Landscape Ecol
DOI 10.1007/s10980-007-9118-2
RESEARCH ARTICLE
Functional connectivity defined through cost-distance
and genetic analyses: a case study for the rock-dwelling
mountain vizcacha (Lagidium viscacia) in Patagonia,
Argentina
R. Susan Walker Æ Andrés J. Novaro Æ Lyn C. Branch
Received: 7 November 2006 / Accepted: 27 May 2007
Springer Science+Business Media B.V. 2007
Abstract Landscape connectivity can have profound consequences for distribution and persistence
of populations and metapopulations. Evaluating
functional connectivity of a landscape for a species
requires a measure of dispersal rates through landscape elements at a spatial scale sufficient to encompass movement capabilities of individuals over the
entire landscape. We evaluated functional connectivity for a rock-dwelling mammal, the mountain
vizcacha (Lagidium viscacia), in northern Patagonia.
Because of the strict association of mountain vizcachas with rocks, we hypothesized that connectivity
for this species would be influenced by geology. We
used molecular genetic estimates of gene flow to test
spatially explicit models of connectivity created with
GIS cost-distance analysis of landscape resistance to
movement. We analyzed the spatial arrangement of
cliffs with join counts and local k-function analyses.
We did not capture and genotype individuals, but
sampled at the population level through non-invasive
collection of feces of mountain vizcachas. The model
of landscape connectivity for mountain vizcachas
based on geology was corroborated by the pattern of
genetic structure, supporting the hypothesis that
functional connectivity for mountain vizcachas is
influenced by geology, particularly by the distribution
of appropriate volcanic rocks. Analysis of spatial
arrangement of cliffs indicated that occupied cliffs
are clustered and confirmed that rivers act as barriers
to dispersal for mountain vizcachas. Our methods
could be used, within certain constraints, to study
functional landscape connectivity in other organisms,
and may be particularly useful for cryptic or endangered species, or those that are difficult or expensive
to capture.
R. S. Walker L. C. Branch
Department of Wildlife Ecology and Conservation,
University of Florida, 110 Newins-Ziegler Hall,
Gainesville, FL 32611, USA
Keywords Landscape connectivity Microsatellites Non-invasive sampling South America
R. S. Walker (&) A. J. Novaro
Wildlife Conservation Society, Centro de Ecologı́a
Aplicada del Neuquén, Calle Curruhue y Rı́o Chimehuı́n,
Junı́n de los Andes 8371 Neuquen, Argentina
e-mail: [email protected]
Introduction
A. J. Novaro
Consejo Nacional de Investigaciones Cientı́ficas y
Técnicas, Centro de Ecologı́a Aplicada del Neuquén, C.C.
7, Junı́n de los Andes 8371 Neuquen, Argentina
Landscape connectivity affects the distribution and
persistence of populations and metapopulations
(Tischendorf and Fahrig 2000). The concept of
functional connectivity incorporates the combined
effects on dispersal of landscape structure, ability of a
species to use and move through the landscape, and
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Landscape Ecol
risk of mortality in different landscape elements, and
is therefore species- as well as landscape-specific
(Taylor et al. 1993; Tischendorf and Fahrig 2000).
Thus, evaluating the connectivity of a landscape for a
given species requires a measure of dispersal rates
through different landscape elements at a spatial scale
sufficient to encompass movement capabilities of
individuals over the entire landscape (Merriam 1995;
Pither and Taylor 1998).
The emerging field of landscape genetics provides
tools appropriate for this scale of analysis (Manel
et al. 2003). Measures of gene flow can be used to
estimate the dispersal component of connectivity
when the time scale of existence of habitat patches is
long relative to generation length of the species under
study and the mutation rate of the genetic marker
used (Michels et al. 2001; Vos et al. 2001). Costdistance modeling with GIS can be used to model
how individuals of a species perceive the permeability of a landscape by including variable travel costs
for different features of the landscape, based on the
known or assumed ability of that species to successfully traverse different landscape features (Ferreras
2001; Graham 2001; Michels et al. 2001; Chardon
et al 2003; Broquet et al. 2006). The costs are based
on geographic information about the landscape, and
behavioral, morphological, and ecological aspects of
the species being evaluated (Adriaensen et al. 2003).
Models of functional connectivity created with costdistance analysis can be tested with genetic analysis
of highly variable markers to determine past history
of dispersal through the landscape (Coulon et al.
2004; Vignieri 2005; Broquet et al. 2006).
