A comparison of Eurasian red squirrel distribution in different
fragmented landscapes
ALEJ AND RO RODRI GUEZ* and HENRTK ANDRE N
Grimso” Wildlife Research Station, Department of Conservation Biology, Swedish University of Agricultural
Sciences, 730 91 Riddarhyttan, Sweden
Summary
1. The occurrence of species vulnerable to habitat fragmentation is likely to depend on the size and
separation of the fragments. However, the shape of the function that relates occurrence to these
landscape parameters may be affected by other fac- tors that are less easily measured, in which case
relationships with size and separa- tion in one area may predict occurrence elsewhere only poorly.
2. We explored how well the distribution of red squirrels Sciurus vulgaris in frag- mented woodlands
was predicted by simple logistic regression models empirically derived in other fragmented landscapes.
3. Comparisons between predictions lead us to identify thresholds in fragment size (> 10 ha) and
distance to a source (< 600 m) where the probability of squirrel occupancy was at least 0 9 in all
landscapes. These values may reflect squirrel mini- mum habitat requirements for home range and
dispersal in the worst study area.
4. For fragments < 10 ha (outside shared thresholds), models developed in a land- scape could predict
squirrel occupancy elsewhere only in 17% of cases, as other factors such as demography or habitat
quality might become relevant in very small and isolated fragments.
5. The predictive ability for small fragments also improved when the range of frag- ment sizes in the area
of observation fell within the range of sizes in the area where the model was developed.
6. Some models gave correct between-year predictions of squirrel distribution in the same landscape
despite noticeable changes in regional squirrel population den- sity.
7. When size and distance thresholds were met, we found that models could be used successfully
elsewhere. Tn addition, threshold values indicate how large forest fragments should be and how they
should be arranged to favour squirrel occur- rence in a landscape.
Key-words: habitat fragmentation, incidence models, predictive ability, Sciurus vul- garis, thresholds in
landscape attributes.
Introduction
The predicted effects of different management measures must be known for environmental decision
making. Specific models are often lacking and, con-
Correspondence author: Dr Alejandro Rodriguez,
Grimso Wildlife Research Station, 730 91 Riddarhyttan,
Sweden.
*present address: Department of Applied Biology,
Estacion Biologica de Donana, CSTC, Avda. Maria Luisa
s/n, 41013 Sevilla, Spain. E-mail: alrodrieebd.csic.es
sequently, a crucial question in applied biology is to
what extent information obtained under similar conditions but in other places can be used to make decisions. Existing empirical models frequently address
site-specific problems. Although these models may
be helpful in solving the local problems they were
built for, their usefulness increases as their predictions become general and can therefore be applied
across a range of different ecological contexts, that
is, when the same pattern occurs in different places
(Beeby 1993). However, there is a trade-off between
the accuracy (often related to the number of predictors and refinements, i.e. the model complexity) and
the potential for the predictions to be generally
applied. For instance, it has been recommended that
attempts at testing complex models that describe
animal responses to variation in their habitat
(Dunning et al. 1995; see also examples in Verner,
Morrison & Ralph 1986) should be ‘conducted
under conditions that do not differ greatly from
those under which the model was constructed’
(Conroy et al. 1995). Tn practice, this means that
quantitative tests usually do not go beyond the
model performance in the area where data were collected for parameter estimation
(Fahrig
&
paloheimo 1988; Norris et al. 1997). The conclusions
of qualitative tests may make more room for generalization (pausas, Austin & Noble 1997), but at the
cost of reduced accuracy in the predictions and
therefore limited general usefulness. Tt would be reasonable to expect a better general applicability of
predictions from simple models.
Tsland biogeography (MacArthur & Wilson 1967)
and metapopulation theories (Gilpin & Hanski
1991) predict that the probability of a species’ occurrence in a habitat patch is positively related to patch
size and negatively related to patch isolation.
Although these predictions have received extensive
empirical support (e.g. Opdam, Rijsdijk & Hustings
1985; Bright, Mitchell & Morris 1994; Arnold,
Weeldenburg & Ng 1995), the typical practical question in conservation is about the parameters of these
relationships in a particular case, i.e. how large and
how isolated patches should be to achieve a given
response by the species. This information is mainly
obtained from existing empirically derived relationships describing the distribution of a species in a
fragmented habitat, and one may ask about the predictive value of such simple, two-variable models.
However, so far models built in one area have been
rarely used to predict the effects of habitat fragmentation on the same species elsewhere.
The Eurasian red squirrel Sciurus vulgaris L. is
restricted to forested areas (Gurnell 1987). Although
deciduous, coniferous, or mixed forests can be suitable habitat for red squirrels, they prefer forest with
old coniferous trees where available (Andren &
Delin 1994). The response of this species to forest
fragmentation has been studied in several places (see
Wauters 1997; for a review) that differ in both the
proportion and the spatial arrangement of forest left
in the landscape. By using simulated fragmented
landscapes, Andren (1994, 1996) has shown that the
proportion of occupied patches of suitable habitat
used by a species (i.e. the population response to
fragmentation) depends upon the total proportion
of suitable habitat in the landscape. From this
hypothesis, it can be expected that the response of
the red squirrel to forest fragmentation will be simi-
lar in landscapes having also similar proportions of
forest.
