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Landscape Ecology 18: 187–194, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
Research article
Effects of patch attributes, barriers, and distance between patches on the
distribution of a rock-dwelling rodent (Lagidium viscacia)
R. Susan Walker 1,2,*, Andrés J. Novaro 2 and Lyn C. Branch 1
1
Department of Wildlife Ecology and Conservation, University of Florida, Gainesville, FL 32611, USA;
Wildlife Conservation Society, at Neuquén Applied Ecology Center, Junín de los Andes, Neuquén, 8371,
Argentina; *Author for correspondence (e-mail: [email protected])
2
Received 4 January 2002; accepted in revised form 31 January 2003
Key words: Argentina, Barriers, Chinchillidae, Habitat quality, Isolation, Lagidium, Matrix, Metapopulation,
Mountain vizcacha, Patagonia, Patch size
Abstract
We tested whether size of habitat patches and distance between patches are sufficient to predict the distribution
of the mountain vizcacha Lagidium viscacia a large, rock-dwelling rodent of the Patagonian steppe Argentina, or
whether information on other patch and landscape characteristics also is required. A logistic regression model
including the distance between rock crevices and depth of crevices, distance between a patch and the nearest
occupied patch, and whether or not there was a river separating it from the nearest occupied patch was a better
predictor of patch occupancy by mountain vizcachas than was a model based only on patch size and distance
between patches. Our results indicate that a simple metapopulation analysis based on size of habitat patches and
distance between patches may not provide an accurate representation of regional population dynamics if patches
vary in habitat quality independently of patch size and features in the matrix alter connectivity.
Introduction
The size of habitat patches and distance between
patches are important predictors of patch occupancy
for a variety of species in patchily distributed habitats (Micol et al. 1994; van Apeldoorn et al. 1994;
Arnold et al. 1995; Hill et al. 1996; Hokit et al. 1999).
The dynamics of metapopulations of different species
in real landscapes have been modeled using only
these two variables and the presence/absence of the
species in a patch (Hanski 1994; Hanski et al. 1995;
Moilanen et al. 1998; Hokit et al. 2001). The size of
the patch is considered an indication of the size of the
population inhabiting that patch, with small patches
less likely to be occupied because small populations
have a higher probability of extinction than large populations (Wilcox 1980). The distance between patches
is used as a measure of the isolation of the patch. Isolated patches may be unoccupied because coloniza-
tion of empty patches and demographic rescue of isolated populations are limited.
Nevertheless, for strict habitat specialists the most
basic limitation to distribution is the availability of
appropriate habitat. Characteristics of a patch other
than its size, such as the availability of some limiting
resource, may be more important in determining population size. In studies reviewed by Mazerolle and
Villard (1999) that examined effects of both size and
habitat characteristics of patches on population size,
population size was significantly correlated with habitat characteristics, but not with patch size, in 71% of
animal taxa. Also, factors other than population size,
such as human-generated deterministic processes
(Sjögren-Gulve and Ray 1996; Fleishman et al. 2002)
or habitat characteristics of patches (Kindvall 1996;
Sjögren-Gulve and Ray 1996), may be important determinants of extinction probability.
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In addition, patch isolation and the probability of
colonization may be influenced by factors other than
distance between patches (Sjögren-Gulve and Ray
1996). Movement of individuals among patches may
be constrained by the composition as well as the configuration of the landscape (Wiens 1997). Characteristics of the matrix may result in effective isolation of
a patch that is greater or less than that expected based
only on distance (Roland et al. 2000; Jonsen et al.
2001; Ricketts 2001).
Moilanen and Hanski (1998) incorporated the effects of habitat quality and matrix structure, as well
as patch size and distance between patches, into their
metapopulation model for the Glanville fritillary butterfly (Melitaea cinxia). They found that this complex
model did not perform much better than a basic model
with only patch size and distance between patches.
Likewise, for the forest carabid Abax parallelepipedus distance to the nearest occupied site was a highly
significant predictor of patch occupancy, and the inclusion of habitat structure and quality as explanatory
variables improved the predictive model only slightly
(Petit and Burel 1998). However, for the butterfly
Speyreria nokomis apacheana, patch occupancy and
extinction were best modeled by measures of habitat
quality, rather than by patch size and isolation (Fleishman et al. 2002).