In this study, we evaluated functional connectivity
for a rock-dwelling mammal, the mountain vizcacha
(Lagidium viscacia, Family Chinchillidae), in northern Patagonia. Rock-dwelling mammals have morphological adaptations, such as more heavily-padded
feet and reduced claws, for living among rocks that
make movement across other substrates more difficult
(Mares and Lacher 1987). Studies of such species in
Africa and Australia suggest that their movement
through the non-rocky matrix is limited (Hoeck 1982;
Pope et al. 1996). Because they have evolved in a
naturally-fragmented habitat with patches that are
stable over long periods of time, gene frequencies of
these species reflect a long history of dispersal among
populations. We used molecular genetic estimates
of gene flow to test spatially explicit models of
123
connectivity created with GIS cost-distance analysis
of landscape resistance to and facilitation of movement. Unlike in recent studies using similar techniques (Coulon et al. 2004; Vignieri 2005; Broquet
et al. 2006), we did not capture and genotype
individuals, but sampled at the population level
through non-invasive collection of feces of mountain
vizcachas.
Mountain vizcachas, large rodents with a body
mass of about 2.5 kg (R.S. Walker, unpublished
data), live in small kin groups within larger colonies.
The species is distributed along the Andean cordillera
of South America from Bolivia to northern Patagonia
in Chile and Argentina and throughout the northern
Patagonian steppe. Because of the strict association
of mountain vizcachas with rocks, we hypothesized
that landscape connectivity for this species would be
influenced by geology. We defined landscape composition as the mosaic of different lithological
categories of surface geology, and landscape configuration as the distribution of rivers, which could be
barriers to dispersal by mountain vizcachas (Walker
et al. 2003), cliffs, and rock outcrops.
Materials and methods
Study area
We conducted the genetics sampling for the study in
a 12,000-km2 area of semi-arid Patagonia in the
southern portion of the province of Neuquén, Argentina (39.58S and 718W), and the analysis of occupancy by mountain vizcachas in an 8,800-km2
portion of the same area. The habitat is grass-shrub
steppe (León et al. 1998) interspersed with numerous
rock outcrops, many in the form of cliffs with vertical
faces and flat tops. The geology has been determined
by Pleistocene glaciations and volcanic activity along
the Andean cordillera during the last 20 million years.
Several rivers ranging from 10 to 100 m wide
traverse the area.
Landscape geology and cliff occupancy
We digitized cliffs and rivers from topographic maps
(1:100,000) of the study area in ARCVIEW (ESRI,
Redlands, CA, USA), and rasterized these digitized
maps and a map of polygons delimiting different
Landscape Ecol
categories of surface geology in IDRISI 32 (Clark
Labs, Worcester, MA, USA). The raster images had a
resolution of 332 m. A sample of 36 cliffs that were
surveyed in a previous study had a mean length of
4,540 m, with a range of 320 m to 52 km (unpublished data). Therefore we considered the resolution
of this image to be adequate for capturing most cliffs
in the area. We overlaid raster images of cliffs and
geological categories, and assigned each cliff to one
of the geological categories listed in Table 1. In order
to evaluate which geological categories contained
cliffs occupied by mountain vizcachas, we determined occupancy status for cliffs (n = 208) through
field surveys and interviews (Fig. 1). In the course of
the study, we conducted field surveys at 100 cliffs,
and determined whether another 108 cliffs were
occupied by mountain vizcachas based on interviews.
Mountain vizcachas are diurnal and highly visible, so
their presence is known to people who live near the
cliffs. Field surveys were conducted for all cliffs
where information on cliff occupancy was questionable. We tested whether occupancy of a cliff
by mountain vizcachas was related to geological
category with a {2 test of independence.
Spatial analysis
We evaluated the spatial arrangement of occupied
and unoccupied cliffs with join count and local
k-function analyses. These analyses are based on
point patterns, so we converted the cliffs to points by
placing a point in the center of each of the 208 cliffs
where occupancy was determined. With the join
count we tested whether occupied and unoccupied
cliffs were distributed independently (Cliff and Ord
Table 1 Geological
categories where cliffs were
located in southern
Neuquén Province,
Argentina, and the percent
of these cliffs occupied by
mountain vizcachas
Fig. 1 Details of the study area, indicating the 8,800-km2 area
where occupancy of cliffs by mountain vizcachas was
determined and the seven sites where samples for genetic
analysis were collected in Neuquén, Argentina. Inset shows
location of Neuquén province in Argentina
1973; p. 17). We created a minimum spanning tree
among all 208 cliffs, and calculated the join count
based on the resulting connections matrix with the
program PASSAGE (Rosenberg 2001).
