The Journal of Wildlife Management 80(2):192–194; 2016; DOI: 10.1002/jwmg.1022
Letter to the Editor
A Broader Definition of Occupancy:
Comment on Hayes and Monfils
QURESH S. LATIF,1 Rocky Mountain Research Station, U.S. Forest Service, 1648 S. Seventh Avenue, Bozeman, MT 59717, USA
MARTHA M. ELLIS, Rocky Mountain Research Station, U.S. Forest Service, 1648 S. Seventh Avenue, Bozeman, MT 59717, USA
COURTNEY L. AMUNDSON, U.S. Geological Survey, Alaska Science Center, 4210 University Dr., Anchorage, AK 99508, USA
Occupancy models are widely used to analyze presence–absence
data for a variety of taxa while accounting for observation error
(MacKenzie et al. 2002, 2006; Tyre et al. 2003; Royle and
Dorazio 2008). Hayes and Monfils (2015) question their use for
analyzing avian point count data based on purported violations
of model assumptions incurred by avian mobility. Animal
mobility is an important consideration, not just for occupancy
models, but for a variety of population and habitat models
(Boyce 2006, Royle et al. 2009, Manning and Goldberg 2010,
Dormann et al. 2013, Renner et al. 2015). Nevertheless, we
believe the ultimate conclusions of Hayes and Monfils are
shortsighted mainly due to a narrow interpretation of
occupancy. Rather than turn away from the use of occupancy
models, we believe they remain an appropriate method for
analyzing many data sets collected from avian point count
surveys. Further, we suggest that there is value in having a
broader and more nuanced interpretation of occupancy that
incorporates the potential for animal movement.
Our disagreement with Hayes and Monfils stems from
their incomplete examination of avian point count methods
used in conjunction with occupancy modeling and their
interpretations of occupancy model parameters. The authors
dismiss single-survey methods that include supplemental
information to estimate detection probability (e.g., distance
sampling, double observer) as too cumbersome and not
applicable to many historical data sets. Instead, they favor the
basic occupancy model of MacKenzie et al. (2002), which
requires repeat surveys across a season. Hayes and Monfils
then suggest that in order to meet closure assumptions, the
occupancy status of a site must remain constant between
surveys within a season (i.e., the period within which closure
is assumed; MacKenzie et al. 2002, 2006). They strictly
equate occupancy status with whether or not 1 individuals
are physically present within a prescribed survey plot during
the entire season in which surveys are repeated. This view is
best suited to analyses focused on sessile organisms, nests,
burrows, or dens, which remain fixed for an entire season.
For mobile animals, the implication of this view is that data
must be collected instantaneously (during a snapshot) or else
Received: 31 August 2015; Accepted: 2 October 2015
1
E-mail: qlatif@fs.fed.us
192
the survey plot must be large enough to encompass the
animals’ movements during the season; otherwise, movement will cause changes in physical presence between
surveys, thus violating the closure assumption and rendering
useless any inference from occupancy models. Single-survey
methods are arguably more appropriate for estimating
occupancy during a snapshot in time and may fit Hayes
and Monfils’ definition of occupancy. In fact, although they
did not formally assess these methods, the authors suggest
that analysis of single-survey data could improve occupancy
estimates. In contrast, others offer a broader definition of
occupancy: species presence at some point within a specified
timeframe, the length of which depends on the question of
interest (Tyre et al. 2003, MacKenzie and Royle 2005, Lele
et al. 2013). For mobile animals, the probability of occupancy
over an extended timeframe (i.e., probability of use in
MacKenzie and Royle 2005) can be of equal or greater
interest than that during a snapshot. For example, whether
sites are occupied over the course of a breeding season (i.e.,
intersect the breeding range of 1 individuals) or even
multiple seasons may be most relevant for identifying or
characterizing important breeding habitats (Royle and Kery
2007, White et al. 2013, Latif et al. 2015). Hayes and
Monfils review studies that suggest alternate interpretations
of the occupancy probability parameter but then ultimately
brush off these distinctions: “We fail to see the distinction
between physical occurrence and usage” (Hayes and Monfils
2015:1367). In fact, sampling affects interpretation of
estimated parameters in virtually all efforts to quantify
animal use of space and habitat. Whether one uses logistic
regression, point-process, or occupancy models to analyze
survey data, animal movement can result in individuals being
observed at multiple sampling units, which changes the
interpretation of the predicted parameter.
How one interprets occupancy probability affects the
definition of truth and estimation bias in simulations.
Based on their comparison of occupancy parameter
estimates in their figures 6, 7, and 8 with purported
truth, we infer that Hayes and Monfils equate truth with
occupancy probabilities when animals are immobile. In
fact, they repeatedly reference estimation bias but fail to
clearly describe their definition of truth other than to claim
“. . .a complete census of all possible sites [allowed] a direct
evaluation of the bias and consistency of the estimators”
The Journal of Wildlife Management
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(Hayes and Monfils 2015:1363). Following their implied
definition of truth, Hayes and Monfils infer positive bias
from the fact that occupancy estimates increase as
organisms become mobile, which is typical for animals.