The purpose of this study was to test whether the
size of habitat patches and distance between patches
is sufficient to predict the distribution of a mammalian specialist for rocky habitat, the mountain vizcacha (Lagidium viscacia, family Chinchillidae), or
whether information on other patch and landscape
characteristics also is required. The mountain vizcachas (Lagidium spp.) comprise three or four species
of South American rodents, all very similar in appearance, and restricted to rocky habitats. Little research
has been conducted on the ecology of these species
(Pearson 1948; Galende and Grigera 1998; Galende
et al. 1998; Puig et al. 1998; Walker et al. 2000), but
all appear to be colonial, living in kin groups within
colonies (Walker 2001). The species that is the subject of this study is a large, rabbit-sized (2–2.5 kg)
mountain vizcacha found in the southern Andes and
Patagonian steppe (Redford and Eisenberg 1992).
Patch characteristics included in our analysis were
the density, depth, and width of rock crevices, which
are used for dens and as refuge from predators, height
and slope of cliffs, which may influence predation
risk (Walker et al. 2000), and orientation of cliffs,
which is an important factor for habitat suitability for
the closely related chinchilla, another rock specialist
(Jiménez 1995). Food availability also can be an important factor determining the presence of a species,
but is a difficult variable to assess for a generalist
herbivore such as the mountain vizcacha (Sinclair et
al. 1982). Local habitat use by mountain vizcachas
within the study area appears to be more constrained
by factors related to predation risk rather than food
availability (Walker et al. 2000), so we did not include this variable in the analysis of patch occupancy.
The landscape characteristic included in the analysis
was the presence of rivers in the matrix between
patches. Movement of mountain vizcachas across rivers appears to be limited (Walker 2001), so we hypothesized that the presence of a river between two
patches could affect their probability of colonization,
increasing isolation beyond that of distance alone.
Methods
Study area
The study was conducted in an 8,000-km 2 area in
southern Neuquén and western Río Negro provinces
of Argentina (near Junín de los Andes, 39.5° S and
71° W; Figure 1). This area is semiarid, grass-shrub
steppe with an average ground cover of about 50%
(León et al. 1998). The steppe is interspersed with
rocky cliffs, mostly of volcanic origin, that provide
patchily distributed habitat for mountain vizcachas.
Cliffs often are found at the tops of hills and have flat
tops and relatively vertical faces. They range in size
from less than 100 m to greater than 50 km long.
Several rivers ranging from 10 to 100 m wide traverse
the area.
Analysis of patch occupancy
Our analysis of patch occupancy by mountain vizcachas was based on sampling of 36 cliffs that were selected randomly from throughout the study area (Figure 1). The occupancy of a patch by mountain
vizcachas is easily discerned by the presence of their
feces. Mountain vizcachas defecate in sunning spots
near their dens in the rocks, and their feces are distinct from feces of any other animal in the region
(Pearson 1948). Patches were considered occupied if
feces were found on the rocks, and unoccupied if not.
To evaluate rock crevices and height and slope of
cliffs, we took measurements along transects placed
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Figure 1. Location of study area in southern Neuquén and western Río Negro provinces, Argentina, and the locations of 36 randomly-chosen
patches that were surveyed to evaluate patch and landscape factors affecting distribution of the mountain vizcacha.
on the tops of the cliffs. Transects were 400 m long,
except cliffs less than 400 m in length were sampled
in their entirety. At two randomly-chosen points
within each 100 m of transect, we measured the
height and slope of the cliff, and the distance between,
depth of, and width of the first five rock crevices encountered from that point on. The distance between
crevices was used as a measure of crevice density.
These measurements were averaged for each transect.
In addition we recorded the overall orientation of the
cliff, and determined whether or not there was a river
between each patch and its nearest occupied neighbor. We surveyed additional patches as needed to
identify the occupied patch nearest each of the ran-
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domly chosen patches. To estimate the size of the
patch, we averaged the height at all sampling points
along the transect and multiplied this by cliff length.
Lengths of cliffs and distances to nearest occupied
neighbors were measured from a digitized map of the
study area using ARCVIEW GIS software (ESRI,
Redlands, CA).