The local k-function tests for spatial randomness
by determining the proportion of all possible pairs of
points whose members are within a specified distance
from each point i, and comparing with the proportion
Lithology
Number of
cliffs
%
Occupied
Unstratified and stratified drift (till), ritmite
27
0
Conglomerates, gravel, blocks, sand
27
7
Andesite, basandesite, basalt, tuff, breccia, fine-grained ash
conglomerate, sandstone
60
72
Basalt, andesite, ignimbrite
28
82
Tuff, ignimbrite and basalt
17
71
9
33
Andesite, basandesite, basalt, tuff, conglomerates, sand, clay
Breccia, volcanic agglomerate, ignimbrite, tuff
Granite, granodiarite and tonalite, sienite and migmatite
35
57
6
33
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Landscape Ecol
obtained in simulations of random distributions of the
points (Getis and Franklin 1987). We used the
program Point Pattern Analysis (Chen and Getis
1998) to calculate local k-functions for all 208 points
and for the 104 occupied points and determine 95%
confidence intervals from 99 simulations. The distance to the nearest cliff occupied by mountain
vizcachas is greater for cliffs not occupied by
mountain vizcachas than for occupied cliffs (Walker
et al. 2003). Distances between occupied cliffs in a
previous study ranged from 200 m to 7.1 km,
compared to a range of 500 m to 19 km of distances
between unoccupied cliffs and the nearest occupied
cliff. As the distances between points in this analysis
are overestimations of the actual distances between
cliffs due to the conversion of linear cliffs to points in
the center of the cliff, we assumed 10 km between
points to be the critical distance for isolation. The
local k-functions were calculated at intervals of 1 km
to a maximum distance of 10 km. In ArcView we
mapped 10-km buffers around those cliffs that had
more cliffs within 10 km than the upper limit of the
confidence interval, and overlaid these with the map
of geological categories preferred by mountain
vizcachas.
Genetic analysis
We collected samples for genetic analysis at 28 cliffs
from seven sites, chosen to provide samples from
both sides of the major rivers in the study area: one
each to the east (Aluminé) and west (Abra Ancha) of
the Aluminé River (approximately 45-m wide), two
to the east (Catan Lil and Collón Cura) and one to the
west (Quilquihue) of the Collón Curá River (approximately 95-m wide), and one each to the north
(Traful) and south (Rı́o Negro) of the Limay River
(approximately 50-m wide; Fig. 1). Mountain vizcachas are difficult to capture in this area because their
rocky refuges are usually in crevices on the face of
vertical cliffs and they rarely entered traps away from
the rock (unpublished data). Therefore, we obtained
samples for genetic analyses from feces. Mountain
vizcachas defecate in piles at sunning spots near the
tops of cliffs, and feces dry quickly in the arid
environment. Fresh fecal pellets are easily collected
and discrete piles come from a single individual.
Studies using hair and feces as sources of DNA
have encountered allelic dropout, in which samples
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are falsely determined to be homozygous because
only one of the two alleles present amplified, and
false alleles, which are erroneous genotypes of both
homozygous and heterozygous genotypes (Broquet
and Petit 2004). This problem seems to be due to the
minute quantities of DNA sometimes obtained from
this type of sample or to degradation of the DNA. In
this study, we evaluated allelic dropout and false
alleles both by comparing the feces-based genotype
with a reference genotype obtained from tissue from
a captive mountain vizcacha, and through repeated
genotyping of DNA from fecal samples. DNA
amplified from tissue and feces of the captured
mountain vizcacha produced the same genotype at all
four microsatellite loci. For the repeated amplifications we used the unbiased weighted estimators for
L
L
P
P
allelic dropout, p ¼
Dj = Ahetj , where Dj is the
j¼1
j¼1
number of amplifications missing one allele at locus j,
and Ahetj is the total number of amplifications of
individuals heterozygous at locus j, and p is the
weighted average of the frequency of allelic dropout
L
L
P
P
over L loci, and for false alleles, f ¼
Fj = A j ,
j¼1
j¼1
where Fj is the number of amplifications with one or
more false alleles at locus j, and Aj is the total number
of amplifications (Broquet and Petit 2004). Repeated
(n = 10) amplifications of four loci of 20 samples
from fecal DNA indicated a 10.5% rate of allelic
dropout and a 9.7% rate of false alleles. As we were
comparing populations, not genotyping individuals
for comparison, we accepted these rates of potential
error, assuming they would not bias comparisons
among populations because they would be similar
across populations. Nevertheless, the high error rate
may create considerable background noise, reducing
power to detect differences among populations.
We extracted DNA from feces using magnetic
beads (Dynabeads DNA Direct, Dynal AS, Oslo,
Norway). We washed three to four fecal pellets in a
1.5-mL Eppendorf tube containing approximately
600 mL phosphate-buffered saline. We transferred the
supernatant to a clean tube, added 200 mL (1 U) of
Dynabeads, and performed the extraction according
to manufacturer’s protocol. We eluted extracted DNA
in 40 mL TE for 5 min at 658C (Flagstad et al. 1999).