Recently, Rushton et al. (1997) modelled the distribution of red and grey S. carolinensis Gmelin
squirrels at the landscape scale combining spatial
variables and species’ life-history traits. These
authors state (quoting Wiens 1989) that reliable predictions of squirrel distribution can hardly be
obtained from what they call ‘associative models’
that only incorporate the spatial configuration of
forest patches in the landscape. Therefore, they
opted for developing a population dynamics model
that, undoubtedly, helps to understand the ecological mechanisms underlying changes in squirrel distribution. Rushton et al. (1997), however, acknowledge
that the performance of their model is very sensitive
to the accuracy in the estimation of inputs such as
dispersal
distance,
mortality,
or
fecundity.
Consequently, although the approach they propose
can be generalized, the predictions of their particular
model could hardly be validated elsewhere because
accurate life-history data are not available in most
squirrel populations (Armitage et al. 1997). Tn contrast, several simple, site-specific, associative models
explaining red squirrel distribution already exist
(e.g. Celada et al. 1994; van Apeldoorn, Celada &
Nieuwenhuizen 1994; Wauters et al. 1997a; Delin &
Andren 1999), and can be readily tested elsewhere
because presence—absence data are easy to obtain.
Therefore, from a practical point of view it would
be useful to test the predictive performance of this
commonly used approach.
Tn this paper we first examine whether there was
any general agreement between predictions of logistic regression models describing the distribution of
red squirrels in six fragmented landscapes. We investigate the relative effects of (i) the total proportion
of suitable habitat in the landscape; (ii) fragment
size; (iii) distance to a source population; (iv) relative population density; and (v) quality of matrix
habitat, on variation in predicted probabilities of
occupancy. Secondly, we test how well the pattern
of fragment occupancy in a particular landscape
matches predictions given by models which were
built in other landscapes.
Methods
STUDY STTES
The effects of fragment size and distance from the
forest fragment to the nearest permanently occupied
forest (source) on the distribution of red squirrels
have been studied in six landscapes: one in the
Netherlands (Twente; Verboom & van Apeldoorn
1990; van Apeldoorn, Celada & Nieuwenhuizen
1994), three in northern Ttaly (Apennines and po
plain; Celada et al. 1994; piedmont; Wauters et al.
1997a), and two in central Sweden (Grimso and
Table 1. Characteristics of six fragmented landscapes where Eurasian red squirrels occur. The ranges of size and distance to
the nearest source are given for each sample of forest fragments. Tn Apennines, po plain, Twente, and piedmont study area
size and percentage of forest left in the landscape were either given in the literature or estimated from published sketches of
the study areas. Sources: Grimso (Delin & Andren 1999), Fellingsbro (this study), Apennines and po plain (Celada et al.
1994), Twente (Verboom & van Apeldoorn 1990; van Apeldoorn, Celada & Nieuwenhuizen 1994), and piedmont (Wauters
et al. 1997a)
Fragments
Study area
Size
(km2)
Dominant
habitat
Forest
(%)
Number of
fragments
Size (ha)
Distance (m)
Matrix
Forest quality
Grimso
Fellingsbro
Apennines
po plain
Twente
piedmont
450
32
135
4675
150
350
Forest
Farmland
Farmland
Farmland
Farmland
Farmland
69
26
25
13
8
8
46
45
34
46
49
61
0 1—500
0 5—79
0 5—32
2 4—120
0 5—14
0 2—70
24—585
25—1200
10—2530
1000—16000
40—3500
10—13000
Young stands
Open fields
Hedgerows
Open fields
Hedgerows
Hedgerows
Mainly conifers
Mainly conifers
Deciduous trees
Deciduous trees
Mixed forest
Deciduous trees
Fellingsbro; Delin & Andren 1999; this study).
These landscapes differ in their total proportion of
forest as well as in the ranges of fragment size and
fragment distance to a source (Table 1). Both connectivity and the spatial arrangement of forest
patches also vary between landscapes with similar
proportion of forest. The proportion of forest in
Fellingsbro compares to that in the Apennines
(Table 1), but while in the former site forest patches
are completely isolated by farmland, in the latter
most woodlots are interconnected by hedgerows or
rows of trees (Celada et al. 1994). The percentage of
forest is also similar in Twente, piedmont and po
plain (Table 1), but source forests are small (up to
200 ha) and lie close to the fragments in Twente (see
Fig. 2 in van Apeldoorn, Celada & Nieuwenhuizen
1994), whilst sources are large continuous forests
(> 16000 ha; Fig. 2 in Celada et al. 1994) or river
woodland belts (L. Wauters, personal communication) quite far from some of the studied fragments
in the po plain and piedmont. Connectivity between
fragments through forested corridors is high in
Twente (Verboom & van Apeldoorn 1990), lower in
piedmont (Wauters et al. 1997b), and virtually
absent in the po plain (Celada et al. 1994). There are
differences in forest quality as well. The forest is
dominated by deciduous tree species in the Ttalian
sites whereas mixed or coniferous forest dominates
in the other study areas (Table 1).