To ascertain how well patch size and distance between patches explained patch occupancy, we performed a logistic regression with those two variables
as explanatory variables and patch occupancy as the
dependent variable. To determine if a model with additional patch and landscape characteristics would
better predict occupancy, we then performed a stepwise logistic regression, including as potential explanatory variables the size of and distance between
patches as well as the patch and landscape variables
described above. Because north-facing cliffs receive
the most sunlight at this latitude, and presence of the
chinchilla was associated with north-facing slopes in
Chile (Jiménez 1995), we used the cosine of the orientation of the cliff as a measure of ⬙northness⬙ in the
model (Roberts 1986). From among these variables
we selected patch and landscape variables for the initial regression model using univariate tests (logistic
regression for continuous variables and cross tabulation for the presence of a river between patches; Hosmer and Lemeshow (1989)). All variables with a
probability less than 0.10 in the univariate tests were
entered into the initial model. We then used a backwards stepwise selection procedure to choose the set
of explanatory variables that best modeled the occupancy of patches by mountain vizcachas. We set the
critical significance level at 0.10 for removing variables, as a more stringent level might exclude variables that could greatly improve the model’s explanatory power (Hosmer and Lemeshow 1989; SjögrenGulve and Ray 1996; Fleishman et al. 2002). Models
with more variables were retained if the Wald’s ␹ 2 for
the coefficients of all the variables were significant
and the improvement of the model over a simpler
model was significant at the 0.05 level. We determined the improvement of the model by comparing
the difference between the −2*log-likelihoods of the
two models to a ␹ 2 distribution (Hosmer and Lemeshow 1989).
For comparison between the model with only
patch size and distance between patches and the final
model resulting from the stepwise analysis, we examined for each model the deviance goodness-of-fit, the
proportion of patches correctly predicted as occupied
or unoccupied, and the strength of association between the explanatory variables and patch occupancy
in each model as measured by Nagelkerke’s R 2
(Nagelkerke 1991). The deviance goodness-of-fit is a
measure of the unexplained variance of the dependent
variable, analogous to the error sum of squares in
least squares regression. The higher the probability,
the less unexplained variance, and the better the fit of
the model. Nagelkerke’s R 2 is an analog of the R 2 coefficient of determination in least squares regression
and is based on the log likelihood for a model compared to the log likelihood for the baseline model.
Statistical analysis of patch occupancy was performed
with SPSS v. 10.0.1 software (SPSS Inc. 1999).
Results
The model based on patch size and distance between
patches was a significant predictor of patch occupancy by mountain vizcachas (Model ␹ 2 = 20.1, df =
2, p < 0.001). The probability of occupancy of a patch
by mountain vizcachas decreased with distance to the
nearest occupied neighboring patch and increased
with increasing size of the patch (Tables 1 and 2). Inclusion of patch size significantly improved the model
(Wald’s ␹ 2 = 3.03, p = 0.08) over a model with distance alone (Model ␹ 2 = 6.75, df = 1, p = 0.009), but
patch occupancy was more strongly associated with
distance between patches (R 2 = 0.42) than with size
(R 2 = 0.21).
The model incorporating additional patch and
landscape characteristics was much better at describing patch occupancy by mountain vizcachas. This
model, resulting from the stepwise regression, included density and depth of rock crevices, rivers as
barriers in the matrix, and distance between patches
(Model ␹ 2 = 36.27, df = 2, p < 0.001; Table 2). Patch
size, cliff orientation, and width of rock crevices were
excluded in univariate analyses (Table 1), and slope
was excluded in the stepwise multiple regression.
This more complex model had a better fit, correctly
predicted occupancy for a greater percentage of
patches, and had a much higher R 2 than the model
based only on size and distance between patches (Table 2). In this model, mountain vizcachas were more
likely to be found on patches with more and deeper
crevices, that were nearer other occupied patches, and
that were not separated from those occupied patches
by a river (Tables 1 and 2).
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Table 1. Means ± standard errors of measurements for patches that were occupied and not occupied by mountain vizcachas in Neuquén and
Río Negro provinces, Argentina.
Distance between crevices (cm)*
Depth of crevices (cm)*
Width of crevices (cm)
Slope of cliff (degrees)*
Height of cliff (m)
Size (ha)
Distance to nearest occupied patch (km)*
Orientation
Rivers 1*
Occupied Patches (n = 20)
Unoccupied Patches (n = 16)
93.3
38.0
13.4
37.9
14.3
6.9
2.1
38.5°
0.05
127.6
24.9
13.1
32.8
8.4
1.2
7.1
32.5°
0.69
±
±
±
±
±
±
±
±
18.6
5.0
3.5
1.5
2.9
2.6
0.5
3.4
±
±
±
±
±
±
±
±
17.0
3.4
2.3
1.3
1.3
0.3
1.4
4.6
1
Proportion of patches separated from the nearest occupied patch by a river.
*Significant at the 0.10 level in the univariate tests.
Table 2. Characteristics of logistic regression models of patch occupancy (n = 36 patches) by mountain vizcachas based only on patch size
and distance between patches (Size/Distance), and based on the full model (Distance/River/Rock Crevices) resulting from the stepwise logistic regression with distance between patches, presence or absence of rivers between patches, distance between crevices, and depth of rock
crevices.