We amplified four microsatellite loci (LV1, LV4,
LV5, and LV8) with primers developed for this
species (Walker et al. 2000a) and labeled fluores-
Landscape Ecol
cently with dyes 6-FAM and HEX. We performed
polymerase chain reaction thermocycling with 0.5 mL
of template in 12.5-mL reactions [10· Buffer with
1.5 mM MgCl (Finnzymes), 100 to 200 mM dNTPs,
0.1–0.2 mM primer, 0.2 U DyNazymeTM Thermostable DNA Polymerase (Finnzymes)]. Cycling conditions were 958C for 3 min, 948C for 15 s, optimal
annealing temperature of the primer (50–588C;
Walker et al. 2000a) for 30 s, 728C for 45 s, for 50
cycles (Ernest et al. 2000). Alleles were resolved by
electrophoresis using a 4.5% polyacrylamide gel on
an automated DNA sequencer [Applied Biosystems
Inc. (ABI, Foster City, CA, USA)-Prism 373]. We
analyzed these data using GENESCAN 2.0.2 and
GENOTYPER 2.0 (ABI) software.
Ninety percent of isolations from feces amplified
at least once with either microsatellite primers or
‘‘universal’’ cytochrome b primers. However, the rate
of amplifications per locus was low (28% for LV1,
30% for LV4, 64% for LV5, 31% for LV8). Because
of the large number of samples initially processed
and limited budget, we were unable to do repeated
amplifications of all samples. This resulted in greatly
reduced sample sizes of individuals (Aluminé, n = 46;
Abra Ancha, n = 28; Catan Lil, n = 49; Collón Cura,
n = 19; Quilquihue, n = 14; Traful, n = 13; and Rı́o
Negro, n = 17).
If two loci are located on the same chromosome,
or their inheritance is linked in some other manner,
they do not provide independent information for
analysis of genetic structure. To test for this linkage
disequilibrium among loci, we performed Fisher’s
exact test with a Markov chain using GENEPOP 3.2
(Raymond and Rousset 1995a, b).
We tested for random mating within sites by
calculating Fis, which is the reduction in heterozygosity of individuals relative to subpopulations (sites,
in this analysis), and for population subdivision by
calculating Fst, which estimates differentiation
among subpopulations (sites) relative to the entire
population (Hartl and Clark 1997; p. 117). Rst is
analogous to Fst, but is specifically applicable to
microsatellite data, in which the sizes of alleles are
known, because it is based on variance in allele size
between populations rather than heterozygosity (Slatkin 1995). By considering differences in the sizes of
alleles, Rst incorporates information on the mutational
history of alleles in the population. Gaggiotti et al.
(1999) found that in simulations Rst overestimated
population subdivision when sample sizes were small
and the number of loci examined was low (<20), as in
this study. Nevertheless, we report both Fst and Rst
here for comparisons with other studies. We calculated Weir and Cockerham’s (1984) F statistics with
FSTAT version 2.9.1 (Goudet 2000), and Rst with
RSTCALC (Goodman 1997), permuting genotypes
among samples 5,000 times to test the significance of
Fst and Rst. We adjusted the rejection threshold with
Bonferroni corrections for all multiple tests (Rice
1989).
Landscape connectivity
We compared four different models of connectivity
for mountain vizcachas in this landscape. The models
represented different dispersal costs for mountain
vizcachas over the entire landscape. The first model
(Distance) was a simple isolation-by-distance model
that assumed all features of the matrix (the unsuitable
habitat between habitat patches) were equally permeable to mountain vizcachas, i.e. that the cost of
dispersal through all landscape features is the same.
The second model (Rivers) incorporated rivers as
barriers that were difficult for mountain vizcachas to
cross in addition to the effect of distance. The third
model (Geology) incorporated differential effects of
geological composition of the matrix in addition to
distance, and the fourth model (Geology + Rivers)
includes the geological composition of the matrix as
well as the effect of distance and rivers as barriers.
For the ‘‘Distance’’ model, we measured Euclidean
distances (linear distance with no friction) between
genetics sampling areas in ARCVIEW. For the other
models, we created friction surfaces with IDRISI by
assigning friction values to geological surface categories and rivers, based on the estimated difficulty, or
cost, for mountain vizcachas of moving through these
landscape features relative to movement across the
rocky cliffs that are their major habitat. These friction
surfaces had the same resolution (332 m) as the base
images. We estimated these relative costs considering
the biological characteristics and behavior of the
species. Habitat use by mountain vizcachas is concentrated close to cliffs, with decreasing use with
increasing distance from the cliff, and greater probability of use of areas with higher percent rock cover
and presence of large rocks (Walker et al. 2000b).
