the area size N to be finite, and the other allowing detectability errors, with probability δ . The results in Green & Young are recovered by taking N → ∞ and δ = 0. Not taking into consideration the finite size of the area, if known, leads to an overestimation of n , which is vital to avoid if sampling is expensive or difficult, while assuming that there are no detectability errors, if they really exist, produces an undesirable bias. Our approximation manages to skirt both problems, for the Poisson and the Negative Binomial.
... The use of indices is attractive because estimation techniques such as markrecapture are not always practical or cost-efficient to robustly determine population parameters. However, it is well known that animal counts vary from the proportion of the true number counted and that this detection process (detectability) varies across space and time (MacKenzie et al., 2002). Ignoring detectability with respect to counts of small carnivores (or any population for that matter) and extrapolating from the index to abundance or density of the entire population places the interpretation of such results on unstable ground with respect to making inference about the target population(s) (Guillera-Arroita et al., 2014). ...
The absences of large carnivores from many ecosystems, human‐induced landscape changes, and resource supplementation have been theorized to increase the abundance of small carnivore species around the world. Overabundant and/or unconstrained small carnivores can have significant effects on specific prey species that, in some cases, can cascade through entire ecosystems. Here, we review the effects of small carnivores on threatened species. We focus on four well‐studied families (Procyonidae, Mephitidae, Mustelidae, and Herpestidae) and emphasize that this is a global conservation issue with consequences for biodiversity. We review and compare the impacts that small carnivores can have on a variety of prey taxa including small mammals, nesting avian and reptilian species, and rare invertebrates. We differentiate between native and exotic small carnivores because this is often an important distinction in terms of the impact severity and range of effects. In addition to direct lethal effects (i.e. predation), small carnivores can also impact threatened species as disease vectors and through competition or overexploitation, which can disrupt communities via ecological release or extinction. Furthermore, we explore other case studies in which small carnivores have had positive effects on threatened species and discuss studies that reveal other taxa responsible for exerting stronger negative effects on threatened prey. We offer some concluding remarks about global small carnivore conservation and emphasize the need for decision‐analytic approaches and robust analyses that can improve our assessment of how populations of threatened species can be affected. To date, indirect effects are especially difficult to measure in the field and many studies have provided only anecdotal or correlative results, signalling a need for improving our scientific methodologies and management approaches.
... All covariates were centre scaled. All analyses were conducted in R using the package 'unmarked' (MacKenzie et al., 2002). ...
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Tigers (Panthera tigris) have disappeared from over 90% of their historical range, and extant populations face habitat loss, direct poaching, and prey depletion in otherwise suitable habitats. In Thailand, tiger numbers continue to decline due to prey depletion, yet a few strongholds remain. Recently, tigers have been detected in the Southern Western Forest Complex (sWEFCOM), following intensification of conservation efforts. However, there is still a lack of primary data on the status of tigers and their prey in the sWEFCOM. To fill this knowledge gap, we conducted camera trapping surveys between 2019 and 2020 in Khuean Srinagarindra National Park (KSR) and Salakphra Wildlife Sanctuary (SLP). Located near a tiger source population in Thungyai Naresuan and Huai Kha Khaeng, these areas are potential areas for tiger recovery. In particular, our study assessed the status of prey, a prerequisite to the persistence and recovery of tigers. Based on relative abundance indices, time overlap and occupancy models, we analysed the effect of anthropogenic and ecological factors on the spatial and temporal habitat use of the main prey species. We highlight that anthropogenic factor impacted species-specific habitat relationships. Mainly, shifts in ungulate temporal and spatial habitat use was linked to human activities. These relationships, however, differed between the two protected areas. As tiger recovery depends on prey recovery, we suggest that increased conservation law enforcement and greater engagement with villages within and adjacent to protected areas are essential to minimising unsustainable resource use practices that currently affect prey.