Model
Occupancy logit
Goodness of fit
Percentage predicted correctly
Nagelkerke’s R 2
Distance/Size
Distance/River/Rock Crevices
−0.56 (Distance) + 0.8 (Size)
−1.26 (Distance) −5.25 (River)
−0.06 (Distance between crevices)
+0.3 (Depth of crevices)
0.70
0.99
80.0
91.4
0.58
0.88
The occupancy status of only one patch (#37) was
predicted incorrectly by both models (Table 3). This
patch was predicted to be occupied, but was not. The
model based on the size of and distance between
patches incorrectly predicted the occupancy of seven
patches. Of the five patches predicted to be occupied
that were not, four were separated from the nearest
occupied patch by a river. Two patches (#7 and 22)
were incorrectly predicted to be unoccupied by the
size and distance model, and both had deep and abundant crevices.
The more complex model incorrectly predicted occupancy of three patches. One patch (#26) was incorrectly predicted to be unoccupied. In this case the
crevices appeared to be inadequate (sparse and shallow), but the patch was a large one, and not isolated
by a great distance or a river. An examination of individual measurements for this patch revealed that in
some parts of the patch crevices were deeper and
more abundant, but the average was affected by some
extreme values. Of the two patches incorrectly predicted to be occupied, one (#32) was very small and
isolated by distance, and the other (#37) was the patch
that also was predicted incorrectly to be occupied by
the size and distance model. This patch was the closest patch in the sample to a human dwelling (< 500
m), and the lack of mountain vizcachas at this site
could have been because of human disturbance.
Discussion
For the rock-dwelling mountain vizcacha, a model
based on patch characteristics related to habitat quality (density and depth of rock crevices), barriers in the
matrix (rivers), and distance between patches was a
better predictor of occupancy than patch size and distance between patches. Our results indicate that a
simple metapopulation analysis based on patch size
and distance between patches may not provide an accurate representation of regional population dynamics if patches vary in habitat quality independently of
patch size and if features in the matrix alter connectivity.
Based on their analysis of the metapopulation dynamics of the Glanville fritillary butterfly, Moilanen
and Hanski (1998) concluded that knowledge of patch
size and distance between habitat patches may be suf-
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Table 3. Patches incorrectly predicted as occupied or unoccupied by mountain vizcachas by one (for size/distance model, n = 7; for full
model, n = 3) or both models (n = 1), and values for explanatory variables used in the models. Total number of patches analyzed was 36.
Crevice
Incorrectly predicted
Patch#
Nearest
(km)
7
22
23
26
29
31
32
37
43
4
7.1
5.5
2
3.3
1.5
5
0.5
2.3
1
Size
(ha)
Spacing
(cm)
0.5
2.4
4
9.4
1.1
0.7
0.1
1
0.8
43
26
72
106
40
86
30
163
62
2
Depth
River
40
28
28
16
23
19
16
30
16
No
No
Yes
No
Yes
Yes
No
No
Yes
3
Occupied
Size/Distance 4
Yes
Yes
No
Yes
No
No
No
No
No
X
X
X
Full 5
X
X
X
X
X
X
X
1
Distance to nearest occupied patch
Average distance between rock crevices
3
Presence of a river between the patch and the nearest occupied patch
4
Model with patch size and distance between patches as explanatory variables
5
Full model resulting from the stepwise logistic regression with distance between patches, presence of rivers between patches, and rock
measurements as explanatory variables.
2
ficient for the study of metapopulation dynamics of
most species. However, they suggest that their model
based on patch size and isolation by distance was not
improved much by the addition of habitat quality because the most important habitat variables had already been incorporated into the process of choosing
which habitat patches would be included in the analysis. The basic model was not improved by the incorporation of landscape structure, but the satellite images they used to characterize the matrix structure
appeared to be inadequate for detecting aspects of the
landscape that were most relevant to the species.
In contrast, in the case of the mountain vizcacha it
would be difficult to incorporate habitat characteristics into the process of choosing which patches should
be used in an analysis of regional dynamics, and the
presence or absence of a river between two patches is
an easily measured characteristic of the matrix that is
biologically relevant. The habitat characteristics that
were most important to mountain vizcachas were the
abundance and depth of rock crevices. Patches with
more and deeper crevices had a higher probability of
being occupied by mountain vizcachas, but some
patches with a low density of crevices and a low average depth of crevices were occupied. As it would
never be possible to measure all crevices in a patch,
some sampling and measure of summary, such as an
average, are necessary to characterize the nature of
the crevices.