Cost values were assigned assuming that (1) there is
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Landscape Ecol
no cost to mountain vizcachas of movement on cliffs
(friction value = 1), (2) rivers may be passable by
mountain vizcachas, at least during times of drought
or in places with many exposed rocks that can be
used as a ‘‘bridge’’, but are not passable or crossed
only with great risk or low frequency when water is
high and swift, and (3) mountain vizcachas are at
much greater risk of predation and have more
difficulty traveling through the matrix away from
rocky cliffs (personal observation). Friction values
for the matrix away from cliffs varied according to
the model.
For the ‘‘Rivers’’ model, which considered only
rivers as major barriers and the rest of the matrix as
permeable, but with much greater cost than travel on
cliffs, medium ( 45 m wide) and large (>45 m
wide) rivers were assigned high friction values (500
and 1,000, respectively), and all of the geological
categories in the matrix were given a value (100)
lower than the rivers but much greater than the cliffs.
For the ‘‘Geology’’ and ‘‘Geology + Rivers’’ models,
we assumed that mountain vizcachas prefer habitats
that present them with lower movement costs. We
used the presence–absence data obtained in the cliff
surveys to assign increasingly greater friction values
to areas comprised of geological categories that were
most used by mountain vizcachas (50), that were
sometimes used (100), that had no cliffs used by
mountain vizcachas (500), and that had no cliffs at all
(1,000), and for the ‘‘Geology + Rivers’’ model we
also incorporated friction values of rivers as in the
‘‘Rivers’’ model.
With the friction maps for each model we used a
pushbroom algorithm to construct a separate costdistance image of the study area for each area where
we did genetic sampling (Eastman 1989). In the
pushbroom system, processing sweeps from one
corner of the image to the other, proceeding sequen-
Table 2 Matrix of pairwise
Fst’s among populations of
mountain vizcachas in the
seven areas of genetic
sampling in Neuquén
Province, Argentina
123
Catan Lil
tially row by row, and accumulating information on
distance from features as it goes. The images for each
area of genetic sampling assigned the lowest possible
‘‘cost’’ of travel from that area to every other pixel in
the image. The cost incorporates both distance and
the frictions (resistance) encountered in movement
from the sampling area to that pixel. Using the
images created for each sampling area, we measured
the cost-distance between that sampling area and
each of the other sampling areas according to each
model (Knaapen et al. 1992; Sutcliffe et al. 2003;
Adriaensen et al. 2003).
To determine if there were significant correlations
between dispersal patterns of mountain vizcachas as
inferred from genetics data and our models of
connectivity, we used Mantel regressions (Mantel
1967) between a pairwise Fst matrix, representing the
genetic distance between each pair of areas (Table 2),
and matrices of cost-distance according to each of the
models. Following the recommendation of Rousset
(1997) for two-dimensional isolation-by-distance
models, we used the natural log of the distances
and did 10,000 permutations for each model. The
Mantel analysis was done with the program TFPGA
(Miller 1997).
Results
Landscape geology and cliff occupancy
Fifty percent of cliffs (n = 208) were occupied
(Fig. 2). Eight of the 17 geological categories found
in the study area contained cliffs, and seven of these
contained cliffs occupied by mountain vizcachas
(Table 1). The presence of mountain vizcachas at
cliffs was strongly associated with specific geological
categories ({2 = 68.87, df = 8, P < 0.0001). Most
Collón Cura
Abra Ancha
Aluminé
Quilquihue
Collón Cura
0.002
Abra Ancha
0.025
0.017
Aluminé
0.042
0.008
0.003
Quilquihue
0.062
0.056
0.076
Traful
0.006
0.018
0.036
0.029
0.241
Rı́o Negro
0.044
0.006
0.060
0.073
0.086
Traful
0.117
0.038
Landscape Ecol
Table 3 Expected and observed number of joins between
occupied and unoccupied points
Expected
Observed
SD
T
P
Occupied to
occupied
51.5
91
4.27
9.26
<0.000
Occupied to
unoccupied
104
23
7.19
11.27
<0.000
Unoccupied to
unoccupied
51.5
93
4.27
9.73
<0.000
Spatial structure
Fig. 2 Occupancy by mountain vizcachas of cliffs in the study
area in Neuquén, Argentina, with 10-km buffers around cliffs
with more cliffs than expected within a 10-km radius
Join count analysis indicated significant clustering of
occupied and unoccupied cliffs (Table 3). Occupied
cliffs were more likely to be next to other occupied
cliffs, and unoccupied cliffs were more likely to be
next to other unoccupied cliffs, whereas occupied and
unoccupied cliffs were less likely to be next to
each other than would be expected with a random
distribution.