The relationship between mobility and occupancy makes
intuitive sense and is well studied (Chandler et al. 2011,
Amundson et al. 2014, Ramsey et al. 2015) but only
constitutes evidence of bias given the narrow definition of
occupancy presented by Hayes and Monfils. With a
broader definition, when home range size (i.e., mobility)
increases, individuals actually occupy more space such that
occupancy probabilities truly increase as reflected in the
results reported by Hayes and Monfils. Conversely,
detectability truly decreases with increasing mobility
because individuals occupying more area are less likely
to be present at any one site during a given survey. Low
detectability can incur actual bias (MacKenzie et al. 2002,
McKann et al. 2013, Hutchinson et al. 2015), so more
surveys may be needed to ensure reliable estimation as the
timeframe over which occupancy is estimated or subject
mobility increase. With broader interpretation of model
parameters, Hayes and Monfils would not have misconstrued the effects of movement on occupancy as bias and
also might have offered useful insights for sampling
design.
In addition to their narrow view of occupancy, Hayes and
Monfils overgeneralize from simulations with limited
relevance to the subject of interest: analysis of avian point
count data. Hayes and Monfils simulate a scenario involving
grid-based sampling whereby sites (i.e., cells) are juxtaposed
with no spacing between them. Although grid-based
sampling schemes are employed (Tipton et al. 2008, Ellis
et al. 2014), Hayes and Monfils’ simulations do not emulate
any specific study. Rather, they claim to simulate the generic
case of “arbitrary plots in continuous habitat” (Efford and
Dawson 2012:1). Although this concept is germane, the
relevance of Hayes and Monfils’ simulations to avian point
counts stops there. Ornithologists typically space point count
stations some distance apart to reduce the possibility of
a single individual occupying >1 station and to encourage
some statistical independence among stations (Ralph et al.
1993, Dudley and Saab 2003). Without any spacing between
sampled cells, movement induces much more spatial
dependency among sampling units than would be expected
for typical point count data. Spatially explicit models can
leverage spatial dependency to improve spatial prediction
(Chandler and Royle 2013, Ramsey et al. 2015), although
such models may be unnecessary if desired inference is of the
number of cells occupied. Regardless, point count data are
unlikely to reflect the level of spatial dependency in
occupancy reflected in Hayes and Monfils’ simulations and
discussed at length in their paper.
A broader view of occupancy would be more useful for
analyzing point count data, and targeted simulation work
could inform ecological inference. Hayes and Monfils
suggest that modeling options are currently limited,
particularly when analyzing historical datasets that do not
contain auxiliary data necessary to support models that
Latif et al.
Broader Definition of Occupancy
account for movement (e.g., temporary emigration models;
Chandler et al. 2011, Amundson et al. 2014, Ramsey et al.
2015). Developing biologically realistic models may be a
worthwhile venture, but until such developments materialize
for existing data, we suggest making the best use of available
models. For example, when forced to use models incapable of
explicitly accounting for movement (e.g., simple occupancy
models, logistic regression, or point-process models),
researchers should, nevertheless, acknowledge the potential
effects of movement when interpreting model parameters.
For example, although Hayes and Monfils strictly interpret
detectability (p) as reflecting the observation process, we
suggest detectability should be interpreted as the product of
availability and perceptibility (Amundson et al. 2014) given
any potential for within-season movement. Given their
interests, Hayes and Monfils could have simulated marsh
bird populations while explicitly representing parameters of
interest (e.g., occupancy at the desired scale of inference),
nuisance parameters (e.g., availability), and the observation
process under attainable sampling schemes (e.g., perceptibility). Such simulations could have suggested how
parameter estimates from simple models would likely reflect
b ¼ occupancy availunderlying processes (e.g., whether C
ability or b
p ¼ availability perceptibility for a given sampling
scheme). Additionally, simulations could be used to assess
the feasibility of sampling to support more complex models
that explicitly estimate parameters representing additional
levels of information (Nichols et al. 2008, Chandler et al.
2011, Amundson et al. 2014). Such work could be extremely
useful for studies of marsh birds given their intractability
(Conway and Gibbs 2005, 2011). Although Hayes and
Monfils discuss their results primarily in terms of bias relative
to occupancy, their main concern may instead relate to how
well the resulting estimates of occupancy reflect the
underlying density of animals across the landscape being
sampled. Indeed, estimating densities of animals across
multiple visits requires closure to movement unless the
models account explicitly for immigration and emigration
(Amundson et al. 2014). The relationships between
occupancy and abundance are the subject of much study
and, as alluded to by Hayes and Monfils, depend on how
sampling corresponds with spatial ecology of the species of
interest (Joseph et al. 2006, Clare et al. 2015). Spatially
explicit simulation tools and approaches capable of informing
inference of abundance from occupancy patterns for specific
systems are the subject of ongoing research (Ellis et al. 2014,
2015). We encourage researchers to think about the
inferences they can make from available models by critically
examining how model-based estimates reflect data and
underlying ecological processes within spatial and temporal
frames of interest.
ACKNOWLEDGMENTS
We thank J. A. Royle, M. Kery, and C. Handel for helpful
comments during conception and editing of this paper. In
the interest of disclosing any potential conflicts of interest,
we note that C. Amundson is an associate editor for the
Journal of Wildlife Management.
193
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Associate Editor: Michael Morrison.
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