The weak effect of patch size on occupancy by
mountain vizcachas may occur because population
size is not linearly related to patch size, or because
some factor other than population size is a more important determinant of extinction probability within
patches. The carrying capacity of a patch for mountain vizcachas may be influenced more by the number of appropriate crevices in the rocks than by the
absolute size of the patch, as in some cases smaller
patches could have more crevices than large ones.
Extinction risk could also be greater at patches with
fewer and shallower crevices, due to greater susceptibility of mountain vizcachas to predation where
crevices that provide adequate shelter are lacking.
In some other studies characteristics of a patch
other than its size have been found to be more important correlates with patch occupancy. For bush-crickets, habitat heterogeneity within a patch was found to
compensate for patch size in terms of extinction probability (Kindvall 1996). Smaller, but more heterogeneous patches had lower extinction probabilities than
larger, more homogeneous ones because different
habitat types were optimal under different climatic
conditions over time. Patch occupation and extinction
were strongly related to habitat quality, but not to
patch size, in Speyreria nokomis apacheana butter-
193
flies (Fleishman et al. 2002). In other studies habitat
characteristics were important predictors of occupancy in addition to patch size (van Apeldoorn et al.
1994; Arnold et al. 1995).
Isolation by distance was also a significant factor
affecting distribution of mountain vizcachas, but the
effect of distance was accentuated by the presence of
a river between two patches. Rivers may be absolute
barriers for mountain vizcachas except in places
where water level drops seasonally to expose rocks
that could provide substrate for mountain vizcachas
to cross. Several recent studies have demonstrated
that the probability of colonization of vacant habitat
patches, or of immigration that ’rescues’ doomed populations, can be affected by characteristics of the matrix that limit or enhance the movement of individuals. Studies using mark and recapture methods have
found that for some butterfly and beetle species,
patches separated from occupied patches by inhospitable habitat in the matrix have lower probabilities of
colonization than patches the same distance apart but
with hospitable intervening habitat (Roland et al.
2000; Jonsen et al. 2001; Ricketts 2001). A logistic
regression analysis revealed that patch occupancy of
the pool frog was correlated with human disturbance
in the matrix, which created barriers to movement by
the frogs (Sjögren-Gulve and Ray 1996). Studies of
genetic structure and gene flow also have provided
evidence for limited movement of individuals of
some species through different habitat types (Keyghobadi et al. 1999) and across barriers in the matrix
(King 1987; Vos et al. 2001).
An analysis of population genetics of mountain
vizcachas in our study area offers additional evidence
that movement is constrained by the structure of the
landscape (Walker 2001). Genetic structure of mountain vizcachas was correlated more highly with a distance measure that incorporated the cost of crossing
rivers and traveling over different geological surfaces
than with straight-line distance. A finer-scale analysis
of genetic structure within a 32-km 2 portion of the
study area indicated that movement among patches
also is restricted at this scale. Movement of males was
less restricted than that of females, though, and all
habitat patches were occupied. Thus, different population structures and dynamics may be observed according to the scale of the study (Hill et al. 1996) and
the landscape configuration of the particular study
area (Stith et al. 1996). Nevertheless, it is clear that
among-patch processes play a major role in the population dynamics of mountain vizcachas.
Data on patch size and distance between patches
is generally easy to obtain, and there is no doubt that
these variables are often important and sometimes
sufficient to explain the distribution of a species.
However, for studies of distribution and persistence
of little-known species in patchy habitats, it is prudent to evaluate both patch characteristics and landscape context of habitat patches whenever possible.
The distribution of a species cannot be assumed to be
based solely on the availability of appropriate habitat
(Mazerolle and Villard 1999), but neither can it be
assumed to be explained only by patch size and distance between habitat patches. Efforts should be made
to evaluate relevant patch characteristics and factors
that determine connectivity for such species.
Acknowledgements
We thank the Neuquén Applied Ecology Center for
logistical support and for permission to work in the
province of Neuquén, and the Delegación Regional
Patagonia de la Administración de Parques Nacionales of Argentina for permission to work in Parques
Nacionales Lanín and Nahuel Huapi. We also thank
all the landowners and inhabitants who allowed us to
survey cliffs on their properties. J. Harrison and G.
Jones of the IFAS Statistics Dept. at the University of
Florida provided statistical advice and help with analysis. M. Biongiorno, O. Monsalvo, J. SchachterBroide, V. Pancotto, and G. Ackermann assisted in the
field. Funding was provided by the Lincoln Park Zoo
Scott Neotropic Fund, Sigma Xi – The Research Society, the American Society of Mammalogy, and the
University of Florida. Additional support was provided by the Wildlife Conservation Society, and Patagonia, Inc. provided some equipment. This is Florida
Agricultural Experiment Station Journal Series No.
R-09220.
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