SQUTRREL SURVEYS
649—662
Tn the published studies, searching for dreys
(Wauters & Dhondt 1988) was used to determine
squirrel presence in each fragment. Tn the Swedish
study areas, squirrel occurrence was determined by
searching for the remains of eaten Norway spruce
Picea abies and Scots pine Pinus sylvestris cones
which were produced during the year of the survey
(Delin & Andren 1999). Forest fragments were monitored during 4 consecutive years in Twente (1988—
91; van Apeldoorn, Celada & Nieuwenhuizen 1994)
and Grimso (1990—93; Delin & Andren 1999), and
for 2 years in Fellingsbro (1994, 1996). The three
Ttalian fragment systems were monitored in only 1
year (Celada et al. 1994; Wauters et al. 1997a).
Delin & Andren (1999) estimated the changes in
relative squirrel density at Grimso using an index
based on sightings. They found that the index in
1990 was six times higher than in 1991, and intermediate in the other years (Table 2). Changes in
squirrel regional density, conifer seed crop, and the
pattern of fragment occupancy, led van Apeldoorn,
Celada & Nieuwenhuizen (1994) to suggest that
there was a continuous increase in squirrel population density in Twente between 1988 and 1991.
However, this increase in density was not quantified.
No attempt was made to estimate temporal changes
in density at Fellingsbro.
MODELS OF SQUT RREL OCCUR RENC E
Tn Twente, Apennines, po plain, and piedmont,
logistic regression models have been fitted, with presence—absence of squirrel as the response variable
and landscape attributes as explanatory variables
(Celada et al. 1994; van Apeldoorn, Celada &
Nieuwenhuizen 1994; Wauters et al. 1997a). Among
the landscape variables, and in the absence of grey
squirrels, fragment size and fragment distance to a
source yielded the highest percentages of explained
variation. Thus, we chose the models containing
these two variables when their effect was significant.
When not published, details of the models (estimated parameters and errors) were provided by R.
van Apeldoorn, C. Celada, and L. Wauters (personal communication). We used stepwise logistic
regression and the same explanatory variables as
predictors of squirrel distribution in Grimso and
Fellingsbro. The parameters of the fitted models and
their variation are shown in Table 2.
Fig. 1. predicted probabilities of squirrel occurrence in forest fragments as a function of (a) fragment size in ha (at three
fixed distances), and (b) distance to the nearest source in km (at three fixed sizes). HD and LD denote high and low squirrel
population density.
Tt has been suggested that male squirrel home
ranges might be determined by the density and dispersion of females (Wauters & Dhondt 1992;
Andren & Delin 1994), while female home range
size, which is probably determined by food availability, might indicate the area requirements of an
adult individual squirrel (Andren & Delin 1994).
Female home range size has been found to be about
4 ha both in forest (Wauters & Dhondt 1992) and
farmland dominated landscapes (Wauters, Casale &
Dhondt 1994). A similar value was found in
Fellingsbro (Delin & Andren 1996). Squirrel space
use was unknown in both the Dutch and Ttalian
study areas, but as landscapes there were similar to
those studied by Wauters and co-workers, we
assumed that female squirrels have a home range of
about 4 ha. Tn Grimso, however, the average size of
female home ranges is 23 ha (Andren & Delin 1994).
This figure is unexpectedly large. As habitat quality
at Grimso is superior to the other landscapes considered here (fragments contain > 95% conifers,
Andren & Delin 1994) it is unlikely that squirrels
have to expand their home ranges to get enough
resources. Rather, large ranges may simply reflect a
low cost (e.g. in terms of predation risk) to access
preferred patches of old spruce, because these
patches are embedded in a matrix of young forest
instead of open land (Andren & Delin 1994; Andren
1997). Squirrel home ranges are not defended as
exclusive territories (Wauters & Dhondt 1992;
Andren & Delin 1994) and thereby energy expenditure costs linked to the defence of large areas are
also unlikely. As home range size may affect fragment occupancy, fragment size in Grimso was corrected (divided by a factor of 23/4 = 5 7) for home
range size before fitting regression models (Table 2),
and before calculating predicted probabilities in
Grimso from other models (see next section).
COMpARTNG pR EDTC TTON S
The predicted probabilities of fragment occupancy
by squirrels were plotted together for the six study
areas in order to look for differences in the behaviour of the models. Tn Grimso and Twente, only
the models obtained in years with the highest and
the lowest squirrel relative densities were used to
make such predictions. For each model, we simulated variation in the coefficients by randomly drawing 10 sets of parameters from a normal distribution
with mean and standard error as shown in Table 2.
Then predictions were calculated at three values of
fragment size (0 1, 1, and 10 ha) and three values of
distance to source (30, 100, and 600 m). Values of
size were chosen at three different orders of magnitude that encompass observed variation in fragment
size, the highest value representing enough area for
at least one squirrel home range. Values of distance
were spaced within the range of the species daily
movements (Andren & Delin 1994). The 10 predictions per model were considered as replicates in an
ANOVA with which we analysed differences in average predictions between study areas, controlling for
landscape attributes (i.e. fragment size and distance
to source; see Table 3). Another ANOVA was performed replacing the factor ‘study area’ by the factor ‘connectivity’ (three levels of matrix quality:
young woodland, fields with hedges, and open fields;
see Table 4). Grimso is the only landscape where
fragments are connected by woodland. Hence, connectivity and study area could not be analysed
together because of confounding effects.
