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Keywords:

  • habitat fragmentation;
  • incidence models;
  • predictive ability;
  • Sciurus vulgaris;
  • thresholds in landscape attributes

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

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 factors that are less easily measured, in which case relationships with size and separation in one area may predict occurrence elsewhere only poorly.

2. We explored how well the distribution of red squirrels Sciurus vulgaris in fragmented 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 minimum habitat requirements for home range and dispersal in the worst study area.

4. For fragments < 10 ha (outside shared thresholds), models developed in a landscape 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 fragment 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 density.

7. When size and distance thresholds were met, we found that models could be used successfully elsewhere. In addition, threshold values indicate how large forest fragments should be and how they should be arranged to favour squirrel occurrence in a landscape.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The predicted effects of different management measures must be known for environmental decision making. Specific models are often lacking and, consequently, 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). In 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. It would be reasonable to expect a better general applicability of predictions from simple models.

Island 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 (Andrén & 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, Andrén (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 similar 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). In 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 & Andrén 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.

In 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

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Study sites

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 Italy (Apennines and Po Plain; Celada et al. 1994; Piedmont; Wauters et al. 1997a), and two in central Sweden (Grimsö and Fellingsbro; Delin & Andrén 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 Italian sites whereas mixed or coniferous forest dominates in the other study areas (Table 1).

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. In 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: Grimsö (Delin & Andrén 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)
Study areaSize (km2) Dominant habitat Forest (%) Number of fragments Fragments Size (ha) Distance (m)MatrixForest quality
Grimsö450Forest69460·1–50024–585 Young standsMainly conifers
Fellingsbro32Farmland26450·5–7925–1200 Open fieldsMainly conifers
Apennines135Farmland25340·5–3210–2530 HedgerowsDeciduous trees
Po Plain4675Farmland13462·4–1201000–16000 Open fieldsDeciduous trees
Twente150Farmland8490·5–1440–3500 HedgerowsMixed forest
Piedmont350Farmland8610·2–7010–13000 HedgerowsDeciduous trees
imageimage

Figure 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). In (a) landscapes are ordered by the percentage of forest left (given within the bars). HD = high density. LD = low density.

Squirrel surveys

In the published studies, searching for dreys (Wauters & Dhondt 1988) was used to determine squirrel presence in each fragment. In 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 & Andrén 1999). Forest fragments were monitored during 4 consecutive years in Twente (1988–91; van Apeldoorn, Celada & Nieuwenhuizen 1994) and Grimsö (1990–93; Delin & Andrén 1999), and for 2 years in Fellingsbro (1994, 1996). The three Italian fragment systems were monitored in only 1 year (Celada et al. 1994; Wauters et al. 1997a).

Delin & Andrén (1999) estimated the changes in relative squirrel density at Grimsö 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.

Table 2.  Coefficients of logistic regression models describing the distribution of the red squirrel in fragmented landscapes. Logit = β0 + β1 X1 + β2 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 Grimsö 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 yearβ0SEβ1SEβ2SE% explained devianceDensity rank
Grimsö 19901·290·43 0·520·22  144
Grimsö 19911·180·43 0·660·24  201
Grimsö 1992       3
Grimsö 1993 1·190·42 0·550·22  162
Fellingsbro 1994
Fellingsbro 199630·6513·61  –4·462·02 48 
Apennines–2·19 1·09 2·260·96  20 
Po Plain15·14 6·45  –1·820·73 14 
Twente 1988 4·37 2·35 4·901·57 –0·960·43 401
Twente 1989 2·87 2·01 3·791·29 –0·620·35 302
Twente 1990 1·90 1·94 3·801·48 –0·390·33 223
Twente 1991 4·67 2·09 1·870·89 –0·700·34 154
Piedmont 3·79 2·01  –0·670·26 16 

Models of squirrel occurrence

In 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 Grimsö and Fellingsbro. The parameters of the fitted models and their variation are shown in Table 2.

It has been suggested that male squirrel home ranges might be determined by the density and dispersion of females (Wauters & Dhondt 1992; Andrén & Delin 1994), while female home range size, which is probably determined by food availability, might indicate the area requirements of an adult individual squirrel (Andrén & 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 & Andrén 1996). Squirrel space use was unknown in both the Dutch and Italian 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. In Grimsö, however, the average size of female home ranges is 23 ha (Andrén & Delin 1994). This figure is unexpectedly large. As habitat quality at Grimsö is superior to the other landscapes considered here (fragments contain > 95% conifers, Andrén & 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 (Andrén & Delin 1994; Andrén 1997). Squirrel home ranges are not defended as exclusive territories (Wauters & Dhondt 1992; Andrén & 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 Grimsö 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 Grimsö from other models (see next section).

Comparing predictions

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. In Grimsö 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 (Andrén & 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). Grimsö is the only landscape where fragments are connected by woodland. Hence, connectivity and study area could not be analysed together because of confounding effects.