The distance to the nearest neighbor for both
points representing all cliffs and for those representing only cliffs occupied by mountain vizcachas was
2 km. The distance at which clustering of some points
began to appear was 5 km for occupied cliffs and
6 km for all cliffs, and the proportion of clustered
points was higher for occupied compared to unoccupied cliffs up to 10 km (Fig. 3). The buffer areas of
these cliffs crossed the Aluminé River and overlapped with some unoccupied points on the other side
of the river. The map of 10-km buffers around all
cliffs that were significantly clustered formed three
large, distinct clusters (Fig. 2). All three clusters
contained both occupied and unoccupied cliffs.
Within the two larger of these clusters, occupied
cliffs occupied by mountain vizcachas (98%) were of
four categories, mainly of rocks of volcanic origin
(Table 1). Many unoccupied cliffs (40%) were also of
these categories. Most occupied cliffs were to the east
of the Aluminé and Collón Cura rivers, and most
unoccupied cliffs of the preferred geological categories were to the west, on the same geological
formations as occupied cliffs on the other side of
the rivers (Fig. 2).
Number of cliffs
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
Distance (km)
All cliffs
Occupied cliffs
Fig. 3 Number of cliffs with more cliffs than expected within
increments of 1 km up to 10 km
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Table 4 The F-statistics (Fst and Fis), Rst, and number of
alleles per locus for mountain vizcachas from seven sites in
southern Neuquén, Argentina
Locus
Fst
Fis
Rst
Alleles
LV1
0.04 ± 0.03
0.33 ± 0.03
0.20
13
LV4
0.01 ± 0.02
0.17 ± 0.04
0.01
12
LV5
0.02 ± 0.01
0.10 ± 0.06
0.10
13
LV8
0.09 ± 0.04
0.45 ± 0.07
0.17
10
Overall
0.04a
0.26a
0.12a
a
Significant at a = 0.01 after sequential Bonferroni correction
for multiple testing (Rice 1989)
Genetic structure
Loci used in the analysis sorted independently, as
there was no evidence of linkage disequilibrium
(P = 0.45–0.99). Gene diversity per locus and
population was high, as is common with microsatellite data, ranging from 0.67 to 0.97. Genetic differentiation (Fst = 0.04 and Rst = 0.12) among the
sampling areas was significant (Tables 2, 4). The Rst
value greater than the Fst is consistent with an
underestimation of population subdivision when Fst is
used for microsatellite data, and with an overestimation of subdivision with Rst with a small sample size
and low number of loci. The significant Fis (0.26)
indicates a deficit of heterozygotes within areas,
which to some extent could be due to allelic dropout.
Landscape connectivity
Fig. 4 Occupancy by mountain vizcachas of cliffs in the study
area in Neuquén, Argentina, with 10-km buffers around
occupied cliffs with more occupied cliffs than expected within
a 10-km radius
and unoccupied cliffs were separated by a river. In
the second largest cluster, however, cliffs to the west
of the Collón Curá River were not on a geological
category preferred by mountain vizcachas. The map
of 10-km buffers around occupied, clustered points
formed a single large cluster, and cliffs contained
in the buffers were all on geological categories
preferred by mountain vizcachas (Fig. 4).
123
Euclidean distances between cliffs sampled ranged
from 7.8 to 173 km. Genetic structure was correlated
with Euclidean distance between areas at a probability of 0.054, which, given the low power of the
Mantel test for seven populations and the loss of
Table 5 Results of Mantel regressions testing for correlation
between genetic distances and the cost-distance among the
areas (n = 7) sampled for mountain vizcachas according to
four different models
Model
r
P
Distance
0.26
0.054
Rivers
0.29
0.066
Geology
0.40
0.008a
Geology + rivers
0.39
0.006a
a
Significant at a = 0.01 after sequential Bonferroni correction
for multiple testing (Rice 1989)
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power due to allelic dropout and amplification
failures, probably indicates a significant correlation
under the ‘‘Distance’’ model (Table 5). The ‘‘Rivers’’
model, in which rivers were assumed to be very
difficult to cross and the rest of the matrix was given
the same weight, was correlated with genetic structure at a probability of 0.66, and increased the slope
of the regression only to a small degree. On the other
hand, the ‘‘Geology’’ model, which incorporated
costs of dispersal by mountain vizcachas through
different surface geological categories, and the
‘‘Geology + Rivers’’ model, which incorporated
rivers as barriers in addition to the effects of geology,
were both correlated with genetic structure to a much
higher degree (P < 0.01 and r = 0.40 and 0.39).