TEST OF pREDTCTTONS
,
649—662
Fig. 2. Mean (±1 SD) predicted probability of squirrel
presence in forest fragments regarding (a) study area, (b)
fragment size, (c) distance to the nearest source, and (d)
type of matrix habitat. Sample size per level is 90 (a), 240
(b,c), 180 (d, levels woodland and open), and 360 (d, level
hedges). Tn (a) landscapes are ordered by the percentage of
forest left (given within the bars). HD = high density.
LD = low density.
The models in Table 2 were used to predict the probabilities of a forest fragment being occupied by
squirrels in an area different from that where the
model was built. predictions were also calculated
within study areas between years with different
squirrel density. Again, in Grimso and Twente only
predictions from years of extreme squirrel relative
density were used.
predictions were tested with our observations in
Grimso and Fellingsbro as well as the observations
in the three Ttalian study areas (C. Celada & L.
Wauters, personal communication). Observed values
were one if squirrels were present in the fragment
Table 2. Coefficients of logistic regression models describing the distribution of the red squirrel in fragmented landscapes.
Logit = $0 + $1 X1 + $2 X2 , where X1 = ln(fragment size), and X2 = ln(distance to the nearest forest permanently inhabited
by squirrels). Temporal differences in relative squirrel density are ranked in the last column, the highest rank corresponds
to the highest density. Empty cells indicate that explanatory variables did not have a significant effect. Fragment size at
Grimso was divided by 5 7 before fitting the regression model, in order to account for differences in squirrel home range
size between study areas. Values for Apennines and po plain after Celada et al. (1994) and C. Celada (personal communication). Values for Twente after van Apeldoorn, Celada & Nieuwenhuizen (1994) and R.C. van Apeldoorn (personal communication). Values for piedmont after L. Wauters (personal communication)
Site and year
Grimso 1990
Grimso 1991
Grimso 1992
Grimso 1993
Fellingsbro 1994
Fellingsbro 1996
Apennines
po plain
Twente 1988
Twente 1989
Twente 1990
Twente 1991
piedmont
$0
SE
$1
SE
$2
SE
% explained deviance
1 29
1 18
0 43
0 43
0 52
0 66
0 22
0 24
14
20
1 19
0 42
0 55
0 22
16
30 65
—2 19
15 14
4 37
2 87
1 90
4 67
3 79
13 61
1 09
6 45
2 35
2 01
1 94
2 09
2 01
2 26
0 96
4 90
3 79
3 80
1 87
1 57
1 29
1 48
0 89
—4 46
2 02
—1 82
—0 96
—0 62
—0 39
—0 70
—0 67
0 73
0 43
0 35
0 33
0 34
0 26
Density rank
4
1
3
2
48
20
14
40
30
22
15
16
1
2
3
4
Table 3. ANOVA table showing the effects of the study area, fragment size, and distance to the nearest source on predicted
probabilities of squirrel forest occupancy. N = 10 per level combination
SS
d.f.
MS
F
P
Main effects
Study area
Size
Distance
39 957
45 503
2 983
7
2
2
5 708
22 572
1 491
55 869
238 626
15 642
< 0 001
< 0 001
< 0 001
Area x Size
Area x Distance
Size x Distance
46 563
2 250
0 101
64 453
14
14
4
676
3 326
0 161
0 025
0 095
34 883
1 685
0 266
< 0 001
0 054
0 900
Tnteractions
Error
Table 4. ANOVA table showing the effects of connectivity, fragment size, and distance to the nearest source on predicted
probabilities of squirrel forest occupancy. N = 10 per level combination
SS
d.f.
MS
F
P
Main effects
Connectivity
Size
Distance
28 197
26 222
2 664
2
2
2
14 099
13 111
1 332
95 473
88 783
9 020
< 0 001
< 0 001
< 0 001
20 042
1 465
0 101
103 518
4
4
4
701
5 010
0 366
0 025
0 148
33 930
2 479
0 171
< 0 001
0 043
0 953
Tnteractions
Connectivity x Size
Connectivity x Distance
Size x Distance
Error
Journal of Applied
Ecology, 36,
649—662
and zero if absent. predicted and observed data series were ordered according to fragment size, if this
variable was present in the model, and then to distance to the nearest source, otherwise they were
ordered first according to distance. Then predicted
and observed means were calculated in groups of
five consecutive values. Fit was assessed by plotting
observed means against predicted ones, and testing
Fig. 3. Examples of significant departures from a perfect fit (dotted line) of the regression line between predicted and
observed frequencies of fragment occupancy. (a) predictions from Twente (low squirrel density) and observations at Grimso
(low density). (b) predictions from po plain and observations at Fellingsbro. (c) predictions from Fellingsbro and observations at Apennines. (d) predictions from Fellingsbro and observations at po plain. Figures indicate how many points are
too close to be discerned.
for correlation between them (see Fig. 3). When
there was a significant correlation we further tested
for departures from a perfect fit, i.e. the null hypothesis that the slope and the intercept of the regression
line were equal to one and zero, respectively.