... Six of these species were species typical of forests (from here 'forest' species To estimate the influence of vegetation structure on birds we used hierarchical single-species occupancy models with a Bayesian approach, considering points nested within farms. Occupancy estimation accounts for imperfect detection probabilities of the species so that if a species is not observed at a certain point, it can be either truly absent or present but undetected (MacKenzie et al., 2006(MacKenzie et al., , 2002. ...
Ground birds are strongly associated with the vegetation structure in natural environments under livestock grazing. Birds that fed on the ground may be the most affected by overgrazing, while those that fed on the shrub layer may respond positively to shrub encroachment in open xerophytic forest. Therefore, evaluating changes in bird species associated with a particular stratum can provide valuable information on the health, productivity, and functionality of the ecosystem. Here, we explore the relationships between vegetation structure and grazing intensity with the individual responses of terrestrial bird species in forests of Central-East Argentina. We tested the hypothesis that vegetation structure and grazing intensity affect the occupancy of 12 ground-foraging bird species. We used hierarchical single-species occupancy models with a Bayesian approach, considering points nested within farms, to estimate the influence of vegetation structure and grazing intensity on the bird occupancy. Vegetation structure variables were related to the occupancy of 11 out of 12 species. Three of these species also responded to grazing intensity. Occupancy of most open country bird species was favored by increasing grass cover but disfavored by increasing shrubs and tree density. Therefore overgrazing, with its consequent low grass cover, negatively affected the presence of open country bird species. On the other hand, occupancy of forest species was favored by either shrub or tree density or by forest age (larger diameter of trees at breast height - dbh). Based on specific responses of bird species, we propose that species directly related to grass cover and grazing intensity, such as the Spotted Nothura (Nothura maculosa), are potential indicator of low grazing intensity in forests of central-east Argentina. In turn, the Ultramarine Grosbeak (Cyanoloxia brissonii), a forest species associated with dense woody sites with high grazing intensity and low grass cover, could be a good indicator of overgrazing in these forests. Livestock management in these forests should promote environmental heterogeneity inside farms. Maintaining minimal livestock grazing in semi-open areas with mature trees and conserving areas of dense forest will be fundamental for achieving satisfactory compromises between the conservation of ground-foraging birds and livestock farming.
... Errors associated with sign surveys, such as observation (e.g., species misidentification) or detection error (e.g., animal was present but went undetected) lead to biased estimates of occupancy, density, or abundance [3][4][5]. Recently, statistical advances have attempted to account for these errors [6,7]. For example, the advent of methods to account for differences in detection and movement skyrocketed with the use of camera traps [3]. ...
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Counting is not always a simple exercise. Specimens can be misidentified or not detected when they are present, giving rise to unidentified sources of error. Deer pellet group counts are a common method to monitor abundance, density, and population trend. Yet, detection errors and observer bias could introduce error into sometimes very large (spatially, temporally) datasets. For example, in Scandinavia, moose ( Alces alces ) pellet group counts are conducted by volunteer hunters and students, but it is unknown how much uncertainty observer error introduces into these datasets. Our objectives were to 1) estimate the detection probability of moose pellet groups; 2) identify the primary variables leading to detection errors including prior observer experience; and 3) compare density estimates using single and double observer counts. We selected a subset of single observer plots from a long-term monitoring project to be conducted as dependent double observer surveys, where primary and secondary observers worked simultaneously in the field. We did this to quantify detection errors for moose pellet groups, which were previously unknown in Scandinavia, and to identify covariates which introduced variation into our estimates. Our study area was in the boreal forests of southern Norway where we had a nested grid of 100-m ² plots that we surveyed each spring. Our observers were primarily inexperienced. We found that when pellet groups were detected by the primary observer, the secondary observer saw additional pellet groups 42% of the time. We found search time was the primary covariate influencing detection. We also found density estimates from double observer counts were 1.4 times higher than single observer counts, for the same plots. This density underestimation from single observer surveys could have consequences to managers, who sometimes use pellet counts to set harvest quotas. We recommend specific steps to improve future moose pellet counts.