Nevertheless, there was no improvement to the
‘‘Geology’’ model with the addition of the effects
of rivers in the ‘‘Geology + Rivers’’ model.
Discussion
Our results support the hypothesis that functional
connectivity for mountain vizcachas is influenced by
geology of the landscape. The model of landscape
connectivity for mountain vizcachas based on geology was corroborated by the pattern of genetic
structure. Gene flow followed the model of isolation
by distance and the model incorporating the barrier
effect of rivers into a cost-distance measure to some
degree, but the models that included differential costs
for different classes of surface geology were more
highly correlated to genetic structure. The inclusion
of the effect of rivers as barriers did not improve the
model based on geology alone, indicating that
geology is more significant in determining landscape
permeability from the point of view of mountain
vizcachas. This suggests that dispersal of mountain
vizcachas is constrained mostly by the pattern of
surface geology in this landscape.
The distribution of unoccupied cliffs on preferred
geological categories and clustering of cliffs as
illustrated with the local k-function analysis
(Figs. 2, 4) suggest that the lower Aluminé and the
Collón Cura rivers are ‘‘hard’’ barriers for mountain
vizcachas (Merriam 1995). The Collón Cura is the
largest river in the region and the Aluminé is the
fastest flowing. These rivers either prevented colonization of appropriate habitat to the west or prevented
successful recolonization once populations to the
west went extinct. Cliffs separated from the nearest
occupied cliff by a river are less likely to be occupied
by mountain vizcachas (Walker et al. 2003). However, the barrier effect of rivers was not sufficient to
explain the pattern of genetic structure of mountain
vizcachas in the area. This could be because the
lower Aluminé and Collón Cura Rivers were such
complete barriers that there were no mountain
vizcachas to sample from both sides of those rivers.
The smaller rivers, which had mountain vizcachas on
both sides, were perhaps less effective barriers.
In the simplest models of patch occupancy and
connectivity, Euclidean distance between patches is
used as a measure of patch isolation, the inverse of
connectivity, without considering the nature of the
matrix between patches (Moilanen and Niemenin
2002). However, most species experience some
environmental or intrinsic biological restrictions to
their movement pathways. Adjustments of distance
measures to incorporate the isolating effects of
characteristics of the matrix have improved different
measures of connectivity for a variety of organisms
(Keyghobadi et al. 1999; Roland et al. 2000; Jonsen
et al. 2001; Verbeylen et al. 2003).
Our results add to the growing body of evidence
indicating that the cost of travel over a landscape is
an important factor in limiting and directing movement of individuals of a species (Chardon et al. 2003;
Coulon et al. 2003; Vignieri 2005; Broquet et al.
2006). The cost of travel over a landscape is an
analog for functional connectivity of the landscape
(Bélisle 2005), and is species-specific, as species
have different capabilities for moving across different
landscape features. Travel costs may vary across a
landscape because landscape features present differences in probability of predation, ease of movement,
and availability of shelter, food, or other resources to
dispersing individuals of a species.
Differences in cost of travel for mountain vizcachas through different geological categories may be
due to differences in the amounts of exposed rock.
Movements of mountain vizcachas away from cliffs
are strongly associated with the amount of rocky
substrate (Walker et al. 2000b), and greater amounts
of exposed rock in some geological categories may
enhance the probability or success of dispersal. The
response of mountain vizcachas to the proximity of
potential predators is to run until they reach some sort
123
Landscape Ecol
of rock, no matter how effective a shelter that may be
(personal observation). Volcanic rocks that have
abundant, wide crevices provide the best shelter for
mountain vizcachas (Walker et al. 2000b, 2003). The
geological categories that mountain vizcachas
selected in this study may provide more and better
rock crevices within cliffs, and more rocky shelters in
the matrix, than those that were not used or used less.
Another possibility is that there is a difference in
topography among geological categories. Mountain
vizcachas tend to use portions of cliffs with steeper
slopes below them (Walker et al. 200b). Their rocky
habitats are three-dimensional, but in this study we
did not evaluate landscape topography.