Another test of fit was done by visual inspection
of the distribution of fragments with and without
squirrels in a scattergram of fragment size by distance to the nearest source. Tn this graph, models in
Table 2 were used to plot isolines of predicted probability of occurrence, set at three values: 0 25, 0 5,
and 0 75. Tf observations fit predictions, most occupied fragments should be above the 0 5 probability
line, and most empty patches below it (see Fig. 4).
We looked at the proportion of correctly classified
fragments to test model predictions.
Results
COMpARTSONS BETWEEN pREDTCTTONS
Journal of Applied
Ecology, 36,
649—662
Noticeable variation in the predictions of the five
models that were sensitive to fragment size only
took place when size was in the range 0—10 ha. Tn
forests larger than 10 ha all models predicted a probability of squirrel occupancy higher than 0 9
(Fig. 1a), under the assumption that individual
home range sizes were similar in all landscapes.
Logistic models uncorrected for home range size at
Grimso gave actual probabilities of occupancy
higher than 0 9 when fragment size was at least 27
and 33 ha, for low and high squirrel density years,
respectively. Hence, the only effect of using uncorrected models would be a displacement to the right
of the Grimso curves in Fig. 1a, thus increasing the
size threshold for agreement between all models up
to about 30 ha. Amongst the models that were
insensitive to fragment size those built in
Fellingsbro and po plain also predicted probabilities
higher than 0 9 if the distance to the nearest source
was shorter than 590 m and 1226 m, respectively
(Fig. 1b). The equivalent distance for the piedmont
model was 2 m. That is, all models but the one built
in piedmont agree in the following: given that a
fragment is large enough ( 10 ha), it is highly probable ( 0 9) that the red squirrel will be present if
the nearest source is not further than 590 m. Tn
piedmont, virtually no fragment had a predicted
probability of occupancy
0 9 (Fig. 1). While there
seemed to be a common threshold for fragment size,
it did not exist for the distance to a source. Given a
very small forest fragment (0 1 ha), there was not a
very short distance to a source within which all
models predicted a high probability of finding squir-
656
Red squirrel
distribution in
fragmented
landscapes
Fig. 4. The distribution of forest fragments with (.) and without (0) red squirrels in relation to fragment size and distance to the nearest source forest. Lines indicate predicted probabilities of occupancy.
Under the hypothesis of a perfect fit between observations and predictions, continuous lines (P = 0 5) should divide occupied (above) from empty fragments (below). (a) predictions from Grimso (high squirrel density) and observations at Grimso (low density). (b) predictions from Grimso (high density) and observations at Fellingsbro. (c) predictions from Twente (high density) and observations at Fellingsbro.
(d) predictions from Grimso (high density) and observations at Apennines. predictions were not corrected for home range size in Grimso within-area comparisons (a).
Journal of Applied
Ecology, 36,
649—662
rels in the fragment. When the distance to the nearest source was high (> 2500 m) the predicted
chances of finding squirrels varied among study
areas, especially when fragment size was small
(Fig. 1b).
Model predictions were compared across areas
(n = 8, two models in Grimso and Twente) to examine variation of the squirrel response to fragment
size in the range 0—10 ha, and taking 600 m as the
upper limit of distance, as this was the maximum
distance to the nearest source common to all the
study areas (Table 1). Above that limit, distance
effects started to operate even in large fragments
(Fig. 1). All factors (study area, size, and distance)
had a significant effect on predicted probabilities of
occupancy (Table 3). The ANOVA model, including
main effects and first order interactions, explained
68% of the variation in these predictions. When
study area was replaced by connectivity this percentage dropped to 49%, though the effect of connectivity was also significant (Table 4).
Differences between areas in the mean probability
of finding squirrels in a fragment did not show any
relationship with the proportion of forest in the
landscape (only high-density years were considered;
both variables were arcsin transformed; r = 0 01,
d.f. = 5, P = 0 99; see Fig. 2a). A posteriori contrasts (Tukey test on all eight situations) revealed
four homogeneous and significantly different groups
of means. These groups were, from the lowest to the
highest mean probability of occupancy: (1)
Apennines; (2) piedmont and Twente when squirrel
density was low; (3) Twente (high density) and
Grimso (both density levels); and (4) po plain and
Fellingsbro. Mean predicted probabilities increased
sharply with fragment size (Fig. 2b; all three comparisons between pairs of means resulted in significant differences; Tukey test) and decreased
moderately with distance to the nearest source
(Fig. 2c; the mean at 600 m was significantly smaller
than the means at lower distances; Tukey test).
Significant interactions (Table 3) reflected the different predicted responses of the squirrel to variation
in fragment size and, less clearly, distance to source
between study areas (Fig. 1). Size and distance did
not interact because most models were insensitive to
both variables at the same time (Table 2). When
study area was replaced by connectivity, the results
of the ANOVA did not change qualitatively
(Table 4). For fragments
10 ha the mean predicted
probability of occupancy did not increase with
increasing degree of connectivity either (Fig. 2d).