Passive recording technologies have become a valuable tool for ecologists to accumulate large data sets on vocalizing species assemblages and to study the response of biodiversity to regional and global environmental change. However, the process of interpreting these recordings and identifying species can be time-consuming. To automate this process, and to derive diversity metrics directly from the audio files, soundscape ecologists developed and published many bioacoustics indices, which are calculated using computer algorithms that mathematically summarize the acoustic energy in a recording. Of these indices, the acoustic complexity index (ACI) is perhaps the most widely proposed surrogate of bird species richness. Although several studies have shown the ACI to have positive correlations with species richness, it remains unknown how well the ACI will perform over large, habitat-diverse, regions. Our aim, here, was to examine whether site-level bird species richness (alpha diversity) correlated with the ACI across a large heterogenous mountain region. Further, we explored whether the elevational trends for alpha diversity and the ACI exhibited similar unimodal patterns with corresponding maximums and whether any shifts in the elevation of these maximums could be tracked over time in response to climate change. We deployed recording devices along two extensive transects on the Pacific Crest Trail in California, USA; these included a 689-km trail section in northern California and a 531-km section in southern California. Point counts for birds from the field were combined with the interpretation of the recordings to estimate alpha diversity using a Bayesian multispecies occupancy model. We found that alpha diversity exhibited a positive linear relationship with the ACI on both trail sections. However, these relationships were not strong (low R² values). Similar mid-elevation maximums for alpha diversity and the ACI were observed along the northern trail section. Power analysis revealed that with repeated annual surveys using our protocols, we could detect an average shift in the elevation of either maximum species richness or ACI of approximately 100 m over 20 years (i.e., 5 m/yr), which could be improved in precision to 50 m (i.e., 2.5 m/yr) with a 5-fold increase in survey effort. Although there was considerable unexplained variation in our diversity- and ACI-elevation trends, which we suspect was due to microhabitat and microclimate effects, we concluded that the ACI was a useful, albeit coarse, surrogate of alpha diversity across large regions. The ACI warrants consideration by ecologists and land managers for application in large-scale monitoring programs.
The conversion of native forest to forestry plantations is a worldwide practice, affecting biodiversity and host-parasite interactions. One of the most common timber plantations in the world are monocultures of Monterey pine (Pinus radiata). Using occupancy models, we analyzed the occurrence and prevalence of Cryptosporidium spp. oocysts and Giardia spp. cysts in fecal samples of wild rodents from a landscape dominated by extensive Monterey pine plantations in central Chile. We aimed to assess drivers of parasite infection such as habitat type, abundance of rodent hosts, species richness, and season. Small mammals were sampled seasonally for two years in three habitat types: native forests, adult pine plantations and young pine plantations. A total of 1091 fecal samples from seven small mammal species were analyzed by coprological analysis. Occurrence probability of Cryptosporidium spp. and Giardia spp. was similar for the most abundant rodent species (Abrothrix longipilis, A. olivacea, and Oligoryzomys longicaudatus) and for all habitat types. For Cryptosporidium spp., variation in prevalence was mostly explained by season with higher prevalence during winter season and lower during spring. For Giardia spp., the prevalence was significantly higher in young pine plantations, followed by adult pine plantations and native forests. In addition, higher prevalence of Giardia spp. was associated with lower host richness, suggesting a possible dilution effect. Our findings reveal that Monterey pine plantations increase Giardia spp. transmission among rodents, but has no clear effect on Cryptosporidium spp., providing evidence that the impact of land use on parasitism can be idiosyncratic. Since both parasites have zoonotic potential, our findings may be useful for land use planning and management considering health issues.