Cliffs occupied by mountain vizcachas were not
randomly distributed, and were more likely to be near
other occupied cliffs. The largest area of all clustered
cliffs was also the largest area of occupied cliffs that
were clustered. The second largest cluster of cliffs
that did not contain many occupied cliffs was on a
geological category that was not preferred. In addition to the structure and composition of the matrix,
connectivity of a landscape for a species is also
affected by the abundance and spatial arrangement of
habitat patches. As the number of successful dispersers that reach a patch is a product of the number of
individuals attempting dispersal and the probability
of successful movement between patches, increased
gene flow within some geological categories could be
due to effects of population size—some areas contain
more habitable cliffs and therefore produce a greater
number of dispersing individuals. Therefore, the
correlation between genetic structure and cost distance through different geological categories could be
related to differences between the categories in the
abundance, size, and spatial arrangement of suitable
cliffs, rather than—or in addition to—cost of travel
through the matrix (D’Eon et al. 2002).
Connectivity can have profound consequences for
distribution and persistence of populations and
metapopulations (Tischendorf and Fahrig 2000), and
must be taken into consideration when evaluating the
status of and planning conservation measures for
those populations. The results of our habitat patch
survey and previous studies suggest that connectivity
influences the distribution of mountain vizcachas in
this landscape. Although presence of mountain vizcachas was strongly associated with certain geological categories, 40 % of the cliffs of the four preferred
123
categories were not occupied by mountain vizcachas,
signifying that habitat availability is not the only
factor determining their presence. The significant
genetic differentiation among populations and the
correlation of genetic structure with surface geology
imply that mountain vizcachas are dispersing among
cliffs, but within constraints of the landscape composition. Isolation of cliffs is inversely related to the
presence of mountain vizcachas (Walker et al. 2003).
Therefore, dispersal, dispersal routes, and connectivity may be key factors affecting cliff occupancy.
Both components of our methodology—non-invasive genetic sampling and cost-distance analysis—
have limitations which may restrict their use in some
cases for other studies. Non-invasive genetic sampling is plagued by the problems of allelic dropout
and a general reduction in sample size due to nonamplifying samples or those that do not amplify for a
sufficient number of loci (Taberlet et al. 1999). In our
study we experienced both of these problems. Allelic
dropout and small sample size greatly reduce the
statistical power to test differences among populations and their relationships to geographical and cost
distances. Therefore to test connectivity for some
species, very large sample sizes may be needed, and a
large budget that allows repeated amplifications of
samples to reduce the impact of allelic dropout and
maximize the utility of samples collected.
In cost-distance modeling, assignment of friction
values may be difficult or impossible for some
species. The process is usually subjective, depending
on expert judgment based on data available in the
literature and existing knowledge about the natural
history of the organism of interest (Adriaensen et al.
2003; Broquet et al. 2006). In some cases actual field
data on animal movements from radio-telemetry,
mark-recapture, or observations can be used to
estimate friction values (Ferreras 2001; Michels
et al. 2001; Graham 2001; Sutcliffe et al. 2003). In
this study, we used empirical data from field surveys
(Chardon et al. 2003; Broquet et al. 2006), to assign
different friction values to geological features according to their degree of use by mountain vizcachas.
However, the grain resolution and rank order of the
friction values are probably more critical than the
actual values used (Knaapen et al. 1992; Sutcliffe
et al. 2003; Broquet et al. 2006). The use of the costdistance method depends on the availability of
suitable maps of landscape features that are relevant
Landscape Ecol
to the biology of the species, and the arbitrary nature
of the assignment of friction values may complicate
the identification of underlying biological processes.
Despite its limitations, the approach we describe to
define species-specific connectivity for mountain
vizcachas in an explicit landscape in the Patagonian
steppe can be applied to study connectivity for other
organisms in other landscapes, where working within
the constraints of the methodology is feasible. It may
be particularly useful for cryptic or endangered
species, or those that are difficult or expensive to
capture. The cost and difficulty of reliable genetic
analysis of samples obtained non-invasively must be
weighed against the cost of capture of these species.
Acknowledgments We thank the Centro de Ecologı́a
Aplicada del Neuquén for logistical support in the field. We
thank J. Ayesa and the Lab de Teledetección de INTABariloche for the digitized geological map, and O. Monsalvo, J.
Schachter-Broide, V. Pancotto, G. Ackerman, and M.
Biongiorno for assistance in the field. We thank landowners
and the Delegación Regional Patagonia de Administración de
Parques Nacionales de Argentina for permission to carry out
the study. Funding was provided by the Lincoln Park Zoo Scott
Neotropic Fund, Sigma Xi, the American Society of
Mammalogists, and National Science Foundation doctoral
dissertation improvement grant number DEB-9972717.
Additional support was provided by the Wildlife
Conservation Society and the University of Florida. We
especially thank A. Clark, B. Bowen, W. Farmerie, D.
Moraga Amador, and D. Brazeau for guidance in the lab.
Finally, we thank B. Bowen, G. Tanner, M. Sunquist, C.
Chapman, and two anonymous reviewers for helpful comments
on the manuscript.
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