Contrasts showed that the means for all three categories of connectivity were significantly different
(Tukey test). However, the highest mean corresponded to landscapes with an open matrix and the
lowest to landscapes where forest fragments were
connected by hedges or treerows (Fig. 2d).
When logistic equations were fitted to data in the
same area (Twente and Grimso) but under different
squirrel population densities, they produced quite
similar predictions, at least compared to models
built in different areas (Fig. 1). Tn Twente, predictions from the high- and low-density models differed
substantially only as a function of distance when
fragment size was around 1 ha (Fig. 1b). A six-fold
change in relative density did not result in a poor
agreement between predictions and observations at
Grimso (Fig. 1, Table 5).
T E S T O F PREDICTIONS
Overall, 83% of the 42 comparisons that were carried out indicated disagreement between predicted
probabilities and observed frequencies of fragment
occupancy. Tn 24 cases there was no correlation
between predictions and observations, and when
they were correlated, in 11 further cases the hypothesis of a fit to a regression line with both intercept
zero and slope one was rejected (Table 5). When
models included the effect of fragment size, this lack
of fit often occurred because predicted probabilities
at low values of fragment size underestimated actual
frequencies of occurrence, while predicted probabilities and observed frequencies were similar (around
1 0), close to the highest values of fragment size (five
cases in Table 5; an example is shown in Fig. 3a).
The only exceptions were the observations in
piedmont, which were much lower than predictions
from Twente (low-density) at intervals including
large forest fragments. Likewise, predictions from
the po plain model, which included only the effect
of distance to the nearest source, agreed with actual
frequencies of occupancy in Fellingsbro at low-distance values, but overestimated them at high-distance values (Fig. 3b). predictions of other models
based on distance, however, produced different disparities, overestimating observed frequencies at low
values of distance and underestimating them at high
values (Fig. 3c), or underestimating them all over
the range of values (Fig. 3d; this was also the case
for the pair po plain vs. piedmont). Tn areas with
large forest fragments (or very short distances
between fragments and sources), where both predicted probabilities and corresponding observed frequencies were close to one, underestimation or
overestimation in the intervals including the smallest
fragments (or longest distances) caused the intercept
to deviate from zero and, as a consequence, forced
the slope to deviate from one (Fig. 3a,b). Neither
predictions nor observations from po plain and
piedmont study areas were involved in a good fit
(Table 5).
The model developed in Twente with high population density was able successfully to predict fragment occupancy at Fellingsbro (Table 5). Models
Slope < 1**
Uncorrelated
Slope < 1***
Slope > 1*
Uncorrelated
Uncorrelated
Uncorrelated
Tntercept < 0*
Slope > 1*
Uncorrelated
Uncorrelated
Uncorrelated
Slope < 1**
Tntercept > 0*
Slope < 1*
Uncorrelated
Uncorrelated
Uncorrelated
Uncorrelated
Good fit
Tntercept > 0**
Slope < 1**
Tntercept > 0*
Slope > 1**
Uncorrelated
Uncorrelated
Uncorrelated
Uncorrelated
Uncorrelated
Discussion
Good fit
Uncorrelated
Good fit
Apennines
Fellingsbro
Grimso LD
predictions
Grimso HD
© 1999 British
Ecological Society
from Grimso predicted the distribution of squirrels
quite well in Fellingsbro and, less clearly, in the
Apennines but, interestingly, predictions from these
two areas did not fit observations at Grimso. The
apparent correctness of predictions in some models
was, however, weakened after the examination of
scattergrams. Models were quite good in classifying
fragments with squirrels but they failed to correctly
classify most empty forest fragments. Ninety per
cent of occupied fragments at Grimso when squirrel
density was low lay above the 0 5 probability line
predicted by the model developed at Grimso when
density was high, while only 33% of empty fragments were below that line (Fig. 4a). Figures were
88% and 46%, respectively, when squirrel density
was high at Grimso regarding predictions made by
the model built in the low-density year. Almost all
occupied patches (97—100%) at Fellingsbro were
above the 0 5 probability line predicted by models
from Grimso or Twente (high density), whereas at
most one empty fragment (0—20%) stayed below the
line (Fig. 4b,c). Tn the Apennines all the occupied
patches were above the 0 75 probability line predicted by models from Grimso (high — Fig. 4d — and
low density) and only three out of the 13 empty
patches (23%) occurred below it.
The fact that predictions and observations were
compared in landscapes with a similar proportion
of forest (Fellingsbro—Apennines, Twente—po plain—
piedmont) did not result in an acceptable model performance (Table 5).
The correctness of predictions might be negatively
affected by extrapolation out of the range of values
of fragment attributes (size and distance) in the area
where the model was developed. This hypothesis
was supported for fragment size, but not for distance to the nearest source. The proportion of correct predictions (0 86, n = 7) was significantly higher
(G = 8 20, d.f. = 1, P = 0 004) when the prediction
was not extrapolated out of the fragment size range
than in cases when it was extrapolated (0 29,
n = 35). The equivalent proportions for the largest
distance to the nearest source were 0 43 (n = 7) and
0 60 (n = 23), respectively, and they were not significantly different (G = 0 69, d.f. = 1, P = 0 405).