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
  SSd.f.MSF P
Main effects
 Study area39·9577 5·708 55·869  < 0·001
 Size45·503222·572238·626  < 0·001
 Distance 2·9832 1·491 15·642  < 0·001
Interactions
 Area × Size 46·56314 3·32634·883  < 0·001
 Area × Distance 2·25014 0·161 1·685 0·054
 Size × Distance 0·1014 0·025 0·266 0·900
Error 64·453676 0·095  
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
 SSd.f.MSF P 
Main effects
 Connectivity28·197214·09995·473  < 0·001
 Size26·222213·11188·783  < 0·001
 Distance 2·6642 1·332 9·020  < 0·001
Interactions
 Connectivity × Size 20·0424 5·01033·930  < 0·001
 Connectivity × Distance 1·4654 0·366 2·479 0·043
 Size × Distance 0·1014 0·025 0·171 0·953
Error 103·518701 0·148  

Test of predictions

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 Grimsö and Twente only predictions from years of extreme squirrel relative density were used.

Predictions were tested with our observations in Grimsö and Fellingsbro as well as the observations in the three Italian study areas (C. Celada & L. Wauters, personal communication). Observed values were one if squirrels were present in the fragment 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 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.

image

Figure 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 Grimsö (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.

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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. In 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. If 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.

image

Figure 4. The distribution of forest fragments with (●) and without (○) 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 Grimsö (high squirrel density) and observations at Grimsö (low density). (b) Predictions from Grimsö (high density) and observations at Fellingsbro. (c) Predictions from Twente (high density) and observations at Fellingsbro. (d) Predictions from Grimsö (high density) and observations at Apennines. Predictions were not corrected for home range size in Grimsö within-area comparisons (a).

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Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Comparisons between predictions

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. In 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 Grimsö 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 Grimsö 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. In 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 squirrels 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).

image

Figure 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.

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Model predictions were compared across areas (n = 8, two models in Grimsö 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 Grimsö (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 Grimsö) but under different squirrel population densities, they produced quite similar predictions, at least compared to models built in different areas (Fig. 1). In 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 Grimsö (Fig. 1, Table 5).

Table 5.  Assessment of the fit between predicted probabilities and observed frequencies of forest fragment occupancy by red squirrels. Fit was rejected (t-test) either if the intercept of the regression line between both variables was different from zero or its slope was different from one. HD: high relative squirrel density. LD = low relative squirrel density
ObservationsPredictions Grimsö HDGrimsö LDFellingsbroApenninesPo PlainTwente HDTwente LDPiedmont
  • *

    P < 0·05;

  • **

    P < 0·01;

  • ***

    P < 0·001.

Grimsö HD Good fitUncorrelatedUncorrelatedUncorrelated Slope < 1**Intercept > 0***UncorrelatedUncorrelated
Grimsö LDGood fit UncorrelatedIntercept > 0*** UncorrelatedUncorrelatedIntercept > 0*** Slope < 1**Uncorrelated 
FellingsbroGood fitGood fit Intercept > 0*** Slope < 1***Intercept < 0* Slope > 1*Good fitIntercept > 0* Slope < 1*Uncorrelated
ApenninesGood fitGood fitIntercept > 0** Slope < 1** UncorrelatedUncorrelatedUncorrelatedUncorrelated
Po PlainUncorrelatedUncorrelatedIntercept > 0* Slope > 1**Uncorrelated UncorrelatedUncorrelatedSlope > 1*
PiedmontUncorrelatedUncorrelatedUncorrelatedUncorrelatedSlope < 1**UncorrelatedSlope < 1*** 

Test of predictions

Overall, 83% of the 42 comparisons that were carried out indicated disagreement between predicted probabilities and observed frequencies of fragment occupancy. In 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). In 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 from Grimsö 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 Grimsö. 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 Grimsö when squirrel density was low lay above the 0·5 probability line predicted by the model developed at Grimsö 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 Grimsö 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 Grimsö or Twente (high density), whereas at most one empty fragment (0–20%) stayed below the line (Fig. 4b,c). In the Apennines all the occupied patches were above the 0·75 probability line predicted by models from Grimsö (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).

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

After allowing for the large home-range size at Grimsö, 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. In 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 habitat 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; Andrén & 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 (Andrén & 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; Åberg 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 Grimsö, despite large fluctuations in squirrel population density. Between-year consistency of predictions was less clear at Twente. In Twente, crowding might have forced some individuals to venture into risky unsuitable matrix habitats to reach distant fragments, in order to improve their survival and breeding chances. In Grimsö, 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. In fact, at Grimsö the squirrel habitat was not functionally fragmented (Andrén & 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 Grimsö (Delin & Andrén 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 (Andrén 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 (Andrén 1994).

Andrén (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 & Nieuwenhuizen 1994; Wauters et al. 1997a,b). Again, the responses of the squirrel were different between these landscapes. Ignoring the special situation 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 (Andrén 1996). However, mean predicted probabilities of occupancy did not follow the gradient of forest proportion in the landscape. In 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 Andrén (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 Grimsö worked in Fellingsbro and Apennines and not vice versa. Thus, none of the predictions in Andrén (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 Grimsö 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). If 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. In 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; Andrén 1996) in the proportion of forest in the landscape.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

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 Tellería, 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 Dirección General de Enseñanza Superior, Spanish Ministry of Education.

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  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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