We developed a Markov process model for colony-site dynamics of Gull-billed Terns (Sterna nilotica). From 1993 through 1996, we monitored breeding numbers of Gullbilled Terns and their frequent colony associates. Common Terns (Sterna hirundo) and Black Skimmers (Rynchops niger), at colony sites along 80 km of the barrier island region of coastal Virginia. We also monitored flooding events and renesting. We developed the model for colony survival, extinction, and recolonization at potential colony sites over the four-year period. We then used data on annual site occupation by Gull-billed Terns to estimate model parameters and tested for differences between nesting substrates (barrier island vs. shellpile). Results revealed a dynamic system but provided no evidence that the dynamics were Markovian, i.e. the probability that a site was occupied in one year was not influenced by whether it had been occupied in the previous year. Nor did colony-level reproductive success the previous season seem to affect the probability of site occupancy. Site survival and recolonization rates were similar, and the estimated overall annual probability of a site being occupied was 0.59. Of the 25 sites that were used during the four-year period, 16 were used in one or two years only, and only three were used in all four years. Flooding and renesting were frequent in both habitat types in all years. The frequent flooding of nests on shell-piles argues for more effective management; augmentation with shell and sand to increase elevations as little as 20 cm could have reduced flooding at a number of sites. The low colony-site fidelity that we observed suggests that an effective management approach would be to provide a large number of sand and / or shellpile sites for use by nesting terns. Sites not used in one year may still be used in subsequent years.
This chapter focuses on metapopulation dynamics and metapopulations, essentially agreeing with the classical concept. In an increasing number of species, the spatial structure of populations is somehow consequential to their dynamics. Many studies have demonstrated that small populations in small habitat fragments have a high risk of extinction. Populations in nature exhibit continuous variation in their spatial structures. Species may persist at a spatial scale larger than the local population due to the “spreading of the risk” process, which involves movements among asynchronously fluctuating local populations. The consequences of this spreading of the risk in space will include a relative reduction in the amplitude of fluctuations of animal numbers in the entire population. However, it is not possible to have long-term persistence even in a metapopulation without some density dependence in local dynamics, given that local population sizes are restricted, as they always are, below some maximum value. Incidence of density dependence may be low in some persisting metapopulations, in comparison with the incidence of density dependence necessary for long-term persistence of isolated local populations. In metapopulations, the combination of long persistence time with little density dependence is associated with high turnover rate, and frequent local extinctions and colonizations.
Preface. Basic Concepts. Sampling Designs and Related Topics. Enumeration Methods. Community Surveys. Detection of a Trend in Population Estimates. Guidelines for Planning Surveys. Fish. Amphibians and Reptiles. Birds. Mammals. Glossary of Terms. Glossary of Notation. Sampling Estimators. Common and Scientific Names of Cited Vertebrates. Subject Index.
The practical value of a predictive metapopulation model is much affected by the amount of data required for parameter estimation. Some metapopulation models require information on population turnover events for parameterization, whereas other models, such as the incidence function model that is used in this study, can be parameterized with spatial data on patch occupancy. The latter data are more readily available. The original method of using spatial pattern data to parameterize the incidence function and other patch models has been criticized for involving potentially troublesome assumptions, such as the independence of habitat patches and constant colonization probabilities. This study describes an improved parameter estimation method that is not affected by these problems. The proposed method is based on Monte Carlo inference for implicit statistical models, and it can be adapted to any stochastic patch occupancy model of metapopulation dynamics. As an additional advantage, the new method allows the estimation of the amplitude of regional stochasticity. Tested with simulated data, the new method was found to produce substantially more accurate parameter estimates than the original method. The new approach is applied to two empirical metapopulations, the false heath fritillary butterfly in Finland and the American pika at Bodie, California.
We discuss a simple method, based on maximum likelihood, to estimate the rates of extinction and recolonization of a species, for example, on an island. Our method applies to both regular and sporadic surveys and thus allows one to use time series with missing data. When only a few surveys have been conducted, it may be possible to lump data from several species. The shape of the likelihood surface may indicate whether the lumping is appropriate.