After allowing for the large home-range size at
Grimso, all models but the one built in piedmont
predicted a very high probability of finding squirrels
in a forest fragment when its size was over 10 ha
and when the nearest source was within 600 m. Tn
this range of values, any model could successfully
predict the squirrel distribution elsewhere. These
thresholds in fragment attributes might reflect the
species minimum requirements when habitat quality
for home range and dispersal was low, i.e. the habi-
© 1999 British
tat quality in the worst of the examined study areas.
A forest of 10 ha may be close in size to the largest
average home range reported (6 8 ha; Wauters,
Casale & Dhondt 1994) when habitat is suboptimal
(i.e. deciduous tree species and young conifers;
Wauters & Dhondt 1990; Andren & Delin 1994). A
distance of 600 m is close to the maximum daily distance (680 m) that females cover across a functionally continuous forest, and males also move within
600 m on more than 80% of days (Andren & Delin
1994). Moreover, although dispersing individuals
can reach up to 4 5 km from their natal range (G.
Verbeylen, unpublished data), most young squirrels
disperse within 1 km in fragmented landscapes
where many forest patches are interconnected by
habitat corridors (Wauters, Casale & Dhondt 1994;
G. Verbeylen, unpublished data). The dispersive
ability of a species depends on how well it moves
across matrix habitats (Taylor et al. 1993; Aberg
et al. 1995). Thus, it is plausible to expect the mode
in dispersal distances to be lower than 1 km (perhaps
closer to 600 m) when corridors between patches are
absent in a matrix of cultivated fields, as for
instance in the Fellingsbro or po plain study areas.
The anomalous behaviour of the piedmont model is
clearly due to the fact that the squirrel distribution
in that study area is primarily determined by an
external deterministic factor, i.e. its displacement by
an expanding population of introduced grey squirrels (Wauters et al. 1997a).
For fragments under the size threshold of 10 ha,
mean predicted probabilities of occupancy increased
sharply with fragment size. Sufficient size is
obviously the principal necessary condition for a
fragment to be occupied. Consequently, as long as
this condition was not fulfilled, other factors were
less important: mean
predicted
probabilities
decreased with distance at a lower rate and did not
tend to increase with the total proportion of forest
or the degree of connectivity between fragments in
the landscape. Although connectivity could be relevant in explaining squirrel occupancy above the size
threshold (see below), mean predictions under 10 ha
were better explained by study area than by connectivity. The first reason is statistical, as the model
including connectivity has fewer parameters (hence
less explanatory power). The second is ecological, as
connectivity is only one of the landscape features
affecting occupancy, all of them implicitly contained
in the factor study area (a similar situation was
found by Asferg et al. 1997).
Models were useful to predict between-year distribution at Grimso, despite large fluctuations in squirrel population density. Between-year consistency of
predictions was less clear at Twente. Tn Twente,
survival and breeding chances. Tn Grimso, however,
squirrels could probably reach and exploit distant
fragments at a lower risk, even when population
density was low, as matrix habitats were suboptimal
(mainly young forest) but not unsuitable. Tn fact, at
Grimso the squirrel habitat was not functionally
fragmented (Andren & Delin 1994). The random
sample hypothesis predicts equal probabilities of
finding an animal within equally sized sampling
habitat plots, regardless the degree of habitat fragmentation in the landscape (Connor & McCoy
1979; Haila 1983). The random sample hypothesis
gave a good description of squirrel patch occupancy
at Grimso (Delin & Andren 1999).
On the other hand, fragmentation clearly affected
squirrel distribution in landscapes with less than
15% of forest left (Celada et al. 1994; van
Apeldoorn, Celada & Nieuwenhuizen 1994). This
effect might have been obscured in the piedmont
study area because of the displacement of red by
grey squirrels (Wauters et al. 1997a). The effects of
habitat fragmentation on animal distribution at the
regional scale start to operate below certain thresholds in the proportion of total habitat available in
the landscape (Andren 1994). The proportion of forest at Fellingsbro (26%) might indicate a fragmentation threshold for the squirrel, as in 1994
fragmentation effects were not detected (see
Table 2), and there was 89% occupancy of fragments in 1996 (see Fig. 4b,c). Furthermore, 26% is
close to 30%, the maximum fragmentation threshold empirically observed in mammals (Andren
1994).
Andren (1996) predicted that models from landscapes with similar proportions of suitable habitat
should be similar. However, we did not find a good
fit between model predictions and squirrel occupancy in landscapes having a similar proportion of
forest. Fellingsbro and Apennines study areas had
similar proportions of forest, but in Fellingsbro connectivity between fragments was low in a matrix of
agricultural unsuitable
habitat,
while in the
Apennines hedgerows and rows of trees connected
forest fragments (Celada et al. 1994), allowing squirrels to move as if their habitat was not fragmented.
These differences resulted in varied responses by
squirrels: they were sensitive only to fragment size in
the Apennines, and only to distance to the nearest
source in Fellingsbro. The proportion of forest was
comparable in the po plain, Twente, and piedmont
study areas, but its spatial arrangement was quite
different, most of the forest was extremely concentrated in two large fragments in the first area
(Celada et al. 1994) and more evenly distributed in
the
others
(van
Apeldoorn,
Celada
&
crowding might have forced some individuals to
venture into risky unsuitable matrix habitats to
reach distant fragments, in order to improve their
Nieuwenhuizen 1994; Wauters et al. 1997a,b).
Again, the responses of the squirrel were different
between these landscapes. Tgnoring the special situa-
Journal of Applied
Ecology, 36,
649—662
tion at piedmont, these differences might also be
due to the fact that the proportion of remaining forest was probably under the threshold for habitat
fragmentation, where a small reduction in the proportion of forest (i.e. from 13% in po plain to 8%
in Twente) might result in a large decrease in the
probability of squirrel occurrence in fragments
(Andren 1996). However, mean predicted probabilities of occupancy did not follow the gradient of forest proportion in the landscape. Tn other words, the
observed poor fit is not necessarily a consequence of
non-linearity in the relationship between squirrel
incidence and the proportion of suitable habitat.
Our results indicate that squirrel distribution is not
only affected by the total proportion of forest, but
also by the spatial arrangement of the remaining
forest fragments and the quality of the matrix habitat.
The simulations in Andren (1996) also suggested
that models from landscapes with low proportions
of suitable habitat could predict the outcome in
landscapes with a higher proportion of suitable
habitat, but not the other way round. However, the
opposite directionality in predictive ability was
observed. Surprisingly, models from Grimso worked
in Fellingsbro and Apennines and not vice versa.
Thus, none of the predictions in Andren (1996) were
supported, probably because his simulations were
made in ideal landscapes where suitable habitat was
randomly distributed in a matrix of unsuitable habitat, while real landscapes, as the ones we have considered, are usually more complex (O’Neill et al.
1988; Gardner & O’Neill 1991).
As fragment size became smaller than 10 ha and
distance to the nearest source larger than 600 m, the
ability of models to predict squirrel distribution outside the area in which they were developed generally
decreased. Yet, 17% of the comparisons resulted in
a reasonable matching between predicted probabilities and observed occupation frequencies. When the
range of fragment sizes in the area of observation
was within the range of fragment sizes in the area
from which the model comes, matching was
favoured, suggesting that predictions can hardly be
extrapolated outside their own range. A similar relationship was not found regarding distance, possibly
because this variable was not present in the Grimso
models, which produced most of the correct predictions.
Although average probabilities of squirrel occupancy could sometimes be predicted in size and distance intervals, predictions in particular fragments
were less satisfactory. A high proportion of empty
patches was wrongly classified. predictions may
point out the fragments that have the potential to
harbour squirrels, according to their spatial characteristics, but actual occurrence in a particular fragment also depends on factors not related to the
landscape pattern, such as population density
(Hinsley et al. 1996), variation in resource quality
within the patch (FitzGibbon 1997), interspecific
competition (Wauters et al. 1997a), or predation
pressure (Barbour & Litvaitis 1993), which were
ignored by the models. These uncontrolled factors
presumably represent much of the 52—86% of variation in squirrel distribution that was not explained
(Table 2).
We conclude that, assuming that squirrel home
range sizes are similar, predictions from empirically
derived logistic regression models can be used outside the area they were built in a broad range of forest sizes (> 10 ha), and a more limited range of
distances to a source forest (< 600 m). Tf both conditions are met, the chances of red squirrel survival
will be very high despite large variation in the proportion of forest in the landscape, forest composition (within-patch habitat quality), matrix features
(between-patch habitat
quality), and the spatial
arrangement of fragments in the landscape. Tn general, setting these kinds of thresholds is relevant to
the practical conservation of species and their habitats. Outside these thresholds — that is, for very
small and isolated forest fragments — models cannot
predict squirrel distribution elsewhere, probably
because squirrel demography, habitat quality, and
many other uncontrolled factors become relevant.
predictions may be more reliable in the same place
at different times, but they can be sensitive to fluctuations in population density, especially in landscapes with a small proportion of forest. Specific
predictions about the presence of the squirrel in a
particular fragment are always difficult to make, as
factors other than size and distance affect actual
occurrence (e.g. interspecific competition, Wauters
et al. 1997a). Comparing the predictions of logistic
models from different areas can be useful in identifying the role of uncontrolled factors on squirrel distribution as well as in determining fragmentation
and extinction thresholds (Lande 1987; Andren
1996) in the proportion of forest in the landscape.
Acknowledgements
We thank Annika Delin, Gunnar Jansson and Eva
Elfgren for helping with the fieldwork at
Fellingsbro,
and Claudio
Celada, Rob van
Apeldoorn, and Luc Wauters for providing unpublished information about squirrel distribution and
model parameters in their study areas. We are also
grateful to Lennart Hansson, peter Lurz, Michael L.
Morrison, J. Luis Telleria, Luc Wauters, and an
anonymous referee for their constructive comments
on the manuscript. This research was supported by
the Swedish Environmental protection Agency, the
Swedish Foundation for Strategic Environmental
Research, and the private foundation ‘Olle och
Signhild Engkvists Stiftelser’. personal support to
AR was provided by a postdoctoral grant from the
Direccion General de Ensenanza Superior, Spanish
Ministry of Education.
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